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	diff --git a/HiddenCode/hidden_code_nb_deflection.py b/HiddenCode/hidden_code_nb_deflection.py
	index f9be657..e042572 100644
	--- a/HiddenCode/hidden_code_nb_deflection.py
	+++ b/HiddenCode/hidden_code_nb_deflection.py
	@@ -1,1025 +1,1033 @@
	import math
	import numpy as np
	from bokeh.layouts import layout, column, row
	from bokeh.models.annotations import Label, Arrow
	from bokeh.models.arrow_heads import VeeHead
	-from bokeh.models import Div, CustomJS, Slider, Spacer, Text
	+from bokeh.models import Div, CustomJS, Slider, Spacer, Text, HoverTool
	from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup
	from bokeh.plotting import figure, show, ColumnDataSource
	from bokeh.io import output_notebook
	from cienpy import simplebeam as sb
	from cienpy import rectangular_section as beam_section
	from cienpy import stress_strain_elastic as stst
	from cienpy import models
	from cienpy import javascriptcodes as js

	output_notebook()


	def main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, E_steel, fy, fy_steel, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr):
	########################################################
	# Initialisation
	########################################################
	# constants for the visualisation
	SCALE = 10
	OFFSET_Q = q
	MAX_B = 3*b
	MAX_H = 3*h
	MAX_Q = q/4*5
	SCALE_DEFL = 100


	# store the values in a specific format
	data_beam = dict(
	x=[0, L],
	y=[0, 0]
	)

	data_scheme_beam = dict(
	x=[0, L*SCALE],
	y=[0, 0]
	)

	data_scheme_q = dict(
	x=[0, 0, LSCALE, LSCALE],
	y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],
	x_fade=[0, 0, LSCALE, LSCALE]
	)

	data_section_scheme = dict(
	x=[0, 0],
	y=[0, h]
	)

	initial_position = L
	initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC
	initial_FBD = 0 # right=0 left=1
	data = dict( # stores every useful single variable
	state=[initial_state],
	FBD=[initial_FBD],
	SCALE=[SCALE],
	L=[L],
	b=[b],
	h=[h],
	E=[E],
	A=[A],
	Iy=[Iy],
	Iz=[Iz],
	yG=[yG],
	y_n_axis=[y_n_axis],
	P=[P],
	x=[initial_position],
	y=[0],
	q=[q],
	Rx=[Rx],
	Ry_l=[Ry_l],
	Ry_r=[Ry_r],
	N=[N],
	V=[V],
	M=[M],
	xF=[L*SCALE]
	)

	source_beam = ColumnDataSource(data_beam)
	source_scheme_beam = ColumnDataSource(data_scheme_beam)
	source_scheme_q = ColumnDataSource(data_scheme_q)
	source_section_scheme = ColumnDataSource(data_section_scheme)
	source = ColumnDataSource(data)


	########################################################
	# Define figures, widgets and renderers as from the previous notebook
	########################################################
	FIG_H_B = 200 # height figure beam
	FIG_B_B = 700 # width figure beam
	FIG_H_S = FIG_H_B # height figure scheme
	FIG_B_S = FIG_B_B # width figure scheme
	FIG_H_SEC = 600 # height figure section
	DIV_B_GEO = 170
	DIV_B_FORCES = 170

	options = dict(
	toolbar_location=None
	)

	# figure for the beam
	paddingx = 0.2*L
	int_x_b = (0-paddingx, L+paddingx)
	int_y_b = (-OFFSET_Q/SCALESCALE_DEFL, (MAX_Q+OFFSET_Q)/SCALESCALE_DEFL)
	fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,
	f_h=FIG_H_B, f_b=FIG_B_B)


	# figure for the cross-section
	fig_section = sb.define_fig_section(MAX_B0.8, MAX_H0.8, options, FIG_H_SEC)


	# beam
	(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,
	ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)

	# section
	section = beam_section.draw_section(fig_section, b, h)


	# show mechanical parameters
	div_geo = Div(width= DIV_B_GEO,
	text=beam_section.div_text_geo(round(h), round(b), round(L),
	"{:.2e}".format(A),
	"{:.2e}".format(Iy),
	"{:.2e}".format(Iz)))


	# change geometry
	slider_b = Slider(
	title="Change the width b [mm]",
	start=10,
	end=MAX_B,
	step=10,
	value=b
	)
	slider_h = Slider(
	title="Change the height h [mm]",
	start=20,
	end=MAX_H,
	step=20,
	value=h
	)

	# reference system
	axis_arrow_length = 0.8
	axis_arrow_scale = 100
	models.force_vector(fig_section, axis_arrow_length10, 0, 0, 0, axis_arrow_lengthaxis_arrow_scale*1.6, 'gray') # y axis
	fig_section.text(x=[0], y=[axis_arrow_lengthaxis_arrow_scale1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2)
	models.force_vector(fig_section, axis_arrow_length10, 0, -axis_arrow_lengthaxis_arrow_scale, 0, 0, 'gray') # z axis
	fig_section.text(x=[-axis_arrow_lengthaxis_arrow_scale1.1], y=[0], text=["z"], text_color='gray', text_align='right', text_baseline='middle')


	# figure for the forces and moments
	fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)


	# uniform load (beam)
	u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALESCALE_DEFL], width=L, height=q/SCALESCALE_DEFL,
	fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)
	label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE*SCALE_DEFL], text=["q"], text_color="blue")


	# axial force (beam)
	axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')
	label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2*SCALE_DEFL], text=["P"], text_color="green")


	# position point
	pos_opt = dict(
	source=source,
	size=10,
	fill_alpha=0.5,
	fill_color="magenta",
	color="magenta",
	alpha=0.5
	)
	# CHAGED: moved below for correct display order of glyphs
	# beam_position = fig_beam.circle('x', 'y', **pos_opt)
	forces_position = fig_scheme.circle('xF', 'y', **pos_opt)


	# beam (scheme)
	scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')
	scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)
	# uniform load (scheme)
	scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',
	fill_alpha=0.3, alpha=0.3)
	scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',
	color='navy', fill_alpha=0.3, alpha=0.3)
	# axial force (scheme)
	scheme_axial_force = models.force_vector(fig_scheme, P, LSCALE+P, LSCALE, 0, 0, 'green')
	# Reactions (scheme)
	scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, LSCALE, LSCALE, -Ry_r, 0, 'orange')
	scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')
	scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')
	# force N
	scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# force V
	scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# moment M
	(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)


	# change the uniform load q
	slider_q = Slider(
	title="Change the uniform load q [kN/m]",
	start=0.1,
	end=MAX_Q,
	step=0.1,
	value=q
	)


	# choose position of interest
	slider_position = Slider(
	title="Change the position x along the beam [m]",
	start=0,
	end=L,
	step=0.02,
	value=L
	)


	# choose left or right FBD
	div_rg_FBD = Div(text="Free-body diagram (FBD):")
	radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)


	# choose axial force or not
	div_cb_P = Div(text=f"Axial force P={P} kN (applied)")
	checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])


	# show values of forces and moments
	div_forces = Div(width=DIV_B_FORCES,
	text=sb.div_text_forces(P, P, Ry_l, Ry_r, "No cross section analysed.", 0, 0, 0))


	# figures for the diagrams
	options_diag = dict(
	toolbar_location=None,
	x_axis_label="Position [m]",
	plot_width=FIG_B_B,
	x_range=fig_beam.x_range
	)
	fig_N = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Axial force", "@y kN")],
	y_axis_label="Axial force N [kN]",
	plot_height=int(FIG_H_B*0.8),
	title="N V M Diagrams")
	fig_V = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Shear force", "@y kN")],
	y_axis_label="Shear force V [kN]",
	plot_height=int(FIG_H_B*0.8))
	fig_M = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Bending moment", "@y kNm")],
	y_axis_label="Bending moment M [kNm]",
	plot_height=FIG_H_B)
	fig_N.xaxis.visible = False
	fig_V.xaxis.visible = False


	# plot N V M
	N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)
	+ fig_N.add_tools(HoverTool(renderers=[N_diag],
	+ tooltips= [("Position", "@x m"), ("Axial force", "@y kN")]))
	+
	V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)
	+ fig_V.add_tools(HoverTool(renderers=[V_diag],
	+ tooltips= [("Position", "@x m"), ("Shear force", "@y kN")]))
	+
	M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)
	+ fig_M.add_tools(HoverTool(renderers=[M_diag],
	+ tooltips= [("Position", "@x m"), ("Bending moment", "@y kNm")]))

	# point that shows the position that it's analyzed
	N_position = fig_N.circle('x', 'N', **pos_opt)
	V_position = fig_V.circle('x', 'V', **pos_opt)
	M_position = fig_M.circle('x', 'M', **pos_opt)

	# figures for the stresses and strains
	FIG_B_ss = 200
	FIG_H_ss = 200
	options_stress_strain = dict(
	toolbar_location=None,
	y_axis_label="Height h [mm]",
	plot_width=FIG_B_ss,
	plot_height=FIG_H_ss
	)
	fig_stress_N = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Axial stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2099 [MPa]")
	fig_stress_N.yaxis.visible = False
	fig_axial_strain = figure(**options_stress_strain,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Axial strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2099 [%]",
	y_range=fig_stress_N.y_range)
	fig_axial_strain.yaxis.visible = False
	fig_stress_M = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Bending stress and centroid",
	y_range=fig_stress_N.y_range,
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2098 [MPa]")
	fig_stress_M.yaxis.visible = False
	fig_bending_strain = figure(**options_stress_strain,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Bending strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2098 [%]",
	y_range=fig_stress_N.y_range)
	fig_bending_strain.yaxis.visible = False
	fig_stress_V = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Shear stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU}\u1d65 [MPa]")
	fig_stress_V.yaxis.visible = False
	fig_stress_sigma = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress \N{GREEK SMALL LETTER SIGMA} and neutral axis",
	y_range=fig_stress_N.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA} [MPa]")
	fig_stress_tau = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress \N{GREEK SMALL LETTER TAU}",
	y_range=fig_stress_V.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU} [MPa]")

	# plot stress N V M
	- discr_stress_strain = 10
	+ discr_stress_strain = 201
	scale_x = 25
	y_discr = np.linspace(0, h, discr_stress_strain)
	sigma_N = stst.compute_sigma_axial(y_discr, 0, A)
	N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,
	source_section_scheme, scale_x=scale_x/10)
	+ fig_stress_N.add_tools(HoverTool(renderers=[N_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	sigma_M = stst.compute_sigma_bending(y_discr, 0, Iy, yG)
	(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,
	source_section_scheme, True, yG, scale_x=scale_x)
	+ fig_stress_M.add_tools(HoverTool(renderers=[M_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, yG)
	tau_V = stst.compute_tau_shear(y_discr, 0, S_rect, Iy, b)
	V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)
	+ fig_stress_V.add_tools(HoverTool(renderers=[V_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot stress sigma and tau
	sigma_total = sigma_M + sigma_N
	(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,
	source_section_scheme,True, yG, scale_x=scale_x)
	+ fig_stress_sigma.add_tools(HoverTool(renderers=[sigma_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	tau_total = tau_V
	tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,
	source_section_scheme, scale_x=1)
	+ fig_stress_tau.add_tools(HoverTool(renderers=[tau_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot strain N M
	strain_axial = stst.compute_epsilon_axial(y_discr, sigma_N, E)
	axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)
	+ fig_axial_strain.add_tools(HoverTool(renderers=[axial_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))
	+
	strain_bending = stst.compute_epsilon_bending(y_discr, sigma_M, E)
	bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)
	+ fig_bending_strain.add_tools(HoverTool(renderers=[bending_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))


	# figures for NVM
	fig_NM_section = figure(**options_stress_strain,
	title="N and M at position x",
	match_aspect=True)
	fig_NM_section.axis.visible = False
	fig_NM_section.grid.grid_line_alpha = 0

	fig_V_section = figure(**options_stress_strain,
	title="V at position x",
	match_aspect=True)
	fig_V_section.axis.visible = False
	fig_V_section.grid.grid_line_alpha = 0

	# section with NVM
	models.section_diagram(fig_NM_section)
	models.section_diagram(fig_V_section)

	# NVM in section
	section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')
	section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')
	(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)

	# NVM label in section
	OFFSET_N = 1
	label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[""], text_color="red", text_baseline='bottom')
	label_M_section = fig_NM_section.text(x=[OFFSET_N6], y=[-OFFSET_N5], text=[""], text_color="red", text_baseline='top')
	label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[0], text=[""], text_color="red", text_baseline='middle')


	########################################################
	# Define the new figures, widgets and renderers
	########################################################
	# deflection of the beam
	fig_beam.title.text = "Simple supported beam with deflection under uniform load"
	fig_beam.ygrid.grid_line_alpha = 1
	fig_beam.yaxis.visible = True
	fig_beam.yaxis.axis_label = "Deflection [mm]"


	# line 70-76 removed: uniform load (beam) and axial force (beam) in the simple beam


	# Change the beam in the beam figure to gray and line width smaller and add new line
	beam.glyph.line_width = 1
	beam.glyph.line_color = "gray"
	beam_defl = fig_beam.line(x=x_discr,
	y=sb.compute_deflection_uniform_load(x_discr, q, L, Iy, E),
	line_width=6, color='black')
	-
	+ fig_beam.add_tools(HoverTool(renderers=[beam_defl],
	+ tooltips= [("Position", "@x m"), ("Deflection", "@y mm")]))
	+
	# FROM ABOVE: position point
	beam_position = fig_beam.circle('x', 'y', **pos_opt)


	# choose different elastic modulus
	E_wood = 8e3 # [MPa]
	E_concrete = 26e3 # [MPa]
	E_ceramic = 300e3 # [MPa]
	slider_elastic = Slider(
	title="Change the elastic modulus [MPa]",
	start=E_wood,
	end=E_ceramic,
	step=1e3,
	value=E,
	margin=(5, 5, 0, 5)
	)


	# show values of E
	div_E = Div(margin=(0, 5, 0, 5),
	text=f"""
	<p style='font-size:12px'>
	E<sub>wood</sub> = {math.trunc(E_wood/1e3)} GPa; E<sub>concrete</sub> = {math.trunc(E_concrete/1e3)} GPa<br>
	E<sub>steel</sub> = {math.trunc(E_steel/1e3)} GPa; E<sub>ceramic</sub> = {math.trunc(E_ceramic/1e3)} GPa</p>
	""")


	########################################################
	# Configurethe logics
	########################################################
	args_slider_pos = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	s_M=source_M,
	arr_head=scheme_M_head,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_slider_pos = f"""
	// retrieve data
	const db = source.data
	const data_sb = s_sb.data
	const data_q = s_q.data
	const FBD = db['FBD'][0]
	const pos = cb_obj.value
	const q = db['q'][0]
	const L = db['L'][0]

	// update data
	db['N'][0] = compute_N(db['P'][0])
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['x'][0] = pos

	// check state
	check_state(db)

	// update:
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// apply the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	// declare functions
	{sb.implement_compute_NJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_growthJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_NVM_diagramJS()}
	{models.implement_check_stateJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_sigma_axialJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_tau_shearJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_update_NVM_sectionJS()}
	"""
	updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)


	args_slider_b = dict(source=source,
	s_b=source_beam,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	beam_defl=beam_defl)
	code_change_b = f"""
	// retrieve data used
	const db = source.data
	const b = cb_obj.value // value of the slider
	const h = db['h'][0]
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)
	const yG = db['yG'][0]
	const N = db['N'][0]
	const M = db['M'][0]

	// apply the changes
	db['b'][0] = b
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_deflection_beam(db, beam_defl)

	// emit the changes
	source.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_deflection_beamJS(discr_NVM)}
	{sb.implement_compute_deflection_uniform_loadJS()}
	"""
	update_b = CustomJS(args=args_slider_b, code=code_change_b)


	args_slider_h = dict(source=source,
	s_b=source_beam,
	s_ss=source_section_scheme,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	beam_defl=beam_defl)
	code_change_h = f"""
	// retrieve data used
	const db = source.data
	const data_ss = s_ss.data
	const b = db['b'][0]
	const h = cb_obj.value // value of the slider
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)
	const N = db['N'][0]
	const M = db['M'][0]
	const yG = compute_centroid_y(h)

	// apply the changes
	db['h'][0] = h
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)
	db['yG'][0] = yG
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)
	data_ss['y'][1] = h // change the height of the section in the diagrams

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_deflection_beam(db, beam_defl)

	// emit the changes
	source.change.emit()
	s_ss.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{js.implement_update_deflection_beamJS(discr_NVM)}
	{sb.implement_compute_deflection_uniform_loadJS()}
	"""
	update_h = CustomJS(args=args_slider_h, code=code_change_h)


	args_checkbox_P = dict(source=source,
	s_M=source_M,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	N_diag=N_diag,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_checkbox_P = f"""
	// retrieve var from the object that uses callback
	var f = cb_obj.active // checkbox P
	if (f.length==0) f = [1]
	const db = source.data

	// apply the changes
	db['P'][0] = {P}*(1-f)
	db['N'][0] = compute_N(db['P'][0])
	db['Rx'][0] = compute_Rx(db['P'][0])

	// update
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_N_diagram(db, N_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// emit the changes
	source.change.emit()

	// declare functions
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_compute_RxJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_compute_NJS()}
	{sb.implement_update_N_diagramJS(discr_NVM)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_neutral_axisJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)


	args_radiogroup_FBD = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	s_M=source_M,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_radiogroup_FBD = f"""
	// retrieve data
	const db = source.data
	const FBD = cb_obj.active
	const data_sb = s_sb.data
	const data_q = s_q.data
	const pos = db['x'][0]

	// apply the changes
	db['FBD'][0] = FBD

	// update
	check_state(db)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// emit the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	{models.implement_check_stateJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)


	args_slider_q = dict(source=source,
	s_q=source_scheme_q,
	s_M=source_M,
	div_f=div_forces,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	V_diag=V_diag,
	M_diag=M_diag,
	centroid=centroid,
	neutral_axis=neutral_axis,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section,
	beam_defl=beam_defl)
	code_slider_q = f"""
	// retrieve data
	const db = source.data
	const q = cb_obj.value
	const pos = db['x'][0]
	const L = db['L'][0]

	// update q
	db['q'][0] = q
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['Ry_l'][0] = compute_Ry_l(q, L)
	db['Ry_r'][0] = compute_Ry_r(q, L)

	// update
	update_u_load(db, s_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_V_diagram(db, V_diag)
	update_M_diagram(db, M_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)
	update_deflection_beam(db, beam_defl)

	// apply changes
	source.change.emit()

	// declare functions
	{js.implement_update_arrowJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_compute_Ry_lJS()}
	{sb.implement_compute_Ry_rJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_update_V_diagramJS(discr_NVM)}
	{sb.implement_update_M_diagramJS(discr_NVM)}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_u_loadJS(OFFSET_Q)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_neutral_axisJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	{js.implement_update_deflection_beamJS(discr_NVM)}
	{sb.implement_compute_deflection_uniform_loadJS()}
	"""
	update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)


	args_slider_elastic = dict(source=source,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	centroid=centroid,
	beam_defl=beam_defl)
	# code_slider_elastic = ""
	code_slider_elastic = f"""
	// retrieve data
	const db = source.data
	const E = cb_obj.value

	// update E
	db['E'][0] = E

	// update
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_deflection_beam(db, beam_defl)

	// apply changes
	source.change.emit()

	// declare functions
	{js.implement_linspaceJS()}
	{sb.implement_compute_NJS()}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{js.implement_update_deflection_beamJS(discr_NVM)}
	{sb.implement_compute_deflection_uniform_loadJS()}
	"""
	update_slider_elastic = CustomJS(args=args_slider_elastic, code=code_slider_elastic)


	# apply the logics
	slider_b.js_on_change('value', update_b)
	slider_h.js_on_change('value', update_h)
	slider_position.js_on_change('value', updade_slider_pos)
	checkbox_P.js_on_click(update_checkbox_P)
	radiogroup_FBD.js_on_click(update_radiogroup_FBD)
	slider_q.js_on_change('value', update_slider_q)
	slider_elastic.js_on_change('value', update_slider_elastic)


	########################################################
	# Build the layout
	########################################################
	padding_layout = 10
	layout1 = layout([
	[column(row(column(fig_scheme,
	row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout*3),
	slider_b,
	slider_h,
	slider_position,
	slider_q,
	slider_elastic,
	div_E,
	div_rg_FBD,
	radiogroup_FBD,
	div_cb_P,
	checkbox_P))),
	column(fig_beam,
	Spacer(height=padding_layout),
	fig_N,
	fig_V,
	fig_M)),
	row(column(
	row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_stress_sigma),
	row(fig_V_section, Spacer(width=FIG_B_ss), fig_stress_V, Spacer(width=FIG_B_ss), Spacer(width=FIG_B_ss), fig_stress_tau),
	))
	),
	],
	])

	show(layout1)
	\ No newline at end of file
	diff --git a/HiddenCode/hidden_code_nb_diagrams.py b/HiddenCode/hidden_code_nb_diagrams.py
	index bf32433..1bb167f 100644
	--- a/HiddenCode/hidden_code_nb_diagrams.py
	+++ b/HiddenCode/hidden_code_nb_diagrams.py
	@@ -1,599 +1,601 @@
	import math
	import numpy as np
	from bokeh.layouts import layout, column, row
	from bokeh.models.annotations import Label, Arrow
	from bokeh.models.arrow_heads import VeeHead
	-from bokeh.models import Div, CustomJS, Slider, Spacer, Text
	+from bokeh.models import Div, CustomJS, Slider, Spacer, Text, HoverTool
	from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup
	from bokeh.plotting import figure, show, ColumnDataSource
	from bokeh.io import output_notebook
	from cienpy import simplebeam as sb
	from cienpy import rectangular_section as beam_section
	from cienpy import models
	from cienpy import javascriptcodes as js

	output_notebook()


	def main_code(L, h, b, A, Iy, Iz, q, P, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr):
	########################################################
	# Initialisation
	########################################################
	# constants for the visualisation
	SCALE = 10
	OFFSET_Q = q
	MAX_B = 3*b
	MAX_H = 3*h
	MAX_Q = q/4*5

	# store the values in a specific format
	data_beam = dict(
	x=[0, L],
	y=[0, 0]
	)

	data_scheme_beam = dict(
	x=[0, L*SCALE],
	y=[0, 0]
	)

	data_scheme_q = dict(
	x=[0, 0, LSCALE, LSCALE],
	y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],
	x_fade=[0, 0, LSCALE, LSCALE]
	)

	initial_position = L
	initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC
	initial_FBD = 0 # right=0 left=1
	data = dict( # stores every useful single variable
	state=[initial_state],
	FBD=[initial_FBD],
	SCALE=[SCALE],
	L=[L],
	b=[b],
	h=[h],
	A=[A],
	Iy=[Iy],
	Iz=[Iz],
	P=[P],
	x=[initial_position],
	y=[0],
	q=[q],
	Rx=[Rx],
	Ry_l=[Ry_l],
	Ry_r=[Ry_r],
	N=[N],
	V=[V],
	M=[M],
	xF=[L*SCALE]
	)

	source_beam = ColumnDataSource(data_beam)
	source_scheme_beam = ColumnDataSource(data_scheme_beam)
	source_scheme_q = ColumnDataSource(data_scheme_q)
	source = ColumnDataSource(data)


	########################################################
	# Define figures, widgets and renderers as from the previous notebook
	########################################################
	FIG_H_B = 200 # height figure beam
	FIG_B_B = 700 # width figure beam
	FIG_H_S = FIG_H_B # height figure scheme
	FIG_B_S = FIG_B_B # width figure scheme
	FIG_H_SEC = 600 # height figure section

	options = dict(
	toolbar_location=None
	)

	# figure for the beam
	paddingx = 0.2*L
	int_x_b = (0-paddingx, L+paddingx)
	int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)
	fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,
	f_h=FIG_H_B, f_b=FIG_B_B)


	# figure for the cross-section
	fig_section = sb.define_fig_section(MAX_B, MAX_H*0.8, options, FIG_H_SEC)


	# beam
	(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,
	ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)


	# section
	section = beam_section.draw_section(fig_section, b, h)


	# show mechanical parameters
	div_geo = Div(text=beam_section.div_text_geo(round(h), round(b), round(L),
	"{:.2e}".format(A),
	"{:.2e}".format(Iy),
	"{:.2e}".format(Iz)))


	# change geometry
	slider_b = Slider(
	title="Change the width b [mm]",
	start=10,
	end=MAX_B,
	step=10,
	value=b
	)
	slider_h = Slider(
	title="Change the height h [mm]",
	start=20,
	end=MAX_H,
	step=20,
	value=h
	)

	# reference system
	axis_arrow_length = 0.8
	axis_arrow_scale = 100
	models.force_vector(fig_section, axis_arrow_length10, 0, 0, 0, axis_arrow_lengthaxis_arrow_scale*1.6, 'gray') # y axis
	fig_section.text(x=[0], y=[axis_arrow_lengthaxis_arrow_scale1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2)
	models.force_vector(fig_section, axis_arrow_length10, 0, -axis_arrow_lengthaxis_arrow_scale, 0, 0, 'gray') # z axis
	fig_section.text(x=[-axis_arrow_lengthaxis_arrow_scale1.1], y=[0], text=["z"], text_color='gray', text_align='right', text_baseline='middle')


	# figure for the forces and moments
	fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)


	# uniform load (beam)
	u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE], width=L, height=q/SCALE,
	fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)
	label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE], text=["q"], text_color="blue")


	# axial force (beam)
	axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')
	label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=["P"], text_color="green")


	# position point
	pos_opt = dict(
	source=source,
	size=10,
	fill_alpha=0.5,
	fill_color="magenta",
	color="magenta",
	alpha=0.5
	)
	beam_position = fig_beam.circle('x', 'y', **pos_opt)
	forces_position = fig_scheme.circle('xF', 'y', **pos_opt)


	# beam (scheme)
	scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')
	scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)
	# uniform load (scheme)
	scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',
	fill_alpha=0.3, alpha=0.3)
	scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',
	color='navy', fill_alpha=0.3, alpha=0.3)
	# axial force (scheme)
	scheme_axial_force = models.force_vector(fig_scheme, P, LSCALE+P, LSCALE, 0, 0, 'green')
	# Reactions (scheme)
	scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, LSCALE, LSCALE, -Ry_r, 0, 'orange')
	scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')
	scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')
	# force N
	scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# force V
	scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# moment M
	(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)


	# change the uniform load q
	slider_q = Slider(
	title="Change the uniform load q [kN/m]",
	start=0.1,
	end=MAX_Q,
	step=0.1,
	value=q
	)


	# choose position of interest
	slider_position = Slider(
	title="Change the position x along the beam [m]",
	start=0,
	end=L,
	step=0.02,
	value=L
	)


	# choose left or right FBD
	div_rg_FBD = Div(text="Free-body diagram (FBD):")
	radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)


	# choose axial force or not
	div_cb_P = Div(text=f"Axial force P={P} kN (applied)")
	checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])


	# show values of forces and moments
	div_forces = Div(text=sb.div_text_forces(P, P, Ry_l, Ry_r, "No cross section analysed.", 0, 0, 0))


	########################################################
	# Define the new figures, widgets and renderers
	########################################################
	# figures for the diagrams
	options_diag = dict(
	toolbar_location=None,
	x_axis_label="Position [m]",
	plot_width=FIG_B_B,
	x_range=fig_beam.x_range
	)
	fig_N = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Axial force", "@y kN")],
	y_axis_label="Axial force N [kN]",
	plot_height=int(FIG_H_B*0.8),
	title="N V M Diagrams")
	fig_V = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Shear force", "@y kN")],
	y_axis_label="Shear force V [kN]",
	plot_height=int(FIG_H_B*0.8))
	fig_M = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Bending moment", "@y kNm")],
	y_axis_label="Bending moment M [kNm]",
	plot_height=FIG_H_B)
	fig_N.xaxis.visible = False
	fig_V.xaxis.visible = False


	# plot N V M
	N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)
	+ fig_N.add_tools(HoverTool(renderers=[N_diag],
	+ tooltips= [("Position", "@x m"), ("Axial force", "@y kN")]))
	+
	V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)
	+ fig_V.add_tools(HoverTool(renderers=[V_diag],
	+ tooltips= [("Position", "@x m"), ("Shear force", "@y kN")]))
	+
	M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)
	+ fig_M.add_tools(HoverTool(renderers=[M_diag],
	+ tooltips= [("Position", "@x m"), ("Bending moment", "@y kNm")]))

	# point that shows the position that it's analyzed
	N_position = fig_N.circle('x', 'N', **pos_opt)
	V_position = fig_V.circle('x', 'V', **pos_opt)
	M_position = fig_M.circle('x', 'M', **pos_opt)


	########################################################
	# Configurethe logics
	########################################################
	args_slider_pos = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	s_M=source_M,
	arr_head=scheme_M_head)
	code_slider_pos = f"""
	// retrieve data
	const db = source.data
	const data_sb = s_sb.data
	const data_q = s_q.data
	const FBD = db['FBD'][0]
	const pos = cb_obj.value
	const q = db['q'][0]
	const L = db['L'][0]

	// update data
	db['N'][0] = compute_N(db['P'][0])
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['x'][0] = pos

	// check state
	check_state(db)

	// update:
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_div_forces(db, div_f)

	// apply the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	// declare functions
	{sb.implement_compute_NJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_growthJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_NVM_diagramJS()}
	{models.implement_check_stateJS()}
	"""
	updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)


	args_slider_b_h = dict(source=source,
	s_b=source_beam,
	div=div_geo,
	section=section,
	support_r=support_r)
	code_change_b = f"""
	// retrieve data used
	const db = source.data
	const b = cb_obj.value // value of the slider
	const h = db['h'][0]
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)

	// apply the changes
	db['b'][0] = b
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)

	// update
	update_div_geo(db, div)
	update_section(db, section)

	// emit the changes
	source.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	"""
	update_b = CustomJS(args=args_slider_b_h, code=code_change_b)


	code_change_h = f"""
	// retrieve data used
	const db = source.data
	const b = db['b'][0]
	const h = cb_obj.value // value of the slider
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)

	// apply the changes
	db['h'][0] = h
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)

	// update
	update_div_geo(db, div)
	update_section(db, section)

	// emit the changes
	source.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	"""
	update_h = CustomJS(args=args_slider_b_h, code=code_change_h)


	args_checkbox_P = dict(source=source,
	s_M=source_M,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	N_diag=N_diag)
	code_checkbox_P = f"""
	// retrieve var from the object that uses callback
	var f = cb_obj.active // checkbox P
	if (f.length==0) f = [1]
	const db = source.data

	// apply the changes
	db['P'][0] = {P}*(1-f)
	db['N'][0] = compute_N(db['P'][0])
	db['Rx'][0] = compute_Rx(db['P'][0])

	// update
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_N_diagram(db, N_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)

	// emit the changes
	source.change.emit()

	// declare functions
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_compute_RxJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_compute_NJS()}
	{sb.implement_update_N_diagramJS(discr_NVM)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)


	args_radiogroup_FBD = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	s_M=source_M,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head)
	code_radiogroup_FBD = f"""
	// retrieve data
	const db = source.data
	const FBD = cb_obj.active
	const data_sb = s_sb.data
	const data_q = s_q.data
	const pos = db['x'][0]

	// apply the changes
	db['FBD'][0] = FBD

	// update
	check_state(db)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)

	// emit the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	{models.implement_check_stateJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)


	args_slider_q = dict(source=source,
	s_q=source_scheme_q,
	s_M=source_M,
	div_f=div_forces,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	V_diag=V_diag,
	M_diag=M_diag)
	code_slider_q = f"""
	// retrieve data
	const db = source.data
	const q = cb_obj.value
	const pos = db['x'][0]
	const L = db['L'][0]

	// update q
	db['q'][0] = q
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['Ry_l'][0] = compute_Ry_l(q, L)
	db['Ry_r'][0] = compute_Ry_r(q, L)

	// update
	update_u_load(db, s_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_V_diagram(db, V_diag)
	update_M_diagram(db, M_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)

	// apply changes
	source.change.emit()

	// declare functions
	{js.implement_update_arrowJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_compute_Ry_lJS()}
	{sb.implement_compute_Ry_rJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_update_V_diagramJS(discr_NVM)}
	{sb.implement_update_M_diagramJS(discr_NVM)}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_u_loadJS(OFFSET_Q)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)


	# apply the logics
	slider_b.js_on_change('value', update_b)
	slider_h.js_on_change('value', update_h)
	slider_position.js_on_change('value', updade_slider_pos)
	checkbox_P.js_on_click(update_checkbox_P)
	radiogroup_FBD.js_on_click(update_radiogroup_FBD)
	slider_q.js_on_change('value', update_slider_q)


	########################################################
	# Build the layout
	########################################################
	padding_layout = 10
	layout1 = layout([
	[column(row(column(fig_scheme,
	row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout),
	slider_b,
	slider_h,
	div_geo,
	Spacer(height=padding_layout),
	slider_position,
	slider_q,
	div_rg_FBD,
	radiogroup_FBD,
	div_cb_P,
	checkbox_P))),
	column(fig_beam,
	Spacer(height=padding_layout),
	fig_N,
	fig_V,
	fig_M,
	div_forces))
	)],
	])

	show(layout1)
	\ No newline at end of file
	diff --git a/HiddenCode/hidden_code_nb_mohr.py b/HiddenCode/hidden_code_nb_mohr.py
	index b1f5396..6dcfc61 100644
	--- a/HiddenCode/hidden_code_nb_mohr.py
	+++ b/HiddenCode/hidden_code_nb_mohr.py
	@@ -1,1700 +1,1709 @@
	import math
	import numpy as np
	from bokeh.layouts import layout, column, row
	from bokeh.models.annotations import Label, Arrow
	from bokeh.models.arrow_heads import VeeHead
	-from bokeh.models import Div, CustomJS, Slider, Spacer
	+from bokeh.models import Div, CustomJS, Slider, Spacer, HoverTool
	from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup
	from bokeh.plotting import figure, show, ColumnDataSource, output_file, save
	from bokeh.io import output_notebook
	from cienpy import simplebeam as sb
	from cienpy import rectangular_section as beam_section
	from cienpy import stress_strain_elastic as stst
	from cienpy import models
	from cienpy import javascriptcodes as js
	from cienpy import mohrcircle

	output_notebook()


	def main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr, initial_y, initial_theta_element, sigma_axial, sigma_bending, sigma_tau, sigma_x0, sigma_y0, tau_0, sigma_average_mohr, r_circle_mohr, theta_principal, initial_theta, new_state):
	########################################################
	# Initialisation
	########################################################
	# constants for the visualisation
	SCALE = 10
	OFFSET_Q = q
	MAX_B = 2*b
	MAX_H = 2*h
	MAX_Q = q/4*5
	MAX_STRESS = 60
	MAX_STRESS_MOHR = 10
	MAX_DIM_STRESS_STATE = MAX_STRESS*2.5

	# store the values in a specific format
	data_beam = dict(
	x=[0, L],
	y=[0, 0]
	)

	data_scheme_beam = dict(
	x=[0, L*SCALE],
	y=[0, 0]
	)

	data_scheme_q = dict(
	x=[0, 0, LSCALE, LSCALE],
	y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],
	x_fade=[0, 0, LSCALE, LSCALE]
	)

	data_section_scheme = dict(
	x=[0, 0],
	y=[0, h]
	)

	initial_position = L
	initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC
	initial_FBD = 0 # right=0 left=1
	data = dict( # stores every useful single variable
	state=[initial_state],
	FBD=[initial_FBD],
	SCALE=[SCALE],
	L=[L],
	b=[b],
	h=[h],
	E=[E],
	A=[A],
	Iy=[Iy],
	Iz=[Iz],
	yG=[yG],
	y_n_axis=[y_n_axis],
	P=[P],
	x=[initial_position],
	y=[0],
	y_var=[initial_y],
	theta_element=[initial_theta_element], # rad
	theta=[initial_theta], # rad
	sigma_x0=[sigma_x0],
	sigma_y0=[sigma_y0],
	tau_0=[tau_0],
	sigma_average=[sigma_average_mohr],
	r_circle_mohr=[r_circle_mohr],
	sigma_x=[new_state[0]],
	sigma_y=[new_state[1]],
	tau=[new_state[2]],
	q=[q],
	Rx=[Rx],
	Ry_l=[Ry_l],
	Ry_r=[Ry_r],
	N=[N],
	V=[V],
	M=[M],
	xF=[L*SCALE]
	)

	source_beam = ColumnDataSource(data_beam)
	source_scheme_beam = ColumnDataSource(data_scheme_beam)
	source_scheme_q = ColumnDataSource(data_scheme_q)
	source_section_scheme = ColumnDataSource(data_section_scheme)
	source = ColumnDataSource(data)

	# Constants
	FIG_H_B = 200 # height figure beam
	FIG_B_B = 600 # width figure beam
	FIG_H_S = FIG_H_B # height figure scheme
	FIG_B_S = FIG_B_B # width figure scheme
	FIG_H_SEC = 500 # height figure section
	DIV_B_GEO = 170
	DIV_B_FORCES = 170
	FIG_MOHR = 600
	FIG_STRESS_STATE = 600


	########################################################
	# Define figures, widgets and renderers as from the previous notebook
	########################################################
	options = dict(
	toolbar_location=None
	)



	######################## Start modifications
	# figure for the beam
	paddingx = 0.2*L
	int_x_b = (0-paddingx, L+paddingx)
	int_y_b = (-MAX_H0.2, MAX_H1.4)
	fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,
	f_h=FIG_H_B, f_b=FIG_B_B)

	# modify beam
	#TODO: add to cienpy
	def draw_beam_2D(fig, L: float, h: float, b_supp=0.25, ratio = 1.0):
	"""
	Function that draws the simple beam in a figure.

	@param fig (bokeh.plotting.figure.Figure): Figure that will be the canvas for the plot.
	@param src (bokeh.models.sources.ColumnDataSource): Source of the coordinates.
	@param L (float): Length of the beam in m.
	@param x (str): Key for the x values. Defaults to 'x'.
	@param y (str): Key for the y values. Defaults to 'y'.
	@param b_supp (float, optional): Size of the supports in x. Defaults to 0.3.
	@param ratio (float, optional): Ratio of the figure (interval_y/height*100). Defaults to 1.0 (axis equal).

	@return tuple: Tuple with the renderers of the beam and supports.
	"""
	beam = fig.rect([L/2], [h/2], width=L, height=h,
	fill_color='lightgray', color='black', line_width=1)
	supp_opt = dict(
	fill_color='white',
	line_color='black'
	)
	support_l = models.define_pinned(fig, 0, 0, b_supp, ratio, supp_opt)
	support_r = models.define_roller(fig, L, 0, b_supp, ratio, supp_opt)

	return (beam, support_l, support_r)

	(beam, support_l, support_r) = draw_beam_2D(fig_beam, L, h,
	ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)

	# uniform load (beam)
	if q!=0:
	fig_beam.rect([L/2], [(int_y_b[1]+MAX_H)/2], width=L, height=(0.99*(int_y_b[1]-MAX_H)),
	fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)
	fig_beam.text(x=[-0.2], y=[MAX_H], text=["q"], text_color="blue")

	####################### End modification



	# figure for the cross-section
	fig_section = sb.define_fig_section(MAX_B0.8, MAX_H0.8, options, FIG_H_SEC)


	# section
	section = beam_section.draw_section(fig_section, b, h)


	# show mechanical parameters
	div_geo = Div(width= DIV_B_GEO,
	text=beam_section.div_text_geo(round(h), round(b), round(L),
	"{:.2e}".format(A),
	"{:.2e}".format(Iy),
	"{:.2e}".format(Iz)))


	# change geometry
	slider_b = Slider(
	title="Change the width b [mm]",
	start=10,
	end=MAX_B,
	step=10,
	value=b
	)
	slider_h = Slider(
	title="Change the height h [mm]",
	start=20,
	end=MAX_H,
	step=20,
	value=h
	)

	# reference system
	axis_arrow_length = 0.8
	axis_arrow_scale = 100
	models.force_vector(fig_section, axis_arrow_length10, 0, 0, 0, axis_arrow_lengthaxis_arrow_scale*1.6, 'gray') # y axis
	fig_section.text(x=[0], y=[axis_arrow_lengthaxis_arrow_scale1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2)
	models.force_vector(fig_section, axis_arrow_length10, 0, -axis_arrow_lengthaxis_arrow_scale, 0, 0, 'gray') # z axis
	fig_section.text(x=[-axis_arrow_lengthaxis_arrow_scale1.1], y=[0], text=["z"], text_color='gray', text_align='right', text_baseline='middle')


	# figure for the forces and moments
	fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)


	# axial force (beam)
	axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')
	label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=["P"], text_color="green")


	# position point
	pos_opt = dict(
	source=source,
	size=10,
	fill_alpha=0.5,
	fill_color="magenta",
	color="magenta",
	alpha=0.5
	)
	forces_position = fig_scheme.circle('xF', 'y', **pos_opt)


	# beam (scheme)
	scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')
	scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)
	# uniform load (scheme)
	scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',
	fill_alpha=0.3, alpha=0.3)
	scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',
	color='navy', fill_alpha=0.3, alpha=0.3)
	# axial force (scheme)
	scheme_axial_force = models.force_vector(fig_scheme, P, LSCALE+P, LSCALE, 0, 0, 'green')
	# Reactions (scheme)
	scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, LSCALE, LSCALE, -Ry_r, 0, 'orange')
	scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')
	scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')
	# force N
	scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# force V
	scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# moment M
	(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)


	# change the uniform load q
	slider_q = Slider(
	title="Change the uniform load q [kN/m]",
	start=0.1,
	end=MAX_Q,
	step=0.1,
	value=q
	)


	# choose position of interest
	slider_position = Slider(
	title="Change the position x along the beam [m]",
	start=0,
	end=L,
	step=0.02,
	value=L
	)


	# choose left or right FBD
	div_rg_FBD = Div(text="Free-body diagram (FBD):")
	radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)


	# choose axial force or not
	div_cb_P = Div(text=f"Axial force P={P} kN (applied)")
	checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])


	# show values of forces and moments
	div_forces = Div(width=DIV_B_FORCES,
	text=sb.div_text_forces(P, P, Ry_l, Ry_r, "No cross section analysed.", 0, 0, 0))


	# figures for the diagrams
	options_diag = dict(
	toolbar_location=None,
	x_axis_label="Position [m]",
	plot_width=FIG_B_B,
	x_range=fig_beam.x_range
	)
	fig_N = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Axial force", "@y kN")],
	y_axis_label="Axial force N [kN]",
	plot_height=int(FIG_H_B*0.8),
	title="N V M Diagrams")
	fig_V = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Shear force", "@y kN")],
	y_axis_label="Shear force V [kN]",
	plot_height=int(FIG_H_B*0.8))
	fig_M = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Bending moment", "@y kNm")],
	y_axis_label="Bending moment M [kNm]",
	plot_height=FIG_H_B)
	fig_N.xaxis.visible = False
	fig_V.xaxis.visible = False


	# plot N V M
	N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)
	+ fig_N.add_tools(HoverTool(renderers=[N_diag],
	+ tooltips= [("Position", "@x m"), ("Axial force", "@y kN")]))
	+
	V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)
	+ fig_V.add_tools(HoverTool(renderers=[V_diag],
	+ tooltips= [("Position", "@x m"), ("Shear force", "@y kN")]))
	+
	M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)
	+ fig_M.add_tools(HoverTool(renderers=[M_diag],
	+ tooltips= [("Position", "@x m"), ("Bending moment", "@y kNm")]))

	# point that shows the position that it's analyzed
	N_position = fig_N.circle('x', 'N', **pos_opt)
	V_position = fig_V.circle('x', 'V', **pos_opt)
	M_position = fig_M.circle('x', 'M', **pos_opt)


	# figures for the stresses and strains
	FIG_B_ss = 200
	FIG_H_ss = 200
	options_stress_strain = dict(
	toolbar_location=None,
	y_axis_label="Height h [mm]",
	plot_width=FIG_B_ss,
	plot_height=FIG_H_ss
	)
	fig_stress_N = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Axial stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2099 [MPa]")
	fig_stress_N.yaxis.visible = False
	fig_axial_strain = figure(**options_stress_strain,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Axial strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2099 [%]",
	y_range=fig_stress_N.y_range)
	fig_axial_strain.yaxis.visible = False
	fig_stress_M = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Bending stress and centroid",
	y_range=fig_stress_N.y_range,
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2098 [MPa]")
	fig_stress_M.yaxis.visible = False
	fig_bending_strain = figure(**options_stress_strain,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Bending strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2098 [%]",
	y_range=fig_stress_N.y_range)
	fig_bending_strain.yaxis.visible = False
	fig_stress_V = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Shear stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU}\u1d65 [MPa]")
	fig_stress_V.yaxis.visible = False
	fig_stress_sigma = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress \N{GREEK SMALL LETTER SIGMA} and neutral axis",
	y_range=fig_stress_N.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA} [MPa]")
	fig_stress_tau = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress \N{GREEK SMALL LETTER TAU}",
	y_range=fig_stress_V.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU} [MPa]")

	# plot stress N V M
	- discr_stress_strain = 10
	+ discr_stress_strain = 201
	scale_x = 25
	y_discr = np.linspace(0, h, discr_stress_strain)
	sigma_N = stst.compute_sigma_axial(y_discr, 0, A)
	N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,
	source_section_scheme, scale_x=scale_x/10)
	+ fig_stress_N.add_tools(HoverTool(renderers=[N_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	sigma_M = stst.compute_sigma_bending(y_discr, 0, Iy, yG)
	(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,
	source_section_scheme, True, yG, scale_x=scale_x)
	+ fig_stress_M.add_tools(HoverTool(renderers=[M_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, yG)
	tau_V = stst.compute_tau_shear(y_discr, 0, S_rect, Iy, b)
	V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)
	+ fig_stress_V.add_tools(HoverTool(renderers=[V_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot stress sigma and tau
	sigma_total = sigma_M + sigma_N
	(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,
	source_section_scheme,True, yG, scale_x=scale_x)
	+ fig_stress_sigma.add_tools(HoverTool(renderers=[sigma_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	tau_total = tau_V
	tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,
	source_section_scheme, scale_x=1)
	+ fig_stress_tau.add_tools(HoverTool(renderers=[tau_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot strain N M
	strain_axial = stst.compute_epsilon_axial(y_discr, sigma_N, E)
	axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)
	+ fig_axial_strain.add_tools(HoverTool(renderers=[axial_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))
	+
	strain_bending = stst.compute_epsilon_bending(y_discr, sigma_M, E)
	bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)
	+ fig_bending_strain.add_tools(HoverTool(renderers=[bending_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))


	# figures for NVM
	fig_NM_section = figure(**options_stress_strain,
	title="N and M at position x",
	match_aspect=True)
	fig_NM_section.axis.visible = False
	fig_NM_section.grid.grid_line_alpha = 0

	fig_V_section = figure(**options_stress_strain,
	title="V at position x",
	match_aspect=True)
	fig_V_section.axis.visible = False
	fig_V_section.grid.grid_line_alpha = 0

	# section with NVM
	models.section_diagram(fig_NM_section)
	models.section_diagram(fig_V_section)

	# NVM in section
	section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')
	section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')
	(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)

	# NVM label in section
	OFFSET_N = 1
	label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[""], text_color="red", text_baseline='bottom')
	label_M_section = fig_NM_section.text(x=[OFFSET_N6], y=[-OFFSET_N5], text=[""], text_color="red", text_baseline='top')
	label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[0], text=[""], text_color="red", text_baseline='middle')


	########################################################
	# Define the new figures, widgets and renderers
	########################################################
	SCALE_TAU = 5

	# Modify the beam figure and plots (see in the previous code cell)


	# Modifiy focus point to square in beam
	beam_position = fig_beam.square('x', 'y_var', **pos_opt)


	# choose height of interest
	slider_y = Slider(
	title="Change the height y along the section [mm]",
	start=0,
	end=h,
	step=1,
	value=initial_y
	)


	# choose angle theta of interest
	slider_theta_element = Slider(
	title="Change the angle \N{GREEK SMALL LETTER THETA} of the element [°]",
	start=0,
	end=90,
	step=0.5,
	value=initial_theta_element
	)


	# figure Mohr circle
	fig_Mohr_circle = figure(toolbar_location=None,
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA} [MPa]",
	y_axis_label="Stress \N{GREEK SMALL LETTER TAU} [MPa]",
	plot_height=FIG_MOHR,
	plot_width=FIG_MOHR,
	match_aspect=True,
	# x_range=[-MAX_STRESS_MOHR, MAX_STRESS_MOHR],
	title="Mohr circle, x axis: stress \N{GREEK SMALL LETTER SIGMA} [MPa], y axis: stress \N{GREEK SMALL LETTER TAU} [MPa]"
	)
	fig_Mohr_circle.axis.fixed_location = 0


	# figure stress state element
	fig_stress_state = figure(toolbar_location=None,
	plot_height=FIG_STRESS_STATE,
	plot_width=FIG_STRESS_STATE,
	match_aspect=True,
	title="Stress state"
	)
	fig_stress_state.grid.grid_line_alpha = 0
	fig_stress_state.axis.visible = False
	fig_stress_state.min_border_left = 0
	fig_stress_state.rect([MAX_DIM_STRESS_STATE0.4], [MAX_DIM_STRESS_STATE0.4],
	width=MAX_DIM_STRESS_STATE*1.2,
	height=MAX_DIM_STRESS_STATE*1.2,
	alpha=0,
	fill_alpha=0)


	# stress state (theta 0)
	fig_stress_state.rect([0], [0],
	width=MAX_STRESS/2,
	height=MAX_STRESS/2,
	angle=0,
	fill_alpha=0, color='black', line_width=2)
	fig_stress_state.text([0], [0],
	text=["Fixed \nelement"],
	text_align="center", text_baseline="middle",
	text_font_size="14px")


	# stress state variable
	stress_state_theta = fig_stress_state.rect([MAX_STRESS*2], [0],
	width=MAX_STRESS/2,
	height=MAX_STRESS/2,
	angle=initial_theta_element,
	fill_alpha=0, color='black', line_width=2)
	label_stress_state_theta = fig_stress_state.text([MAX_STRESS*2], [0],
	text=["Rotating \nelement"],
	text_align="center", text_baseline="middle",
	text_font_size="14px")

	# rotating axis
	rotating_axis = fig_stress_state.line([0, MAX_DIM_STRESS_STATE], [0, 0],
	line_dash="4 4", line_color="black", line_width=0.5)


	# arc and label theta in stress state
	arc_theta_element = fig_stress_state.arc(x=[0], y=[0],
	radius=MAX_STRESS, start_angle=0, end_angle=0,
	line_color="gray", line_dash="2 5")
	label_theta_element = fig_stress_state.text([MAX_STRESS], [0],
	text=[""],
	text_baseline="middle", x_offset=5, text_font_size="14px")

	# fixed axis
	fig_stress_state.line([0, MAX_DIM_STRESS_STATE], [0, 0],
	line_dash="4 4", line_color="black", line_width=0.5)


	# stress state arrows
	arrows_stress_state = models.set_arrows_stress_state(fig_stress_state, sigma_x0, sigma_y0, tau_0, MAX_STRESS/2,
	SCALE_TAU)


	# stress state theta arrows
	arrows_stress_state_theta = models.set_arrows_stress_state(fig_stress_state, sigma_x0, sigma_y0, tau_0, MAX_STRESS/2,
	SCALE_TAU, MAX_STRESS*2)

	# Mohr circle
	Mohr_circle = fig_Mohr_circle.circle([sigma_average_mohr], [0],
	radius=r_circle_mohr,
	fill_alpha=0, color="gray")


	# arc and label theta in Mohr circle
	arc_theta_Mohr = fig_Mohr_circle.arc(x=[sigma_average_mohr], y=[0],
	radius=r_circle_mohr/2, start_angle=0, end_angle=0,
	line_color="gray", line_dash="2 5")
	label_theta_Mohr = fig_Mohr_circle.text([sigma_average_mohr+r_circle_mohr/2], [0],
	text=[""],
	text_baseline="middle", x_offset=5, text_font_size="14px")
	arc_theta_p_Mohr = fig_Mohr_circle.arc(x=[sigma_average_mohr], y=[0],
	radius=r_circle_mohr/2, start_angle=0, end_angle=0,
	line_color="gray", line_dash="2 5")
	label_theta_p_Mohr = fig_Mohr_circle.text([sigma_average_mohr+r_circle_mohr/5*2], [0],
	text=[""],
	text_baseline="middle", x_offset=5, text_font_size="14px")


	# linking line and two points from current stress state
	mohr_points_opt = dict(
	size=5,
	fill_alpha=0.5,
	alpha=0.5
	)
	line_stress_state = fig_Mohr_circle.line([sigma_x0, tau_0], [sigma_y0, -tau_0],
	line_dash="4 4", line_color="blue", line_width=0.5)
	points_stress_state = fig_Mohr_circle.circle([sigma_x0, tau_0], [sigma_y0, -tau_0],
	**mohr_points_opt, color="blue", fill_color="blue")
	str_label_stress_state1 = "Fixed element \n(\N{GREEK SMALL LETTER SIGMA}\N{LATIN SUBSCRIPT SMALL LETTER X}\N{SUBSCRIPT ZERO}, \N{GREEK SMALL LETTER TAU}\N{SUBSCRIPT ZERO})"
	# NB: no subscript of latin y, so use gamma (very similar in the display)
	str_label_stress_state2 = "Fixed element \n(\N{GREEK SMALL LETTER SIGMA}\N{Greek Subscript Small Letter Gamma}\N{SUBSCRIPT ZERO}, -\N{GREEK SMALL LETTER TAU}\N{SUBSCRIPT ZERO})"
	label_points_stress_state = fig_Mohr_circle.text([sigma_x0, tau_0], [sigma_y0, -tau_0],
	text=[str_label_stress_state1, str_label_stress_state2],
	color="blue", x_offset=5, y_offset=18, text_font_size="14px")


	# linking line and two points from stress state in function of theta
	line_stress_state_theta = fig_Mohr_circle.line([sigma_x0, tau_0], [sigma_y0, -tau_0],
	line_dash="4 4", line_color="red", line_width=0.5)
	points_stress_state_theta = fig_Mohr_circle.circle([sigma_x0, tau_0], [sigma_y0, -tau_0],
	**mohr_points_opt, color="red", fill_color="red")
	str_label_stress_state_theta1 = "Rotating element \n(\N{GREEK SMALL LETTER SIGMA}\N{LATIN SUBSCRIPT SMALL LETTER X}, \N{GREEK SMALL LETTER TAU})"
	# NB: no subscript of latin y, so use gamma (very similar in the display)
	str_label_stress_state_theta2 = "Rotating element \n(\N{GREEK SMALL LETTER SIGMA}\N{Greek Subscript Small Letter Gamma}, -\N{GREEK SMALL LETTER TAU})"
	label_points_stress_state_theta = fig_Mohr_circle.text([sigma_x0, tau_0], [sigma_y0, -tau_0],
	text=[str_label_stress_state_theta1, str_label_stress_state_theta2],
	text_align="right",
	color="red", x_offset=-5, y_offset=18, text_font_size="14px")
	-
	+ # add hover for 4 points
	+ fig_Mohr_circle.add_tools(HoverTool(renderers=[points_stress_state, points_stress_state_theta],
	+ tooltips= [("Sigma", "@x MPa"), ("Tau", "@y MPa")]))
	+

	########################################################
	# Configurethe logics
	########################################################
	update_circle_mohr = f"""
	const y_var = db['y_var'][0]
	const A = db['A'][0]
	const b = db['b'][0]
	const h = db['h'][0]
	const yG = db['yG'][0]
	const Iy = db['Iy'][0]
	const theta_element = db['theta_element'][0]
	const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))
	const sigma_y0 = 0
	const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))
	const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)
	const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)
	const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)
	const theta = compute_theta_mohr(theta_element, theta_principal)
	const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)

	// update data
	db['sigma_x0'][0] = sigma_x0
	db['sigma_y0'][0] = sigma_y0
	db['tau_0'][0] = tau_0
	db['sigma_average'][0] = sigma_average
	db['r_circle_mohr'][0] = r_circle
	db['sigma_x'][0] = new_state[0]
	db['sigma_y'][0] = new_state[1]
	db['tau'][0] = new_state[2]
	db['theta'][0] = theta

	update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)
	"""
	args_slider_pos = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	s_M=source_M,
	arr_head=scheme_M_head,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section,
	Mohr_circle=Mohr_circle,
	line_stress_state=line_stress_state,
	line_stress_state_theta=line_stress_state_theta,
	points_stress_state=points_stress_state,
	points_stress_state_theta=points_stress_state_theta,
	label_points_stress_state=label_points_stress_state,
	label_points_stress_state_theta=label_points_stress_state_theta,
	arc_theta_Mohr=arc_theta_Mohr,
	label_theta_Mohr=label_theta_Mohr,
	arc_theta_p_Mohr=arc_theta_p_Mohr,
	label_theta_p_Mohr=label_theta_p_Mohr,
	arrow_sigma_x1=arrows_stress_state[0],
	arrow_sigma_x2=arrows_stress_state[1],
	arrow_sigma_y1=arrows_stress_state[2],
	arrow_sigma_y2=arrows_stress_state[3],
	arrow_tau_x1=arrows_stress_state[4],
	arrow_tau_x2=arrows_stress_state[5],
	arrow_tau_y1=arrows_stress_state[6],
	arrow_tau_y2=arrows_stress_state[7],
	arrow_sigma_x1_theta=arrows_stress_state_theta[0],
	arrow_sigma_x2_theta=arrows_stress_state_theta[1],
	arrow_sigma_y1_theta=arrows_stress_state_theta[2],
	arrow_sigma_y2_theta=arrows_stress_state_theta[3],
	arrow_tau_x1_theta=arrows_stress_state_theta[4],
	arrow_tau_x2_theta=arrows_stress_state_theta[5],
	arrow_tau_y1_theta=arrows_stress_state_theta[6],
	arrow_tau_y2_theta=arrows_stress_state_theta[7])
	code_slider_pos = f"""
	// retrieve data
	const db = source.data
	const data_sb = s_sb.data
	const data_q = s_q.data
	const FBD = db['FBD'][0]
	const pos = cb_obj.value
	const q = db['q'][0]
	const L = db['L'][0]
	const N = compute_N(db['P'][0])
	const V = compute_V(pos, q, L)
	const M = compute_M(pos, q, L)

	// update data
	db['N'][0] = N
	db['V'][0] = V
	db['M'][0] = M
	db['x'][0] = pos

	// check state
	check_state(db)

	// update:
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)
	{update_circle_mohr}
	update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)
	update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)
	update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)
	update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)
	update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)
	update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)

	// apply the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	// declare functions
	{sb.implement_compute_NJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_growthJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_NVM_diagramJS()}
	{models.implement_check_stateJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_sigma_axialJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_tau_shearJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_neutral_axisJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_update_NVM_sectionJS()}
	{mohrcircle.implement_compute_radius_mohrJS()}
	{mohrcircle.implement_compute_sigma_average_mohrJS()}
	{mohrcircle.implement_compute_stress_state_mohrJS()}
	{mohrcircle.implement_compute_principal_theta_mohrJS()}
	{mohrcircle.implement_compute_theta_mohrJS()}
	{mohrcircle.implement_update_circle_mohrJS()}
	{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}
	{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}
	"""
	updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)


	args_slider_b = dict(source=source,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	Mohr_circle=Mohr_circle,
	line_stress_state=line_stress_state,
	points_stress_state=points_stress_state,
	points_stress_state_theta=points_stress_state_theta,
	line_stress_state_theta=line_stress_state_theta,
	label_points_stress_state=label_points_stress_state,
	label_points_stress_state_theta=label_points_stress_state_theta,
	arc_theta_Mohr=arc_theta_Mohr,
	label_theta_Mohr=label_theta_Mohr,
	arc_theta_p_Mohr=arc_theta_p_Mohr,
	label_theta_p_Mohr=label_theta_p_Mohr,
	arrow_sigma_x1=arrows_stress_state[0],
	arrow_sigma_x2=arrows_stress_state[1],
	arrow_sigma_y1=arrows_stress_state[2],
	arrow_sigma_y2=arrows_stress_state[3],
	arrow_tau_x1=arrows_stress_state[4],
	arrow_tau_x2=arrows_stress_state[5],
	arrow_tau_y1=arrows_stress_state[6],
	arrow_tau_y2=arrows_stress_state[7],
	arrow_sigma_x1_theta=arrows_stress_state_theta[0],
	arrow_sigma_x2_theta=arrows_stress_state_theta[1],
	arrow_sigma_y1_theta=arrows_stress_state_theta[2],
	arrow_sigma_y2_theta=arrows_stress_state_theta[3],
	arrow_tau_x1_theta=arrows_stress_state_theta[4],
	arrow_tau_x2_theta=arrows_stress_state_theta[5],
	arrow_tau_y1_theta=arrows_stress_state_theta[6],
	arrow_tau_y2_theta=arrows_stress_state_theta[7])
	code_change_b = f"""
	// retrieve data used
	const db = source.data
	const b = cb_obj.value // value of the slider
	const h = db['h'][0]
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)
	const yG = db['yG'][0]
	const N = db['N'][0]
	const M = db['M'][0]
	const V = db['V'][0]
	const y_var = db['y_var'][0]
	const theta_element = db['theta_element'][0]
	const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))
	const sigma_y0 = 0
	const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))
	const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)
	const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)
	const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)
	const theta = compute_theta_mohr(theta_element, theta_principal)
	const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)

	// apply the changes
	db['b'][0] = b
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)
	db['sigma_x0'][0] = sigma_x0
	db['sigma_y0'][0] = sigma_y0
	db['tau_0'][0] = tau_0
	db['sigma_average'][0] = sigma_average
	db['r_circle_mohr'][0] = r_circle
	db['sigma_x'][0] = new_state[0]
	db['sigma_y'][0] = new_state[1]
	db['tau'][0] = new_state[2]
	db['theta'][0] = theta

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	// Mohr circle
	update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)
	// stress state
	update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)
	update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)
	update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)
	// stress state (theta)
	update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)
	update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)
	update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)

	// emit the changes
	source.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_arrow_growthJS()}
	{mohrcircle.implement_compute_radius_mohrJS()}
	{mohrcircle.implement_compute_stress_state_mohrJS()}
	{mohrcircle.implement_compute_sigma_average_mohrJS()}
	{mohrcircle.implement_compute_principal_theta_mohrJS()}
	{mohrcircle.implement_compute_theta_mohrJS()}
	{mohrcircle.implement_update_circle_mohrJS()}
	{js.implement_update_arrowJS()}
	{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}
	{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}
	"""
	update_b = CustomJS(args=args_slider_b, code=code_change_b)


	args_slider_h = dict(source=source,
	s_ss=source_section_scheme,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	slider_y=slider_y,
	beam=beam,
	Mohr_circle=Mohr_circle,
	line_stress_state=line_stress_state,
	points_stress_state=points_stress_state,
	points_stress_state_theta=points_stress_state_theta,
	line_stress_state_theta=line_stress_state_theta,
	label_points_stress_state=label_points_stress_state,
	label_points_stress_state_theta=label_points_stress_state_theta,
	arc_theta_Mohr=arc_theta_Mohr,
	label_theta_Mohr=label_theta_Mohr,
	arc_theta_p_Mohr=arc_theta_p_Mohr,
	label_theta_p_Mohr=label_theta_p_Mohr,
	arrow_sigma_x1=arrows_stress_state[0],
	arrow_sigma_x2=arrows_stress_state[1],
	arrow_sigma_y1=arrows_stress_state[2],
	arrow_sigma_y2=arrows_stress_state[3],
	arrow_tau_x1=arrows_stress_state[4],
	arrow_tau_x2=arrows_stress_state[5],
	arrow_tau_y1=arrows_stress_state[6],
	arrow_tau_y2=arrows_stress_state[7],
	arrow_sigma_x1_theta=arrows_stress_state_theta[0],
	arrow_sigma_x2_theta=arrows_stress_state_theta[1],
	arrow_sigma_y1_theta=arrows_stress_state_theta[2],
	arrow_sigma_y2_theta=arrows_stress_state_theta[3],
	arrow_tau_x1_theta=arrows_stress_state_theta[4],
	arrow_tau_x2_theta=arrows_stress_state_theta[5],
	arrow_tau_y1_theta=arrows_stress_state_theta[6],
	arrow_tau_y2_theta=arrows_stress_state_theta[7])
	code_change_h = f"""
	// solve sliders conflict
	const db = source.data
	const h = cb_obj.value // value of the slider
	if (h < db['y_var'][0]) {{
	db['y_var'][0] = h
	}}
	slider_y.end = h
	if (h < slider_y.value) {{
	slider_y.value = h
	}}

	// retrieve data used
	const data_ss = s_ss.data
	const b = db['b'][0]
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)
	const N = db['N'][0]
	const V = db['V'][0]
	const M = db['M'][0]
	const yG = compute_centroid_y(h)
	const y_var = db['y_var'][0]
	const theta_element = db['theta_element'][0]
	const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))
	const sigma_y0 = 0
	const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))
	const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)
	const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)
	const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)
	const theta = compute_theta_mohr(theta_element, theta_principal)
	const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)

	// apply the changes
	db['h'][0] = h
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)
	db['yG'][0] = yG
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)
	beam.glyph.height = h // change the beam height
	beam.glyph.y = h/2
	data_ss['y'][1] = h // change the height of the section in the diagrams
	db['sigma_x0'][0] = sigma_x0
	db['sigma_y0'][0] = sigma_y0
	db['tau_0'][0] = tau_0
	db['sigma_average'][0] = sigma_average
	db['r_circle_mohr'][0] = r_circle
	db['sigma_x'][0] = new_state[0]
	db['sigma_y'][0] = new_state[1]
	db['tau'][0] = new_state[2]
	db['theta'][0] = theta

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	// Mohr circle
	update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)
	// stress state
	update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)
	update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)
	update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)
	// stress state (theta)
	update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)
	update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)
	update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)

	// emit the changes
	source.change.emit()
	s_ss.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{js.implement_arrow_growthJS()}
	{mohrcircle.implement_compute_radius_mohrJS()}
	{mohrcircle.implement_compute_stress_state_mohrJS()}
	{mohrcircle.implement_compute_sigma_average_mohrJS()}
	{mohrcircle.implement_compute_principal_theta_mohrJS()}
	{mohrcircle.implement_compute_theta_mohrJS()}
	{mohrcircle.implement_update_circle_mohrJS()}
	{js.implement_update_arrowJS()}
	{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}
	{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}
	"""
	update_h = CustomJS(args=args_slider_h, code=code_change_h)


	args_checkbox_P = dict(source=source,
	s_M=source_M,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	N_diag=N_diag,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section,
	Mohr_circle=Mohr_circle,
	line_stress_state=line_stress_state,
	points_stress_state=points_stress_state,
	points_stress_state_theta=points_stress_state_theta,
	line_stress_state_theta=line_stress_state_theta,
	label_points_stress_state=label_points_stress_state,
	label_points_stress_state_theta=label_points_stress_state_theta,
	arc_theta_Mohr=arc_theta_Mohr,
	label_theta_Mohr=label_theta_Mohr,
	arc_theta_p_Mohr=arc_theta_p_Mohr,
	label_theta_p_Mohr=label_theta_p_Mohr,
	arrow_sigma_x1=arrows_stress_state[0],
	arrow_sigma_x2=arrows_stress_state[1],
	arrow_sigma_y1=arrows_stress_state[2],
	arrow_sigma_y2=arrows_stress_state[3],
	arrow_sigma_x1_theta=arrows_stress_state_theta[0],
	arrow_sigma_x2_theta=arrows_stress_state_theta[1],
	arrow_sigma_y1_theta=arrows_stress_state_theta[2],
	arrow_sigma_y2_theta=arrows_stress_state_theta[3],
	arrow_tau_x1_theta=arrows_stress_state_theta[4],
	arrow_tau_x2_theta=arrows_stress_state_theta[5],
	arrow_tau_y1_theta=arrows_stress_state_theta[6],
	arrow_tau_y2_theta=arrows_stress_state_theta[7])
	code_checkbox_P = f"""
	// retrieve var from the object that uses callback
	var f = cb_obj.active // checkbox P
	if (f.length==0) f = [1]
	const P = {P}*(1-f)
	const db = source.data
	const N = compute_N(P)
	const M = db['M'][0]
	const A = db['A'][0]
	const Iy = db['Iy'][0]
	const yG = db['yG'][0]
	const y_var = db['y_var'][0]
	const theta_element = db['theta_element'][0]
	const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))
	const sigma_y0 = 0
	const tau_0 = db['tau_0'][0]
	const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)
	const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)
	const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)
	const theta = compute_theta_mohr(theta_element, theta_principal)
	const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)

	// apply the changes
	db['P'][0] = P
	db['N'][0] = N
	db['Rx'][0] = compute_Rx(db['P'][0])
	db['sigma_x0'][0] = sigma_x0
	db['sigma_y0'][0] = sigma_y0
	db['sigma_average'][0] = sigma_average
	db['r_circle_mohr'][0] = r_circle
	db['sigma_x'][0] = new_state[0]
	db['sigma_y'][0] = new_state[1]
	db['tau'][0] = new_state[2]
	db['theta'][0] = theta

	// update
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_N_diagram(db, N_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)
	// Mohr circle
	update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)
	// stress state
	update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)
	update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)
	// stress state (theta)
	update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)
	update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)
	update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)

	// emit the changes
	source.change.emit()

	// declare functions
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_compute_RxJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_compute_NJS()}
	{sb.implement_update_N_diagramJS(discr_NVM)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_neutral_axisJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{stst.implement_compute_total_tauJS()}
	{js.implement_arrow_growthJS()}
	{mohrcircle.implement_compute_radius_mohrJS()}
	{mohrcircle.implement_compute_stress_state_mohrJS()}
	{mohrcircle.implement_compute_sigma_average_mohrJS()}
	{mohrcircle.implement_compute_principal_theta_mohrJS()}
	{mohrcircle.implement_compute_theta_mohrJS()}
	{mohrcircle.implement_update_circle_mohrJS()}
	{js.implement_update_arrowJS()}
	{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}
	"""
	update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)


	args_radiogroup_FBD = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	s_M=source_M,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_radiogroup_FBD = f"""
	// retrieve data
	const db = source.data
	const FBD = cb_obj.active
	const data_sb = s_sb.data
	const data_q = s_q.data
	const pos = db['x'][0]

	// apply the changes
	db['FBD'][0] = FBD

	// update
	check_state(db)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// emit the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	{models.implement_check_stateJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)


	args_slider_q = dict(source=source,
	s_q=source_scheme_q,
	s_M=source_M,
	div_f=div_forces,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	V_diag=V_diag,
	M_diag=M_diag,
	centroid=centroid,
	neutral_axis=neutral_axis,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section,
	Mohr_circle=Mohr_circle,
	line_stress_state=line_stress_state,
	points_stress_state=points_stress_state,
	points_stress_state_theta=points_stress_state_theta,
	line_stress_state_theta=line_stress_state_theta,
	label_points_stress_state=label_points_stress_state,
	label_points_stress_state_theta=label_points_stress_state_theta,
	arc_theta_Mohr=arc_theta_Mohr,
	label_theta_Mohr=label_theta_Mohr,
	arc_theta_p_Mohr=arc_theta_p_Mohr,
	label_theta_p_Mohr=label_theta_p_Mohr,
	arrow_sigma_x1=arrows_stress_state[0],
	arrow_sigma_x2=arrows_stress_state[1],
	arrow_sigma_y1=arrows_stress_state[2],
	arrow_sigma_y2=arrows_stress_state[3],
	arrow_tau_x1=arrows_stress_state[4],
	arrow_tau_x2=arrows_stress_state[5],
	arrow_tau_y1=arrows_stress_state[6],
	arrow_tau_y2=arrows_stress_state[7],
	arrow_sigma_x1_theta=arrows_stress_state_theta[0],
	arrow_sigma_x2_theta=arrows_stress_state_theta[1],
	arrow_sigma_y1_theta=arrows_stress_state_theta[2],
	arrow_sigma_y2_theta=arrows_stress_state_theta[3],
	arrow_tau_x1_theta=arrows_stress_state_theta[4],
	arrow_tau_x2_theta=arrows_stress_state_theta[5],
	arrow_tau_y1_theta=arrows_stress_state_theta[6],
	arrow_tau_y2_theta=arrows_stress_state_theta[7])
	code_slider_q = f"""
	// retrieve data
	const db = source.data
	const q = cb_obj.value
	const pos = db['x'][0]
	const L = db['L'][0]
	const N = db['N'][0]
	const V = compute_V(pos, q, L)
	const M = compute_M(pos, q, L)
	const y_var = db['y_var'][0]
	const A = db['A'][0]
	const b = db['b'][0]
	const h = db['h'][0]
	const yG = db['yG'][0]
	const Iy = db['Iy'][0]
	const theta_element = db['theta_element'][0]
	const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))
	const sigma_y0 = 0
	const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))
	const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)
	const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)
	const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)
	const theta = compute_theta_mohr(theta_element, theta_principal)
	const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)

	// update data
	db['q'][0] = q
	db['V'][0] = V
	db['M'][0] = M
	db['Ry_l'][0] = compute_Ry_l(q, L)
	db['Ry_r'][0] = compute_Ry_r(q, L)
	db['sigma_x0'][0] = sigma_x0
	db['sigma_y0'][0] = sigma_y0
	db['tau_0'][0] = tau_0
	db['sigma_average'][0] = sigma_average
	db['r_circle_mohr'][0] = r_circle
	db['sigma_x'][0] = new_state[0]
	db['sigma_y'][0] = new_state[1]
	db['tau'][0] = new_state[2]
	db['theta'][0] = theta

	// update
	update_u_load(db, s_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_V_diagram(db, V_diag)
	update_M_diagram(db, M_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)
	// Mohr circle
	update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)
	// stress state
	update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)
	update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)
	update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)
	// stress state (theta)
	update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)
	update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)
	update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)

	// apply changes
	source.change.emit()

	// declare functions
	{js.implement_update_arrowJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_compute_Ry_lJS()}
	{sb.implement_compute_Ry_rJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_update_V_diagramJS(discr_NVM)}
	{sb.implement_update_M_diagramJS(discr_NVM)}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_u_loadJS(OFFSET_Q)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_neutral_axisJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	{mohrcircle.implement_compute_radius_mohrJS()}
	{mohrcircle.implement_compute_stress_state_mohrJS()}
	{mohrcircle.implement_compute_sigma_average_mohrJS()}
	{mohrcircle.implement_compute_principal_theta_mohrJS()}
	{mohrcircle.implement_compute_theta_mohrJS()}
	{mohrcircle.implement_update_circle_mohrJS()}
	{js.implement_update_arrowJS()}
	{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}
	{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}
	"""
	update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)


	args_slider_theta = dict(source=source,
	Mohr_circle=Mohr_circle,
	line_stress_state=line_stress_state,
	points_stress_state=points_stress_state,
	line_stress_state_theta=line_stress_state_theta,
	points_stress_state_theta=points_stress_state_theta,
	label_points_stress_state=label_points_stress_state,
	label_points_stress_state_theta=label_points_stress_state_theta,
	stress_state_theta=stress_state_theta,
	label_stress_state_theta=label_stress_state_theta,
	arc_theta_element=arc_theta_element,
	label_theta_element= label_theta_element,
	arc_theta_Mohr=arc_theta_Mohr,
	label_theta_Mohr=label_theta_Mohr,
	arc_theta_p_Mohr=arc_theta_p_Mohr,
	label_theta_p_Mohr=label_theta_p_Mohr,
	rotating_axis=rotating_axis,
	beam_position=beam_position,
	arrow_sigma_x1_theta=arrows_stress_state_theta[0],
	arrow_sigma_x2_theta=arrows_stress_state_theta[1],
	arrow_sigma_y1_theta=arrows_stress_state_theta[2],
	arrow_sigma_y2_theta=arrows_stress_state_theta[3],
	arrow_tau_x1_theta=arrows_stress_state_theta[4],
	arrow_tau_x2_theta=arrows_stress_state_theta[5],
	arrow_tau_y1_theta=arrows_stress_state_theta[6],
	arrow_tau_y2_theta=arrows_stress_state_theta[7])
	code_slider_theta = f"""
	// retrieve data
	const db = source.data
	const theta_element = cb_obj.value/180*Math.PI
	const sigma_x0 = db['sigma_x0'][0]
	const sigma_y0 = db['sigma_y0'][0]
	const tau_0 = db['tau_0'][0]
	const sigma_average = db['sigma_average'][0]
	const r_circle = db['r_circle_mohr'][0]
	const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)
	const theta = compute_theta_mohr(theta_element, theta_principal)
	const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)

	// update data
	db['sigma_x'][0] = new_state[0]
	db['sigma_y'][0] = new_state[1]
	db['tau'][0] = new_state[2]
	db['theta_element'][0] = theta_element
	db['theta'][0] = theta

	// update
	// square point:
	beam_position.glyph.angle = theta_element
	// stress state element
	update_stress_state_elements(db, stress_state_theta, rotating_axis, label_stress_state_theta, arc_theta_element, label_theta_element)
	// stress state (theta)
	update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)
	update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)
	update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)
	// update Mohr circle
	update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)

	// apply changes
	source.change.emit()

	// declare functions
	{mohrcircle.implement_update_stress_state_elementsJS(MAX_STRESS, MAX_DIM_STRESS_STATE)}
	{js.implement_arrow_growthJS()}
	{mohrcircle.implement_compute_stress_state_mohrJS()}
	{mohrcircle.implement_compute_principal_theta_mohrJS()}
	{mohrcircle.implement_compute_theta_mohrJS()}
	{mohrcircle.implement_update_circle_mohrJS()}
	{js.implement_update_arrowJS()}
	{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}
	"""
	update_slider_theta = CustomJS(args=args_slider_theta, code=code_slider_theta)


	args_slider_y = dict(source=source,
	Mohr_circle=Mohr_circle,
	line_stress_state=line_stress_state,
	points_stress_state=points_stress_state,
	line_stress_state_theta=line_stress_state_theta,
	points_stress_state_theta=points_stress_state_theta,
	label_points_stress_state=label_points_stress_state,
	label_points_stress_state_theta=label_points_stress_state_theta,
	arc_theta_Mohr=arc_theta_Mohr,
	label_theta_Mohr=label_theta_Mohr,
	arc_theta_p_Mohr=arc_theta_p_Mohr,
	label_theta_p_Mohr=label_theta_p_Mohr,
	beam_position=beam_position,
	arrow_sigma_x1=arrows_stress_state[0],
	arrow_sigma_x2=arrows_stress_state[1],
	arrow_sigma_y1=arrows_stress_state[2],
	arrow_sigma_y2=arrows_stress_state[3],
	arrow_tau_x1=arrows_stress_state[4],
	arrow_tau_x2=arrows_stress_state[5],
	arrow_tau_y1=arrows_stress_state[6],
	arrow_tau_y2=arrows_stress_state[7],
	arrow_sigma_x1_theta=arrows_stress_state_theta[0],
	arrow_sigma_x2_theta=arrows_stress_state_theta[1],
	arrow_sigma_y1_theta=arrows_stress_state_theta[2],
	arrow_sigma_y2_theta=arrows_stress_state_theta[3],
	arrow_tau_x1_theta=arrows_stress_state_theta[4],
	arrow_tau_x2_theta=arrows_stress_state_theta[5],
	arrow_tau_y1_theta=arrows_stress_state_theta[6],
	arrow_tau_y2_theta=arrows_stress_state_theta[7])
	code_slider_y = f"""
	// retrieve data
	const db = source.data
	const y_var = cb_obj.value
	const N = db['N'][0]
	const V = db['V'][0]
	const M = db['M'][0]
	const A = db['A'][0]
	const b = db['b'][0]
	const h = db['h'][0]
	const yG = db['yG'][0]
	const Iy = db['Iy'][0]
	const theta_element = db['theta_element'][0]
	const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))
	const sigma_y0 = 0
	const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))
	const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)
	const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)
	const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)
	const theta = compute_theta_mohr(theta_element, theta_principal)
	const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)

	// update data
	db['y_var'][0] = y_var
	db['sigma_x0'][0] = sigma_x0
	db['sigma_y0'][0] = sigma_y0
	db['tau_0'][0] = tau_0
	db['sigma_average'][0] = sigma_average
	db['r_circle_mohr'][0] = r_circle
	db['sigma_x'][0] = new_state[0]
	db['sigma_y'][0] = new_state[1]
	db['tau'][0] = new_state[2]
	db['theta'][0] = theta

	// update
	// square point:
	beam_position.glyph.y = y_var
	// update Mohr circle
	update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)
	// stress state
	update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)
	update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)
	update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)
	// stress state (theta)
	update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)
	update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)
	update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)

	// apply changes
	source.change.emit()

	// declare functions
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_sigma_axialJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_tau_shearJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{js.implement_arrow_growthJS()}
	{mohrcircle.implement_compute_radius_mohrJS()}
	{mohrcircle.implement_compute_stress_state_mohrJS()}
	{mohrcircle.implement_compute_sigma_average_mohrJS()}
	{mohrcircle.implement_compute_principal_theta_mohrJS()}
	{mohrcircle.implement_compute_theta_mohrJS()}
	{mohrcircle.implement_update_circle_mohrJS()}
	{js.implement_update_arrowJS()}
	{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}
	{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}
	{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}
	{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}
	"""
	update_slider_y = CustomJS(args=args_slider_y, code=code_slider_y)


	# apply the logics
	slider_b.js_on_change('value', update_b)
	slider_h.js_on_change('value', update_h)
	slider_position.js_on_change('value', updade_slider_pos)
	checkbox_P.js_on_click(update_checkbox_P)
	radiogroup_FBD.js_on_click(update_radiogroup_FBD)
	slider_q.js_on_change('value', update_slider_q)
	slider_theta_element.js_on_change('value', update_slider_theta)
	slider_y.js_on_change('value', update_slider_y)


	########################################################
	# Build the layout
	########################################################
	padding_layout = 10
	layout1 = layout([
	[column(row(column(fig_scheme,
	row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout),
	slider_b,
	slider_h,
	# row(div_geo, div_forces),
	slider_y,
	slider_theta_element,
	Spacer(height=padding_layout),
	slider_position,
	slider_q,
	div_rg_FBD,
	radiogroup_FBD,
	div_cb_P,
	checkbox_P))),
	column(fig_beam,
	Spacer(height=padding_layout),
	fig_N,
	fig_V,
	fig_M)),
	row(column(
	row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_stress_sigma),
	row(fig_V_section, Spacer(width=FIG_B_ss), fig_stress_V, Spacer(width=FIG_B_ss), Spacer(width=FIG_B_ss), fig_stress_tau),
	))
	),
	column(fig_Mohr_circle, fig_stress_state)
	],
	])

	show(layout1)
	\ No newline at end of file
	diff --git a/HiddenCode/hidden_code_nb_plastic.py b/HiddenCode/hidden_code_nb_plastic.py
	index 8cf8c6f..6f31687 100644
	--- a/HiddenCode/hidden_code_nb_plastic.py
	+++ b/HiddenCode/hidden_code_nb_plastic.py
	@@ -1,1183 +1,1188 @@
	import math
	import numpy as np
	from bokeh.layouts import layout, column, row
	from bokeh.models.annotations import Label, Arrow
	from bokeh.models.arrow_heads import VeeHead
	-from bokeh.models import Div, CustomJS, Slider, Spacer, Text
	+from bokeh.models import Div, CustomJS, Slider, Spacer, Text, HoverTool
	from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup
	from bokeh.plotting import figure, show, ColumnDataSource
	from bokeh.io import output_notebook
	from cienpy import simplebeam as sb
	from cienpy import rectangular_section as beam_section
	from cienpy import stress_strain_elastic as ststel
	from cienpy import stress_strain_plastic as ststpl
	from cienpy import models
	from cienpy import javascriptcodes as js

	output_notebook()


	def main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, E_steel, fy, fy_steel, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr):
	########################################################
	# Initialisation
	########################################################
	# constants for the visualisation
	SCALE = 10
	OFFSET_Q = q
	MAX_B = 3*b
	MAX_H = 3*h
	MAX_Q = q/4*5

	# store the values in a specific format
	data_beam = dict(
	x=[0, L],
	y=[0, 0]
	)

	data_scheme_beam = dict(
	x=[0, L*SCALE],
	y=[0, 0]
	)

	data_scheme_q = dict(
	x=[0, 0, LSCALE, LSCALE],
	y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],
	x_fade=[0, 0, LSCALE, LSCALE]
	)

	data_section_scheme = dict(
	x=[0, 0],
	y=[0, h]
	)

	initial_position = L
	initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC
	initial_FBD = 0 # right=0 left=1
	data = dict( # stores every useful single variable
	state=[initial_state],
	FBD=[initial_FBD],
	SCALE=[SCALE],
	L=[L],
	b=[b],
	h=[h],
	E=[E],
	fy=[fy],
	A=[A],
	Iy=[Iy],
	Iz=[Iz],
	yG=[yG],
	y_n_axis=[y_n_axis],
	P=[P],
	x=[initial_position],
	y=[0],
	q=[q],
	Rx=[Rx],
	Ry_l=[Ry_l],
	Ry_r=[Ry_r],
	N=[N],
	V=[V],
	M=[M],
	xF=[L*SCALE]
	)

	source_beam = ColumnDataSource(data_beam)
	source_scheme_beam = ColumnDataSource(data_scheme_beam)
	source_scheme_q = ColumnDataSource(data_scheme_q)
	source_section_scheme = ColumnDataSource(data_section_scheme)
	source = ColumnDataSource(data)


	########################################################
	# Define figures, widgets and renderers as from the previous notebook
	########################################################
	FIG_H_B = 200 # height figure beam
	FIG_B_B = 700 # width figure beam
	FIG_H_S = FIG_H_B # height figure scheme
	FIG_B_S = FIG_B_B # width figure scheme
	FIG_H_SEC = 600 # height figure section
	DIV_B_GEO = 170
	DIV_B_FORCES = 170

	options = dict(
	toolbar_location=None
	)

	# figure for the beam
	paddingx = 0.2*L
	int_x_b = (0-paddingx, L+paddingx)
	int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)
	fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,
	f_h=FIG_H_B, f_b=FIG_B_B)


	# figure for the cross-section
	fig_section = sb.define_fig_section(MAX_B0.8, MAX_H0.8, options, FIG_H_SEC)


	# beam
	(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,
	ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)

	# section
	section = beam_section.draw_section(fig_section, b, h)


	# show mechanical parameters
	div_geo = Div(width= DIV_B_GEO,
	text=beam_section.div_text_geo(round(h), round(b), round(L),
	"{:.2e}".format(A),
	"{:.2e}".format(Iy),
	"{:.2e}".format(Iz)))


	# change geometry
	slider_b = Slider(
	title="Change the width b [mm]",
	start=10,
	end=MAX_B,
	step=10,
	value=b
	)
	slider_h = Slider(
	title="Change the height h [mm]",
	start=20,
	end=MAX_H,
	step=20,
	value=h
	)

	# reference system
	axis_arrow_length = 0.8
	axis_arrow_scale = 100
	models.force_vector(fig_section, axis_arrow_length10, 0, 0, 0, axis_arrow_lengthaxis_arrow_scale*1.6, 'gray') # y axis
	fig_section.text(x=[0], y=[axis_arrow_lengthaxis_arrow_scale1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2)
	models.force_vector(fig_section, axis_arrow_length10, 0, -axis_arrow_lengthaxis_arrow_scale, 0, 0, 'gray') # z axis
	fig_section.text(x=[-axis_arrow_lengthaxis_arrow_scale1.1], y=[0], text=["z"], text_color='gray', text_align='right', text_baseline='middle')


	# figure for the forces and moments
	fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)


	# uniform load (beam)
	u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE], width=L, height=q/SCALE,
	fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)
	label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE], text=["q"], text_color="blue")


	# axial force (beam)
	axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')
	label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=["P"], text_color="green")


	# position point
	pos_opt = dict(
	source=source,
	size=10,
	fill_alpha=0.5,
	fill_color="magenta",
	color="magenta",
	alpha=0.5
	)
	beam_position = fig_beam.circle('x', 'y', **pos_opt)
	forces_position = fig_scheme.circle('xF', 'y', **pos_opt)


	# beam (scheme)
	scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')
	scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)
	# uniform load (scheme)
	scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',
	fill_alpha=0.3, alpha=0.3)
	scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',
	color='navy', fill_alpha=0.3, alpha=0.3)
	# axial force (scheme)
	scheme_axial_force = models.force_vector(fig_scheme, P, LSCALE+P, LSCALE, 0, 0, 'green')
	# Reactions (scheme)
	scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, LSCALE, LSCALE, -Ry_r, 0, 'orange')
	scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')
	scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')
	# force N
	scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# force V
	scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# moment M
	(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)


	# change the uniform load q
	slider_q = Slider(
	title="Change the uniform load q [kN/m]",
	start=0.1,
	end=MAX_Q,
	step=0.1,
	value=q
	)


	# choose position of interest
	slider_position = Slider(
	title="Change the position x along the beam [m]",
	start=0,
	end=L,
	step=0.02,
	value=L
	)


	# choose left or right FBD
	div_rg_FBD = Div(text="Free-body diagram (FBD):")
	radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)


	# choose axial force or not
	div_cb_P = Div(text=f"Axial force P={P} kN (applied)")
	checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])


	# show values of forces and moments
	div_forces = Div(width=DIV_B_FORCES,
	text=sb.div_text_forces(P, P, Ry_l, Ry_r, "No cross section analysed.", 0, 0, 0))


	# figures for the diagrams
	options_diag = dict(
	toolbar_location=None,
	x_axis_label="Position [m]",
	plot_width=FIG_B_B,
	x_range=fig_beam.x_range
	)
	fig_N = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Axial force", "@y kN")],
	y_axis_label="Axial force N [kN]",
	plot_height=int(FIG_H_B*0.8),
	title="N V M Diagrams")
	fig_V = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Shear force", "@y kN")],
	y_axis_label="Shear force V [kN]",
	plot_height=int(FIG_H_B*0.8))
	fig_M = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Bending moment", "@y kNm")],
	y_axis_label="Bending moment M [kNm]",
	plot_height=FIG_H_B)
	fig_N.xaxis.visible = False
	fig_V.xaxis.visible = False


	# plot N V M
	N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)
	+ fig_N.add_tools(HoverTool(renderers=[N_diag],
	+ tooltips= [("Position", "@x m"), ("Axial force", "@y kN")]))
	+
	V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)
	+ fig_V.add_tools(HoverTool(renderers=[V_diag],
	+ tooltips= [("Position", "@x m"), ("Shear force", "@y kN")]))
	+
	M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)
	+ fig_M.add_tools(HoverTool(renderers=[M_diag],
	+ tooltips= [("Position", "@x m"), ("Bending moment", "@y kNm")]))

	# point that shows the position that it's analyzed
	N_position = fig_N.circle('x', 'N', **pos_opt)
	V_position = fig_V.circle('x', 'V', **pos_opt)
	M_position = fig_M.circle('x', 'M', **pos_opt)


	# figures for the stresses and strains
	FIG_B_ss = 200
	FIG_H_ss = 200
	options_stress_strain = dict(
	toolbar_location=None,
	y_axis_label="Height h [mm]",
	plot_height=FIG_H_ss
	)
	fig_stress_N = figure(**options_stress_strain,
	plot_width=FIG_B_ss,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Axial stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2099 [MPa]")
	fig_stress_N.yaxis.visible = False
	fig_axial_strain = figure(**options_stress_strain,
	plot_width=FIG_B_ss,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Axial strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2099 [%]",
	y_range=fig_stress_N.y_range)
	fig_axial_strain.yaxis.visible = False
	fig_stress_M = figure(**options_stress_strain,
	plot_width=FIG_B_ss,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Bending stress and centroid",
	y_range=fig_stress_N.y_range,
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2098 [MPa]")
	fig_stress_M.yaxis.visible = False
	fig_bending_strain = figure(**options_stress_strain,
	plot_width=FIG_B_ss,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Bending strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2098 [%]",
	y_range=fig_stress_N.y_range)
	fig_bending_strain.yaxis.visible = False
	fig_stress_V = figure(**options_stress_strain,
	plot_width=FIG_B_ss,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Shear stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU}\u1d65 [MPa]")
	fig_stress_V.yaxis.visible = False
	fig_stress_sigma = figure(**options_stress_strain,
	plot_width=int(FIG_B_ss*1.2),
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress (green=yield) and N.A.",
	y_range=fig_stress_N.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA} [MPa]")
	fig_stress_tau = figure(**options_stress_strain,
	plot_width=int(FIG_B_ss*1.2),
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress \N{GREEK SMALL LETTER TAU}",
	y_range=fig_stress_V.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU} [MPa]")

	# plot stress N V M
	- discr_stress_strain = 10
	+ discr_stress_strain = 201
	scale_x = 25
	y_discr = np.linspace(0, h, discr_stress_strain)
	sigma_N = ststel.compute_sigma_axial(y_discr, 0, A)
	N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,
	source_section_scheme, scale_x=scale_x/10)
	+ fig_stress_N.add_tools(HoverTool(renderers=[N_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	sigma_M = ststel.compute_sigma_bending(y_discr, 0, Iy, yG)
	(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,
	source_section_scheme, True, yG, scale_x=scale_x)
	+ fig_stress_M.add_tools(HoverTool(renderers=[M_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, yG)
	tau_V = ststel.compute_tau_shear(y_discr, 0, S_rect, Iy, b)
	V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)
	+ fig_stress_V.add_tools(HoverTool(renderers=[V_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot stress sigma (moved below) and tau
	tau_total = tau_V
	tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,
	source_section_scheme, scale_x=1)
	+ fig_stress_tau.add_tools(HoverTool(renderers=[tau_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot strain N M
	strain_axial = ststel.compute_epsilon_axial(y_discr, sigma_N, E)
	axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)
	+ fig_axial_strain.add_tools(HoverTool(renderers=[axial_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))
	+
	strain_bending = ststel.compute_epsilon_bending(y_discr, sigma_M, E)
	bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)
	+ fig_bending_strain.add_tools(HoverTool(renderers=[bending_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))


	# figures for NVM
	fig_NM_section = figure(**options_stress_strain,
	plot_width=FIG_B_ss,
	title="N and M at position x",
	match_aspect=True)
	fig_NM_section.axis.visible = False
	fig_NM_section.grid.grid_line_alpha = 0

	fig_V_section = figure(**options_stress_strain,
	plot_width=FIG_B_ss,
	title="V at position x",
	match_aspect=True)
	fig_V_section.axis.visible = False
	fig_V_section.grid.grid_line_alpha = 0

	# section with NVM
	models.section_diagram(fig_NM_section)
	models.section_diagram(fig_V_section)

	# NVM in section
	section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')
	section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')
	(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)

	# NVM label in section
	OFFSET_N = 1
	label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[""], text_color="red", text_baseline='bottom')
	label_M_section = fig_NM_section.text(x=[OFFSET_N6], y=[-OFFSET_N5], text=[""], text_color="red", text_baseline='top')
	label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[0], text=[""], text_color="red", text_baseline='middle')


	########################################################
	# Define the new figures, widgets and renderers
	########################################################
	# choose different elastic modulus
	E_wood = 8e3 # [MPa]
	E_concrete = 26e3 # [MPa]
	E_ceramic = 300e3 # [MPa]
	slider_elastic = Slider(
	title="Change the elastic modulus [MPa]",
	start=E_wood,
	end=E_ceramic,
	step=1e3,
	value=E,
	margin=(5, 5, 0, 5)
	)


	# show values of E
	div_E = Div(margin=(0, 5, 0, 5),
	text=f"""
	<p style='font-size:12px'>
	E<sub>wood</sub> = {math.trunc(E_wood/1e3)} GPa; E<sub>concrete</sub> = {math.trunc(E_concrete/1e3)} GPa<br>
	E<sub>steel</sub> = {math.trunc(E_steel/1e3)} GPa; E<sub>ceramic</sub> = {math.trunc(E_ceramic/1e3)} GPa</p>
	""")


	# choose different yield strength
	fy_wood = 16 # [MPa] (bending)
	fy_concrete = 25 # [MPa]
	fy_glass = 1000 # [MPa] (compressive)
	slider_yield = Slider(
	title="Change the yield strength [MPa]",
	start=fy_wood,
	end=fy_glass,
	step=1,
	value=fy,
	margin=(0, 5, 0, 5)
	)


	# show values of fy
	div_fy = Div(margin=(0, 5, 0, 5),
	text=f"""
	<p style='font-size:12px'>
	f<sub>y,wood</sub> = {math.trunc(fy_wood)} MPa; f<sub>y,concrete</sub> = {math.trunc(fy_concrete)} MPa<br>
	f<sub>y,steel</sub> = {math.trunc(fy_steel)} MPa; f<sub>y,glass</sub> = {math.trunc(fy_glass)} MPa</p>
	""")


	# add total strain epsilon
	fig_total_strain = figure(**options_stress_strain,
	plot_width=FIG_B_ss,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Total strain (green=yield)",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON} [%]",
	y_range=fig_stress_N.y_range)
	fig_total_strain.yaxis.visible = False


	# add the strain and stress with yield implemented
	# plastic
	- discr_pl = 2000
	+ discr_pl = 2001
	(stress_pl, strain_pl, y_discr_pl, yNA_pl) = ststpl.compute_total_stress_strain(discr_pl, h, fy, E, N, M, A, Iy, yG)
	tmp_y = np.linspace(0, h, len(stress_pl))
	total_stress_pl_diag = fig_stress_sigma.line([0, stress_pl, 0], [0, tmp_y, h], color='green')
	total_strain_pl_diag = fig_total_strain.line(strain_pl*0, y_discr_pl, color='green')
	# elastic
	total_strain = ststel.compute_total_epsilon(strain_axial, strain_bending)
	total_strain_diag = models.strain_diagram(fig_total_strain, total_strain, h, source_section_scheme)
	+ fig_total_strain.add_tools(HoverTool(renderers=[total_strain_diag, total_strain_pl_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))
	+
	# (moved from above, total stress sigma elastic)
	sigma_total = sigma_M + sigma_N
	(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,
	source_section_scheme,True, yG, scale_x=scale_x)
	+ fig_stress_sigma.add_tools(HoverTool(renderers=[sigma_stress_diag, total_stress_pl_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+


	########################################################
	# Configurethe logics
	########################################################
	args_slider_pos = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	discr_stress=discr_stress_strain,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	s_M=source_M,
	arr_head=scheme_M_head,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section,
	total_strain_diag=total_strain_diag,
	total_stress_pl_diag=total_stress_pl_diag,
	total_strain_pl_diag=total_strain_pl_diag)
	code_slider_pos = f"""
	// retrieve data
	const db = source.data
	const data_sb = s_sb.data
	const data_q = s_q.data
	const FBD = db['FBD'][0]
	const pos = cb_obj.value
	const q = db['q'][0]
	const L = db['L'][0]

	// update data
	db['N'][0] = compute_N(db['P'][0])
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['x'][0] = pos

	// check state
	check_state(db)

	// update:
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)
	update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)

	// apply the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	// declare functions
	{sb.implement_compute_NJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_growthJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_NVM_diagramJS()}
	{models.implement_check_stateJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{ststel.implement_compute_sigma_axialJS()}
	{ststel.implement_compute_sigma_bendingJS()}
	{ststel.implement_compute_tau_shearJS()}
	{ststel.implement_compute_epsilon_axialJS()}
	{ststel.implement_compute_epsilon_bendingJS()}
	{ststel.implement_compute_total_sigmaJS()}
	{ststel.implement_compute_total_tauJS()}
	{ststel.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_update_plastic_stress_strainJS(discr_pl)}
	{ststpl.implement_compute_NyJS()}
	{ststpl.implement_compute_MyJS()}
	{ststpl.implement_compute_total_stress_strainJS()}
	{ststpl.implement_support_function_plasticJS()}
	{ststel.implement_compute_total_epsilonJS()}
	"""
	updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)


	args_slider_b = dict(source=source,
	s_b=source_beam,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	total_strain_diag=total_strain_diag,
	total_stress_pl_diag=total_stress_pl_diag,
	total_strain_pl_diag=total_strain_pl_diag)
	code_change_b = f"""
	// retrieve data used
	const db = source.data
	const b = cb_obj.value // value of the slider
	const h = db['h'][0]
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)
	const yG = db['yG'][0]
	const N = db['N'][0]
	const M = db['M'][0]

	// apply the changes
	db['b'][0] = b
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)

	// emit the changes
	source.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{ststel.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{ststel.implement_compute_epsilon_axialJS()}
	{ststel.implement_compute_epsilon_bendingJS()}
	{ststel.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{ststel.implement_compute_sigma_bendingJS()}
	{ststel.implement_compute_total_sigmaJS()}
	{ststel.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{ststel.implement_compute_tau_shearJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{ststel.implement_compute_neutral_axisJS()}
	{js.implement_update_plastic_stress_strainJS(discr_pl)}
	{ststpl.implement_compute_NyJS()}
	{ststpl.implement_compute_MyJS()}
	{ststpl.implement_compute_total_stress_strainJS()}
	{ststpl.implement_support_function_plasticJS()}
	{ststel.implement_compute_total_epsilonJS()}
	"""
	update_b = CustomJS(args=args_slider_b, code=code_change_b)


	args_slider_h = dict(source=source,
	s_b=source_beam,
	s_ss=source_section_scheme,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	total_strain_diag=total_strain_diag,
	total_stress_pl_diag=total_stress_pl_diag,
	total_strain_pl_diag=total_strain_pl_diag)
	code_change_h = f"""
	// retrieve data used
	const db = source.data
	const data_ss = s_ss.data
	const b = db['b'][0]
	const h = cb_obj.value // value of the slider
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)
	const N = db['N'][0]
	const M = db['M'][0]
	const yG = compute_centroid_y(h)

	// apply the changes
	db['h'][0] = h
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)
	db['yG'][0] = yG
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)
	data_ss['y'][1] = h // change the height of the section in the diagrams

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)

	// emit the changes
	source.change.emit()
	s_ss.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{ststel.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{ststel.implement_compute_epsilon_axialJS()}
	{ststel.implement_compute_epsilon_bendingJS()}
	{ststel.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{ststel.implement_compute_sigma_bendingJS()}
	{ststel.implement_compute_total_sigmaJS()}
	{ststel.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{ststel.implement_compute_tau_shearJS()}
	{js.implement_update_plastic_stress_strainJS(discr_pl)}
	{ststpl.implement_compute_NyJS()}
	{ststpl.implement_compute_MyJS()}
	{ststpl.implement_compute_total_stress_strainJS()}
	{ststpl.implement_support_function_plasticJS()}
	{ststel.implement_compute_total_epsilonJS()}
	"""
	update_h = CustomJS(args=args_slider_h, code=code_change_h)


	args_checkbox_P = dict(source=source,
	s_M=source_M,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	N_diag=N_diag,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section,
	total_strain_diag=total_strain_diag,
	total_stress_pl_diag=total_stress_pl_diag,
	total_strain_pl_diag=total_strain_pl_diag)
	code_checkbox_P = f"""
	// retrieve var from the object that uses callback
	var f = cb_obj.active // checkbox P
	if (f.length==0) f = [1]
	const db = source.data

	// apply the changes
	db['P'][0] = {P}*(1-f)
	db['N'][0] = compute_N(db['P'][0])
	db['Rx'][0] = compute_Rx(db['P'][0])

	// update
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_N_diagram(db, N_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)
	update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)

	// emit the changes
	source.change.emit()

	// declare functions
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_compute_RxJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_compute_NJS()}
	{sb.implement_update_N_diagramJS(discr_NVM)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{ststel.implement_compute_epsilon_axialJS()}
	{ststel.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{ststel.implement_compute_neutral_axisJS()}
	{ststel.implement_compute_sigma_bendingJS()}
	{ststel.implement_compute_total_sigmaJS()}
	{ststel.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{ststel.implement_compute_tau_shearJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	{js.implement_update_plastic_stress_strainJS(discr_pl)}
	{ststpl.implement_compute_NyJS()}
	{ststpl.implement_compute_MyJS()}
	{ststpl.implement_compute_total_stress_strainJS()}
	{ststpl.implement_support_function_plasticJS()}
	{ststel.implement_compute_total_epsilonJS()}
	{ststel.implement_compute_epsilon_bendingJS()}
	"""
	update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)


	args_radiogroup_FBD = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	s_M=source_M,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_radiogroup_FBD = f"""
	// retrieve data
	const db = source.data
	const FBD = cb_obj.active
	const data_sb = s_sb.data
	const data_q = s_q.data
	const pos = db['x'][0]

	// apply the changes
	db['FBD'][0] = FBD

	// update
	check_state(db)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// emit the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	{models.implement_check_stateJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)


	args_slider_q = dict(source=source,
	s_q=source_scheme_q,
	s_M=source_M,
	div_f=div_forces,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	V_diag=V_diag,
	M_diag=M_diag,
	centroid=centroid,
	neutral_axis=neutral_axis,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section,
	total_strain_diag=total_strain_diag,
	total_stress_pl_diag=total_stress_pl_diag,
	total_strain_pl_diag=total_strain_pl_diag)
	code_slider_q = f"""
	// retrieve data
	const db = source.data
	const q = cb_obj.value
	const pos = db['x'][0]
	const L = db['L'][0]

	// update q
	db['q'][0] = q
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['Ry_l'][0] = compute_Ry_l(q, L)
	db['Ry_r'][0] = compute_Ry_r(q, L)

	// update
	update_u_load(db, s_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_V_diagram(db, V_diag)
	update_M_diagram(db, M_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)
	update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)

	// apply changes
	source.change.emit()

	// declare functions
	{js.implement_update_arrowJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_compute_Ry_lJS()}
	{sb.implement_compute_Ry_rJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_update_V_diagramJS(discr_NVM)}
	{sb.implement_update_M_diagramJS(discr_NVM)}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_u_loadJS(OFFSET_Q)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{ststel.implement_compute_epsilon_bendingJS()}
	{ststel.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{ststel.implement_compute_neutral_axisJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{ststel.implement_compute_sigma_bendingJS()}
	{ststel.implement_compute_total_sigmaJS()}
	{ststel.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{ststel.implement_compute_tau_shearJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	{js.implement_update_plastic_stress_strainJS(discr_pl)}
	{ststpl.implement_compute_NyJS()}
	{ststpl.implement_compute_MyJS()}
	{ststpl.implement_compute_total_stress_strainJS()}
	{ststpl.implement_support_function_plasticJS()}
	{ststel.implement_compute_total_epsilonJS()}
	{ststel.implement_compute_epsilon_axialJS()}
	"""
	update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)


	args_slider_yield = dict(source=source,
	total_strain_diag=total_strain_diag,
	total_stress_pl_diag=total_stress_pl_diag,
	total_strain_pl_diag=total_strain_pl_diag)
	code_slider_yield = f"""
	// retrieve data
	const db = source.data
	const fy = cb_obj.value
	const L = db['L'][0]

	// update q
	db['fy'][0] = fy

	// update
	update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)

	// apply changes
	source.change.emit()

	// declare functions
	{js.implement_update_plastic_stress_strainJS(discr_pl)}
	{ststpl.implement_compute_NyJS()}
	{ststpl.implement_compute_MyJS()}
	{ststpl.implement_compute_total_stress_strainJS()}
	{ststpl.implement_support_function_plasticJS()}
	{ststel.implement_compute_total_epsilonJS()}
	{js.implement_linspaceJS()}
	{ststel.implement_compute_epsilon_axialJS()}
	{ststel.implement_compute_epsilon_bendingJS()}
	{ststel.implement_compute_sigma_axialJS()}
	{ststel.implement_compute_sigma_bendingJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	"""
	update_slider_yield = CustomJS(args=args_slider_yield, code=code_slider_yield)

	# for the implementation in the other nbs!!!
	# args_slider_elastic = dict(source=source,
	# N_stress_diag=N_stress_diag,
	# axial_strain_diag=axial_strain_diag,
	# M_stress_diag=M_stress_diag,
	# bending_strain_diag=bending_strain_diag,
	# centroid=centroid)
	# code_slider_elastic = f"""
	# // retrieve data
	# const db = source.data
	# const E = cb_obj.value

	# // update E
	# db['E'][0] = E

	# // update
	# update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	# update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)

	# // apply changes
	# source.change.emit()

	# // declare functions
	# {js.implement_linspaceJS()}
	# {sb.implement_compute_NJS()}
	# {js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	# {js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	# {ststel.implement_compute_epsilon_bendingJS()}
	# {ststel.implement_compute_epsilon_axialJS()}
	# {ststel.implement_compute_sigma_axialJS()}
	# {js.implement_update_stress_diagramJS()}
	# {js.implement_update_strain_diagramJS()}
	# {ststel.implement_compute_sigma_bendingJS()}
	# """
	# update_slider_elastic = CustomJS(args=args_slider_elastic, code=code_slider_elastic)

	# slider_elastic.js_on_change('value', update_slider_elastic)

	args_slider_elastic = dict(source=source,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	centroid=centroid,
	total_strain_diag=total_strain_diag,
	total_stress_pl_diag=total_stress_pl_diag,
	total_strain_pl_diag=total_strain_pl_diag)
	code_slider_elastic = f"""
	// retrieve data
	const db = source.data
	const E = cb_obj.value

	// update E
	db['E'][0] = E

	// update
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)

	// apply changes
	source.change.emit()

	// declare functions
	{js.implement_linspaceJS()}
	{sb.implement_compute_NJS()}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{ststel.implement_compute_epsilon_bendingJS()}
	{ststel.implement_compute_epsilon_axialJS()}
	{ststel.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{ststel.implement_compute_sigma_bendingJS()}
	{js.implement_update_plastic_stress_strainJS(discr_pl)}
	{ststpl.implement_compute_NyJS()}
	{ststpl.implement_compute_MyJS()}
	{ststpl.implement_compute_total_stress_strainJS()}
	{ststpl.implement_support_function_plasticJS()}
	{ststel.implement_compute_total_epsilonJS()}
	"""
	update_slider_elastic = CustomJS(args=args_slider_elastic, code=code_slider_elastic)

	# apply the logics
	slider_b.js_on_change('value', update_b)
	slider_h.js_on_change('value', update_h)
	slider_position.js_on_change('value', updade_slider_pos)
	checkbox_P.js_on_click(update_checkbox_P)
	radiogroup_FBD.js_on_click(update_radiogroup_FBD)
	slider_q.js_on_change('value', update_slider_q)
	slider_elastic.js_on_change('value', update_slider_elastic)
	slider_yield.js_on_change('value', update_slider_yield)


	########################################################
	# Build the layout
	########################################################
	padding_layout = 10
	layout1 = layout([
	[column(row(column(fig_scheme,
	row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout*3),
	slider_b,
	slider_h,
	# row(div_geo, div_forces),
	slider_position,
	slider_q,
	slider_elastic,
	div_E,
	slider_yield,
	div_fy,
	# Spacer(height=padding_layout),
	div_rg_FBD,
	radiogroup_FBD,
	div_cb_P,
	checkbox_P))),
	column(fig_beam,
	Spacer(height=padding_layout),
	fig_N,
	fig_V,
	fig_M)),
	row(column(
	row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_total_strain, fig_stress_sigma),
	row(fig_V_section, Spacer(width=FIG_B_ss), fig_stress_V, Spacer(width=FIG_B_ss), Spacer(width=FIG_B_ss), Spacer(width=FIG_B_ss), fig_stress_tau),
	))
	),
	],
	])

	show(layout1)
	\ No newline at end of file
	diff --git a/HiddenCode/hidden_code_nb_stress.py b/HiddenCode/hidden_code_nb_stress.py
	index 8f4675f..5b9e3f4 100644
	--- a/HiddenCode/hidden_code_nb_stress.py
	+++ b/HiddenCode/hidden_code_nb_stress.py
	@@ -1,923 +1,929 @@
	import math
	import numpy as np
	from bokeh.layouts import layout, column, row
	from bokeh.models.annotations import Label, Arrow
	from bokeh.models.arrow_heads import VeeHead
	-from bokeh.models import Div, CustomJS, Slider, Spacer, Text
	+from bokeh.models import Div, CustomJS, Slider, Spacer, Text, HoverTool
	from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup
	from bokeh.plotting import figure, show, ColumnDataSource
	from bokeh.io import output_notebook
	from cienpy import simplebeam as sb
	from cienpy import rectangular_section as beam_section
	from cienpy import stress_strain_elastic as stst
	from cienpy import models
	from cienpy import javascriptcodes as js

	output_notebook()


	def main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr):
	########################################################
	# Initialisation
	########################################################
	# constants for the visualisation
	SCALE = 10
	OFFSET_Q = q
	MAX_B = 3*b
	MAX_H = 3*h
	MAX_Q = q/4*5

	# store the values in a specific format
	data_beam = dict(
	x=[0, L],
	y=[0, 0]
	)

	data_scheme_beam = dict(
	x=[0, L*SCALE],
	y=[0, 0]
	)

	data_scheme_q = dict(
	x=[0, 0, LSCALE, LSCALE],
	y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],
	x_fade=[0, 0, LSCALE, LSCALE]
	)

	data_section_scheme = dict(
	x=[0, 0],
	y=[0, h]
	)

	initial_position = L
	initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC
	initial_FBD = 0 # right=0 left=1
	data = dict( # stores every useful single variable
	state=[initial_state],
	FBD=[initial_FBD],
	SCALE=[SCALE],
	L=[L],
	b=[b],
	h=[h],
	E=[E],
	A=[A],
	Iy=[Iy],
	Iz=[Iz],
	yG=[yG],
	y_n_axis=[y_n_axis],
	P=[P],
	x=[initial_position],
	y=[0],
	q=[q],
	Rx=[Rx],
	Ry_l=[Ry_l],
	Ry_r=[Ry_r],
	N=[N],
	V=[V],
	M=[M],
	xF=[L*SCALE]
	)

	source_beam = ColumnDataSource(data_beam)
	source_scheme_beam = ColumnDataSource(data_scheme_beam)
	source_scheme_q = ColumnDataSource(data_scheme_q)
	source_section_scheme = ColumnDataSource(data_section_scheme)
	source = ColumnDataSource(data)


	########################################################
	# Define figures, widgets and renderers as from the previous notebook
	########################################################
	FIG_H_B = 200 # height figure beam
	FIG_B_B = 700 # width figure beam
	FIG_H_S = FIG_H_B # height figure scheme
	FIG_B_S = FIG_B_B # width figure scheme
	FIG_H_SEC = 600 # height figure section
	DIV_B_GEO = 170
	DIV_B_FORCES = 170

	options = dict(
	toolbar_location=None
	)

	# figure for the beam
	paddingx = 0.2*L
	int_x_b = (0-paddingx, L+paddingx)
	int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)
	fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,
	f_h=FIG_H_B, f_b=FIG_B_B)


	# figure for the cross-section
	fig_section = sb.define_fig_section(MAX_B0.8, MAX_H0.8, options, FIG_H_SEC)


	# beam
	(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,
	ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)

	# section
	section = beam_section.draw_section(fig_section, b, h)


	# show mechanical parameters
	div_geo = Div(width= DIV_B_GEO,
	text=beam_section.div_text_geo(round(h), round(b), round(L),
	"{:.2e}".format(A),
	"{:.2e}".format(Iy),
	"{:.2e}".format(Iz)))


	# change geometry
	slider_b = Slider(
	title="Change the width b [mm]",
	start=10,
	end=MAX_B,
	step=10,
	value=b
	)
	slider_h = Slider(
	title="Change the height h [mm]",
	start=20,
	end=MAX_H,
	step=20,
	value=h
	)

	# reference system
	axis_arrow_length = 0.8
	axis_arrow_scale = 100
	models.force_vector(fig_section, axis_arrow_length10, 0, 0, 0, axis_arrow_lengthaxis_arrow_scale*1.6, 'gray') # y axis
	fig_section.text(x=[0], y=[axis_arrow_lengthaxis_arrow_scale1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2)
	models.force_vector(fig_section, axis_arrow_length10, 0, -axis_arrow_lengthaxis_arrow_scale, 0, 0, 'gray') # z axis
	fig_section.text(x=[-axis_arrow_lengthaxis_arrow_scale1.1], y=[0], text=["z"], text_color='gray', text_align='right', text_baseline='middle')


	# figure for the forces and moments
	fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)


	# uniform load (beam)
	u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE], width=L, height=q/SCALE,
	fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)
	label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE], text=["q"], text_color="blue")


	# axial force (beam)
	axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')
	label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=["P"], text_color="green")


	# position point
	pos_opt = dict(
	source=source,
	size=10,
	fill_alpha=0.5,
	fill_color="magenta",
	color="magenta",
	alpha=0.5
	)
	beam_position = fig_beam.circle('x', 'y', **pos_opt)
	forces_position = fig_scheme.circle('xF', 'y', **pos_opt)


	# beam (scheme)
	scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')
	scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)
	# uniform load (scheme)
	scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',
	fill_alpha=0.3, alpha=0.3)
	scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',
	color='navy', fill_alpha=0.3, alpha=0.3)
	# axial force (scheme)
	scheme_axial_force = models.force_vector(fig_scheme, P, LSCALE+P, LSCALE, 0, 0, 'green')
	# Reactions (scheme)
	scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, LSCALE, LSCALE, -Ry_r, 0, 'orange')
	scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')
	scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')
	# force N
	scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# force V
	scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# moment M
	(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)


	# change the uniform load q
	slider_q = Slider(
	title="Change the uniform load q [kN/m]",
	start=0.1,
	end=MAX_Q,
	step=0.1,
	value=q
	)


	# choose position of interest
	slider_position = Slider(
	title="Change the position x along the beam [m]",
	start=0,
	end=L,
	step=0.02,
	value=L
	)


	# choose left or right FBD
	div_rg_FBD = Div(text="Free-body diagram (FBD):")
	radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)


	# choose axial force or not
	div_cb_P = Div(text=f"Axial force P={P} kN (applied)")
	checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])


	# show values of forces and moments
	div_forces = Div(width=DIV_B_FORCES,
	text=sb.div_text_forces(P, P, Ry_l, Ry_r, "No cross section analysed.", 0, 0, 0))


	# figures for the diagrams
	options_diag = dict(
	toolbar_location=None,
	x_axis_label="Position [m]",
	plot_width=FIG_B_B,
	x_range=fig_beam.x_range
	)
	fig_N = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Axial force", "@y kN")],
	y_axis_label="Axial force N [kN]",
	plot_height=int(FIG_H_B*0.8),
	title="N V M Diagrams")
	fig_V = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Shear force", "@y kN")],
	y_axis_label="Shear force V [kN]",
	plot_height=int(FIG_H_B*0.8))
	fig_M = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Bending moment", "@y kNm")],
	y_axis_label="Bending moment M [kNm]",
	plot_height=FIG_H_B)
	fig_N.xaxis.visible = False
	fig_V.xaxis.visible = False


	# plot N V M
	N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)
	+ fig_N.add_tools(HoverTool(renderers=[N_diag],
	+ tooltips= [("Position", "@x m"), ("Axial force", "@y kN")]))
	+
	V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)
	+ fig_V.add_tools(HoverTool(renderers=[V_diag],
	+ tooltips= [("Position", "@x m"), ("Shear force", "@y kN")]))
	+
	M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)
	+ fig_M.add_tools(HoverTool(renderers=[M_diag],
	+ tooltips= [("Position", "@x m"), ("Bending moment", "@y kNm")]))

	# point that shows the position that it's analyzed
	N_position = fig_N.circle('x', 'N', **pos_opt)
	V_position = fig_V.circle('x', 'V', **pos_opt)
	M_position = fig_M.circle('x', 'M', **pos_opt)


	########################################################
	# Define the new figures, widgets and renderers
	########################################################
	# figures for the stresses and strains
	FIG_B_ss = 200
	FIG_H_ss = 200
	options_stress_strain = dict(
	toolbar_location=None,
	y_axis_label="Height h [mm]",
	plot_width=FIG_B_ss,
	plot_height=FIG_H_ss
	)
	fig_stress_N = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Axial stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2099 [MPa]")
	fig_stress_N.yaxis.visible = False
	fig_axial_strain = figure(**options_stress_strain,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Axial strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2099 [%]",
	y_range=fig_stress_N.y_range)
	fig_axial_strain.yaxis.visible = False
	fig_stress_M = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Bending stress and centroid",
	y_range=fig_stress_N.y_range,
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2098 [MPa]")
	fig_stress_M.yaxis.visible = False
	fig_bending_strain = figure(**options_stress_strain,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Bending strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2098 [%]",
	y_range=fig_stress_N.y_range)
	fig_bending_strain.yaxis.visible = False
	fig_stress_V = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Shear stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU}\u1d65 [MPa]")
	fig_stress_V.yaxis.visible = False
	fig_stress_sigma = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress \N{GREEK SMALL LETTER SIGMA} and neutral axis",
	y_range=fig_stress_N.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA} [MPa]")
	fig_stress_tau = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress \N{GREEK SMALL LETTER TAU}",
	y_range=fig_stress_V.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU} [MPa]")

	# plot stress N V M
	- discr_stress_strain = 10
	+ discr_stress_strain = 201
	scale_x = 25
	y_discr = np.linspace(0, h, discr_stress_strain)
	sigma_N = stst.compute_sigma_axial(y_discr, 0, A)
	N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,
	source_section_scheme, scale_x=scale_x/10)
	+ fig_stress_N.add_tools(HoverTool(renderers=[N_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	sigma_M = stst.compute_sigma_bending(y_discr, 0, Iy, yG)
	(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,
	source_section_scheme, True, yG, scale_x=scale_x)
	+ fig_stress_M.add_tools(HoverTool(renderers=[M_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, yG)
	tau_V = stst.compute_tau_shear(y_discr, 0, S_rect, Iy, b)
	V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)
	+ fig_stress_V.add_tools(HoverTool(renderers=[V_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot stress sigma and tau
	sigma_total = sigma_M + sigma_N
	(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,
	source_section_scheme,True, yG, scale_x=scale_x)
	+ fig_stress_sigma.add_tools(HoverTool(renderers=[sigma_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	tau_total = tau_V
	tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,
	source_section_scheme, scale_x=1)
	+ fig_stress_tau.add_tools(HoverTool(renderers=[tau_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot strain N M
	strain_axial = stst.compute_epsilon_axial(y_discr, sigma_N, E)
	axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)
	+ fig_axial_strain.add_tools(HoverTool(renderers=[axial_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))
	+
	strain_bending = stst.compute_epsilon_bending(y_discr, sigma_M, E)
	bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)
	+ fig_bending_strain.add_tools(HoverTool(renderers=[bending_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))


	# figures for NVM
	fig_NM_section = figure(**options_stress_strain,
	title="N and M at position x",
	match_aspect=True)
	fig_NM_section.axis.visible = False
	fig_NM_section.grid.grid_line_alpha = 0

	fig_V_section = figure(**options_stress_strain,
	title="V at position x",
	match_aspect=True)
	fig_V_section.axis.visible = False
	fig_V_section.grid.grid_line_alpha = 0

	# section with NVM
	models.section_diagram(fig_NM_section)
	models.section_diagram(fig_V_section)

	# NVM in section
	section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')
	section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')
	(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)

	# NVM label in section
	OFFSET_N = 1
	label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[""], text_color="red", text_baseline='bottom')
	label_M_section = fig_NM_section.text(x=[OFFSET_N6], y=[-OFFSET_N5], text=[""], text_color="red", text_baseline='top')
	label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[0], text=[""], text_color="red", text_baseline='middle')


	########################################################
	# Configurethe logics
	########################################################
	args_slider_pos = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	s_M=source_M,
	arr_head=scheme_M_head,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_slider_pos = f"""
	// retrieve data
	const db = source.data
	const data_sb = s_sb.data
	const data_q = s_q.data
	const FBD = db['FBD'][0]
	const pos = cb_obj.value
	const q = db['q'][0]
	const L = db['L'][0]

	// update data
	db['N'][0] = compute_N(db['P'][0])
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['x'][0] = pos

	// check state
	check_state(db)

	// update:
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// apply the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	// declare functions
	{sb.implement_compute_NJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_growthJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_NVM_diagramJS()}
	{models.implement_check_stateJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_sigma_axialJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_tau_shearJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_update_NVM_sectionJS()}
	"""
	updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)


	args_slider_b = dict(source=source,
	s_b=source_beam,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag)
	code_change_b = f"""
	// retrieve data used
	const db = source.data
	const b = cb_obj.value // value of the slider
	const h = db['h'][0]
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)
	const yG = db['yG'][0]
	const N = db['N'][0]
	const M = db['M'][0]

	// apply the changes
	db['b'][0] = b
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)

	// emit the changes
	source.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_neutral_axisJS()}
	"""
	update_b = CustomJS(args=args_slider_b, code=code_change_b)


	args_slider_h = dict(source=source,
	s_b=source_beam,
	s_ss=source_section_scheme,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag)
	code_change_h = f"""
	// retrieve data used
	const db = source.data
	const data_ss = s_ss.data
	const b = db['b'][0]
	const h = cb_obj.value // value of the slider
	const A = compute_area(b, h)
	const Iy = compute_inertia_y(b, h)
	const N = db['N'][0]
	const M = db['M'][0]
	const yG = compute_centroid_y(h)

	// apply the changes
	db['h'][0] = h
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h)
	db['yG'][0] = yG
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)
	data_ss['y'][1] = h // change the height of the section in the diagrams

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)

	// emit the changes
	source.change.emit()
	s_ss.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	"""
	update_h = CustomJS(args=args_slider_h, code=code_change_h)


	args_checkbox_P = dict(source=source,
	s_M=source_M,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	N_diag=N_diag,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_checkbox_P = f"""
	// retrieve var from the object that uses callback
	var f = cb_obj.active // checkbox P
	if (f.length==0) f = [1]
	const db = source.data

	// apply the changes
	db['P'][0] = {P}*(1-f)
	db['N'][0] = compute_N(db['P'][0])
	db['Rx'][0] = compute_Rx(db['P'][0])

	// update
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_N_diagram(db, N_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// emit the changes
	source.change.emit()

	// declare functions
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_compute_RxJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_compute_NJS()}
	{sb.implement_update_N_diagramJS(discr_NVM)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_neutral_axisJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)


	args_radiogroup_FBD = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	s_M=source_M,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_radiogroup_FBD = f"""
	// retrieve data
	const db = source.data
	const FBD = cb_obj.active
	const data_sb = s_sb.data
	const data_q = s_q.data
	const pos = db['x'][0]

	// apply the changes
	db['FBD'][0] = FBD

	// update
	check_state(db)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// emit the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	{models.implement_check_stateJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)


	args_slider_q = dict(source=source,
	s_q=source_scheme_q,
	s_M=source_M,
	div_f=div_forces,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	V_diag=V_diag,
	M_diag=M_diag,
	centroid=centroid,
	neutral_axis=neutral_axis,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_slider_q = f"""
	// retrieve data
	const db = source.data
	const q = cb_obj.value
	const pos = db['x'][0]
	const L = db['L'][0]

	// update q
	db['q'][0] = q
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['Ry_l'][0] = compute_Ry_l(q, L)
	db['Ry_r'][0] = compute_Ry_r(q, L)

	// update
	update_u_load(db, s_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_V_diagram(db, V_diag)
	update_M_diagram(db, M_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// apply changes
	source.change.emit()

	// declare functions
	{js.implement_update_arrowJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_compute_Ry_lJS()}
	{sb.implement_compute_Ry_rJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_update_V_diagramJS(discr_NVM)}
	{sb.implement_update_M_diagramJS(discr_NVM)}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_u_loadJS(OFFSET_Q)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain)}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_neutral_axisJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)

	# apply the logics
	slider_b.js_on_change('value', update_b)
	slider_h.js_on_change('value', update_h)
	slider_position.js_on_change('value', updade_slider_pos)
	checkbox_P.js_on_click(update_checkbox_P)
	radiogroup_FBD.js_on_click(update_radiogroup_FBD)
	slider_q.js_on_change('value', update_slider_q)


	########################################################
	# Build the layout
	########################################################
	padding_layout = 10
	layout1 = layout([
	[column(row(column(fig_scheme,
	row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout),
	slider_b,
	slider_h,
	row(div_geo, div_forces),
	Spacer(height=padding_layout),
	slider_position,
	slider_q,
	div_rg_FBD,
	radiogroup_FBD,
	div_cb_P,
	checkbox_P))),
	column(fig_beam,
	Spacer(height=padding_layout),
	fig_N,
	fig_V,
	fig_M)),
	row(column(
	row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_stress_sigma),
	row(fig_V_section, Spacer(width=FIG_B_ss), fig_stress_V, Spacer(width=FIG_B_ss), Spacer(width=FIG_B_ss), fig_stress_tau),
	))
	)],
	])

	show(layout1)
	\ No newline at end of file
	diff --git a/HiddenCode/hidden_code_nb_torsion.py b/HiddenCode/hidden_code_nb_torsion.py
	index b266e65..d2d8c4b 100644
	--- a/HiddenCode/hidden_code_nb_torsion.py
	+++ b/HiddenCode/hidden_code_nb_torsion.py
	@@ -1,1194 +1,1199 @@
	import math
	import numpy as np
	from bokeh.layouts import layout, column, row
	from bokeh.models.annotations import Label, Arrow
	from bokeh.models.arrow_heads import VeeHead
	-from bokeh.models import Div, CustomJS, Slider, Spacer, Text
	+from bokeh.models import Div, CustomJS, Slider, Spacer, Text, HoverTool
	from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup
	from bokeh.plotting import figure, show, ColumnDataSource
	from bokeh.io import output_notebook
	from cienpy import simplebeam as sb
	from cienpy import hollow_rectangular_section as beam_section
	from cienpy import stress_strain_elastic as stst
	from cienpy import models
	from cienpy import javascriptcodes as js

	output_notebook()


	def main_code(L, h, b, t, A, Iy, Iz, yG, y_n_axis, q, P, Mt, E, N, V, M, T, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr, T_discr):
	########################################################
	# Initialisation
	########################################################
	# constants for the visualisation
	SCALE = 10
	SCALE_T = 10
	OFFSET_Q = q
	MAX_B = 3*b
	MAX_H = 3*h
	MAX_T = 2*t
	MAX_Q = q/4*5

	# store the values in a specific format
	data_beam = dict(
	x=[0, L],
	y=[0, 0]
	)

	data_scheme_beam = dict(
	x=[0, L*SCALE],
	y=[0, 0]
	)

	data_scheme_q = dict(
	x=[0, 0, LSCALE, LSCALE],
	y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],
	x_fade=[0, 0, LSCALE, LSCALE]
	)

	data_section_scheme = dict(
	x=[0, 0],
	y=[0, h]
	)

	initial_position = L
	initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC
	initial_FBD = 0 # right=0 left=1
	data = dict( # stores every useful single variable
	state=[initial_state],
	FBD=[initial_FBD],
	SCALE=[SCALE],
	L=[L],
	b=[b],
	h=[h],
	t=[t],
	E=[E],
	A=[A],
	Iy=[Iy],
	Iz=[Iz],
	yG=[yG],
	y_n_axis=[y_n_axis],
	P=[P],
	x=[initial_position],
	y=[0],
	q=[q],
	Mt=[Mt],
	Rx=[Rx],
	Ry_l=[Ry_l],
	Ry_r=[Ry_r],
	N=[N],
	V=[V],
	M=[M],
	T=[T],
	xF=[L*SCALE]
	)

	source_beam = ColumnDataSource(data_beam)
	source_scheme_beam = ColumnDataSource(data_scheme_beam)
	source_scheme_q = ColumnDataSource(data_scheme_q)
	source_section_scheme = ColumnDataSource(data_section_scheme)
	source = ColumnDataSource(data)

	# Constants
	FIG_H_B = 200 # height figure beam
	FIG_B_B = 700 # width figure beam
	FIG_H_S = FIG_H_B # height figure scheme
	FIG_B_S = FIG_B_B # width figure scheme
	FIG_H_SEC = 600 # height figure section
	DIV_B_GEO = 170
	DIV_B_FORCES = 170


	########################################################
	# Define figures, widgets and renderers as from the previous notebook
	########################################################
	options = dict(
	toolbar_location=None
	)

	# figure for the beam
	paddingx = 0.2*L
	int_x_b = (0-paddingx, L+paddingx)
	int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)
	fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,
	f_h=FIG_H_B, f_b=FIG_B_B)


	# figure for the cross-section
	fig_section = sb.define_fig_section(MAX_B0.8, MAX_H0.8, options, FIG_H_SEC)


	# beam
	(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,
	ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)

	# section
	section = beam_section.draw_section(fig_section, b, h, t)


	# show mechanical parameters
	div_geo = Div(width= DIV_B_GEO,
	text=beam_section.div_text_geo(round(h), round(b), round(t), round(L),
	"{:.2e}".format(A),
	"{:.2e}".format(Iy),
	"{:.2e}".format(Iz)))


	# change geometry
	slider_b = Slider(
	title="Change the width b [mm]",
	start=MAX_T*2+10,
	end=MAX_B,
	step=10,
	value=b
	)
	slider_h = Slider(
	title="Change the height h [mm]",
	start=MAX_T*2+10,
	end=MAX_H,
	step=10,
	value=h
	)

	# reference system
	axis_arrow_length = 0.8
	axis_arrow_scale = 100
	models.force_vector(fig_section, axis_arrow_length10, 0, 0, 0, axis_arrow_lengthaxis_arrow_scale*1.6, 'gray') # y axis
	fig_section.text(x=[0], y=[axis_arrow_lengthaxis_arrow_scale1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2)
	models.force_vector(fig_section, axis_arrow_length10, 0, -axis_arrow_lengthaxis_arrow_scale, 0, 0, 'gray') # z axis
	fig_section.text(x=[-axis_arrow_lengthaxis_arrow_scale1.1], y=[0], text=["z"], text_color='gray', text_align='right', text_baseline='middle')


	# figure for the forces and moments
	fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)


	# uniform load (beam)
	u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE], width=L, height=q/SCALE,
	fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)
	label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE], text=["q"], text_color="blue")


	# axial force (beam)
	axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')
	label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/4], text=["P"], text_color="green")


	# position point
	pos_opt = dict(
	source=source,
	size=10,
	fill_alpha=0.5,
	fill_color="magenta",
	color="magenta",
	alpha=0.5
	)
	beam_position = fig_beam.circle('x', 'y', **pos_opt)
	forces_position = fig_scheme.circle('xF', 'y', **pos_opt)


	# beam (scheme)
	scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')
	scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)
	# uniform load (scheme)
	scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',
	fill_alpha=0.3, alpha=0.3)
	scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',
	color='navy', fill_alpha=0.3, alpha=0.3)
	# axial force (scheme)
	scheme_axial_force = models.force_vector(fig_scheme, P, LSCALE+P, LSCALE, 0, 0, 'green')
	# Reactions (scheme)
	scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, LSCALE, LSCALE, -Ry_r, 0, 'orange')
	scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')
	scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')
	# force N
	scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# force V
	scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')
	# moment M
	(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)


	# change the uniform load q
	slider_q = Slider(
	title="Change the uniform load q [kN/m]",
	start=0.1,
	end=MAX_Q,
	step=0.1,
	value=q
	)


	# choose position of interest
	slider_position = Slider(
	title="Change the position x along the beam [m]",
	start=0,
	end=L,
	step=0.02,
	value=L
	)


	# choose left or right FBD
	div_rg_FBD = Div(text="Free-body diagram (FBD):")
	radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)


	# choose axial force or not
	div_cb_P = Div(text=f"Axial force P={P} kN (applied)")
	checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])


	# show values of forces and moments
	div_forces = Div(width=DIV_B_FORCES,
	text=sb.div_text_forces(P, P, Ry_l, Ry_r, "No cross section analysed.", 0, 0, 0))


	# figures for the diagrams
	options_diag = dict(
	toolbar_location=None,
	x_axis_label="Position [m]",
	plot_width=FIG_B_B,
	x_range=fig_beam.x_range
	)
	fig_N = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Axial force", "@y kN")],
	y_axis_label="Axial force N [kN]",
	plot_height=int(FIG_H_B*0.8),
	title="N V M Diagrams")
	fig_V = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Shear force", "@y kN")],
	y_axis_label="Shear force V [kN]",
	plot_height=int(FIG_H_B*0.8))
	fig_M = figure(**options_diag,
	- tooltips= [("Position", "@x m"),
	- ("Bending moment", "@y kNm")],
	y_axis_label="Bending moment M [kNm]",
	plot_height=FIG_H_B)
	fig_N.xaxis.visible = False
	fig_V.xaxis.visible = False


	# plot N V M
	N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)
	+ fig_N.add_tools(HoverTool(renderers=[N_diag],
	+ tooltips= [("Position", "@x m"), ("Axial force", "@y kN")]))
	+
	V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)
	+ fig_V.add_tools(HoverTool(renderers=[V_diag],
	+ tooltips= [("Position", "@x m"), ("Shear force", "@y kN")]))
	+
	M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)
	+ fig_M.add_tools(HoverTool(renderers=[M_diag],
	+ tooltips= [("Position", "@x m"), ("Bending moment", "@y kNm")]))


	# point that shows the position that it's analyzed
	N_position = fig_N.circle('x', 'N', **pos_opt)
	V_position = fig_V.circle('x', 'V', **pos_opt)
	M_position = fig_M.circle('x', 'M', **pos_opt)


	# figures for the stresses and strains
	FIG_B_ss = 200
	FIG_H_ss = 200
	options_stress_strain = dict(
	toolbar_location=None,
	y_axis_label="Height h [mm]",
	plot_width=FIG_B_ss,
	plot_height=FIG_H_ss,
	)
	fig_stress_N = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Axial stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2099 [MPa]")
	fig_stress_N.yaxis.visible = False
	fig_axial_strain = figure(**options_stress_strain,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Axial strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2099 [%]",
	y_range=fig_stress_N.y_range)
	fig_axial_strain.yaxis.visible = False
	fig_stress_M = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Bending stress and centroid",
	y_range=fig_stress_N.y_range,
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA}\u2098 [MPa]")
	fig_stress_M.yaxis.visible = False
	fig_bending_strain = figure(**options_stress_strain,
	- tooltips= [("Strain", "@x %"),
	- ("Height", "@y mm")],
	title="Bending strain",
	x_axis_label="Strain \N{GREEK SMALL LETTER EPSILON}\u2098 [%]",
	y_range=fig_stress_N.y_range)
	fig_bending_strain.yaxis.visible = False
	fig_stress_V = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Shear stress",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU}\u1d65 [MPa]")
	fig_stress_V.yaxis.visible = False
	fig_stress_sigma = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress \N{GREEK SMALL LETTER SIGMA} and neutral axis",
	y_range=fig_stress_N.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER SIGMA} [MPa]")
	fig_stress_tau = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Total stress \N{GREEK SMALL LETTER TAU}",
	y_range=fig_stress_V.y_range,
	y_axis_location="right",
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU} [MPa]")


	# plot stress N V M
	- discr_stress_strain = 50
	+ discr_stress_strain = 201
	scale_x = 25
	y_discr = np.linspace(0, h, discr_stress_strain)
	sigma_N = stst.compute_sigma_axial(y_discr, N, A)
	N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,
	source_section_scheme, scale_x=scale_x/10)
	+ fig_stress_N.add_tools(HoverTool(renderers=[N_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	sigma_M = stst.compute_sigma_bending(y_discr, 0, Iy, yG)
	(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,
	source_section_scheme, True, yG, scale_x=scale_x)
	+ fig_stress_M.add_tools(HoverTool(renderers=[M_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, t, yG)
	tau_V = stst.compute_tau_shear(y_discr, 0, S_rect, Iy, b)
	V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)
	-
	+ fig_stress_V.add_tools(HoverTool(renderers=[V_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot stress sigma and tau
	sigma_total = sigma_M + sigma_N
	(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,
	source_section_scheme,True, yG, scale_x=scale_x)
	+ fig_stress_sigma.add_tools(HoverTool(renderers=[sigma_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	tau_total = tau_V
	tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,
	source_section_scheme, scale_x=1)
	+ fig_stress_tau.add_tools(HoverTool(renderers=[tau_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))

	# plot strain N M
	strain_axial = stst.compute_epsilon_axial(y_discr, sigma_N, E)
	axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)
	+ fig_axial_strain.add_tools(HoverTool(renderers=[axial_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))
	+
	strain_bending = stst.compute_epsilon_bending(y_discr, sigma_M, E)
	bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)
	+ fig_bending_strain.add_tools(HoverTool(renderers=[bending_strain_diag],
	+ tooltips= [("Strain", "@x %"), ("Height", "@y mm")]))


	# figures for NVM
	fig_NM_section = figure(**options_stress_strain,
	title="N and M at position x",
	match_aspect=True)
	fig_NM_section.axis.visible = False
	fig_NM_section.grid.grid_line_alpha = 0

	fig_V_section = figure(**options_stress_strain,
	title="V at position x",
	match_aspect=True)
	fig_V_section.axis.visible = False
	fig_V_section.grid.grid_line_alpha = 0


	# section with NVM
	models.section_diagram(fig_NM_section)
	models.section_diagram(fig_V_section)


	# NVM in section
	section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')
	section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')
	(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)


	# NVM label in section
	OFFSET_N = 1
	label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[""], text_color="red", text_baseline='bottom')
	label_M_section = fig_NM_section.text(x=[OFFSET_N6], y=[-OFFSET_N5], text=[""], text_color="red", text_baseline='top')
	label_V_section = fig_V_section.text(x=[OFFSET_N5], y=[OFFSET_N4], text=[""], text_color="red", text_baseline='middle')


	########################################################
	# Define the new figures, widgets and renderers
	########################################################
	# applied torsion Mt
	str_Mt = "M\N{LATIN SUBSCRIPT SMALL LETTER T}"
	div_cb_T = Div(text=f"Torsion {str_Mt}={Mt} kNm (applied)")
	checkbox_T = CheckboxButtonGroup(labels=[f'Apply or remove torsion {str_Mt}'], active=[0])


	# torsion diagram
	fig_M.plot_height = int(FIG_H_B*0.8)
	fig_M.xaxis.visible = False
	fig_T = figure(**options_diag,
	- tooltips= [("Position:", "@x m"),
	- ("Torsion:", "@y kNm")],
	y_axis_label="Torsion T [kNm]",
	plot_height=FIG_H_B)


	# change geometry (thickness)
	slider_t = Slider(
	title="Change the thicknes t [mm]",
	start=2,
	end=MAX_T,
	step=1,
	value=t
	)


	# plot T
	T_diag = models.NVM_diagram(fig_T, x_discr, T_discr, L, source_beam)
	+ fig_T.add_tools(HoverTool(renderers=[T_diag],
	+ tooltips= [("Position", "@x m"), ("Torsion", "@y kNm")]))


	# point that shows the position that it's analyzed
	T_position = fig_T.circle('x', 'T', **pos_opt)


	# figure for the stress tau_T
	fig_stress_T = figure(**options_stress_strain,
	- tooltips= [("Stress", "@x MPa"),
	- ("Height", "@y mm")],
	title="Torsional stress",
	y_range=fig_stress_V.y_range,
	x_axis_label="Stress \N{GREEK SMALL LETTER TAU}\N{LATIN SUBSCRIPT SMALL LETTER T} [MPa]")
	fig_stress_T.yaxis.visible = False


	# torsion in the section
	(section_torsion_line, section_torsion_head, section_torsion_source) = models.define_curvedArrow(fig_section, 0, T4/SCALE_T, abs(T3/SCALE_T), size_head=20)


	# moment Mt in beam
	PIXEL2UNIT_BEAM = 100
	(beam_torsion_line, beam_torsion_head, source_beam_torsion) = models.define_doubleArrow(fig_beam, L/2, L/2+Mt/SCALE/10, 0, 0,
	arrow_color="green", pixel2unit=PIXEL2UNIT_BEAM)
	# label
	label_Mt_force = fig_beam.text(x=[L/2+Mt/2/SCALE/SCALE_T], y=[OFFSET_Q/4/SCALE/SCALE_T], text=[str_Mt], text_color="green")


	# add torsion in section stress
	T_DOUBLE_HEAD_SIZE = 10
	(section_T_line, section_T_head, section_T_source) = models.define_doubleArrow(fig_V_section, OFFSET_N4-T/SCALE_T, OFFSET_N4, 0, 0, size_head=T_DOUBLE_HEAD_SIZE)
	# label
	label_T_section = fig_V_section.text(x=[Mt*1.1/SCALE_T], y=[OFFSET_N], text=["T"], text_color="red", text_baseline='bottom')


	# tau stress torsion
	tau_T = beam_section.compute_tau_torsion(y_discr, T, b, h, t)
	T_stress_diag = models.stress_diagram(fig_stress_T, tau_T, h, source_section_scheme, scale_x=1)
	-
	+ fig_stress_T.add_tools(HoverTool(renderers=[T_stress_diag],
	+ tooltips= [("Stress", "@x MPa"), ("Height", "@y mm")]))
	+
	# Easter egg
	EasterEgg1 = fig_N.text(x=[2], y=[-4], text=[""], text_color="purple", text_font_size="10px", angle=math.pi/10)


	########################################################
	# Configurethe logics
	########################################################
	args_slider_pos = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	s_M=source_M,
	arr_head=scheme_M_head,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section,
	section_T_line=section_T_line,
	section_T_head=section_T_head,
	section_T_source=section_T_source,
	section_torsion_head=section_torsion_head,
	section_torsion_source=section_torsion_source,
	label_T_section=label_T_section,
	div_T=div_cb_T,
	T_stress_diag=T_stress_diag)
	code_slider_pos = f"""
	// retrieve data
	const db = source.data
	const data_sb = s_sb.data
	const data_q = s_q.data
	const FBD = db['FBD'][0]
	const pos = cb_obj.value
	const q = db['q'][0]
	const L = db['L'][0]
	const Mt = db['Mt'][0]

	// update data
	db['N'][0] = compute_N(db['P'][0])
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['T'][0] = compute_T(pos, Mt, L)
	db['x'][0] = pos

	// check state
	check_state(db)

	// update:
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)
	update_T_section(db, section_torsion_head, section_torsion_source, section_T_line, section_T_head, section_T_source, div_T, label_T_section)
	update_torsional_stress(db, T_stress_diag)

	// apply the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	// declare functions
	{sb.implement_compute_NJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_growthJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_NVM_diagramJS()}
	{js.implement_update_stress_diagramJS()}
	{models.implement_check_stateJS()}
	{js.implement_update_strain_diagramJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_sigma_axialJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_tau_shearJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}
	{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}
	{js.implement_update_NVM_sectionJS()}
	{sb.implement_update_T_sectionJS(scale_T=SCALE_T)}
	{js.implement_update_doubleArrowJS()}
	{sb.implement_compute_TJS()}
	{beam_section.implement_compute_tau_torsionJS()}
	{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}
	"""
	updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)


	args_slider_b = dict(source=source,
	s_b=source_beam,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	T_stress_diag=T_stress_diag,
	div_P=div_cb_P)
	code_change_b = f"""
	// retrieve data used
	const db = source.data
	const b = cb_obj.value // value of the slider
	const h = db['h'][0]
	const t = db['t'][0]
	const A = compute_area(b, h, t)
	const Iy = compute_inertia_y(b, h, t)
	const yG = db['yG'][0]
	const N = db['N'][0]
	const M = db['M'][0]

	// Easter egg
	const str_Doge = " such width"
	const str_tmp = div_P.text
	if (b == {MAX_B}) {{
	div_P.text = str_tmp+str_Doge
	}} else {{
	div_P.text = str_tmp.replace(str_Doge, '')
	}}

	// apply the changes
	db['b'][0] = b
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h, t)
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_torsional_stress(db, T_stress_diag)

	// emit the changes
	source.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}
	{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_neutral_axisJS()}
	{beam_section.implement_compute_tau_torsionJS()}
	{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}
	"""
	update_b = CustomJS(args=args_slider_b, code=code_change_b)


	args_slider_h = dict(source=source,
	s_b=source_beam,
	s_ss=source_section_scheme,
	div=div_geo,
	section=section,
	support_r=support_r,
	centroid=centroid,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	T_stress_diag=T_stress_diag,
	div_T=div_cb_T,
	EE1=EasterEgg1)
	code_change_h = f"""
	// retrieve data used
	const db = source.data
	const data_ss = s_ss.data
	const b = db['b'][0]
	const t = db['t'][0]
	const h = cb_obj.value // value of the slider
	const A = compute_area(b, h, t)
	const Iy = compute_inertia_y(b, h, t)
	const N = db['N'][0]
	const M = db['M'][0]
	const yG = compute_centroid_y(h)

	// Easter egg
	/*const str_Doge = " much wow"
	const str_tmp = div_T.text
	if (h == {MAX_H}) {{
	div_T.text = str_tmp+str_Doge
	}} else {{
	div_T.text = str_tmp.replace(str_Doge, '')
	}}*/
	if (h == {MAX_H}) {{
	EE1.glyph.text = "much wow"
	}} else {{
	EE1.glyph.text = ""
	}}

	// apply the changes
	db['h'][0] = h
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h, t)
	db['yG'][0] = yG
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)
	data_ss['y'][1] = h // change the height of the section in the diagrams

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_torsional_stress(db, T_stress_diag)

	// emit the changes
	source.change.emit()
	s_ss.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}
	{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{beam_section.implement_compute_tau_torsionJS()}
	{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}
	"""
	update_h = CustomJS(args=args_slider_h, code=code_change_h)


	args_checkbox_P = dict(source=source,
	s_M=source_M,
	div_P=div_cb_P,
	div_f=div_forces,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	N_diag=N_diag,
	neutral_axis=neutral_axis,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_checkbox_P = f"""
	// retrieve var from the object that uses callback
	var f = cb_obj.active // checkbox P
	if (f.length==0) f = [1]
	const db = source.data

	// apply the changes
	db['P'][0] = {P}*(1-f)
	db['N'][0] = compute_N(db['P'][0])
	db['Rx'][0] = compute_Rx(db['P'][0])

	// update
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_N_diagram(db, N_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// emit the changes
	source.change.emit()

	// declare functions
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_compute_RxJS()}
	{js.implement_update_arrowJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_compute_NJS()}
	{sb.implement_update_N_diagramJS(discr_NVM)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_neutral_axisJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	{beam_section.implement_compute_tau_torsionJS()}
	"""
	update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)


	args_radiogroup_FBD = dict(source=source,
	s_sb=source_scheme_beam,
	s_q=source_scheme_q,
	s_M=source_M,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	tau_stress_diag=tau_stress_diag)
	code_radiogroup_FBD = f"""
	// retrieve data
	const db = source.data
	const FBD = cb_obj.active
	const data_sb = s_sb.data
	const data_q = s_q.data
	const pos = db['x'][0]

	// apply the changes
	db['FBD'][0] = FBD

	// update
	check_state(db)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_scheme_position(db, data_sb, data_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)

	// emit the changes
	source.change.emit()
	s_sb.change.emit()
	s_q.change.emit()

	{models.implement_check_stateJS()}
	{sb.implement_update_internal_forcesJS()}
	{sb.implement_update_scheme_positionJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	"""
	update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)


	args_slider_q = dict(source=source,
	s_q=source_scheme_q,
	s_M=source_M,
	div_f=div_forces,
	div_P=div_cb_P,
	fP=scheme_axial_force,
	fRx=scheme_Rx_l,
	fRyl=scheme_Ry_l,
	fRyr=scheme_Ry_r,
	fN=scheme_N,
	fV=scheme_V,
	arr_head=scheme_M_head,
	V_diag=V_diag,
	M_diag=M_diag,
	centroid=centroid,
	neutral_axis=neutral_axis,
	V_stress_diag=V_stress_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	section_N=section_N,
	section_V=section_V,
	section_M_head=section_M_head,
	s_section_M=source_section_M,
	label_N_section=label_N_section,
	label_V_section=label_V_section,
	label_M_section=label_M_section)
	code_slider_q = f"""
	// retrieve data
	const db = source.data
	const q = cb_obj.value
	const pos = db['x'][0]
	const L = db['L'][0]

	// update q
	db['q'][0] = q
	db['V'][0] = compute_V(pos, q, L)
	db['M'][0] = compute_M(pos, q, L)
	db['Ry_l'][0] = compute_Ry_l(q, L)
	db['Ry_r'][0] = compute_Ry_r(q, L)

	// update
	update_u_load(db, s_q)
	update_reactions(db, fRx, fRyl, fRyr)
	update_external_forces(db, fP, div_P)
	update_V_diagram(db, V_diag)
	update_M_diagram(db, M_diag)
	update_internal_forces(db, fN, fV, arr_head, s_M)
	update_div_forces(db, div_f)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)

	// apply changes
	source.change.emit()

	// declare functions
	{js.implement_update_arrowJS()}
	{js.implement_linspaceJS()}
	{js.implement_parabolaJS()}
	{js.implement_arrow_alphaJS()}
	{js.implement_update_arrowJS()}
	{sb.implement_compute_VJS()}
	{sb.implement_compute_MJS()}
	{sb.implement_compute_Ry_lJS()}
	{sb.implement_compute_Ry_rJS()}
	{js.implement_update_NVM_diagramJS()}
	{sb.implement_update_V_diagramJS(discr_NVM)}
	{sb.implement_update_M_diagramJS(discr_NVM)}
	{sb.implement_update_reactionsJS()}
	{sb.implement_update_external_forcesJS()}
	{sb.implement_update_u_loadJS(OFFSET_Q)}
	{sb.implement_update_internal_forcesJS()}
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}
	{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_neutral_axisJS()}
	{beam_section.implement_compute_centroid_yJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{sb.implement_update_div_forcesJS()}
	{js.implement_update_NVM_sectionJS()}
	{js.implement_arrow_growthJS()}
	{beam_section.implement_compute_tau_torsionJS()}
	"""
	update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)


	args_checkbox_T = dict(source=source,
	T_diag=T_diag,
	div_T=div_cb_T,
	label_T_section=label_T_section,
	section_T_line=section_T_line,
	section_T_head=section_T_head,
	section_T_source=section_T_source,
	section_torsion_head=section_torsion_head,
	section_torsion_source=section_torsion_source,
	neutral_axis=neutral_axis,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	T_stress_diag=T_stress_diag)
	code_checkbox_T = f"""
	// retrieve var from the object that uses callback
	var f = cb_obj.active // checkbox Mt
	if (f.length==0) f = [1]
	const db = source.data
	const L = db['L'][0]
	const x = db['x'][0]

	// apply the changes
	db['Mt'][0] = {Mt}*(1-f)
	db['T'][0] = compute_T(x, db['Mt'][0], L)

	// update
	update_torsional_stress(db, T_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)
	update_T_diagram(db, T_diag)
	update_T_section(db, section_torsion_head, section_torsion_source, section_T_line, section_T_head, section_T_source, div_T, label_T_section)

	// emit the changes
	source.change.emit()

	// declare functions
	{js.implement_update_curvedArrowJS()}
	{js.implement_update_doubleArrowJS()}
	{js.implement_arrow_growthJS()}
	{sb.implement_update_T_sectionJS(scale_T=SCALE_T)}
	{sb.implement_compute_TJS()}
	{sb.implement_update_T_diagramJS(discr_NVM)}
	{js.implement_linspaceJS()}
	{js.implement_update_NVM_diagramJS()}
	{beam_section.implement_compute_tau_torsionJS()}
	{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}
	{stst.implement_compute_neutral_axisJS()}
	{stst.implement_compute_sigma_axialJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{js.implement_update_stress_diagramJS()}
	{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}
	"""
	update_checkbox_T = CustomJS(args=args_checkbox_T, code=code_checkbox_T)


	args_slider_t = dict(source=source,
	div=div_geo,
	section=section,
	N_stress_diag=N_stress_diag,
	axial_strain_diag=axial_strain_diag,
	M_stress_diag=M_stress_diag,
	bending_strain_diag=bending_strain_diag,
	centroid=centroid,
	V_stress_diag=V_stress_diag,
	sigma_stress_diag=sigma_stress_diag,
	tau_stress_diag=tau_stress_diag,
	neutral_axis=neutral_axis,
	T_stress_diag=T_stress_diag)
	code_change_t = f"""
	// retrieve data used
	const db = source.data
	const t = cb_obj.value // value of the slider
	const b = db['b'][0]
	const h = db['h'][0]
	const A = compute_area(b, h, t)
	const Iy = compute_inertia_y(b, h, t)
	const yG = db['yG'][0]
	const N = db['N'][0]
	const M = db['M'][0]

	// apply the changes
	db['t'][0] = t
	db['A'][0] = A
	db['Iy'][0] = Iy
	db['Iz'][0] = compute_inertia_z(b, h, t)
	db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)

	// update
	update_div_geo(db, div)
	update_section(db, section)
	update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)
	update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)
	update_shear_stress(db, V_stress_diag)
	update_torsional_stress(db, T_stress_diag)
	update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)

	// emit the changes
	source.change.emit()

	{beam_section.implement_update_div_geoJS()}
	{beam_section.implement_update_sectionJS()}
	{beam_section.implement_compute_areaJS()}
	{beam_section.implement_compute_inertia_yJS()}
	{beam_section.implement_compute_inertia_zJS()}
	{stst.implement_compute_neutral_axisJS()}
	{js.implement_update_axial_stress_strainJS(discr_stress_strain)}
	{js.implement_update_bending_stress_strainJS(discr_stress_strain)}
	{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}
	{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}
	{js.implement_linspaceJS()}
	{stst.implement_compute_epsilon_axialJS()}
	{stst.implement_compute_epsilon_bendingJS()}
	{stst.implement_compute_sigma_axialJS()}
	{js.implement_update_stress_diagramJS()}
	{js.implement_update_strain_diagramJS()}
	{stst.implement_compute_sigma_bendingJS()}
	{stst.implement_compute_total_sigmaJS()}
	{stst.implement_compute_total_tauJS()}
	{beam_section.implement_compute_first_moment_of_areaJS()}
	{beam_section.implement_compute_first_moment_of_area_implicitJS()}
	{stst.implement_compute_tau_shearJS()}
	{beam_section.implement_compute_tau_torsionJS()}
	{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}
	"""
	update_t = CustomJS(args=args_slider_t, code=code_change_t)



	# apply the logics
	slider_b.js_on_change('value', update_b)
	slider_h.js_on_change('value', update_h)
	slider_position.js_on_change('value', updade_slider_pos)
	checkbox_P.js_on_click(update_checkbox_P)
	radiogroup_FBD.js_on_click(update_radiogroup_FBD)
	slider_q.js_on_change('value', update_slider_q)
	slider_t.js_on_change('value', update_t)
	checkbox_T.js_on_click(update_checkbox_T)


	########################################################
	# Build the layout
	########################################################
	padding_layout = 10
	layout1 = layout([
	[column(row(column(fig_scheme,
	row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout*3),
	slider_b,
	slider_h,
	slider_t,
	# row(div_geo, div_forces),
	slider_position,
	slider_q,
	Spacer(height=padding_layout*3),
	div_rg_FBD,
	radiogroup_FBD,
	div_cb_P,
	checkbox_P,
	Spacer(height=padding_layout*3),
	div_cb_T,
	checkbox_T))),
	column(fig_beam,
	Spacer(height=padding_layout),
	fig_N,
	fig_V,
	fig_M,
	fig_T)),
	row(column(
	row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_stress_sigma),
	row(fig_V_section, Spacer(width=FIG_B_ss), fig_stress_V, Spacer(width=FIG_B_ss), fig_stress_T, fig_stress_tau),
	))
	),
	],
	])

	show(layout1)
	\ No newline at end of file
	diff --git a/Simple Beam DEMOs/sb_geo.ipynb b/Simple Beam DEMOs/01-sb_geo.ipynb
	similarity index 97%
	rename from Simple Beam DEMOs/sb_geo.ipynb
	rename to Simple Beam DEMOs/01-sb_geo.ipynb
	index 0af35d2..e14468c 100644
	--- a/Simple Beam DEMOs/sb_geo.ipynb
	+++ b/Simple Beam DEMOs/01-sb_geo.ipynb
	@@ -1,541 +1,548 @@
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"# Simple beam - Geometry\n",
	"\n",
	"## Description\n",
	"In this first notebook, the geometry and some mechanical parameters of a simple beam with constant rectangular section are explored. The main idea of this DEMO and the following ones is to actively learn the Structural Mechanics by thinking and playing with an interactive visualisation tool. Considering the complexity of the code to generate this tool (that uses Python for the initialisation and Javascript for the dynamic interactiy), the code is hidden but can be easily accessed in the folder \"HiddenCode\" for the most curious ones."
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## Goals\n",
	"\n",
	- "* Introduce the structure and the main concepts of this set of DEMOs, that will be incrementally enriched step-by-step with more information, theories, diagrams, etc with each notebook\n",
	- "* Gain familiarity with the subject of our following analysis (form, section, static scheme)"
	+ "* Identify the structure and the main concepts of this set of DEMOs, that will be incrementally enriched step-by-step with more information, theories, diagrams, etc with each notebook\n",
	+ "* Gain familiarity with the subject (form, section, static scheme) of our analysis in the next DEMOs"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {
	"tags": []
	},
	"source": [
	"## Tasks and exercises\n",
	"\n",
	"Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	"\n",
	"1. Which static system is studied?\n",
	"\n",
	" <details>\n",
	" <summary style=\"color: red\">Solution:</summary>\n",
	" The beam is supported by a roller (right) and pinned (left), thus the static system is simply supported.\n",
	" </details>\n",
	"\n",
	"<br>\n",
	"\n",
	"2. If our objective is to increase the area to 30'000 mm², which geometric parameters (height, width, length) can we change to achieve the desired configuration? The configuration found is the only one? \n",
	"\n",
	" <details>\n",
	" <summary style=\"color: red\">Solution:</summary>\n",
	" By using the slider for the length (L), it is possible to note that the length has no impact in any mechanical parameter, because the cross-section is constant along the beam, thus the getmetric paraemter has no impact in the area. On the other hand, by changing the value of b and h with the correlated slider, we note the direct correlation with the area, thus by manipulating just the width, the configuration b=150 mm and h=200 mm has an area of 30'000 mm².\n",
	" \n",
	" No, it is not the only configuration possible because there the width and the height of the section have the same influence in the area and without any other condition, there is an infinite number of combination to achieve the desired configuration. For example by swapping the value of b and h, we can have the same area.\n",
	" </details>\n",
	" \n",
	"<br>\n",
	"\n",
	"3. If our objective is to have the inertia with respect to the strong axis (y) equals to 9.0x10⁸ mm⁴ by keeping the area equals to 30'000 mm², which combination of parameters achieves the desired configuration? The configuration found is the only one? \n",
	"\n",
	" <details>\n",
	" <summary style=\"color: red\">Solution:</summary>\n",
	" By playing with the sliders of height and width, the combinationation found b=50 mm and h=600 mm.\n",
	" \n",
	" Yes, because only this combination satisfy both the area and inertia conditions. In this case, swapping the value of b and h has a major impact on the inertia y, thus this combination is not possible.\n",
	" </details>\n",
	"\n",
	"<br>"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## Build the interactive visualisation tool"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {},
	"outputs": [
	{
	"data": {
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	" <div class=\"bk-root\">\n",
	" <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	" <span id=\"1002\">Loading BokehJS ...</span>\n",
	" </div>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	},
	{
	"data": {
	"application/javascript": [
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	" root._bokeh_is_loading = undefined;\n",
	" }\n",
	"\n",
	" const JS_MIME_TYPE = 'application/javascript';\n",
	" const HTML_MIME_TYPE = 'text/html';\n",
	" const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	" const CLASS_NAME = 'output_bokeh rendered_html';\n",
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	"\n",
	" if (server_id !== undefined) {\n",
	" // Clean up Bokeh references\n",
	" const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	" cell.notebook.kernel.execute(cmd_clean, {\n",
	" iopub: {\n",
	" output: function(msg) {\n",
	" const id = msg.content.text.trim();\n",
	" if (id in Bokeh.index) {\n",
	" Bokeh.index[id].model.document.clear();\n",
	" delete Bokeh.index[id];\n",
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	" const output_area = handle.output_area;\n",
	" const output = handle.output;\n",
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	" if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	" return\n",
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	"\n",
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	" // store reference to server id on output_area\n",
	" output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
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	" // create a DOM node to render to\n",
	" const toinsert = this.create_output_subarea(\n",
	" metadata,\n",
	" CLASS_NAME,\n",
	" EXEC_MIME_TYPE\n",
	" );\n",
	" this.keyboard_manager.register_events(toinsert);\n",
	" // Render to node\n",
	" const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	" render(props, toinsert[toinsert.length - 1]);\n",
	" element.append(toinsert);\n",
	" return toinsert\n",
	" }\n",
	"\n",
	" /* Handle when an output is cleared or removed */\n",
	" events.on('clear_output.CodeCell', handleClearOutput);\n",
	" events.on('delete.Cell', handleClearOutput);\n",
	"\n",
	" /* Handle when a new output is added */\n",
	" events.on('output_added.OutputArea', handleAddOutput);\n",
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	" * Register the mime type and append_mime function with output_area\n",
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	" /* Is output safe? */\n",
	" safe: true,\n",
	" /* Index of renderer in `output_area.display_order` */\n",
	" index: 0\n",
	" });\n",
	" }\n",
	"\n",
	" // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	" if (root.Jupyter !== undefined) {\n",
	" const events = require('base/js/events');\n",
	" const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	"\n",
	" if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
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	" root._bokeh_failed_load = false;\n",
	" }\n",
	"\n",
	" const NB_LOAD_WARNING = {'data': {'text/html':\n",
	" \"<div style='background-color: #fdd'>\\n\"+\n",
	" \"<p>\\n\"+\n",
	" \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	" \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	" \"</p>\\n\"+\n",
	" \"<ul>\\n\"+\n",
	" \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	" \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	" \"</ul>\\n\"+\n",
	" \"<code>\\n\"+\n",
	" \"from bokeh.resources import INLINE\\n\"+\n",
	" \"output_notebook(resources=INLINE)\\n\"+\n",
	" \"</code>\\n\"+\n",
	" \"</div>\"}};\n",
	"\n",
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	" if (root.Bokeh !== undefined) {\n",
	" if (el != null) {\n",
	" el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
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	" } else if (Date.now() < root._bokeh_timeout) {\n",
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	" });\n",
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	" delete root._bokeh_onload_callbacks\n",
	" }\n",
	" console.debug(\"Bokeh: all callbacks have finished\");\n",
	" }\n",
	"\n",
	" function load_libs(css_urls, js_urls, callback) {\n",
	" if (css_urls == null) css_urls = [];\n",
	" if (js_urls == null) js_urls = [];\n",
	"\n",
	" root._bokeh_onload_callbacks.push(callback);\n",
	" if (root._bokeh_is_loading > 0) {\n",
	" console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	" return null;\n",
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	" if (js_urls == null \|\| js_urls.length === 0) {\n",
	" run_callbacks();\n",
	" return null;\n",
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	" console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	" root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	"\n",
	" function on_load() {\n",
	" root._bokeh_is_loading--;\n",
	" if (root._bokeh_is_loading === 0) {\n",
	" console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	" run_callbacks()\n",
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	"\n",
	" for (let i = 0; i < css_urls.length; i++) {\n",
	" const url = css_urls[i];\n",
	" const element = document.createElement(\"link\");\n",
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	" element.onerror = on_error.bind(null, url);\n",
	" element.rel = \"stylesheet\";\n",
	" element.type = \"text/css\";\n",
	" element.href = url;\n",
	" console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	" document.body.appendChild(element);\n",
	" }\n",
	"\n",
	" for (let i = 0; i < js_urls.length; i++) {\n",
	" const url = js_urls[i];\n",
	" const element = document.createElement('script');\n",
	" element.onload = on_load;\n",
	" element.onerror = on_error.bind(null, url);\n",
	" element.async = false;\n",
	" element.src = url;\n",
	" console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	" document.head.appendChild(element);\n",
	" }\n",
	" };\n",
	"\n",
	" function inject_raw_css(css) {\n",
	" const element = document.createElement(\"style\");\n",
	" element.appendChild(document.createTextNode(css));\n",
	" document.body.appendChild(element);\n",
	" }\n",
	"\n",
	" \n",
	" const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
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	" Bokeh.set_log_level(\"info\");\n",
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	" \n",
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	" run_inline_js();\n",
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	" load_libs(css_urls, js_urls, function() {\n",
	" console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	" run_inline_js();\n",
	" });\n",
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	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"# Import the packages needed\n",
	"import sys\n",
	"sys.path.append('../HiddenCode')\n",
	"import hidden_code_nb_geo\n",
	"import math\n",
	"import numpy as np \n",
	"from cienpy import simplebeam as sb\n",
	"from cienpy import rectangular_section as beam_section"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"Define the geometry and compute the initial configuration:"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {},
	"outputs": [],
	"source": [
	"# Choose the dimensions\n",
	"L = 6 # [m]\n",
	"h = 200 # [mm]\n",
	"b = 100 # [mm]\n",
	"\n",
	"# compute the parameters\n",
	"A = beam_section.compute_area(b, h) # [mm2]\n",
	"Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	"Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"Run the complex code to generate the interactive visualisation tool:"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {},
	"outputs": [
	{
	"data": {
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pe\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":6,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1083\",\"type\":\"Line\"},{\"attributes\":{\"fill_alpha\":0.1,\"fill_color\":\"white\",\"hatch_alpha\":0.1,\"line_alpha\":0.1,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1088\",\"type\":\"Patch\"},{\"attributes\":{\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1112\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"1162\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Cross-section of the beam\"},\"id\":\"1039\",\"type\":\"Title\"},{\"attributes\":{\"source\":{\"id\":\"1111\"}},\"id\":\"1116\",\"type\":\"CDSView\"},{\"attributes\":{\"source\":{\"id\":\"1003\"}},\"id\":\"1085\",\"type\":\"CDSView\"},{\"attributes\":{\"fill_color\":{\"value\":\"white\"},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":200},\"line_width\":{\"value\":3},\"width\":{\"value\":100},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1099\",\"type\":\"Rect\"},{\"attributes\":{},\"id\":\"1163\",\"type\":\"Selection\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_alpha\":{\"value\":0.2},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1123\",\"type\":\"Text\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1086\"},\"glyph\":{\"id\":\"1087\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1089\"},\"nonselection_glyph\":{\"id\":\"1088\"},\"view\":{\"id\":\"1091\"}},\"id\":\"1090\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"fill_color\":\"white\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1087\",\"type\":\"Patch\"},{\"attributes\":{},\"id\":\"1060\",\"type\":\"SaveTool\"},{\"attributes\":{\"data\":{\"x\":[0,0.15,-0.15],\"y\":[0,-0.25980762113533157,-0.25980762113533157]},\"selected\":{\"id\":\"1163\"},\"selection_policy\":{\"id\":\"1162\"}},\"id\":\"1086\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"data\":{\"x\":[6],\"y\":[-0.15]},\"selected\":{\"id\":\"1165\"},\"selection_policy\":{\"id\":\"1164\"}},\"id\":\"1092\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_color\":{\"value\":\"white\"},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1093\",\"type\":\"Circle\"},{\"attributes\":{\"fill_alpha\":0.2,\"fill_color\":\"white\",\"hatch_alpha\":0.2,\"line_alpha\":0.2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1089\",\"type\":\"Patch\"},{\"attributes\":{\"data\":{\"x\":[0],\"y\":[0]},\"selected\":{\"id\":\"1174\"},\"selection_policy\":{\"id\":\"1173\"}},\"id\":\"1098\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"source\":{\"id\":\"1086\"}},\"id\":\"1091\",\"type\":\"CDSView\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1114\",\"type\":\"Text\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.1},\"line_alpha\":{\"value\":0.1},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1094\",\"type\":\"Circle\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.2},\"line_alpha\":{\"value\":0.2},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1095\",\"type\":\"Circle\"},{\"attributes\":{\"tools\":[{\"id\":\"1057\"},{\"id\":\"1058\"},{\"id\":\"1059\"},{\"id\":\"1060\"},{\"id\":\"1061\"},{\"id\":\"1062\"}]},\"id\":\"1064\",\"type\":\"Toolbar\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1092\"},\"glyph\":{\"id\":\"1093\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1095\"},\"nonselection_glyph\":{\"id\":\"1094\"},\"view\":{\"id\":\"1097\"}},\"id\":\"1096\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":200},\"line_alpha\":{\"value\":0.1},\"line_width\":{\"value\":3},\"width\":{\"value\":100},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1100\",\"type\":\"Rect\"},{\"attributes\":{\"end\":300,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1136\"}]},\"start\":10,\"step\":10,\"title\":\"Change the width b [mm]\",\"value\":100},\"id\":\"1105\",\"type\":\"Slider\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1098\"},\"glyph\":{\"id\":\"1099\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1101\"},\"nonselection_glyph\":{\"id\":\"1100\"},\"view\":{\"id\":\"1103\"}},\"id\":\"1102\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"fill_color\":{\"value\":\"gray\"},\"line_color\":{\"value\":\"gray\"},\"size\":{\"value\":4.114506654314834}},\"id\":\"1108\",\"type\":\"VeeHead\"},{\"attributes\":{},\"id\":\"1164\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"height\":300,\"text\":\"<p style='font-size:16px'><b>Geometrical and mechanical parameters</b></p>\\n h = 200 mm<br>\\n b = 100 mm<br>\\n L = 6 m<br>\\n A = 2.00e+04 mm<sup>2</sup><br>\\n Iy = 6.67e+07 mm<sup>4</sup><br>\\n Iz = 1.67e+07 mm<sup>4</sup>\",\"width\":300},\"id\":\"1104\",\"type\":\"Div\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":200},\"line_alpha\":{\"value\":0.2},\"line_width\":{\"value\":3},\"width\":{\"value\":100},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1101\",\"type\":\"Rect\"},{\"attributes\":{\"source\":{\"id\":\"1098\"}},\"id\":\"1103\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1165\",\"type\":\"Selection\"},{\"attributes\":{\"end\":7,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1135\"}]},\"start\":1,\"step\":0.1,\"title\":\"Change the length L [m]\",\"value\":6},\"id\":\"1107\",\"type\":\"Slider\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1108\"},\"group\":null,\"line_color\":{\"value\":\"gray\"},\"line_width\":{\"value\":0.5877866649021191},\"source\":{\"id\":\"1153\"},\"start\":null,\"x_end\":{\"value\":6.8},\"x_start\":{\"value\":6},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1109\",\"type\":\"Arrow\"},{\"attributes\":{\"end\":600,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1137\"}]},\"start\":20,\"step\":20,\"title\":\"Change the height h [mm]\",\"value\":200},\"id\":\"1106\",\"type\":\"Slider\"},{\"attributes\":{},\"id\":\"1180\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"data\":{\"text\":[\"y axis\"],\"x\":[0],\"y\":[136.0]},\"selected\":{\"id\":\"1176\"},\"selection_policy\":{\"id\":\"1175\"}},\"id\":\"1120\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"source\":{\"id\":\"1129\"}},\"id\":\"1134\",\"type\":\"CDSView\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1120\"},\"glyph\":{\"id\":\"1121\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1123\"},\"nonselection_glyph\":{\"id\":\"1122\"},\"view\":{\"id\":\"1125\"}},\"id\":\"1124\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1181\",\"type\":\"Selection\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1111\"},\"glyph\":{\"id\":\"1112\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1114\"},\"nonselection_glyph\":{\"id\":\"1113\"},\"view\":{\"id\":\"1116\"}},\"id\":\"1115\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"1120\"}},\"id\":\"1125\",\"type\":\"CDSView\"},{\"attributes\":{\"data\":{\"text\":[\"x axis\"],\"x\":[6.4],\"y\":[0.1]},\"selected\":{\"id\":\"1167\"},\"selection_policy\":{\"id\":\"1166\"}},\"id\":\"1111\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_alpha\":{\"value\":0.1},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1122\",\"type\":\"Text\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1121\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"1182\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1117\"},\"group\":null,\"line_color\":{\"value\":\"gray\"},\"line_width\":{\"value\":2.1972245773362196},\"source\":{\"id\":\"1158\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":128.0},\"y_start\":{\"value\":0}},\"id\":\"1118\",\"type\":\"Arrow\"},{\"attributes\":{\"fill_color\":{\"value\":\"gray\"},\"line_color\":{\"value\":\"gray\"},\"size\":{\"value\":15.380572041353537}},\"id\":\"1126\",\"type\":\"VeeHead\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1126\"},\"group\":null,\"line_color\":{\"value\":\"gray\"},\"line_width\":{\"value\":2.1972245773362196},\"source\":{\"id\":\"1159\"},\"start\":null,\"x_end\":{\"value\":-80.0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1127\",\"type\":\"Arrow\"},{\"attributes\":{\"overlay\":{\"id\":\"1063\"}},\"id\":\"1059\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"1183\",\"type\":\"Selection\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1130\",\"type\":\"Text\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_alpha\":{\"value\":0.2},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1132\",\"type\":\"Text\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_alpha\":{\"value\":0.1},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1131\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"1166\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"children\":[{\"id\":\"1005\"}]},\"id\":\"1142\",\"type\":\"Row\"},{\"attributes\":{\"axis_label\":\"Height h [mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"1154\"},\"group\":null,\"major_label_policy\":{\"id\":\"1155\"},\"ticker\":{\"id\":\"1077\"}},\"id\":\"1053\",\"type\":\"LinearAxis\"},{\"attributes\":{\"text_alpha\":{\"value\":0.1},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1113\",\"type\":\"Text\"},{\"attributes\":{\"data\":{\"text\":[\"z axis\"],\"x\":[-88.0],\"y\":[0]},\"selected\":{\"id\":\"1178\"},\"selection_policy\":{\"id\":\"1177\"}},\"id\":\"1129\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1062\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1184\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1129\"},\"glyph\":{\"id\":\"1130\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1132\"},\"nonselection_glyph\":{\"id\":\"1131\"},\"view\":{\"id\":\"1134\"}},\"id\":\"1133\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1167\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1104\"},\"s_b\":{\"id\":\"1003\"},\"s_s\":{\"id\":\"1004\"},\"section\":{\"id\":\"1102\"},\"support_r\":{\"id\":\"1096\"},\"x_axis_arrow\":{\"id\":\"1109\"},\"x_axis_label\":{\"id\":\"1115\"}},\"code\":\"\\n // retrieve data used\\n const data_b = s_b.data\\n const data_s = s_s.data\\n // retrieve the var from the object that uses callback\\n const f = cb_obj.value // value of the slider\\n // compute the parameters and dimensions\\n const L = Math.round(f10)/10\\n const b = Math.round(data_s['b'])\\n const h = Math.round(data_s['h'])\\n const A = bh\\n const Iy = Math.round(Math.pow(h, 3)b/12)\\n const Iz = Math.round(Math.pow(b, 3)h/12)\\n div.text = \\\"<p style='font-size:16px'><b>Geometrical and mechanical parameters:</b></p> h = \\\"+h+\\n \\\" mm<br> b = \\\"+b+\\n \\\" mm<br> L = \\\"+L+\\n \\\" m<br> A = \\\"+A.toExponential()+\\n \\\" mm<sup>2</sup><br> Iy = \\\"+Iy.toExponential()+\\n \\\" mm<sup>4</sup><br> Iz = \\\"+Iz.toExponential()+\\n \\\" mm<sup>4</sup>\\\"\\n // change the plot of the section\\n section.glyph.width = b\\n section.glyph.height = h\\n // change the plot of the beam\\n data_b['x'][1] = L\\n support_r.glyph.x = L\\n \\n // change the position of the x axis arrow and text\\n x_axis_arrow.x_start = L\\n x_axis_arrow.x_end = L+0.8\\n x_axis_label.glyph.x = L+0.8/2\\n \\n // apply the changes\\n data_s['L'] = f\\n data_s['A'] = A\\n data_s['Iy'] = Iy\\n data_s['Iz'] = Iz\\n s_s.change.emit()\\n s_b.change.emit()\\n \"},\"id\":\"1135\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1185\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1104\"},\"s_b\":{\"id\":\"1003\"},\"s_s\":{\"id\":\"1004\"},\"section\":{\"id\":\"1102\"},\"support_r\":{\"id\":\"1096\"}},\"code\":\"\\n // retrieve data used\\n const data_b = s_b.data\\n const data_s = s_s.data\\n // retrieve the var from the object that uses callback\\n const f = cb_obj.value // value of the slider\\n // compute the parameters and dimensions\\n const L = Math.round(data_s['L']10)/10\\n const b = Math.round(f)\\n const h = Math.round(data_s['h'])\\n const A = bh\\n const Iy = Math.round(Math.pow(h, 3)b/12)\\n const Iz = Math.round(Math.pow(b, 3)h/12)\\n div.text = \\\"<p style='font-size:16px'><b>Geometrical and mechanical parameters:</b></p> h = \\\"+h+\\n \\\" mm<br> b = \\\"+b+\\n \\\" mm<br> L = \\\"+L+\\n \\\" m<br> A = \\\"+A.toExponential()+\\n \\\" mm<sup>2</sup><br> Iy = \\\"+Iy.toExponential()+\\n \\\" mm<sup>4</sup><br> Iz = \\\"+Iz.toExponential()+\\n \\\" mm<sup>4</sup>\\\"\\n // change the plot of the section\\n section.glyph.width = b\\n section.glyph.height = h\\n // change the plot of the beam\\n data_b['x'][1] = L\\n support_r.glyph.x = L\\n \\n // apply the changes\\n data_s['b'] = f\\n data_s['A'] = A\\n data_s['Iy'] = Iy\\n data_s['Iz'] = Iz\\n s_s.change.emit()\\n s_b.change.emit()\\n \"},\"id\":\"1136\",\"type\":\"CustomJS\"},{\"attributes\":{\"axis\":{\"id\":\"1049\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1052\",\"type\":\"Grid\"},{\"attributes\":{\"fill_color\":{\"value\":\"gray\"},\"line_color\":{\"value\":\"gray\"},\"size\":{\"value\":15.380572041353537}},\"id\":\"1117\",\"type\":\"VeeHead\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1104\"},\"s_b\":{\"id\":\"1003\"},\"s_s\":{\"id\":\"1004\"},\"section\":{\"id\":\"1102\"},\"support_r\":{\"id\":\"1096\"}},\"code\":\"\\n // retrieve data used\\n const data_b = s_b.data\\n const data_s = s_s.data\\n // retrieve the var from the object that uses callback\\n const f = cb_obj.value // value of the slider\\n // compute the parameters and dimensions\\n const L = Math.round(data_s['L']10)/10\\n const b = Math.round(data_s['b'])\\n const h = Math.round(f)\\n const A = bh\\n const Iy = Math.round(Math.pow(h, 3)b/12)\\n const Iz = Math.round(Math.pow(b, 3)h/12)\\n div.text = \\\"<p style='font-size:16px'><b>Geometrical and mechanical parameters:</b></p> h = \\\"+h+\\n \\\" mm<br> b = \\\"+b+\\n \\\" mm<br> L = \\\"+L+\\n \\\" m<br> A = \\\"+A.toExponential()+\\n \\\" mm<sup>2</sup><br> Iy = \\\"+Iy.toExponential()+\\n \\\" mm<sup>4</sup><br> Iz = \\\"+Iz.toExponential()+\\n \\\" mm<sup>4</sup>\\\"\\n // change the plot of the section\\n section.glyph.width = b\\n section.glyph.height = h\\n // change the plot of the beam\\n data_b['x'][1] = L\\n support_r.glyph.x = L\\n \\n // apply the changes\\n data_s['h'] = f\\n data_s['A'] = A\\n data_s['Iy'] = Iy\\n data_s['Iz'] = Iz\\n s_s.change.emit()\\n s_b.change.emit()\\n \"},\"id\":\"1137\",\"type\":\"CustomJS\"},{\"attributes\":{\"width\":20},\"id\":\"1138\",\"type\":\"Spacer\"},{\"attributes\":{\"height\":50},\"id\":\"1139\",\"type\":\"Spacer\"},{\"attributes\":{\"height\":50},\"id\":\"1140\",\"type\":\"Spacer\"},{\"attributes\":{\"children\":[{\"id\":\"1139\"},{\"id\":\"1107\"},{\"id\":\"1105\"},{\"id\":\"1106\"},{\"id\":\"1140\"},{\"id\":\"1104\"}]},\"id\":\"1141\",\"type\":\"Column\"}],\"root_ids\":[\"1144\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n",
	" const render_items = [{\"docid\":\"92c2f2f8-9928-41ef-8c17-faf92aab2e85\",\"root_ids\":[\"1144\"],\"roots\":{\"1144\":\"f61d0e24-9628-47a2-9b21-fb274f4324bf\"}}];\n",
	" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	"\n",
	" }\n",
	" if (root.Bokeh !== undefined) {\n",
	" embed_document(root);\n",
	" } else {\n",
	" let attempts = 0;\n",
	" const timer = setInterval(function(root) {\n",
	" if (root.Bokeh !== undefined) {\n",
	" clearInterval(timer);\n",
	" embed_document(root);\n",
	" } else {\n",
	" attempts++;\n",
	" if (attempts > 100) {\n",
	" clearInterval(timer);\n",
	" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	" }\n",
	" }\n",
	" }, 10, root)\n",
	" }\n",
	"})(window);"
	],
	"application/vnd.bokehjs_exec.v0+json": ""
	},
	"metadata": {
	"application/vnd.bokehjs_exec.v0+json": {
	"id": "1144"
	}
	},
	"output_type": "display_data"
	}
	],
	"source": [
	"hidden_code_nb_geo.main_code(L, h, b, A, Iy, Iz)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## Legend\n",
	"\n",
	"Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder. \n",
	"\n",
	"* Slider of the length L: move the slider to change the length L of the beam.\n",
	"* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	"* Slider of the height h: move the slider to change the height h of the cross-section of the beam.\n",
	"* Textbox \"Geometrical and mechanical parameters: small summary with the value of h, b, L, A (area), Iy (inertia with respect to the strong axis) and Iz (inertia with respect to the weak axis).\n",
	"* Figure \"Simple supported beam\": in this figure, the static scheme, the length and x axis are presented. This figure serves to have a dynamic representation of the studied case.\n",
	"* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	"\n",
	+ "### Help and Information on the functions\n",
	+ "\n",
	+ "In Jupyter Notebooks the user can learn more about a function by using the question mark after the target function. One question mark shows some useful information on the function and two question marks show in addition also the code of the function, revealing it's content.\n",
	+ "For example, by creating a Code cell and pasting \"beam_section.compute_area?\" or \"beam_section.compute_area??\", it's possible to see how this feature works.\n",
	+ "\n",
	"### Recommendations\n",
	"\n",
	+ "If you have problem visualizing the entirety of the tool, you can maximize the window size by using Ctrl+B to hide/show the left explorer panel and by using F11 to go to the full-page mode and back in the browser (NB: it could not work in the tab with NOTO; just use F11 in another tab and come back in the NOTO tab). If you're using a very sall display and it's not enough, you can zoom out the browser tab.\n",
	+ "\n",
	"Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully."
	]
	}
	],
	"metadata": {
	"interpreter": {
	"hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	},
	"kernelspec": {
	"display_name": "cienpy venv",
	"language": "python",
	"name": "cienpy_venv"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.8.10"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 4
	}
	diff --git a/Simple Beam DEMOs/sb_actions.ipynb b/Simple Beam DEMOs/02-sb_actions.ipynb
	similarity index 98%
	rename from Simple Beam DEMOs/sb_actions.ipynb
	rename to Simple Beam DEMOs/02-sb_actions.ipynb
	index 7096771..d45e343 100644
	--- a/Simple Beam DEMOs/sb_actions.ipynb
	+++ b/Simple Beam DEMOs/02-sb_actions.ipynb
	@@ -1,562 +1,569 @@
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"# Simple beam - Actions\n",
	- "In this second notebook, different actions are applied on the simple supported beam presented in the previous DEMO called \"sb_geo\". The internal forces and moments can be visuallized along the beam. "
	+ "In this second notebook, different actions are applied on the simple supported beam presented in the previous DEMO called \"01-sb_geo\". The internal forces and moments can be visuallized along the beam. "
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## Goals\n",
	"\n",
	- "* Learn the effect of different actions inside an element\n",
	- "* Note how some parameters impact the internal forces\n",
	- "* Improve the understanding of how the free-body diagram is used and the (frequently) unclear sign convention"
	+ "* Describe the effect of different actions inside an element\n",
	+ "* Identify which parameters impact the internal forces\n",
	+ "* Explain how the free-body diagram is used and the (frequently) unclear sign convention"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {
	"tags": []
	},
	"source": [
	"## Tasks and exercises\n",
	"\n",
	"Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	"\n",
	"1. Which consequences does the applied force P have on the internal and external forces?\n",
	"\n",
	" <details>\n",
	" <summary style=\"color: red\">Solution:</summary>\n",
	" The external force P has direct influence on the horizontal reaction force R and the axial force N. There is no correlation with the shear force V and the bending moment M. Note that this affirmation does not hold for more complex cases.\n",
	" </details>\n",
	"\n",
	"<br>\n",
	"\n",
	"2. Is there a position along the beam where the norm of the internal forces changes between right-hand and left-hand free-body diagram? What can you note about the sign?\n",
	"\n",
	" <details>\n",
	" <summary style=\"color: red\">Solution:</summary>\n",
	" No, because the equilibrium must be met in every position and the magnitude of the internal forces in each point should be the same independently of the side chosen for the equilibrium.\n",
	" \n",
	" The sign for the axial and shear forces flip between the two equilibrium. Instead, the sign of the moment remains the same.\n",
	" </details>\n",
	" \n",
	"<br>\n",
	"\n",
	"3. Does the cross-section influence the internal forces? By changing the length of the beam to 8 m, do you ascertain any changes?\n",
	"\n",
	" <details>\n",
	" <summary style=\"color: red\">Solution:</summary>\n",
	" No, the cross-section has no impact on the internal forces in this case. This is true because the system is isostatic; if the system was hyperstatic, the cross-section could have an impact on the internal forces.\n",
	" \n",
	" By increasing the length of the beam, the shear force and bending moment increase; on the other hand the axial force remains the same.\n",
	" </details>\n",
	"\n",
	"<br>"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## Build the interactive visualisation tool"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/html": [
	"\n",
	" <div class=\"bk-root\">\n",
	" <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	" <span id=\"1002\">Loading BokehJS ...</span>\n",
	" </div>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	},
	{
	"data": {
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	" function now() {\n",
	" return new Date();\n",
	" }\n",
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	" const force = true;\n",
	"\n",
	" if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	" root._bokeh_onload_callbacks = [];\n",
	" root._bokeh_is_loading = undefined;\n",
	" }\n",
	"\n",
	" const JS_MIME_TYPE = 'application/javascript';\n",
	" const HTML_MIME_TYPE = 'text/html';\n",
	" const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	" const CLASS_NAME = 'output_bokeh rendered_html';\n",
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	" */\n",
	" function render(props, node) {\n",
	" const script = document.createElement(\"script\");\n",
	" node.appendChild(script);\n",
	" }\n",
	"\n",
	" /**\n",
	" * Handle when an output is cleared or removed\n",
	" */\n",
	" function handleClearOutput(event, handle) {\n",
	" const cell = handle.cell;\n",
	"\n",
	" const id = cell.output_area._bokeh_element_id;\n",
	" const server_id = cell.output_area._bokeh_server_id;\n",
	" // Clean up Bokeh references\n",
	" if (id != null && id in Bokeh.index) {\n",
	" Bokeh.index[id].model.document.clear();\n",
	" delete Bokeh.index[id];\n",
	" }\n",
	"\n",
	" if (server_id !== undefined) {\n",
	" // Clean up Bokeh references\n",
	" const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	" cell.notebook.kernel.execute(cmd_clean, {\n",
	" iopub: {\n",
	" output: function(msg) {\n",
	" const id = msg.content.text.trim();\n",
	" if (id in Bokeh.index) {\n",
	" Bokeh.index[id].model.document.clear();\n",
	" delete Bokeh.index[id];\n",
	" }\n",
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	" });\n",
	" // Destroy server and session\n",
	" const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	" cell.notebook.kernel.execute(cmd_destroy);\n",
	" }\n",
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	" if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
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	" if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
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	" output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
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	" const bk_div = document.createElement(\"div\");\n",
	" bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
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	"\n",
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	"\n",
	" function append_mime(data, metadata, element) {\n",
	" // create a DOM node to render to\n",
	" const toinsert = this.create_output_subarea(\n",
	" metadata,\n",
	" CLASS_NAME,\n",
	" EXEC_MIME_TYPE\n",
	" );\n",
	" this.keyboard_manager.register_events(toinsert);\n",
	" // Render to node\n",
	" const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	" render(props, toinsert[toinsert.length - 1]);\n",
	" element.append(toinsert);\n",
	" return toinsert\n",
	" }\n",
	"\n",
	" /* Handle when an output is cleared or removed */\n",
	" events.on('clear_output.CodeCell', handleClearOutput);\n",
	" events.on('delete.Cell', handleClearOutput);\n",
	"\n",
	" /* Handle when a new output is added */\n",
	" events.on('output_added.OutputArea', handleAddOutput);\n",
	"\n",
	" /**\n",
	" * Register the mime type and append_mime function with output_area\n",
	" */\n",
	" OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	" /* Is output safe? */\n",
	" safe: true,\n",
	" /* Index of renderer in `output_area.display_order` */\n",
	" index: 0\n",
	" });\n",
	" }\n",
	"\n",
	" // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	" if (root.Jupyter !== undefined) {\n",
	" const events = require('base/js/events');\n",
	" const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	"\n",
	" if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	" register_renderer(events, OutputArea);\n",
	" }\n",
	" }\n",
	"\n",
	" \n",
	" if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	" root._bokeh_timeout = Date.now() + 5000;\n",
	" root._bokeh_failed_load = false;\n",
	" }\n",
	"\n",
	" const NB_LOAD_WARNING = {'data': {'text/html':\n",
	" \"<div style='background-color: #fdd'>\\n\"+\n",
	" \"<p>\\n\"+\n",
	" \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	" \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	" \"</p>\\n\"+\n",
	" \"<ul>\\n\"+\n",
	" \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	" \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	" \"</ul>\\n\"+\n",
	" \"<code>\\n\"+\n",
	" \"from bokeh.resources import INLINE\\n\"+\n",
	" \"output_notebook(resources=INLINE)\\n\"+\n",
	" \"</code>\\n\"+\n",
	" \"</div>\"}};\n",
	"\n",
	" function display_loaded() {\n",
	" const el = document.getElementById(\"1002\");\n",
	" if (el != null) {\n",
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	" if (el != null) {\n",
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	" }\n",
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	" try {\n",
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	" if (callback != null)\n",
	" callback();\n",
	" });\n",
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	" delete root._bokeh_onload_callbacks\n",
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	" console.debug(\"Bokeh: all callbacks have finished\");\n",
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	"\n",
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	"\n",
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	" if (root._bokeh_is_loading > 0) {\n",
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	" return null;\n",
	" }\n",
	" if (js_urls == null \|\| js_urls.length === 0) {\n",
	" run_callbacks();\n",
	" return null;\n",
	" }\n",
	" console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	" root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	"\n",
	" function on_load() {\n",
	" root._bokeh_is_loading--;\n",
	" if (root._bokeh_is_loading === 0) {\n",
	" console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	" run_callbacks()\n",
	" }\n",
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	" }\n",
	"\n",
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	" element.rel = \"stylesheet\";\n",
	" element.type = \"text/css\";\n",
	" element.href = url;\n",
	" console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	" document.body.appendChild(element);\n",
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	"\n",
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	" console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	" document.head.appendChild(element);\n",
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	" };\n",
	"\n",
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	" element.appendChild(document.createTextNode(css));\n",
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	" \n",
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	" const css_urls = [];\n",
	" \n",
	"\n",
	" const inline_js = [\n",
	" function(Bokeh) {\n",
	" Bokeh.set_log_level(\"info\");\n",
	" },\n",
	" function(Bokeh) {\n",
	" \n",
	" \n",
	" }\n",
	" ];\n",
	"\n",
	" function run_inline_js() {\n",
	" \n",
	" if (root.Bokeh !== undefined \|\| force === true) {\n",
	" \n",
	" for (let i = 0; i < inline_js.length; i++) {\n",
	" inline_js[i].call(root, root.Bokeh);\n",
	" }\n",
	" if (force === true) {\n",
	" display_loaded();\n",
	" }} else if (Date.now() < root._bokeh_timeout) {\n",
	" setTimeout(run_inline_js, 100);\n",
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	}
	],
	"source": [
	"# Import the packages needed\n",
	"import sys\n",
	"sys.path.append('../HiddenCode')\n",
	"import hidden_code_nb_actions\n",
	"import math\n",
	"import numpy as np\n",
	"from cienpy import simplebeam as sb\n",
	"from cienpy import rectangular_section as beam_section"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"Define the geometry, the external actions and compute the initial configuration."
	]
	},
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {},
	"outputs": [],
	"source": [
	"# Choose the dimensions\n",
	"L = 6 # [m]\n",
	"h = 200 # [mm]\n",
	"b = 100 # [mm]\n",
	"q = 4; # [kN/m]\n",
	"P = 10; # [kN]\n",
	"\n",
	"# compute the internal forces (at x=L)\n",
	"discr_NVM = 100\n",
	"x_discr = np.linspace(0, L, discr_NVM)\n",
	"N_discr = sb.compute_N(x_discr, P)\n",
	"V_discr = sb.compute_V(x_discr, q, L)\n",
	"M_discr = sb.compute_M(x_discr, q, L)\n",
	"N = N_discr[-1]\n",
	"V = V_discr[-1]\n",
	"M = M_discr[-1]\n",
	"\n",
	"# compute the parameters\n",
	"A = beam_section.compute_area(b, h) # [mm2]\n",
	"Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	"Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	"\n",
	"# compute the reactions\n",
	"Rx = sb.compute_Rx(P)\n",
	"Ry_l = sb.compute_Ry_l(q, L)\n",
	"Ry_r = sb.compute_Ry_r(q, L)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"Run the complex code to generate the interactive visualisation tool:"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {},
	"outputs": [
	{
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Scheme\"},\"id\":\"1902\",\"type\":\"Title\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"2009\"},\"group\":null,\"line_color\":{\"value\":\"red\"},\"line_width\":{\"value\":0.0},\"source\":{\"id\":\"2156\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"2010\",\"type\":\"Arrow\"},{\"attributes\":{\"fill_color\":{\"value\":\"red\"},\"line_color\":{\"value\":\"red\"},\"size\":{\"value\":0.0}},\"id\":\"2012\",\"type\":\"VeeHead\"},{\"attributes\":{\"tools\":[{\"id\":\"1833\"},{\"id\":\"1834\"},{\"id\":\"1835\"},{\"id\":\"1836\"},{\"id\":\"1837\"},{\"id\":\"1838\"}]},\"id\":\"1840\",\"type\":\"Toolbar\"},{\"attributes\":{\"source\":{\"id\":\"1779\"}},\"id\":\"1996\",\"type\":\"CDSView\"},{\"attributes\":{\"fill_color\":{\"value\":\"orange\"},\"line_color\":{\"value\":\"orange\"},\"size\":{\"value\":17.954645502230758}},\"id\":\"2003\",\"type\":\"VeeHead\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2199\"},\"selection_policy\":{\"id\":\"2198\"}},\"id\":\"2154\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_color\":{\"value\":\"red\"},\"line_color\":{\"value\":\"red\"},\"size\":{\"value\":0.0}},\"id\":\"2009\",\"type\":\"VeeHead\"},{\"attributes\":{},\"id\":\"2164\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"fill_color\":{\"value\":\"orange\"},\"line_color\":{\"value\":\"orange\"},\"size\":{\"value\":16.785266909588593}},\"id\":\"2006\",\"type\":\"VeeHead\"},{\"attributes\":{\"text\":\"\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = 200 mm<br>\\n b = 100 mm<br>\\n L = 6 m<br>\\n A = 2.00e+04 mm<sup>2</sup><br>\\n Iy = 6.67e+07 mm<sup>4</sup><br>\\n Iz = 1.67e+07 mm<sup>4</sup>\"},\"id\":\"1880\",\"type\":\"Div\"},{\"attributes\":{},\"id\":\"2165\",\"type\":\"Selection\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_alpha\":{\"value\":0.2},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1898\",\"type\":\"Text\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"2015\"},\"glyph\":{\"id\":\"2017\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"2019\"},\"nonselection_glyph\":{\"id\":\"2018\"},\"view\":{\"id\":\"2021\"}},\"id\":\"2020\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"height\":10},\"id\":\"2042\",\"type\":\"Spacer\"},{\"attributes\":{},\"id\":\"2206\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"end\":300,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"2036\"}]},\"start\":10,\"step\":10,\"title\":\"Change the width b [mm]\",\"value\":100},\"id\":\"1881\",\"type\":\"Slider\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"red\",\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2018\",\"type\":\"Line\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2201\"},\"selection_policy\":{\"id\":\"2200\"}},\"id\":\"2155\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"red\",\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2019\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"2173\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"red\"},\"hatch_alpha\":{\"value\":0.1},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"red\"},\"marker\":{\"value\":\"triangle\"},\"size\":{\"value\":0},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2024\",\"type\":\"Scatter\"},{\"attributes\":{\"height\":10},\"id\":\"2043\",\"type\":\"Spacer\"},{\"attributes\":{\"source\":{\"id\":\"1934\"}},\"id\":\"1939\",\"type\":\"CDSView\"},{\"attributes\":{\"source\":{\"id\":\"2015\"}},\"id\":\"2021\",\"type\":\"CDSView\"},{\"attributes\":{\"source\":{\"id\":\"2022\"}},\"id\":\"2027\",\"type\":\"CDSView\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2203\"},\"selection_policy\":{\"id\":\"2202\"}},\"id\":\"2156\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"2174\",\"type\":\"Selection\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0.2},\"height\":{\"value\":18.0},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":72.0},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1937\",\"type\":\"Rect\"},{\"attributes\":{\"fill_color\":{\"value\":\"red\"},\"line_color\":{\"value\":\"red\"},\"marker\":{\"value\":\"triangle\"},\"size\":{\"value\":0},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2023\",\"type\":\"Scatter\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0.2},\"height\":{\"value\":480.0},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":300},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1850\",\"type\":\"Rect\"},{\"attributes\":{\"fill_alpha\":0.2,\"fill_color\":\"white\",\"hatch_alpha\":0.2,\"line_alpha\":0.2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1865\",\"type\":\"Patch\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"red\"},\"hatch_alpha\":{\"value\":0.2},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"red\"},\"marker\":{\"value\":\"triangle\"},\"size\":{\"value\":0},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2025\",\"type\":\"Scatter\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1934\"},\"glyph\":{\"id\":\"1935\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1937\"},\"nonselection_glyph\":{\"id\":\"1936\"},\"view\":{\"id\":\"1939\"}},\"id\":\"1938\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"2166\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"2022\"},\"glyph\":{\"id\":\"2023\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"2025\"},\"nonselection_glyph\":{\"id\":\"2024\"},\"view\":{\"id\":\"2027\"}},\"id\":\"2026\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2205\"},\"selection_policy\":{\"id\":\"2204\"}},\"id\":\"2157\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"end\":5.0,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"2040\"}]},\"start\":0.1,\"step\":0.1,\"title\":\"Change the uniform load q [kN/m]\",\"value\":4},\"id\":\"2028\",\"type\":\"Slider\"},{\"attributes\":{},\"id\":\"2167\",\"type\":\"Selection\"},{\"attributes\":{\"text\":\"Free-body diagram (FBD):\"},\"id\":\"2030\",\"type\":\"Div\"},{\"attributes\":{},\"id\":\"2202\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1904\",\"type\":\"DataRange1d\"},{\"attributes\":{\"end\":6,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"2035\"}]},\"start\":0,\"step\":0.02,\"title\":\"Change the position x along the beam [m]\",\"value\":6},\"id\":\"2029\",\"type\":\"Slider\"},{\"attributes\":{\"active\":0,\"js_property_callbacks\":{\"change:active\":[{\"id\":\"2039\"}]},\"labels\":[\"Right-hand\",\"Left-hand\"]},\"id\":\"2031\",\"type\":\"RadioButtonGroup\"},{\"attributes\":{\"tools\":[{\"id\":\"1920\"},{\"id\":\"1921\"},{\"id\":\"1922\"},{\"id\":\"1923\"},{\"id\":\"1924\"},{\"id\":\"1925\"}]},\"id\":\"1927\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"2158\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"text\":\"Axial force P=10 kN (applied)\"},\"id\":\"2032\",\"type\":\"Div\"},{\"attributes\":{\"fill_alpha\":0.2,\"fill_color\":\"blue\",\"hatch_alpha\":0.2,\"hatch_color\":\"navy\",\"line_alpha\":0.2,\"line_color\":\"navy\",\"x\":{\"field\":\"x_fade\"},\"y\":{\"field\":\"y\"}},\"id\":\"1994\",\"type\":\"Patch\"},{\"attributes\":{\"text\":\"\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = 10 kN<br>\\n Rx = 10 kN<br>\\n Ry (left) = 12.0 kN<br>\\n Ry (right) = 12.0 kN<br>\\n No cross section analysed.<br>\\n N = 0 kN<br>\\n V = 0 kN<br>\\n M = 0 kNm\\n \\n \"},\"id\":\"2034\",\"type\":\"Div\"},{\"attributes\":{\"source\":{\"id\":\"1847\"}},\"id\":\"1852\",\"type\":\"CDSView\"},{\"attributes\":{\"data\":{\"x\":[3.0],\"y\":[0.6]},\"selected\":{\"id\":\"2165\"},\"selection_policy\":{\"id\":\"2164\"}},\"id\":\"1940\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1874\"},\"glyph\":{\"id\":\"1875\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1877\"},\"nonselection_glyph\":{\"id\":\"1876\"},\"view\":{\"id\":\"1879\"}},\"id\":\"1878\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.1},\"line_alpha\":{\"value\":0.1},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1870\",\"type\":\"Circle\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1940\"},\"glyph\":{\"id\":\"1941\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1943\"},\"nonselection_glyph\":{\"id\":\"1942\"},\"view\":{\"id\":\"1945\"}},\"id\":\"1944\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1880\"},\"s_b\":{\"id\":\"1777\"},\"section\":{\"id\":\"1878\"},\"source\":{\"id\":\"1780\"},\"support_r\":{\"id\":\"1872\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \"},\"id\":\"2036\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1862\"},\"glyph\":{\"id\":\"1863\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1865\"},\"nonselection_glyph\":{\"id\":\"1864\"},\"view\":{\"id\":\"1867\"}},\"id\":\"1866\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"data\":{\"x\":[6],\"y\":[-0.0975]},\"selected\":{\"id\":\"2163\"},\"selection_policy\":{\"id\":\"2162\"}},\"id\":\"1868\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"blue\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_color\":{\"value\":\"navy\"},\"height\":{\"value\":0.4},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"navy\"},\"width\":{\"value\":6},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1942\",\"type\":\"Rect\"},{\"attributes\":{\"fill_color\":{\"value\":\"green\"},\"line_color\":{\"value\":\"green\"},\"size\":{\"value\":16.785266909588593}},\"id\":\"1952\",\"type\":\"VeeHead\"},{\"attributes\":{\"active\":[0],\"js_property_callbacks\":{\"change:active\":[{\"id\":\"2038\"}]},\"labels\":[\"Apply or remove axial force P\"]},\"id\":\"2033\",\"type\":\"CheckboxButtonGroup\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"2026\"},\"div_P\":{\"id\":\"2032\"},\"div_f\":{\"id\":\"2034\"},\"fN\":{\"id\":\"2010\"},\"fP\":{\"id\":\"1998\"},\"fRx\":{\"id\":\"2007\"},\"fRyl\":{\"id\":\"2004\"},\"fRyr\":{\"id\":\"2001\"},\"fV\":{\"id\":\"2013\"},\"s_M\":{\"id\":\"2015\"},\"s_q\":{\"id\":\"1779\"},\"s_sb\":{\"id\":\"1778\"},\"source\":{\"id\":\"1780\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \"},\"id\":\"2035\",\"type\":\"CustomJS\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"blue\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_color\":{\"value\":\"navy\"},\"height\":{\"value\":0.4},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"navy\"},\"width\":{\"value\":6},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1943\",\"type\":\"Rect\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Cross-section of the beam\"},\"id\":\"1815\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"2159\",\"type\":\"Selection\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1946\"},\"glyph\":{\"id\":\"1947\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1949\"},\"nonselection_glyph\":{\"id\":\"1948\"},\"view\":{\"id\":\"1951\"}},\"id\":\"1950\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":6,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1859\",\"type\":\"Line\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":200},\"line_alpha\":{\"value\":0.1},\"line_width\":{\"value\":3},\"width\":{\"value\":100},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1876\",\"type\":\"Rect\"},{\"attributes\":{\"data\":{\"text\":[\"q\"],\"x\":[-0.2],\"y\":[0.4]},\"selected\":{\"id\":\"2167\"},\"selection_policy\":{\"id\":\"2166\"}},\"id\":\"1946\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1913\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"2161\",\"type\":\"Selection\"},{\"attributes\":{\"fill_color\":{\"value\":\"white\"},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1869\",\"type\":\"Circle\"},{\"attributes\":{\"source\":{\"id\":\"1940\"}},\"id\":\"1945\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"2168\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"source\":{\"id\":\"1862\"}},\"id\":\"1867\",\"type\":\"CDSView\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"green\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1958\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"2203\",\"type\":\"Selection\"},{\"attributes\":{\"text_color\":{\"value\":\"blue\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1947\",\"type\":\"Text\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1886\"},\"glyph\":{\"id\":\"1887\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1889\"},\"nonselection_glyph\":{\"id\":\"1888\"},\"view\":{\"id\":\"1891\"}},\"id\":\"1890\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1880\"},\"s_b\":{\"id\":\"1777\"},\"section\":{\"id\":\"1878\"},\"source\":{\"id\":\"1780\"},\"support_r\":{\"id\":\"1872\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const b = db['b'][0]\\n const h = cb_obj.value // value of the slider\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \"},\"id\":\"2037\",\"type\":\"CustomJS\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.2},\"line_alpha\":{\"value\":0.2},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1871\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"2169\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"2207\",\"type\":\"Selection\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1868\"},\"glyph\":{\"id\":\"1869\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1871\"},\"nonselection_glyph\":{\"id\":\"1870\"},\"view\":{\"id\":\"1873\"}},\"id\":\"1872\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"1946\"}},\"id\":\"1951\",\"type\":\"CDSView\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"2026\"},\"div_P\":{\"id\":\"2032\"},\"div_f\":{\"id\":\"2034\"},\"fN\":{\"id\":\"2010\"},\"fP\":{\"id\":\"1998\"},\"fRx\":{\"id\":\"2007\"},\"fRyl\":{\"id\":\"2004\"},\"fRyr\":{\"id\":\"2001\"},\"fV\":{\"id\":\"2013\"},\"s_M\":{\"id\":\"2015\"},\"source\":{\"id\":\"1780\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"2038\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1952\"},\"group\":null,\"line_color\":{\"value\":\"green\"},\"line_width\":{\"value\":2.3978952727983707},\"source\":{\"id\":\"2144\"},\"start\":null,\"x_end\":{\"value\":6},\"x_start\":{\"value\":7.0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1953\",\"type\":\"Arrow\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_alpha\":{\"value\":0.1},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1897\",\"type\":\"Text\"},{\"attributes\":{\"text_alpha\":{\"value\":0.1},\"text_color\":{\"value\":\"blue\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1948\",\"type\":\"Text\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":200},\"line_alpha\":{\"value\":0.2},\"line_width\":{\"value\":3},\"width\":{\"value\":100},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1877\",\"type\":\"Rect\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"2026\"},\"div_P\":{\"id\":\"2032\"},\"fN\":{\"id\":\"2010\"},\"fP\":{\"id\":\"1998\"},\"fRx\":{\"id\":\"2007\"},\"fRyl\":{\"id\":\"2004\"},\"fRyr\":{\"id\":\"2001\"},\"fV\":{\"id\":\"2013\"},\"s_M\":{\"id\":\"2015\"},\"s_q\":{\"id\":\"1779\"},\"s_sb\":{\"id\":\"1778\"},\"source\":{\"id\":\"1780\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"2039\",\"type\":\"CustomJS\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.5},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.5},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1962\",\"type\":\"Circle\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1892\"},\"group\":null,\"line_color\":{\"value\":\"gray\"},\"line_width\":{\"value\":2.1972245773362196},\"source\":{\"id\":\"2180\"},\"start\":null,\"x_end\":{\"value\":-80.0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1893\",\"type\":\"Arrow\"},{\"attributes\":{},\"id\":\"1834\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"blue\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1949\",\"type\":\"Text\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"2026\"},\"div_P\":{\"id\":\"2032\"},\"div_f\":{\"id\":\"2034\"},\"fN\":{\"id\":\"2010\"},\"fP\":{\"id\":\"1998\"},\"fRx\":{\"id\":\"2007\"},\"fRyl\":{\"id\":\"2004\"},\"fRyr\":{\"id\":\"2001\"},\"fV\":{\"id\":\"2013\"},\"s_M\":{\"id\":\"2015\"},\"s_q\":{\"id\":\"1779\"},\"source\":{\"id\":\"1780\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]*10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"2040\",\"type\":\"CustomJS\"},{\"attributes\":{\"text_alpha\":{\"value\":0.1},\"text_color\":{\"value\":\"green\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1957\",\"type\":\"Text\"},{\"attributes\":{\"width\":10},\"id\":\"2041\",\"type\":\"Spacer\"},{\"attributes\":{\"fill_color\":{\"value\":\"green\"},\"line_color\":{\"value\":\"green\"},\"size\":{\"value\":16.785266909588593}},\"id\":\"1997\",\"type\":\"VeeHead\"},{\"attributes\":{\"source\":{\"id\":\"1886\"}},\"id\":\"1891\",\"type\":\"CDSView\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1955\"},\"glyph\":{\"id\":\"1956\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1958\"},\"nonselection_glyph\":{\"id\":\"1957\"},\"view\":{\"id\":\"1960\"}},\"id\":\"1959\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"2160\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_alpha\":{\"value\":0.2},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1889\",\"type\":\"Text\"},{\"attributes\":{\"text_color\":{\"value\":\"green\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1956\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"2175\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"source\":{\"id\":\"1955\"}},\"id\":\"1960\",\"type\":\"CDSView\"},{\"attributes\":{\"data\":{\"text\":[\"P\"],\"x\":[6.5],\"y\":[0.2]},\"selected\":{\"id\":\"2169\"},\"selection_policy\":{\"id\":\"2168\"}},\"id\":\"1955\",\"type\":\"ColumnDataSource\"}],\"root_ids\":[\"2052\"]},\"title\":\"Bokeh 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	" const render_items = [{\"docid\":\"c3490bd5-5d4b-47ec-80cf-f488a75f6246\",\"root_ids\":[\"2052\"],\"roots\":{\"2052\":\"6c600490-fe9d-47f0-9390-e76787d544b5\"}}];\n",
	" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	"\n",
	" }\n",
	" if (root.Bokeh !== undefined) {\n",
	" embed_document(root);\n",
	" } else {\n",
	" let attempts = 0;\n",
	" const timer = setInterval(function(root) {\n",
	" if (root.Bokeh !== undefined) {\n",
	" clearInterval(timer);\n",
	" embed_document(root);\n",
	" } else {\n",
	" attempts++;\n",
	" if (attempts > 100) {\n",
	" clearInterval(timer);\n",
	" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	" }\n",
	" }\n",
	" }, 10, root)\n",
	" }\n",
	"})(window);"
	],
	"application/vnd.bokehjs_exec.v0+json": ""
	},
	"metadata": {
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	"output_type": "display_data"
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	"source": [
	"hidden_code_nb_actions.main_code(L, h, b, A, Iy, Iz, q, P, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr)"
	]
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	{
	"cell_type": "markdown",
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	"source": [
	"## Legend\n",
	"\n",
	"Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder. \n",
	"\n",
	"* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	"* Slider of height h: move the slider to change the height h of the cross-section of the beam.\n",
	"* Slider of the position x: move the slider to change the position x along the beam.\n",
	"* Slider of the uniform load q: move the slider to change the uniform load q.\n",
	"* Textbox \"Geometrical and mechanical parameters: small summary with the value of h, b, L, A (area), Iy (inertia with respect to the strong axis) and Iz (inertia with respect to the weak axis).\n",
	"* Textbox \"Forces and Moments: small summary with the value of the magnitude of the reaction forces and the internal forces at the position x.\n",
	"* Figure \"Simple supported beam\": in this figure, the initial state is presented with the static scheme, the length of the beam, the horizontal force P and the uniform load q.\n",
	"* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	"* Figure \"Forces and Moments Scheme\": this figure has a dynamic representation of the studied case with the position x indicated by a magenta dot, the internal forces shown in with red arrows, the reaction forces with yellow arrows, the external force P with a green arrow and the uniform load q in blue.\n",
	"* Radio buttons of the FBD: choose between right-hand or left-hand free-body diagram.\n",
	"* Button of the force P: apply or remove the external force P.\n",
	"\n",
	+ "### Help and Information on the functions\n",
	+ "\n",
	+ "In Jupyter Notebooks the user can learn more about a function by using the question mark after the target function. One question mark shows some useful information on the function and two question marks show in addition also the code of the function, revealing it's content.\n",
	+ "For example, by creating a Code cell and pasting \"beam_section.compute_area?\" or \"beam_section.compute_area??\", it's possible to see how this feature works.\n",
	+ "\n",
	"### Recommendations\n",
	"\n",
	+ "If you have problem visualizing the entirety of the tool, you can maximize the window size by using Ctrl+B to hide/show the left explorer panel and by using F11 to go to the full-page mode and back in the browser (NB: it could not work in the tab with NOTO; just use F11 in another tab and come back in the NOTO tab). If you're using a very sall display and it's not enough, you can zoom out the browser tab.\n",
	+ "\n",
	"Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully."
	]
	}
	],
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	diff --git a/Simple Beam DEMOs/03-sb_diagrams.ipynb b/Simple Beam DEMOs/03-sb_diagrams.ipynb
	new file mode 100644
	index 0000000..724946b
	--- /dev/null
	+++ b/Simple Beam DEMOs/03-sb_diagrams.ipynb
	@@ -0,0 +1,572 @@
	+{
	+ "cells": [
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "# Simple beam - N V M Diagrams\n",
	+ "In this third notebook, the internal axial force N, shear force V and bending moment M diagrams are studied on the same system, external force P and the uniform load q introduced in the DEMO \"02-sb_actions\"."
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Goals\n",
	+ "\n",
	+ "* Analyze the N V M diagrams\n",
	+ "* Describe the relations between the three diagrams\n",
	+ "* Identify the direct correlation of the diagrams with the internal forces"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Tasks and exercises\n",
	+ "\n",
	+ "Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	+ "\n",
	+ "1. In which position the bending moment M is the highest? Does the shear force V have correlation with the behaviour of the bending moment M?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " The bending moment is the highest in the middle of the beam, at x = 3 m.\n",
	+ " \n",
	+ " Yes, in fact we can note that the shear force V is 0 when the moment is maximum and that the slope of the moment is directily correlated with the shear force V. The relation between V and M is the following $\\frac{dM}{dx} = V$.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>\n",
	+ "\n",
	+ "2. In this case, does changing the uniform load q have any impact on the internal force N? What else do you note?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " No, q has no influece with the axial force N, but it has direct impact with the shear force V, the bending moment M and the left and right vertical reaction.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>\n",
	+ "\n",
	+ "3. Which impact has the chosen free-body diagram on the N V M diagrams?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " None, beacuse the N V M diagrams are independent on the free-body diagram used to compute the equilibium. The signs of the diagrams are computed by following a sign conention, presented below:\n",
	+ " <br>\n",
	+ " <img src=\"img/Sign_convention.png\" alt=\"drawing\" width=\"600\"/>\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Build the interactive visualisation tool"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 1,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ " <div class=\"bk-root\">\n",
	+ " <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	+ " <span id=\"1002\">Loading BokehJS ...</span>\n",
	+ " </div>"
	+ ]
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ },
	+ {
	+ "data": {
	+ "application/javascript": [
	+ "\n",
	+ "(function(root) {\n",
	+ " function now() {\n",
	+ " return new Date();\n",
	+ " }\n",
	+ "\n",
	+ " const force = true;\n",
	+ "\n",
	+ " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_onload_callbacks = [];\n",
	+ " root._bokeh_is_loading = undefined;\n",
	+ " }\n",
	+ "\n",
	+ " const JS_MIME_TYPE = 'application/javascript';\n",
	+ " const HTML_MIME_TYPE = 'text/html';\n",
	+ " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	+ " const CLASS_NAME = 'output_bokeh rendered_html';\n",
	+ "\n",
	+ " /**\n",
	+ " * Render data to the DOM node\n",
	+ " */\n",
	+ " function render(props, node) {\n",
	+ " const script = document.createElement(\"script\");\n",
	+ " node.appendChild(script);\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
	+ " * Handle when an output is cleared or removed\n",
	+ " */\n",
	+ " function handleClearOutput(event, handle) {\n",
	+ " const cell = handle.cell;\n",
	+ "\n",
	+ " const id = cell.output_area._bokeh_element_id;\n",
	+ " const server_id = cell.output_area._bokeh_server_id;\n",
	+ " // Clean up Bokeh references\n",
	+ " if (id != null && id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ "\n",
	+ " if (server_id !== undefined) {\n",
	+ " // Clean up Bokeh references\n",
	+ " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	+ " cell.notebook.kernel.execute(cmd_clean, {\n",
	+ " iopub: {\n",
	+ " output: function(msg) {\n",
	+ " const id = msg.content.text.trim();\n",
	+ " if (id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ " }\n",
	+ " }\n",
	+ " });\n",
	+ " // Destroy server and session\n",
	+ " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	+ " cell.notebook.kernel.execute(cmd_destroy);\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
	+ " * Handle when a new output is added\n",
	+ " */\n",
	+ " function handleAddOutput(event, handle) {\n",
	+ " const output_area = handle.output_area;\n",
	+ " const output = handle.output;\n",
	+ "\n",
	+ " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	+ " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	+ " return\n",
	+ " }\n",
	+ "\n",
	+ " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
	+ "\n",
	+ " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	+ " // store reference to embed id on output_area\n",
	+ " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
	+ " }\n",
	+ " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	+ " const bk_div = document.createElement(\"div\");\n",
	+ " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	+ " const script_attrs = bk_div.children[0].attributes;\n",
	+ " for (let i = 0; i < script_attrs.length; i++) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	+ " }\n",
	+ " // store reference to server id on output_area\n",
	+ " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function register_renderer(events, OutputArea) {\n",
	+ "\n",
	+ " function append_mime(data, metadata, element) {\n",
	+ " // create a DOM node to render to\n",
	+ " const toinsert = this.create_output_subarea(\n",
	+ " metadata,\n",
	+ " CLASS_NAME,\n",
	+ " EXEC_MIME_TYPE\n",
	+ " );\n",
	+ " this.keyboard_manager.register_events(toinsert);\n",
	+ " // Render to node\n",
	+ " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	+ " render(props, toinsert[toinsert.length - 1]);\n",
	+ " element.append(toinsert);\n",
	+ " return toinsert\n",
	+ " }\n",
	+ "\n",
	+ " /* Handle when an output is cleared or removed */\n",
	+ " events.on('clear_output.CodeCell', handleClearOutput);\n",
	+ " events.on('delete.Cell', handleClearOutput);\n",
	+ "\n",
	+ " /* Handle when a new output is added */\n",
	+ " events.on('output_added.OutputArea', handleAddOutput);\n",
	+ "\n",
	+ " /**\n",
	+ " * Register the mime type and append_mime function with output_area\n",
	+ " */\n",
	+ " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	+ " /* Is output safe? */\n",
	+ " safe: true,\n",
	+ " /* Index of renderer in `output_area.display_order` */\n",
	+ " index: 0\n",
	+ " });\n",
	+ " }\n",
	+ "\n",
	+ " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	+ " if (root.Jupyter !== undefined) {\n",
	+ " const events = require('base/js/events');\n",
	+ " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	+ "\n",
	+ " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	+ " register_renderer(events, OutputArea);\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " \n",
	+ " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_timeout = Date.now() + 5000;\n",
	+ " root._bokeh_failed_load = false;\n",
	+ " }\n",
	+ "\n",
	+ " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	+ " \"<div style='background-color: #fdd'>\\n\"+\n",
	+ " \"<p>\\n\"+\n",
	+ " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	+ " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	+ " \"</p>\\n\"+\n",
	+ " \"<ul>\\n\"+\n",
	+ " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	+ " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	+ " \"</ul>\\n\"+\n",
	+ " \"<code>\\n\"+\n",
	+ " \"from bokeh.resources import INLINE\\n\"+\n",
	+ " \"output_notebook(resources=INLINE)\\n\"+\n",
	+ " \"</code>\\n\"+\n",
	+ " \"</div>\"}};\n",
	+ "\n",
	+ " function display_loaded() {\n",
	+ " const el = document.getElementById(\"1002\");\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS is loading...\";\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	+ " }\n",
	+ " } else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(display_loaded, 100)\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ "\n",
	+ " function run_callbacks() {\n",
	+ " try {\n",
	+ " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	+ " if (callback != null)\n",
	+ " callback();\n",
	+ " });\n",
	+ " } finally {\n",
	+ " delete root._bokeh_onload_callbacks\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: all callbacks have finished\");\n",
	+ " }\n",
	+ "\n",
	+ " function load_libs(css_urls, js_urls, callback) {\n",
	+ " if (css_urls == null) css_urls = [];\n",
	+ " if (js_urls == null) js_urls = [];\n",
	+ "\n",
	+ " root._bokeh_onload_callbacks.push(callback);\n",
	+ " if (root._bokeh_is_loading > 0) {\n",
	+ " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	+ " return null;\n",
	+ " }\n",
	+ " if (js_urls == null \|\| js_urls.length === 0) {\n",
	+ " run_callbacks();\n",
	+ " return null;\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	+ " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	+ "\n",
	+ " function on_load() {\n",
	+ " root._bokeh_is_loading--;\n",
	+ " if (root._bokeh_is_loading === 0) {\n",
	+ " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	+ " run_callbacks()\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function on_error(url) {\n",
	+ " console.error(\"failed to load \" + url);\n",
	+ " }\n",
	+ "\n",
	+ " for (let i = 0; i < css_urls.length; i++) {\n",
	+ " const url = css_urls[i];\n",
	+ " const element = document.createElement(\"link\");\n",
	+ " element.onload = on_load;\n",
	+ " element.onerror = on_error.bind(null, url);\n",
	+ " element.rel = \"stylesheet\";\n",
	+ " element.type = \"text/css\";\n",
	+ " element.href = url;\n",
	+ " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	+ " document.body.appendChild(element);\n",
	+ " }\n",
	+ "\n",
	+ " for (let i = 0; i < js_urls.length; i++) {\n",
	+ " const url = js_urls[i];\n",
	+ " const element = document.createElement('script');\n",
	+ " element.onload = on_load;\n",
	+ " element.onerror = on_error.bind(null, url);\n",
	+ " element.async = false;\n",
	+ " element.src = url;\n",
	+ " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	+ " document.head.appendChild(element);\n",
	+ " }\n",
	+ " };\n",
	+ "\n",
	+ " function inject_raw_css(css) {\n",
	+ " const element = document.createElement(\"style\");\n",
	+ " element.appendChild(document.createTextNode(css));\n",
	+ " document.body.appendChild(element);\n",
	+ " }\n",
	+ "\n",
	+ " \n",
	+ " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	+ " const css_urls = [];\n",
	+ " \n",
	+ "\n",
	+ " const inline_js = [\n",
	+ " function(Bokeh) {\n",
	+ " Bokeh.set_log_level(\"info\");\n",
	+ " },\n",
	+ " function(Bokeh) {\n",
	+ " \n",
	+ " \n",
	+ " }\n",
	+ " ];\n",
	+ "\n",
	+ " function run_inline_js() {\n",
	+ " \n",
	+ " if (root.Bokeh !== undefined \|\| force === true) {\n",
	+ " \n",
	+ " for (let i = 0; i < inline_js.length; i++) {\n",
	+ " inline_js[i].call(root, root.Bokeh);\n",
	+ " }\n",
	+ " if (force === true) {\n",
	+ " display_loaded();\n",
	+ " }} else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(run_inline_js, 100);\n",
	+ " } else if (!root._bokeh_failed_load) {\n",
	+ " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
	+ " root._bokeh_failed_load = true;\n",
	+ " } else if (force !== true) {\n",
	+ " const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
	+ " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
	+ " }\n",
	+ "\n",
	+ " }\n",
	+ "\n",
	+ " if (root._bokeh_is_loading === 0) {\n",
	+ " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
	+ " run_inline_js();\n",
	+ " } else {\n",
	+ " load_libs(css_urls, js_urls, function() {\n",
	+ " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	+ " run_inline_js();\n",
	+ " });\n",
	+ " }\n",
	+ "}(window));"
	+ ],
	+ "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n function now() {\n return new Date();\n }\n\n const force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n \n\n \n if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n const NB_LOAD_WARNING = {'data': {'text/html':\n \"<div style='background-color: #fdd'>\\n\"+\n \"<p>\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"</p>\\n\"+\n \"<ul>\\n\"+\n \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n \"<li>use INLINE resources instead, as so:</li>\\n\"+\n \"</ul>\\n\"+\n \"<code>\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"</code>\\n\"+\n \"</div>\"}};\n\n function display_loaded() {\n const el = document.getElementById(\"1002\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null \|\| js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error(url) {\n console.error(\"failed to load \" + url);\n }\n\n for (let i = 0; i < css_urls.length; i++) {\n const url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n \n const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n const css_urls = [];\n \n\n const inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n function(Bokeh) {\n \n \n }\n ];\n\n function run_inline_js() {\n \n if (root.Bokeh !== undefined \|\| force === true) {\n \n for (let i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\n if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));"
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "# Import the packages needed\n",
	+ "import sys\n",
	+ "sys.path.append('../HiddenCode')\n",
	+ "import hidden_code_nb_diagrams\n",
	+ "import math\n",
	+ "import numpy as np \n",
	+ "from cienpy import simplebeam as sb\n",
	+ "from cienpy import rectangular_section as beam_section"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Define the geometry, the external actions and compute the initial configuration."
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 2,
	+ "metadata": {},
	+ "outputs": [],
	+ "source": [
	+ "# Choose the dimensions\n",
	+ "L = 6 # [m]\n",
	+ "h = 200 # [mm]\n",
	+ "b = 100 # [mm]\n",
	+ "q = 4; # [kN/m]\n",
	+ "P = 10; # [kN]\n",
	+ "\n",
	+ "# compute the internal forces (at x=L)\n",
	+ "discr_NVM = 101\n",
	+ "x_discr = np.linspace(0, L, discr_NVM)\n",
	+ "N_discr = sb.compute_N(x_discr, P)\n",
	+ "V_discr = sb.compute_V(x_discr, q, L)\n",
	+ "M_discr = sb.compute_M(x_discr, q, L)\n",
	+ "N = N_discr[-1]\n",
	+ "V = V_discr[-1]\n",
	+ "M = M_discr[-1]\n",
	+ "\n",
	+ "# compute the parameters\n",
	+ "A = beam_section.compute_area(b, h) # [mm2]\n",
	+ "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	+ "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	+ "\n",
	+ "# compute the reactions\n",
	+ "Rx = sb.compute_Rx(P)\n",
	+ "Ry_l = sb.compute_Ry_l(q, L)\n",
	+ "Ry_r = sb.compute_Ry_r(q, L)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Run the complex code to generate the interactive visualisation tool:"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 3,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ " <div class=\"bk-root\" id=\"d6b57e37-d080-48b1-abe8-d03e60a7816c\" data-root-id=\"1430\"></div>\n"
	+ ]
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ },
	+ {
	+ "data": {
	+ "application/javascript": [
	+ "(function(root) {\n",
	+ " function embed_document(root) {\n",
	+ " \n",
	+ " const docs_json = 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442\"},\"group\":null,\"major_label_policy\":{\"id\":\"1443\"},\"ticker\":{\"id\":\"1139\"},\"visible\":false},\"id\":\"1138\",\"type\":\"LinearAxis\"},{\"attributes\":{\"axis\":{\"id\":\"1142\"},\"coordinates\":null,\"dimension\":1,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1145\",\"type\":\"Grid\"},{\"attributes\":{\"axis\":{\"id\":\"1138\"},\"coordinates\":null,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1141\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1139\",\"type\":\"BasicTicker\"},{\"attributes\":{\"coordinates\":null,\"formatter\":{\"id\":\"1439\"},\"group\":null,\"major_label_policy\":{\"id\":\"1440\"},\"ticker\":{\"id\":\"1143\"},\"visible\":false},\"id\":\"1142\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1519\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1520\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1533\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1534\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1535\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1536\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1522\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1523\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1524\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1537\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1538\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1525\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1539\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1540\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1016\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1014\",\"type\":\"LinearScale\"},{\"attributes\":{\"fill_alpha\":{\"value\":0},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0},\"height\":{\"value\":480.0},\"line_alpha\":{\"value\":0},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":300},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1074\",\"type\":\"Rect\"},{\"attributes\":{\"coordinates\":null,\"group\":null},\"id\":\"1434\",\"type\":\"Title\"},{\"attributes\":{\"end\":0.9,\"start\":-0.4},\"id\":\"1012\",\"type\":\"Range1d\"},{\"attributes\":{\"axis\":{\"id\":\"1018\"},\"coordinates\":null,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1021\",\"type\":\"Grid\"},{\"attributes\":{\"coordinates\":null,\"group\":null},\"id\":\"1436\",\"type\":\"Title\"},{\"attributes\":{\"end\":7.2,\"start\":-1.2000000000000002},\"id\":\"1010\",\"type\":\"Range1d\"},{\"attributes\":{\"below\":[{\"id\":\"1051\"}],\"center\":[{\"id\":\"1054\"},{\"id\":\"1058\"},{\"id\":\"1110\"},{\"id\":\"1119\"}],\"left\":[{\"id\":\"1055\"}],\"match_aspect\":true,\"renderers\":[{\"id\":\"1077\"},{\"id\":\"1104\"},{\"id\":\"1116\"},{\"id\":\"1125\"}],\"title\":{\"id\":\"1041\"},\"toolbar\":{\"id\":\"1066\"},\"toolbar_location\":null,\"width\":375,\"x_range\":{\"id\":\"1043\"},\"x_scale\":{\"id\":\"1047\"},\"y_range\":{\"id\":\"1045\"},\"y_scale\":{\"id\":\"1049\"}},\"id\":\"1040\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"1019\",\"type\":\"BasicTicker\"},{\"attributes\":{\"axis_label\":\"Position [m]\",\"coordinates\":null,\"formatter\":{\"id\":\"1455\"},\"group\":null,\"major_label_policy\":{\"id\":\"1456\"},\"ticker\":{\"id\":\"1019\"}},\"id\":\"1018\",\"type\":\"LinearAxis\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Simple supported beam\"},\"id\":\"1008\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"1439\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1440\",\"type\":\"AllLabels\"},{\"attributes\":{},\"id\":\"1151\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1147\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1146\",\"type\":\"PanTool\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1345\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"data\":{\"A\":[20000],\"FBD\":[0],\"Iy\":[66666666.666666664],\"Iz\":[16666666.666666666],\"L\":[6],\"M\":[0.0],\"N\":[-10.0],\"P\":[10],\"Rx\":[10],\"Ry_l\":[12.0],\"Ry_r\":[12.0],\"SCALE\":[10],\"V\":[12.0],\"b\":[100],\"h\":[200],\"q\":[4],\"state\":[\"IDLE\"],\"x\":[6],\"xF\":[60],\"y\":[0]},\"selected\":{\"id\":\"1479\"},\"selection_policy\":{\"id\":\"1478\"}},\"id\":\"1006\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"overlay\":{\"id\":\"1152\"}},\"id\":\"1148\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"1149\",\"type\":\"SaveTool\"},{\"attributes\":{\"data\":{\"x\":[0,60],\"y\":[0,0]},\"selected\":{\"id\":\"1481\"},\"selection_policy\":{\"id\":\"1480\"}},\"id\":\"1004\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1150\",\"type\":\"ResetTool\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"1357\"},\"arr_head\":{\"id\":\"1252\"},\"div_P\":{\"id\":\"1258\"},\"div_f\":{\"id\":\"1260\"},\"fN\":{\"id\":\"1236\"},\"fP\":{\"id\":\"1224\"},\"fRx\":{\"id\":\"1233\"},\"fRyl\":{\"id\":\"1230\"},\"fRyr\":{\"id\":\"1227\"},\"fV\":{\"id\":\"1239\"},\"s_M\":{\"id\":\"1241\"},\"source\":{\"id\":\"1006\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=101) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n 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// retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \"},\"id\":\"1414\",\"type\":\"CustomJS\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"blue\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1175\",\"type\":\"Text\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"xF\"},\"y\":{\"field\":\"y\"}},\"id\":\"1196\",\"type\":\"Circle\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1376\",\"type\":\"Line\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1006\"},\"glyph\":{\"id\":\"1194\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1196\"},\"nonselection_glyph\":{\"id\":\"1195\"},\"view\":{\"id\":\"1198\"}},\"id\":\"1197\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1374\",\"type\":\"Line\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1181\"},\"glyph\":{\"id\":\"1182\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1184\"},\"nonselection_glyph\":{\"id\":\"1183\"},\"view\":{\"id\":\"1186\"}},\"id\":\"1185\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"1006\"}},\"id\":\"1198\",\"type\":\"CDSView\"},{\"attributes\":{\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1382\",\"type\":\"Line\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1004\"},\"glyph\":{\"id\":\"1200\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1202\"},\"nonselection_glyph\":{\"id\":\"1201\"},\"view\":{\"id\":\"1204\"}},\"id\":\"1203\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.5},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.5},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"M\"}},\"id\":\"1408\",\"type\":\"Circle\"},{\"attributes\":{\"data\":{\"text\":[\"P\"],\"x\":[6.5],\"y\":[0.2]},\"selected\":{\"id\":\"1520\"},\"selection_policy\":{\"id\":\"1519\"}},\"id\":\"1181\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1384\",\"type\":\"Line\"},{\"attributes\":{\"text_color\":{\"value\":\"green\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1182\",\"type\":\"Text\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1252\"},\"div_P\":{\"id\":\"1258\"},\"div_f\":{\"id\":\"1260\"},\"fN\":{\"id\":\"1236\"},\"fP\":{\"id\":\"1224\"},\"fRx\":{\"id\":\"1233\"},\"fRyl\":{\"id\":\"1230\"},\"fRyr\":{\"id\":\"1227\"},\"fV\":{\"id\":\"1239\"},\"s_M\":{\"id\":\"1241\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"source\":{\"id\":\"1006\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \"},\"id\":\"1413\",\"type\":\"CustomJS\"},{\"attributes\":{\"source\":{\"id\":\"1181\"}},\"id\":\"1186\",\"type\":\"CDSView\"},{\"attributes\":{\"text_alpha\":{\"value\":0.1},\"text_color\":{\"value\":\"green\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1183\",\"type\":\"Text\"},{\"attributes\":{\"source\":{\"id\":\"1003\"}},\"id\":\"1378\",\"type\":\"CDSView\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.5},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.5},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"xF\"},\"y\":{\"field\":\"y\"}},\"id\":\"1194\",\"type\":\"Circle\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1381\"},\"glyph\":{\"id\":\"1382\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1384\"},\"nonselection_glyph\":{\"id\":\"1383\"},\"view\":{\"id\":\"1386\"}},\"id\":\"1385\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"green\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1184\",\"type\":\"Text\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1229\"},\"group\":null,\"line_color\":{\"value\":\"orange\"},\"line_width\":{\"value\":2.5649493574615367},\"source\":{\"id\":\"1446\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":-12.0}},\"id\":\"1230\",\"type\":\"Arrow\"},{\"attributes\":{\"callback\":null,\"renderers\":[{\"id\":\"1371\"}],\"tooltips\":[[\"Position\",\"@x m\"],[\"Shear force\",\"@y 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1227\"},\"fV\":{\"id\":\"1239\"},\"s_M\":{\"id\":\"1241\"},\"s_q\":{\"id\":\"1005\"},\"source\":{\"id\":\"1006\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1418\",\"type\":\"CustomJS\"},{\"attributes\":{\"fill_alpha\":0.3,\"fill_color\":\"blue\",\"hatch_alpha\":0.3,\"hatch_color\":\"navy\",\"line_alpha\":0.3,\"line_color\":\"navy\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1212\",\"type\":\"Patch\"},{\"attributes\":{\"data\":{\"x\":[0.0],\"y\":[0.0]},\"selected\":{\"id\":\"1489\"},\"selection_policy\":{\"id\":\"1488\"}},\"id\":\"1248\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_alpha\":0.1,\"fill_color\":\"blue\",\"hatch_alpha\":0.1,\"hatch_color\":\"navy\",\"line_alpha\":0.1,\"line_color\":\"navy\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1213\",\"type\":\"Patch\"},{\"attributes\":{},\"id\":\"1465\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"fill_alpha\":0.3,\"fill_color\":\"blue\",\"hatch_alpha\":0.3,\"hatch_color\":\"navy\",\"line_alpha\":0.3,\"line_color\":\"navy\",\"x\":{\"field\":\"x_fade\"},\"y\":{\"field\":\"y\"}},\"id\":\"1218\",\"type\":\"Patch\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"V\"}},\"id\":\"1404\",\"type\":\"Circle\"},{\"attributes\":{\"fill_color\":{\"value\":\"red\"},\"line_color\":{\"value\":\"red\"},\"marker\":{\"value\":\"triangle\"},\"size\":{\"value\":0},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1249\",\"type\":\"Scatter\"},{\"attributes\":{\"fill_alpha\":0.1,\"fill_color\":\"blue\",\"hatch_alpha\":0.1,\"hatch_color\":\"navy\",\"line_alpha\":0.1,\"line_color\":\"navy\",\"x\":{\"field\":\"x_fade\"},\"y\":{\"field\":\"y\"}},\"id\":\"1219\",\"type\":\"Patch\"},{\"attributes\":{\"source\":{\"id\":\"1006\"}},\"id\":\"1406\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1466\",\"type\":\"AllLabels\"},{\"attributes\":{\"fill_alpha\":0.2,\"fill_color\":\"blue\",\"hatch_alpha\":0.2,\"hatch_color\":\"navy\",\"line_alpha\":0.2,\"line_color\":\"navy\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1214\",\"type\":\"Patch\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"red\",\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1244\",\"type\":\"Line\"},{\"attributes\":{\"source\":{\"id\":\"1241\"}},\"id\":\"1247\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1468\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1513\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1005\"},\"glyph\":{\"id\":\"1218\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1220\"},\"nonselection_glyph\":{\"id\":\"1219\"},\"view\":{\"id\":\"1222\"}},\"id\":\"1221\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"1005\"}},\"id\":\"1222\",\"type\":\"CDSView\"},{\"attributes\":{\"fill_color\":{\"value\":\"orange\"},\"line_color\":{\"value\":\"orange\"},\"size\":{\"value\":17.954645502230758}},\"id\":\"1226\",\"type\":\"VeeHead\"},{\"attributes\":{},\"id\":\"1469\",\"type\":\"AllLabels\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1252\"},\"div_P\":{\"id\":\"1258\"},\"fN\":{\"id\":\"1236\"},\"fP\":{\"id\":\"1224\"},\"fRx\":{\"id\":\"1233\"},\"fRyl\":{\"id\":\"1230\"},\"fRyr\":{\"id\":\"1227\"},\"fV\":{\"id\":\"1239\"},\"s_M\":{\"id\":\"1241\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"source\":{\"id\":\"1006\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]*data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1417\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1223\"},\"group\":null,\"line_color\":{\"value\":\"green\"},\"line_width\":{\"value\":2.3978952727983707},\"source\":{\"id\":\"1444\"},\"start\":null,\"x_end\":{\"value\":60},\"x_start\":{\"value\":70},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1224\",\"type\":\"Arrow\"},{\"attributes\":{},\"id\":\"1514\",\"type\":\"Selection\"},{\"attributes\":{\"fill_alpha\":0.2,\"fill_color\":\"blue\",\"hatch_alpha\":0.2,\"hatch_color\":\"navy\",\"line_alpha\":0.2,\"line_color\":\"navy\",\"x\":{\"field\":\"x_fade\"},\"y\":{\"field\":\"y\"}},\"id\":\"1220\",\"type\":\"Patch\"},{\"attributes\":{\"children\":[{\"id\":\"1420\"},{\"id\":\"1107\"},{\"id\":\"1108\"},{\"id\":\"1106\"},{\"id\":\"1421\"},{\"id\":\"1255\"},{\"id\":\"1254\"},{\"id\":\"1256\"},{\"id\":\"1257\"},{\"id\":\"1258\"},{\"id\":\"1259\"}]},\"id\":\"1422\",\"type\":\"Column\"},{\"attributes\":{\"fill_color\":{\"value\":\"green\"},\"line_color\":{\"value\":\"green\"},\"size\":{\"value\":16.785266909588593}},\"id\":\"1223\",\"type\":\"VeeHead\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"red\",\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1245\",\"type\":\"Line\"},{\"attributes\":{\"height\":10},\"id\":\"1420\",\"type\":\"Spacer\"},{\"attributes\":{},\"id\":\"1530\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"height\":10},\"id\":\"1421\",\"type\":\"Spacer\"},{\"attributes\":{\"end\":6,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1413\"}]},\"start\":0,\"step\":0.02,\"title\":\"Change the position x along the beam [m]\",\"value\":6},\"id\":\"1255\",\"type\":\"Slider\"},{\"attributes\":{\"children\":[{\"id\":\"1040\"},{\"id\":\"1419\"},{\"id\":\"1422\"}]},\"id\":\"1423\",\"type\":\"Row\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1226\"},\"group\":null,\"line_color\":{\"value\":\"orange\"},\"line_width\":{\"value\":2.5649493574615367},\"source\":{\"id\":\"1445\"},\"start\":null,\"x_end\":{\"value\":60},\"x_start\":{\"value\":60},\"y_end\":{\"value\":0},\"y_start\":{\"value\":-12.0}},\"id\":\"1227\",\"type\":\"Arrow\"},{\"attributes\":{},\"id\":\"1531\",\"type\":\"Selection\"},{\"attributes\":{\"line_color\":\"red\",\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1243\",\"type\":\"Line\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"red\"},\"hatch_alpha\":{\"value\":0.1},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"red\"},\"marker\":{\"value\":\"triangle\"},\"size\":{\"value\":0},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1250\",\"type\":\"Scatter\"},{\"attributes\":{\"children\":[{\"id\":\"1427\"}]},\"id\":\"1428\",\"type\":\"Column\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1248\"},\"glyph\":{\"id\":\"1249\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1251\"},\"nonselection_glyph\":{\"id\":\"1250\"},\"view\":{\"id\":\"1253\"}},\"id\":\"1252\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"children\":[{\"id\":\"1127\"},{\"id\":\"1423\"}]},\"id\":\"1424\",\"type\":\"Column\"},{\"attributes\":{\"text\":\"Free-body diagram (FBD):\"},\"id\":\"1256\",\"type\":\"Div\"},{\"attributes\":{\"end\":5.0,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1418\"}]},\"start\":0.1,\"step\":0.1,\"title\":\"Change the uniform load q [kN/m]\",\"value\":4},\"id\":\"1254\",\"type\":\"Slider\"},{\"attributes\":{\"height\":10},\"id\":\"1425\",\"type\":\"Spacer\"},{\"attributes\":{\"source\":{\"id\":\"1248\"}},\"id\":\"1253\",\"type\":\"CDSView\"},{\"attributes\":{\"children\":[{\"id\":\"1007\"},{\"id\":\"1425\"},{\"id\":\"1261\"},{\"id\":\"1293\"},{\"id\":\"1323\"},{\"id\":\"1260\"}]},\"id\":\"1426\",\"type\":\"Column\"},{\"attributes\":{\"children\":[{\"id\":\"1424\"},{\"id\":\"1426\"}]},\"id\":\"1427\",\"type\":\"Row\"},{\"attributes\":{\"active\":0,\"js_property_callbacks\":{\"change:active\":[{\"id\":\"1417\"}]},\"labels\":[\"Right-hand\",\"Left-hand\"]},\"id\":\"1257\",\"type\":\"RadioButtonGroup\"},{\"attributes\":{},\"id\":\"1267\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1515\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"text\":\"Axial force P=10 kN (applied)\"},\"id\":\"1258\",\"type\":\"Div\"},{\"attributes\":{\"text\":\"\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = 10 kN<br>\\n Rx = 10 kN<br>\\n Ry (left) = 12.0 kN<br>\\n Ry (right) = 12.0 kN<br>\\n No cross section analysed.<br>\\n N = 0 kN<br>\\n V = 0 kN<br>\\n M = 0 kNm\\n \\n \"},\"id\":\"1260\",\"type\":\"Div\"},{\"attributes\":{},\"id\":\"1516\",\"type\":\"Selection\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1003\"},\"glyph\":{\"id\":\"1360\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1362\"},\"nonselection_glyph\":{\"id\":\"1361\"},\"view\":{\"id\":\"1364\"}},\"id\":\"1363\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"active\":[0],\"js_property_callbacks\":{\"change:active\":[{\"id\":\"1416\"}]},\"labels\":[\"Apply or remove axial force 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V M Diagrams\"},\"id\":\"1262\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"1269\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1280\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"axis_label\":\"Position [m]\",\"coordinates\":null,\"formatter\":{\"id\":\"1462\"},\"group\":null,\"major_label_policy\":{\"id\":\"1463\"},\"ticker\":{\"id\":\"1272\"},\"visible\":false},\"id\":\"1271\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1272\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"1471\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"axis_label\":\"Axial force N 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Application\",\"version\":\"2.4.2\"}};\n",
	+ " const render_items = [{\"docid\":\"fc24d7bf-4243-4c13-a069-6fd9b7de0638\",\"root_ids\":[\"1430\"],\"roots\":{\"1430\":\"d6b57e37-d080-48b1-abe8-d03e60a7816c\"}}];\n",
	+ " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	+ "\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " let attempts = 0;\n",
	+ " const timer = setInterval(function(root) {\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " clearInterval(timer);\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " attempts++;\n",
	+ " if (attempts > 100) {\n",
	+ " clearInterval(timer);\n",
	+ " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	+ " }\n",
	+ " }\n",
	+ " }, 10, root)\n",
	+ " }\n",
	+ "})(window);"
	+ ],
	+ "application/vnd.bokehjs_exec.v0+json": ""
	+ },
	+ "metadata": {
	+ "application/vnd.bokehjs_exec.v0+json": {
	+ "id": "1430"
	+ }
	+ },
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "hidden_code_nb_diagrams.main_code(L, h, b, A, Iy, Iz, q, P, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Legend\n",
	+ "\n",
	+ "Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder.\n",
	+ "\n",
	+ "* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	+ "* Slider of height h: move the slider to change the height h of the cross-section of the beam.\n",
	+ "* Slider of the position x: move the slider to change the position x along the beam.\n",
	+ "* Slider of the uniform load q: move the slider to change the uniform load q.\n",
	+ "* Textbox \"Geometrical and mechanical parameters: small summary with the value of h, b, L, A (area), Iy (inertia with respect to the strong axis) and Iz (inertia with respect to the weak axis).\n",
	+ "* Textbox \"Forces and Moments: small summary with the value of the magnitude of the reaction forces and the internal forces at the position x.\n",
	+ "* Figure \"Simple supported beam\": in this figure, the initial state is presented with the static scheme, the length of the beam, the horizontal force P and the uniform load q.\n",
	+ "* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	+ "* Figure \"Forces and Moments Scheme\": this figure has a dynamic representation of the studied case with the position x indicated by a magenta dot, the internal forces shown in with red arrows, the reaction forces with yellow arrows, the external force P with a green arrow and the uniform load q in blue.\n",
	+ "* Radio buttons of the FBD: choose between right-hand or left-hand free-body diagram.\n",
	+ "* Button of the force P: apply or remove the external force P.\n",
	+ "* Figures \"N V M Diagrams\": plots that show the axial force N, shear force V and bending moment M diagrams, with a magenta dot that represents the x position. By hovering with the cursor over the desired position, a small window will show the position and the value of the internal force.\n",
	+ "\n",
	+ "### Help and Information on the functions\n",
	+ "\n",
	+ "In Jupyter Notebooks the user can learn more about a function by using the question mark after the target function. One question mark shows some useful information on the function and two question marks show in addition also the code of the function, revealing it's content.\n",
	+ "For example, by creating a Code cell and pasting \"beam_section.compute_area?\" or \"beam_section.compute_area??\", it's possible to see how this feature works.\n",
	+ "\n",
	+ "### Recommendations\n",
	+ "\n",
	+ "If you have problem visualizing the entirety of the tool, you can maximize the window size by using Ctrl+B to hide/show the left explorer panel and by using F11 to go to the full-page mode and back in the browser (NB: it could not work in the tab with NOTO; just use F11 in another tab and come back in the NOTO tab). If you're using a very sall display and it's not enough, you can zoom out the browser tab.\n",
	+ "\n",
	+ "Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully."
	+ ]
	+ }
	+ ],
	+ "metadata": {
	+ "interpreter": {
	+ "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	+ },
	+ "kernelspec": {
	+ "display_name": "Python 3 (ipykernel)",
	+ "language": "python",
	+ "name": "python3"
	+ },
	+ "language_info": {
	+ "codemirror_mode": {
	+ "name": "ipython",
	+ "version": 3
	+ },
	+ "file_extension": ".py",
	+ "mimetype": "text/x-python",
	+ "name": "python",
	+ "nbconvert_exporter": "python",
	+ "pygments_lexer": "ipython3",
	+ "version": "3.8.10"
	+ }
	+ },
	+ "nbformat": 4,
	+ "nbformat_minor": 4
	+}
	diff --git a/Simple Beam DEMOs/04-sb_stress.ipynb b/Simple Beam DEMOs/04-sb_stress.ipynb
	new file mode 100644
	index 0000000..03d61f0
	--- /dev/null
	+++ b/Simple Beam DEMOs/04-sb_stress.ipynb
	@@ -0,0 +1,608 @@
	+{
	+ "cells": [
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "# Simple beam - Stress and Strain\n",
	+ "In this fourth notebook, the stresses and strains inside the element are studied. For any civil engineer, the deep understanding of the behaviour of stress and strain inside an element is essential. For this reason, after completing this DEMO, you'll be equipped with the preliminary and fundamental knowledge to be able to tackle the next important concepts and theories. \n",
	+ "The system, geometry and actions are the same presented in the previous DEMO \"03-sb_diagrams\"."
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Goals\n",
	+ "\n",
	+ "* Describe the differences between the various strains and stresses\n",
	+ "* Explain the relations between them\n",
	+ "* Identify which parameters influence their behaviour"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Tasks and exercises\n",
	+ "\n",
	+ "Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	+ "\n",
	+ "1. What are the differences between the centroid and the neutral axis? Is there a way to superimpose them in this studied case?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " The centroid is dependent only on the geometry of the section; on the other hand, the neutral axis is function of the centroid and the internal forces.\n",
	+ " \n",
	+ " Yes, if the external horizontal force P is removed and the axial force N becomes zero, the neutral axis is in the same position of the centroid.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>\n",
	+ "\n",
	+ "2. Does the cross-section influence the maximal stresses and strains? By changing the length of the beam to 8 m, do you ascertain any changes?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " Yes; the internal forces do not change, but the resistance of the section (area and inertia) is directly influenced by h and b. Note that increasing h has a bigger impact only on the bending strain and bending stress (power of 2); on the other hand b and h have the same influence, because the axial stress and strain is dependent only on the area: $\\sigma_N = N/A$ and $\\epsilon_N = \\sigma_N/E$ and the shear stress is also only dependent on the area: $\\tau_{max} = \\frac{V S}{I_y b} = \\frac{V\\frac{bh^2}{8}}{\\frac{bh^3}{12}b} = \\frac{3V}{2bh} = \\frac{3V}{2A}$.\n",
	+ " \n",
	+ " Yes; the parameters responsible for the resistance of the section (area and inertia) do not change, but the amplitude of the shear and the bending moment increase, thus the stress and strain inside the section increase, except for the axial strain and stress, that are independent of the length of the beam and they remain the same.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>\n",
	+ "\n",
	+ "3. Consider the starting configuration; assume that the beam is composed of a material with a yield strength of 27.2 MPa.\n",
	+ " 1. Will the beam remain elastic everywhere?\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " No, at the position where the bending moment is maximum, the stress in the top compressed fiber is equal to 27.5 MPa, that is bigger than 27.2 MPa.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 2. Where will it yield?\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " At the center of the beam, where the bending moment is the highest.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 3. If you can change only one parameter to assure that the beam remains always elastic, what will you do?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " The possible solution are:\n",
	+ " <ul>\n",
	+ " <li>Increase h</li>\n",
	+ " <li>Increase b</li>\n",
	+ " <li>Decrease L</li>\n",
	+ " <li>Remove (or decrease) the external horizontal force P</li>\n",
	+ " <li>Decrease the uniform load q</li>\n",
	+ " </ul>\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Build the interactive visualisation tool"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 1,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ " <div class=\"bk-root\">\n",
	+ " <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	+ " <span id=\"1002\">Loading BokehJS ...</span>\n",
	+ " </div>"
	+ ]
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ },
	+ {
	+ "data": {
	+ "application/javascript": [
	+ "\n",
	+ "(function(root) {\n",
	+ " function now() {\n",
	+ " return new Date();\n",
	+ " }\n",
	+ "\n",
	+ " const force = true;\n",
	+ "\n",
	+ " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_onload_callbacks = [];\n",
	+ " root._bokeh_is_loading = undefined;\n",
	+ " }\n",
	+ "\n",
	+ " const JS_MIME_TYPE = 'application/javascript';\n",
	+ " const HTML_MIME_TYPE = 'text/html';\n",
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	+ " const CLASS_NAME = 'output_bokeh rendered_html';\n",
	+ "\n",
	+ " /**\n",
	+ " * Render data to the DOM node\n",
	+ " */\n",
	+ " function render(props, node) {\n",
	+ " const script = document.createElement(\"script\");\n",
	+ " node.appendChild(script);\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
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	+ " */\n",
	+ " function handleClearOutput(event, handle) {\n",
	+ " const cell = handle.cell;\n",
	+ "\n",
	+ " const id = cell.output_area._bokeh_element_id;\n",
	+ " const server_id = cell.output_area._bokeh_server_id;\n",
	+ " // Clean up Bokeh references\n",
	+ " if (id != null && id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ "\n",
	+ " if (server_id !== undefined) {\n",
	+ " // Clean up Bokeh references\n",
	+ " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	+ " cell.notebook.kernel.execute(cmd_clean, {\n",
	+ " iopub: {\n",
	+ " output: function(msg) {\n",
	+ " const id = msg.content.text.trim();\n",
	+ " if (id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
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	+ " });\n",
	+ " // Destroy server and session\n",
	+ " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	+ " cell.notebook.kernel.execute(cmd_destroy);\n",
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	+ " const output = handle.output;\n",
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	+ " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	+ " return\n",
	+ " }\n",
	+ "\n",
	+ " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
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	+ " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
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	+ " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	+ " const bk_div = document.createElement(\"div\");\n",
	+ " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	+ " const script_attrs = bk_div.children[0].attributes;\n",
	+ " for (let i = 0; i < script_attrs.length; i++) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	+ " }\n",
	+ " // store reference to server id on output_area\n",
	+ " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function register_renderer(events, OutputArea) {\n",
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	+ " function append_mime(data, metadata, element) {\n",
	+ " // create a DOM node to render to\n",
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	+ " CLASS_NAME,\n",
	+ " EXEC_MIME_TYPE\n",
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	+ " this.keyboard_manager.register_events(toinsert);\n",
	+ " // Render to node\n",
	+ " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	+ " render(props, toinsert[toinsert.length - 1]);\n",
	+ " element.append(toinsert);\n",
	+ " return toinsert\n",
	+ " }\n",
	+ "\n",
	+ " /* Handle when an output is cleared or removed */\n",
	+ " events.on('clear_output.CodeCell', handleClearOutput);\n",
	+ " events.on('delete.Cell', handleClearOutput);\n",
	+ "\n",
	+ " /* Handle when a new output is added */\n",
	+ " events.on('output_added.OutputArea', handleAddOutput);\n",
	+ "\n",
	+ " /**\n",
	+ " * Register the mime type and append_mime function with output_area\n",
	+ " */\n",
	+ " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	+ " /* Is output safe? */\n",
	+ " safe: true,\n",
	+ " /* Index of renderer in `output_area.display_order` */\n",
	+ " index: 0\n",
	+ " });\n",
	+ " }\n",
	+ "\n",
	+ " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	+ " if (root.Jupyter !== undefined) {\n",
	+ " const events = require('base/js/events');\n",
	+ " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	+ "\n",
	+ " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	+ " register_renderer(events, OutputArea);\n",
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	+ " }\n",
	+ "\n",
	+ " \n",
	+ " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_timeout = Date.now() + 5000;\n",
	+ " root._bokeh_failed_load = false;\n",
	+ " }\n",
	+ "\n",
	+ " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	+ " \"<div style='background-color: #fdd'>\\n\"+\n",
	+ " \"<p>\\n\"+\n",
	+ " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	+ " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	+ " \"</p>\\n\"+\n",
	+ " \"<ul>\\n\"+\n",
	+ " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	+ " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	+ " \"</ul>\\n\"+\n",
	+ " \"<code>\\n\"+\n",
	+ " \"from bokeh.resources import INLINE\\n\"+\n",
	+ " \"output_notebook(resources=INLINE)\\n\"+\n",
	+ " \"</code>\\n\"+\n",
	+ " \"</div>\"}};\n",
	+ "\n",
	+ " function display_loaded() {\n",
	+ " const el = document.getElementById(\"1002\");\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS is loading...\";\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	+ " }\n",
	+ " } else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(display_loaded, 100)\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ "\n",
	+ " function run_callbacks() {\n",
	+ " try {\n",
	+ " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	+ " if (callback != null)\n",
	+ " callback();\n",
	+ " });\n",
	+ " } finally {\n",
	+ " delete root._bokeh_onload_callbacks\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: all callbacks have finished\");\n",
	+ " }\n",
	+ "\n",
	+ " function load_libs(css_urls, js_urls, callback) {\n",
	+ " if (css_urls == null) css_urls = [];\n",
	+ " if (js_urls == null) js_urls = [];\n",
	+ "\n",
	+ " root._bokeh_onload_callbacks.push(callback);\n",
	+ " if (root._bokeh_is_loading > 0) {\n",
	+ " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	+ " return null;\n",
	+ " }\n",
	+ " if (js_urls == null \|\| js_urls.length === 0) {\n",
	+ " run_callbacks();\n",
	+ " return null;\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	+ " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	+ "\n",
	+ " function on_load() {\n",
	+ " root._bokeh_is_loading--;\n",
	+ " if (root._bokeh_is_loading === 0) {\n",
	+ " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	+ " run_callbacks()\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function on_error(url) {\n",
	+ " console.error(\"failed to load \" + url);\n",
	+ " }\n",
	+ "\n",
	+ " for (let i = 0; i < css_urls.length; i++) {\n",
	+ " const url = css_urls[i];\n",
	+ " const element = document.createElement(\"link\");\n",
	+ " element.onload = on_load;\n",
	+ " element.onerror = on_error.bind(null, url);\n",
	+ " element.rel = \"stylesheet\";\n",
	+ " element.type = \"text/css\";\n",
	+ " element.href = url;\n",
	+ " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	+ " document.body.appendChild(element);\n",
	+ " }\n",
	+ "\n",
	+ " for (let i = 0; i < js_urls.length; i++) {\n",
	+ " const url = js_urls[i];\n",
	+ " const element = document.createElement('script');\n",
	+ " element.onload = on_load;\n",
	+ " element.onerror = on_error.bind(null, url);\n",
	+ " element.async = false;\n",
	+ " element.src = url;\n",
	+ " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	+ " document.head.appendChild(element);\n",
	+ " }\n",
	+ " };\n",
	+ "\n",
	+ " function inject_raw_css(css) {\n",
	+ " const element = document.createElement(\"style\");\n",
	+ " element.appendChild(document.createTextNode(css));\n",
	+ " document.body.appendChild(element);\n",
	+ " }\n",
	+ "\n",
	+ " \n",
	+ " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	+ " const css_urls = [];\n",
	+ " \n",
	+ "\n",
	+ " const inline_js = [\n",
	+ " function(Bokeh) {\n",
	+ " Bokeh.set_log_level(\"info\");\n",
	+ " },\n",
	+ " function(Bokeh) {\n",
	+ " \n",
	+ " \n",
	+ " }\n",
	+ " ];\n",
	+ "\n",
	+ " function run_inline_js() {\n",
	+ " \n",
	+ " if (root.Bokeh !== undefined \|\| force === true) {\n",
	+ " \n",
	+ " for (let i = 0; i < inline_js.length; i++) {\n",
	+ " inline_js[i].call(root, root.Bokeh);\n",
	+ " }\n",
	+ " if (force === true) {\n",
	+ " display_loaded();\n",
	+ " }} else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(run_inline_js, 100);\n",
	+ " } else if (!root._bokeh_failed_load) {\n",
	+ " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
	+ " root._bokeh_failed_load = true;\n",
	+ " } else if (force !== true) {\n",
	+ " const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
	+ " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
	+ " }\n",
	+ "\n",
	+ " }\n",
	+ "\n",
	+ " if (root._bokeh_is_loading === 0) {\n",
	+ " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
	+ " run_inline_js();\n",
	+ " } else {\n",
	+ " load_libs(css_urls, js_urls, function() {\n",
	+ " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	+ " run_inline_js();\n",
	+ " });\n",
	+ " }\n",
	+ "}(window));"
	+ ],
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	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "# Import the packages needed\n",
	+ "import sys\n",
	+ "sys.path.append('../HiddenCode')\n",
	+ "import hidden_code_nb_stress\n",
	+ "import math\n",
	+ "import numpy as np\n",
	+ "from cienpy import simplebeam as sb\n",
	+ "from cienpy import rectangular_section as beam_section\n",
	+ "from cienpy import stress_strain_elastic as stst"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Define the geometry, the external actions, the mechanical property and compute the initial configuration."
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 2,
	+ "metadata": {},
	+ "outputs": [],
	+ "source": [
	+ "# Choose the dimensions\n",
	+ "L = 6 # [m]\n",
	+ "h = 200 # [mm]\n",
	+ "b = 100 # [mm]\n",
	+ "q = 4; # [kN/m]\n",
	+ "P = 10; # [kN]\n",
	+ "\n",
	+ "# Choose the material parameters\n",
	+ "E = 200e3 # [MPa]\n",
	+ "\n",
	+ "# compute the internal forces (at x=L)\n",
	+ "discr_NVM = 101\n",
	+ "x_discr = np.linspace(0, L, discr_NVM)\n",
	+ "N_discr = sb.compute_N(x_discr, P)\n",
	+ "V_discr = sb.compute_V(x_discr, q, L)\n",
	+ "M_discr = sb.compute_M(x_discr, q, L)\n",
	+ "N = N_discr[-1]\n",
	+ "V = V_discr[-1]\n",
	+ "M = M_discr[-1]\n",
	+ "\n",
	+ "# compute the parameters\n",
	+ "A = beam_section.compute_area(b, h) # [mm2]\n",
	+ "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	+ "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	+ "yG = beam_section.compute_centroid_y(h)\n",
	+ "y_n_axis = stst.compute_neutral_axis(N, A, Iy, M, yG)\n",
	+ "\n",
	+ "# compute the reactions\n",
	+ "Rx = sb.compute_Rx(P)\n",
	+ "Ry_l = sb.compute_Ry_l(q, L)\n",
	+ "Ry_r = sb.compute_Ry_r(q, L)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Run the complex code to generate the interactive visualisation tool:"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 3,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
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// retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \"},\"id\":\"1900\",\"type\":\"CustomJS\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"red\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1896\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"1283\",\"type\":\"SaveTool\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1777\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1833\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"1284\",\"type\":\"ResetTool\"},{\"attributes\":{\"source\":{\"id\":\"1762\"}},\"id\":\"1767\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1841\",\"type\":\"HelpTool\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"red\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1764\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1836\",\"type\":\"PanTool\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1664\"},\"N_stress_diag\":{\"id\":\"1644\"},\"V_stress_diag\":{\"id\":\"1684\"},\"arr_head\":{\"id\":\"1253\"},\"axial_strain_diag\":{\"id\":\"1744\"},\"bending_strain_diag\":{\"id\":\"1766\"},\"centroid\":{\"id\":\"1676\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1716\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \"},\"id\":\"1899\",\"type\":\"CustomJS\"},{\"attributes\":{\"overlay\":{\"id\":\"1842\"}},\"id\":\"1838\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1286\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1769\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1839\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1840\",\"type\":\"ResetTool\"},{\"attributes\":{\"axis_label\":\"Position [m]\",\"coordinates\":null,\"formatter\":{\"id\":\"1962\"},\"group\":null,\"major_label_policy\":{\"id\":\"1963\"},\"ticker\":{\"id\":\"1303\"},\"visible\":false},\"id\":\"1302\",\"type\":\"LinearAxis\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1664\"},\"N_stress_diag\":{\"id\":\"1644\"},\"V_stress_diag\":{\"id\":\"1684\"},\"axial_strain_diag\":{\"id\":\"1744\"},\"bending_strain_diag\":{\"id\":\"1766\"},\"centroid\":{\"id\":\"1676\"},\"div\":{\"id\":\"1107\"},\"neutral_axis\":{\"id\":\"1716\"},\"s_b\":{\"id\":\"1003\"},\"s_ss\":{\"id\":\"1006\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1099\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const h = cb_obj.value // value of the slider\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \"},\"id\":\"1901\",\"type\":\"CustomJS\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1033\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"source\":{\"id\":\"1774\"}},\"id\":\"1779\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1776\",\"type\":\"Line\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"1358\"},\"N_stress_diag\":{\"id\":\"1644\"},\"arr_head\":{\"id\":\"1253\"},\"axial_strain_diag\":{\"id\":\"1744\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1716\"},\"s_M\":{\"id\":\"1242\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=101) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1902\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_alpha\":0,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1775\",\"type\":\"Line\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1842\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"1313\",\"type\":\"SaveTool\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1253\"},\"div_P\":{\"id\":\"1259\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1903\",\"type\":\"CustomJS\"},{\"attributes\":{\"data\":{\"x\":[-0.00012,0.00012],\"y\":[0,0]},\"selected\":{\"id\":\"2131\"},\"selection_policy\":{\"id\":\"2130\"}},\"id\":\"1774\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1386\"},\"M_stress_diag\":{\"id\":\"1664\"},\"V_diag\":{\"id\":\"1372\"},\"V_stress_diag\":{\"id\":\"1684\"},\"arr_head\":{\"id\":\"1253\"},\"bending_strain_diag\":{\"id\":\"1766\"},\"centroid\":{\"id\":\"1676\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1716\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n 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Application\",\"version\":\"2.4.2\"}};\n",
	+ " const render_items = [{\"docid\":\"8cb004cd-7d18-4bc4-989a-350d46a80772\",\"root_ids\":[\"1924\"],\"roots\":{\"1924\":\"84fa22ec-cc0c-4de4-9dfa-2f183159d7e8\"}}];\n",
	+ " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	+ "\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " let attempts = 0;\n",
	+ " const timer = setInterval(function(root) {\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " clearInterval(timer);\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " attempts++;\n",
	+ " if (attempts > 100) {\n",
	+ " clearInterval(timer);\n",
	+ " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	+ " }\n",
	+ " }\n",
	+ " }, 10, root)\n",
	+ " }\n",
	+ "})(window);"
	+ ],
	+ "application/vnd.bokehjs_exec.v0+json": ""
	+ },
	+ "metadata": {
	+ "application/vnd.bokehjs_exec.v0+json": {
	+ "id": "1924"
	+ }
	+ },
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "hidden_code_nb_stress.main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Legend\n",
	+ "\n",
	+ "Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder.\n",
	+ "\n",
	+ "* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	+ "* Slider of height h: move the slider to change the height h of the cross-section of the beam.\n",
	+ "* Slider of the position x: move the slider to change the position x along the beam.\n",
	+ "* Slider of the uniform load q: move the slider to change the uniform load q.\n",
	+ "* Textbox \"Geometrical and mechanical parameters: small summary with the value of h, b, L, A (area), Iy (inertia with respect to the strong axis) and Iz (inertia with respect to the weak axis).\n",
	+ "* Textbox \"Forces and Moments: small summary with the value of the magnitude of the reaction forces and the internal forces at the position x.\n",
	+ "* Figure \"Simple supported beam\": in this figure, the initial state is presented with the static scheme, the length of the beam, the horizontal force P and the uniform load q.\n",
	+ "* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	+ "* Figure \"Forces and Moments Scheme\": this figure has a dynamic representation of the studied case with the position x indicated by a magenta dot, the internal forces shown in with red arrows, the reaction forces with yellow arrows, the external force P with a green arrow and the uniform load q in blue.\n",
	+ "* Radio buttons of the FBD: choose between right-hand or left-hand free-body diagram.\n",
	+ "* Button of the force P: apply or remove the external force P.\n",
	+ "* Figures \"N V M Diagrams\": plots that show the axial force N, shear force V and bending moment M diagrams, with a magenta dot that represents the x position. By hovering with the cursor over the desired position, a small window will show the position and the value of the internal force.\n",
	+ "* 9 small bottom figures: plots that show the strains, stresses and right-hand free-body diagram section (with N, V and M). By hovering with the cursor over the desired position, a small window will show the height and the value of the stress or strain.\n",
	+ "\n",
	+ "### Help and Information on the functions\n",
	+ "\n",
	+ "In Jupyter Notebooks the user can learn more about a function by using the question mark after the target function. One question mark shows some useful information on the function and two question marks show in addition also the code of the function, revealing it's content.\n",
	+ "For example, by creating a Code cell and pasting \"beam_section.compute_area?\" or \"beam_section.compute_area??\", it's possible to see how this feature works.\n",
	+ "\n",
	+ "### Recommendations\n",
	+ "\n",
	+ "If you have problem visualizing the entirety of the tool, you can maximize the window size by using Ctrl+B or Cmd+B to hide/show the left explorer panel and by using F11 to go to the full-page mode and back in the browser (NB: it could not work in the tab with NOTO; just use F11 in another tab and come back in the NOTO tab). If you're using a very sall display and it's not enough, you can zoom out the browser tab.\n",
	+ "\n",
	+ "Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully.\n",
	+ "\n",
	+ "### EXTRA: Note on the slow reactivity of the tool\n",
	+ "\n",
	+ "The slow reactivity of the tool is given by the two textboxes (called Div Widgets) which automatically call a specific funtion every time they are modified. This function redraws everything in the tool (figures, plots, diagrams, textboxes, sliders, ...), generating this problem. Considering that a real solution does not exist in the current version of the lib used (Bokeh 2.4.2), these textboxes will be removed in the next DEMOs."
	+ ]
	+ }
	+ ],
	+ "metadata": {
	+ "interpreter": {
	+ "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	+ },
	+ "kernelspec": {
	+ "display_name": "Python 3 (ipykernel)",
	+ "language": "python",
	+ "name": "python3"
	+ },
	+ "language_info": {
	+ "codemirror_mode": {
	+ "name": "ipython",
	+ "version": 3
	+ },
	+ "file_extension": ".py",
	+ "mimetype": "text/x-python",
	+ "name": "python",
	+ "nbconvert_exporter": "python",
	+ "pygments_lexer": "ipython3",
	+ "version": "3.8.10"
	+ }
	+ },
	+ "nbformat": 4,
	+ "nbformat_minor": 4
	+}
	diff --git a/Simple Beam DEMOs/05-sb_torsion.ipynb b/Simple Beam DEMOs/05-sb_torsion.ipynb
	new file mode 100644
	index 0000000..dc98c40
	--- /dev/null
	+++ b/Simple Beam DEMOs/05-sb_torsion.ipynb
	@@ -0,0 +1,595 @@
	+{
	+ "cells": [
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "# Simple beam - Torsion\n",
	+ "In this fifth notebook, the torsion is analysed. The system and part of the geometry and actions are taken from the previous DEMO \"04-sb_stress\", with the following changes:\n",
	+ "\n",
	+ "* the cross-section is now an hollow rectangular section\n",
	+ "* in the middle of the beam, a torsional moment Mt is applied\n",
	+ "* both supports are fixed with respect to the torsion\n",
	+ "\n",
	+ "To analyse correctly the interaction of the torsional stress and strain with the other ones, the left/right webs and the top/bottom flanges should be inspected individually, but considering the complexity of the problem (new cross-section geometry and the introduction of the torsion), the focus of this notebook is placed only on the left web."
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Goals\n",
	+ "\n",
	+ "* Explain the influence of the introduction of a torsional moment on the analysis of the beam\n",
	+ "* Identify the differences that arise with this new cross-section\n",
	+ "* Describe the tau stress and its origin"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Tasks and exercises\n",
	+ "\n",
	+ "Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	+ "\n",
	+ "1. Consider the starting configuration, but with q = 1 kN/m and h = 100 mm. In the \"Total stress $\\tau$\" figure, try to explain the cause of the two couple of jumps in stress by computing by hand the equation that describes the total stress $\\tau$.\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " The first jump is due to the constant torsional stress $\\tau_T$ applied on the left web; the second jump is caused in the calculation of the shear stress $\\tau_V$ by the immediate shape change at height equals to h-t and t. The equations are:\n",
	+ " <br>\n",
	+ " $$ \\tau = \\tau_T + \\tau_V $$\n",
	+ " <br>\n",
	+ " $$ \\tau_T = \\frac{T}{2t(b-t)(h-t)} $$\n",
	+ " <br>\n",
	+ " $$\\tau_V=\\begin{cases}\n",
	+ " \\frac{VS}{I_y2t}, S = \\frac{b}{2}(\\frac{h^2}{4}-(y-y_G)^2), & \\text{if $y\\in[t;h-t]$}.\\\\\n",
	+ " \\frac{VS}{I_yb}, S = \\frac{b}{2}(h-t)^t + t(\\frac{(h-2t)^2}{4}-(y-y_G)^2), & \\text{otherwise}.\n",
	+ " \\end{cases}$$\n",
	+ " With $y_G$ the position of the centroid from below, that is equal to h/2.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ "\n",
	+ "2. Why is $\\tau_T$ (stress generated by the torsion T) combinated with $\\tau_V$ (stress generated by shear force V) and not with $\\sigma_N$ (axial stress) or $\\sigma_M$ (bending stress)?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " The shear force and the torsion produce shear stress (called $\\tau$), on the other hand the axial force and the bending moment produce normal stress (called $\\sigma$). For this reason, the $\\tau_T$ is superimposed with $\\tau_V$. You will see how to visualize and combine togheter normal and shear stresses using the Mohr circle in the next DEMO.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>\n",
	+ "\n",
	+ "3. For what reasons the left web is the chosen one to be analysed?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " The web was chosen instead of the flange beacause given the direction in which the beam is bent, analysing the flange would have been less interesting. Secondly, the left web is critical considering that the superposition between the torsional stress and the shear stress results in a higher maximal stress.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Build the interactive visualisation tool"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 1,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ " <div class=\"bk-root\">\n",
	+ " <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	+ " <span id=\"1002\">Loading BokehJS ...</span>\n",
	+ " </div>"
	+ ]
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ },
	+ {
	+ "data": {
	+ "application/javascript": [
	+ "\n",
	+ "(function(root) {\n",
	+ " function now() {\n",
	+ " return new Date();\n",
	+ " }\n",
	+ "\n",
	+ " const force = true;\n",
	+ "\n",
	+ " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_onload_callbacks = [];\n",
	+ " root._bokeh_is_loading = undefined;\n",
	+ " }\n",
	+ "\n",
	+ " const JS_MIME_TYPE = 'application/javascript';\n",
	+ " const HTML_MIME_TYPE = 'text/html';\n",
	+ " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	+ " const CLASS_NAME = 'output_bokeh rendered_html';\n",
	+ "\n",
	+ " /**\n",
	+ " * Render data to the DOM node\n",
	+ " */\n",
	+ " function render(props, node) {\n",
	+ " const script = document.createElement(\"script\");\n",
	+ " node.appendChild(script);\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
	+ " * Handle when an output is cleared or removed\n",
	+ " */\n",
	+ " function handleClearOutput(event, handle) {\n",
	+ " const cell = handle.cell;\n",
	+ "\n",
	+ " const id = cell.output_area._bokeh_element_id;\n",
	+ " const server_id = cell.output_area._bokeh_server_id;\n",
	+ " // Clean up Bokeh references\n",
	+ " if (id != null && id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ "\n",
	+ " if (server_id !== undefined) {\n",
	+ " // Clean up Bokeh references\n",
	+ " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	+ " cell.notebook.kernel.execute(cmd_clean, {\n",
	+ " iopub: {\n",
	+ " output: function(msg) {\n",
	+ " const id = msg.content.text.trim();\n",
	+ " if (id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ " }\n",
	+ " }\n",
	+ " });\n",
	+ " // Destroy server and session\n",
	+ " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	+ " cell.notebook.kernel.execute(cmd_destroy);\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
	+ " * Handle when a new output is added\n",
	+ " */\n",
	+ " function handleAddOutput(event, handle) {\n",
	+ " const output_area = handle.output_area;\n",
	+ " const output = handle.output;\n",
	+ "\n",
	+ " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	+ " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	+ " return\n",
	+ " }\n",
	+ "\n",
	+ " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
	+ "\n",
	+ " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	+ " // store reference to embed id on output_area\n",
	+ " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
	+ " }\n",
	+ " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	+ " const bk_div = document.createElement(\"div\");\n",
	+ " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	+ " const script_attrs = bk_div.children[0].attributes;\n",
	+ " for (let i = 0; i < script_attrs.length; i++) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	+ " }\n",
	+ " // store reference to server id on output_area\n",
	+ " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function register_renderer(events, OutputArea) {\n",
	+ "\n",
	+ " function append_mime(data, metadata, element) {\n",
	+ " // create a DOM node to render to\n",
	+ " const toinsert = this.create_output_subarea(\n",
	+ " metadata,\n",
	+ " CLASS_NAME,\n",
	+ " EXEC_MIME_TYPE\n",
	+ " );\n",
	+ " this.keyboard_manager.register_events(toinsert);\n",
	+ " // Render to node\n",
	+ " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	+ " render(props, toinsert[toinsert.length - 1]);\n",
	+ " element.append(toinsert);\n",
	+ " return toinsert\n",
	+ " }\n",
	+ "\n",
	+ " /* Handle when an output is cleared or removed */\n",
	+ " events.on('clear_output.CodeCell', handleClearOutput);\n",
	+ " events.on('delete.Cell', handleClearOutput);\n",
	+ "\n",
	+ " /* Handle when a new output is added */\n",
	+ " events.on('output_added.OutputArea', handleAddOutput);\n",
	+ "\n",
	+ " /**\n",
	+ " * Register the mime type and append_mime function with output_area\n",
	+ " */\n",
	+ " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	+ " /* Is output safe? */\n",
	+ " safe: true,\n",
	+ " /* Index of renderer in `output_area.display_order` */\n",
	+ " index: 0\n",
	+ " });\n",
	+ " }\n",
	+ "\n",
	+ " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	+ " if (root.Jupyter !== undefined) {\n",
	+ " const events = require('base/js/events');\n",
	+ " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	+ "\n",
	+ " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	+ " register_renderer(events, OutputArea);\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " \n",
	+ " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_timeout = Date.now() + 5000;\n",
	+ " root._bokeh_failed_load = false;\n",
	+ " }\n",
	+ "\n",
	+ " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	+ " \"<div style='background-color: #fdd'>\\n\"+\n",
	+ " \"<p>\\n\"+\n",
	+ " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	+ " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	+ " \"</p>\\n\"+\n",
	+ " \"<ul>\\n\"+\n",
	+ " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	+ " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	+ " \"</ul>\\n\"+\n",
	+ " \"<code>\\n\"+\n",
	+ " \"from bokeh.resources import INLINE\\n\"+\n",
	+ " \"output_notebook(resources=INLINE)\\n\"+\n",
	+ " \"</code>\\n\"+\n",
	+ " \"</div>\"}};\n",
	+ "\n",
	+ " function display_loaded() {\n",
	+ " const el = document.getElementById(\"1002\");\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS is loading...\";\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	+ " }\n",
	+ " } else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(display_loaded, 100)\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ "\n",
	+ " function run_callbacks() {\n",
	+ " try {\n",
	+ " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	+ " if (callback != null)\n",
	+ " callback();\n",
	+ " });\n",
	+ " } finally {\n",
	+ " delete root._bokeh_onload_callbacks\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: all callbacks have finished\");\n",
	+ " }\n",
	+ "\n",
	+ " function load_libs(css_urls, js_urls, callback) {\n",
	+ " if (css_urls == null) css_urls = [];\n",
	+ " if (js_urls == null) js_urls = [];\n",
	+ "\n",
	+ " root._bokeh_onload_callbacks.push(callback);\n",
	+ " if (root._bokeh_is_loading > 0) {\n",
	+ " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	+ " return null;\n",
	+ " }\n",
	+ " if (js_urls == null \|\| js_urls.length === 0) {\n",
	+ " run_callbacks();\n",
	+ " return null;\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	+ " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	+ "\n",
	+ " function on_load() {\n",
	+ " root._bokeh_is_loading--;\n",
	+ " if (root._bokeh_is_loading === 0) {\n",
	+ " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	+ " run_callbacks()\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function on_error(url) {\n",
	+ " console.error(\"failed to load \" + url);\n",
	+ " }\n",
	+ "\n",
	+ " for (let i = 0; i < css_urls.length; i++) {\n",
	+ " const url = css_urls[i];\n",
	+ " const element = document.createElement(\"link\");\n",
	+ " element.onload = on_load;\n",
	+ " element.onerror = on_error.bind(null, url);\n",
	+ " element.rel = \"stylesheet\";\n",
	+ " element.type = \"text/css\";\n",
	+ " element.href = url;\n",
	+ " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	+ " document.body.appendChild(element);\n",
	+ " }\n",
	+ "\n",
	+ " for (let i = 0; i < js_urls.length; i++) {\n",
	+ " const url = js_urls[i];\n",
	+ " const element = document.createElement('script');\n",
	+ " element.onload = on_load;\n",
	+ " element.onerror = on_error.bind(null, url);\n",
	+ " element.async = false;\n",
	+ " element.src = url;\n",
	+ " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	+ " document.head.appendChild(element);\n",
	+ " }\n",
	+ " };\n",
	+ "\n",
	+ " function inject_raw_css(css) {\n",
	+ " const element = document.createElement(\"style\");\n",
	+ " element.appendChild(document.createTextNode(css));\n",
	+ " document.body.appendChild(element);\n",
	+ " }\n",
	+ "\n",
	+ " \n",
	+ " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	+ " const css_urls = [];\n",
	+ " \n",
	+ "\n",
	+ " const inline_js = [\n",
	+ " function(Bokeh) {\n",
	+ " Bokeh.set_log_level(\"info\");\n",
	+ " },\n",
	+ " function(Bokeh) {\n",
	+ " \n",
	+ " \n",
	+ " }\n",
	+ " ];\n",
	+ "\n",
	+ " function run_inline_js() {\n",
	+ " \n",
	+ " if (root.Bokeh !== undefined \|\| force === true) {\n",
	+ " \n",
	+ " for (let i = 0; i < inline_js.length; i++) {\n",
	+ " inline_js[i].call(root, root.Bokeh);\n",
	+ " }\n",
	+ " if (force === true) {\n",
	+ " display_loaded();\n",
	+ " }} else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(run_inline_js, 100);\n",
	+ " } else if (!root._bokeh_failed_load) {\n",
	+ " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
	+ " root._bokeh_failed_load = true;\n",
	+ " } else if (force !== true) {\n",
	+ " const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
	+ " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
	+ " }\n",
	+ "\n",
	+ " }\n",
	+ "\n",
	+ " if (root._bokeh_is_loading === 0) {\n",
	+ " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
	+ " run_inline_js();\n",
	+ " } else {\n",
	+ " load_libs(css_urls, js_urls, function() {\n",
	+ " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	+ " run_inline_js();\n",
	+ " });\n",
	+ " }\n",
	+ "}(window));"
	+ ],
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	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "# Import the packages needed\n",
	+ "import sys\n",
	+ "sys.path.append('../HiddenCode')\n",
	+ "import hidden_code_nb_torsion\n",
	+ "import math\n",
	+ "import numpy as np\n",
	+ "from cienpy import simplebeam as sb\n",
	+ "from cienpy import hollow_rectangular_section as beam_section\n",
	+ "from cienpy import stress_strain_elastic as stst"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Define the geometry, the external actions, the mechanical property and compute the initial configuration."
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 2,
	+ "metadata": {},
	+ "outputs": [],
	+ "source": [
	+ "# Choose the dimensions\n",
	+ "L = 6 # [m]\n",
	+ "h = 200 # [mm]\n",
	+ "b = 100 # [mm]\n",
	+ "t = 10 # [mm]\n",
	+ "q = 4 # [kN/m]\n",
	+ "P = 10 # [kN]\n",
	+ "Mt = 100 # [kNm]\n",
	+ "\n",
	+ "# Choose the material parameters\n",
	+ "E = 200e3 # [MPa]\n",
	+ "\n",
	+ "# compute the internal forces (at x=L)\n",
	+ "discr_NVM = 101\n",
	+ "x_discr = np.linspace(0, L, discr_NVM)\n",
	+ "N_discr = sb.compute_N(x_discr, P)\n",
	+ "V_discr = sb.compute_V(x_discr, q, L)\n",
	+ "M_discr = sb.compute_M(x_discr, q, L)\n",
	+ "T_discr = sb.compute_T(x_discr, Mt, L)\n",
	+ "N = N_discr[-1]\n",
	+ "V = V_discr[-1]\n",
	+ "M = M_discr[-1]\n",
	+ "T = T_discr[-1]\n",
	+ "\n",
	+ "# compute the parameters\n",
	+ "A = beam_section.compute_area(b, h, t) # [mm2]\n",
	+ "Iy = beam_section.compute_inertia_y(b, h, t) # [mm4] strong axis\n",
	+ "Iz = beam_section.compute_inertia_z(b, h, t) # [mm4] weak axis\n",
	+ "yG = beam_section.compute_centroid_y(h)\n",
	+ "y_n_axis = stst.compute_neutral_axis(N, A, Iy, M, yG)\n",
	+ "\n",
	+ "# compute the reactions\n",
	+ "Rx = sb.compute_Rx(P)\n",
	+ "Ry_l = sb.compute_Ry_l(q, L)\n",
	+ "Ry_r = sb.compute_Ry_r(q, L)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Run the complex code to generate the interactive visualisation tool:"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 3,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ " <div class=\"bk-root\" id=\"8de2cdc4-bf81-4ebc-b851-aa49955eb6f9\" data-root-id=\"2087\"></div>\n"
	+ ]
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ },
	+ {
	+ "data": {
	+ "application/javascript": [
	+ "(function(root) {\n",
	+ " function embed_document(root) {\n",
	+ " \n",
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// retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const t = db['t'][0]\\n const A = compute_area(b, h, t)\\n const Iy = compute_inertia_y(b, h, t)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n\\n // Easter egg\\n const str_Doge = \\\" such width\\\"\\n const str_tmp = div_P.text\\n if (b == 300) {\\n div_P.text = str_tmp+str_Doge\\n } else {\\n div_P.text = str_tmp.replace(str_Doge, '')\\n }\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h, t)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_torsional_stress(db, T_stress_diag)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const t = Math.round(data['t'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n t = `+t+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n const src = glyph_section.data_source\\n const t = data['t'][0]\\n const b = data['b'][0]\\n const h = data['h'][0]\\n src.data.xs = [[[ [b/2, b/2, -b/2, -b/2], [b/2-t, b/2-t, -b/2+t, -b/2+t] ]]]\\n src.data.ys = [[[ [h/2, -h/2, -h/2, h/2], [h/2-t, -h/2+t, -h/2+t, h/2-t] ]]]\\n src.change.emit()\\n }\\n \\n \\n function compute_area(b, h, t) {\\n return bh - (b-t2)(h-2t)\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12 - (b-2t)(h-2t)*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h, t) {\\n return hb*3/12 - (h-2t)(b-2t)*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_torsion, y_discr)\\n }\\n \\n \"},\"id\":\"2062\",\"type\":\"CustomJS\"},{\"attributes\":{\"source\":{\"id\":\"1660\"}},\"id\":\"1665\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1311\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"overlay\":{\"id\":\"1066\"}},\"id\":\"1062\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"overlay\":{\"id\":\"1316\"}},\"id\":\"1312\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"1313\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"2313\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"angle\":{\"value\":0.3141592653589793},\"text_alpha\":{\"value\":0.1},\"text_color\":{\"value\":\"purple\"},\"text_font_size\":{\"value\":\"10px\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2057\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"1314\",\"type\":\"ResetTool\"},{\"attributes\":{\"angle\":{\"value\":0.3141592653589793},\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"purple\"},\"text_font_size\":{\"value\":\"10px\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2058\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"2314\",\"type\":\"Selection\"},{\"attributes\":{\"tools\":[{\"id\":\"1060\"},{\"id\":\"1061\"},{\"id\":\"1062\"},{\"id\":\"1063\"},{\"id\":\"1064\"},{\"id\":\"1065\"}]},\"id\":\"1067\",\"type\":\"Toolbar\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1316\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1664\"},\"N_stress_diag\":{\"id\":\"1644\"},\"T_stress_diag\":{\"id\":\"2039\"},\"V_stress_diag\":{\"id\":\"1684\"},\"arr_head\":{\"id\":\"1253\"},\"axial_strain_diag\":{\"id\":\"1744\"},\"bending_strain_diag\":{\"id\":\"1766\"},\"centroid\":{\"id\":\"1676\"},\"div_P\":{\"id\":\"1259\"},\"div_T\":{\"id\":\"1899\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_T_section\":{\"id\":\"2033\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1716\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_T_head\":{\"id\":\"2027\"},\"section_T_line\":{\"id\":\"2021\"},\"section_T_source\":{\"id\":\"2016\"},\"section_V\":{\"id\":\"1866\"},\"section_torsion_head\":{\"id\":\"1995\"},\"section_torsion_source\":{\"id\":\"1984\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n const Mt = db['Mt'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['T'][0] = compute_T(pos, Mt, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_T_section(db, section_torsion_head, section_torsion_source, section_T_line, section_T_head, section_T_source, div_T, label_T_section)\\n update_torsional_stress(db, T_stress_diag)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function update_T_section(data, head_T_curved, source_T_curved, line_T, head_T, source_T, div_T, label_T_section, offset_T=4, pixel2unit=10, scale_T=10) {\\n const Mt = data['Mt'][0]\\n const T = data['T'][0]\\n \\n if (T > 0) {\\n update_doubleArrow(offset_T, offset_T+T/scale_T, 0, 0, source_T, head_T)\\n } else {\\n update_doubleArrow(offset_T-T/scale_T, offset_T, 0, 0, source_T, head_T)\\n }\\n \\n // update visibility\\n if (Mt==0) {\\n div_T.text = \\\"Torsion M<sub>t</sub>=0 kNm (removed)\\\"\\n line_T.glyph.line_alpha = 0 // T\\n head_T.glyph.line_alpha = 0\\n head_T.glyph.fill_alpha = 0\\n // T in cross-section\\n update_curvedArrow(0, 0, 0, 0, 0, source_T_curved, head_T_curved)\\n } else {\\n div_T.text = \\\"Torsion M<sub>t</sub>=\\\"+Mt+\\\" kNm (applied)\\\"\\n line_T.glyph.line_alpha = 1 // T\\n head_T.glyph.line_alpha = 1\\n head_T.glyph.fill_alpha = 1\\n // T in cross-section\\n update_curvedArrow(0, T4/scale_T, Math.abs(T3/scale_T), 0, 0, source_T_curved, head_T_curved)\\n }\\n \\n if (T==0) {\\n label_T_section.glyph.text=''\\n } else {\\n label_T_section.glyph.text='T'\\n }\\n }\\n \\n \\n function update_doubleArrow(x_start, x_end, y_start, y_end, source, arr_heads, AHF=6, pixel2unit=10) {\\n // compute the angle of the line\\n const delta_x = x_end-x_start\\n const delta_y = y_end-y_start\\n if (delta_x==0) {\\n if (delta_y > 0) {\\n var theta = Math.PI/2\\n } else {\\n var theta = Math.PI3/2\\n }\\n } else if (delta_x > 0) {\\n var theta = Math.atan(delta_y/delta_x)\\n } else {\\n var theta = Math.atan(delta_y/delta_x)+Math.PI\\n }\\n \\n // head adjust\\n const length_arr = Math.sqrt(delta_x2 + delta_y2)\\n const size_head = arrow_growth(length_arr)AHF\\n const head_x = size_head/pixel2unitMath.cos(theta)\\n const head_y = size_head/pixel2unitMath.sin(theta)\\n \\n // update line\\n const data_line = source.data\\n data_line['x'] = [x_start, x_end]\\n data_line['y'] = [y_start, y_end]\\n source.change.emit()\\n \\n // heads\\n arr_heads.glyph.size = size_head\\n arr_heads.glyph.angle = theta+Math.PI/6\\n //arr_heads.glyph.x = [x_end-head_x/2, x_end-head_x/23]\\n //arr_heads.glyph.y = [y_end-head_y/2, y_end-head_y/23]\\n const source_h = arr_heads.data_source\\n source_h.data['x'] = [x_end-head_x/2, x_end-head_x/23]\\n source_h.data['y'] = [y_end-head_y/2, y_end-head_y/23]\\n source_h.change.emit()\\n }\\n \\n \\n function compute_T(x, Mt, L) {\\n if (x<L/2) {\\n return Mt/2\\n } else {\\n return -Mt/2\\n }\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_torsion, y_discr)\\n }\\n \\n \"},\"id\":\"2061\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1354\"},\"glyph\":{\"id\":\"1355\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1357\"},\"nonselection_glyph\":{\"id\":\"1356\"},\"view\":{\"id\":\"1359\"}},\"id\":\"1358\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"2055\"},\"glyph\":{\"id\":\"2056\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"2058\"},\"nonselection_glyph\":{\"id\":\"2057\"},\"view\":{\"id\":\"2060\"}},\"id\":\"2059\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"2055\"}},\"id\":\"2060\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1064\",\"type\":\"ResetTool\"},{\"attributes\":{\"callback\":null,\"renderers\":[{\"id\":\"1372\"}],\"tooltips\":[[\"Position\",\"@x m\"],[\"Shear force\",\"@y kN\"]]},\"id\":\"1380\",\"type\":\"HoverTool\"},{\"attributes\":{},\"id\":\"1614\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1063\",\"type\":\"SaveTool\"},{\"attributes\":{\"args\":{\"EE1\":{\"id\":\"2059\"},\"M_stress_diag\":{\"id\":\"1664\"},\"N_stress_diag\":{\"id\":\"1644\"},\"T_stress_diag\":{\"id\":\"2039\"},\"V_stress_diag\":{\"id\":\"1684\"},\"axial_strain_diag\":{\"id\":\"1744\"},\"bending_strain_diag\":{\"id\":\"1766\"},\"centroid\":{\"id\":\"1676\"},\"div\":{\"id\":\"1107\"},\"div_T\":{\"id\":\"1899\"},\"neutral_axis\":{\"id\":\"1716\"},\"s_b\":{\"id\":\"1003\"},\"s_ss\":{\"id\":\"1006\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1099\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const t = db['t'][0]\\n const h = cb_obj.value // value of the slider\\n const A = compute_area(b, h, t)\\n const Iy = compute_inertia_y(b, h, t)\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n\\n // Easter egg\\n /const str_Doge = \\\" much wow\\\"\\n const str_tmp = div_T.text\\n if (h == 600) {\\n div_T.text = str_tmp+str_Doge\\n } else {\\n div_T.text = str_tmp.replace(str_Doge, '')\\n }/\\n if (h == 600) {\\n EE1.glyph.text = \\\"much wow\\\"\\n } else {\\n EE1.glyph.text = \\\"\\\"\\n }\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h, t)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_torsional_stress(db, T_stress_diag)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const t = Math.round(data['t'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n t = `+t+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n const src = glyph_section.data_source\\n const t = data['t'][0]\\n const b = data['b'][0]\\n const h = data['h'][0]\\n src.data.xs = [[[ [b/2, b/2, -b/2, -b/2], [b/2-t, b/2-t, -b/2+t, -b/2+t] ]]]\\n src.data.ys = [[[ [h/2, -h/2, -h/2, h/2], [h/2-t, -h/2+t, -h/2+t, h/2-t] ]]]\\n src.change.emit()\\n }\\n \\n \\n function compute_area(b, h, t) {\\n return bh - (b-t2)(h-2t)\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12 - (b-2t)(h-2t)*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h, t) {\\n return hb*3/12 - (h-2t)(b-2t)*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_torsion, y_discr)\\n }\\n \\n \"},\"id\":\"2063\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2354\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1377\",\"type\":\"Line\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1640\"},\"glyph\":{\"id\":\"1641\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1643\"},\"nonselection_glyph\":{\"id\":\"1642\"},\"view\":{\"id\":\"1645\"}},\"id\":\"1644\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"1358\"},\"N_stress_diag\":{\"id\":\"1644\"},\"arr_head\":{\"id\":\"1253\"},\"axial_strain_diag\":{\"id\":\"1744\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1716\"},\"s_M\":{\"id\":\"1242\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=101) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n 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// retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"2065\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1061\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1386\"},\"M_stress_diag\":{\"id\":\"1664\"},\"V_diag\":{\"id\":\"1372\"},\"V_stress_diag\":{\"id\":\"1684\"},\"arr_head\":{\"id\":\"1253\"},\"bending_strain_diag\":{\"id\":\"1766\"},\"centroid\":{\"id\":\"1676\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1716\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \"},\"id\":\"2066\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1619\",\"type\":\"BasicTicker\"},{\"attributes\":{\"line_alpha\":0.1,\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1376\",\"type\":\"Line\"},{\"attributes\":{\"axis\":{\"id\":\"1618\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1621\",\"type\":\"Grid\"},{\"attributes\":{\"args\":{\"T_diag\":{\"id\":\"1936\"},\"T_stress_diag\":{\"id\":\"2039\"},\"div_T\":{\"id\":\"1899\"},\"label_T_section\":{\"id\":\"2033\"},\"neutral_axis\":{\"id\":\"1716\"},\"section_T_head\":{\"id\":\"2027\"},\"section_T_line\":{\"id\":\"2021\"},\"section_T_source\":{\"id\":\"2016\"},\"section_torsion_head\":{\"id\":\"1995\"},\"section_torsion_source\":{\"id\":\"1984\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox Mt\\n if (f.length==0) f = [1]\\n const db = source.data\\n const L = db['L'][0]\\n const x = db['x'][0]\\n\\n // apply the changes\\n db['Mt'][0] = 100(1-f)\\n db['T'][0] = compute_T(x, db['Mt'][0], L)\\n\\n // update\\n update_torsional_stress(db, T_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_T_diagram(db, T_diag)\\n update_T_section(db, section_torsion_head, section_torsion_source, section_T_line, section_T_head, section_T_source, div_T, label_T_section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_doubleArrow(x_start, x_end, y_start, y_end, source, arr_heads, AHF=6, pixel2unit=10) {\\n // compute the angle of the line\\n const delta_x = x_end-x_start\\n const delta_y = y_end-y_start\\n if (delta_x==0) {\\n if (delta_y > 0) {\\n var theta = Math.PI/2\\n } else {\\n var theta = Math.PI3/2\\n }\\n } else if (delta_x > 0) {\\n var theta = Math.atan(delta_y/delta_x)\\n } else {\\n var theta = Math.atan(delta_y/delta_x)+Math.PI\\n }\\n \\n // head adjust\\n const length_arr = Math.sqrt(delta_x2 + delta_y2)\\n const size_head = arrow_growth(length_arr)AHF\\n const head_x = size_head/pixel2unitMath.cos(theta)\\n const head_y = size_head/pixel2unitMath.sin(theta)\\n \\n // update line\\n const data_line = source.data\\n data_line['x'] = [x_start, x_end]\\n data_line['y'] = [y_start, y_end]\\n source.change.emit()\\n \\n // heads\\n arr_heads.glyph.size = size_head\\n arr_heads.glyph.angle = theta+Math.PI/6\\n //arr_heads.glyph.x = [x_end-head_x/2, x_end-head_x/23]\\n //arr_heads.glyph.y = [y_end-head_y/2, y_end-head_y/23]\\n const source_h = arr_heads.data_source\\n source_h.data['x'] = [x_end-head_x/2, x_end-head_x/23]\\n source_h.data['y'] = [y_end-head_y/2, y_end-head_y/23]\\n source_h.change.emit()\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_T_section(data, head_T_curved, source_T_curved, line_T, head_T, source_T, div_T, label_T_section, offset_T=4, pixel2unit=10, scale_T=10) {\\n const Mt = data['Mt'][0]\\n const T = data['T'][0]\\n \\n if (T > 0) {\\n update_doubleArrow(offset_T, offset_T+T/scale_T, 0, 0, source_T, head_T)\\n } else {\\n update_doubleArrow(offset_T-T/scale_T, offset_T, 0, 0, source_T, head_T)\\n }\\n \\n // update visibility\\n if (Mt==0) {\\n div_T.text = \\\"Torsion M<sub>t</sub>=0 kNm (removed)\\\"\\n line_T.glyph.line_alpha = 0 // T\\n head_T.glyph.line_alpha = 0\\n head_T.glyph.fill_alpha = 0\\n // T in cross-section\\n update_curvedArrow(0, 0, 0, 0, 0, source_T_curved, head_T_curved)\\n } else {\\n div_T.text = \\\"Torsion M<sub>t</sub>=\\\"+Mt+\\\" kNm (applied)\\\"\\n line_T.glyph.line_alpha = 1 // T\\n head_T.glyph.line_alpha = 1\\n head_T.glyph.fill_alpha = 1\\n // T in cross-section\\n update_curvedArrow(0, T4/scale_T, Math.abs(T3/scale_T), 0, 0, source_T_curved, head_T_curved)\\n }\\n \\n if (T==0) {\\n label_T_section.glyph.text=''\\n } else {\\n label_T_section.glyph.text='T'\\n }\\n }\\n \\n \\n function compute_T(x, Mt, L) {\\n if (x<L/2) {\\n return Mt/2\\n } else {\\n return -Mt/2\\n }\\n }\\n \\n \\n function update_T_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const Mt = data['Mt'][0]\\n const x = linspace(0, L, 101)\\n const T_discr = Array.from({length: discr}, (_, i) => compute_T(x[i], Mt, L))\\n update_NVM_diagram(glyph, T_discr)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_torsion, y_discr)\\n }\\n \\n \"},\"id\":\"2067\",\"type\":\"CustomJS\"},{\"attributes\":{\"data\":{\"x\":[0],\"y\":[0]},\"selected\":{\"id\":\"2280\"},\"selection_policy\":{\"id\":\"2279\"}},\"id\":\"1074\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"axis\":{\"id\":\"1332\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1335\",\"type\":\"Grid\"},{\"attributes\":{\"axis_label\":\"Width b [mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"2180\"},\"group\":null,\"major_label_policy\":{\"id\":\"2181\"},\"ticker\":{\"id\":\"1080\"}},\"id\":\"1052\",\"type\":\"LinearAxis\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1664\"},\"N_stress_diag\":{\"id\":\"1644\"},\"T_stress_diag\":{\"id\":\"2039\"},\"V_stress_diag\":{\"id\":\"1684\"},\"axial_strain_diag\":{\"id\":\"1744\"},\"bending_strain_diag\":{\"id\":\"1766\"},\"centroid\":{\"id\":\"1676\"},\"div\":{\"id\":\"1107\"},\"neutral_axis\":{\"id\":\"1716\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1704\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const t = cb_obj.value // value of the slider\\n const b = db['b'][0]\\n const h = db['h'][0]\\n const A = compute_area(b, h, t)\\n const Iy = compute_inertia_y(b, h, t)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n\\n // apply the changes\\n db['t'][0] = t\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h, t)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_torsional_stress(db, T_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const t = Math.round(data['t'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n t = `+t+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n const src = glyph_section.data_source\\n const t = data['t'][0]\\n const b = data['b'][0]\\n const h = data['h'][0]\\n src.data.xs = [[[ [b/2, b/2, -b/2, -b/2], [b/2-t, b/2-t, -b/2+t, -b/2+t] ]]]\\n src.data.ys = [[[ [h/2, -h/2, -h/2, h/2], [h/2-t, -h/2+t, -h/2+t, h/2-t] ]]]\\n src.change.emit()\\n }\\n \\n \\n function compute_area(b, h, t) {\\n return bh - (b-t2)(h-2t)\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12 - (b-2t)(h-2t)*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h, t) {\\n return hb*3/12 - (h-2t)(b-2t)*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))*1000\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_torsion, y_discr)\\n }\\n \\n \"},\"id\":\"2068\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Total stress \\u03c4\"},\"id\":\"1609\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"2249\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1627\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"width\":10},\"id\":\"2069\",\"type\":\"Spacer\"},{\"attributes\":{},\"id\":\"1616\",\"type\":\"LinearScale\"},{\"attributes\":{\"axis_label\":\"Position 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stress \\u03c3 and neutral axis\"},\"id\":\"1577\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"1584\",\"type\":\"LinearScale\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1007\"},\"glyph\":{\"id\":\"1409\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1411\"},\"nonselection_glyph\":{\"id\":\"1410\"},\"view\":{\"id\":\"1413\"}},\"id\":\"1412\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"tools\":[{\"id\":\"1594\"},{\"id\":\"1595\"},{\"id\":\"1596\"},{\"id\":\"1597\"},{\"id\":\"1598\"},{\"id\":\"1599\"},{\"id\":\"1718\"}]},\"id\":\"1601\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"1470\",\"type\":\"HelpTool\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2173\"},\"selection_policy\":{\"id\":\"2172\"}},\"id\":\"2106\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"M\"}},\"id\":\"1410\",\"type\":\"Circle\"},{\"attributes\":{\"axis_label\":\"Stress 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stress\"},\"id\":\"1415\",\"type\":\"Title\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1600\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"axis\":{\"id\":\"1425\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1428\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1421\",\"type\":\"LinearScale\"},{\"attributes\":{\"axis_label\":\"Stress \\u03c3\\u2099 [MPa]\",\"coordinates\":null,\"formatter\":{\"id\":\"2235\"},\"group\":null,\"major_label_policy\":{\"id\":\"2236\"},\"ticker\":{\"id\":\"1426\"}},\"id\":\"1425\",\"type\":\"LinearAxis\"},{\"attributes\":{\"axis_label\":\"Height h [mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"2232\"},\"group\":null,\"major_label_policy\":{\"id\":\"2233\"},\"ticker\":{\"id\":\"1430\"},\"visible\":false},\"id\":\"1429\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1485\",\"type\":\"LinearScale\"}],\"root_ids\":[\"2087\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n",
	+ " const render_items = [{\"docid\":\"c22caa71-b155-4e16-ad9c-7384d8f7826e\",\"root_ids\":[\"2087\"],\"roots\":{\"2087\":\"8de2cdc4-bf81-4ebc-b851-aa49955eb6f9\"}}];\n",
	+ " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	+ "\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " let attempts = 0;\n",
	+ " const timer = setInterval(function(root) {\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " clearInterval(timer);\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " attempts++;\n",
	+ " if (attempts > 100) {\n",
	+ " clearInterval(timer);\n",
	+ " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	+ " }\n",
	+ " }\n",
	+ " }, 10, root)\n",
	+ " }\n",
	+ "})(window);"
	+ ],
	+ "application/vnd.bokehjs_exec.v0+json": ""
	+ },
	+ "metadata": {
	+ "application/vnd.bokehjs_exec.v0+json": {
	+ "id": "2087"
	+ }
	+ },
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "hidden_code_nb_torsion.main_code(L, h, b, t, A, Iy, Iz, yG, y_n_axis, q, P, Mt, E, N, V, M, T, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr, T_discr)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Legend\n",
	+ "\n",
	+ "Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder.\n",
	+ "\n",
	+ "* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	+ "* Slider of height h: move the slider to change the height h of the cross-section of the beam.\n",
	+ "* Slider of thickness t: move the slider to change the thickness t of the cross-section of the beam.\n",
	+ "* Slider of the position x: move the slider to change the position x along the beam.\n",
	+ "* Slider of the uniform load q: move the slider to change the uniform load q.\n",
	+ "* Figure \"Simple supported beam\": in this figure, the initial state is presented with the static scheme, the length of the beam, the horizontal force P and the uniform load q.\n",
	+ "* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	+ "* Figure \"Forces and Moments Scheme\": this figure has a dynamic representation of the studied case with the position x indicated by a magenta dot, the internal forces shown in with red arrows, the reaction forces with yellow arrows, the external force P with a green arrow and the uniform load q in blue.\n",
	+ "* Radio buttons of the FBD: choose between right-hand or left-hand free-body diagram.\n",
	+ "* Button of the force P: apply or remove the external force P.\n",
	+ "* Button of the torsional moment Mt: apply or remove the external torsional moment Mt.\n",
	+ "* Figures \"N V M T Diagrams\": plots that show the axial force N, shear force V, bending moment M and the torsion T diagrams, with a magenta dot that represents the x position. By hovering with the cursor over the desired position, a small window will show the position and the value of the internal force.\n",
	+ "* 10 small bottom figures: plots that show the strains, stresses and right-hand free-body diagram section (with N, V, M and T) only of the left web. By hovering with the cursor over the desired position, a small window will show the height and the value of the stress or strain.\n",
	+ "\n",
	+ "### Help and Information on the functions\n",
	+ "\n",
	+ "In Jupyter Notebooks the user can learn more about a function by using the question mark after the target function. One question mark shows some useful information on the function and two question marks show in addition also the code of the function, revealing it's content.\n",
	+ "For example, by creating a Code cell and pasting \"beam_section.compute_area?\" or \"beam_section.compute_area??\", it's possible to see how this feature works.\n",
	+ "\n",
	+ "### Recommendations\n",
	+ "\n",
	+ "If you have problem visualizing the entirety of the tool, you can maximize the window size by using Ctrl+B or Cmd+B to hide/show the left explorer panel and by using F11 to go to the full-page mode and back in the browser (NB: it could not work in the tab with NOTO; just use F11 in another tab and come back in the NOTO tab). If you're using a very sall display and it's not enough, you can zoom out the browser tab.\n",
	+ "\n",
	+ "Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully."
	+ ]
	+ }
	+ ],
	+ "metadata": {
	+ "interpreter": {
	+ "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	+ },
	+ "kernelspec": {
	+ "display_name": "Python 3 (ipykernel)",
	+ "language": "python",
	+ "name": "python3"
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	+ "codemirror_mode": {
	+ "name": "ipython",
	+ "version": 3
	+ },
	+ "file_extension": ".py",
	+ "mimetype": "text/x-python",
	+ "name": "python",
	+ "nbconvert_exporter": "python",
	+ "pygments_lexer": "ipython3",
	+ "version": "3.8.10"
	+ }
	+ },
	+ "nbformat": 4,
	+ "nbformat_minor": 4
	+}
	diff --git a/Simple Beam DEMOs/06-sb_mohr.ipynb b/Simple Beam DEMOs/06-sb_mohr.ipynb
	new file mode 100644
	index 0000000..c88d9e9
	--- /dev/null
	+++ b/Simple Beam DEMOs/06-sb_mohr.ipynb
	@@ -0,0 +1,669 @@
	+{
	+ "cells": [
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "# Simple beam - Mohr Circle\n",
	+ "In this sixth notebook, the Mohr circle is explored. The system, geometry and actions are taken from the previous DEMO \"04-sb_stress\"."
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Goals\n",
	+ "\n",
	+ "* Describe the Mohr circle and its different parameters\n",
	+ "* Identify the relationships between the normal and shear stress using the Mohr circle\n",
	+ "* Explain the importance of the orientation of the stress element analysed"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Tasks and exercises\n",
	+ "\n",
	+ "Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	+ "\n",
	+ "1. What are $\\theta_p$ and $\\theta$? Is it correct that there's a 2 multiplier in fornt of the angles in the Mohr circle plot?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " $\\theta_p$ is the principal angle, that characterises the plane that experiences zero shear stress; $\\theta$ is the angle of the rotating stress element with respect to the fixed stress element. It is defined with the reference position set horizontally and the positive direction set counter-clockwise.\n",
	+ " \n",
	+ " <br>\n",
	+ " \n",
	+ " Yes, because in the representation of the stress element in a 2D cartesian graph with $\\sigma$ vs. $\\tau$, the angle in the plot is the double of the real inclination of the stress element studied.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>\n",
	+ "\n",
	+ "2. Consider the starting configuration and the stress element in the point at y = 150 mm and x = 5.30 m.\n",
	+ "\n",
	+ " 1. Are the stresses in the fixed stress element principal?\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " No, because the principal stresses corresponds to the stress state with zero shear stress and in the fixed stress element the $\\tau$ stress is not zero.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 2. Which angle $\\theta$ corresponds to a rotating stress element with stresses approximately equal to the principal ones?\n",
	+ " \n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " By rotating the stress element counter-clockwise by 85.0 degrees, the shear stress are approximately zero, thus the element has stresses approximately equal to the principal ones. The same result could be obtained by rotating the element clockwise by $90-85 = 5$ degrees.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 3. Compute the principal stresses $\\sigma_1$ and $\\sigma_2$ and the principal angle. Can you formulate a relation between the angle of the rotating element $\\theta$ and the principal angle $\\theta_p$ when the stresses inside the rotating element are equal to the principal ones? \n",
	+ " \n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " The equations to compute the principal stresses are the following:\n",
	+ " \n",
	+ " $$ \\sigma_{avg} = \\frac{\\sigma_{x0}+\\sigma_{y0}}{2} $$\n",
	+ " $$ r_{circle} = \\sqrt{\\tau_0^2 + \\frac{(\\sigma_{x0}-\\sigma_{y0})^2}{4}} $$\n",
	+ " $$ \\sigma_1 = \\sigma_{avg} - r_{circle} $$\n",
	+ " $$ \\sigma_2 = \\sigma_{avg} + r_{circle} $$\n",
	+ " \n",
	+ " The equation to compute the principal angle $\\theta_p$ is the following:\n",
	+ " \n",
	+ " $$ \\theta_p = \\arctan(\\frac{2\\tau_0}{\\sigma_{y0}-\\sigma_{x0}})/2 $$\n",
	+ " \n",
	+ " With $\\tau_0 = -0.518 MPa$, $\\sigma_{x0} = -6.065 MPa$ and $\\sigma_{y0} = 0 MPa$, the principal stresses are $\\sigma_1 = 0.044 MPa$ and $\\sigma_2 = -6.109 MPa$ and the principal angle is $\\theta_p = -4.84$ degrees.\n",
	+ " It's possible to check the results with the stresses inside the rotating element with theta = 85 degrees.\n",
	+ " \n",
	+ " <br>\n",
	+ " <br>\n",
	+ " \n",
	+ " To formulate the relation between $\\theta$ and $\\theta_p$, let's define the angle $\\theta'$ with the reference position set vertically and the positive direction set counter-clockwise. The relation with the principal angle $\\theta_p$ would be:\n",
	+ " $$ \\theta_p = \\theta'$$\n",
	+ " The relation between the angle $\\theta'$ and $\\theta$ is the following:\n",
	+ " $$\\theta' = \\theta + \\pi/2$$\n",
	+ " Thus, the relation between the angle theta and the principal angle theta p is the following:\n",
	+ " $$ \\theta_p = \\pi/2 + \\theta $$\n",
	+ " This can also be observed in the Mohr circle plot by multiplying the equation above by 2:\n",
	+ " $$ 2\\theta_p = \\pi + 2\\theta $$\n",
	+ " \n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ "\n",
	+ "3. Consider the starting configuration but with q = 5 kN/m and a cross-section with b = 30 mm and h = 300 mm; analyse the welds presented in the figures below.\n",
	+ "\n",
	+ " 1. Assume a vertical weld positioned at $L_1 = 5 m$ illustrated in red in the figure below.\n",
	+ " \n",
	+ " <br>\n",
	+ " <img src=\"img/Weld1.png\" alt=\"drawing\" width=\"600\"/>\n",
	+ " <br>\n",
	+ " \n",
	+ " In which point the stress state is critical for the design of the weld? Define the minimal normal yield strength of the weld material. \n",
	+ " \n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " By analysing the stresses along the weld, the critical point is positioned at an height of 0 mm; here the tensile stress is maximum.\n",
	+ " <br>\n",
	+ " The minimal normal yield strength of the weld material needs to be bigger that the maxiaml tensile stress that is equal to 26.67 MPa, thus a metal with 30 MPa normal yield strength works.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 2. Consider the new weld with an angle $\\beta$ = 55 degrees presented in red the green dot positioned at $L_2 = 0.5 m$ and $h_2 = 80 mm$.\n",
	+ " \n",
	+ " <br>\n",
	+ " <img src=\"img/Weld2.png\" alt=\"drawing\" width=\"600\"/>\n",
	+ " <br>\n",
	+ " \n",
	+ " Define the minimal shear and normal yield strength of the weld material, assuming that the green dot is the critical point. \n",
	+ " \n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " To define the material characteristics, the critical stress state needs to be studied. The coordinates are defined as x = 0.5 m and y = 80 mm, but in this case, the default stress element ($\\theta$ = 0) is not the correct one, because the plane of the weld is oblique. By rotating the element by 55 degrees, the critical stresses are exposed: tensile stress of 5.57 MPa and shear stress of 2.27 MPa. The weld can be designed by using a metal with 6 MPa normal yield strength and 2.5 MPa shear yield strength.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Build the interactive visualisation tool"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 1,
	+ "metadata": {},
	+ "outputs": [
	+ {
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	+ " <span id=\"1002\">Loading BokehJS ...</span>\n",
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	+ " cell.notebook.kernel.execute(cmd_clean, {\n",
	+ " iopub: {\n",
	+ " output: function(msg) {\n",
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	+ " function append_mime(data, metadata, element) {\n",
	+ " // create a DOM node to render to\n",
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	+ " render(props, toinsert[toinsert.length - 1]);\n",
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	+ " return toinsert\n",
	+ " }\n",
	+ "\n",
	+ " /* Handle when an output is cleared or removed */\n",
	+ " events.on('clear_output.CodeCell', handleClearOutput);\n",
	+ " events.on('delete.Cell', handleClearOutput);\n",
	+ "\n",
	+ " /* Handle when a new output is added */\n",
	+ " events.on('output_added.OutputArea', handleAddOutput);\n",
	+ "\n",
	+ " /**\n",
	+ " * Register the mime type and append_mime function with output_area\n",
	+ " */\n",
	+ " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	+ " /* Is output safe? */\n",
	+ " safe: true,\n",
	+ " /* Index of renderer in `output_area.display_order` */\n",
	+ " index: 0\n",
	+ " });\n",
	+ " }\n",
	+ "\n",
	+ " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	+ " if (root.Jupyter !== undefined) {\n",
	+ " const events = require('base/js/events');\n",
	+ " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	+ "\n",
	+ " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	+ " register_renderer(events, OutputArea);\n",
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	+ "\n",
	+ " \n",
	+ " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_timeout = Date.now() + 5000;\n",
	+ " root._bokeh_failed_load = false;\n",
	+ " }\n",
	+ "\n",
	+ " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	+ " \"<div style='background-color: #fdd'>\\n\"+\n",
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	+ " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	+ " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	+ " \"</p>\\n\"+\n",
	+ " \"<ul>\\n\"+\n",
	+ " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	+ " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	+ " \"</ul>\\n\"+\n",
	+ " \"<code>\\n\"+\n",
	+ " \"from bokeh.resources import INLINE\\n\"+\n",
	+ " \"output_notebook(resources=INLINE)\\n\"+\n",
	+ " \"</code>\\n\"+\n",
	+ " \"</div>\"}};\n",
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	+ " if (root._bokeh_is_loading > 0) {\n",
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	+ " element.src = url;\n",
	+ " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	+ " document.head.appendChild(element);\n",
	+ " }\n",
	+ " };\n",
	+ "\n",
	+ " function inject_raw_css(css) {\n",
	+ " const element = document.createElement(\"style\");\n",
	+ " element.appendChild(document.createTextNode(css));\n",
	+ " document.body.appendChild(element);\n",
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	+ "\n",
	+ " \n",
	+ " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
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	+ " \n",
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	+ " const inline_js = [\n",
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	+ " Bokeh.set_log_level(\"info\");\n",
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	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "# Import the packages needed\n",
	+ "import sys\n",
	+ "sys.path.append('../HiddenCode')\n",
	+ "import hidden_code_nb_mohr\n",
	+ "import math\n",
	+ "import numpy as np\n",
	+ "from cienpy import simplebeam as sb\n",
	+ "from cienpy import rectangular_section as beam_section\n",
	+ "from cienpy import stress_strain_elastic as stst\n",
	+ "from cienpy import mohrcircle"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Define the geometry, the external actions, the mechanical property and compute the initial configuration."
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 2,
	+ "metadata": {},
	+ "outputs": [],
	+ "source": [
	+ "# Choose the dimensions\n",
	+ "L = 6 # [m]\n",
	+ "h = 200 # [mm]\n",
	+ "b = 100 # [mm]\n",
	+ "q = 4; # [kN/m]\n",
	+ "P = 10; # [kN]\n",
	+ "\n",
	+ "# Choose the material parameters\n",
	+ "E = 200e3 # [MPa]\n",
	+ "\n",
	+ "# compute the internal forces (at x=L)\n",
	+ "discr_NVM = 101\n",
	+ "x_discr = np.linspace(0, L, discr_NVM)\n",
	+ "N_discr = sb.compute_N(x_discr, P)\n",
	+ "V_discr = sb.compute_V(x_discr, q, L)\n",
	+ "M_discr = sb.compute_M(x_discr, q, L)\n",
	+ "N = N_discr[-1]\n",
	+ "V = V_discr[-1]\n",
	+ "M = M_discr[-1]\n",
	+ "\n",
	+ "# compute the parameters\n",
	+ "A = beam_section.compute_area(b, h) # [mm2]\n",
	+ "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	+ "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	+ "yG = beam_section.compute_centroid_y(h)\n",
	+ "y_n_axis = stst.compute_neutral_axis(N, A, Iy, M, yG)\n",
	+ "\n",
	+ "# compute the reactions\n",
	+ "Rx = sb.compute_Rx(P)\n",
	+ "Ry_l = sb.compute_Ry_l(q, L)\n",
	+ "Ry_r = sb.compute_Ry_r(q, L)\n",
	+ "\n",
	+ "# compute Mohr circle parameters\n",
	+ "initial_y = h\n",
	+ "initial_theta_element = 0\n",
	+ "sigma_axial = stst.compute_sigma_axial(initial_y, N, A)\n",
	+ "sigma_bending = stst.compute_sigma_bending(initial_y, M, Iy, yG)\n",
	+ "S = beam_section. compute_first_moment_of_area(initial_y, b, h, yG)\n",
	+ "sigma_tau = stst.compute_tau_shear(initial_y, V, S, Iy, b)\n",
	+ "sigma_x0 = stst.compute_total_sigma(sigma_axial, sigma_bending)\n",
	+ "sigma_y0 = 0 # no vertical axial forces\n",
	+ "tau_0 = stst.compute_total_tau(sigma_tau)\n",
	+ "sigma_average_mohr = mohrcircle.compute_sigma_average_mohr(sigma_x0, sigma_y0)\n",
	+ "r_circle_mohr = mohrcircle.compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\n",
	+ "theta_principal = mohrcircle.compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\n",
	+ "initial_theta = mohrcircle.compute_theta_mohr(initial_theta_element, theta_principal)\n",
	+ "\n",
	+ "# stress state in function of theta\n",
	+ "new_state = mohrcircle.compute_stress_state_mohr(sigma_average_mohr, r_circle_mohr, initial_theta)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Run the complex code to generate the interactive visualisation tool:"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 3,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
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	+ "\n",
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// retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n const N = compute_N(db['P'][0])\\n const V = compute_V(pos, q, L)\\n const M = compute_M(pos, q, L)\\n\\n // update data\\n db['N'][0] = N\\n db['V'][0] = V\\n db['M'][0] = M\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n \\n const y_var = db['y_var'][0]\\n const A = db['A'][0]\\n const b = db['b'][0]\\n const h = db['h'][0]\\n const yG = db['yG'][0]\\n const Iy = db['Iy'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // update data\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n \\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2137\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"2129\"},\"glyph\":{\"id\":\"2130\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"2132\"},\"nonselection_glyph\":{\"id\":\"2131\"},\"view\":{\"id\":\"2134\"}},\"id\":\"2133\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2345\"},\"selection_policy\":{\"id\":\"2344\"}},\"id\":\"2285\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_color\":\"blue\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1715\",\"type\":\"Line\"},{\"attributes\":{\"source\":{\"id\":\"2129\"}},\"id\":\"2134\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"2239\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2387\",\"type\":\"AllLabels\"},{\"attributes\":{\"line_alpha\":0.1,\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1722\",\"type\":\"Line\"},{\"attributes\":{\"callback\":null,\"renderers\":[{\"id\":\"1718\"}],\"tooltips\":[[\"Stress\",\"@x MPa\"],[\"Height\",\"@y mm\"]]},\"id\":\"1732\",\"type\":\"HoverTool\"},{\"attributes\":{},\"id\":\"2440\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1658\"},\"Mohr_circle\":{\"id\":\"2073\"},\"N_stress_diag\":{\"id\":\"1638\"},\"V_stress_diag\":{\"id\":\"1678\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1\":{\"id\":\"2034\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2\":{\"id\":\"2037\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1\":{\"id\":\"2040\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2\":{\"id\":\"2043\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"axial_strain_diag\":{\"id\":\"1738\"},\"bending_strain_diag\":{\"id\":\"1760\"},\"centroid\":{\"id\":\"1670\"},\"div\":{\"id\":\"1119\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"neutral_axis\":{\"id\":\"1710\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"section\":{\"id\":\"1117\"},\"sigma_stress_diag\":{\"id\":\"1698\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1057\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const V = db['V'][0]\\n const y_var = db['y_var'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n // Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2138\",\"type\":\"CustomJS\"},{\"attributes\":{\"source\":{\"id\":\"1714\"}},\"id\":\"1719\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"2240\",\"type\":\"Selection\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"blue\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1716\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"2441\",\"type\":\"Selection\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2347\"},\"selection_policy\":{\"id\":\"2346\"}},\"id\":\"2286\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1790\",\"type\":\"BasicTicker\"},{\"attributes\":{\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1721\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1787\",\"type\":\"LinearScale\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1658\"},\"Mohr_circle\":{\"id\":\"2073\"},\"N_stress_diag\":{\"id\":\"1638\"},\"V_stress_diag\":{\"id\":\"1678\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1\":{\"id\":\"2034\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2\":{\"id\":\"2037\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1\":{\"id\":\"2040\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2\":{\"id\":\"2043\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"axial_strain_diag\":{\"id\":\"1738\"},\"beam\":{\"id\":\"1045\"},\"bending_strain_diag\":{\"id\":\"1760\"},\"centroid\":{\"id\":\"1670\"},\"div\":{\"id\":\"1119\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"neutral_axis\":{\"id\":\"1710\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"s_ss\":{\"id\":\"1006\"},\"section\":{\"id\":\"1117\"},\"sigma_stress_diag\":{\"id\":\"1698\"},\"slider_y\":{\"id\":\"1899\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1057\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // solve sliders conflict\\n const db = source.data\\n const h = cb_obj.value // value of the slider\\n if (h < db['y_var'][0]) {\\n db['y_var'][0] = h\\n }\\n slider_y.end = h\\n if (h < slider_y.value) {\\n slider_y.value = h\\n }\\n\\n // retrieve data used\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const N = db['N'][0]\\n const V = db['V'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n const y_var = db['y_var'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n beam.glyph.height = h // change the beam height\\n beam.glyph.y = h/2\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n // Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2139\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_color\":\"red\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1735\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"2479\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2241\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2349\"},\"selection_policy\":{\"id\":\"2348\"}},\"id\":\"2287\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"axis_label\":\"Strain \\u03b5\\u2099 [%]\",\"coordinates\":null,\"formatter\":{\"id\":\"2392\"},\"group\":null,\"major_label_policy\":{\"id\":\"2393\"},\"ticker\":{\"id\":\"1752\"}},\"id\":\"1451\",\"type\":\"LinearAxis\"},{\"attributes\":{\"args\":{\"Mohr_circle\":{\"id\":\"2073\"},\"N_diag\":{\"id\":\"1352\"},\"N_stress_diag\":{\"id\":\"1638\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arr_head\":{\"id\":\"1247\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"axial_strain_diag\":{\"id\":\"1738\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"neutral_axis\":{\"id\":\"1710\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"s_M\":{\"id\":\"1236\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1698\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const P = 10(1-f)\\n const db = source.data\\n const N = compute_N(P)\\n const M = db['M'][0]\\n const A = db['A'][0]\\n const Iy = db['Iy'][0]\\n const yG = db['yG'][0]\\n const y_var = db['y_var'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = db['tau_0'][0]\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // apply the changes\\n db['P'][0] = P\\n db['N'][0] = N\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n // Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=101) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2140\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1723\",\"type\":\"Line\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1729\",\"type\":\"Line\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1247\"},\"div_P\":{\"id\":\"1253\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"2141\",\"type\":\"CustomJS\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2461\"},\"selection_policy\":{\"id\":\"2460\"}},\"id\":\"2388\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"source\":{\"id\":\"1006\"}},\"id\":\"1725\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1727\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"2480\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1380\"},\"M_stress_diag\":{\"id\":\"1658\"},\"Mohr_circle\":{\"id\":\"2073\"},\"V_diag\":{\"id\":\"1366\"},\"V_stress_diag\":{\"id\":\"1678\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arr_head\":{\"id\":\"1247\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1\":{\"id\":\"2034\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2\":{\"id\":\"2037\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1\":{\"id\":\"2040\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2\":{\"id\":\"2043\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"bending_strain_diag\":{\"id\":\"1760\"},\"centroid\":{\"id\":\"1670\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"neutral_axis\":{\"id\":\"1710\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1698\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n const N = db['N'][0]\\n const V = compute_V(pos, q, L)\\n const M = compute_M(pos, q, L)\\n const y_var = db['y_var'][0]\\n const A = db['A'][0]\\n const b = db['b'][0]\\n const h = db['h'][0]\\n const yG = db['yG'][0]\\n const Iy = db['Iy'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // update data\\n db['q'][0] = q\\n db['V'][0] = V\\n db['M'][0] = M\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n // Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2142\",\"type\":\"CustomJS\"},{\"attributes\":{\"data\":{\"x\":[-1.2,1.2],\"y\":[0,0]},\"selected\":{\"id\":\"2504\"},\"selection_policy\":{\"id\":\"2503\"}},\"id\":\"1726\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"args\":{\"Mohr_circle\":{\"id\":\"2073\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_element\":{\"id\":\"2007\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"beam_position\":{\"id\":\"1897\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_stress_state_theta\":{\"id\":\"1995\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_element\":{\"id\":\"2013\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"rotating_axis\":{\"id\":\"2001\"},\"source\":{\"id\":\"1007\"},\"stress_state_theta\":{\"id\":\"1989\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const theta_element = cb_obj.value/180Math.PI\\n const sigma_x0 = db['sigma_x0'][0]\\n const sigma_y0 = db['sigma_y0'][0]\\n const tau_0 = db['tau_0'][0]\\n const sigma_average = db['sigma_average'][0]\\n const r_circle = db['r_circle_mohr'][0]\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // update data\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta_element'][0] = theta_element\\n db['theta'][0] = theta\\n\\n // update\\n // square point:\\n beam_position.glyph.angle = theta_element\\n // stress state element\\n update_stress_state_elements(db, stress_state_theta, rotating_axis, label_stress_state_theta, arc_theta_element, label_theta_element)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n // update Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_stress_state_elements(data, glyph_stress_state_theta, glyph_axis, glyph_label_element_theta, glyph_arc_theta, glyph_label_theta, max_stress=60, max_dim=150.0) {\\n // set variables\\n const theta_element = data['theta_element'][0]\\n const x_new = max_stressMath.cos(theta_element)\\n const y_new = max_stressMath.sin(theta_element)\\n \\n \\n // update rotating axis\\n const src_axis = glyph_axis.data_source\\n src_axis.data.x = [0, x_newmax_dim/max_stress]\\n src_axis.data.y = [0, y_newmax_dim/max_stress]\\n src_axis.change.emit()\\n \\n // update stress state theta\\n glyph_stress_state_theta.glyph.angle = theta_element\\n glyph_stress_state_theta.glyph.x = x_new2\\n glyph_stress_state_theta.glyph.y = y_new2\\n \\n // label element\\n const src_label_element = glyph_label_element_theta.data_source\\n src_label_element.data.x = [x_new2]\\n src_label_element.data.y = [y_new2]\\n src_label_element.change.emit()\\n \\n // arc theta (stress state)\\n glyph_arc_theta.glyph.end_angle = theta_element\\n \\n // label theta (stress state)\\n if (theta_element==0) {\\n glyph_label_theta.glyph.text = \\\"\\\"\\n } else {\\n glyph_label_theta.glyph.text = \\\"\\u03b8\\\"\\n const src_label_theta = glyph_label_theta.data_source\\n src_label_theta.data.x = [max_stressMath.cos(theta_element/2)]\\n src_label_theta.data.y = [max_stressMath.sin(theta_element/2)]\\n src_label_theta.change.emit()\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2143\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1726\"},\"glyph\":{\"id\":\"1727\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1729\"},\"nonselection_glyph\":{\"id\":\"1728\"},\"view\":{\"id\":\"1731\"}},\"id\":\"1730\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"2442\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1734\"},\"glyph\":{\"id\":\"1735\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1737\"},\"nonselection_glyph\":{\"id\":\"1736\"},\"view\":{\"id\":\"1739\"}},\"id\":\"1738\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"args\":{\"Mohr_circle\":{\"id\":\"2073\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1\":{\"id\":\"2034\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2\":{\"id\":\"2037\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1\":{\"id\":\"2040\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2\":{\"id\":\"2043\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"beam_position\":{\"id\":\"1897\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"source\":{\"id\":\"1007\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const y_var = cb_obj.value\\n const N = db['N'][0]\\n const V = db['V'][0]\\n const M = db['M'][0]\\n const A = db['A'][0]\\n const b = db['b'][0]\\n const h = db['h'][0]\\n const yG = db['yG'][0]\\n const Iy = db['Iy'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // update data\\n db['y_var'][0] = y_var\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n // square point:\\n beam_position.glyph.y = y_var\\n // update Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n 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<p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = 200 mm<br>\\n b = 100 mm<br>\\n L = 6 m<br>\\n A = 2.00e+04 mm<sup>2</sup><br>\\n Iy = 6.67e+07 mm<sup>4</sup><br>\\n Iz = 1.67e+07 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Application\",\"version\":\"2.4.2\"}};\n",
	+ " const render_items = [{\"docid\":\"21595604-136d-47e8-80bc-7b0b2dcec6f8\",\"root_ids\":[\"2164\"],\"roots\":{\"2164\":\"cf97d42a-8a40-4f6d-aba3-358d43f1dbe1\"}}];\n",
	+ " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	+ "\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " let attempts = 0;\n",
	+ " const timer = setInterval(function(root) {\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " clearInterval(timer);\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " attempts++;\n",
	+ " if (attempts > 100) {\n",
	+ " clearInterval(timer);\n",
	+ " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	+ " }\n",
	+ " }\n",
	+ " }, 10, root)\n",
	+ " }\n",
	+ "})(window);"
	+ ],
	+ "application/vnd.bokehjs_exec.v0+json": ""
	+ },
	+ "metadata": {
	+ "application/vnd.bokehjs_exec.v0+json": {
	+ "id": "2164"
	+ }
	+ },
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "hidden_code_nb_mohr.main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr, initial_y, initial_theta_element, sigma_axial, sigma_bending, sigma_tau, sigma_x0, sigma_y0, tau_0, sigma_average_mohr, r_circle_mohr, theta_principal, initial_theta, new_state)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Legend\n",
	+ "\n",
	+ "Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder.\n",
	+ "\n",
	+ "* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	+ "* Slider of height h: move the slider to change the height h of the cross-section of the beam.\n",
	+ "* Slider of the hight y: move the slider to change the height y along h starting from the bottom.\n",
	+ "* Slider of the angle $\\theta$: move the slider to change the angle of the rotating stress element.\n",
	+ "* Slider of the position x: move the slider to change the position x along the beam.\n",
	+ "* Slider of the uniform load q: move the slider to change the uniform load q.\n",
	+ "* Figure \"Simple supported beam\": in this figure, the initial state is presented with the static scheme, the length of the beam, the horizontal force P and the uniform load q.\n",
	+ "* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	+ "* Figure \"Forces and Moments Scheme\": this figure has a dynamic representation of the studied case with the position x indicated by a magenta dot, the internal forces shown in with red arrows, the reaction forces with yellow arrows, the external force P with a green arrow and the uniform load q in blue.\n",
	+ "* Radio buttons of the FBD: choose between right-hand or left-hand free-body diagram.\n",
	+ "* Button of the force P: apply or remove the external force P.\n",
	+ "* Figures \"N V M Diagrams\": plots that show the axial force N, shear force V and bending moment M diagrams, with a magenta dot that represents the x position. By hovering with the cursor over the desired position, a small window will show the position and the value of the internal force.\n",
	+ "* 9 small bottom figures: plots that show the strains, stresses and right-hand free-body diagram section (with N, V and M). By hovering with the cursor over the desired position, a small window will show the height and the value of the stress or strain.\n",
	+ "* Figure \"Mohr circle\": plot that shows the Mohr circle of the stress element in the position x, y. By hovering with the cursor over the desired position, a small window will show the shear and normal stress.\n",
	+ "* Figures \"Stress state\": figure that shows the stress element with an angle fixed of 0 (characterized by the stresses $\\sigma_{x0}$ = total stress, $\\sigma_{y0}$ = 0 and $\\tau_{0}$ = total shear) and the stress element rotated by the angle $\\theta$. $\\theta_p$ is the principal stress.\n",
	+ "\n",
	+ "### Help and Information on the functions\n",
	+ "\n",
	+ "In Jupyter Notebooks the user can learn more about a function by using the question mark after the target function. One question mark shows some useful information on the function and two question marks show in addition also the code of the function, revealing it's content.\n",
	+ "For example, by creating a Code cell and pasting \"beam_section.compute_area?\" or \"beam_section.compute_area??\", it's possible to see how this feature works.\n",
	+ "\n",
	+ "### Recommendations\n",
	+ "\n",
	+ "If you have problem visualizing the entirety of the tool, you can maximize the window size by using Ctrl+B or Cmd+B to hide/show the left explorer panel and by using F11 to go to the full-page mode and back in the browser (NB: it could not work in the tab with NOTO; just use F11 in another tab and come back in the NOTO tab). If you're using a very sall display and it's not enough, you can zoom out the browser tab.\n",
	+ "\n",
	+ "Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully."
	+ ]
	+ }
	+ ],
	+ "metadata": {
	+ "interpreter": {
	+ "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	+ },
	+ "kernelspec": {
	+ "display_name": "Python 3 (ipykernel)",
	+ "language": "python",
	+ "name": "python3"
	+ },
	+ "language_info": {
	+ "codemirror_mode": {
	+ "name": "ipython",
	+ "version": 3
	+ },
	+ "file_extension": ".py",
	+ "mimetype": "text/x-python",
	+ "name": "python",
	+ "nbconvert_exporter": "python",
	+ "pygments_lexer": "ipython3",
	+ "version": "3.8.10"
	+ }
	+ },
	+ "nbformat": 4,
	+ "nbformat_minor": 4
	+}
	diff --git a/Simple Beam DEMOs/07-sb_plastic.ipynb b/Simple Beam DEMOs/07-sb_plastic.ipynb
	new file mode 100644
	index 0000000..02e8268
	--- /dev/null
	+++ b/Simple Beam DEMOs/07-sb_plastic.ipynb
	@@ -0,0 +1,635 @@
	+{
	+ "cells": [
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "# Simple beam - Plastic Analysis\n",
	+ "In this seventh notebook, the plastic analysis is presented. The system, geometry and actions are taken from the previous DEMO \"04-sb_stress\"."
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Goals\n",
	+ "\n",
	+ "* Describe the difference in the elastic and plastic analysis\n",
	+ "* Analyse the influence of the material parameters\n",
	+ "* Explore the evolution of the stress after the elastic limit"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Tasks and exercises\n",
	+ "\n",
	+ "Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	+ "\n",
	+ "1. Consider the starting configuration but with q = 5 kN/m, b = 90 mm and h = 100 mm.\n",
	+ " \n",
	+ " 1. By analysing the stresses inside the section, do you think that the beam is designed correctly? \n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " No, because the section and material chosen are enough resistant for the beam to remain elastic (no collapse), but the beam is clearly oversized.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 2. By changing only one parameter, is there a configuration with the critical stress slightly below the yield strength (maxiaml elastic resistant)?\n",
	+ " \n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " Yes, there are different solutions:\n",
	+ " <ul>\n",
	+ " <li>Decrease b to 40 mm (55.6 % reduction)</li>\n",
	+ " <li>Decrease h to 80 mm (20.0 % reduction)</li>\n",
	+ " <li>Decrease yield strength $f_y$ to 152 MPa (57.2 % reduction)</li>\n",
	+ " <li>Increase L to 9 m (50.0 % increase)</li>\n",
	+ " </ul>\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 3. By changing only the same parameter of the previous question, is it possible to reduce costs even more by yielding the section? What is the limit?\n",
	+ " \n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " Yes, there are different solutions:\n",
	+ " <ul>\n",
	+ " <li>Decrease b from 40 mm to 30 mm (25.0 % reduction)</li>\n",
	+ " <li>Decrease h from 80 mm to 60 mm (25.0 % reduction)</li>\n",
	+ " <li>Decrease yield strength $f_y$ from 152 MPa to 101 MPa (33.6 % reduction)</li>\n",
	+ " <li>Increase L from 9 m to 11 m (22.2 % increase)</li>\n",
	+ " </ul>\n",
	+ " The beam collapses if a plastic hinge is formed, considering that the system is isostatic. Thus, the limit is achieved when the plastic strain becomes infinite and the section is completely yielded.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 4. Find which parameter does not influence the critical stress and explain the reasons.\n",
	+ " \n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " It's easy to observe that the elastic modulus E does not influence the stress distribution inside the section. Considering that the system is isostaic, the parameter E is directly proportional to the strain.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ "\n",
	+ "2. Explore different configurations and observe the position of the elastic neutral axis.\n",
	+ "\n",
	+ " 1. Does it coincide with the position of the plastic neautral axis (not shown explicitly in the plots)?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " By analysing a configuration with very slender section (20 mm x 160 mm), x=L/2, yield strength = 16 MPa and q = 5 kN/m, the position of the elastic neutral axis is clearly not the same of the plastic neutral axis.\n",
	+ " \n",
	+ " If the section remains elastic, the two neutral axis overlap; when the section yields, the plastic neutral axis can move, due to the redistribution of stresses inside the section, resulting in a differnet position of the two neutral axis.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 2. Show elastic and plastic neutral axis are computed differently (formulas).\n",
	+ " \n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " \n",
	+ " Elastic neutral axis: \n",
	+ " $$ y_{Ne} = yG - \\frac{NI_y}{AM} = \\frac{h}{2} - \\frac{N}{M}\\frac{h^2}{12} $$\n",
	+ " \n",
	+ " Plastic neutral axis (section completely yielded): \n",
	+ " $$ y_{Np} = \\frac{h}{2} - \\frac{N}{2f_yb} $$\n",
	+ " \n",
	+ " This equations show that changing the width of the section influences only the position of the plastic neutral axis (when the section is completely yielded). Thus by using the configuration of the previous answer, it is possible to see hot the plastic neutral axis moves inside the section by changing only b.\n",
	+ " <br>\n",
	+ " Note that the position of the plastic neutral axis depends on the yield status of the section: if the section is not in a elastic or completely yielded status, it is in a transitory status that has a different position of the plastic neutral axis.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Build the interactive visualisation tool"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 1,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ " <div class=\"bk-root\">\n",
	+ " <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	+ " <span id=\"1002\">Loading BokehJS ...</span>\n",
	+ " </div>"
	+ ]
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ },
	+ {
	+ "data": {
	+ "application/javascript": [
	+ "\n",
	+ "(function(root) {\n",
	+ " function now() {\n",
	+ " return new Date();\n",
	+ " }\n",
	+ "\n",
	+ " const force = true;\n",
	+ "\n",
	+ " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_onload_callbacks = [];\n",
	+ " root._bokeh_is_loading = undefined;\n",
	+ " }\n",
	+ "\n",
	+ " const JS_MIME_TYPE = 'application/javascript';\n",
	+ " const HTML_MIME_TYPE = 'text/html';\n",
	+ " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	+ " const CLASS_NAME = 'output_bokeh rendered_html';\n",
	+ "\n",
	+ " /**\n",
	+ " * Render data to the DOM node\n",
	+ " */\n",
	+ " function render(props, node) {\n",
	+ " const script = document.createElement(\"script\");\n",
	+ " node.appendChild(script);\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
	+ " * Handle when an output is cleared or removed\n",
	+ " */\n",
	+ " function handleClearOutput(event, handle) {\n",
	+ " const cell = handle.cell;\n",
	+ "\n",
	+ " const id = cell.output_area._bokeh_element_id;\n",
	+ " const server_id = cell.output_area._bokeh_server_id;\n",
	+ " // Clean up Bokeh references\n",
	+ " if (id != null && id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ "\n",
	+ " if (server_id !== undefined) {\n",
	+ " // Clean up Bokeh references\n",
	+ " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	+ " cell.notebook.kernel.execute(cmd_clean, {\n",
	+ " iopub: {\n",
	+ " output: function(msg) {\n",
	+ " const id = msg.content.text.trim();\n",
	+ " if (id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ " }\n",
	+ " }\n",
	+ " });\n",
	+ " // Destroy server and session\n",
	+ " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	+ " cell.notebook.kernel.execute(cmd_destroy);\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
	+ " * Handle when a new output is added\n",
	+ " */\n",
	+ " function handleAddOutput(event, handle) {\n",
	+ " const output_area = handle.output_area;\n",
	+ " const output = handle.output;\n",
	+ "\n",
	+ " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	+ " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	+ " return\n",
	+ " }\n",
	+ "\n",
	+ " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
	+ "\n",
	+ " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	+ " // store reference to embed id on output_area\n",
	+ " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
	+ " }\n",
	+ " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	+ " const bk_div = document.createElement(\"div\");\n",
	+ " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	+ " const script_attrs = bk_div.children[0].attributes;\n",
	+ " for (let i = 0; i < script_attrs.length; i++) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	+ " }\n",
	+ " // store reference to server id on output_area\n",
	+ " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function register_renderer(events, OutputArea) {\n",
	+ "\n",
	+ " function append_mime(data, metadata, element) {\n",
	+ " // create a DOM node to render to\n",
	+ " const toinsert = this.create_output_subarea(\n",
	+ " metadata,\n",
	+ " CLASS_NAME,\n",
	+ " EXEC_MIME_TYPE\n",
	+ " );\n",
	+ " this.keyboard_manager.register_events(toinsert);\n",
	+ " // Render to node\n",
	+ " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	+ " render(props, toinsert[toinsert.length - 1]);\n",
	+ " element.append(toinsert);\n",
	+ " return toinsert\n",
	+ " }\n",
	+ "\n",
	+ " /* Handle when an output is cleared or removed */\n",
	+ " events.on('clear_output.CodeCell', handleClearOutput);\n",
	+ " events.on('delete.Cell', handleClearOutput);\n",
	+ "\n",
	+ " /* Handle when a new output is added */\n",
	+ " events.on('output_added.OutputArea', handleAddOutput);\n",
	+ "\n",
	+ " /**\n",
	+ " * Register the mime type and append_mime function with output_area\n",
	+ " */\n",
	+ " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	+ " /* Is output safe? */\n",
	+ " safe: true,\n",
	+ " /* Index of renderer in `output_area.display_order` */\n",
	+ " index: 0\n",
	+ " });\n",
	+ " }\n",
	+ "\n",
	+ " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	+ " if (root.Jupyter !== undefined) {\n",
	+ " const events = require('base/js/events');\n",
	+ " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	+ "\n",
	+ " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	+ " register_renderer(events, OutputArea);\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " \n",
	+ " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_timeout = Date.now() + 5000;\n",
	+ " root._bokeh_failed_load = false;\n",
	+ " }\n",
	+ "\n",
	+ " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	+ " \"<div style='background-color: #fdd'>\\n\"+\n",
	+ " \"<p>\\n\"+\n",
	+ " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	+ " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	+ " \"</p>\\n\"+\n",
	+ " \"<ul>\\n\"+\n",
	+ " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	+ " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	+ " \"</ul>\\n\"+\n",
	+ " \"<code>\\n\"+\n",
	+ " \"from bokeh.resources import INLINE\\n\"+\n",
	+ " \"output_notebook(resources=INLINE)\\n\"+\n",
	+ " \"</code>\\n\"+\n",
	+ " \"</div>\"}};\n",
	+ "\n",
	+ " function display_loaded() {\n",
	+ " const el = document.getElementById(\"1002\");\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS is loading...\";\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	+ " }\n",
	+ " } else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(display_loaded, 100)\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ "\n",
	+ " function run_callbacks() {\n",
	+ " try {\n",
	+ " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	+ " if (callback != null)\n",
	+ " callback();\n",
	+ " });\n",
	+ " } finally {\n",
	+ " delete root._bokeh_onload_callbacks\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: all callbacks have finished\");\n",
	+ " }\n",
	+ "\n",
	+ " function load_libs(css_urls, js_urls, callback) {\n",
	+ " if (css_urls == null) css_urls = [];\n",
	+ " if (js_urls == null) js_urls = [];\n",
	+ "\n",
	+ " root._bokeh_onload_callbacks.push(callback);\n",
	+ " if (root._bokeh_is_loading > 0) {\n",
	+ " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	+ " return null;\n",
	+ " }\n",
	+ " if (js_urls == null \|\| js_urls.length === 0) {\n",
	+ " run_callbacks();\n",
	+ " return null;\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	+ " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	+ "\n",
	+ " function on_load() {\n",
	+ " root._bokeh_is_loading--;\n",
	+ " if (root._bokeh_is_loading === 0) {\n",
	+ " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	+ " run_callbacks()\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function on_error(url) {\n",
	+ " console.error(\"failed to load \" + url);\n",
	+ " }\n",
	+ "\n",
	+ " for (let i = 0; i < css_urls.length; i++) {\n",
	+ " const url = css_urls[i];\n",
	+ " const element = document.createElement(\"link\");\n",
	+ " element.onload = on_load;\n",
	+ " element.onerror = on_error.bind(null, url);\n",
	+ " element.rel = \"stylesheet\";\n",
	+ " element.type = \"text/css\";\n",
	+ " element.href = url;\n",
	+ " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	+ " document.body.appendChild(element);\n",
	+ " }\n",
	+ "\n",
	+ " for (let i = 0; i < js_urls.length; i++) {\n",
	+ " const url = js_urls[i];\n",
	+ " const element = document.createElement('script');\n",
	+ " element.onload = on_load;\n",
	+ " element.onerror = on_error.bind(null, url);\n",
	+ " element.async = false;\n",
	+ " element.src = url;\n",
	+ " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	+ " document.head.appendChild(element);\n",
	+ " }\n",
	+ " };\n",
	+ "\n",
	+ " function inject_raw_css(css) {\n",
	+ " const element = document.createElement(\"style\");\n",
	+ " element.appendChild(document.createTextNode(css));\n",
	+ " document.body.appendChild(element);\n",
	+ " }\n",
	+ "\n",
	+ " \n",
	+ " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	+ " const css_urls = [];\n",
	+ " \n",
	+ "\n",
	+ " const inline_js = [\n",
	+ " function(Bokeh) {\n",
	+ " Bokeh.set_log_level(\"info\");\n",
	+ " },\n",
	+ " function(Bokeh) {\n",
	+ " \n",
	+ " \n",
	+ " }\n",
	+ " ];\n",
	+ "\n",
	+ " function run_inline_js() {\n",
	+ " \n",
	+ " if (root.Bokeh !== undefined \|\| force === true) {\n",
	+ " \n",
	+ " for (let i = 0; i < inline_js.length; i++) {\n",
	+ " inline_js[i].call(root, root.Bokeh);\n",
	+ " }\n",
	+ " if (force === true) {\n",
	+ " display_loaded();\n",
	+ " }} else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(run_inline_js, 100);\n",
	+ " } else if (!root._bokeh_failed_load) {\n",
	+ " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
	+ " root._bokeh_failed_load = true;\n",
	+ " } else if (force !== true) {\n",
	+ " const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
	+ " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
	+ " }\n",
	+ "\n",
	+ " }\n",
	+ "\n",
	+ " if (root._bokeh_is_loading === 0) {\n",
	+ " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
	+ " run_inline_js();\n",
	+ " } else {\n",
	+ " load_libs(css_urls, js_urls, function() {\n",
	+ " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	+ " run_inline_js();\n",
	+ " });\n",
	+ " }\n",
	+ "}(window));"
	+ ],
	+ "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n function now() {\n return new Date();\n }\n\n const force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n \n\n \n if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n const NB_LOAD_WARNING = {'data': {'text/html':\n \"<div style='background-color: #fdd'>\\n\"+\n \"<p>\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"</p>\\n\"+\n \"<ul>\\n\"+\n \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n \"<li>use INLINE resources instead, as so:</li>\\n\"+\n \"</ul>\\n\"+\n \"<code>\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"</code>\\n\"+\n \"</div>\"}};\n\n function display_loaded() {\n const el = document.getElementById(\"1002\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null \|\| js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error(url) {\n console.error(\"failed to load \" + url);\n }\n\n for (let i = 0; i < css_urls.length; i++) {\n const url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n \n const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n const css_urls = [];\n \n\n const inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n function(Bokeh) {\n \n \n }\n ];\n\n function run_inline_js() {\n \n if (root.Bokeh !== undefined \|\| force === true) {\n \n for (let i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\n if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));"
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "# Import the packages needed\n",
	+ "import sys\n",
	+ "sys.path.append('../HiddenCode')\n",
	+ "import hidden_code_nb_plastic\n",
	+ "import math\n",
	+ "import numpy as np \n",
	+ "from cienpy import simplebeam as sb\n",
	+ "from cienpy import rectangular_section as beam_section\n",
	+ "from cienpy import stress_strain_elastic as ststel\n",
	+ "from cienpy import stress_strain_plastic as ststpl"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Define the geometry, the external actions, the mechanical property and compute the initial configuration."
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 2,
	+ "metadata": {},
	+ "outputs": [],
	+ "source": [
	+ "# Choose the dimensions\n",
	+ "L = 6 # [m]\n",
	+ "h = 200 # [mm]\n",
	+ "b = 100 # [mm]\n",
	+ "q = 4; # [kN/m]\n",
	+ "P = 10; # [kN]\n",
	+ "\n",
	+ "# Choose the material parameters\n",
	+ "E_steel = 200e3 # [MPa] steel\n",
	+ "fy_steel = 355 # [MPa] steel\n",
	+ "E = E_steel\n",
	+ "fy = fy_steel\n",
	+ "\n",
	+ "# compute the internal forces (at x=L)\n",
	+ "discr_NVM = 101\n",
	+ "x_discr = np.linspace(0, L, discr_NVM)\n",
	+ "N_discr = sb.compute_N(x_discr, P)\n",
	+ "V_discr = sb.compute_V(x_discr, q, L)\n",
	+ "M_discr = sb.compute_M(x_discr, q, L)\n",
	+ "N = N_discr[-1]\n",
	+ "V = V_discr[-1]\n",
	+ "M = M_discr[-1]\n",
	+ "\n",
	+ "# compute the parameters\n",
	+ "A = beam_section.compute_area(b, h) # [mm2]\n",
	+ "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	+ "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	+ "yG = beam_section.compute_centroid_y(h)\n",
	+ "y_n_axis = ststel.compute_neutral_axis(N, A, Iy, M, yG)\n",
	+ "\n",
	+ "# compute the reactions\n",
	+ "Rx = sb.compute_Rx(P)\n",
	+ "Ry_l = sb.compute_Ry_l(q, L)\n",
	+ "Ry_r = sb.compute_Ry_r(q, L)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Run the complex code to generate the interactive visualisation tool:"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 3,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ "\n",
	+ " <div class=\"bk-root\" id=\"b4d05515-c356-42ea-b8bb-80d4c028fd3a\" data-root-id=\"1995\"></div>\n"
	+ ]
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ },
	+ {
	+ "data": {
	+ "application/javascript": [
	+ "(function(root) {\n",
	+ " function embed_document(root) {\n",
	+ " \n",
	+ " const docs_json = 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style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = 200 mm<br>\\n b = 100 mm<br>\\n L = 6 m<br>\\n A = 2.00e+04 mm<sup>2</sup><br>\\n Iy = 6.67e+07 mm<sup>4</sup><br>\\n Iz = 1.67e+07 mm<sup>4</sup>\",\"width\":170},\"id\":\"1107\",\"type\":\"Div\"},{\"attributes\":{},\"id\":\"1821\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1563\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"end\":600,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1971\"}]},\"start\":20,\"step\":20,\"title\":\"Change the height h 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[mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"2156\"},\"group\":null,\"major_label_policy\":{\"id\":\"2157\"},\"ticker\":{\"id\":\"1559\"},\"visible\":false},\"id\":\"1558\",\"type\":\"LinearAxis\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_alpha\":{\"value\":0.1},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1115\",\"type\":\"Text\"},{\"attributes\":{\"overlay\":{\"id\":\"1822\"}},\"id\":\"1818\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"source\":{\"id\":\"1113\"}},\"id\":\"1118\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"red\",\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1851\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1819\",\"type\":\"SaveTool\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1113\"},\"glyph\":{\"id\":\"1114\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1116\"},\"nonselection_glyph\":{\"id\":\"1115\"},\"view\":{\"id\":\"1118\"}},\"id\":\"1117\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"2105\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1820\",\"type\":\"ResetTool\"},{\"attributes\":{\"tools\":[{\"id\":\"1562\"},{\"id\":\"1563\"},{\"id\":\"1564\"},{\"id\":\"1565\"},{\"id\":\"1566\"},{\"id\":\"1567\"},{\"id\":\"1698\"}]},\"id\":\"1569\",\"type\":\"Toolbar\"},{\"attributes\":{\"data\":{\"text\":[\"z\"],\"x\":[-88.0],\"y\":[0]},\"selected\":{\"id\":\"2174\"},\"selection_policy\":{\"id\":\"2173\"}},\"id\":\"1122\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1566\",\"type\":\"ResetTool\"},{\"attributes\":{\"tools\":[{\"id\":\"1816\"},{\"id\":\"1817\"},{\"id\":\"1818\"},{\"id\":\"1819\"},{\"id\":\"1820\"},{\"id\":\"1821\"}]},\"id\":\"1823\",\"type\":\"Toolbar\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_alpha\":{\"value\":0.2},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1116\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"1559\",\"type\":\"BasicTicker\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_alpha\":{\"value\":0.1},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1124\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"2106\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1567\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1562\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"2218\",\"type\":\"Selection\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1822\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"fill_alpha\":{\"value\":0},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0},\"height\":{\"value\":18.0},\"line_alpha\":{\"value\":0},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":72.0},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1162\",\"type\":\"Rect\"},{\"attributes\":{\"overlay\":{\"id\":\"1568\"}},\"id\":\"1564\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1664\"},\"N_stress_diag\":{\"id\":\"1644\"},\"V_stress_diag\":{\"id\":\"1684\"},\"axial_strain_diag\":{\"id\":\"1724\"},\"bending_strain_diag\":{\"id\":\"1746\"},\"centroid\":{\"id\":\"1676\"},\"div\":{\"id\":\"1107\"},\"neutral_axis\":{\"id\":\"1965\"},\"s_b\":{\"id\":\"1003\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1953\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1099\"},\"tau_stress_diag\":{\"id\":\"1704\"},\"total_strain_diag\":{\"id\":\"1931\"},\"total_strain_pl_diag\":{\"id\":\"1925\"},\"total_stress_pl_diag\":{\"id\":\"1919\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2001) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm*2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n 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// retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2001) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm*2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \"},\"id\":\"1969\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2191\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2028\",\"type\":\"AllLabels\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1003\"},\"glyph\":{\"id\":\"1084\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1086\"},\"nonselection_glyph\":{\"id\":\"1085\"},\"view\":{\"id\":\"1088\"}},\"id\":\"1087\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"2192\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"2193\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2184\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"axis_label\":\"Width b [mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"2080\"},\"group\":null,\"major_label_policy\":{\"id\":\"2081\"},\"ticker\":{\"id\":\"1080\"}},\"id\":\"1052\",\"type\":\"LinearAxis\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1664\"},\"N_stress_diag\":{\"id\":\"1644\"},\"V_stress_diag\":{\"id\":\"1684\"},\"axial_strain_diag\":{\"id\":\"1724\"},\"bending_strain_diag\":{\"id\":\"1746\"},\"centroid\":{\"id\":\"1676\"},\"div\":{\"id\":\"1107\"},\"neutral_axis\":{\"id\":\"1965\"},\"s_b\":{\"id\":\"1003\"},\"s_ss\":{\"id\":\"1006\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1953\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1099\"},\"tau_stress_diag\":{\"id\":\"1704\"},\"total_strain_diag\":{\"id\":\"1931\"},\"total_strain_pl_diag\":{\"id\":\"1925\"},\"total_stress_pl_diag\":{\"id\":\"1919\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const h = cb_obj.value // value of the slider\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2001) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \"},\"id\":\"1971\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2194\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"1358\"},\"N_stress_diag\":{\"id\":\"1644\"},\"arr_head\":{\"id\":\"1253\"},\"axial_strain_diag\":{\"id\":\"1724\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1871\"},\"label_N_section\":{\"id\":\"1865\"},\"label_V_section\":{\"id\":\"1877\"},\"neutral_axis\":{\"id\":\"1965\"},\"s_M\":{\"id\":\"1242\"},\"s_section_M\":{\"id\":\"1848\"},\"section_M_head\":{\"id\":\"1859\"},\"section_N\":{\"id\":\"1843\"},\"section_V\":{\"id\":\"1846\"},\"sigma_stress_diag\":{\"id\":\"1953\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1704\"},\"total_strain_diag\":{\"id\":\"1931\"},\"total_strain_pl_diag\":{\"id\":\"1925\"},\"total_stress_pl_diag\":{\"id\":\"1919\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=101) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2001) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm*2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \"},\"id\":\"1972\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2185\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1253\"},\"div_P\":{\"id\":\"1259\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1871\"},\"label_N_section\":{\"id\":\"1865\"},\"label_V_section\":{\"id\":\"1877\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1848\"},\"section_M_head\":{\"id\":\"1859\"},\"section_N\":{\"id\":\"1843\"},\"section_V\":{\"id\":\"1846\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1704\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1973\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1386\"},\"M_stress_diag\":{\"id\":\"1664\"},\"V_diag\":{\"id\":\"1372\"},\"V_stress_diag\":{\"id\":\"1684\"},\"arr_head\":{\"id\":\"1253\"},\"bending_strain_diag\":{\"id\":\"1746\"},\"centroid\":{\"id\":\"1676\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1871\"},\"label_N_section\":{\"id\":\"1865\"},\"label_V_section\":{\"id\":\"1877\"},\"neutral_axis\":{\"id\":\"1965\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_section_M\":{\"id\":\"1848\"},\"section_M_head\":{\"id\":\"1859\"},\"section_N\":{\"id\":\"1843\"},\"section_V\":{\"id\":\"1846\"},\"sigma_stress_diag\":{\"id\":\"1953\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1704\"},\"total_strain_diag\":{\"id\":\"1931\"},\"total_strain_pl_diag\":{\"id\":\"1925\"},\"total_stress_pl_diag\":{\"id\":\"1919\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2001) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm*2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \"},\"id\":\"1974\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2226\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"args\":{\"source\":{\"id\":\"1007\"},\"total_strain_diag\":{\"id\":\"1931\"},\"total_strain_pl_diag\":{\"id\":\"1925\"},\"total_stress_pl_diag\":{\"id\":\"1919\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const fy = cb_obj.value\\n const L = db['L'][0]\\n\\n // update q\\n db['fy'][0] = fy\\n\\n // update\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2001) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \"},\"id\":\"1975\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2084\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2227\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1664\"},\"N_stress_diag\":{\"id\":\"1644\"},\"axial_strain_diag\":{\"id\":\"1724\"},\"bending_strain_diag\":{\"id\":\"1746\"},\"centroid\":{\"id\":\"1676\"},\"source\":{\"id\":\"1007\"},\"total_strain_diag\":{\"id\":\"1931\"},\"total_strain_pl_diag\":{\"id\":\"1925\"},\"total_stress_pl_diag\":{\"id\":\"1919\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const E = cb_obj.value\\n\\n // update E\\n db['E'][0] = E\\n\\n // update\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2001) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n 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<p style='font-size:12px'>\\n f<sub>y,wood</sub> = 16 MPa; f<sub>y,concrete</sub> = 25 MPa<br>\\n f<sub>y,steel</sub> = 355 MPa; f<sub>y,glass</sub> = 1000 MPa</p>\\n \"},\"id\":\"1882\",\"type\":\"Div\"},{\"attributes\":{\"source\":{\"id\":\"1003\"}},\"id\":\"1379\",\"type\":\"CDSView\"},{\"attributes\":{\"axis_label\":\"Axial force N [kN]\",\"coordinates\":null,\"formatter\":{\"id\":\"2024\"},\"group\":null,\"major_label_policy\":{\"id\":\"2025\"},\"ticker\":{\"id\":\"1277\"}},\"id\":\"1276\",\"type\":\"LinearAxis\"},{\"attributes\":{\"end\":300000.0,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1976\"}]},\"margin\":[5,5,0,5],\"start\":8000.0,\"step\":1000.0,\"title\":\"Change the elastic modulus [MPa]\",\"value\":200000.0},\"id\":\"1879\",\"type\":\"Slider\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1384\",\"type\":\"Line\"},{\"attributes\":{\"axis\":{\"id\":\"1276\"},\"coordinates\":null,\"dimension\":1,\"group\":null,\"ticker\":null},\"id\":\"1279\",\"type\":\"Grid\"},{\"attributes\":{\"line_alpha\":0.1,\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1376\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1277\",\"type\":\"BasicTicker\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1377\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1889\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1283\",\"type\":\"SaveTool\"},{\"attributes\":{\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1375\",\"type\":\"Line\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1006\"},\"glyph\":{\"id\":\"1934\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1936\"},\"nonselection_glyph\":{\"id\":\"1935\"},\"view\":{\"id\":\"1938\"}},\"id\":\"1937\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1382\"},\"glyph\":{\"id\":\"1383\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1385\"},\"nonselection_glyph\":{\"id\":\"1384\"},\"view\":{\"id\":\"1387\"}},\"id\":\"1386\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"overlay\":{\"id\":\"1286\"}},\"id\":\"1282\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"1280\",\"type\":\"PanTool\"}],\"root_ids\":[\"1995\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n",
	+ " const render_items = [{\"docid\":\"c3f311ba-a0da-40e7-945f-9d5df57dacdd\",\"root_ids\":[\"1995\"],\"roots\":{\"1995\":\"b4d05515-c356-42ea-b8bb-80d4c028fd3a\"}}];\n",
	+ " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	+ "\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " let attempts = 0;\n",
	+ " const timer = setInterval(function(root) {\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " clearInterval(timer);\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " attempts++;\n",
	+ " if (attempts > 100) {\n",
	+ " clearInterval(timer);\n",
	+ " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	+ " }\n",
	+ " }\n",
	+ " }, 10, root)\n",
	+ " }\n",
	+ "})(window);"
	+ ],
	+ "application/vnd.bokehjs_exec.v0+json": ""
	+ },
	+ "metadata": {
	+ "application/vnd.bokehjs_exec.v0+json": {
	+ "id": "1995"
	+ }
	+ },
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "hidden_code_nb_plastic.main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, E_steel, fy, fy_steel, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Legend\n",
	+ "\n",
	+ "Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder.\n",
	+ "\n",
	+ "* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	+ "* Slider of height h: move the slider to change the height h of the cross-section of the beam.\n",
	+ "* Slider of the position x: move the slider to change the position x along the beam.\n",
	+ "* Slider of the uniform load q: move the slider to change the uniform load q.\n",
	+ "* Slider of the elastic modulus E: move the slider to change the elastic modulus of the section.\n",
	+ "* Slider of the yield strength $f_y$: move the slider to change the yield strength of the section.\n",
	+ "* Figure \"Simple supported beam\": in this figure, the initial state is presented with the static scheme, the length of the beam, the horizontal force P and the uniform load q.\n",
	+ "* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	+ "* Figure \"Forces and Moments Scheme\": this figure has a dynamic representation of the studied case with the position x indicated by a magenta dot, the internal forces shown in with red arrows, the reaction forces with yellow arrows, the external force P with a green arrow and the uniform load q in blue.\n",
	+ "* Radio buttons of the FBD: choose between right-hand or left-hand free-body diagram.\n",
	+ "* Button of the force P: apply or remove the external force P.\n",
	+ "* Figures \"N V M Diagrams\": plots that show the axial force N, shear force V and bending moment M diagrams, with a magenta dot that represents the x position. By hovering with the cursor over the desired position, a small window will show the position and the value of the internal force.\n",
	+ "* 10 small bottom figures: plots that show the strains, stresses and right-hand free-body diagram section (with N, V and M). By hovering with the cursor over the desired position, a small window will show the height and the value of the stress or strain.\n",
	+ "\n",
	+ "### Help and Information on the functions\n",
	+ "\n",
	+ "In Jupyter Notebooks the user can learn more about a function by using the question mark after the target function. One question mark shows some useful information on the function and two question marks show in addition also the code of the function, revealing it's content.\n",
	+ "For example, by creating a Code cell and pasting \"beam_section.compute_area?\" or \"beam_section.compute_area??\", it's possible to see how this feature works.\n",
	+ "\n",
	+ "### Recommendations\n",
	+ "\n",
	+ "If you have problem visualizing the entirety of the tool, you can maximize the window size by using Ctrl+B or Cmd+B to hide/show the left explorer panel and by using F11 to go to the full-page mode and back in the browser (NB: it could not work in the tab with NOTO; just use F11 in another tab and come back in the NOTO tab). If you're using a very sall display and it's not enough, you can zoom out the browser tab.\n",
	+ "\n",
	+ "Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully."
	+ ]
	+ }
	+ ],
	+ "metadata": {
	+ "interpreter": {
	+ "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	+ },
	+ "kernelspec": {
	+ "display_name": "Python 3 (ipykernel)",
	+ "language": "python",
	+ "name": "python3"
	+ },
	+ "language_info": {
	+ "codemirror_mode": {
	+ "name": "ipython",
	+ "version": 3
	+ },
	+ "file_extension": ".py",
	+ "mimetype": "text/x-python",
	+ "name": "python",
	+ "nbconvert_exporter": "python",
	+ "pygments_lexer": "ipython3",
	+ "version": "3.8.10"
	+ }
	+ },
	+ "nbformat": 4,
	+ "nbformat_minor": 4
	+}
	diff --git a/Simple Beam DEMOs/08-sb_deflection.ipynb b/Simple Beam DEMOs/08-sb_deflection.ipynb
	new file mode 100644
	index 0000000..77ff15c
	--- /dev/null
	+++ b/Simple Beam DEMOs/08-sb_deflection.ipynb
	@@ -0,0 +1,575 @@
	+{
	+ "cells": [
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "# Simple beam - Deflection\n",
	+ "In this eigth notebook, the deflection of a simple supported beam is studied. The system, geometry and actions are taken from the previous DEMO \"04-sb_stress\"."
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Goals\n",
	+ "\n",
	+ "* Explain how the deflection of a simple beam works\n",
	+ "* Identify the parameters directly influencing to the rigidity of the system\n",
	+ "* Describe the effect of the Young modulus E and it's importance for the design of an element"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Tasks and exercises\n",
	+ "\n",
	+ "Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	+ "\n",
	+ "1. Is it possible for the neutral axis to be located outside of the section?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " Yes, in the graphical tool it's possible to observe that when the bending stress are of the same magnitude of the axial stress (at the extremes with the starting configuration), the neautral axis is outside. This is possible only if an axial load is applied.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>\n",
	+ "\n",
	+ "2. Consider the starting configuration but with a square section (200 mm x 200 mm); change the height h and the width b and observe the deflection, axial, bending and shear stresses. How do these geometric parameters influence these values? \n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " First we note down the results with the square section. Secondly we change the width to 100 mm, then to 50 mm, we note the results and we reset the width to 200 mm. Then we change the height to 100 mm, to 400 mm and we note the results. By analysing the trends of the results with the changes of h and b we can conclude that:\n",
	+ " <ul>\n",
	+ " <li> Deflection: $ v \\propto 1/b \\cdot 1/h^3 $ </li>\n",
	+ " <li> Normal stress: $ \\sigma_N \\propto 1/b \\cdot 1/h $ </li>\n",
	+ " <li> Bending stress: $ \\sigma_M \\propto 1/b \\cdot 1/h^2 $ </li>\n",
	+ " <li> Shear stress: $ \\tau_V \\propto 1/b \\cdot 1/h $ </li>\n",
	+ " </ul>\n",
	+ " It is clear to see that the height plays an essential role. For this reason, the form is of the I beam is optimal.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Build the interactive visualisation tool"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 1,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ " <div class=\"bk-root\">\n",
	+ " <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	+ " <span id=\"1002\">Loading BokehJS ...</span>\n",
	+ " </div>"
	+ ]
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ },
	+ {
	+ "data": {
	+ "application/javascript": [
	+ "\n",
	+ "(function(root) {\n",
	+ " function now() {\n",
	+ " return new Date();\n",
	+ " }\n",
	+ "\n",
	+ " const force = true;\n",
	+ "\n",
	+ " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_onload_callbacks = [];\n",
	+ " root._bokeh_is_loading = undefined;\n",
	+ " }\n",
	+ "\n",
	+ " const JS_MIME_TYPE = 'application/javascript';\n",
	+ " const HTML_MIME_TYPE = 'text/html';\n",
	+ " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	+ " const CLASS_NAME = 'output_bokeh rendered_html';\n",
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	+ " /**\n",
	+ " * Render data to the DOM node\n",
	+ " */\n",
	+ " function render(props, node) {\n",
	+ " const script = document.createElement(\"script\");\n",
	+ " node.appendChild(script);\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
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	+ " */\n",
	+ " function handleClearOutput(event, handle) {\n",
	+ " const cell = handle.cell;\n",
	+ "\n",
	+ " const id = cell.output_area._bokeh_element_id;\n",
	+ " const server_id = cell.output_area._bokeh_server_id;\n",
	+ " // Clean up Bokeh references\n",
	+ " if (id != null && id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ "\n",
	+ " if (server_id !== undefined) {\n",
	+ " // Clean up Bokeh references\n",
	+ " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	+ " cell.notebook.kernel.execute(cmd_clean, {\n",
	+ " iopub: {\n",
	+ " output: function(msg) {\n",
	+ " const id = msg.content.text.trim();\n",
	+ " if (id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
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	+ " }\n",
	+ " });\n",
	+ " // Destroy server and session\n",
	+ " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	+ " cell.notebook.kernel.execute(cmd_destroy);\n",
	+ " }\n",
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	+ "\n",
	+ " /**\n",
	+ " * Handle when a new output is added\n",
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	+ " function handleAddOutput(event, handle) {\n",
	+ " const output_area = handle.output_area;\n",
	+ " const output = handle.output;\n",
	+ "\n",
	+ " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	+ " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	+ " return\n",
	+ " }\n",
	+ "\n",
	+ " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
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	+ " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	+ " // store reference to embed id on output_area\n",
	+ " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
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	+ " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	+ " const bk_div = document.createElement(\"div\");\n",
	+ " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	+ " const script_attrs = bk_div.children[0].attributes;\n",
	+ " for (let i = 0; i < script_attrs.length; i++) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	+ " }\n",
	+ " // store reference to server id on output_area\n",
	+ " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function register_renderer(events, OutputArea) {\n",
	+ "\n",
	+ " function append_mime(data, metadata, element) {\n",
	+ " // create a DOM node to render to\n",
	+ " const toinsert = this.create_output_subarea(\n",
	+ " metadata,\n",
	+ " CLASS_NAME,\n",
	+ " EXEC_MIME_TYPE\n",
	+ " );\n",
	+ " this.keyboard_manager.register_events(toinsert);\n",
	+ " // Render to node\n",
	+ " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	+ " render(props, toinsert[toinsert.length - 1]);\n",
	+ " element.append(toinsert);\n",
	+ " return toinsert\n",
	+ " }\n",
	+ "\n",
	+ " /* Handle when an output is cleared or removed */\n",
	+ " events.on('clear_output.CodeCell', handleClearOutput);\n",
	+ " events.on('delete.Cell', handleClearOutput);\n",
	+ "\n",
	+ " /* Handle when a new output is added */\n",
	+ " events.on('output_added.OutputArea', handleAddOutput);\n",
	+ "\n",
	+ " /**\n",
	+ " * Register the mime type and append_mime function with output_area\n",
	+ " */\n",
	+ " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	+ " /* Is output safe? */\n",
	+ " safe: true,\n",
	+ " /* Index of renderer in `output_area.display_order` */\n",
	+ " index: 0\n",
	+ " });\n",
	+ " }\n",
	+ "\n",
	+ " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	+ " if (root.Jupyter !== undefined) {\n",
	+ " const events = require('base/js/events');\n",
	+ " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	+ "\n",
	+ " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	+ " register_renderer(events, OutputArea);\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " \n",
	+ " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_timeout = Date.now() + 5000;\n",
	+ " root._bokeh_failed_load = false;\n",
	+ " }\n",
	+ "\n",
	+ " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	+ " \"<div style='background-color: #fdd'>\\n\"+\n",
	+ " \"<p>\\n\"+\n",
	+ " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	+ " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	+ " \"</p>\\n\"+\n",
	+ " \"<ul>\\n\"+\n",
	+ " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	+ " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	+ " \"</ul>\\n\"+\n",
	+ " \"<code>\\n\"+\n",
	+ " \"from bokeh.resources import INLINE\\n\"+\n",
	+ " \"output_notebook(resources=INLINE)\\n\"+\n",
	+ " \"</code>\\n\"+\n",
	+ " \"</div>\"}};\n",
	+ "\n",
	+ " function display_loaded() {\n",
	+ " const el = document.getElementById(\"1002\");\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS is loading...\";\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	+ " }\n",
	+ " } else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(display_loaded, 100)\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ "\n",
	+ " function run_callbacks() {\n",
	+ " try {\n",
	+ " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	+ " if (callback != null)\n",
	+ " callback();\n",
	+ " });\n",
	+ " } finally {\n",
	+ " delete root._bokeh_onload_callbacks\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: all callbacks have finished\");\n",
	+ " }\n",
	+ "\n",
	+ " function load_libs(css_urls, js_urls, callback) {\n",
	+ " if (css_urls == null) css_urls = [];\n",
	+ " if (js_urls == null) js_urls = [];\n",
	+ "\n",
	+ " root._bokeh_onload_callbacks.push(callback);\n",
	+ " if (root._bokeh_is_loading > 0) {\n",
	+ " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	+ " return null;\n",
	+ " }\n",
	+ " if (js_urls == null \|\| js_urls.length === 0) {\n",
	+ " run_callbacks();\n",
	+ " return null;\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	+ " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	+ "\n",
	+ " function on_load() {\n",
	+ " root._bokeh_is_loading--;\n",
	+ " if (root._bokeh_is_loading === 0) {\n",
	+ " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	+ " run_callbacks()\n",
	+ " }\n",
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	+ " element.rel = \"stylesheet\";\n",
	+ " element.type = \"text/css\";\n",
	+ " element.href = url;\n",
	+ " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
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	+ " }\n",
	+ "\n",
	+ " for (let i = 0; i < js_urls.length; i++) {\n",
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	+ "\n",
	+ " function inject_raw_css(css) {\n",
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	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "# Import the packages needed\n",
	+ "import sys\n",
	+ "sys.path.append('../HiddenCode')\n",
	+ "import hidden_code_nb_deflection\n",
	+ "import math\n",
	+ "import numpy as np\n",
	+ "from cienpy import simplebeam as sb\n",
	+ "from cienpy import rectangular_section as beam_section\n",
	+ "from cienpy import stress_strain_elastic as stst"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Define the geometry, the external actions, the mechanical property and compute the initial configuration."
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 2,
	+ "metadata": {},
	+ "outputs": [],
	+ "source": [
	+ "# Choose the dimensions\n",
	+ "L = 6 # [m]\n",
	+ "h = 200 # [mm]\n",
	+ "b = 100 # [mm]\n",
	+ "q = 4; # [kN/m]\n",
	+ "P = 10; # [kN]\n",
	+ "\n",
	+ "# Choose the material parameters\n",
	+ "E_steel = 200e3 # [MPa] steel\n",
	+ "fy_steel = 355 # [MPa] steel\n",
	+ "E = E_steel\n",
	+ "fy = fy_steel\n",
	+ "\n",
	+ "# compute the internal forces (at x=L)\n",
	+ "discr_NVM = 101\n",
	+ "x_discr = np.linspace(0, L, discr_NVM)\n",
	+ "N_discr = sb.compute_N(x_discr, P)\n",
	+ "V_discr = sb.compute_V(x_discr, q, L)\n",
	+ "M_discr = sb.compute_M(x_discr, q, L)\n",
	+ "N = N_discr[-1]\n",
	+ "V = V_discr[-1]\n",
	+ "M = M_discr[-1]\n",
	+ "\n",
	+ "# compute the parameters\n",
	+ "A = beam_section.compute_area(b, h) # [mm2]\n",
	+ "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	+ "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	+ "yG = beam_section.compute_centroid_y(h)\n",
	+ "y_n_axis = stst.compute_neutral_axis(N, A, Iy, M, yG)\n",
	+ "\n",
	+ "# compute the reactions\n",
	+ "Rx = sb.compute_Rx(P)\n",
	+ "Ry_l = sb.compute_Ry_l(q, L)\n",
	+ "Ry_r = sb.compute_Ry_r(q, L)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Run the complex code to generate the interactive visualisation tool:"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 3,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
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// retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_deflection_beam(db, beam_defl)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_deflection_beam(data, glyph_beam, discr=101) {\\n const q = data['q'][0]\\n const E = data['E'][0]\\n const L = data['L'][0]\\n const Iy = data['Iy'][0]\\n \\n const x = linspace(0, L, discr)\\n const defl = new Array(discr)\\n for(var i = 0; i < discr; i++) {\\n defl[i] = compute_deflection_uniform_load(x[i], q, L, Iy, E)\\n }\\n \\n const source = glyph_beam.data_source\\n source.data.x = x\\n source.data.y = defl\\n source.change.emit()\\n }\\n \\n \\n function compute_deflection_uniform_load(x, q, L, Iy, E) {\\n return -qx / (24EIy) (L*3-2Lx2+x3)1e12\\n }\\n \\n \"},\"id\":\"1910\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2131\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"fill_color\":{\"value\":\"orange\"},\"line_color\":{\"value\":\"orange\"},\"size\":{\"value\":17.954645502230758}},\"id\":\"1221\",\"type\":\"VeeHead\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1658\"},\"N_stress_diag\":{\"id\":\"1638\"},\"V_stress_diag\":{\"id\":\"1678\"},\"arr_head\":{\"id\":\"1247\"},\"axial_strain_diag\":{\"id\":\"1738\"},\"bending_strain_diag\":{\"id\":\"1760\"},\"centroid\":{\"id\":\"1670\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"neutral_axis\":{\"id\":\"1710\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1698\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \"},\"id\":\"1909\",\"type\":\"CustomJS\"},{\"attributes\":{\"axis_label\":\"Shear force V [kN]\",\"coordinates\":null,\"formatter\":{\"id\":\"1968\"},\"group\":null,\"major_label_policy\":{\"id\":\"1969\"},\"ticker\":{\"id\":\"1301\"}},\"id\":\"1300\",\"type\":\"LinearAxis\"},{\"attributes\":{\"fill_alpha\":0.2,\"fill_color\":\"blue\",\"hatch_alpha\":0.2,\"hatch_color\":\"navy\",\"line_alpha\":0.2,\"line_color\":\"navy\",\"x\":{\"field\":\"x_fade\"},\"y\":{\"field\":\"y\"}},\"id\":\"1215\",\"type\":\"Patch\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1859\"},\"group\":null,\"line_color\":{\"value\":\"red\"},\"line_width\":{\"value\":0.0},\"source\":{\"id\":\"2088\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1860\",\"type\":\"Arrow\"},{\"attributes\":{},\"id\":\"2132\",\"type\":\"Selection\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1218\"},\"group\":null,\"line_color\":{\"value\":\"green\"},\"line_width\":{\"value\":2.3978952727983707},\"source\":{\"id\":\"1947\"},\"start\":null,\"x_end\":{\"value\":60},\"x_start\":{\"value\":70},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1219\",\"type\":\"Arrow\"},{\"attributes\":{\"fill_alpha\":0.1,\"fill_color\":\"blue\",\"hatch_alpha\":0.1,\"hatch_color\":\"navy\",\"line_alpha\":0.1,\"line_color\":\"navy\",\"x\":{\"field\":\"x_fade\"},\"y\":{\"field\":\"y\"}},\"id\":\"1214\",\"type\":\"Patch\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1658\"},\"N_stress_diag\":{\"id\":\"1638\"},\"V_stress_diag\":{\"id\":\"1678\"},\"axial_strain_diag\":{\"id\":\"1738\"},\"beam_defl\":{\"id\":\"1897\"},\"bending_strain_diag\":{\"id\":\"1760\"},\"centroid\":{\"id\":\"1670\"},\"div\":{\"id\":\"1107\"},\"neutral_axis\":{\"id\":\"1710\"},\"s_b\":{\"id\":\"1003\"},\"s_ss\":{\"id\":\"1006\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1698\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1099\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const h = cb_obj.value // value of the slider\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_deflection_beam(db, beam_defl)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_deflection_beam(data, glyph_beam, discr=101) {\\n const q = data['q'][0]\\n const E = data['E'][0]\\n const L = data['L'][0]\\n const Iy = data['Iy'][0]\\n \\n const x = linspace(0, L, discr)\\n const defl = new Array(discr)\\n for(var i = 0; i < discr; i++) {\\n defl[i] = compute_deflection_uniform_load(x[i], q, L, Iy, E)\\n }\\n \\n const source = glyph_beam.data_source\\n source.data.x = x\\n source.data.y = defl\\n source.change.emit()\\n }\\n \\n \\n function compute_deflection_uniform_load(x, q, L, Iy, E) {\\n return -qx / (24EIy) * (L*3-2Lx2+x3)1e12\\n }\\n \\n \"},\"id\":\"1911\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_alpha\":0.1,\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1852\",\"type\":\"Line\"},{\"attributes\":{\"fill_color\":{\"value\":\"orange\"},\"line_color\":{\"value\":\"orange\"},\"size\":{\"value\":17.954645502230758}},\"id\":\"1224\",\"type\":\"VeeHead\"},{\"attributes\":{\"fill_color\":{\"value\":\"green\"},\"line_color\":{\"value\":\"green\"},\"size\":{\"value\":16.785266909588593}},\"id\":\"1218\",\"type\":\"VeeHead\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"1352\"},\"N_stress_diag\":{\"id\":\"1638\"},\"arr_head\":{\"id\":\"1247\"},\"axial_strain_diag\":{\"id\":\"1738\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"neutral_axis\":{\"id\":\"1710\"},\"s_M\":{\"id\":\"1236\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1698\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=101) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1912\",\"type\":\"CustomJS\"},{\"attributes\":{\"fill_color\":{\"value\":\"red\"},\"line_color\":{\"value\":\"red\"},\"size\":{\"value\":0.0}},\"id\":\"1230\",\"type\":\"VeeHead\"},{\"attributes\":{\"fill_color\":{\"value\":\"orange\"},\"line_color\":{\"value\":\"orange\"},\"size\":{\"value\":16.785266909588593}},\"id\":\"1227\",\"type\":\"VeeHead\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1247\"},\"div_P\":{\"id\":\"1253\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1913\",\"type\":\"CustomJS\"},{\"attributes\":{\"callback\":null,\"renderers\":[{\"id\":\"1658\"}],\"tooltips\":[[\"Stress\",\"@x MPa\"],[\"Height\",\"@y mm\"]]},\"id\":\"1672\",\"type\":\"HoverTool\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1230\"},\"group\":null,\"line_color\":{\"value\":\"red\"},\"line_width\":{\"value\":0.0},\"source\":{\"id\":\"1951\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1231\",\"type\":\"Arrow\"},{\"attributes\":{},\"id\":\"2060\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1528\",\"type\":\"HelpTool\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1221\"},\"group\":null,\"line_color\":{\"value\":\"orange\"},\"line_width\":{\"value\":2.5649493574615367},\"source\":{\"id\":\"1948\"},\"start\":null,\"x_end\":{\"value\":60},\"x_start\":{\"value\":60},\"y_end\":{\"value\":0},\"y_start\":{\"value\":-12.0}},\"id\":\"1222\",\"type\":\"Arrow\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1850\"},\"glyph\":{\"id\":\"1851\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1853\"},\"nonselection_glyph\":{\"id\":\"1852\"},\"view\":{\"id\":\"1855\"}},\"id\":\"1854\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1380\"},\"M_stress_diag\":{\"id\":\"1658\"},\"V_diag\":{\"id\":\"1366\"},\"V_stress_diag\":{\"id\":\"1678\"},\"arr_head\":{\"id\":\"1247\"},\"beam_defl\":{\"id\":\"1897\"},\"bending_strain_diag\":{\"id\":\"1760\"},\"centroid\":{\"id\":\"1670\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"neutral_axis\":{\"id\":\"1710\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1698\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1718\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_deflection_beam(db, beam_defl)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=101) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 101)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=201) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_deflection_beam(data, glyph_beam, discr=101) {\\n const q = data['q'][0]\\n const E = data['E'][0]\\n const L = data['L'][0]\\n const Iy = data['Iy'][0]\\n \\n const x = linspace(0, L, discr)\\n const defl = new Array(discr)\\n for(var i = 0; i < discr; i++) {\\n defl[i] = compute_deflection_uniform_load(x[i], q, L, Iy, E)\\n }\\n \\n const source = glyph_beam.data_source\\n source.data.x = x\\n source.data.y = defl\\n source.change.emit()\\n }\\n \\n \\n function compute_deflection_uniform_load(x, q, L, Iy, E) {\\n return -qx / (24EIy) (L*3-2Lx2+x3)1e12\\n }\\n \\n \"},\"id\":\"1914\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1233\"},\"group\":null,\"line_color\":{\"value\":\"red\"},\"line_width\":{\"value\":0.0},\"source\":{\"id\":\"1952\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1234\",\"type\":\"Arrow\"},{\"attributes\":{},\"id\":\"2023\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2163\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1224\"},\"group\":null,\"line_color\":{\"value\":\"orange\"},\"line_width\":{\"value\":2.5649493574615367},\"source\":{\"id\":\"1949\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":-12.0}},\"id\":\"1225\",\"type\":\"Arrow\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1658\"},\"N_stress_diag\":{\"id\":\"1638\"},\"axial_strain_diag\":{\"id\":\"1738\"},\"beam_defl\":{\"id\":\"1897\"},\"bending_strain_diag\":{\"id\":\"1760\"},\"centroid\":{\"id\":\"1670\"},\"source\":{\"id\":\"1007\"}},\"code\":\"\\n 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<p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = 200 mm<br>\\n b = 100 mm<br>\\n L = 6 m<br>\\n A = 2.00e+04 mm<sup>2</sup><br>\\n Iy = 6.67e+07 mm<sup>4</sup><br>\\n Iz = 1.67e+07 mm<sup>4</sup>\",\"width\":170},\"id\":\"1107\",\"type\":\"Div\"},{\"attributes\":{\"desired_num_ticks\":3,\"num_minor_ticks\":2},\"id\":\"1774\",\"type\":\"AdaptiveTicker\"},{\"attributes\":{\"source\":{\"id\":\"1101\"}},\"id\":\"1106\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"2156\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"data\":{\"x\":[-30.0,30.0],\"y\":[100.0,100.0]},\"selected\":{\"id\":\"2147\"},\"selection_policy\":{\"id\":\"2146\"}},\"id\":\"1666\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1988\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2157\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1989\",\"type\":\"Selection\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1663\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"2118\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2083\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"2084\",\"type\":\"AllLabels\"},{\"attributes\":{\"source\":{\"id\":\"1006\"}},\"id\":\"1665\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1955\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"2086\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1956\",\"type\":\"AllLabels\"},{\"attributes\":{},\"id\":\"1420\",\"type\":\"BasicTicker\"},{\"attributes\":{\"line_dash\":[4,4],\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1667\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"2087\",\"type\":\"AllLabels\"}],\"root_ids\":[\"1933\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n",
	+ " const render_items = [{\"docid\":\"1ba41f57-afc1-4c1f-adbd-445e1b83b0a8\",\"root_ids\":[\"1933\"],\"roots\":{\"1933\":\"4e250a96-0fc2-4305-9bd2-13fa7feefc9d\"}}];\n",
	+ " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	+ "\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " let attempts = 0;\n",
	+ " const timer = setInterval(function(root) {\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " clearInterval(timer);\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " attempts++;\n",
	+ " if (attempts > 100) {\n",
	+ " clearInterval(timer);\n",
	+ " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	+ " }\n",
	+ " }\n",
	+ " }, 10, root)\n",
	+ " }\n",
	+ "})(window);"
	+ ],
	+ "application/vnd.bokehjs_exec.v0+json": ""
	+ },
	+ "metadata": {
	+ "application/vnd.bokehjs_exec.v0+json": {
	+ "id": "1933"
	+ }
	+ },
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "hidden_code_nb_deflection.main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, E_steel, fy, fy_steel, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Legend\n",
	+ "\n",
	+ "Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder.\n",
	+ "\n",
	+ "* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	+ "* Slider of height h: move the slider to change the height h of the cross-section of the beam.\n",
	+ "* Slider of the position x: move the slider to change the position x along the beam.\n",
	+ "* Slider of the uniform load q: move the slider to change the uniform load q.\n",
	+ "* Slider of the elastic modulus E: move the slider to change the elastic modulus of the section.\n",
	+ "* Figure \"Simple supported beam with deflection under uniform load\": in this figure, the initial state is presented with the static scheme, the length of the beam, the horizontal force P and the uniform load q. In addition the beam can deform, showing the deflection graphically and quantitatively (by hoving over the beam with the cursor).\n",
	+ "* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	+ "* Figure \"Forces and Moments Scheme\": this figure has a dynamic representation of the studied case with the position x indicated by a magenta dot, the internal forces shown in with red arrows, the reaction forces with yellow arrows, the external force P with a green arrow and the uniform load q in blue.\n",
	+ "* Radio buttons of the FBD: choose between right-hand or left-hand free-body diagram.\n",
	+ "* Button of the force P: apply or remove the external force P.\n",
	+ "* Figures \"N V M Diagrams\": plots that show the axial force N, shear force V and bending moment M diagrams, with a magenta dot that represents the x position. By hovering with the cursor over the desired position, a small window will show the position and the value of the internal force.\n",
	+ "* 9 small bottom figures: plots that show the strains, stresses and right-hand free-body diagram section (with N, V and M). By hovering with the cursor over the desired position, a small window will show the height and the value of the stress or strain.\n",
	+ "\n",
	+ "### Help and Information on the functions\n",
	+ "\n",
	+ "In Jupyter Notebooks the user can learn more about a function by using the question mark after the target function. One question mark shows some useful information on the function and two question marks show in addition also the code of the function, revealing it's content.\n",
	+ "For example, by creating a Code cell and pasting \"beam_section.compute_area?\" or \"beam_section.compute_area??\", it's possible to see how this feature works.\n",
	+ "\n",
	+ "### Recommendations\n",
	+ "\n",
	+ "If you have problem visualizing the entirety of the tool, you can maximize the window size by using Ctrl+B or Cmd+B to hide/show the left explorer panel and by using F11 to go to the full-page mode and back in the browser (NB: it could not work in the tab with NOTO; just use F11 in another tab and come back in the NOTO tab). If you're using a very sall display and it's not enough, you can zoom out the browser tab.\n",
	+ "\n",
	+ "Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully."
	+ ]
	+ }
	+ ],
	+ "metadata": {
	+ "interpreter": {
	+ "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	+ },
	+ "kernelspec": {
	+ "display_name": "Python 3 (ipykernel)",
	+ "language": "python",
	+ "name": "python3"
	+ },
	+ "language_info": {
	+ "codemirror_mode": {
	+ "name": "ipython",
	+ "version": 3
	+ },
	+ "file_extension": ".py",
	+ "mimetype": "text/x-python",
	+ "name": "python",
	+ "nbconvert_exporter": "python",
	+ "pygments_lexer": "ipython3",
	+ "version": "3.8.10"
	+ }
	+ },
	+ "nbformat": 4,
	+ "nbformat_minor": 4
	+}
	diff --git a/Simple Beam DEMOs/09-sb_buckling.ipynb b/Simple Beam DEMOs/09-sb_buckling.ipynb
	new file mode 100644
	index 0000000..eff2ef2
	--- /dev/null
	+++ b/Simple Beam DEMOs/09-sb_buckling.ipynb
	@@ -0,0 +1,592 @@
	+{
	+ "cells": [
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "# Simple beam - Buckling\n",
	+ "In this last notebook, the instability of a simple beam under constant axial load is studied. The system, geometry and actions are taken from the previous DEMO \"02-sb_actions\" except for the uniform load that is removed."
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Goals\n",
	+ "\n",
	+ "* Explore the concept of instability of an element\n",
	+ "* Identify the major aspects of the buckling phenomena\n",
	+ "* Describe the consequences of the instability in the design of an element"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Tasks and exercises\n",
	+ "\n",
	+ "Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	+ "\n",
	+ "1. Why do the interactive visualization tool emphasizes on analysing the beam in the two planes x-y and x-z?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " In the analysis of an element under axial load that can buckle, it's essential to study individually the strong and weak axis instability, because one is independent of the other one.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>\n",
	+ "\n",
	+ "2. Consider the starting configuration with an axial force of 200 kN; the section is composed of a material with a yield strength $f_y$ = 50 MPa.\n",
	+ "\n",
	+ " 1. Does the section yield under the axial load?\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " No, because the axial load $P$ is 350 kN and the resisting axial force $N_{Ry}$ is computed below:\n",
	+ " $$ N_{Ry} = Af_y = bhf_y = 250 kN $$\n",
	+ " Given that the axial load is smaller that the resisting axial force, we can conlude that the section does not yield under axial load.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ " \n",
	+ " 2. Can you assume that the element is designed correctly? If not, what would you change to avoid collapse of the beam?\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " As seen in the previous question, the section does not yield under axial load, but it's possible to observe in the tool that in the x-z plane, the beam buckles under the force P. The beam is unstable and will collapse under the slightest out-of-plane perturbation. It's essential to underline that the real elements that engineers design always have imprecisions (during constructions, during production, etc), thus the beam is not designed correctly.\n",
	+ " <br>\n",
	+ " There are different solutions to avoid the collapse:\n",
	+ " <ul>\n",
	+ " <li> Increase the height of the section beyond 300 mm (at least 440 mm) </li>\n",
	+ " <li> Increase the width of the section to 80 mm </li>\n",
	+ " <li> Decrease the length of the beam to 3.2 m </li>\n",
	+ " <li> Add one brace in the middle of the beam </li>\n",
	+ " </ul>\n",
	+ " Note that increasing the resistance of the material has <strong>no positive impact</strong> in the instability.\n",
	+ " </details>\n",
	+ "\n",
	+ " <br>\n",
	+ "\n",
	+ "3. Is it possible to compute analytically the amount of out-of-plane deflection due to buckling?\n",
	+ "\n",
	+ " <details>\n",
	+ " <summary style=\"color: red\">Solution:</summary>\n",
	+ " No, because the analitic shape of a buckled element is based on the following differential equation:\n",
	+ " $$ \\frac{d^2v}{dx^2} + k^2v = 0 $$\n",
	+ " With $v$ the deflection out-of-plane, $x$ the position across the element and $k = \\frac{N}{EI}$. The general solution of this equation is:\n",
	+ " $$ y = C_1sinkx + C_2coskx $$\n",
	+ " With $C_1$ and $C_2$ the constants of integration. It is not possible to compute the value of these constants; even so, this equation is important to extrapolate the mode shape of buckling.\n",
	+ " </details>\n",
	+ "\n",
	+ "<br>\n"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "## Build the interactive visualisation tool"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 1,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
	+ "text/html": [
	+ "\n",
	+ " <div class=\"bk-root\">\n",
	+ " <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	+ " <span id=\"1002\">Loading BokehJS ...</span>\n",
	+ " </div>"
	+ ]
	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ },
	+ {
	+ "data": {
	+ "application/javascript": [
	+ "\n",
	+ "(function(root) {\n",
	+ " function now() {\n",
	+ " return new Date();\n",
	+ " }\n",
	+ "\n",
	+ " const force = true;\n",
	+ "\n",
	+ " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_onload_callbacks = [];\n",
	+ " root._bokeh_is_loading = undefined;\n",
	+ " }\n",
	+ "\n",
	+ " const JS_MIME_TYPE = 'application/javascript';\n",
	+ " const HTML_MIME_TYPE = 'text/html';\n",
	+ " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	+ " const CLASS_NAME = 'output_bokeh rendered_html';\n",
	+ "\n",
	+ " /**\n",
	+ " * Render data to the DOM node\n",
	+ " */\n",
	+ " function render(props, node) {\n",
	+ " const script = document.createElement(\"script\");\n",
	+ " node.appendChild(script);\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
	+ " * Handle when an output is cleared or removed\n",
	+ " */\n",
	+ " function handleClearOutput(event, handle) {\n",
	+ " const cell = handle.cell;\n",
	+ "\n",
	+ " const id = cell.output_area._bokeh_element_id;\n",
	+ " const server_id = cell.output_area._bokeh_server_id;\n",
	+ " // Clean up Bokeh references\n",
	+ " if (id != null && id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ "\n",
	+ " if (server_id !== undefined) {\n",
	+ " // Clean up Bokeh references\n",
	+ " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	+ " cell.notebook.kernel.execute(cmd_clean, {\n",
	+ " iopub: {\n",
	+ " output: function(msg) {\n",
	+ " const id = msg.content.text.trim();\n",
	+ " if (id in Bokeh.index) {\n",
	+ " Bokeh.index[id].model.document.clear();\n",
	+ " delete Bokeh.index[id];\n",
	+ " }\n",
	+ " }\n",
	+ " }\n",
	+ " });\n",
	+ " // Destroy server and session\n",
	+ " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	+ " cell.notebook.kernel.execute(cmd_destroy);\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " /**\n",
	+ " * Handle when a new output is added\n",
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	+ " function handleAddOutput(event, handle) {\n",
	+ " const output_area = handle.output_area;\n",
	+ " const output = handle.output;\n",
	+ "\n",
	+ " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	+ " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	+ " return\n",
	+ " }\n",
	+ "\n",
	+ " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
	+ "\n",
	+ " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	+ " // store reference to embed id on output_area\n",
	+ " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
	+ " }\n",
	+ " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	+ " const bk_div = document.createElement(\"div\");\n",
	+ " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	+ " const script_attrs = bk_div.children[0].attributes;\n",
	+ " for (let i = 0; i < script_attrs.length; i++) {\n",
	+ " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	+ " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	+ " }\n",
	+ " // store reference to server id on output_area\n",
	+ " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " function register_renderer(events, OutputArea) {\n",
	+ "\n",
	+ " function append_mime(data, metadata, element) {\n",
	+ " // create a DOM node to render to\n",
	+ " const toinsert = this.create_output_subarea(\n",
	+ " metadata,\n",
	+ " CLASS_NAME,\n",
	+ " EXEC_MIME_TYPE\n",
	+ " );\n",
	+ " this.keyboard_manager.register_events(toinsert);\n",
	+ " // Render to node\n",
	+ " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	+ " render(props, toinsert[toinsert.length - 1]);\n",
	+ " element.append(toinsert);\n",
	+ " return toinsert\n",
	+ " }\n",
	+ "\n",
	+ " /* Handle when an output is cleared or removed */\n",
	+ " events.on('clear_output.CodeCell', handleClearOutput);\n",
	+ " events.on('delete.Cell', handleClearOutput);\n",
	+ "\n",
	+ " /* Handle when a new output is added */\n",
	+ " events.on('output_added.OutputArea', handleAddOutput);\n",
	+ "\n",
	+ " /**\n",
	+ " * Register the mime type and append_mime function with output_area\n",
	+ " */\n",
	+ " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	+ " /* Is output safe? */\n",
	+ " safe: true,\n",
	+ " /* Index of renderer in `output_area.display_order` */\n",
	+ " index: 0\n",
	+ " });\n",
	+ " }\n",
	+ "\n",
	+ " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	+ " if (root.Jupyter !== undefined) {\n",
	+ " const events = require('base/js/events');\n",
	+ " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	+ "\n",
	+ " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	+ " register_renderer(events, OutputArea);\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ " \n",
	+ " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	+ " root._bokeh_timeout = Date.now() + 5000;\n",
	+ " root._bokeh_failed_load = false;\n",
	+ " }\n",
	+ "\n",
	+ " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	+ " \"<div style='background-color: #fdd'>\\n\"+\n",
	+ " \"<p>\\n\"+\n",
	+ " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	+ " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	+ " \"</p>\\n\"+\n",
	+ " \"<ul>\\n\"+\n",
	+ " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	+ " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	+ " \"</ul>\\n\"+\n",
	+ " \"<code>\\n\"+\n",
	+ " \"from bokeh.resources import INLINE\\n\"+\n",
	+ " \"output_notebook(resources=INLINE)\\n\"+\n",
	+ " \"</code>\\n\"+\n",
	+ " \"</div>\"}};\n",
	+ "\n",
	+ " function display_loaded() {\n",
	+ " const el = document.getElementById(\"1002\");\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS is loading...\";\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " if (el != null) {\n",
	+ " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	+ " }\n",
	+ " } else if (Date.now() < root._bokeh_timeout) {\n",
	+ " setTimeout(display_loaded, 100)\n",
	+ " }\n",
	+ " }\n",
	+ "\n",
	+ "\n",
	+ " function run_callbacks() {\n",
	+ " try {\n",
	+ " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	+ " if (callback != null)\n",
	+ " callback();\n",
	+ " });\n",
	+ " } finally {\n",
	+ " delete root._bokeh_onload_callbacks\n",
	+ " }\n",
	+ " console.debug(\"Bokeh: all callbacks have finished\");\n",
	+ " }\n",
	+ "\n",
	+ " function load_libs(css_urls, js_urls, callback) {\n",
	+ " if (css_urls == null) css_urls = [];\n",
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	+ },
	+ "metadata": {},
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "# Import the packages needed\n",
	+ "import sys\n",
	+ "sys.path.append('../HiddenCode')\n",
	+ "import hidden_code_nb_buckling\n",
	+ "import numpy as np\n",
	+ "import math\n",
	+ "from cienpy import simplebeam as sb\n",
	+ "from cienpy import rectangular_section as beam_section\n",
	+ "from cienpy import buckling"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Define the geometry, the external actions, the mechanical property and compute the initial configuration."
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 2,
	+ "metadata": {},
	+ "outputs": [],
	+ "source": [
	+ "# Choose the dimensions\n",
	+ "L = 6 # [m]\n",
	+ "h = 100 # [mm]\n",
	+ "b = 50 # [mm]\n",
	+ "P = 10; # [kN]\n",
	+ "\n",
	+ "# Material parameter\n",
	+ "E = 200e3 # MPa\n",
	+ "\n",
	+ "# compute the internal forces (at x=L)\n",
	+ "discr_NVM = 101\n",
	+ "x_discr = np.linspace(0, L, discr_NVM)\n",
	+ "N = sb.compute_N(L, P)\n",
	+ "\n",
	+ "# compute the parameters\n",
	+ "A = beam_section.compute_area(b, h) # [mm2]\n",
	+ "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	+ "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	+ "\n",
	+ "# compute the reactions\n",
	+ "Rx = sb.compute_Rx(P)\n",
	+ "\n",
	+ "# compute buckling resistance\n",
	+ "n_bracey = 0\n",
	+ "n_bracez = 0\n",
	+ "Ncrity = buckling.compute_N_buckling_y(E, Iy, L, n_bracey)\n",
	+ "Ncritz = buckling.compute_N_buckling_z(E, Iz, L, n_bracez)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {},
	+ "source": [
	+ "Run the complex code to generate the interactive visualisation tool:"
	+ ]
	+ },
	+ {
	+ "cell_type": "code",
	+ "execution_count": 3,
	+ "metadata": {},
	+ "outputs": [
	+ {
	+ "data": {
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[m]\",\"coordinates\":null,\"formatter\":{\"id\":\"1384\"},\"group\":null,\"major_label_policy\":{\"id\":\"1385\"},\"ticker\":{\"id\":\"1247\"}},\"id\":\"1246\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1247\",\"type\":\"BasicTicker\"},{\"attributes\":{\"coordinates\":null,\"formatter\":{\"id\":\"1381\"},\"group\":null,\"major_label_policy\":{\"id\":\"1382\"},\"ticker\":{\"id\":\"1251\"},\"visible\":false},\"id\":\"1250\",\"type\":\"LinearAxis\"},{\"attributes\":{\"axis\":{\"id\":\"1250\"},\"coordinates\":null,\"dimension\":1,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1253\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1251\",\"type\":\"BasicTicker\"},{\"attributes\":{\"data\":{\"x\":[],\"y\":[]},\"selected\":{\"id\":\"1442\"},\"selection_policy\":{\"id\":\"1441\"}},\"id\":\"1331\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1255\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1254\",\"type\":\"PanTool\"},{\"attributes\":{\"overlay\":{\"id\":\"1260\"}},\"id\":\"1256\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"1257\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1402\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1258\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1403\",\"type\":\"Selection\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1260\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"tools\":[{\"id\":\"1254\"},{\"id\":\"1255\"},{\"id\":\"1256\"},{\"id\":\"1257\"},{\"id\":\"1258\"},{\"id\":\"1259\"}]},\"id\":\"1261\",\"type\":\"Toolbar\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"red\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_color\":{\"value\":\"red\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"red\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1333\",\"type\":\"Circle\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"red\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_color\":{\"value\":\"red\"},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"red\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1334\",\"type\":\"Circle\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1331\"},\"glyph\":{\"id\":\"1332\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1334\"},\"nonselection_glyph\":{\"id\":\"1333\"},\"view\":{\"id\":\"1336\"}},\"id\":\"1335\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"1331\"}},\"id\":\"1336\",\"type\":\"CDSView\"},{\"attributes\":{\"text_color\":{\"value\":\"green\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1129\",\"type\":\"Text\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"gray\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1314\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1057\",\"type\":\"PanTool\"},{\"attributes\":{\"text\":\"\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = 10 kN<br>\\n Rx = 10 kN<br>\\n N = -10 kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = 228.46 kN<br>\\n N<sub>crit,z</sub> = 57.12 kN<br>\\n Instability: No\\n \",\"width\":170},\"id\":\"1324\",\"type\":\"Div\"},{\"attributes\":{},\"id\":\"1058\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"below\":[{\"id\":\"1145\"}],\"center\":[{\"id\":\"1148\"},{\"id\":\"1152\"},{\"id\":\"1186\"},{\"id\":\"1213\"},{\"id\":\"1222\"}],\"height\":200,\"left\":[{\"id\":\"1149\"}],\"min_border_left\":0,\"renderers\":[{\"id\":\"1171\"},{\"id\":\"1177\"},{\"id\":\"1183\"},{\"id\":\"1192\"},{\"id\":\"1219\"},{\"id\":\"1228\"}],\"title\":{\"id\":\"1135\"},\"toolbar\":{\"id\":\"1160\"},\"toolbar_location\":null,\"width\":700,\"x_range\":{\"id\":\"1008\"},\"x_scale\":{\"id\":\"1141\"},\"y_range\":{\"id\":\"1139\"},\"y_scale\":{\"id\":\"1143\"}},\"id\":\"1134\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1321\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1062\",\"type\":\"HelpTool\"},{\"attributes\":{\"source\":{\"id\":\"1128\"}},\"id\":\"1133\",\"type\":\"CDSView\"},{\"attributes\":{\"line_color\":\"gray\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1313\",\"type\":\"Line\"},{\"attributes\":{\"data\":{\"text\":[\"P\"],\"x\":[6.5],\"y\":[0.2]},\"selected\":{\"id\":\"1405\"},\"selection_policy\":{\"id\":\"1404\"}},\"id\":\"1128\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"gray\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1315\",\"type\":\"Line\"},{\"attributes\":{\"overlay\":{\"id\":\"1063\"}},\"id\":\"1059\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1319\",\"type\":\"Line\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1128\"},\"glyph\":{\"id\":\"1129\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1131\"},\"nonselection_glyph\":{\"id\":\"1130\"},\"view\":{\"id\":\"1133\"}},\"id\":\"1132\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"1003\"}},\"id\":\"1317\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1060\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1061\",\"type\":\"ResetTool\"},{\"attributes\":{\"text_alpha\":{\"value\":0.1},\"text_color\":{\"value\":\"green\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1130\",\"type\":\"Text\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1104\"},\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"section\":{\"id\":\"1102\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const h = cb_obj.value // value of the slider\\n const b = db['b'][0]\\n const L = db['L'][0]\\n const E = db['E'][0]\\n const n_bracey = db['n_bracey'][0]\\n const n_bracez = db['n_bracez'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const Iz = compute_inertia_z(b, h)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = Iz\\n db['Ncrity'][0] = compute_N_buckling_y(E, Iy, L, n_bracey)\\n db['Ncritz'][0] = compute_N_buckling_z(E, Iz, L, n_bracez)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_div_buckling(db, div_buckling)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)*2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=101, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1338\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1003\"},\"glyph\":{\"id\":\"1168\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1170\"},\"nonselection_glyph\":{\"id\":\"1169\"},\"view\":{\"id\":\"1172\"}},\"id\":\"1171\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1318\"},\"glyph\":{\"id\":\"1319\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1321\"},\"nonselection_glyph\":{\"id\":\"1320\"},\"view\":{\"id\":\"1323\"}},\"id\":\"1322\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1439\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"green\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1131\",\"type\":\"Text\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1063\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1185\"},\"group\":null,\"line_color\":{\"value\":\"green\"},\"line_width\":{\"value\":2.3978952727983707},\"source\":{\"id\":\"1377\"},\"start\":null,\"x_end\":{\"value\":6},\"x_start\":{\"value\":7.0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1186\",\"type\":\"Arrow\"},{\"attributes\":{\"data\":{\"x\":[0,6],\"y\":[0,0]},\"selected\":{\"id\":\"1440\"},\"selection_policy\":{\"id\":\"1439\"}},\"id\":\"1318\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"axis_label\":\"Position [m]\",\"coordinates\":null,\"formatter\":{\"id\":\"1375\"},\"group\":null,\"major_label_policy\":{\"id\":\"1376\"},\"ticker\":{\"id\":\"1146\"}},\"id\":\"1145\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1440\",\"type\":\"Selection\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Simple supported beam: x-z plane\"},\"id\":\"1135\",\"type\":\"Title\"},{\"attributes\":{\"source\":{\"id\":\"1318\"}},\"id\":\"1323\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1158\",\"type\":\"HelpTool\"},{\"attributes\":{\"line_alpha\":0.1,\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1320\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1143\",\"type\":\"LinearScale\"},{\"attributes\":{\"line_width\":6,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1081\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1146\",\"type\":\"BasicTicker\"},{\"attributes\":{\"axis\":{\"id\":\"1145\"},\"coordinates\":null,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1148\",\"type\":\"Grid\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_alpha\":{\"value\":0.2},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1122\",\"type\":\"Text\"},{\"attributes\":{\"coordinates\":null,\"formatter\":{\"id\":\"1372\"},\"group\":null,\"major_label_policy\":{\"id\":\"1373\"},\"ticker\":{\"id\":\"1150\"},\"visible\":false},\"id\":\"1149\",\"type\":\"LinearAxis\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1104\"},\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"section\":{\"id\":\"1102\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const L = db['L'][0]\\n const E = db['E'][0]\\n const n_bracey = db['n_bracey'][0]\\n const n_bracez = db['n_bracez'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const Iz = compute_inertia_z(b, h)\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = Iz\\n db['Ncrity'][0] = compute_N_buckling_y(E, Iy, L, n_bracey)\\n db['Ncritz'][0] = compute_N_buckling_z(E, Iz, L, n_bracez)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_div_buckling(db, div_buckling)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)*2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=101, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1337\",\"type\":\"CustomJS\"},{\"attributes\":{\"axis\":{\"id\":\"1149\"},\"coordinates\":null,\"dimension\":1,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1152\",\"type\":\"Grid\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":6,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1083\",\"type\":\"Line\"},{\"attributes\":{\"args\":{\"axial_force_y\":{\"id\":\"1126\"},\"axial_force_z\":{\"id\":\"1186\"},\"div\":{\"id\":\"1104\"},\"div_buckling\":{\"id\":\"1324\"},\"label_P_force_y\":{\"id\":\"1132\"},\"label_P_force_z\":{\"id\":\"1192\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"point_brace_y\":{\"id\":\"1329\"},\"point_brace_z\":{\"id\":\"1335\"},\"s_b\":{\"id\":\"1003\"},\"source\":{\"id\":\"1004\"},\"support_r_y\":{\"id\":\"1096\"},\"support_r_z\":{\"id\":\"1183\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_b = s_b.data\\n const L = cb_obj.value // value of the slider\\n const E = db['E'][0]\\n const Iy = db['Iy'][0]\\n const Iz = db['Iz'][0]\\n const n_bracey = db['n_bracey'][0]\\n const n_bracez = db['n_bracez'][0]\\n\\n // apply the changes\\n data_b['x'][1] = L\\n db['L'][0] = L\\n db['Ncrity'][0] = compute_N_buckling_y(E, Iy, L, n_bracey)\\n db['Ncritz'][0] = compute_N_buckling_z(E, Iz, L, n_bracez)\\n\\n // update\\n update_div_geo(db, div)\\n update_div_buckling(db, div_buckling)\\n support_r_y.glyph.x = L\\n support_r_z.glyph.x = L\\n axial_force_y.x_start = L+1.0\\n axial_force_y.x_end = L\\n label_P_force_y.glyph.x = L+1.0/2\\n axial_force_z.x_start = L+1.0\\n axial_force_z.x_end = L\\n label_P_force_z.glyph.x = L+1.0/2\\n update_point_brace(point_brace_y, n_bracey)\\n update_point_brace(point_brace_z, n_bracez)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n s_b.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)*2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function update_point_brace(point_brace, n_brace) {\\n switch(n_brace) {\\n case 0:\\n var x_ = []\\n var y_ = []\\n break\\n case 1:\\n var x_ = [L/2]\\n var y_ = [0]\\n break\\n case 2:\\n var x_ = [L/3, 2L/3]\\n var y_ = [0, 0]\\n break\\n default:\\n console.error(\\\"Number of braces \\\"+n_brace+\\\" exceeds the implemented limit (2)\\\")\\n }\\n const src_point = point_brace.data_source\\n src_point.data.x = x_\\n src_point.data.y = y_\\n src_point.change.emit()\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=101, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1339\",\"type\":\"CustomJS\"},{\"attributes\":{\"fill_alpha\":0.1,\"fill_color\":\"white\",\"hatch_alpha\":0.1,\"line_alpha\":0.1,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1088\",\"type\":\"Patch\"},{\"attributes\":{},\"id\":\"1150\",\"type\":\"BasicTicker\"},{\"attributes\":{\"fill_alpha\":0.1,\"fill_color\":\"white\",\"hatch_alpha\":0.1,\"line_alpha\":0.1,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1175\",\"type\":\"Patch\"},{\"attributes\":{\"args\":{\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n const db = source.data\\n const P = cb_obj.value // value of the slider\\n\\n // apply the changes\\n db['P'][0] = P\\n db['N'][0] = compute_N(P)\\n db['Rx'][0] = compute_Rx(P)\\n\\n // update\\n update_div_buckling(db, div_buckling)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=101, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1340\",\"type\":\"CustomJS\"},{\"attributes\":{\"fill_color\":{\"value\":\"white\"},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":100},\"line_width\":{\"value\":3},\"width\":{\"value\":50},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1099\",\"type\":\"Rect\"},{\"attributes\":{},\"id\":\"1154\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"args\":{\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"point_brace\":{\"id\":\"1329\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const n_brace = cb_obj.active\\n const E = db['E'][0]\\n const L = db['L'][0]\\n const I = db['Iy'][0]\\n\\n // apply the changes\\n db['n_bracey'][0] = n_brace\\n db['Ncrity'][0] = compute_N_buckling_y(E, I, L, n_brace)\\n\\n // update\\n update_div_buckling(db, div_buckling)\\n update_point_brace(point_brace, n_brace)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function update_point_brace(point_brace, n_brace) {\\n switch(n_brace) {\\n case 0:\\n var x_ = []\\n var y_ = []\\n break\\n case 1:\\n var x_ = [L/2]\\n var y_ = [0]\\n break\\n case 2:\\n var x_ = [L/3, 2L/3]\\n var y_ = [0, 0]\\n break\\n default:\\n console.error(\\\"Number of braces \\\"+n_brace+\\\" exceeds the implemented limit (2)\\\")\\n }\\n const src_point = point_brace.data_source\\n src_point.data.x = x_\\n src_point.data.y = y_\\n src_point.change.emit()\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=101, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1341\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1153\",\"type\":\"PanTool\"},{\"attributes\":{\"data\":{\"x\":[0,0.15,-0.15],\"y\":[0,-0.16887495373796552,-0.16887495373796552]},\"selected\":{\"id\":\"1401\"},\"selection_policy\":{\"id\":\"1400\"}},\"id\":\"1086\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"overlay\":{\"id\":\"1159\"}},\"id\":\"1155\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"args\":{\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"point_brace\":{\"id\":\"1335\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const n_brace = cb_obj.active\\n const E = db['E'][0]\\n const L = db['L'][0]\\n const I = db['Iz'][0]\\n\\n // apply the changes\\n db['n_bracez'][0] = n_brace\\n db['Ncritz'][0] = compute_N_buckling_z(E, I, L, n_brace)\\n\\n // update\\n update_div_buckling(db, div_buckling)\\n update_point_brace(point_brace, n_brace)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function update_point_brace(point_brace, n_brace) {\\n switch(n_brace) {\\n case 0:\\n var x_ = []\\n var y_ = []\\n break\\n case 1:\\n var x_ = [L/2]\\n var y_ = [0]\\n break\\n case 2:\\n var x_ = [L/3, 2L/3]\\n var y_ = [0, 0]\\n break\\n default:\\n console.error(\\\"Number of braces \\\"+n_brace+\\\" exceeds the implemented limit (2)\\\")\\n }\\n const src_point = point_brace.data_source\\n src_point.data.x = x_\\n src_point.data.y = y_\\n src_point.change.emit()\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=101, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n 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Application\",\"version\":\"2.4.2\"}};\n",
	+ " const render_items = [{\"docid\":\"e8780aad-6871-4f40-8880-fb642db884e1\",\"root_ids\":[\"1356\"],\"roots\":{\"1356\":\"3841a4e9-dcab-4bd3-b1e0-b95fd367dcf4\"}}];\n",
	+ " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	+ "\n",
	+ " }\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " let attempts = 0;\n",
	+ " const timer = setInterval(function(root) {\n",
	+ " if (root.Bokeh !== undefined) {\n",
	+ " clearInterval(timer);\n",
	+ " embed_document(root);\n",
	+ " } else {\n",
	+ " attempts++;\n",
	+ " if (attempts > 100) {\n",
	+ " clearInterval(timer);\n",
	+ " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	+ " }\n",
	+ " }\n",
	+ " }, 10, root)\n",
	+ " }\n",
	+ "})(window);"
	+ ],
	+ "application/vnd.bokehjs_exec.v0+json": ""
	+ },
	+ "metadata": {
	+ "application/vnd.bokehjs_exec.v0+json": {
	+ "id": "1356"
	+ }
	+ },
	+ "output_type": "display_data"
	+ }
	+ ],
	+ "source": [
	+ "hidden_code_nb_buckling.main_code(L, h, b, A, Iy, Iz, P, E, N, Rx, discr_NVM, x_discr, n_bracey, n_bracez, Ncrity, Ncritz)"
	+ ]
	+ },
	+ {
	+ "cell_type": "markdown",
	+ "metadata": {
	+ "tags": []
	+ },
	+ "source": [
	+ "## Legend\n",
	+ "\n",
	+ "Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder.\n",
	+ "\n",
	+ "* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	+ "* Slider of the height h: move the slider to change the height h of the cross-section of the beam.\n",
	+ "* Slider of the axial force P: move the slider to change the axial force P applied on the beam.\n",
	+ "* Slider of the length L: move the slider to change the length L of the beam.\n",
	+ "* Textbox \"Geometrical and mechanical parameters: small summary with the value of h, b, L, A (area), Iy (inertia with respect to the strong axis) and Iz (inertia with respect to the weak axis).\n",
	+ "* Textbox \"Forces and Instability: small summary with the value of the reaction forces, the internal forces, external forces, critical buckling loads and the information on the instability of the element.\n",
	+ "* Radio buttons of the number of braces: choose between zero, one and two braces (equally spaced) in the y or z direction.\n",
	+ "* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	+ "* 2 Figures \"Simple supported beam\": in this figures, the initial system is presented with the static scheme, the length of the beam, the horizontal force P and the x and y/z axis.\n",
	+ "* 2 Figures \"Beam instability\": in this figures, if buckling occurs, the shape of the beam is presented. The red dots represent the position of the braces.\n",
	+ "\n",
	+ "### Help and Information on the functions\n",
	+ "\n",
	+ "In Jupyter Notebooks the user can learn more about a function by using the question mark after the target function. One question mark shows some useful information on the function and two question marks show in addition also the code of the function, revealing it's content.\n",
	+ "For example, by creating a Code cell and pasting \"beam_section.compute_area?\" or \"beam_section.compute_area??\", it's possible to see how this feature works.\n",
	+ "\n",
	+ "### Recommendations\n",
	+ "\n",
	+ "If you have problem visualizing the entirety of the tool, you can maximize the window size by using Ctrl+B or Cmd+B to hide/show the left explorer panel and by using F11 to go to the full-page mode and back in the browser (NB: it could not work in the tab with NOTO; just use F11 in another tab and come back in the NOTO tab). If you're using a very sall display and it's not enough, you can zoom out the browser tab.\n",
	+ "\n",
	+ "Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully."
	+ ]
	+ }
	+ ],
	+ "metadata": {
	+ "interpreter": {
	+ "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	+ },
	+ "kernelspec": {
	+ "display_name": "Python 3 (ipykernel)",
	+ "language": "python",
	+ "name": "python3"
	+ },
	+ "language_info": {
	+ "codemirror_mode": {
	+ "name": "ipython",
	+ "version": 3
	+ },
	+ "file_extension": ".py",
	+ "mimetype": "text/x-python",
	+ "name": "python",
	+ "nbconvert_exporter": "python",
	+ "pygments_lexer": "ipython3",
	+ "version": "3.8.10"
	+ }
	+ },
	+ "nbformat": 4,
	+ "nbformat_minor": 4
	+}
	diff --git a/Simple Beam DEMOs/img/Weld1.png b/Simple Beam DEMOs/img/Weld1.png
	new file mode 100644
	index 0000000..655027a
	Binary files /dev/null and b/Simple Beam DEMOs/img/Weld1.png differ
	diff --git a/Simple Beam DEMOs/img/Weld2.png b/Simple Beam DEMOs/img/Weld2.png
	new file mode 100644
	index 0000000..736ce51
	Binary files /dev/null and b/Simple Beam DEMOs/img/Weld2.png differ
	diff --git a/Simple Beam DEMOs/sb_buckling.ipynb b/Simple Beam DEMOs/sb_buckling.ipynb
	deleted file mode 100644
	index f8111e4..0000000
	--- a/Simple Beam DEMOs/sb_buckling.ipynb
	+++ /dev/null
	@@ -1,479 +0,0 @@
	-{
	- "cells": [
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "# Simple beam - Buckling\n",
	- "In this last notebook, the instability of a simple beam under constant axial load is studied. "
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	- " if (server_id !== undefined) {\n",
	- " // Clean up Bokeh references\n",
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	- " cell.notebook.kernel.execute(cmd_clean, {\n",
	- " iopub: {\n",
	- " output: function(msg) {\n",
	- " const id = msg.content.text.trim();\n",
	- " if (id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
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	- " events.on('clear_output.CodeCell', handleClearOutput);\n",
	- " events.on('delete.Cell', handleClearOutput);\n",
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	- " /* Handle when a new output is added */\n",
	- " events.on('output_added.OutputArea', handleAddOutput);\n",
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	- " \n",
	- " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_timeout = Date.now() + 5000;\n",
	- " root._bokeh_failed_load = false;\n",
	- " }\n",
	- "\n",
	- " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	- " \"<div style='background-color: #fdd'>\\n\"+\n",
	- " \"<p>\\n\"+\n",
	- " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	- " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	- " \"</p>\\n\"+\n",
	- " \"<ul>\\n\"+\n",
	- " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	- " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	- " \"</ul>\\n\"+\n",
	- " \"<code>\\n\"+\n",
	- " \"from bokeh.resources import INLINE\\n\"+\n",
	- " \"output_notebook(resources=INLINE)\\n\"+\n",
	- " \"</code>\\n\"+\n",
	- " \"</div>\"}};\n",
	- "\n",
	- " function display_loaded() {\n",
	- " const el = document.getElementById(\"1002\");\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS is loading...\";\n",
	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	- " }\n",
	- " } else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(display_loaded, 100)\n",
	- " }\n",
	- " }\n",
	- "\n",
	- "\n",
	- " function run_callbacks() {\n",
	- " try {\n",
	- " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	- " if (callback != null)\n",
	- " callback();\n",
	- " });\n",
	- " } finally {\n",
	- " delete root._bokeh_onload_callbacks\n",
	- " }\n",
	- " console.debug(\"Bokeh: all callbacks have finished\");\n",
	- " }\n",
	- "\n",
	- " function load_libs(css_urls, js_urls, callback) {\n",
	- " if (css_urls == null) css_urls = [];\n",
	- " if (js_urls == null) js_urls = [];\n",
	- "\n",
	- " root._bokeh_onload_callbacks.push(callback);\n",
	- " if (root._bokeh_is_loading > 0) {\n",
	- " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	- " return null;\n",
	- " }\n",
	- " if (js_urls == null \|\| js_urls.length === 0) {\n",
	- " run_callbacks();\n",
	- " return null;\n",
	- " }\n",
	- " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	- " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	- "\n",
	- " function on_load() {\n",
	- " root._bokeh_is_loading--;\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	- " run_callbacks()\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function on_error(url) {\n",
	- " console.error(\"failed to load \" + url);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < css_urls.length; i++) {\n",
	- " const url = css_urls[i];\n",
	- " const element = document.createElement(\"link\");\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.rel = \"stylesheet\";\n",
	- " element.type = \"text/css\";\n",
	- " element.href = url;\n",
	- " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < js_urls.length; i++) {\n",
	- " const url = js_urls[i];\n",
	- " const element = document.createElement('script');\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.async = false;\n",
	- " element.src = url;\n",
	- " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	- " document.head.appendChild(element);\n",
	- " }\n",
	- " };\n",
	- "\n",
	- " function inject_raw_css(css) {\n",
	- " const element = document.createElement(\"style\");\n",
	- " element.appendChild(document.createTextNode(css));\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " \n",
	- " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	- " const css_urls = [];\n",
	- " \n",
	- "\n",
	- " const inline_js = [\n",
	- " function(Bokeh) {\n",
	- " Bokeh.set_log_level(\"info\");\n",
	- " },\n",
	- " function(Bokeh) {\n",
	- " \n",
	- " \n",
	- " }\n",
	- " ];\n",
	- "\n",
	- " function run_inline_js() {\n",
	- " \n",
	- " if (root.Bokeh !== undefined \|\| force === true) {\n",
	- " \n",
	- " for (let i = 0; i < inline_js.length; i++) {\n",
	- " inline_js[i].call(root, root.Bokeh);\n",
	- " }\n",
	- " if (force === true) {\n",
	- " display_loaded();\n",
	- " }} else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(run_inline_js, 100);\n",
	- " } else if (!root._bokeh_failed_load) {\n",
	- " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
	- " root._bokeh_failed_load = true;\n",
	- " } else if (force !== true) {\n",
	- " const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
	- " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
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	- "\n",
	- " }\n",
	- "\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
	- " run_inline_js();\n",
	- " } else {\n",
	- " load_libs(css_urls, js_urls, function() {\n",
	- " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	- " run_inline_js();\n",
	- " });\n",
	- " }\n",
	- "}(window));"
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	- },
	- "metadata": {},
	- "output_type": "display_data"
	- }
	- ],
	- "source": [
	- "# Import the packages needed\n",
	- "import sys\n",
	- "sys.path.append('../HiddenCode')\n",
	- "import hidden_code_nb_buckling\n",
	- "import numpy as np\n",
	- "import math\n",
	- "from cienpy import simplebeam as sb\n",
	- "from cienpy import rectangular_section as beam_section\n",
	- "from cienpy import buckling"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Define the geometry and uniform load. Note that given the graphical nature of the notebook, extreme cases can cause the figures to not be displayed."
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 2,
	- "metadata": {},
	- "outputs": [],
	- "source": [
	- "# Choose the dimensions\n",
	- "L = 6 # [m]\n",
	- "h = 100 # [mm]\n",
	- "b = 50 # [mm]\n",
	- "P = 10; # [kN]\n",
	- "\n",
	- "# Material parameter\n",
	- "E = 200e3 # MPa\n",
	- "\n",
	- "# compute the internal forces (at x=L)\n",
	- "discr_NVM = 100\n",
	- "x_discr = np.linspace(0, L, discr_NVM)\n",
	- "N = sb.compute_N(L, P)\n",
	- "\n",
	- "# compute the parameters\n",
	- "A = beam_section.compute_area(b, h) # [mm2]\n",
	- "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	- "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	- "\n",
	- "# compute the reactions\n",
	- "Rx = sb.compute_Rx(P)\n",
	- "\n",
	- "# compute buckling resistance\n",
	- "n_bracey = 0\n",
	- "n_bracez = 0\n",
	- "Ncrity = buckling.compute_N_buckling_y(E, Iy, L, n_bracey)\n",
	- "Ncritz = buckling.compute_N_buckling_z(E, Iz, L, n_bracez)"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Run the complex code for the interactive visualisation:"
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 3,
	- "metadata": {},
	- "outputs": [
	- {
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":\"CDSView\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Beam instability in z direction\"},\"id\":\"1281\",\"type\":\"Title\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":6,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1083\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1288\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1286\",\"type\":\"LinearScale\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1003\"},\"glyph\":{\"id\":\"1313\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1315\"},\"nonselection_glyph\":{\"id\":\"1314\"},\"view\":{\"id\":\"1317\"}},\"id\":\"1316\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1284\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"1303\",\"type\":\"HelpTool\"},{\"attributes\":{\"axis_label\":\"Position [m]\",\"coordinates\":null,\"formatter\":{\"id\":\"1390\"},\"group\":null,\"major_label_policy\":{\"id\":\"1391\"},\"ticker\":{\"id\":\"1291\"}},\"id\":\"1290\",\"type\":\"LinearAxis\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"red\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_color\":{\"value\":\"red\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"red\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1327\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1436\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"tools\":[{\"id\":\"1057\"},{\"id\":\"1058\"},{\"id\":\"1059\"},{\"id\":\"1060\"},{\"id\":\"1061\"},{\"id\":\"1062\"}]},\"id\":\"1064\",\"type\":\"Toolbar\"},{\"attributes\":{\"data\":{\"x\":[],\"y\":[]},\"selected\":{\"id\":\"1437\"},\"selection_policy\":{\"id\":\"1436\"}},\"id\":\"1325\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_color\":{\"value\":\"white\"},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":100},\"line_width\":{\"value\":3},\"width\":{\"value\":50},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1099\",\"type\":\"Rect\"},{\"attributes\":{},\"id\":\"1143\",\"type\":\"LinearScale\"},{\"attributes\":{\"coordinates\":null,\"formatter\":{\"id\":\"1387\"},\"group\":null,\"major_label_policy\":{\"id\":\"1388\"},\"ticker\":{\"id\":\"1295\"},\"visible\":false},\"id\":\"1294\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1437\",\"type\":\"Selection\"},{\"attributes\":{\"axis\":{\"id\":\"1294\"},\"coordinates\":null,\"dimension\":1,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1297\",\"type\":\"Grid\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.1},\"line_alpha\":{\"value\":0.1},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1094\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1295\",\"type\":\"BasicTicker\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1098\"},\"glyph\":{\"id\":\"1099\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1101\"},\"nonselection_glyph\":{\"id\":\"1100\"},\"view\":{\"id\":\"1103\"}},\"id\":\"1102\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"data\":{\"x\":[0,0.15,-0.15],\"y\":[0,-0.16887495373796552,-0.16887495373796552]},\"selected\":{\"id\":\"1401\"},\"selection_policy\":{\"id\":\"1400\"}},\"id\":\"1086\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1086\"},\"glyph\":{\"id\":\"1087\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1089\"},\"nonselection_glyph\":{\"id\":\"1088\"},\"view\":{\"id\":\"1091\"}},\"id\":\"1090\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"data\":{\"x\":[0],\"y\":[0]},\"selected\":{\"id\":\"1447\"},\"selection_policy\":{\"id\":\"1446\"}},\"id\":\"1098\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"data\":{\"x\":[6],\"y\":[-0.0975]},\"selected\":{\"id\":\"1403\"},\"selection_policy\":{\"id\":\"1402\"}},\"id\":\"1092\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1299\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"fill_color\":{\"value\":\"white\"},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1093\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1298\",\"type\":\"PanTool\"},{\"attributes\":{\"overlay\":{\"id\":\"1304\"}},\"id\":\"1300\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1107\"},\"group\":null,\"line_color\":{\"value\":\"gray\"},\"line_width\":{\"value\":2.1972245773362196},\"source\":{\"id\":\"1396\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":128.0},\"y_start\":{\"value\":0}},\"id\":\"1108\",\"type\":\"Arrow\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.2},\"line_alpha\":{\"value\":0.2},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1095\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1301\",\"type\":\"SaveTool\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":100},\"line_alpha\":{\"value\":0.1},\"line_width\":{\"value\":3},\"width\":{\"value\":50},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1100\",\"type\":\"Rect\"},{\"attributes\":{},\"id\":\"1302\",\"type\":\"ResetTool\"},{\"attributes\":{\"fill_color\":{\"value\":\"gray\"},\"line_color\":{\"value\":\"gray\"},\"size\":{\"value\":15.380572041353537}},\"id\":\"1107\",\"type\":\"VeeHead\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1092\"},\"glyph\":{\"id\":\"1093\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1095\"},\"nonselection_glyph\":{\"id\":\"1094\"},\"view\":{\"id\":\"1097\"}},\"id\":\"1096\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1304\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"source\":{\"id\":\"1092\"}},\"id\":\"1097\",\"type\":\"CDSView\"},{\"attributes\":{\"tools\":[{\"id\":\"1298\"},{\"id\":\"1299\"},{\"id\":\"1300\"},{\"id\":\"1301\"},{\"id\":\"1302\"},{\"id\":\"1303\"}]},\"id\":\"1305\",\"type\":\"Toolbar\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":100},\"line_alpha\":{\"value\":0.2},\"line_width\":{\"value\":3},\"width\":{\"value\":50},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1101\",\"type\":\"Rect\"},{\"attributes\":{\"end\":300,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1338\"}]},\"start\":20,\"step\":20,\"title\":\"Change the height h [mm]\",\"value\":100},\"id\":\"1106\",\"type\":\"Slider\"},{\"attributes\":{\"end\":150,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1337\"}]},\"start\":10,\"step\":10,\"title\":\"Change the width b [mm]\",\"value\":50},\"id\":\"1105\",\"type\":\"Slider\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1111\",\"type\":\"Text\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"red\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_color\":{\"value\":\"red\"},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"red\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1328\",\"type\":\"Circle\"},{\"attributes\":{\"source\":{\"id\":\"1098\"}},\"id\":\"1103\",\"type\":\"CDSView\"},{\"attributes\":{\"tools\":[{\"id\":\"1024\"},{\"id\":\"1025\"},{\"id\":\"1026\"},{\"id\":\"1027\"},{\"id\":\"1028\"},{\"id\":\"1029\"}]},\"id\":\"1031\",\"type\":\"Toolbar\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1030\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"source\":{\"id\":\"1071\"}},\"id\":\"1076\",\"type\":\"CDSView\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1071\"},\"glyph\":{\"id\":\"1072\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1074\"},\"nonselection_glyph\":{\"id\":\"1073\"},\"view\":{\"id\":\"1076\"}},\"id\":\"1075\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"gray\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1314\",\"type\":\"Line\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1321\",\"type\":\"Line\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"gray\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1315\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1387\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1104\"},\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"section\":{\"id\":\"1102\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const h = cb_obj.value // value of the slider\\n const b = db['b'][0]\\n const L = db['L'][0]\\n const E = db['E'][0]\\n const n_bracey = db['n_bracey'][0]\\n const n_bracez = db['n_bracez'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const Iz = compute_inertia_z(b, h)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = Iz\\n db['Ncrity'][0] = compute_N_buckling_y(E, Iy, L, n_bracey)\\n db['Ncritz'][0] = compute_N_buckling_z(E, Iz, L, n_bracez)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_div_buckling(db, div_buckling)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)*2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=100, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1338\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_color\":\"gray\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1313\",\"type\":\"Line\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1318\"},\"glyph\":{\"id\":\"1319\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1321\"},\"nonselection_glyph\":{\"id\":\"1320\"},\"view\":{\"id\":\"1323\"}},\"id\":\"1322\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1388\",\"type\":\"AllLabels\"},{\"attributes\":{\"source\":{\"id\":\"1003\"}},\"id\":\"1317\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1390\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1104\"},\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"section\":{\"id\":\"1102\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const L = db['L'][0]\\n const E = db['E'][0]\\n const n_bracey = db['n_bracey'][0]\\n const n_bracez = db['n_bracez'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const Iz = compute_inertia_z(b, h)\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = Iz\\n db['Ncrity'][0] = compute_N_buckling_y(E, Iy, L, n_bracey)\\n db['Ncritz'][0] = compute_N_buckling_z(E, Iz, L, n_bracez)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_div_buckling(db, div_buckling)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)*2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=100, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1337\",\"type\":\"CustomJS\"},{\"attributes\":{\"text\":\"\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = 10 kN<br>\\n Rx = 10 kN<br>\\n N = -10 kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = 228.46 kN<br>\\n N<sub>crit,z</sub> = 57.12 kN<br>\\n Instability: No\\n \",\"width\":170},\"id\":\"1324\",\"type\":\"Div\"},{\"attributes\":{\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1319\",\"type\":\"Line\"},{\"attributes\":{\"data\":{\"x\":[0,6],\"y\":[0,0]},\"selected\":{\"id\":\"1440\"},\"selection_policy\":{\"id\":\"1439\"}},\"id\":\"1318\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1391\",\"type\":\"AllLabels\"},{\"attributes\":{\"source\":{\"id\":\"1318\"}},\"id\":\"1323\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.1,\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1320\",\"type\":\"Line\"},{\"attributes\":{\"source\":{\"id\":\"1331\"}},\"id\":\"1336\",\"type\":\"CDSView\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1331\"},\"glyph\":{\"id\":\"1332\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1334\"},\"nonselection_glyph\":{\"id\":\"1333\"},\"view\":{\"id\":\"1336\"}},\"id\":\"1335\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"args\":{\"axial_force_y\":{\"id\":\"1126\"},\"axial_force_z\":{\"id\":\"1186\"},\"div\":{\"id\":\"1104\"},\"div_buckling\":{\"id\":\"1324\"},\"label_P_force_y\":{\"id\":\"1132\"},\"label_P_force_z\":{\"id\":\"1192\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"point_brace_y\":{\"id\":\"1329\"},\"point_brace_z\":{\"id\":\"1335\"},\"s_b\":{\"id\":\"1003\"},\"source\":{\"id\":\"1004\"},\"support_r_y\":{\"id\":\"1096\"},\"support_r_z\":{\"id\":\"1183\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_b = s_b.data\\n const L = cb_obj.value // value of the slider\\n const E = db['E'][0]\\n const Iy = db['Iy'][0]\\n const Iz = db['Iz'][0]\\n const n_bracey = db['n_bracey'][0]\\n const n_bracez = db['n_bracez'][0]\\n\\n // apply the changes\\n data_b['x'][1] = L\\n db['L'][0] = L\\n db['Ncrity'][0] = compute_N_buckling_y(E, Iy, L, n_bracey)\\n db['Ncritz'][0] = compute_N_buckling_z(E, Iz, L, n_bracez)\\n\\n // update\\n update_div_geo(db, div)\\n update_div_buckling(db, div_buckling)\\n support_r_y.glyph.x = L\\n support_r_z.glyph.x = L\\n axial_force_y.x_start = L+1.0\\n axial_force_y.x_end = L\\n label_P_force_y.glyph.x = L+1.0/2\\n axial_force_z.x_start = L+1.0\\n axial_force_z.x_end = L\\n label_P_force_z.glyph.x = L+1.0/2\\n update_point_brace(point_brace_y, n_bracey)\\n update_point_brace(point_brace_z, n_bracez)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n s_b.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)*2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function update_point_brace(point_brace, n_brace) {\\n switch(n_brace) {\\n case 0:\\n var x_ = []\\n var y_ = []\\n break\\n case 1:\\n var x_ = [L/2]\\n var y_ = [0]\\n break\\n case 2:\\n var x_ = [L/3, 2L/3]\\n var y_ = [0, 0]\\n break\\n default:\\n console.error(\\\"Number of braces \\\"+n_brace+\\\" exceeds the implemented limit (2)\\\")\\n }\\n const src_point = point_brace.data_source\\n src_point.data.x = x_\\n src_point.data.y = y_\\n src_point.change.emit()\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=100, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1339\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n const db = source.data\\n const P = cb_obj.value // value of the slider\\n\\n // apply the changes\\n db['P'][0] = P\\n db['N'][0] = compute_N(P)\\n db['Rx'][0] = compute_Rx(P)\\n\\n // update\\n update_div_buckling(db, div_buckling)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=100, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1340\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"point_brace\":{\"id\":\"1329\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const n_brace = cb_obj.active\\n const E = db['E'][0]\\n const L = db['L'][0]\\n const I = db['Iy'][0]\\n\\n // apply the changes\\n db['n_bracey'][0] = n_brace\\n db['Ncrity'][0] = compute_N_buckling_y(E, I, L, n_brace)\\n\\n // update\\n update_div_buckling(db, div_buckling)\\n update_point_brace(point_brace, n_brace)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function update_point_brace(point_brace, n_brace) {\\n switch(n_brace) {\\n case 0:\\n var x_ = []\\n var y_ = []\\n break\\n case 1:\\n var x_ = [L/2]\\n var y_ = [0]\\n break\\n case 2:\\n var x_ = [L/3, 2L/3]\\n var y_ = [0, 0]\\n break\\n default:\\n console.error(\\\"Number of braces \\\"+n_brace+\\\" exceeds the implemented limit (2)\\\")\\n }\\n const src_point = point_brace.data_source\\n src_point.data.x = x_\\n src_point.data.y = y_\\n src_point.change.emit()\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=100, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1341\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"div_buckling\":{\"id\":\"1324\"},\"mode_shape_y\":{\"id\":\"1278\"},\"mode_shape_z\":{\"id\":\"1322\"},\"point_brace\":{\"id\":\"1335\"},\"source\":{\"id\":\"1004\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const n_brace = cb_obj.active\\n const E = db['E'][0]\\n const L = db['L'][0]\\n const I = db['Iz'][0]\\n\\n // apply the changes\\n db['n_bracez'][0] = n_brace\\n db['Ncritz'][0] = compute_N_buckling_z(E, I, L, n_brace)\\n\\n // update\\n update_div_buckling(db, div_buckling)\\n update_point_brace(point_brace, n_brace)\\n update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_buckling(data, div) {\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const N = data['N'][0]\\n const Ncrity = Math.round(data['Ncrity'][0]10)/10\\n const Ncritz = Math.round(data['Ncritz'][0]10)/10\\n if ((-N<Ncrity) && (-N<Ncritz)) {\\n var str_insta = \\\"No\\\"\\n } else {\\n var str_insta = \\\"Yes\\\"\\n }\\n div.text = `\\n <p style='font-size:14px'><b>Forces and Instability:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n N = `+N+` kN<br>\\n V = 0 kN<br>\\n M = 0 kNm<br>\\n N<sub>crit,y</sub> = `+Ncrity+` kN<br>\\n N<sub>crit,z</sub> = `+Ncritz+` kN<br>\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_N_buckling_y(E, Iy, L, n_bracey) {\\n return ((n_bracey+1)Math.PI)2EIy/L2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)Math.PI)*2EIz/L2/1e9\\n }\\n \\n \\n function update_point_brace(point_brace, n_brace) {\\n switch(n_brace) {\\n case 0:\\n var x_ = []\\n var y_ = []\\n break\\n case 1:\\n var x_ = [L/2]\\n var y_ = [0]\\n break\\n case 2:\\n var x_ = [L/3, 2L/3]\\n var y_ = [0, 0]\\n break\\n default:\\n console.error(\\\"Number of braces \\\"+n_brace+\\\" exceeds the implemented limit (2)\\\")\\n }\\n const src_point = point_brace.data_source\\n src_point.data.x = x_\\n src_point.data.y = y_\\n src_point.change.emit()\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return CMath.sin((n_brace+1)Math.PIx/L)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function update_mode_shape_N_buckling(data, glyph_ms_y, glyph_ms_z, discr=100, C=1) {\\n const L = data['L'][0]\\n const n_bracey = data['n_bracey'][0]\\n const n_bracez = data['n_bracez'][0]\\n const N = -data['N'][0]\\n const Ncrity = data['Ncrity'][0]\\n const Ncritz = data['Ncritz'][0]\\n const x_discr = linspace(0, L, discr)\\n let mode_shape_y = new Array(discr)\\n let mode_shape_z = new Array(discr)\\n \\n // compute the arrays\\n if (N >= Ncrity) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_y[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracey, C)\\n }\\n } else {\\n mode_shape_y = new Array(discr).fill(0)\\n }\\n if (N >= Ncritz) {\\n for (var i = 0; i < discr; i++) {\\n mode_shape_z[i] = compute_mode_shape_N_buckling(x_discr[i], L, n_bracez, C)\\n }\\n } else {\\n mode_shape_z = new Array(discr).fill(0)\\n }\\n debugger\\n // update the mode shape\\n const src_ms_y = glyph_ms_y.data_source\\n src_ms_y.data.x = x_discr\\n src_ms_y.data.y = mode_shape_y\\n src_ms_y.change.emit()\\n const src_ms_z = glyph_ms_z.data_source\\n src_ms_z.data.x = x_discr\\n src_ms_z.data.y = mode_shape_z\\n src_ms_z.change.emit()\\n }\\n \\n \"},\"id\":\"1342\",\"type\":\"CustomJS\"},{\"attributes\":{\"width\":10},\"id\":\"1343\",\"type\":\"Spacer\"},{\"attributes\":{\"height\":10},\"id\":\"1346\",\"type\":\"Spacer\"},{\"attributes\":{\"height\":10},\"id\":\"1344\",\"type\":\"Spacer\"},{\"attributes\":{\"children\":[{\"id\":\"1104\"},{\"id\":\"1324\"}]},\"id\":\"1345\",\"type\":\"Row\"},{\"attributes\":{\"children\":[{\"id\":\"1038\"},{\"id\":\"1343\"},{\"id\":\"1347\"}]},\"id\":\"1348\",\"type\":\"Row\"},{\"attributes\":{\"children\":[{\"id\":\"1344\"},{\"id\":\"1105\"},{\"id\":\"1106\"},{\"id\":\"1230\"},{\"id\":\"1231\"},{\"id\":\"1345\"},{\"id\":\"1346\"},{\"id\":\"1232\"},{\"id\":\"1233\"},{\"id\":\"1234\"},{\"id\":\"1235\"}]},\"id\":\"1347\",\"type\":\"Column\"},{\"attributes\":{\"children\":[{\"id\":\"1348\"}]},\"id\":\"1349\",\"type\":\"Column\"},{\"attributes\":{\"width\":10},\"id\":\"1350\",\"type\":\"Spacer\"},{\"attributes\":{\"fill_alpha\":0.2,\"fill_color\":\"white\",\"hatch_alpha\":0.2,\"line_alpha\":0.2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1089\",\"type\":\"Patch\"},{\"attributes\":{\"children\":[{\"id\":\"1005\"},{\"id\":\"1134\"},{\"id\":\"1236\"},{\"id\":\"1280\"}]},\"id\":\"1352\",\"type\":\"Column\"},{\"attributes\":{\"children\":[{\"id\":\"1350\"}]},\"id\":\"1351\",\"type\":\"Column\"},{\"attributes\":{\"children\":[{\"id\":\"1349\"},{\"id\":\"1351\"},{\"id\":\"1352\"}]},\"id\":\"1353\",\"type\":\"Row\"},{\"attributes\":{},\"id\":\"1392\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"children\":[{\"id\":\"1353\"}]},\"id\":\"1354\",\"type\":\"Column\"},{\"attributes\":{},\"id\":\"1393\",\"type\":\"AllLabels\"},{\"attributes\":{\"children\":[{\"id\":\"1354\"}]},\"id\":\"1355\",\"type\":\"Row\"},{\"attributes\":{},\"id\":\"1394\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1395\",\"type\":\"AllLabels\"},{\"attributes\":{},\"id\":\"1402\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1403\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1025\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1421\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1422\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1404\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1405\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1423\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"below\":[{\"id\":\"1049\"}],\"center\":[{\"id\":\"1052\"},{\"id\":\"1056\"},{\"id\":\"1108\"},{\"id\":\"1117\"}],\"left\":[{\"id\":\"1053\"}],\"match_aspect\":true,\"renderers\":[{\"id\":\"1075\"},{\"id\":\"1102\"},{\"id\":\"1114\"},{\"id\":\"1123\"}],\"title\":{\"id\":\"1039\"},\"toolbar\":{\"id\":\"1064\"},\"toolbar_location\":null,\"width\":375,\"x_range\":{\"id\":\"1041\"},\"x_scale\":{\"id\":\"1045\"},\"y_range\":{\"id\":\"1043\"},\"y_scale\":{\"id\":\"1047\"}},\"id\":\"1038\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"1424\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1406\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1407\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1425\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1426\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1408\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1409\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1028\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1029\",\"type\":\"HelpTool\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0.2},\"height\":{\"value\":240.0},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":150},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1074\",\"type\":\"Rect\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0.1},\"height\":{\"value\":240.0},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":150},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1073\",\"type\":\"Rect\"},{\"attributes\":{\"overlay\":{\"id\":\"1030\"}},\"id\":\"1026\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"1027\",\"type\":\"SaveTool\"}],\"root_ids\":[\"1356\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n",
	- " const render_items = [{\"docid\":\"c8f06a0a-e584-4717-aa52-b032f08dea83\",\"root_ids\":[\"1356\"],\"roots\":{\"1356\":\"a743359c-c5c2-462d-9c0c-f95ef4d9ace0\"}}];\n",
	- " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	- "\n",
	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " embed_document(root);\n",
	- " } else {\n",
	- " let attempts = 0;\n",
	- " const timer = setInterval(function(root) {\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " clearInterval(timer);\n",
	- " embed_document(root);\n",
	- " } else {\n",
	- " attempts++;\n",
	- " if (attempts > 100) {\n",
	- " clearInterval(timer);\n",
	- " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	- " }\n",
	- " }\n",
	- " }, 10, root)\n",
	- " }\n",
	- "})(window);"
	- ],
	- "application/vnd.bokehjs_exec.v0+json": ""
	- },
	- "metadata": {
	- "application/vnd.bokehjs_exec.v0+json": {
	- "id": "1356"
	- }
	- },
	- "output_type": "display_data"
	- }
	- ],
	- "source": [
	- "hidden_code_nb_buckling.main_code(L, h, b, A, Iy, Iz, P, E, N, Rx, discr_NVM, x_discr, n_bracey, n_bracez, Ncrity, Ncritz)"
	- ]
	- }
	- ],
	- "metadata": {
	- "interpreter": {
	- "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	- },
	- "kernelspec": {
	- "display_name": "Python 3 (ipykernel)",
	- "language": "python",
	- "name": "python3"
	- },
	- "language_info": {
	- "codemirror_mode": {
	- "name": "ipython",
	- "version": 3
	- },
	- "file_extension": ".py",
	- "mimetype": "text/x-python",
	- "name": "python",
	- "nbconvert_exporter": "python",
	- "pygments_lexer": "ipython3",
	- "version": "3.8.10"
	- }
	- },
	- "nbformat": 4,
	- "nbformat_minor": 4
	-}
	diff --git a/Simple Beam DEMOs/sb_deflection.ipynb b/Simple Beam DEMOs/sb_deflection.ipynb
	deleted file mode 100644
	index 7d0e12f..0000000
	--- a/Simple Beam DEMOs/sb_deflection.ipynb
	+++ /dev/null
	@@ -1,486 +0,0 @@
	-{
	- "cells": [
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "# Simple beam - Deflection\n",
	- "In this eigth notebook, the deflection of a simple supported beam is studied."
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 1,
	- "metadata": {},
	- "outputs": [
	- {
	- "data": {
	- "text/html": [
	- "\n",
	- " <div class=\"bk-root\">\n",
	- " <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	- " <span id=\"1002\">Loading BokehJS ...</span>\n",
	- " </div>"
	- ]
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- },
	- {
	- "data": {
	- "application/javascript": [
	- "\n",
	- "(function(root) {\n",
	- " function now() {\n",
	- " return new Date();\n",
	- " }\n",
	- "\n",
	- " const force = true;\n",
	- "\n",
	- " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_onload_callbacks = [];\n",
	- " root._bokeh_is_loading = undefined;\n",
	- " }\n",
	- "\n",
	- " const JS_MIME_TYPE = 'application/javascript';\n",
	- " const HTML_MIME_TYPE = 'text/html';\n",
	- " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	- " const CLASS_NAME = 'output_bokeh rendered_html';\n",
	- "\n",
	- " /**\n",
	- " * Render data to the DOM node\n",
	- " */\n",
	- " function render(props, node) {\n",
	- " const script = document.createElement(\"script\");\n",
	- " node.appendChild(script);\n",
	- " }\n",
	- "\n",
	- " /**\n",
	- " * Handle when an output is cleared or removed\n",
	- " */\n",
	- " function handleClearOutput(event, handle) {\n",
	- " const cell = handle.cell;\n",
	- "\n",
	- " const id = cell.output_area._bokeh_element_id;\n",
	- " const server_id = cell.output_area._bokeh_server_id;\n",
	- " // Clean up Bokeh references\n",
	- " if (id != null && id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- "\n",
	- " if (server_id !== undefined) {\n",
	- " // Clean up Bokeh references\n",
	- " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	- " cell.notebook.kernel.execute(cmd_clean, {\n",
	- " iopub: {\n",
	- " output: function(msg) {\n",
	- " const id = msg.content.text.trim();\n",
	- " if (id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- " }\n",
	- " }\n",
	- " });\n",
	- " // Destroy server and session\n",
	- " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	- " cell.notebook.kernel.execute(cmd_destroy);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " /**\n",
	- " * Handle when a new output is added\n",
	- " */\n",
	- " function handleAddOutput(event, handle) {\n",
	- " const output_area = handle.output_area;\n",
	- " const output = handle.output;\n",
	- "\n",
	- " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	- " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	- " return\n",
	- " }\n",
	- "\n",
	- " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
	- "\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	- " // store reference to embed id on output_area\n",
	- " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
	- " }\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	- " const bk_div = document.createElement(\"div\");\n",
	- " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	- " const script_attrs = bk_div.children[0].attributes;\n",
	- " for (let i = 0; i < script_attrs.length; i++) {\n",
	- " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	- " }\n",
	- " // store reference to server id on output_area\n",
	- " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function register_renderer(events, OutputArea) {\n",
	- "\n",
	- " function append_mime(data, metadata, element) {\n",
	- " // create a DOM node to render to\n",
	- " const toinsert = this.create_output_subarea(\n",
	- " metadata,\n",
	- " CLASS_NAME,\n",
	- " EXEC_MIME_TYPE\n",
	- " );\n",
	- " this.keyboard_manager.register_events(toinsert);\n",
	- " // Render to node\n",
	- " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	- " render(props, toinsert[toinsert.length - 1]);\n",
	- " element.append(toinsert);\n",
	- " return toinsert\n",
	- " }\n",
	- "\n",
	- " /* Handle when an output is cleared or removed */\n",
	- " events.on('clear_output.CodeCell', handleClearOutput);\n",
	- " events.on('delete.Cell', handleClearOutput);\n",
	- "\n",
	- " /* Handle when a new output is added */\n",
	- " events.on('output_added.OutputArea', handleAddOutput);\n",
	- "\n",
	- " /**\n",
	- " * Register the mime type and append_mime function with output_area\n",
	- " */\n",
	- " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	- " /* Is output safe? */\n",
	- " safe: true,\n",
	- " /* Index of renderer in `output_area.display_order` */\n",
	- " index: 0\n",
	- " });\n",
	- " }\n",
	- "\n",
	- " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	- " if (root.Jupyter !== undefined) {\n",
	- " const events = require('base/js/events');\n",
	- " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	- "\n",
	- " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	- " register_renderer(events, OutputArea);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " \n",
	- " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_timeout = Date.now() + 5000;\n",
	- " root._bokeh_failed_load = false;\n",
	- " }\n",
	- "\n",
	- " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	- " \"<div style='background-color: #fdd'>\\n\"+\n",
	- " \"<p>\\n\"+\n",
	- " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	- " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	- " \"</p>\\n\"+\n",
	- " \"<ul>\\n\"+\n",
	- " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	- " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	- " \"</ul>\\n\"+\n",
	- " \"<code>\\n\"+\n",
	- " \"from bokeh.resources import INLINE\\n\"+\n",
	- " \"output_notebook(resources=INLINE)\\n\"+\n",
	- " \"</code>\\n\"+\n",
	- " \"</div>\"}};\n",
	- "\n",
	- " function display_loaded() {\n",
	- " const el = document.getElementById(\"1002\");\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS is loading...\";\n",
	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	- " }\n",
	- " } else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(display_loaded, 100)\n",
	- " }\n",
	- " }\n",
	- "\n",
	- "\n",
	- " function run_callbacks() {\n",
	- " try {\n",
	- " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	- " if (callback != null)\n",
	- " callback();\n",
	- " });\n",
	- " } finally {\n",
	- " delete root._bokeh_onload_callbacks\n",
	- " }\n",
	- " console.debug(\"Bokeh: all callbacks have finished\");\n",
	- " }\n",
	- "\n",
	- " function load_libs(css_urls, js_urls, callback) {\n",
	- " if (css_urls == null) css_urls = [];\n",
	- " if (js_urls == null) js_urls = [];\n",
	- "\n",
	- " root._bokeh_onload_callbacks.push(callback);\n",
	- " if (root._bokeh_is_loading > 0) {\n",
	- " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	- " return null;\n",
	- " }\n",
	- " if (js_urls == null \|\| js_urls.length === 0) {\n",
	- " run_callbacks();\n",
	- " return null;\n",
	- " }\n",
	- " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	- " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	- "\n",
	- " function on_load() {\n",
	- " root._bokeh_is_loading--;\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	- " run_callbacks()\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function on_error(url) {\n",
	- " console.error(\"failed to load \" + url);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < css_urls.length; i++) {\n",
	- " const url = css_urls[i];\n",
	- " const element = document.createElement(\"link\");\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.rel = \"stylesheet\";\n",
	- " element.type = \"text/css\";\n",
	- " element.href = url;\n",
	- " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < js_urls.length; i++) {\n",
	- " const url = js_urls[i];\n",
	- " const element = document.createElement('script');\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.async = false;\n",
	- " element.src = url;\n",
	- " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	- " document.head.appendChild(element);\n",
	- " }\n",
	- " };\n",
	- "\n",
	- " function inject_raw_css(css) {\n",
	- " const element = document.createElement(\"style\");\n",
	- " element.appendChild(document.createTextNode(css));\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " \n",
	- " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	- " const css_urls = [];\n",
	- " \n",
	- "\n",
	- " const inline_js = [\n",
	- " function(Bokeh) {\n",
	- " Bokeh.set_log_level(\"info\");\n",
	- " },\n",
	- " function(Bokeh) {\n",
	- " \n",
	- " \n",
	- " }\n",
	- " ];\n",
	- "\n",
	- " function run_inline_js() {\n",
	- " \n",
	- " if (root.Bokeh !== undefined \|\| force === true) {\n",
	- " \n",
	- " for (let i = 0; i < inline_js.length; i++) {\n",
	- " inline_js[i].call(root, root.Bokeh);\n",
	- " }\n",
	- " if (force === true) {\n",
	- " display_loaded();\n",
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	- },
	- "metadata": {},
	- "output_type": "display_data"
	- }
	- ],
	- "source": [
	- "# Import the packages needed\n",
	- "import sys\n",
	- "sys.path.append('../HiddenCode')\n",
	- "import hidden_code_nb_deflection\n",
	- "import math\n",
	- "import numpy as np\n",
	- "from cienpy import simplebeam as sb\n",
	- "from cienpy import rectangular_section as beam_section\n",
	- "from cienpy import stress_strain_elastic as stst"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Define the geometry and uniform load. Note that given the graphical nature of the notebook, extreme cases can cause the figures to not be displayed."
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 2,
	- "metadata": {},
	- "outputs": [],
	- "source": [
	- "# Choose the dimensions\n",
	- "L = 6 # [m]\n",
	- "h = 200 # [mm]\n",
	- "b = 100 # [mm]\n",
	- "q = 4; # [kN/m]\n",
	- "P = 10; # [kN]\n",
	- "\n",
	- "# Choose the material parameters\n",
	- "E_steel = 200e3 # [MPa] steel\n",
	- "fy_steel = 355 # [MPa] steel\n",
	- "E = E_steel\n",
	- "fy = fy_steel\n",
	- "\n",
	- "# compute the internal forces (at x=L)\n",
	- "discr_NVM = 100\n",
	- "x_discr = np.linspace(0, L, discr_NVM)\n",
	- "N_discr = sb.compute_N(x_discr, P)\n",
	- "V_discr = sb.compute_V(x_discr, q, L)\n",
	- "M_discr = sb.compute_M(x_discr, q, L)\n",
	- "N = N_discr[-1]\n",
	- "V = V_discr[-1]\n",
	- "M = M_discr[-1]\n",
	- "\n",
	- "# compute the parameters\n",
	- "A = beam_section.compute_area(b, h) # [mm2]\n",
	- "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	- "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	- "yG = beam_section.compute_centroid_y(h)\n",
	- "y_n_axis = stst.compute_neutral_axis(N, A, Iy, M, yG)\n",
	- "\n",
	- "# compute the reactions\n",
	- "Rx = sb.compute_Rx(P)\n",
	- "Ry_l = sb.compute_Ry_l(q, L)\n",
	- "Ry_r = sb.compute_Ry_r(q, L)"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Run the complex code for the interactive visualisation:"
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 3,
	- "metadata": {},
	- "outputs": [
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db['M'][0]\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_deflection_beam(db, beam_defl)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_deflection_beam(data, glyph_beam, discr=100) {\\n const q = data['q'][0]\\n const E = data['E'][0]\\n const L = data['L'][0]\\n const Iy = data['Iy'][0]\\n \\n const x = linspace(0, L, discr)\\n const defl = new Array(discr)\\n for(var i = 0; i < discr; i++) {\\n defl[i] = compute_deflection_uniform_load(x[i], q, L, Iy, E)\\n }\\n \\n const source = glyph_beam.data_source\\n source.data.x = x\\n source.data.y = defl\\n source.change.emit()\\n }\\n \\n \\n function compute_deflection_uniform_load(x, q, L, Iy, E) {\\n return -qx / (24EIy) (L*3-2Lx2+x3)1e12\\n }\\n \\n \"},\"id\":\"1908\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1670\"},\"N_stress_diag\":{\"id\":\"1652\"},\"V_stress_diag\":{\"id\":\"1688\"},\"arr_head\":{\"id\":\"1247\"},\"axial_strain_diag\":{\"id\":\"1742\"},\"bending_strain_diag\":{\"id\":\"1762\"},\"centroid\":{\"id\":\"1682\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"neutral_axis\":{\"id\":\"1718\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1706\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \"},\"id\":\"1907\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1994\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1602\",\"type\":\"ResetTool\"},{\"attributes\":{\"source\":{\"id\":\"1844\"}},\"id\":\"1849\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1995\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1670\"},\"N_stress_diag\":{\"id\":\"1652\"},\"V_stress_diag\":{\"id\":\"1688\"},\"axial_strain_diag\":{\"id\":\"1742\"},\"beam_defl\":{\"id\":\"1897\"},\"bending_strain_diag\":{\"id\":\"1762\"},\"centroid\":{\"id\":\"1682\"},\"div\":{\"id\":\"1107\"},\"neutral_axis\":{\"id\":\"1718\"},\"s_b\":{\"id\":\"1003\"},\"s_ss\":{\"id\":\"1006\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1706\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1099\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const h = cb_obj.value // value of the slider\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_deflection_beam(db, beam_defl)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_deflection_beam(data, glyph_beam, discr=100) {\\n const q = data['q'][0]\\n const E = data['E'][0]\\n const L = data['L'][0]\\n const Iy = data['Iy'][0]\\n \\n const x = linspace(0, L, discr)\\n const defl = new Array(discr)\\n for(var i = 0; i < discr; i++) {\\n defl[i] = compute_deflection_uniform_load(x[i], q, L, Iy, E)\\n }\\n \\n const source = glyph_beam.data_source\\n source.data.x = x\\n source.data.y = defl\\n source.change.emit()\\n }\\n \\n \\n function compute_deflection_uniform_load(x, q, L, Iy, E) {\\n return -qx / (24EIy) * (L*3-2Lx2+x3)1e12\\n }\\n \\n \"},\"id\":\"1909\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"1358\"},\"N_stress_diag\":{\"id\":\"1652\"},\"arr_head\":{\"id\":\"1247\"},\"axial_strain_diag\":{\"id\":\"1742\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"neutral_axis\":{\"id\":\"1718\"},\"s_M\":{\"id\":\"1236\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1706\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=100) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1910\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1599\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1247\"},\"div_P\":{\"id\":\"1253\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1911\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1853\",\"type\":\"Line\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1382\"},\"M_stress_diag\":{\"id\":\"1670\"},\"V_diag\":{\"id\":\"1370\"},\"V_stress_diag\":{\"id\":\"1688\"},\"arr_head\":{\"id\":\"1247\"},\"beam_defl\":{\"id\":\"1897\"},\"bending_strain_diag\":{\"id\":\"1762\"},\"centroid\":{\"id\":\"1682\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"neutral_axis\":{\"id\":\"1718\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1706\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_deflection_beam(db, beam_defl)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_deflection_beam(data, glyph_beam, discr=100) {\\n const q = data['q'][0]\\n const E = data['E'][0]\\n const L = data['L'][0]\\n const Iy = data['Iy'][0]\\n \\n const x = linspace(0, L, discr)\\n const defl = new Array(discr)\\n for(var i = 0; i < discr; i++) {\\n defl[i] = compute_deflection_uniform_load(x[i], q, L, Iy, E)\\n }\\n \\n const source = glyph_beam.data_source\\n source.data.x = x\\n source.data.y = defl\\n source.change.emit()\\n }\\n \\n \\n function compute_deflection_uniform_load(x, q, L, Iy, E) {\\n return -qx / (24EIy) (L*3-2Lx2+x3)1e12\\n }\\n \\n \"},\"id\":\"1912\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1598\",\"type\":\"PanTool\"},{\"attributes\":{\"data\":{\"x\":[-1.6666666666666667,0,0,-1.6666666666666667],\"y\":[-10,-10,10,10]},\"selected\":{\"id\":\"2153\"},\"selection_policy\":{\"id\":\"2152\"}},\"id\":\"1850\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1670\"},\"N_stress_diag\":{\"id\":\"1652\"},\"axial_strain_diag\":{\"id\":\"1742\"},\"beam_defl\":{\"id\":\"1897\"},\"bending_strain_diag\":{\"id\":\"1762\"},\"centroid\":{\"id\":\"1682\"},\"source\":{\"id\":\"1007\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const E = cb_obj.value\\n\\n // update E\\n db['E'][0] = E\\n\\n // update\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_deflection_beam(db, beam_defl)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function update_deflection_beam(data, glyph_beam, discr=100) {\\n const q = data['q'][0]\\n const E = data['E'][0]\\n const L = data['L'][0]\\n const Iy = data['Iy'][0]\\n \\n const x = linspace(0, L, discr)\\n const defl = new Array(discr)\\n for(var i = 0; i < discr; i++) {\\n defl[i] = compute_deflection_uniform_load(x[i], q, L, Iy, E)\\n }\\n \\n const source = glyph_beam.data_source\\n source.data.x = x\\n source.data.y = defl\\n source.change.emit()\\n }\\n \\n \\n function compute_deflection_uniform_load(x, q, L, Iy, E) {\\n return -qx / (24EIy) * (L*3-2Lx2+x3)1e12\\n }\\n \\n \"},\"id\":\"1913\",\"type\":\"CustomJS\"},{\"attributes\":{\"width\":10},\"id\":\"1914\",\"type\":\"Spacer\"},{\"attributes\":{},\"id\":\"1591\",\"type\":\"BasicTicker\"},{\"attributes\":{\"callback\":null,\"tooltips\":[[\"Stress\",\"@x MPa\"],[\"Height\",\"@y 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	- "hidden_code_nb_deflection.main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, E_steel, fy, fy_steel, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr)"
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	diff --git a/Simple Beam DEMOs/sb_diagrams.ipynb b/Simple Beam DEMOs/sb_diagrams.ipynb
	deleted file mode 100644
	index 1dbb53c..0000000
	--- a/Simple Beam DEMOs/sb_diagrams.ipynb
	+++ /dev/null
	@@ -1,565 +0,0 @@
	-{
	- "cells": [
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "# Simple beam - N V M Diagrams\n",
	- "In this third notebook, the internal axial force N, shear force V and bending moment M diagrams are studied on the same system, external force P and the uniform load q introduced in the DEMO \"sb_actions\"."
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "## Goals\n",
	- "\n",
	- "* Gain familiarity with the N V M diagrams\n",
	- "* Learn the relations between the three diagrams\n",
	- "* Note the direct correlation of the diagrams with the internal forces"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {
	- "tags": []
	- },
	- "source": [
	- "## Tasks and exercises\n",
	- "\n",
	- "Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	- "\n",
	- "1. In which position the bending moment M is the highest? Does the shear force V have correlation with the behaviour of the bending moment M?\n",
	- "\n",
	- " <details>\n",
	- " <summary style=\"color: red\">Solution:</summary>\n",
	- " The bending moment is the highest in the middle of the beam, at x = 3 m.\n",
	- " \n",
	- " Yes, in fact we can note that the shear force V is 0 when the moment is maximum and that the slope of the moment is directily correlated with the shear force V. The relation between V and M is the following $\\frac{dM}{dx} = V$.\n",
	- " </details>\n",
	- "\n",
	- "<br>\n",
	- "\n",
	- "2. In this case, does changing the uniform load q have any impact on the internal force N? What else do you note?\n",
	- "\n",
	- " <details>\n",
	- " <summary style=\"color: red\">Solution:</summary>\n",
	- " No, q has no influece with the axial force N, but it has direct impact with the shear force V, the bending moment M and the left and right vertical reaction.\n",
	- " </details>\n",
	- "\n",
	- "<br>\n",
	- "\n",
	- "3. Which impact has the chosen free-body diagram on the N V M diagrams?\n",
	- "\n",
	- " <details>\n",
	- " <summary style=\"color: red\">Solution:</summary>\n",
	- " None, beacuse the N V M diagrams are independent on the free-body diagram used to compute the equilibium. The signs of the diagrams are computed by following a sign conention, presented below:\n",
	- " <br>\n",
	- " <img src=\"img/Sign_convention.png\" alt=\"drawing\" width=\"600\"/>\n",
	- " </details>\n",
	- "\n",
	- "<br>"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "## Build the interactive visualisation tool"
	- ]
	- },
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	- "cell_type": "code",
	- "execution_count": 1,
	- "metadata": {},
	- "outputs": [
	- {
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	- " \"from bokeh.resources import INLINE\\n\"+\n",
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	- " }\n",
	- "\n",
	- " function load_libs(css_urls, js_urls, callback) {\n",
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	- "\n",
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	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
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	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.rel = \"stylesheet\";\n",
	- " element.type = \"text/css\";\n",
	- " element.href = url;\n",
	- " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < js_urls.length; i++) {\n",
	- " const url = js_urls[i];\n",
	- " const element = document.createElement('script');\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.async = false;\n",
	- " element.src = url;\n",
	- " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	- " document.head.appendChild(element);\n",
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	- " };\n",
	- "\n",
	- " function inject_raw_css(css) {\n",
	- " const element = document.createElement(\"style\");\n",
	- " element.appendChild(document.createTextNode(css));\n",
	- " document.body.appendChild(element);\n",
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	- },
	- "metadata": {},
	- "output_type": "display_data"
	- }
	- ],
	- "source": [
	- "# Import the packages needed\n",
	- "import sys\n",
	- "sys.path.append('../HiddenCode')\n",
	- "import hidden_code_nb_diagrams\n",
	- "import math\n",
	- "import numpy as np \n",
	- "from cienpy import simplebeam as sb\n",
	- "from cienpy import rectangular_section as beam_section"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Define the geometry, the external actions and compute the initial configuration."
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 2,
	- "metadata": {},
	- "outputs": [],
	- "source": [
	- "# Choose the dimensions\n",
	- "L = 6 # [m]\n",
	- "h = 200 # [mm]\n",
	- "b = 100 # [mm]\n",
	- "q = 4; # [kN/m]\n",
	- "P = 10; # [kN]\n",
	- "\n",
	- "# compute the internal forces (at x=L)\n",
	- "discr_NVM = 100\n",
	- "x_discr = np.linspace(0, L, discr_NVM)\n",
	- "N_discr = sb.compute_N(x_discr, P)\n",
	- "V_discr = sb.compute_V(x_discr, q, L)\n",
	- "M_discr = sb.compute_M(x_discr, q, L)\n",
	- "N = N_discr[-1]\n",
	- "V = V_discr[-1]\n",
	- "M = M_discr[-1]\n",
	- "\n",
	- "# compute the parameters\n",
	- "A = beam_section.compute_area(b, h) # [mm2]\n",
	- "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	- "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	- "\n",
	- "# compute the reactions\n",
	- "Rx = sb.compute_Rx(P)\n",
	- "Ry_l = sb.compute_Ry_l(q, L)\n",
	- "Ry_r = sb.compute_Ry_r(q, L)"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Run the complex code to generate the interactive visualisation tool:"
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 3,
	- "metadata": {},
	- "outputs": [
	- {
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mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \"},\"id\":\"1415\",\"type\":\"CustomJS\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"M\"}},\"id\":\"1409\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1456\",\"type\":\"AllLabels\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"V\"}},\"id\":\"1403\",\"type\":\"Circle\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"M\"}},\"id\":\"1410\",\"type\":\"Circle\"},{\"attributes\":{\"args\":{\"div\":{\"id\":\"1106\"},\"s_b\":{\"id\":\"1003\"},\"section\":{\"id\":\"1104\"},\"source\":{\"id\":\"1006\"},\"support_r\":{\"id\":\"1098\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \"},\"id\":\"1414\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1442\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1006\"},\"glyph\":{\"id\":\"1408\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1410\"},\"nonselection_glyph\":{\"id\":\"1409\"},\"view\":{\"id\":\"1412\"}},\"id\":\"1411\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"1006\"}},\"id\":\"1406\",\"type\":\"CDSView\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1252\"},\"div_P\":{\"id\":\"1258\"},\"div_f\":{\"id\":\"1260\"},\"fN\":{\"id\":\"1236\"},\"fP\":{\"id\":\"1224\"},\"fRx\":{\"id\":\"1233\"},\"fRyl\":{\"id\":\"1230\"},\"fRyr\":{\"id\":\"1227\"},\"fV\":{\"id\":\"1239\"},\"s_M\":{\"id\":\"1241\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"source\":{\"id\":\"1006\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \"},\"id\":\"1413\",\"type\":\"CustomJS\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"magenta\"},\"hatch_alpha\":{\"value\":0.5},\"hatch_color\":{\"value\":\"magenta\"},\"line_alpha\":{\"value\":0.5},\"line_color\":{\"value\":\"magenta\"},\"size\":{\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"M\"}},\"id\":\"1408\",\"type\":\"Circle\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"1363\"},\"arr_head\":{\"id\":\"1252\"},\"div_P\":{\"id\":\"1258\"},\"div_f\":{\"id\":\"1260\"},\"fN\":{\"id\":\"1236\"},\"fP\":{\"id\":\"1224\"},\"fRx\":{\"id\":\"1233\"},\"fRyl\":{\"id\":\"1230\"},\"fRyr\":{\"id\":\"1227\"},\"fV\":{\"id\":\"1239\"},\"s_M\":{\"id\":\"1241\"},\"source\":{\"id\":\"1006\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=100) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1416\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1252\"},\"div_P\":{\"id\":\"1258\"},\"fN\":{\"id\":\"1236\"},\"fP\":{\"id\":\"1224\"},\"fRx\":{\"id\":\"1233\"},\"fRyl\":{\"id\":\"1230\"},\"fRyr\":{\"id\":\"1227\"},\"fV\":{\"id\":\"1239\"},\"s_M\":{\"id\":\"1241\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"source\":{\"id\":\"1006\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1417\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1006\"},\"glyph\":{\"id\":\"1402\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1404\"},\"nonselection_glyph\":{\"id\":\"1403\"},\"view\":{\"id\":\"1406\"}},\"id\":\"1405\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1387\"},\"V_diag\":{\"id\":\"1375\"},\"arr_head\":{\"id\":\"1252\"},\"div_P\":{\"id\":\"1258\"},\"div_f\":{\"id\":\"1260\"},\"fN\":{\"id\":\"1236\"},\"fP\":{\"id\":\"1224\"},\"fRx\":{\"id\":\"1233\"},\"fRyl\":{\"id\":\"1230\"},\"fRyr\":{\"id\":\"1227\"},\"fV\":{\"id\":\"1239\"},\"s_M\":{\"id\":\"1241\"},\"s_q\":{\"id\":\"1005\"},\"source\":{\"id\":\"1006\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]*10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n 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<p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = 200 mm<br>\\n b = 100 mm<br>\\n L = 6 m<br>\\n A = 2.00e+04 mm<sup>2</sup><br>\\n Iy = 6.67e+07 mm<sup>4</sup><br>\\n Iz = 1.67e+07 mm<sup>4</sup>\"},\"id\":\"1106\",\"type\":\"Div\"},{\"attributes\":{},\"id\":\"1498\",\"type\":\"Selection\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_alpha\":{\"value\":0.1},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1123\",\"type\":\"Text\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1118\"},\"group\":null,\"line_color\":{\"value\":\"gray\"},\"line_width\":{\"value\":2.1972245773362196},\"source\":{\"id\":\"1508\"},\"start\":null,\"x_end\":{\"value\":-80.0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1119\",\"type\":\"Arrow\"},{\"attributes\":{\"source\":{\"id\":\"1094\"}},\"id\":\"1099\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1499\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"fill_color\":{\"value\":\"gray\"},\"line_color\":{\"value\":\"gray\"},\"size\":{\"value\":15.380572041353537}},\"id\":\"1109\",\"type\":\"VeeHead\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1109\"},\"group\":null,\"line_color\":{\"value\":\"gray\"},\"line_width\":{\"value\":2.1972245773362196},\"source\":{\"id\":\"1507\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":128.0},\"y_start\":{\"value\":0}},\"id\":\"1110\",\"type\":\"Arrow\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"white\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_pattern\":{\"value\":\"/\"},\"height\":{\"value\":200},\"line_alpha\":{\"value\":0.2},\"line_width\":{\"value\":3},\"width\":{\"value\":100},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1103\",\"type\":\"Rect\"},{\"attributes\":{},\"id\":\"1500\",\"type\":\"Selection\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_alpha\":{\"value\":0.2},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1115\",\"type\":\"Text\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1100\"},\"glyph\":{\"id\":\"1101\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1103\"},\"nonselection_glyph\":{\"id\":\"1102\"},\"view\":{\"id\":\"1105\"}},\"id\":\"1104\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"data\":{\"text\":[\"y\"],\"x\":[0],\"y\":[136.0]},\"selected\":{\"id\":\"1538\"},\"selection_policy\":{\"id\":\"1537\"}},\"id\":\"1112\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"source\":{\"id\":\"1100\"}},\"id\":\"1105\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1501\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"end\":300,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1414\"}]},\"start\":10,\"step\":10,\"title\":\"Change 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	- " const render_items = [{\"docid\":\"9b573d13-698b-4ace-a16d-eea151a69129\",\"root_ids\":[\"1430\"],\"roots\":{\"1430\":\"1bb0cdda-33e0-4f5e-a634-8e50d1c48ecd\"}}];\n",
	- " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	- "\n",
	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " embed_document(root);\n",
	- " } else {\n",
	- " let attempts = 0;\n",
	- " const timer = setInterval(function(root) {\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " clearInterval(timer);\n",
	- " embed_document(root);\n",
	- " } else {\n",
	- " attempts++;\n",
	- " if (attempts > 100) {\n",
	- " clearInterval(timer);\n",
	- " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	- " }\n",
	- " }\n",
	- " }, 10, root)\n",
	- " }\n",
	- "})(window);"
	- ],
	- "application/vnd.bokehjs_exec.v0+json": ""
	- },
	- "metadata": {
	- "application/vnd.bokehjs_exec.v0+json": {
	- "id": "1430"
	- }
	- },
	- "output_type": "display_data"
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	- ],
	- "source": [
	- "hidden_code_nb_diagrams.main_code(L, h, b, A, Iy, Iz, q, P, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr)"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {
	- "tags": []
	- },
	- "source": [
	- "## Legend\n",
	- "\n",
	- "Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder.\n",
	- "\n",
	- "* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	- "* Slider of height h: move the slider to change the height h of the cross-section of the beam.\n",
	- "* Slider of the position x: move the slider to change the position x along the beam.\n",
	- "* Slider of the uniform load q: move the slider to change the uniform load q.\n",
	- "* Textbox \"Geometrical and mechanical parameters: small summary with the value of h, b, L, A (area), Iy (inertia with respect to the strong axis) and Iz (inertia with respect to the weak axis).\n",
	- "* Textbox \"Forces and Moments: small summary with the value of the magnitude of the reaction forces and the internal forces at the position x.\n",
	- "* Figure \"Simple supported beam\": in this figure, the initial state is presented with the static scheme, the length of the beam, the horizontal force P and the uniform load q.\n",
	- "* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	- "* Figure \"Forces and Moments Scheme\": this figure has a dynamic representation of the studied case with the position x indicated by a magenta dot, the internal forces shown in with red arrows, the reaction forces with yellow arrows, the external force P with a green arrow and the uniform load q in blue.\n",
	- "* Radio buttons of the FBD: choose between right-hand or left-hand free-body diagram.\n",
	- "* Button of the force P: apply or remove the external force P.\n",
	- "* Figures \"N V M Diagrams\": plots that show the axial force N, shear force V and bending moment M diagrams, with a magenta dot that represents the x position. By hovering with the cursor over the desired position, a small window will show the position and the value of the internal force.\n",
	- "\n",
	- "### Recommendations\n",
	- "\n",
	- "Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully."
	- ]
	- }
	- ],
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	- "pygments_lexer": "ipython3",
	- "version": "3.8.10"
	- }
	- },
	- "nbformat": 4,
	- "nbformat_minor": 4
	-}
	diff --git a/Simple Beam DEMOs/sb_mohr.ipynb b/Simple Beam DEMOs/sb_mohr.ipynb
	deleted file mode 100644
	index 38281f1..0000000
	--- a/Simple Beam DEMOs/sb_mohr.ipynb
	+++ /dev/null
	@@ -1,502 +0,0 @@
	-{
	- "cells": [
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "# Simple beam - Mohr Circle\n",
	- "In this first notebook, the Mohr circle is presented."
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 1,
	- "metadata": {},
	- "outputs": [
	- {
	- "data": {
	- "text/html": [
	- "\n",
	- " <div class=\"bk-root\">\n",
	- " <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	- " <span id=\"1002\">Loading BokehJS ...</span>\n",
	- " </div>"
	- ]
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- },
	- {
	- "data": {
	- "application/javascript": [
	- "\n",
	- "(function(root) {\n",
	- " function now() {\n",
	- " return new Date();\n",
	- " }\n",
	- "\n",
	- " const force = true;\n",
	- "\n",
	- " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_onload_callbacks = [];\n",
	- " root._bokeh_is_loading = undefined;\n",
	- " }\n",
	- "\n",
	- " const JS_MIME_TYPE = 'application/javascript';\n",
	- " const HTML_MIME_TYPE = 'text/html';\n",
	- " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	- " const CLASS_NAME = 'output_bokeh rendered_html';\n",
	- "\n",
	- " /**\n",
	- " * Render data to the DOM node\n",
	- " */\n",
	- " function render(props, node) {\n",
	- " const script = document.createElement(\"script\");\n",
	- " node.appendChild(script);\n",
	- " }\n",
	- "\n",
	- " /**\n",
	- " * Handle when an output is cleared or removed\n",
	- " */\n",
	- " function handleClearOutput(event, handle) {\n",
	- " const cell = handle.cell;\n",
	- "\n",
	- " const id = cell.output_area._bokeh_element_id;\n",
	- " const server_id = cell.output_area._bokeh_server_id;\n",
	- " // Clean up Bokeh references\n",
	- " if (id != null && id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- "\n",
	- " if (server_id !== undefined) {\n",
	- " // Clean up Bokeh references\n",
	- " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	- " cell.notebook.kernel.execute(cmd_clean, {\n",
	- " iopub: {\n",
	- " output: function(msg) {\n",
	- " const id = msg.content.text.trim();\n",
	- " if (id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- " }\n",
	- " }\n",
	- " });\n",
	- " // Destroy server and session\n",
	- " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	- " cell.notebook.kernel.execute(cmd_destroy);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " /**\n",
	- " * Handle when a new output is added\n",
	- " */\n",
	- " function handleAddOutput(event, handle) {\n",
	- " const output_area = handle.output_area;\n",
	- " const output = handle.output;\n",
	- "\n",
	- " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	- " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	- " return\n",
	- " }\n",
	- "\n",
	- " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
	- "\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	- " // store reference to embed id on output_area\n",
	- " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
	- " }\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	- " const bk_div = document.createElement(\"div\");\n",
	- " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	- " const script_attrs = bk_div.children[0].attributes;\n",
	- " for (let i = 0; i < script_attrs.length; i++) {\n",
	- " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	- " }\n",
	- " // store reference to server id on output_area\n",
	- " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function register_renderer(events, OutputArea) {\n",
	- "\n",
	- " function append_mime(data, metadata, element) {\n",
	- " // create a DOM node to render to\n",
	- " const toinsert = this.create_output_subarea(\n",
	- " metadata,\n",
	- " CLASS_NAME,\n",
	- " EXEC_MIME_TYPE\n",
	- " );\n",
	- " this.keyboard_manager.register_events(toinsert);\n",
	- " // Render to node\n",
	- " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	- " render(props, toinsert[toinsert.length - 1]);\n",
	- " element.append(toinsert);\n",
	- " return toinsert\n",
	- " }\n",
	- "\n",
	- " /* Handle when an output is cleared or removed */\n",
	- " events.on('clear_output.CodeCell', handleClearOutput);\n",
	- " events.on('delete.Cell', handleClearOutput);\n",
	- "\n",
	- " /* Handle when a new output is added */\n",
	- " events.on('output_added.OutputArea', handleAddOutput);\n",
	- "\n",
	- " /**\n",
	- " * Register the mime type and append_mime function with output_area\n",
	- " */\n",
	- " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	- " /* Is output safe? */\n",
	- " safe: true,\n",
	- " /* Index of renderer in `output_area.display_order` */\n",
	- " index: 0\n",
	- " });\n",
	- " }\n",
	- "\n",
	- " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	- " if (root.Jupyter !== undefined) {\n",
	- " const events = require('base/js/events');\n",
	- " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	- "\n",
	- " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	- " register_renderer(events, OutputArea);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " \n",
	- " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_timeout = Date.now() + 5000;\n",
	- " root._bokeh_failed_load = false;\n",
	- " }\n",
	- "\n",
	- " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	- " \"<div style='background-color: #fdd'>\\n\"+\n",
	- " \"<p>\\n\"+\n",
	- " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	- " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	- " \"</p>\\n\"+\n",
	- " \"<ul>\\n\"+\n",
	- " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	- " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	- " \"</ul>\\n\"+\n",
	- " \"<code>\\n\"+\n",
	- " \"from bokeh.resources import INLINE\\n\"+\n",
	- " \"output_notebook(resources=INLINE)\\n\"+\n",
	- " \"</code>\\n\"+\n",
	- " \"</div>\"}};\n",
	- "\n",
	- " function display_loaded() {\n",
	- " const el = document.getElementById(\"1002\");\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS is loading...\";\n",
	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	- " }\n",
	- " } else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(display_loaded, 100)\n",
	- " }\n",
	- " }\n",
	- "\n",
	- "\n",
	- " function run_callbacks() {\n",
	- " try {\n",
	- " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	- " if (callback != null)\n",
	- " callback();\n",
	- " });\n",
	- " } finally {\n",
	- " delete root._bokeh_onload_callbacks\n",
	- " }\n",
	- " console.debug(\"Bokeh: all callbacks have finished\");\n",
	- " }\n",
	- "\n",
	- " function load_libs(css_urls, js_urls, callback) {\n",
	- " if (css_urls == null) css_urls = [];\n",
	- " if (js_urls == null) js_urls = [];\n",
	- "\n",
	- " root._bokeh_onload_callbacks.push(callback);\n",
	- " if (root._bokeh_is_loading > 0) {\n",
	- " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	- " return null;\n",
	- " }\n",
	- " if (js_urls == null \|\| js_urls.length === 0) {\n",
	- " run_callbacks();\n",
	- " return null;\n",
	- " }\n",
	- " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	- " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	- "\n",
	- " function on_load() {\n",
	- " root._bokeh_is_loading--;\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	- " run_callbacks()\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function on_error(url) {\n",
	- " console.error(\"failed to load \" + url);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < css_urls.length; i++) {\n",
	- " const url = css_urls[i];\n",
	- " const element = document.createElement(\"link\");\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.rel = \"stylesheet\";\n",
	- " element.type = \"text/css\";\n",
	- " element.href = url;\n",
	- " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < js_urls.length; i++) {\n",
	- " const url = js_urls[i];\n",
	- " const element = document.createElement('script');\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.async = false;\n",
	- " element.src = url;\n",
	- " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	- " document.head.appendChild(element);\n",
	- " }\n",
	- " };\n",
	- "\n",
	- " function inject_raw_css(css) {\n",
	- " const element = document.createElement(\"style\");\n",
	- " element.appendChild(document.createTextNode(css));\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " \n",
	- " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	- " const css_urls = [];\n",
	- " \n",
	- "\n",
	- " const inline_js = [\n",
	- " function(Bokeh) {\n",
	- " Bokeh.set_log_level(\"info\");\n",
	- " },\n",
	- " function(Bokeh) {\n",
	- " \n",
	- " \n",
	- " }\n",
	- " ];\n",
	- "\n",
	- " function run_inline_js() {\n",
	- " \n",
	- " if (root.Bokeh !== undefined \|\| force === true) {\n",
	- " \n",
	- " for (let i = 0; i < inline_js.length; i++) {\n",
	- " inline_js[i].call(root, root.Bokeh);\n",
	- " }\n",
	- " if (force === true) {\n",
	- " display_loaded();\n",
	- " }} else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(run_inline_js, 100);\n",
	- " } else if (!root._bokeh_failed_load) {\n",
	- " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
	- " root._bokeh_failed_load = true;\n",
	- " } else if (force !== true) {\n",
	- " const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
	- " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
	- " }\n",
	- "\n",
	- " }\n",
	- "\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
	- " run_inline_js();\n",
	- " } else {\n",
	- " load_libs(css_urls, js_urls, function() {\n",
	- " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	- " run_inline_js();\n",
	- " });\n",
	- " }\n",
	- "}(window));"
	- ],
	- "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n function now() {\n return new Date();\n }\n\n const force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n \n\n \n if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n const NB_LOAD_WARNING = {'data': {'text/html':\n \"<div style='background-color: #fdd'>\\n\"+\n \"<p>\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"</p>\\n\"+\n \"<ul>\\n\"+\n \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n \"<li>use INLINE resources instead, as so:</li>\\n\"+\n \"</ul>\\n\"+\n \"<code>\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"</code>\\n\"+\n \"</div>\"}};\n\n function display_loaded() {\n const el = document.getElementById(\"1002\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null \|\| js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error(url) {\n console.error(\"failed to load \" + url);\n }\n\n for (let i = 0; i < css_urls.length; i++) {\n const url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n \n const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n const css_urls = [];\n \n\n const inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n function(Bokeh) {\n \n \n }\n ];\n\n function run_inline_js() {\n \n if (root.Bokeh !== undefined \|\| force === true) {\n \n for (let i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\n if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));"
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- }
	- ],
	- "source": [
	- "# Import the packages needed\n",
	- "import sys\n",
	- "sys.path.append('../HiddenCode')\n",
	- "import hidden_code_nb_mohr\n",
	- "import math\n",
	- "import numpy as np\n",
	- "from cienpy import simplebeam as sb\n",
	- "from cienpy import rectangular_section as beam_section\n",
	- "from cienpy import stress_strain_elastic as stst\n",
	- "from cienpy import mohrcircle"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Define the geometry and uniform load. Note that given the graphical nature of the notebook, extreme cases can cause the figures to not be displayed."
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 2,
	- "metadata": {},
	- "outputs": [],
	- "source": [
	- "# Choose the dimensions\n",
	- "L = 6 # [m]\n",
	- "h = 200 # [mm]\n",
	- "b = 100 # [mm]\n",
	- "q = 4; # [kN/m]\n",
	- "P = 10; # [kN]\n",
	- "\n",
	- "# Choose the material parameters\n",
	- "E = 200e3 # [MPa]\n",
	- "\n",
	- "# compute the internal forces (at x=L)\n",
	- "discr_NVM = 100\n",
	- "x_discr = np.linspace(0, L, discr_NVM)\n",
	- "N_discr = sb.compute_N(x_discr, P)\n",
	- "V_discr = sb.compute_V(x_discr, q, L)\n",
	- "M_discr = sb.compute_M(x_discr, q, L)\n",
	- "N = N_discr[-1]\n",
	- "V = V_discr[-1]\n",
	- "M = M_discr[-1]\n",
	- "\n",
	- "# compute the parameters\n",
	- "A = beam_section.compute_area(b, h) # [mm2]\n",
	- "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	- "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	- "yG = beam_section.compute_centroid_y(h)\n",
	- "y_n_axis = stst.compute_neutral_axis(N, A, Iy, M, yG)\n",
	- "\n",
	- "# compute the reactions\n",
	- "Rx = sb.compute_Rx(P)\n",
	- "Ry_l = sb.compute_Ry_l(q, L)\n",
	- "Ry_r = sb.compute_Ry_r(q, L)\n",
	- "\n",
	- "# compute Mohr circle parameters\n",
	- "initial_y = h\n",
	- "initial_theta_element = 0\n",
	- "sigma_axial = stst.compute_sigma_axial(initial_y, N, A)\n",
	- "sigma_bending = stst.compute_sigma_bending(initial_y, M, Iy, yG)\n",
	- "S = beam_section. compute_first_moment_of_area(initial_y, b, h, yG)\n",
	- "sigma_tau = stst.compute_tau_shear(initial_y, V, S, Iy, b)\n",
	- "sigma_x0 = stst.compute_total_sigma(sigma_axial, sigma_bending)\n",
	- "sigma_y0 = 0 # no vertical axial forces\n",
	- "tau_0 = stst.compute_total_tau(sigma_tau)\n",
	- "sigma_average_mohr = mohrcircle.compute_sigma_average_mohr(sigma_x0, sigma_y0)\n",
	- "r_circle_mohr = mohrcircle.compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\n",
	- "theta_principal = mohrcircle.compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\n",
	- "initial_theta = mohrcircle.compute_theta_mohr(initial_theta_element, theta_principal)\n",
	- "\n",
	- "# stress state in function of theta\n",
	- "new_state = mohrcircle.compute_stress_state_mohr(sigma_average_mohr, r_circle_mohr, initial_theta)"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Run the complex code for the interactive visualisation:"
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 3,
	- "metadata": {},
	- "outputs": [
	- {
	- "data": {
	- "text/html": [
	- "\n",
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	- "\n",
	- "\n",
	- " <div class=\"bk-root\" id=\"2e089feb-3b1b-4ecc-9884-faba18e88063\" data-root-id=\"2162\"></div>\n"
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	- "metadata": {},
	- "output_type": "display_data"
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	- " function embed_document(root) {\n",
	- " \n",
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":\"red\"},\"hatch_alpha\":{\"value\":0.2},\"hatch_color\":{\"value\":\"red\"},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"red\"},\"size\":{\"value\":5},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2126\",\"type\":\"Circle\"},{\"attributes\":{\"source\":{\"id\":\"1770\"}},\"id\":\"1775\",\"type\":\"CDSView\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"red\"},\"hatch_alpha\":{\"value\":0.1},\"hatch_color\":{\"value\":\"red\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"red\"},\"size\":{\"value\":5},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2125\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"2384\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_color\":{\"value\":\"red\"},\"text_font_size\":{\"value\":\"14px\"},\"x\":{\"field\":\"x\"},\"x_offset\":{\"value\":-5},\"y\":{\"field\":\"y\"},\"y_offset\":{\"value\":18}},\"id\":\"2130\",\"type\":\"Text\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"N and M at position x\"},\"id\":\"1779\",\"type\":\"Title\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"2129\"},\"glyph\":{\"id\":\"2130\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"2132\"},\"nonselection_glyph\":{\"id\":\"2131\"},\"view\":{\"id\":\"2134\"}},\"id\":\"2133\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"axis_label\":\"Height h [mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"2381\"},\"group\":null,\"major_label_policy\":{\"id\":\"2382\"},\"ticker\":{\"id\":\"1794\"},\"visible\":false},\"id\":\"1793\",\"type\":\"LinearAxis\"},{\"attributes\":{\"data\":{\"text\":[\"Rotating element \\n(\\u03c3\\u2093, \\u03c4)\",\"Rotating element \\n(\\u03c3\\u1d67, -\\u03c4)\"],\"x\":[-0.5,0.0],\"y\":[0,-0.0]},\"selected\":{\"id\":\"2221\"},\"selection_policy\":{\"id\":\"2220\"}},\"id\":\"2129\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"below\":[{\"id\":\"1822\"}],\"center\":[{\"id\":\"1825\"},{\"id\":\"1829\"},{\"id\":\"1860\"}],\"height\":200,\"left\":[{\"id\":\"1826\"}],\"match_aspect\":true,\"renderers\":[{\"id\":\"1854\"},{\"id\":\"1891\"}],\"title\":{\"id\":\"1812\"},\"toolbar\":{\"id\":\"1837\"},\"toolbar_location\":null,\"width\":200,\"x_range\":{\"id\":\"1814\"},\"x_scale\":{\"id\":\"1818\"},\"y_range\":{\"id\":\"1816\"},\"y_scale\":{\"id\":\"1820\"}},\"id\":\"1811\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"2385\",\"type\":\"AllLabels\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"2123\"},\"glyph\":{\"id\":\"2124\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"2126\"},\"nonselection_glyph\":{\"id\":\"2125\"},\"view\":{\"id\":\"2128\"}},\"id\":\"2127\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"2327\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1794\",\"type\":\"BasicTicker\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_alpha\":{\"value\":0.1},\"text_color\":{\"value\":\"red\"},\"text_font_size\":{\"value\":\"14px\"},\"x\":{\"field\":\"x\"},\"x_offset\":{\"value\":-5},\"y\":{\"field\":\"y\"},\"y_offset\":{\"value\":18}},\"id\":\"2131\",\"type\":\"Text\"},{\"attributes\":{\"source\":{\"id\":\"2129\"}},\"id\":\"2134\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"2328\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1802\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1797\",\"type\":\"PanTool\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1670\"},\"Mohr_circle\":{\"id\":\"2073\"},\"N_stress_diag\":{\"id\":\"1652\"},\"V_stress_diag\":{\"id\":\"1688\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arr_head\":{\"id\":\"1247\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1\":{\"id\":\"2034\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2\":{\"id\":\"2037\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1\":{\"id\":\"2040\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2\":{\"id\":\"2043\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"axial_strain_diag\":{\"id\":\"1742\"},\"bending_strain_diag\":{\"id\":\"1762\"},\"centroid\":{\"id\":\"1682\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"neutral_axis\":{\"id\":\"1718\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1706\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n const N = compute_N(db['P'][0])\\n const V = compute_V(pos, q, L)\\n const M = compute_M(pos, q, L)\\n\\n // update data\\n db['N'][0] = N\\n db['V'][0] = V\\n db['M'][0] = M\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n \\n const y_var = db['y_var'][0]\\n const A = db['A'][0]\\n const b = db['b'][0]\\n const h = db['h'][0]\\n const yG = db['yG'][0]\\n const Iy = db['Iy'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // update data\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n \\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2135\",\"type\":\"CustomJS\"},{\"attributes\":{\"overlay\":{\"id\":\"1803\"}},\"id\":\"1799\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"red\"},\"text_font_size\":{\"value\":\"14px\"},\"x\":{\"field\":\"x\"},\"x_offset\":{\"value\":-5},\"y\":{\"field\":\"y\"},\"y_offset\":{\"value\":18}},\"id\":\"2132\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"1800\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1801\",\"type\":\"ResetTool\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1670\"},\"Mohr_circle\":{\"id\":\"2073\"},\"N_stress_diag\":{\"id\":\"1652\"},\"V_stress_diag\":{\"id\":\"1688\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1\":{\"id\":\"2034\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2\":{\"id\":\"2037\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1\":{\"id\":\"2040\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2\":{\"id\":\"2043\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"axial_strain_diag\":{\"id\":\"1742\"},\"bending_strain_diag\":{\"id\":\"1762\"},\"centroid\":{\"id\":\"1682\"},\"div\":{\"id\":\"1119\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"neutral_axis\":{\"id\":\"1718\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"section\":{\"id\":\"1117\"},\"sigma_stress_diag\":{\"id\":\"1706\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1057\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const V = db['V'][0]\\n const y_var = db['y_var'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n // Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2136\",\"type\":\"CustomJS\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1803\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2459\"},\"selection_policy\":{\"id\":\"2458\"}},\"id\":\"2386\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1670\"},\"Mohr_circle\":{\"id\":\"2073\"},\"N_stress_diag\":{\"id\":\"1652\"},\"V_stress_diag\":{\"id\":\"1688\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1\":{\"id\":\"2034\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2\":{\"id\":\"2037\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1\":{\"id\":\"2040\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2\":{\"id\":\"2043\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"axial_strain_diag\":{\"id\":\"1742\"},\"beam\":{\"id\":\"1045\"},\"bending_strain_diag\":{\"id\":\"1762\"},\"centroid\":{\"id\":\"1682\"},\"div\":{\"id\":\"1119\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"neutral_axis\":{\"id\":\"1718\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"s_ss\":{\"id\":\"1006\"},\"section\":{\"id\":\"1117\"},\"sigma_stress_diag\":{\"id\":\"1706\"},\"slider_y\":{\"id\":\"1899\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1057\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // solve sliders conflict\\n const db = source.data\\n const h = cb_obj.value // value of the slider\\n if (h < db['y_var'][0]) {\\n db['y_var'][0] = h\\n }\\n slider_y.end = h\\n if (h < slider_y.value) {\\n slider_y.value = h\\n }\\n\\n // retrieve data used\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const N = db['N'][0]\\n const V = db['V'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n const y_var = db['y_var'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n beam.glyph.height = h // change the beam height\\n beam.glyph.y = h/2\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n // Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2137\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"Mohr_circle\":{\"id\":\"2073\"},\"N_diag\":{\"id\":\"1358\"},\"N_stress_diag\":{\"id\":\"1652\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arr_head\":{\"id\":\"1247\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"axial_strain_diag\":{\"id\":\"1742\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"neutral_axis\":{\"id\":\"1718\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"s_M\":{\"id\":\"1236\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1706\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const P = 10(1-f)\\n const db = source.data\\n const N = compute_N(P)\\n const M = db['M'][0]\\n const A = db['A'][0]\\n const Iy = db['Iy'][0]\\n const yG = db['yG'][0]\\n const y_var = db['y_var'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = db['tau_0'][0]\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // apply the changes\\n db['P'][0] = P\\n db['N'][0] = N\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n // Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=100) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2138\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1247\"},\"div_P\":{\"id\":\"1253\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"2139\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2329\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"text_baseline\":{\"value\":\"top\"},\"text_color\":{\"value\":\"red\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1882\",\"type\":\"Text\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1382\"},\"M_stress_diag\":{\"id\":\"1670\"},\"Mohr_circle\":{\"id\":\"2073\"},\"V_diag\":{\"id\":\"1370\"},\"V_stress_diag\":{\"id\":\"1688\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arr_head\":{\"id\":\"1247\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1\":{\"id\":\"2034\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2\":{\"id\":\"2037\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1\":{\"id\":\"2040\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2\":{\"id\":\"2043\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"bending_strain_diag\":{\"id\":\"1762\"},\"centroid\":{\"id\":\"1682\"},\"div_P\":{\"id\":\"1253\"},\"div_f\":{\"id\":\"1255\"},\"fN\":{\"id\":\"1231\"},\"fP\":{\"id\":\"1219\"},\"fRx\":{\"id\":\"1228\"},\"fRyl\":{\"id\":\"1225\"},\"fRyr\":{\"id\":\"1222\"},\"fV\":{\"id\":\"1234\"},\"label_M_section\":{\"id\":\"1885\"},\"label_N_section\":{\"id\":\"1879\"},\"label_V_section\":{\"id\":\"1891\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"neutral_axis\":{\"id\":\"1718\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"s_M\":{\"id\":\"1236\"},\"s_q\":{\"id\":\"1005\"},\"s_section_M\":{\"id\":\"1862\"},\"section_M_head\":{\"id\":\"1873\"},\"section_N\":{\"id\":\"1857\"},\"section_V\":{\"id\":\"1860\"},\"sigma_stress_diag\":{\"id\":\"1706\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1724\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n const N = db['N'][0]\\n const V = compute_V(pos, q, L)\\n const M = compute_M(pos, q, L)\\n const y_var = db['y_var'][0]\\n const A = db['A'][0]\\n const b = db['b'][0]\\n const h = db['h'][0]\\n const yG = db['yG'][0]\\n const Iy = db['Iy'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // update data\\n db['q'][0] = q\\n db['V'][0] = V\\n db['M'][0] = M\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n // Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2140\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1875\"},\"glyph\":{\"id\":\"1876\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1878\"},\"nonselection_glyph\":{\"id\":\"1877\"},\"view\":{\"id\":\"1880\"}},\"id\":\"1879\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"2330\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"Mohr_circle\":{\"id\":\"2073\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_element\":{\"id\":\"2007\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"beam_position\":{\"id\":\"1897\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_stress_state_theta\":{\"id\":\"1995\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_element\":{\"id\":\"2013\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"rotating_axis\":{\"id\":\"2001\"},\"source\":{\"id\":\"1007\"},\"stress_state_theta\":{\"id\":\"1989\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const theta_element = cb_obj.value/180Math.PI\\n const sigma_x0 = db['sigma_x0'][0]\\n const sigma_y0 = db['sigma_y0'][0]\\n const tau_0 = db['tau_0'][0]\\n const sigma_average = db['sigma_average'][0]\\n const r_circle = db['r_circle_mohr'][0]\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // update data\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta_element'][0] = theta_element\\n db['theta'][0] = theta\\n\\n // update\\n // square point:\\n beam_position.glyph.angle = theta_element\\n // stress state element\\n update_stress_state_elements(db, stress_state_theta, rotating_axis, label_stress_state_theta, arc_theta_element, label_theta_element)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n // update Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_stress_state_elements(data, glyph_stress_state_theta, glyph_axis, glyph_label_element_theta, glyph_arc_theta, glyph_label_theta, max_stress=60, max_dim=150.0) {\\n // set variables\\n const theta_element = data['theta_element'][0]\\n const x_new = max_stressMath.cos(theta_element)\\n const y_new = max_stressMath.sin(theta_element)\\n \\n \\n // update rotating axis\\n const src_axis = glyph_axis.data_source\\n src_axis.data.x = [0, x_newmax_dim/max_stress]\\n src_axis.data.y = [0, y_newmax_dim/max_stress]\\n src_axis.change.emit()\\n \\n // update stress state theta\\n glyph_stress_state_theta.glyph.angle = theta_element\\n glyph_stress_state_theta.glyph.x = x_new2\\n glyph_stress_state_theta.glyph.y = y_new2\\n \\n // label element\\n const src_label_element = glyph_label_element_theta.data_source\\n src_label_element.data.x = [x_new2]\\n src_label_element.data.y = [y_new2]\\n src_label_element.change.emit()\\n \\n // arc theta (stress state)\\n glyph_arc_theta.glyph.end_angle = theta_element\\n \\n // label theta (stress state)\\n if (theta_element==0) {\\n glyph_label_theta.glyph.text = \\\"\\\"\\n } else {\\n glyph_label_theta.glyph.text = \\\"\\u03b8\\\"\\n const src_label_theta = glyph_label_theta.data_source\\n src_label_theta.data.x = [max_stressMath.cos(theta_element/2)]\\n src_label_theta.data.y = [max_stressMath.sin(theta_element/2)]\\n src_label_theta.change.emit()\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n AHF)\\n }\\n \\n \"},\"id\":\"2141\",\"type\":\"CustomJS\"},{\"attributes\":{\"source\":{\"id\":\"1875\"}},\"id\":\"1880\",\"type\":\"CDSView\"},{\"attributes\":{\"args\":{\"Mohr_circle\":{\"id\":\"2073\"},\"arc_theta_Mohr\":{\"id\":\"2079\"},\"arc_theta_p_Mohr\":{\"id\":\"2091\"},\"arrow_sigma_x1\":{\"id\":\"2022\"},\"arrow_sigma_x1_theta\":{\"id\":\"2046\"},\"arrow_sigma_x2\":{\"id\":\"2025\"},\"arrow_sigma_x2_theta\":{\"id\":\"2049\"},\"arrow_sigma_y1\":{\"id\":\"2028\"},\"arrow_sigma_y1_theta\":{\"id\":\"2052\"},\"arrow_sigma_y2\":{\"id\":\"2031\"},\"arrow_sigma_y2_theta\":{\"id\":\"2055\"},\"arrow_tau_x1\":{\"id\":\"2034\"},\"arrow_tau_x1_theta\":{\"id\":\"2058\"},\"arrow_tau_x2\":{\"id\":\"2037\"},\"arrow_tau_x2_theta\":{\"id\":\"2061\"},\"arrow_tau_y1\":{\"id\":\"2040\"},\"arrow_tau_y1_theta\":{\"id\":\"2064\"},\"arrow_tau_y2\":{\"id\":\"2043\"},\"arrow_tau_y2_theta\":{\"id\":\"2067\"},\"beam_position\":{\"id\":\"1897\"},\"label_points_stress_state\":{\"id\":\"2115\"},\"label_points_stress_state_theta\":{\"id\":\"2133\"},\"label_theta_Mohr\":{\"id\":\"2085\"},\"label_theta_p_Mohr\":{\"id\":\"2097\"},\"line_stress_state\":{\"id\":\"2103\"},\"line_stress_state_theta\":{\"id\":\"2121\"},\"points_stress_state\":{\"id\":\"2109\"},\"points_stress_state_theta\":{\"id\":\"2127\"},\"source\":{\"id\":\"1007\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const y_var = cb_obj.value\\n const N = db['N'][0]\\n const V = db['V'][0]\\n const M = db['M'][0]\\n const A = db['A'][0]\\n const b = db['b'][0]\\n const h = db['h'][0]\\n const yG = db['yG'][0]\\n const Iy = db['Iy'][0]\\n const theta_element = db['theta_element'][0]\\n const sigma_x0 = compute_total_sigma(compute_sigma_axial(N, A), compute_sigma_bending(y_var, M, Iy, yG))\\n const sigma_y0 = 0\\n const tau_0 = compute_total_tau(compute_tau_shear(V, compute_first_moment_of_area(y_var, b, h, yG), Iy, b))\\n const sigma_average = compute_sigma_average_mohr(sigma_x0, sigma_y0)\\n const r_circle = compute_radius_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta_principal = compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0)\\n const theta = compute_theta_mohr(theta_element, theta_principal)\\n const new_state = compute_stress_state_mohr(sigma_average, r_circle, theta)\\n\\n // update data\\n db['y_var'][0] = y_var\\n db['sigma_x0'][0] = sigma_x0\\n db['sigma_y0'][0] = sigma_y0\\n db['tau_0'][0] = tau_0\\n db['sigma_average'][0] = sigma_average\\n db['r_circle_mohr'][0] = r_circle\\n db['sigma_x'][0] = new_state[0]\\n db['sigma_y'][0] = new_state[1]\\n db['tau'][0] = new_state[2]\\n db['theta'][0] = theta\\n\\n // update\\n // square point:\\n beam_position.glyph.y = y_var\\n // update Mohr circle\\n update_circle_mohr(db, Mohr_circle, line_stress_state, points_stress_state, label_points_stress_state, line_stress_state_theta, points_stress_state_theta, label_points_stress_state_theta, arc_theta_Mohr, label_theta_Mohr, arc_theta_p_Mohr, label_theta_p_Mohr)\\n // stress state\\n update_sigmax_state(db, arrow_sigma_x1, arrow_sigma_x2)\\n update_sigmay_state(db, arrow_sigma_y1, arrow_sigma_y2)\\n update_tau_state(db, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2)\\n // stress state (theta)\\n update_sigmax_state_theta(db, arrow_sigma_x1_theta, arrow_sigma_x2_theta)\\n update_sigmay_state_theta(db, arrow_sigma_y1_theta, arrow_sigma_y2_theta)\\n update_tau_state_theta(db, arrow_tau_x1_theta,arrow_tau_x2_theta, arrow_tau_y1_theta, arrow_tau_y2_theta)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_radius_mohr(sigma_x0, sigma_y0, tau_0) {\\n return Math.sqrt(tau_02 + (sigma_x0-sigma_y0)2/4)\\n }\\n \\n \\n function compute_stress_state_mohr(sigma_average, r_circle, theta) {\\n if (sigma_average > 0) {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var tau = -r_circleMath.sin(2theta)\\n } else {\\n var sigma_x = sigma_average + r_circleMath.cos(2theta-Math.PI)\\n var sigma_y = sigma_average + r_circleMath.cos(2theta)\\n var tau = r_circleMath.sin(2theta)\\n }\\n return [sigma_x, sigma_y, tau]\\n }\\n \\n \\n function compute_sigma_average_mohr(sigma_x0, sigma_y0) {\\n return (sigma_x0+sigma_y0)/2\\n }\\n \\n \\n function compute_principal_theta_mohr(sigma_x0, sigma_y0, tau_0) {\\n if ((sigma_x0-sigma_y0)==0) {\\n if (tau_0>0) {\\n return Math.PI/2\\n } else {\\n return -Math.PI/2\\n }\\n } else {\\n return Math.atan(2tau_0/(sigma_y0-sigma_x0))/2\\n }\\n }\\n \\n \\n function compute_theta_mohr(theta_element, theta_principal) {\\n return theta_element+theta_principal\\n }\\n \\n \\n function update_circle_mohr(data, glyph_circle, glyph_line, glyph_points, glyph_label, glyph_line_theta, glyph_points_theta, glyph_label_theta, glyph_arc, glyph_theta_text, glyph_arc_p, glyph_theta_p_text) {\\n // set variables\\n const sigma_average = data['sigma_average'][0]\\n const r_circle = data['r_circle_mohr'][0]\\n const sigma_x0 = data['sigma_x0'][0]\\n const sigma_y0 = data['sigma_y0'][0]\\n const tau_0 = data['tau_0'][0]\\n const sigma_x = data['sigma_x'][0]\\n const sigma_y = data['sigma_y'][0]\\n const tau = data['tau'][0]\\n const theta_element = data['theta_element'][0]\\n const theta = data['theta'][0]\\n \\n // update circle\\n glyph_circle.glyph.x = sigma_average\\n glyph_circle.glyph.radius = r_circle\\n \\n // update points\\n const src_points = glyph_points.data_source\\n src_points.data.x = [sigma_x0, sigma_y0]\\n src_points.data.y = [tau_0, -tau_0]\\n src_points.change.emit()\\n \\n // update lines\\n const src_line = glyph_line.data_source\\n src_line.data.x = [sigma_x0, sigma_y0]\\n src_line.data.y = [tau_0, -tau_0]\\n src_line.change.emit()\\n \\n // update labels\\n const src_labels = glyph_label.data_source\\n src_labels.data.x = [sigma_x0, sigma_y0]\\n src_labels.data.y = [tau_0, -tau_0]\\n src_labels.change.emit()\\n \\n // update points theta\\n const src_points_theta = glyph_points_theta.data_source\\n src_points_theta.data.x = [sigma_x, sigma_y]\\n src_points_theta.data.y = [tau, -tau]\\n src_points_theta.change.emit()\\n \\n // update lines theta\\n const src_line_theta = glyph_line_theta.data_source\\n src_line_theta.data.x = [sigma_x, sigma_y]\\n src_line_theta.data.y = [tau, -tau]\\n src_line_theta.change.emit()\\n \\n // update labels theta\\n const src_labels_theta = glyph_label_theta.data_source\\n src_labels_theta.data.x = [sigma_x, sigma_y]\\n src_labels_theta.data.y = [tau, -tau]\\n src_labels_theta.change.emit()\\n \\n // arc theta (Mohr)\\n const theta_p = theta-theta_element\\n glyph_arc.glyph.start_angle = -2theta\\n glyph_arc.glyph.end_angle = -2theta_p\\n glyph_arc.glyph.x = sigma_average\\n glyph_arc.glyph.radius = r_circle/2\\n \\n // label theta (Mohr)\\n if (theta_element==0) {\\n glyph_theta_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_text.glyph.text = \\\"2\\u03b8\\\"\\n const src_label_theta = glyph_theta_text.data_source\\n src_label_theta.data.x = [sigma_average + r_circleMath.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circleMath.sin(-theta-theta_p)/2]\\n src_label_theta.change.emit()\\n }\\n debugger\\n // arc principal theta (Mohr)\\n if (theta_p < 0) {\\n var theta_p_tmp = Math.PI/2+theta_p\\n } else {\\n var theta_p_tmp = theta_p\\n }\\n glyph_arc_p.glyph.x = sigma_average\\n glyph_arc_p.glyph.radius = r_circle/52\\n glyph_arc_p.glyph.start_angle = -2theta_p_tmp\\n \\n // label principal theta (Mohr)\\n if (theta_p==0) {\\n glyph_theta_p_text.glyph.text = \\\"\\\"\\n } else {\\n glyph_theta_p_text.glyph.text = \\\"2\\u03b8\\u209a\\\"\\n const src_label_theta_p = glyph_theta_p_text.data_source\\n src_label_theta_p.data.x = [sigma_average + r_circleMath.cos(theta_p_tmp)/52]\\n src_label_theta_p.data.y = [r_circleMath.sin(-theta_p_tmp)/52]\\n src_label_theta_p.change.emit()\\n }\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_sigmax_state(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_x0 = data['sigma_x0'][0]\\n const AHF = 4\\n \\n if (sigma_x0 > 0) {\\n update_arrow(arrow_sigma_x1, sigma_x0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_x0, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, sigma_x0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_x0), 0, 0, AHF)\\n } else {\\n update_arrow(arrow_sigma_x1, -sigma_x0, width_element/2+offset_arrows-sigma_x0, width_element/2+offset_arrows, 0, 0, AHF)\\n update_arrow(arrow_sigma_x2, -sigma_x0, -(width_element/2+offset_arrows-sigma_x0), -(width_element/2+offset_arrows), 0, 0, AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0) {\\n const offset_arrows = width_element/3\\n const sigma_y0 = data['sigma_y0'][0]\\n const AHF = 4\\n \\n if (sigma_y0 > 0) {\\n update_arrow(arrow_sigma_y1, sigma_y0, 0, 0, width_element/2+offset_arrows, width_element/2+offset_arrows+sigma_y0, AHF)\\n update_arrow(arrow_sigma_y2, sigma_y0, 0, 0, -(width_element/2+offset_arrows), -(width_element/2+offset_arrows+sigma_y0), AHF)\\n } else {\\n update_arrow(arrow_sigma_y1, -sigma_y0, 0, 0, width_element/2+offset_arrows-sigma_y0, width_element/2+offset_arrows, AHF)\\n update_arrow(arrow_sigma_y2, -sigma_y0, 0, 0, -(width_element/2+offset_arrows-sigma_y0), -(width_element/2+offset_arrows), AHF)\\n }\\n }\\n \\n \\n function update_tau_state(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const tau_0 = data['tau_0'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1, tau_0, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, -tau_0/2, tau_0/2, AHF)\\n update_arrow(arrow_tau_x2, tau_0, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), tau_0/2, -tau_0/2, AHF)\\n update_arrow(arrow_tau_y1, tau_0, -tau_0/2, tau_0/2, width_element/2+offset_arrows/2, width_element/2+offset_arrows/2, AHF)\\n update_arrow(arrow_tau_y2, tau_0, tau_0/2, -tau_0/2, -(width_element/2+offset_arrows/2), -(width_element/2+offset_arrows/2), AHF)\\n }\\n \\n \\n function update_sigmax_state_theta(data, arrow_sigma_x1, arrow_sigma_x2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n var sigma_x = data['sigma_x'][0]\\n const theta = data['theta_element'][0]\\n const AHF = 4\\n \\n if (sigma_x < 0) {\\n var sigma_x = -sigma_x\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_x1,\\n sigma_x,\\n (offset_sigma+center_x)Math.cos(theta),\\n (offset_sigma+center_x+sigma_x)Math.cos(theta),\\n (offset_sigma+center_x)Math.sin(theta),\\n (offset_sigma+center_x+sigma_x)Math.sin(theta),\\n AHF)\\n update_arrow(arrow_sigma_x2,\\n sigma_x,\\n (-offset_sigma+center_x)Math.cos(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.cos(theta),\\n (-offset_sigma+center_x)Math.sin(theta),\\n (-(offset_sigma+sigma_x)+center_x)Math.sin(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_sigmay_state_theta(data, arrow_sigma_y1, arrow_sigma_y2, width_element=30.0, center_x=120) {\\n const offset_arrows = width_element/3\\n const offset_sigma = width_element/2+offset_arrows\\n const theta = data['theta_element'][0]\\n var sigma_y = data['sigma_y'][0]\\n const AHF = 4\\n \\n if (sigma_y<0) {\\n var sigma_y = -sigma_y\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n AHF)\\n } else {\\n update_arrow(arrow_sigma_y1,\\n sigma_y,\\n (center_x)Math.cos(theta)-(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)-(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)+(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)+(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_sigma_y2,\\n sigma_y,\\n (center_x)Math.cos(theta)+(offset_sigma)Math.sin(theta),\\n (center_x)Math.cos(theta)+(offset_sigma+sigma_y)Math.sin(theta),\\n (center_x)Math.sin(theta)-(offset_sigma)Math.cos(theta),\\n (center_x)Math.sin(theta)-(offset_sigma+sigma_y)Math.cos(theta),\\n AHF)\\n }\\n }\\n \\n \\n function update_tau_state_theta(data, arrow_tau_x1, arrow_tau_x2, arrow_tau_y1, arrow_tau_y2, width_element=30.0, center_x=120, scale_tau=5) {\\n const offset_arrows = width_element/3\\n const offset_tau = width_element/2+offset_arrows/2\\n const theta = data['theta_element'][0]\\n const tau = data['tau'][0]scale_tau\\n const AHF = 4\\n \\n update_arrow(arrow_tau_x1,\\n tau,\\n (center_x+offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x+offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n (center_x+offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_x2,\\n tau,\\n (center_x-offset_tau)Math.cos(theta)-(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.cos(theta)+(tau/2)Math.sin(theta),\\n (center_x-offset_tau)Math.sin(theta)+(tau/2)Math.cos(theta),\\n (center_x-offset_tau)Math.sin(theta)-(tau/2)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y1,\\n tau,\\n (center_x-tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.cos(theta)-(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n (center_x+tau/2)Math.sin(theta)+(offset_tau)Math.cos(theta),\\n AHF)\\n update_arrow(arrow_tau_y2,\\n tau,\\n (center_x+tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x-tau/2)Math.cos(theta)+(offset_tau)Math.sin(theta),\\n (center_x+tau/2)Math.sin(theta)-(offset_tau)Math.cos(theta),\\n (center_x-tau/2)Math.sin(theta)-(offset_tau)*Math.cos(theta),\\n AHF)\\n }\\n \\n 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(FBD):\"},\"id\":\"1251\",\"type\":\"Div\"},{\"attributes\":{\"axis\":{\"id\":\"1594\"},\"coordinates\":null,\"dimension\":1,\"group\":null,\"ticker\":null},\"id\":\"1597\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"2477\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2251\"},\"selection_policy\":{\"id\":\"2250\"}},\"id\":\"2181\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"red\"},\"hatch_alpha\":{\"value\":0.2},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"red\"},\"marker\":{\"value\":\"triangle\"},\"size\":{\"value\":0},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1246\",\"type\":\"Scatter\"},{\"attributes\":{\"source\":{\"id\":\"1243\"}},\"id\":\"1248\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"2478\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"2416\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1557\",\"type\":\"BasicTicker\"},{\"attributes\":{\"active\":0,\"js_property_callbacks\":{\"change:active\":[{\"id\":\"2139\"}]},\"labels\":[\"Right-hand\",\"Left-hand\"]},\"id\":\"1252\",\"type\":\"RadioButtonGroup\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2253\"},\"selection_policy\":{\"id\":\"2252\"}},\"id\":\"2182\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"text\":\"Axial force P=10 kN (applied)\"},\"id\":\"1253\",\"type\":\"Div\"},{\"attributes\":{},\"id\":\"2417\",\"type\":\"AllLabels\"},{\"attributes\":{},\"id\":\"2440\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"text\":\"\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = 10 kN<br>\\n Rx = 10 kN<br>\\n Ry (left) = 12.0 kN<br>\\n Ry (right) = 12.0 kN<br>\\n No cross section analysed.<br>\\n N = 0 kN<br>\\n V = 0 kN<br>\\n M = 0 kNm\\n \\n 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or remove axial force P\"]},\"id\":\"1254\",\"type\":\"CheckboxButtonGroup\"},{\"attributes\":{\"below\":[{\"id\":\"1266\"}],\"center\":[{\"id\":\"1269\"},{\"id\":\"1273\"}],\"height\":160,\"left\":[{\"id\":\"1270\"}],\"renderers\":[{\"id\":\"1358\"},{\"id\":\"1364\"},{\"id\":\"1394\"}],\"title\":{\"id\":\"1257\"},\"toolbar\":{\"id\":\"1282\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"1011\"},\"x_scale\":{\"id\":\"1262\"},\"y_range\":{\"id\":\"1260\"},\"y_scale\":{\"id\":\"1264\"}},\"id\":\"1256\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"1554\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"2420\",\"type\":\"AllLabels\"},{\"attributes\":{},\"id\":\"1633\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1260\",\"type\":\"DataRange1d\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2257\"},\"selection_policy\":{\"id\":\"2256\"}},\"id\":\"2184\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1262\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"2348\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"axis\":{\"id\":\"1266\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1269\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1275\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"callback\":null,\"tooltips\":[[\"Position\",\"@x m\"],[\"Axial force\",\"@y kN\"]]},\"id\":\"1281\",\"type\":\"HoverTool\"},{\"attributes\":{},\"id\":\"1548\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"2349\",\"type\":\"AllLabels\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"N V M Diagrams\"},\"id\":\"1257\",\"type\":\"Title\"},{\"attributes\":{\"below\":[{\"id\":\"1556\"}],\"center\":[{\"id\":\"1559\"},{\"id\":\"1563\"}],\"height\":200,\"left\":[{\"id\":\"1560\"}],\"renderers\":[{\"id\":\"1688\"},{\"id\":\"1694\"},{\"id\":\"1700\"}],\"title\":{\"id\":\"1546\"},\"toolbar\":{\"id\":\"1572\"},\"toolbar_location\":null,\"width\":200,\"x_range\":{\"id\":\"1548\"},\"x_scale\":{\"id\":\"1552\"},\"y_range\":{\"id\":\"1550\"},\"y_scale\":{\"id\":\"1554\"}},\"id\":\"1545\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"text\":\"\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = 200 mm<br>\\n b = 100 mm<br>\\n L = 6 m<br>\\n A = 2.00e+04 mm<sup>2</sup><br>\\n Iy = 6.67e+07 mm<sup>4</sup><br>\\n Iz = 1.67e+07 mm<sup>4</sup>\",\"width\":170},\"id\":\"1119\",\"type\":\"Div\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2259\"},\"selection_policy\":{\"id\":\"2258\"}},\"id\":\"2185\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"axis_label\":\"Position [m]\",\"coordinates\":null,\"formatter\":{\"id\":\"2298\"},\"group\":null,\"major_label_policy\":{\"id\":\"2299\"},\"ticker\":{\"id\":\"1267\"},\"visible\":false},\"id\":\"1266\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1550\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"2350\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"2499\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1267\",\"type\":\"BasicTicker\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2493\"},\"selection_policy\":{\"id\":\"2492\"}},\"id\":\"2421\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"axis_label\":\"Height h 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	diff --git a/Simple Beam DEMOs/sb_plastic.ipynb b/Simple Beam DEMOs/sb_plastic.ipynb
	deleted file mode 100644
	index 212d0d9..0000000
	--- a/Simple Beam DEMOs/sb_plastic.ipynb
	+++ /dev/null
	@@ -1,487 +0,0 @@
	-{
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	- "(function(root) {\n",
	- " function now() {\n",
	- " return new Date();\n",
	- " }\n",
	- "\n",
	- " const force = true;\n",
	- "\n",
	- " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_onload_callbacks = [];\n",
	- " root._bokeh_is_loading = undefined;\n",
	- " }\n",
	- "\n",
	- " const JS_MIME_TYPE = 'application/javascript';\n",
	- " const HTML_MIME_TYPE = 'text/html';\n",
	- " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	- " const CLASS_NAME = 'output_bokeh rendered_html';\n",
	- "\n",
	- " /**\n",
	- " * Render data to the DOM node\n",
	- " */\n",
	- " function render(props, node) {\n",
	- " const script = document.createElement(\"script\");\n",
	- " node.appendChild(script);\n",
	- " }\n",
	- "\n",
	- " /**\n",
	- " * Handle when an output is cleared or removed\n",
	- " */\n",
	- " function handleClearOutput(event, handle) {\n",
	- " const cell = handle.cell;\n",
	- "\n",
	- " const id = cell.output_area._bokeh_element_id;\n",
	- " const server_id = cell.output_area._bokeh_server_id;\n",
	- " // Clean up Bokeh references\n",
	- " if (id != null && id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- "\n",
	- " if (server_id !== undefined) {\n",
	- " // Clean up Bokeh references\n",
	- " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	- " cell.notebook.kernel.execute(cmd_clean, {\n",
	- " iopub: {\n",
	- " output: function(msg) {\n",
	- " const id = msg.content.text.trim();\n",
	- " if (id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- " }\n",
	- " }\n",
	- " });\n",
	- " // Destroy server and session\n",
	- " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	- " cell.notebook.kernel.execute(cmd_destroy);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " /**\n",
	- " * Handle when a new output is added\n",
	- " */\n",
	- " function handleAddOutput(event, handle) {\n",
	- " const output_area = handle.output_area;\n",
	- " const output = handle.output;\n",
	- "\n",
	- " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	- " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	- " return\n",
	- " }\n",
	- "\n",
	- " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
	- "\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	- " // store reference to embed id on output_area\n",
	- " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
	- " }\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	- " const bk_div = document.createElement(\"div\");\n",
	- " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	- " const script_attrs = bk_div.children[0].attributes;\n",
	- " for (let i = 0; i < script_attrs.length; i++) {\n",
	- " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	- " }\n",
	- " // store reference to server id on output_area\n",
	- " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function register_renderer(events, OutputArea) {\n",
	- "\n",
	- " function append_mime(data, metadata, element) {\n",
	- " // create a DOM node to render to\n",
	- " const toinsert = this.create_output_subarea(\n",
	- " metadata,\n",
	- " CLASS_NAME,\n",
	- " EXEC_MIME_TYPE\n",
	- " );\n",
	- " this.keyboard_manager.register_events(toinsert);\n",
	- " // Render to node\n",
	- " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	- " render(props, toinsert[toinsert.length - 1]);\n",
	- " element.append(toinsert);\n",
	- " return toinsert\n",
	- " }\n",
	- "\n",
	- " /* Handle when an output is cleared or removed */\n",
	- " events.on('clear_output.CodeCell', handleClearOutput);\n",
	- " events.on('delete.Cell', handleClearOutput);\n",
	- "\n",
	- " /* Handle when a new output is added */\n",
	- " events.on('output_added.OutputArea', handleAddOutput);\n",
	- "\n",
	- " /**\n",
	- " * Register the mime type and append_mime function with output_area\n",
	- " */\n",
	- " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	- " /* Is output safe? */\n",
	- " safe: true,\n",
	- " /* Index of renderer in `output_area.display_order` */\n",
	- " index: 0\n",
	- " });\n",
	- " }\n",
	- "\n",
	- " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	- " if (root.Jupyter !== undefined) {\n",
	- " const events = require('base/js/events');\n",
	- " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	- "\n",
	- " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	- " register_renderer(events, OutputArea);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " \n",
	- " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_timeout = Date.now() + 5000;\n",
	- " root._bokeh_failed_load = false;\n",
	- " }\n",
	- "\n",
	- " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	- " \"<div style='background-color: #fdd'>\\n\"+\n",
	- " \"<p>\\n\"+\n",
	- " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	- " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	- " \"</p>\\n\"+\n",
	- " \"<ul>\\n\"+\n",
	- " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	- " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	- " \"</ul>\\n\"+\n",
	- " \"<code>\\n\"+\n",
	- " \"from bokeh.resources import INLINE\\n\"+\n",
	- " \"output_notebook(resources=INLINE)\\n\"+\n",
	- " \"</code>\\n\"+\n",
	- " \"</div>\"}};\n",
	- "\n",
	- " function display_loaded() {\n",
	- " const el = document.getElementById(\"1002\");\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS is loading...\";\n",
	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	- " }\n",
	- " } else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(display_loaded, 100)\n",
	- " }\n",
	- " }\n",
	- "\n",
	- "\n",
	- " function run_callbacks() {\n",
	- " try {\n",
	- " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	- " if (callback != null)\n",
	- " callback();\n",
	- " });\n",
	- " } finally {\n",
	- " delete root._bokeh_onload_callbacks\n",
	- " }\n",
	- " console.debug(\"Bokeh: all callbacks have finished\");\n",
	- " }\n",
	- "\n",
	- " function load_libs(css_urls, js_urls, callback) {\n",
	- " if (css_urls == null) css_urls = [];\n",
	- " if (js_urls == null) js_urls = [];\n",
	- "\n",
	- " root._bokeh_onload_callbacks.push(callback);\n",
	- " if (root._bokeh_is_loading > 0) {\n",
	- " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	- " return null;\n",
	- " }\n",
	- " if (js_urls == null \|\| js_urls.length === 0) {\n",
	- " run_callbacks();\n",
	- " return null;\n",
	- " }\n",
	- " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	- " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	- "\n",
	- " function on_load() {\n",
	- " root._bokeh_is_loading--;\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	- " run_callbacks()\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function on_error(url) {\n",
	- " console.error(\"failed to load \" + url);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < css_urls.length; i++) {\n",
	- " const url = css_urls[i];\n",
	- " const element = document.createElement(\"link\");\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.rel = \"stylesheet\";\n",
	- " element.type = \"text/css\";\n",
	- " element.href = url;\n",
	- " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < js_urls.length; i++) {\n",
	- " const url = js_urls[i];\n",
	- " const element = document.createElement('script');\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.async = false;\n",
	- " element.src = url;\n",
	- " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	- " document.head.appendChild(element);\n",
	- " }\n",
	- " };\n",
	- "\n",
	- " function inject_raw_css(css) {\n",
	- " const element = document.createElement(\"style\");\n",
	- " element.appendChild(document.createTextNode(css));\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " \n",
	- " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	- " const css_urls = [];\n",
	- " \n",
	- "\n",
	- " const inline_js = [\n",
	- " function(Bokeh) {\n",
	- " Bokeh.set_log_level(\"info\");\n",
	- " },\n",
	- " function(Bokeh) {\n",
	- " \n",
	- " \n",
	- " }\n",
	- " ];\n",
	- "\n",
	- " function run_inline_js() {\n",
	- " \n",
	- " if (root.Bokeh !== undefined \|\| force === true) {\n",
	- " \n",
	- " for (let i = 0; i < inline_js.length; i++) {\n",
	- " inline_js[i].call(root, root.Bokeh);\n",
	- " }\n",
	- " if (force === true) {\n",
	- " display_loaded();\n",
	- " }} else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(run_inline_js, 100);\n",
	- " } else if (!root._bokeh_failed_load) {\n",
	- " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
	- " root._bokeh_failed_load = true;\n",
	- " } else if (force !== true) {\n",
	- " const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
	- " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
	- " }\n",
	- "\n",
	- " }\n",
	- "\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
	- " run_inline_js();\n",
	- " } else {\n",
	- " load_libs(css_urls, js_urls, function() {\n",
	- " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	- " run_inline_js();\n",
	- " });\n",
	- " }\n",
	- "}(window));"
	- ],
	- "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n function now() {\n return new Date();\n }\n\n const force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n \n\n \n if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n const NB_LOAD_WARNING = {'data': {'text/html':\n \"<div style='background-color: #fdd'>\\n\"+\n \"<p>\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"</p>\\n\"+\n \"<ul>\\n\"+\n \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n \"<li>use INLINE resources instead, as so:</li>\\n\"+\n \"</ul>\\n\"+\n \"<code>\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"</code>\\n\"+\n \"</div>\"}};\n\n function display_loaded() {\n const el = document.getElementById(\"1002\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null \|\| js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error(url) {\n console.error(\"failed to load \" + url);\n }\n\n for (let i = 0; i < css_urls.length; i++) {\n const url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n \n const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n const css_urls = [];\n \n\n const inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n function(Bokeh) {\n \n \n }\n ];\n\n function run_inline_js() {\n \n if (root.Bokeh !== undefined \|\| force === true) {\n \n for (let i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\n if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));"
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- }
	- ],
	- "source": [
	- "# Import the packages needed\n",
	- "import sys\n",
	- "sys.path.append('../HiddenCode')\n",
	- "import hidden_code_nb_plastic\n",
	- "import math\n",
	- "import numpy as np \n",
	- "from cienpy import simplebeam as sb\n",
	- "from cienpy import rectangular_section as beam_section\n",
	- "from cienpy import stress_strain_elastic as ststel\n",
	- "from cienpy import stress_strain_plastic as ststpl"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Define the geometry and uniform load. Note that given the graphical nature of the notebook, extreme cases can cause the figures to not be displayed."
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 2,
	- "metadata": {},
	- "outputs": [],
	- "source": [
	- "# Choose the dimensions\n",
	- "L = 6 # [m]\n",
	- "h = 200 # [mm]\n",
	- "b = 100 # [mm]\n",
	- "q = 4; # [kN/m]\n",
	- "P = 10; # [kN]\n",
	- "\n",
	- "# Choose the material parameters\n",
	- "E_steel = 200e3 # [MPa] steel\n",
	- "fy_steel = 355 # [MPa] steel\n",
	- "E = E_steel\n",
	- "fy = fy_steel\n",
	- "\n",
	- "# compute the internal forces (at x=L)\n",
	- "discr_NVM = 100\n",
	- "x_discr = np.linspace(0, L, discr_NVM)\n",
	- "N_discr = sb.compute_N(x_discr, P)\n",
	- "V_discr = sb.compute_V(x_discr, q, L)\n",
	- "M_discr = sb.compute_M(x_discr, q, L)\n",
	- "N = N_discr[-1]\n",
	- "V = V_discr[-1]\n",
	- "M = M_discr[-1]\n",
	- "\n",
	- "# compute the parameters\n",
	- "A = beam_section.compute_area(b, h) # [mm2]\n",
	- "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	- "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	- "yG = beam_section.compute_centroid_y(h)\n",
	- "y_n_axis = ststel.compute_neutral_axis(N, A, Iy, M, yG)\n",
	- "\n",
	- "# compute the reactions\n",
	- "Rx = sb.compute_Rx(P)\n",
	- "Ry_l = sb.compute_Ry_l(q, L)\n",
	- "Ry_r = sb.compute_Ry_r(q, L)"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Run the complex code for the interactive visualisation:"
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 4,
	- "metadata": {},
	- "outputs": [
	- {
	- "data": {
	- "text/html": [
	- "\n",
	- "\n",
	- "\n",
	- "\n",
	- "\n",
	- "\n",
	- " <div class=\"bk-root\" id=\"3c8f723c-8402-4b2c-9417-8d4e32cea55f\" data-root-id=\"4488\"></div>\n"
	- ]
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- },
	- {
	- "data": {
	- "application/javascript": [
	- "(function(root) {\n",
	- " function embed_document(root) {\n",
	- " \n",
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// retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2000) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm*2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n 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// retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2000) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm*2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \"},\"id\":\"4463\",\"type\":\"CustomJS\"},{\"attributes\":{\"source\":{\"id\":\"3499\"}},\"id\":\"4194\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"4196\",\"type\":\"Line\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"4169\"},\"N_stress_diag\":{\"id\":\"4151\"},\"V_stress_diag\":{\"id\":\"4187\"},\"axial_strain_diag\":{\"id\":\"4223\"},\"bending_strain_diag\":{\"id\":\"4243\"},\"centroid\":{\"id\":\"4181\"},\"div\":{\"id\":\"3600\"},\"neutral_axis\":{\"id\":\"4460\"},\"s_b\":{\"id\":\"3496\"},\"s_ss\":{\"id\":\"3499\"},\"section\":{\"id\":\"3598\"},\"sigma_stress_diag\":{\"id\":\"4448\"},\"source\":{\"id\":\"3500\"},\"support_r\":{\"id\":\"3592\"},\"tau_stress_diag\":{\"id\":\"4205\"},\"total_strain_diag\":{\"id\":\"4428\"},\"total_strain_pl_diag\":{\"id\":\"4422\"},\"total_stress_pl_diag\":{\"id\":\"4416\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const h = cb_obj.value // value of the slider\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2000) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \"},\"id\":\"4464\",\"type\":\"CustomJS\"},{\"attributes\":{\"overlay\":{\"id\":\"4284\"}},\"id\":\"4280\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"data\":{\"x\":[-1.2,1.2],\"y\":[0,0]},\"selected\":{\"id\":\"4982\"},\"selection_policy\":{\"id\":\"4981\"}},\"id\":\"4195\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"4195\"},\"glyph\":{\"id\":\"4196\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"4198\"},\"nonselection_glyph\":{\"id\":\"4197\"},\"view\":{\"id\":\"4200\"}},\"id\":\"4199\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"blue\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"4204\",\"type\":\"Line\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"3857\"},\"N_stress_diag\":{\"id\":\"4151\"},\"arr_head\":{\"id\":\"3746\"},\"axial_strain_diag\":{\"id\":\"4223\"},\"div_P\":{\"id\":\"3752\"},\"div_f\":{\"id\":\"3754\"},\"fN\":{\"id\":\"3730\"},\"fP\":{\"id\":\"3718\"},\"fRx\":{\"id\":\"3727\"},\"fRyl\":{\"id\":\"3724\"},\"fRyr\":{\"id\":\"3721\"},\"fV\":{\"id\":\"3733\"},\"label_M_section\":{\"id\":\"4366\"},\"label_N_section\":{\"id\":\"4360\"},\"label_V_section\":{\"id\":\"4372\"},\"neutral_axis\":{\"id\":\"4460\"},\"s_M\":{\"id\":\"3735\"},\"s_section_M\":{\"id\":\"4343\"},\"section_M_head\":{\"id\":\"4354\"},\"section_N\":{\"id\":\"4338\"},\"section_V\":{\"id\":\"4341\"},\"sigma_stress_diag\":{\"id\":\"4448\"},\"source\":{\"id\":\"3500\"},\"tau_stress_diag\":{\"id\":\"4205\"},\"total_strain_diag\":{\"id\":\"4428\"},\"total_strain_pl_diag\":{\"id\":\"4422\"},\"total_stress_pl_diag\":{\"id\":\"4416\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=100) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2000) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm*2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \"},\"id\":\"4465\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"4197\",\"type\":\"Line\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"4201\"},\"glyph\":{\"id\":\"4202\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"4204\"},\"nonselection_glyph\":{\"id\":\"4203\"},\"view\":{\"id\":\"4206\"}},\"id\":\"4205\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"3746\"},\"div_P\":{\"id\":\"3752\"},\"fN\":{\"id\":\"3730\"},\"fP\":{\"id\":\"3718\"},\"fRx\":{\"id\":\"3727\"},\"fRyl\":{\"id\":\"3724\"},\"fRyr\":{\"id\":\"3721\"},\"fV\":{\"id\":\"3733\"},\"label_M_section\":{\"id\":\"4366\"},\"label_N_section\":{\"id\":\"4360\"},\"label_V_section\":{\"id\":\"4372\"},\"s_M\":{\"id\":\"3735\"},\"s_q\":{\"id\":\"3498\"},\"s_sb\":{\"id\":\"3497\"},\"s_section_M\":{\"id\":\"4343\"},\"section_M_head\":{\"id\":\"4354\"},\"section_N\":{\"id\":\"4338\"},\"section_V\":{\"id\":\"4341\"},\"source\":{\"id\":\"3500\"},\"tau_stress_diag\":{\"id\":\"4205\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"4466\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_color\":\"blue\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"4202\",\"type\":\"Line\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"3881\"},\"M_stress_diag\":{\"id\":\"4169\"},\"V_diag\":{\"id\":\"3869\"},\"V_stress_diag\":{\"id\":\"4187\"},\"arr_head\":{\"id\":\"3746\"},\"bending_strain_diag\":{\"id\":\"4243\"},\"centroid\":{\"id\":\"4181\"},\"div_P\":{\"id\":\"3752\"},\"div_f\":{\"id\":\"3754\"},\"fN\":{\"id\":\"3730\"},\"fP\":{\"id\":\"3718\"},\"fRx\":{\"id\":\"3727\"},\"fRyl\":{\"id\":\"3724\"},\"fRyr\":{\"id\":\"3721\"},\"fV\":{\"id\":\"3733\"},\"label_M_section\":{\"id\":\"4366\"},\"label_N_section\":{\"id\":\"4360\"},\"label_V_section\":{\"id\":\"4372\"},\"neutral_axis\":{\"id\":\"4460\"},\"s_M\":{\"id\":\"3735\"},\"s_q\":{\"id\":\"3498\"},\"s_section_M\":{\"id\":\"4343\"},\"section_M_head\":{\"id\":\"4354\"},\"section_N\":{\"id\":\"4338\"},\"section_V\":{\"id\":\"4341\"},\"sigma_stress_diag\":{\"id\":\"4448\"},\"source\":{\"id\":\"3500\"},\"tau_stress_diag\":{\"id\":\"4205\"},\"total_strain_diag\":{\"id\":\"4428\"},\"total_strain_pl_diag\":{\"id\":\"4422\"},\"total_stress_pl_diag\":{\"id\":\"4416\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2000) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm*2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \"},\"id\":\"4467\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_alpha\":0.1,\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"4209\",\"type\":\"Line\"},{\"attributes\":{\"source\":{\"id\":\"4201\"}},\"id\":\"4206\",\"type\":\"CDSView\"},{\"attributes\":{\"args\":{\"source\":{\"id\":\"3500\"},\"total_strain_diag\":{\"id\":\"4428\"},\"total_strain_pl_diag\":{\"id\":\"4422\"},\"total_stress_pl_diag\":{\"id\":\"4416\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const fy = cb_obj.value\\n const L = db['L'][0]\\n\\n // update q\\n db['fy'][0] = fy\\n\\n // update\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2000) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \"},\"id\":\"4468\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"blue\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"4203\",\"type\":\"Line\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"3499\"},\"glyph\":{\"id\":\"4226\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"4228\"},\"nonselection_glyph\":{\"id\":\"4227\"},\"view\":{\"id\":\"4230\"}},\"id\":\"4229\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"4169\"},\"N_stress_diag\":{\"id\":\"4151\"},\"axial_strain_diag\":{\"id\":\"4223\"},\"bending_strain_diag\":{\"id\":\"4243\"},\"centroid\":{\"id\":\"4181\"},\"source\":{\"id\":\"3500\"},\"total_strain_diag\":{\"id\":\"4428\"},\"total_strain_pl_diag\":{\"id\":\"4422\"},\"total_stress_pl_diag\":{\"id\":\"4416\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const E = cb_obj.value\\n\\n // update E\\n db['E'][0] = E\\n\\n // update\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_plastic_stress_strain(db, total_strain_diag, total_strain_pl_diag, total_stress_pl_diag)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function update_plastic_stress_strain(data, glyph_strain_el, glyph_strain_pl, glyph_sigma_pl, discr=2000) { \\n // define parameters\\n const h = data['h'][0]\\n const N = data['N'][0]\\n const M = data['M'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const E = data['E'][0]\\n const fy = data['fy'][0]\\n const y_discr = linspace(0, h, discr)\\n let total_epsilon = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var sigma_axial = compute_sigma_axial(N, A)\\n var sigma_bending = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n var epsilon_bending = compute_epsilon_bending(sigma_bending, E)\\n var epsilon_axial = compute_epsilon_axial(sigma_axial, E)\\n total_epsilon[i] = compute_total_epsilon(epsilon_axial, epsilon_bending)\\n }\\n let [stress_pl, strain_pl, y_discr_strain_pl, yNA] = compute_total_stress_strain(h, fy, E, N, M, A, Iy, yG, discr)\\n \\n \\n // change the diagrams\\n update_strain_diagram(glyph_strain_el, total_epsilon, y_discr)\\n update_stress_diagram(glyph_sigma_pl, stress_pl, y_discr)\\n update_strain_diagram(glyph_strain_pl, strain_pl, y_discr_strain_pl)\\n }\\n \\n \\n function compute_Ny(fy, A) {\\n return fyA/1e3\\n }\\n \\n \\n function compute_My(fy, Iy, yG, H) {\\n if (yG >= H-yG) {\\n var extreme_fiber = yG\\n } else {\\n var extreme_fiber = H-yG\\n }\\n return Iy/extreme_fiberfy/1e6\\n }\\n \\n \\n function compute_total_stress_strain(H, fy, E, N, M, A, Iy, yG, discr) {\\n // initialization\\n const scale_discr_o = 20\\n var y_discr = linspace(0, H, discr)\\n const Ny = compute_Ny(fy, A)\\n const My = compute_My(fy, Iy, yG, H)\\n const M_norm = __compute_M_norm(M, My)\\n const N_norm = __compute_N_norm(N, Ny)\\n const err_inside = new Array(discr).fill(1e30)\\n const err_outside = new Array(discrscale_discr_o).fill(1e30)\\n\\n // compute state (elastic)\\n let strain_el = new Array(discr)\\n let stress_el = new Array(discr)\\n for (var i = 0; i < discr; i++) {\\n var sigma_N_el = compute_sigma_axial(N, A)\\n var sigma_M_el = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n stress_el[i] = sigma_M_el + sigma_N_el\\n strain_el[i] = compute_epsilon_axial(sigma_N_el, E)/100 + compute_epsilon_bending(sigma_M_el, E)/100\\n }\\n if (Math.abs(stress_el[0]) > fy \|\| Math.abs(stress_el.slice(-1)[0]) > fy) {\\n if (__check_limit(M_norm, N_norm)) {\\n // double yield check\\n var h = __compute_h_2Y(N_norm)\\n var yNA = hH\\n var k = __compute_k_2Y(M_norm, N_norm)\\n var chi = __compute_chi_2Y(k, fy, E, H, yNA)\\n var k_prime = __compute_k_prime_2Y(k, h)\\n if (k>=1 && k_prime>=1) {\\n // DOUBLE YIELD CASE\\n console.log(\\\"2 yield case\\\")\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n } else {\\n // one yield, yNA inside check\\n for (var i = 1; i < discr-1; i++) {\\n var yNA = y_discr[i]\\n var h = yNA/H\\n if (__check_validity_yNA(h, N_norm)) {\\n var k = __compute_k_1Y_in(h, N_norm)\\n err_inside[i] = __compute_err_1Y_in(h, k, M_norm, N_norm)\\n }\\n }\\n const index_min_i = err_inside.indexOf(Math.min(...err_inside))\\n var yNA = y_discr[index_min_i]\\n var k = __compute_k_1Y_in(yNA/H, N_norm)\\n var chi = __compute_chi_1Y_in(k, fy, E, H, yNA)\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F = -chi\\n } else {\\n var chi_F = chi\\n }\\n \\n if (index_min_i != 1) {\\n // ONE YIELD (YNA INSIDE) CASE\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // check if it's inside (edge case) or outside\\n const yNA_F_in = yNA_F\\n const chi_F_in = chi_F\\n const err_in = err_inside[index_min_i]\\n \\n const k_discr = linspace(1, 20, discrscale_discr_o)\\n for (var i = 1; i < discrscale_discr_o; i++) {\\n var k = k_discr[i]\\n var h = __compute_h_1Y_out(N_norm, k)\\n err_outside[i] = __compute_err_1Y_out(k, h, M_norm, N_norm)\\n }\\n const index_min_o = err_outside.indexOf(Math.min(...err_outside))\\n var k = k_discr[index_min_o]\\n var h = __compute_h_1Y_out(N_norm, k)\\n var yNA = hH\\n var chi = __compute_chi_1Y_out(k, fy, E, H, yNA)\\n const err_o = err_outside[index_min_o]\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F_o = H+yNA\\n } else {\\n var yNA_F_o = -yNA\\n }\\n if ((N>=0 && M>0) \|\| (N<0 && M>0)) {\\n var chi_F_o = -chi\\n } else {\\n var chi_F_o = chi\\n }\\n \\n if (err_in < err_o) {\\n // ONE YIELD (YNA INSIDE) CASE\\n console.log(\\\"1 yield, yNA in case\\\")\\n var yNA_F = yNA_F_in\\n var chi_F = chi_F_in\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n } else {\\n // ONE YIELD (YNA OUTSIDE) CASE\\n console.log(\\\"1 yield, yNA out case\\\")\\n var yNA_F = yNA_F_o\\n var chi_F = chi_F_o\\n var strain_pl = __compute_strain_pl(y_discr, yNA_F, chi_F)\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yNA_F]\\n \\n }\\n }\\n }\\n } else {\\n // PLASTIC LIMIT CASE\\n console.log(\\\"limit case\\\")\\n var yNA = __compute_h_2Y(N_norm)H\\n if ((N>=0 && M<0) \|\| (N<0 && M>0)) {\\n var yNA_F = H-yNA\\n } else {\\n var yNA_F = yNA\\n }\\n let strain_pl = new Array(discr)\\n if ((N>=0 && M>=0) \|\| (N<0 && M>0)) {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]<yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n } else {\\n for (var i = 0; i < discr; i++) {\\n if (y_discr[i]>yNA_F) {\\n strain_pl[i] = -fy/E\\n } else {\\n strain_pl[i] = fy/E\\n }\\n }\\n }\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n var strain_pl_ = [Math.min(...strain_el)100, Math.max(...strain_el)100]\\n var y_discr = [yNA_F, yNA_F]\\n return [stress_pl, strain_pl_, y_discr, yNA_F]\\n }\\n }else {\\n // ELASTIC CASE\\n console.log(\\\"elastic case\\\")\\n var strain_pl = strain_el\\n var stress_pl = __compute_stress_pl(strain_pl, fy, E)\\n return [stress_pl, strain_pl.map(x => x100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3M_norm+N_norm2\\n if (tmp>1) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_M_norm(M, My){\\n return Math.abs(M/My)\\n }\\n \\n function __compute_N_norm(N, Ny){\\n return Math.abs(N/Ny)\\n }\\n\\n function __compute_strain_pl(y, yNA, chi){\\n return y.map(x => -(x-yNA)chi) \\n }\\n\\n function __compute_stress_pl(epsilon, fy, E){\\n const sigma = new Array(epsilon.length).fill(0)\\n for (var i = 0; i < epsilon.length; i++) {\\n var tmp = epsilon[i]E\\n if (tmp > fy){\\n sigma[i] = fy\\n }else if (tmp < -fy){\\n sigma[i] = -fy\\n }else{\\n sigma[i] = tmp\\n }\\n }\\n return sigma\\n }\\n \\n // double yield\\n function __compute_h_2Y(N_norm){\\n return (1-N_norm)/2\\n }\\n \\n function __compute_k_2Y(M_norm, N_norm){\\n return Math.sqrt((1+2N_norm+N_norm*2) / (3-3N_norm*2-2M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return kh / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return kfy/(E(H-yNA))\\n }\\n\\n \\n // one yield (yNA inside)\\n function __check_validity_yNA(h, N_norm){\\n const tmp = (1-N_norm)2 -2h(1-N_norm)\\n if (tmp<0) {\\n return false\\n }else{\\n return true\\n }\\n }\\n \\n function __compute_k_1Y_in(h, N_norm){\\n return (h-1)( (h-1+N_norm) + Math.sqrt((1-N_norm)*2 -2h(1-N_norm)) ) / h2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3N_norm(1-2h) - 2kh*3/(1-h) - (3k2-1)/k2(1-h)2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return kfy/(E(H-yNA))\\n }\\n\\n // one yield (yNA outside)\\n function __compute_h_1Y_out(N_norm, k){\\n return (k(2-N_norm)-1-kMath.sqrt((k-N_norm)2-(k-1)2)) / (k-1)2\\n }\\n \\n function __compute_chi_1Y_out(k, fy, E, H, yNA){\\n return kfy/(E(H+yNA))\\n }\\n\\n function __compute_err_1Y_out(k, h, M_norm, N_norm){\\n return Math.abs( M_norm + 3(N_norm-1) + (1+h-kh)3 / (k2(1+h)) )\\n }\\n \\n \\n function compute_total_epsilon(epsilon_axial, epsilon_bending) {\\n return epsilon_axial+epsilon_bending\\n }\\n \\n 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	- "hidden_code_nb_plastic.main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, E_steel, fy, fy_steel, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr)"
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	diff --git a/Simple Beam DEMOs/sb_stress.ipynb b/Simple Beam DEMOs/sb_stress.ipynb
	deleted file mode 100644
	index 026fc24..0000000
	--- a/Simple Beam DEMOs/sb_stress.ipynb
	+++ /dev/null
	@@ -1,600 +0,0 @@
	-{
	- "cells": [
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "# Simple beam - Stress and Strain\n",
	- "In this fourth notebook, the stresses and strains inside the element are presented."
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "## Goals\n",
	- "\n",
	- "* Understand the differences between the various strains and stresses\n",
	- "* Learn the relations between them\n",
	- "* Note how some parameters influence their behaviour"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {
	- "tags": []
	- },
	- "source": [
	- "## Tasks and exercises\n",
	- "\n",
	- "Answer to the following questions by using and playing with the interactive visualisation tool (bottom of the notebook).\n",
	- "\n",
	- "1. What are the differences between the centroid and the neutral axis? Is there a way to superimpose them in this studied case?\n",
	- "\n",
	- " <details>\n",
	- " <summary style=\"color: red\">Solution:</summary>\n",
	- " The centroid is dependent only on the geometry of the section; on the other hand, the neutral axis is function of the centroid and the internal forces.\n",
	- " \n",
	- " Yes, if the external horizontal force P is removed and the axial force N becomes zero, the neutral axis is in the same position of the centroid.\n",
	- " </details>\n",
	- "\n",
	- "<br>\n",
	- "\n",
	- "2. Does the cross-section influence the maximal stresses and strains? By changing the length of the beam to 8 m, do you ascertain any changes?\n",
	- "\n",
	- " <details>\n",
	- " <summary style=\"color: red\">Solution:</summary>\n",
	- " Yes; the internal forces do not change, but the resistance of the section (area and inertia) is directly influenced by h and b. Note that increasing h has a bigger impact only on the bending strain and bending stress (power of 2); on the other hand b and h have the same influence, because the axial stress and strain is dependent only on the area: $\\sigma_N = N/A$ and $\\epsilon_N = \\sigma_N/E$ and the shear stress is also only dependent on the area: $\\tau_{max} = \\frac{V S}{I_y b} = \\frac{V\\frac{bh^2}{8}}{\\frac{bh^3}{12}b} = \\frac{3V}{2bh} = \\frac{3V}{2A}$.\n",
	- " \n",
	- " Yes; the parameters responsible for the resistance of the section (area and inertia) do not change, but the amplitude of the shear and the bending moment increase, thus the stress and strain inside the section increase, except for the axial strain and stress, that are independent of the length of the beam and they remain the same.\n",
	- " </details>\n",
	- "\n",
	- "<br>\n",
	- "\n",
	- "3. Consider the starting configuration; assume that the beam is composed of a material with a yield strength of 27.2 MPa.\n",
	- " 1. Will the beam remain elastic everywhere?\n",
	- " <details>\n",
	- " <summary style=\"color: red\">Solution:</summary>\n",
	- " No, at the position where the bending moment is maximum, the stress in the top compressed fiber is equal to 27.5 MPa, that is bigger than 27.2 MPa.\n",
	- " </details>\n",
	- "\n",
	- " <br>\n",
	- " \n",
	- " 2. Where will it yield?\n",
	- " <details>\n",
	- " <summary style=\"color: red\">Solution:</summary>\n",
	- " At the center of the beam, where the bending moment is the highest.\n",
	- " </details>\n",
	- "\n",
	- " <br>\n",
	- " \n",
	- " 3. If you can change only one parameter to assure that the beam remains always elastic, what will you do?\n",
	- "\n",
	- " <details>\n",
	- " <summary style=\"color: red\">Solution:</summary>\n",
	- " The possible solution are:\n",
	- " <ul>\n",
	- " <li>Increase h</li>\n",
	- " <li>Increase b</li>\n",
	- " <li>Decrease L</li>\n",
	- " <li>Remove (or decrease) the external horizontal force P</li>\n",
	- " <li>Decrease the uniform load q</li>\n",
	- " </ul>\n",
	- " </details>\n",
	- "\n",
	- " <br>"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "## Build the interactive visualisation tool"
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 1,
	- "metadata": {},
	- "outputs": [
	- {
	- "data": {
	- "text/html": [
	- "\n",
	- " <div class=\"bk-root\">\n",
	- " <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
	- " <span id=\"1002\">Loading BokehJS ...</span>\n",
	- " </div>"
	- ]
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- },
	- {
	- "data": {
	- "application/javascript": [
	- "\n",
	- "(function(root) {\n",
	- " function now() {\n",
	- " return new Date();\n",
	- " }\n",
	- "\n",
	- " const force = true;\n",
	- "\n",
	- " if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_onload_callbacks = [];\n",
	- " root._bokeh_is_loading = undefined;\n",
	- " }\n",
	- "\n",
	- " const JS_MIME_TYPE = 'application/javascript';\n",
	- " const HTML_MIME_TYPE = 'text/html';\n",
	- " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
	- " const CLASS_NAME = 'output_bokeh rendered_html';\n",
	- "\n",
	- " /**\n",
	- " * Render data to the DOM node\n",
	- " */\n",
	- " function render(props, node) {\n",
	- " const script = document.createElement(\"script\");\n",
	- " node.appendChild(script);\n",
	- " }\n",
	- "\n",
	- " /**\n",
	- " * Handle when an output is cleared or removed\n",
	- " */\n",
	- " function handleClearOutput(event, handle) {\n",
	- " const cell = handle.cell;\n",
	- "\n",
	- " const id = cell.output_area._bokeh_element_id;\n",
	- " const server_id = cell.output_area._bokeh_server_id;\n",
	- " // Clean up Bokeh references\n",
	- " if (id != null && id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- "\n",
	- " if (server_id !== undefined) {\n",
	- " // Clean up Bokeh references\n",
	- " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	- " cell.notebook.kernel.execute(cmd_clean, {\n",
	- " iopub: {\n",
	- " output: function(msg) {\n",
	- " const id = msg.content.text.trim();\n",
	- " if (id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- " }\n",
	- " }\n",
	- " });\n",
	- " // Destroy server and session\n",
	- " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	- " cell.notebook.kernel.execute(cmd_destroy);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " /**\n",
	- " * Handle when a new output is added\n",
	- " */\n",
	- " function handleAddOutput(event, handle) {\n",
	- " const output_area = handle.output_area;\n",
	- " const output = handle.output;\n",
	- "\n",
	- " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	- " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	- " return\n",
	- " }\n",
	- "\n",
	- " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
	- "\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	- " // store reference to embed id on output_area\n",
	- " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
	- " }\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	- " const bk_div = document.createElement(\"div\");\n",
	- " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	- " const script_attrs = bk_div.children[0].attributes;\n",
	- " for (let i = 0; i < script_attrs.length; i++) {\n",
	- " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	- " }\n",
	- " // store reference to server id on output_area\n",
	- " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function register_renderer(events, OutputArea) {\n",
	- "\n",
	- " function append_mime(data, metadata, element) {\n",
	- " // create a DOM node to render to\n",
	- " const toinsert = this.create_output_subarea(\n",
	- " metadata,\n",
	- " CLASS_NAME,\n",
	- " EXEC_MIME_TYPE\n",
	- " );\n",
	- " this.keyboard_manager.register_events(toinsert);\n",
	- " // Render to node\n",
	- " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	- " render(props, toinsert[toinsert.length - 1]);\n",
	- " element.append(toinsert);\n",
	- " return toinsert\n",
	- " }\n",
	- "\n",
	- " /* Handle when an output is cleared or removed */\n",
	- " events.on('clear_output.CodeCell', handleClearOutput);\n",
	- " events.on('delete.Cell', handleClearOutput);\n",
	- "\n",
	- " /* Handle when a new output is added */\n",
	- " events.on('output_added.OutputArea', handleAddOutput);\n",
	- "\n",
	- " /**\n",
	- " * Register the mime type and append_mime function with output_area\n",
	- " */\n",
	- " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	- " /* Is output safe? */\n",
	- " safe: true,\n",
	- " /* Index of renderer in `output_area.display_order` */\n",
	- " index: 0\n",
	- " });\n",
	- " }\n",
	- "\n",
	- " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	- " if (root.Jupyter !== undefined) {\n",
	- " const events = require('base/js/events');\n",
	- " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	- "\n",
	- " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	- " register_renderer(events, OutputArea);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " \n",
	- " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_timeout = Date.now() + 5000;\n",
	- " root._bokeh_failed_load = false;\n",
	- " }\n",
	- "\n",
	- " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	- " \"<div style='background-color: #fdd'>\\n\"+\n",
	- " \"<p>\\n\"+\n",
	- " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	- " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	- " \"</p>\\n\"+\n",
	- " \"<ul>\\n\"+\n",
	- " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	- " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	- " \"</ul>\\n\"+\n",
	- " \"<code>\\n\"+\n",
	- " \"from bokeh.resources import INLINE\\n\"+\n",
	- " \"output_notebook(resources=INLINE)\\n\"+\n",
	- " \"</code>\\n\"+\n",
	- " \"</div>\"}};\n",
	- "\n",
	- " function display_loaded() {\n",
	- " const el = document.getElementById(\"1002\");\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS is loading...\";\n",
	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	- " }\n",
	- " } else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(display_loaded, 100)\n",
	- " }\n",
	- " }\n",
	- "\n",
	- "\n",
	- " function run_callbacks() {\n",
	- " try {\n",
	- " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	- " if (callback != null)\n",
	- " callback();\n",
	- " });\n",
	- " } finally {\n",
	- " delete root._bokeh_onload_callbacks\n",
	- " }\n",
	- " console.debug(\"Bokeh: all callbacks have finished\");\n",
	- " }\n",
	- "\n",
	- " function load_libs(css_urls, js_urls, callback) {\n",
	- " if (css_urls == null) css_urls = [];\n",
	- " if (js_urls == null) js_urls = [];\n",
	- "\n",
	- " root._bokeh_onload_callbacks.push(callback);\n",
	- " if (root._bokeh_is_loading > 0) {\n",
	- " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	- " return null;\n",
	- " }\n",
	- " if (js_urls == null \|\| js_urls.length === 0) {\n",
	- " run_callbacks();\n",
	- " return null;\n",
	- " }\n",
	- " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	- " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	- "\n",
	- " function on_load() {\n",
	- " root._bokeh_is_loading--;\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	- " run_callbacks()\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function on_error(url) {\n",
	- " console.error(\"failed to load \" + url);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < css_urls.length; i++) {\n",
	- " const url = css_urls[i];\n",
	- " const element = document.createElement(\"link\");\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.rel = \"stylesheet\";\n",
	- " element.type = \"text/css\";\n",
	- " element.href = url;\n",
	- " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < js_urls.length; i++) {\n",
	- " const url = js_urls[i];\n",
	- " const element = document.createElement('script');\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.async = false;\n",
	- " element.src = url;\n",
	- " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	- " document.head.appendChild(element);\n",
	- " }\n",
	- " };\n",
	- "\n",
	- " function inject_raw_css(css) {\n",
	- " const element = document.createElement(\"style\");\n",
	- " element.appendChild(document.createTextNode(css));\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " \n",
	- " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	- " const css_urls = [];\n",
	- " \n",
	- "\n",
	- " const inline_js = [\n",
	- " function(Bokeh) {\n",
	- " Bokeh.set_log_level(\"info\");\n",
	- " },\n",
	- " function(Bokeh) {\n",
	- " \n",
	- " \n",
	- " }\n",
	- " ];\n",
	- "\n",
	- " function run_inline_js() {\n",
	- " \n",
	- " if (root.Bokeh !== undefined \|\| force === true) {\n",
	- " \n",
	- " for (let i = 0; i < inline_js.length; i++) {\n",
	- " inline_js[i].call(root, root.Bokeh);\n",
	- " }\n",
	- " if (force === true) {\n",
	- " display_loaded();\n",
	- " }} else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(run_inline_js, 100);\n",
	- " } else if (!root._bokeh_failed_load) {\n",
	- " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
	- " root._bokeh_failed_load = true;\n",
	- " } else if (force !== true) {\n",
	- " const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
	- " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
	- " }\n",
	- "\n",
	- " }\n",
	- "\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
	- " run_inline_js();\n",
	- " } else {\n",
	- " load_libs(css_urls, js_urls, function() {\n",
	- " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	- " run_inline_js();\n",
	- " });\n",
	- " }\n",
	- "}(window));"
	- ],
	- "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n function now() {\n return new Date();\n }\n\n const force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n \n\n \n if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n const NB_LOAD_WARNING = {'data': {'text/html':\n \"<div style='background-color: #fdd'>\\n\"+\n \"<p>\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"</p>\\n\"+\n \"<ul>\\n\"+\n \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n \"<li>use INLINE resources instead, as so:</li>\\n\"+\n \"</ul>\\n\"+\n \"<code>\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"</code>\\n\"+\n \"</div>\"}};\n\n function display_loaded() {\n const el = document.getElementById(\"1002\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null \|\| js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error(url) {\n console.error(\"failed to load \" + url);\n }\n\n for (let i = 0; i < css_urls.length; i++) {\n const url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n \n const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n const css_urls = [];\n \n\n const inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n function(Bokeh) {\n \n \n }\n ];\n\n function run_inline_js() {\n \n if (root.Bokeh !== undefined \|\| force === true) {\n \n for (let i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\n if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));"
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- }
	- ],
	- "source": [
	- "# Import the packages needed\n",
	- "import sys\n",
	- "sys.path.append('../HiddenCode')\n",
	- "import hidden_code_nb_stress\n",
	- "import math\n",
	- "import numpy as np\n",
	- "from cienpy import simplebeam as sb\n",
	- "from cienpy import rectangular_section as beam_section\n",
	- "from cienpy import stress_strain_elastic as stst"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Define the geometry, the external actions, the mechanical property and compute the initial configuration."
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 2,
	- "metadata": {},
	- "outputs": [],
	- "source": [
	- "# Choose the dimensions\n",
	- "L = 6 # [m]\n",
	- "h = 200 # [mm]\n",
	- "b = 100 # [mm]\n",
	- "q = 4; # [kN/m]\n",
	- "P = 10; # [kN]\n",
	- "\n",
	- "# Choose the material parameters\n",
	- "E = 200e3 # [MPa]\n",
	- "\n",
	- "# compute the internal forces (at x=L)\n",
	- "discr_NVM = 100\n",
	- "x_discr = np.linspace(0, L, discr_NVM)\n",
	- "N_discr = sb.compute_N(x_discr, P)\n",
	- "V_discr = sb.compute_V(x_discr, q, L)\n",
	- "M_discr = sb.compute_M(x_discr, q, L)\n",
	- "N = N_discr[-1]\n",
	- "V = V_discr[-1]\n",
	- "M = M_discr[-1]\n",
	- "\n",
	- "# compute the parameters\n",
	- "A = beam_section.compute_area(b, h) # [mm2]\n",
	- "Iy = beam_section.compute_inertia_y(b, h) # [mm4] strong axis\n",
	- "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis\n",
	- "yG = beam_section.compute_centroid_y(h)\n",
	- "y_n_axis = stst.compute_neutral_axis(N, A, Iy, M, yG)\n",
	- "\n",
	- "# compute the reactions\n",
	- "Rx = sb.compute_Rx(P)\n",
	- "Ry_l = sb.compute_Ry_l(q, L)\n",
	- "Ry_r = sb.compute_Ry_r(q, L)"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Run the complex code to generate the interactive visualisation tool:"
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 3,
	- "metadata": {},
	- "outputs": [
	- {
	- "data": {
	- "text/html": [
	- "\n",
	- "\n",
	- "\n",
	- "\n",
	- "\n",
	- "\n",
	- " <div class=\"bk-root\" id=\"d94629b0-ef5a-4113-9780-0052e36c0c72\" data-root-id=\"1924\"></div>\n"
	- ]
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- },
	- {
	- "data": {
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	- "(function(root) {\n",
	- " function embed_document(root) {\n",
	- " \n",
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// retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \"},\"id\":\"1900\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1676\"},\"N_stress_diag\":{\"id\":\"1658\"},\"V_stress_diag\":{\"id\":\"1694\"},\"arr_head\":{\"id\":\"1253\"},\"axial_strain_diag\":{\"id\":\"1748\"},\"bending_strain_diag\":{\"id\":\"1768\"},\"centroid\":{\"id\":\"1688\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1724\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1712\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \"},\"id\":\"1899\",\"type\":\"CustomJS\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1676\"},\"N_stress_diag\":{\"id\":\"1658\"},\"V_stress_diag\":{\"id\":\"1694\"},\"axial_strain_diag\":{\"id\":\"1748\"},\"bending_strain_diag\":{\"id\":\"1768\"},\"centroid\":{\"id\":\"1688\"},\"div\":{\"id\":\"1107\"},\"neutral_axis\":{\"id\":\"1724\"},\"s_b\":{\"id\":\"1003\"},\"s_ss\":{\"id\":\"1006\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1712\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1099\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const h = cb_obj.value // value of the slider\\n const A = compute_area(b, h)\\n const Iy = compute_inertia_y(b, h)\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n glyph_section.glyph.width = data['b'][0]\\n glyph_section.glyph.height = data['h'][0]\\n }\\n \\n \\n function compute_area(b, h) {\\n return bh\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return hb*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \"},\"id\":\"1901\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2140\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"1364\"},\"N_stress_diag\":{\"id\":\"1658\"},\"arr_head\":{\"id\":\"1253\"},\"axial_strain_diag\":{\"id\":\"1748\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1724\"},\"s_M\":{\"id\":\"1242\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1712\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=100) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1902\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2085\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1253\"},\"div_P\":{\"id\":\"1259\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"1903\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2141\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"2086\",\"type\":\"AllLabels\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1388\"},\"M_stress_diag\":{\"id\":\"1676\"},\"V_diag\":{\"id\":\"1376\"},\"V_stress_diag\":{\"id\":\"1694\"},\"arr_head\":{\"id\":\"1253\"},\"bending_strain_diag\":{\"id\":\"1768\"},\"centroid\":{\"id\":\"1688\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1724\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1712\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=10) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n \\n total_tau[i] = compute_total_tau(tau_shear[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y, b, h, yG) {\\n return b/2(h2/4-(y-yG)2)\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n 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	- " const render_items = [{\"docid\":\"01c53cca-b8cd-4ae6-a2a0-b26d6b8dbc69\",\"root_ids\":[\"1924\"],\"roots\":{\"1924\":\"d94629b0-ef5a-4113-9780-0052e36c0c72\"}}];\n",
	- " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
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	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " embed_document(root);\n",
	- " } else {\n",
	- " let attempts = 0;\n",
	- " const timer = setInterval(function(root) {\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " clearInterval(timer);\n",
	- " embed_document(root);\n",
	- " } else {\n",
	- " attempts++;\n",
	- " if (attempts > 100) {\n",
	- " clearInterval(timer);\n",
	- " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	- " }\n",
	- " }\n",
	- " }, 10, root)\n",
	- " }\n",
	- "})(window);"
	- ],
	- "application/vnd.bokehjs_exec.v0+json": ""
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	- "source": [
	- "hidden_code_nb_stress.main_code(L, h, b, A, Iy, Iz, yG, y_n_axis, q, P, E, N, V, M, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr)"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {
	- "tags": []
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	- "source": [
	- "## Legend\n",
	- "\n",
	- "Brief description on how to use the interactive visualization tool. For more information on specific features, check the comments in the desired file in the HiddenCode folder.\n",
	- "\n",
	- "* Slider of the width b: move the slider to change the width b of the cross-section of the beam.\n",
	- "* Slider of height h: move the slider to change the height h of the cross-section of the beam.\n",
	- "* Slider of the position x: move the slider to change the position x along the beam.\n",
	- "* Slider of the uniform load q: move the slider to change the uniform load q.\n",
	- "* Textbox \"Geometrical and mechanical parameters: small summary with the value of h, b, L, A (area), Iy (inertia with respect to the strong axis) and Iz (inertia with respect to the weak axis).\n",
	- "* Textbox \"Forces and Moments: small summary with the value of the magnitude of the reaction forces and the internal forces at the position x.\n",
	- "* Figure \"Simple supported beam\": in this figure, the initial state is presented with the static scheme, the length of the beam, the horizontal force P and the uniform load q.\n",
	- "* Figure \"Cross-section of the beam\": in this figure, the cross section (constant along the beam) and the remaining two axis (y and z) are depicted.\n",
	- "* Figure \"Forces and Moments Scheme\": this figure has a dynamic representation of the studied case with the position x indicated by a magenta dot, the internal forces shown in with red arrows, the reaction forces with yellow arrows, the external force P with a green arrow and the uniform load q in blue.\n",
	- "* Radio buttons of the FBD: choose between right-hand or left-hand free-body diagram.\n",
	- "* Button of the force P: apply or remove the external force P.\n",
	- "* Figures \"N V M Diagrams\": plots that show the axial force N, shear force V and bending moment M diagrams, with a magenta dot that represents the x position. By hovering with the cursor over the desired position, a small window will show the position and the value of the internal force.\n",
	- "* 9 small bottom figures: plots that show the strains, stresses and right-hand free-body diagram section (with N, V and M). By hovering with the cursor over the desired position, a small window will show the height and the value of the stress or strain.\n",
	- "\n",
	- "### Recommendations\n",
	- "\n",
	- "Considering the innate graphical nature of the interactive visualization tool, the input in the definition of the variables with extreme configuration can lead to small glitches or unclear plots; it's recommended to change these values carefully.\n",
	- "\n",
	- "### EXTRA: Note on the slow reactivity of the tool\n",
	- "\n",
	- "The slow reactivity of the tool is given by the two textboxes (called Div Widgets) which automatically call a specific funtion every time they are modified. This function redraws everything in the tool (figures, plots, diagrams, textboxes, sliders, ...), generating this problem. Considering that a real solution does not exist in the current version of the lib used (Bokeh 2.4.2), these textboxes will be removed in the next DEMOs."
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	- "nbformat": 4,
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	diff --git a/Simple Beam DEMOs/sb_torsion.ipynb b/Simple Beam DEMOs/sb_torsion.ipynb
	deleted file mode 100644
	index e136c34..0000000
	--- a/Simple Beam DEMOs/sb_torsion.ipynb
	+++ /dev/null
	@@ -1,488 +0,0 @@
	-{
	- "cells": [
	- {
	- "cell_type": "markdown",
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	- "source": [
	- "# Simple beam - Torsion\n",
	- "In this first notebook, the torsion is presented. Considering the complexity of the problem with this new cross-section geometry and the introduction of the torsion, the focus of the notebook in the stress and strain analysis is placed on the left web."
	- ]
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	- " <span id=\"1002\">Loading BokehJS ...</span>\n",
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	- "\n",
	- " const id = cell.output_area._bokeh_element_id;\n",
	- " const server_id = cell.output_area._bokeh_server_id;\n",
	- " // Clean up Bokeh references\n",
	- " if (id != null && id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- "\n",
	- " if (server_id !== undefined) {\n",
	- " // Clean up Bokeh references\n",
	- " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
	- " cell.notebook.kernel.execute(cmd_clean, {\n",
	- " iopub: {\n",
	- " output: function(msg) {\n",
	- " const id = msg.content.text.trim();\n",
	- " if (id in Bokeh.index) {\n",
	- " Bokeh.index[id].model.document.clear();\n",
	- " delete Bokeh.index[id];\n",
	- " }\n",
	- " }\n",
	- " }\n",
	- " });\n",
	- " // Destroy server and session\n",
	- " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
	- " cell.notebook.kernel.execute(cmd_destroy);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " /**\n",
	- " * Handle when a new output is added\n",
	- " */\n",
	- " function handleAddOutput(event, handle) {\n",
	- " const output_area = handle.output_area;\n",
	- " const output = handle.output;\n",
	- "\n",
	- " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
	- " if ((output.output_type != \"display_data\") \|\| (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
	- " return\n",
	- " }\n",
	- "\n",
	- " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
	- "\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
	- " // store reference to embed id on output_area\n",
	- " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
	- " }\n",
	- " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
	- " const bk_div = document.createElement(\"div\");\n",
	- " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
	- " const script_attrs = bk_div.children[0].attributes;\n",
	- " for (let i = 0; i < script_attrs.length; i++) {\n",
	- " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
	- " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
	- " }\n",
	- " // store reference to server id on output_area\n",
	- " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function register_renderer(events, OutputArea) {\n",
	- "\n",
	- " function append_mime(data, metadata, element) {\n",
	- " // create a DOM node to render to\n",
	- " const toinsert = this.create_output_subarea(\n",
	- " metadata,\n",
	- " CLASS_NAME,\n",
	- " EXEC_MIME_TYPE\n",
	- " );\n",
	- " this.keyboard_manager.register_events(toinsert);\n",
	- " // Render to node\n",
	- " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
	- " render(props, toinsert[toinsert.length - 1]);\n",
	- " element.append(toinsert);\n",
	- " return toinsert\n",
	- " }\n",
	- "\n",
	- " /* Handle when an output is cleared or removed */\n",
	- " events.on('clear_output.CodeCell', handleClearOutput);\n",
	- " events.on('delete.Cell', handleClearOutput);\n",
	- "\n",
	- " /* Handle when a new output is added */\n",
	- " events.on('output_added.OutputArea', handleAddOutput);\n",
	- "\n",
	- " /**\n",
	- " * Register the mime type and append_mime function with output_area\n",
	- " */\n",
	- " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
	- " /* Is output safe? */\n",
	- " safe: true,\n",
	- " /* Index of renderer in `output_area.display_order` */\n",
	- " index: 0\n",
	- " });\n",
	- " }\n",
	- "\n",
	- " // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
	- " if (root.Jupyter !== undefined) {\n",
	- " const events = require('base/js/events');\n",
	- " const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
	- "\n",
	- " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
	- " register_renderer(events, OutputArea);\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " \n",
	- " if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n",
	- " root._bokeh_timeout = Date.now() + 5000;\n",
	- " root._bokeh_failed_load = false;\n",
	- " }\n",
	- "\n",
	- " const NB_LOAD_WARNING = {'data': {'text/html':\n",
	- " \"<div style='background-color: #fdd'>\\n\"+\n",
	- " \"<p>\\n\"+\n",
	- " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
	- " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
	- " \"</p>\\n\"+\n",
	- " \"<ul>\\n\"+\n",
	- " \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
	- " \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
	- " \"</ul>\\n\"+\n",
	- " \"<code>\\n\"+\n",
	- " \"from bokeh.resources import INLINE\\n\"+\n",
	- " \"output_notebook(resources=INLINE)\\n\"+\n",
	- " \"</code>\\n\"+\n",
	- " \"</div>\"}};\n",
	- "\n",
	- " function display_loaded() {\n",
	- " const el = document.getElementById(\"1002\");\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS is loading...\";\n",
	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " if (el != null) {\n",
	- " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
	- " }\n",
	- " } else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(display_loaded, 100)\n",
	- " }\n",
	- " }\n",
	- "\n",
	- "\n",
	- " function run_callbacks() {\n",
	- " try {\n",
	- " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
	- " if (callback != null)\n",
	- " callback();\n",
	- " });\n",
	- " } finally {\n",
	- " delete root._bokeh_onload_callbacks\n",
	- " }\n",
	- " console.debug(\"Bokeh: all callbacks have finished\");\n",
	- " }\n",
	- "\n",
	- " function load_libs(css_urls, js_urls, callback) {\n",
	- " if (css_urls == null) css_urls = [];\n",
	- " if (js_urls == null) js_urls = [];\n",
	- "\n",
	- " root._bokeh_onload_callbacks.push(callback);\n",
	- " if (root._bokeh_is_loading > 0) {\n",
	- " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
	- " return null;\n",
	- " }\n",
	- " if (js_urls == null \|\| js_urls.length === 0) {\n",
	- " run_callbacks();\n",
	- " return null;\n",
	- " }\n",
	- " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
	- " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
	- "\n",
	- " function on_load() {\n",
	- " root._bokeh_is_loading--;\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
	- " run_callbacks()\n",
	- " }\n",
	- " }\n",
	- "\n",
	- " function on_error(url) {\n",
	- " console.error(\"failed to load \" + url);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < css_urls.length; i++) {\n",
	- " const url = css_urls[i];\n",
	- " const element = document.createElement(\"link\");\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.rel = \"stylesheet\";\n",
	- " element.type = \"text/css\";\n",
	- " element.href = url;\n",
	- " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " for (let i = 0; i < js_urls.length; i++) {\n",
	- " const url = js_urls[i];\n",
	- " const element = document.createElement('script');\n",
	- " element.onload = on_load;\n",
	- " element.onerror = on_error.bind(null, url);\n",
	- " element.async = false;\n",
	- " element.src = url;\n",
	- " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
	- " document.head.appendChild(element);\n",
	- " }\n",
	- " };\n",
	- "\n",
	- " function inject_raw_css(css) {\n",
	- " const element = document.createElement(\"style\");\n",
	- " element.appendChild(document.createTextNode(css));\n",
	- " document.body.appendChild(element);\n",
	- " }\n",
	- "\n",
	- " \n",
	- " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
	- " const css_urls = [];\n",
	- " \n",
	- "\n",
	- " const inline_js = [\n",
	- " function(Bokeh) {\n",
	- " Bokeh.set_log_level(\"info\");\n",
	- " },\n",
	- " function(Bokeh) {\n",
	- " \n",
	- " \n",
	- " }\n",
	- " ];\n",
	- "\n",
	- " function run_inline_js() {\n",
	- " \n",
	- " if (root.Bokeh !== undefined \|\| force === true) {\n",
	- " \n",
	- " for (let i = 0; i < inline_js.length; i++) {\n",
	- " inline_js[i].call(root, root.Bokeh);\n",
	- " }\n",
	- " if (force === true) {\n",
	- " display_loaded();\n",
	- " }} else if (Date.now() < root._bokeh_timeout) {\n",
	- " setTimeout(run_inline_js, 100);\n",
	- " } else if (!root._bokeh_failed_load) {\n",
	- " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
	- " root._bokeh_failed_load = true;\n",
	- " } else if (force !== true) {\n",
	- " const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
	- " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
	- " }\n",
	- "\n",
	- " }\n",
	- "\n",
	- " if (root._bokeh_is_loading === 0) {\n",
	- " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
	- " run_inline_js();\n",
	- " } else {\n",
	- " load_libs(css_urls, js_urls, function() {\n",
	- " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
	- " run_inline_js();\n",
	- " });\n",
	- " }\n",
	- "}(window));"
	- ],
	- "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n function now() {\n return new Date();\n }\n\n const force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" \|\| force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n \n\n \n if (typeof (root._bokeh_timeout) === \"undefined\" \|\| force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n const NB_LOAD_WARNING = {'data': {'text/html':\n \"<div style='background-color: #fdd'>\\n\"+\n \"<p>\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"</p>\\n\"+\n \"<ul>\\n\"+\n \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n \"<li>use INLINE resources instead, as so:</li>\\n\"+\n \"</ul>\\n\"+\n \"<code>\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"</code>\\n\"+\n \"</div>\"}};\n\n function display_loaded() {\n const el = document.getElementById(\"1002\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null \|\| js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error(url) {\n console.error(\"failed to load \" + url);\n }\n\n for (let i = 0; i < css_urls.length; i++) {\n const url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n \n const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n const css_urls = [];\n \n\n const inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n function(Bokeh) {\n \n \n }\n ];\n\n function run_inline_js() {\n \n if (root.Bokeh !== undefined \|\| force === true) {\n \n for (let i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\n if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));"
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- }
	- ],
	- "source": [
	- "# Import the packages needed\n",
	- "import sys\n",
	- "sys.path.append('../HiddenCode')\n",
	- "import hidden_code_nb_torsion\n",
	- "import math\n",
	- "import numpy as np\n",
	- "from cienpy import simplebeam as sb\n",
	- "from cienpy import hollow_rectangular_section as beam_section\n",
	- "from cienpy import stress_strain_elastic as stst"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Define the geometry, uniform load and torsion. Both supports are fixed with respect to the torsion.\n",
	- "Note that given the graphical nature of the notebook, extreme cases can cause the figures to not be displayed."
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 2,
	- "metadata": {},
	- "outputs": [],
	- "source": [
	- "# Choose the dimensions\n",
	- "L = 6 # [m]\n",
	- "h = 200 # [mm]\n",
	- "b = 100 # [mm]\n",
	- "t = 10 # [mm]\n",
	- "q = 4 # [kN/m]\n",
	- "P = 10 # [kN]\n",
	- "Mt = 100 # [kNm]\n",
	- "\n",
	- "# Choose the material parameters\n",
	- "E = 200e3 # [MPa]\n",
	- "\n",
	- "# compute the internal forces (at x=L)\n",
	- "discr_NVM = 100\n",
	- "x_discr = np.linspace(0, L, discr_NVM)\n",
	- "N_discr = sb.compute_N(x_discr, P)\n",
	- "V_discr = sb.compute_V(x_discr, q, L)\n",
	- "M_discr = sb.compute_M(x_discr, q, L)\n",
	- "T_discr = sb.compute_T(x_discr, Mt, L)\n",
	- "N = N_discr[-1]\n",
	- "V = V_discr[-1]\n",
	- "M = M_discr[-1]\n",
	- "T = T_discr[-1]\n",
	- "\n",
	- "# compute the parameters\n",
	- "A = beam_section.compute_area(b, h, t) # [mm2]\n",
	- "Iy = beam_section.compute_inertia_y(b, h, t) # [mm4] strong axis\n",
	- "Iz = beam_section.compute_inertia_z(b, h, t) # [mm4] weak axis\n",
	- "yG = beam_section.compute_centroid_y(h)\n",
	- "y_n_axis = stst.compute_neutral_axis(N, A, Iy, M, yG)\n",
	- "\n",
	- "# compute the reactions\n",
	- "Rx = sb.compute_Rx(P)\n",
	- "Ry_l = sb.compute_Ry_l(q, L)\n",
	- "Ry_r = sb.compute_Ry_r(q, L)"
	- ]
	- },
	- {
	- "cell_type": "markdown",
	- "metadata": {},
	- "source": [
	- "Run the complex code for the interactive visualisation:"
	- ]
	- },
	- {
	- "cell_type": "code",
	- "execution_count": 3,
	- "metadata": {},
	- "outputs": [
	- {
	- "data": {
	- "text/html": [
	- "\n",
	- "\n",
	- "\n",
	- "\n",
	- "\n",
	- "\n",
	- " <div class=\"bk-root\" id=\"272a9d88-57a5-466e-b9b2-cd6e1a1520cb\" data-root-id=\"2087\"></div>\n"
	- ]
	- },
	- "metadata": {},
	- "output_type": "display_data"
	- },
	- {
	- "data": {
	- "application/javascript": [
	- "(function(root) {\n",
	- " function embed_document(root) {\n",
	- " \n",
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// retrieve data used\\n const db = source.data\\n const b = cb_obj.value // value of the slider\\n const h = db['h'][0]\\n const t = db['t'][0]\\n const A = compute_area(b, h, t)\\n const Iy = compute_inertia_y(b, h, t)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n\\n // Easter egg\\n const str_Doge = \\\" such width\\\"\\n const str_tmp = div_P.text\\n if (b == 300) {\\n div_P.text = str_tmp+str_Doge\\n } else {\\n div_P.text = str_tmp.replace(str_Doge, '')\\n }\\n\\n // apply the changes\\n db['b'][0] = b\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h, t)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_torsional_stress(db, T_stress_diag)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const t = Math.round(data['t'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n t = `+t+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n const src = glyph_section.data_source\\n const t = data['t'][0]\\n const b = data['b'][0]\\n const h = data['h'][0]\\n src.data.xs = [[[ [b/2, b/2, -b/2, -b/2], [b/2-t, b/2-t, -b/2+t, -b/2+t] ]]]\\n src.data.ys = [[[ [h/2, -h/2, -h/2, h/2], [h/2-t, -h/2+t, -h/2+t, h/2-t] ]]]\\n src.change.emit()\\n }\\n \\n \\n function compute_area(b, h, t) {\\n return bh - (b-t2)(h-2t)\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12 - (b-2t)(h-2t)*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h, t) {\\n return hb*3/12 - (h-2t)(b-2t)*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the 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// retrieve data\\n const db = source.data\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const FBD = db['FBD'][0]\\n const pos = cb_obj.value\\n const q = db['q'][0]\\n const L = db['L'][0]\\n const Mt = db['Mt'][0]\\n\\n // update data\\n db['N'][0] = compute_N(db['P'][0])\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['T'][0] = compute_T(pos, Mt, L)\\n db['x'][0] = pos\\n\\n // check state\\n check_state(db)\\n\\n // update:\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n update_T_section(db, section_torsion_head, section_torsion_source, section_T_line, section_T_head, section_T_source, div_T, label_T_section)\\n update_torsional_stress(db, T_stress_diag)\\n\\n // apply the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n // declare functions\\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function update_T_section(data, head_T_curved, source_T_curved, line_T, head_T, source_T, div_T, label_T_section, offset_T=4, pixel2unit=10, scale_T=10) {\\n const Mt = data['Mt'][0]\\n const T = data['T'][0]\\n \\n if (T > 0) {\\n update_doubleArrow(offset_T, offset_T+T/scale_T, 0, 0, source_T, head_T)\\n } else {\\n update_doubleArrow(offset_T-T/scale_T, offset_T, 0, 0, source_T, head_T)\\n }\\n \\n // update visibility\\n if (Mt==0) {\\n div_T.text = \\\"Torsion M<sub>t</sub>=0 kNm (removed)\\\"\\n line_T.glyph.line_alpha = 0 // T\\n head_T.glyph.line_alpha = 0\\n head_T.glyph.fill_alpha = 0\\n // T in cross-section\\n update_curvedArrow(0, 0, 0, 0, 0, source_T_curved, head_T_curved)\\n } else {\\n div_T.text = \\\"Torsion M<sub>t</sub>=\\\"+Mt+\\\" kNm (applied)\\\"\\n line_T.glyph.line_alpha = 1 // T\\n head_T.glyph.line_alpha = 1\\n head_T.glyph.fill_alpha = 1\\n // T in cross-section\\n update_curvedArrow(0, T4/scale_T, Math.abs(T3/scale_T), 0, 0, source_T_curved, head_T_curved)\\n }\\n \\n if (T==0) {\\n label_T_section.glyph.text=''\\n } else {\\n label_T_section.glyph.text='T'\\n }\\n }\\n \\n \\n function update_doubleArrow(x_start, x_end, y_start, y_end, source, arr_heads, AHF=6, pixel2unit=10) {\\n // compute the angle of the line\\n const delta_x = x_end-x_start\\n const delta_y = y_end-y_start\\n if (delta_x==0) {\\n if (delta_y > 0) {\\n var theta = Math.PI/2\\n } else {\\n var theta = Math.PI3/2\\n }\\n } else if (delta_x > 0) {\\n var theta = Math.atan(delta_y/delta_x)\\n } else {\\n var theta = Math.atan(delta_y/delta_x)+Math.PI\\n }\\n \\n // head adjust\\n const length_arr = Math.sqrt(delta_x2 + delta_y2)\\n const size_head = arrow_growth(length_arr)AHF\\n const head_x = size_head/pixel2unitMath.cos(theta)\\n const head_y = size_head/pixel2unitMath.sin(theta)\\n \\n // update line\\n const data_line = source.data\\n data_line['x'] = [x_start, x_end]\\n data_line['y'] = [y_start, y_end]\\n source.change.emit()\\n \\n // heads\\n arr_heads.glyph.size = size_head\\n arr_heads.glyph.angle = theta+Math.PI/6\\n //arr_heads.glyph.x = [x_end-head_x/2, x_end-head_x/23]\\n //arr_heads.glyph.y = [y_end-head_y/2, y_end-head_y/23]\\n const source_h = arr_heads.data_source\\n source_h.data['x'] = [x_end-head_x/2, x_end-head_x/23]\\n source_h.data['y'] = [y_end-head_y/2, y_end-head_y/23]\\n source_h.change.emit()\\n }\\n \\n \\n function compute_T(x, Mt, L) {\\n if (x<L/2) {\\n return Mt/2\\n } else {\\n return -Mt/2\\n }\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_torsion, y_discr)\\n }\\n \\n \"},\"id\":\"2061\",\"type\":\"CustomJS\"},{\"attributes\":{\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1385\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"2282\",\"type\":\"Selection\"},{\"attributes\":{\"line_alpha\":0.1,\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1852\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"2338\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":1.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1853\",\"type\":\"Line\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2348\"},\"selection_policy\":{\"id\":\"2347\"}},\"id\":\"2260\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"args\":{\"EE1\":{\"id\":\"2059\"},\"M_stress_diag\":{\"id\":\"1676\"},\"N_stress_diag\":{\"id\":\"1658\"},\"T_stress_diag\":{\"id\":\"2041\"},\"V_stress_diag\":{\"id\":\"1694\"},\"axial_strain_diag\":{\"id\":\"1748\"},\"bending_strain_diag\":{\"id\":\"1768\"},\"centroid\":{\"id\":\"1688\"},\"div\":{\"id\":\"1107\"},\"div_T\":{\"id\":\"1899\"},\"neutral_axis\":{\"id\":\"1724\"},\"s_b\":{\"id\":\"1003\"},\"s_ss\":{\"id\":\"1006\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1712\"},\"source\":{\"id\":\"1007\"},\"support_r\":{\"id\":\"1099\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const data_ss = s_ss.data\\n const b = db['b'][0]\\n const t = db['t'][0]\\n const h = cb_obj.value // value of the slider\\n const A = compute_area(b, h, t)\\n const Iy = compute_inertia_y(b, h, t)\\n const N = db['N'][0]\\n const M = db['M'][0]\\n const yG = compute_centroid_y(h)\\n\\n // Easter egg\\n /const str_Doge = \\\" much wow\\\"\\n const str_tmp = div_T.text\\n if (h == 600) {\\n div_T.text = str_tmp+str_Doge\\n } else {\\n div_T.text = str_tmp.replace(str_Doge, '')\\n }/\\n if (h == 600) {\\n EE1.glyph.text = \\\"much wow\\\"\\n } else {\\n EE1.glyph.text = \\\"\\\"\\n }\\n\\n // apply the changes\\n db['h'][0] = h\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h, t)\\n db['yG'][0] = yG\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n data_ss['y'][1] = h // change the height of the section in the diagrams\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_torsional_stress(db, T_stress_diag)\\n\\n // emit the changes\\n source.change.emit()\\n s_ss.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const t = Math.round(data['t'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n t = `+t+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n const src = glyph_section.data_source\\n const t = data['t'][0]\\n const b = data['b'][0]\\n const h = data['h'][0]\\n src.data.xs = [[[ [b/2, b/2, -b/2, -b/2], [b/2-t, b/2-t, -b/2+t, -b/2+t] ]]]\\n src.data.ys = [[[ [h/2, -h/2, -h/2, h/2], [h/2-t, -h/2+t, -h/2+t, h/2-t] ]]]\\n src.change.emit()\\n }\\n \\n \\n function compute_area(b, h, t) {\\n return bh - (b-t2)(h-2t)\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12 - (b-2t)(h-2t)*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h, t) {\\n return hb*3/12 - (h-2t)(b-2t)*3/12\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_torsion, y_discr)\\n }\\n \\n \"},\"id\":\"2063\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2339\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"N_diag\":{\"id\":\"1364\"},\"N_stress_diag\":{\"id\":\"1658\"},\"arr_head\":{\"id\":\"1253\"},\"axial_strain_diag\":{\"id\":\"1748\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1724\"},\"s_M\":{\"id\":\"1242\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1712\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox P\\n if (f.length==0) f = [1]\\n const db = source.data\\n\\n // apply the changes\\n db['P'][0] = 10(1-f)\\n db['N'][0] = compute_N(db['P'][0])\\n db['Rx'][0] = compute_Rx(db['P'][0])\\n\\n // update\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_N_diagram(db, N_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function compute_Rx(P) {\\n return P\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_N(P) {\\n return -P\\n }\\n \\n \\n function update_N_diagram(data, glyph, discr=100) {\\n const P = data['P'][0]\\n const N_discr = Array.from({length: discr}, (_, i) => compute_N(P))\\n update_NVM_diagram(glyph, N_discr)\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \"},\"id\":\"2064\",\"type\":\"CustomJS\"},{\"attributes\":{\"data\":{\"x\":[-1.6666666666666667,0,0,-1.6666666666666667],\"y\":[-10,-10,10,10]},\"selected\":{\"id\":\"2297\"},\"selection_policy\":{\"id\":\"2296\"}},\"id\":\"1850\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"2227\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"args\":{\"arr_head\":{\"id\":\"1253\"},\"div_P\":{\"id\":\"1259\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_sb\":{\"id\":\"1004\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const FBD = cb_obj.active\\n const data_sb = s_sb.data\\n const data_q = s_q.data\\n const pos = db['x'][0]\\n\\n // apply the changes\\n db['FBD'][0] = FBD\\n\\n // update\\n check_state(db)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_scheme_position(db, data_sb, data_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n\\n // emit the changes\\n source.change.emit()\\n s_sb.change.emit()\\n s_q.change.emit()\\n\\n \\n function check_state(data) {\\n const FBD = data['FBD'][0]\\n const pos = data['x'][0]\\n const L = data['L'][0]\\n if (FBD == 0 && pos != L) {\\n data['state'][0] = 'R_SEC'\\n } else if (FBD == 1 && pos != 0) {\\n data['state'][0] = 'L_SEC'\\n } else {\\n data['state'][0] = 'IDLE'\\n }\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_scheme_position(data, data_scheme_beam, data_scheme_q) {\\n const L = data['L'][0]data['SCALE'][0]\\n const pos = data['x'][0]data['SCALE'][0]\\n \\n // move position of the point\\n data['xF'][0] = pos\\n \\n switch(data['state'][0]) {\\n case 'IDLE':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = L\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = L\\n data_scheme_q['x'][3] = L\\n break\\n case 'R_SEC':\\n // beam\\n data_scheme_beam['x'][0] = 0\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = 0\\n data_scheme_q['x'][1] = 0\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n case 'L_SEC':\\n // beam\\n data_scheme_beam['x'][0] = L\\n data_scheme_beam['x'][1] = pos\\n // unif load\\n data_scheme_q['x'][0] = L\\n data_scheme_q['x'][1] = L\\n data_scheme_q['x'][2] = pos\\n data_scheme_q['x'][3] = pos\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c*2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \"},\"id\":\"2065\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2296\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"source\":{\"id\":\"1850\"}},\"id\":\"1855\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"2228\",\"type\":\"AllLabels\"},{\"attributes\":{\"args\":{\"M_diag\":{\"id\":\"1388\"},\"M_stress_diag\":{\"id\":\"1676\"},\"V_diag\":{\"id\":\"1376\"},\"V_stress_diag\":{\"id\":\"1694\"},\"arr_head\":{\"id\":\"1253\"},\"bending_strain_diag\":{\"id\":\"1768\"},\"centroid\":{\"id\":\"1688\"},\"div_P\":{\"id\":\"1259\"},\"div_f\":{\"id\":\"1261\"},\"fN\":{\"id\":\"1237\"},\"fP\":{\"id\":\"1225\"},\"fRx\":{\"id\":\"1234\"},\"fRyl\":{\"id\":\"1231\"},\"fRyr\":{\"id\":\"1228\"},\"fV\":{\"id\":\"1240\"},\"label_M_section\":{\"id\":\"1891\"},\"label_N_section\":{\"id\":\"1885\"},\"label_V_section\":{\"id\":\"1897\"},\"neutral_axis\":{\"id\":\"1724\"},\"s_M\":{\"id\":\"1242\"},\"s_q\":{\"id\":\"1005\"},\"s_section_M\":{\"id\":\"1868\"},\"section_M_head\":{\"id\":\"1879\"},\"section_N\":{\"id\":\"1863\"},\"section_V\":{\"id\":\"1866\"},\"sigma_stress_diag\":{\"id\":\"1712\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve data\\n const db = source.data\\n const q = cb_obj.value\\n const pos = db['x'][0]\\n const L = db['L'][0]\\n\\n // update q\\n db['q'][0] = q\\n db['V'][0] = compute_V(pos, q, L)\\n db['M'][0] = compute_M(pos, q, L)\\n db['Ry_l'][0] = compute_Ry_l(q, L)\\n db['Ry_r'][0] = compute_Ry_r(q, L)\\n\\n // update\\n update_u_load(db, s_q)\\n update_reactions(db, fRx, fRyl, fRyr)\\n update_external_forces(db, fP, div_P)\\n update_V_diagram(db, V_diag)\\n update_M_diagram(db, M_diag)\\n update_internal_forces(db, fN, fV, arr_head, s_M)\\n update_div_forces(db, div_f)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_NVM_section(db, section_N, section_V, section_M_head, s_section_M, label_N_section, label_V_section, label_M_section)\\n\\n // apply changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function parabola(x, a1, a2, a3) {\\n return Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a2 x[i] + a1);\\n }\\n \\n \\n function arrow_alpha(straight_arrow, alpha=1) {\\n straight_arrow.end.line_alpha = alpha\\n straight_arrow.end.fill_alpha = alpha\\n straight_arrow.line_alpha = alpha\\n }\\n \\n \\n function update_arrow(straight_arrow, intensity, x_start=0, x_end=0, y_start=0, y_end=0, AHF=7) {\\n straight_arrow.end.size = arrow_growth(intensity)AHF\\n straight_arrow.x_start = x_start\\n straight_arrow.x_end = x_end\\n straight_arrow.y_start = y_start\\n straight_arrow.y_end = y_end\\n straight_arrow.line_width = arrow_growth(intensity)\\n }\\n \\n \\n function compute_V(x, q, L) {\\n return qx-qL/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return qx/2(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return qL/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return qL/2\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_V_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const V_discr = Array.from({length: discr}, (_, i) => compute_V(x[i], q, L))\\n update_NVM_diagram(glyph, V_discr)\\n }\\n \\n \\n function update_M_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const q = data['q'][0]\\n const x = linspace(0, L, 100)\\n const M_discr = Array.from({length: discr}, (_, i) => compute_M(x[i], q, L))\\n update_NVM_diagram(glyph, M_discr)\\n }\\n \\n \\n function update_reactions(data, glyph_Rx, glyph_Ry_l, glyph_Ry_r, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n const Ry_l = data['Ry_l'][0]\\n const Ry_r = data['Ry_r'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_Rx) // Rx\\n arrow_alpha(glyph_Ry_l) // Ry left\\n arrow_alpha(glyph_Ry_r) // Ry right\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_Rx, 1) // Rx\\n arrow_alpha(glyph_Ry_l, 1) // Ry left\\n arrow_alpha(glyph_Ry_r, alpha) // Ry right\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_Rx, alpha) //Rx\\n arrow_alpha(glyph_Ry_l, alpha) //Ry left\\n arrow_alpha(glyph_Ry_r, 1) // Ry right\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n update_arrow(glyph_Rx, -P, -P, 0, 0, 0) // Rx\\n update_arrow(glyph_Ry_r, Ry_r, L, L, -Ry_r, 0) // Ry right\\n update_arrow(glyph_Ry_l, Ry_l, 0, 0, -Ry_l, 0) // Ry left\\n }\\n \\n \\n function update_external_forces(data, glyph_P, div_P, alpha=0.3) {\\n const P = data['P'][0]\\n const L = data['L'][0]data['SCALE'][0]\\n \\n // update visibility\\n switch(data['state'][0]) {\\n case 'IDLE':\\n arrow_alpha(glyph_P) // P\\n break\\n case 'R_SEC':\\n arrow_alpha(glyph_P, alpha) // P\\n break\\n case 'L_SEC':\\n arrow_alpha(glyph_P, 1) //P\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n \\n // update size\\n if (P==0) {\\n div_P.text = \\\"Axial force P=0 kN (removed)\\\"\\n update_arrow(glyph_P) // P\\n } else {\\n div_P.text = \\\"Axial force P=\\\"+P+\\\" kN (applied)\\\"\\n update_arrow(glyph_P, P, L+P, L, 0, 0) // P\\n }\\n }\\n \\n \\n function update_u_load(data, source_q, OFFSET_Q=4) {\\n const q = data['q'][0]\\n source_q.data['y'][1] = OFFSET_Q+q\\n source_q.data['y'][2] = OFFSET_Q+q\\n source_q.change.emit()\\n }\\n \\n \\n function update_internal_forces(data, glyph_N, glyph_V, glyph_M_head, source_M, lambda=0.25, offset_N=1.5, offset_V=1) {\\n const pos = data['x'][0]\\n const SCALE = data['SCALE'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n switch(data['state'][0]) {\\n case 'IDLE':\\n // internal forces\\n update_arrow(glyph_N)\\n update_arrow(glyph_V)\\n update_curvedArrow(0, 0, 0, 0, 0, source_M, glyph_M_head)\\n break;\\n case 'R_SEC':\\n // internal forces\\n update_arrow(glyph_N, -N, posSCALE-N+offset_N, posSCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, posSCALE+offset_V, posSCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, posSCALE+N-offset_N, posSCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, posSCALE-offset_V, posSCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/20.8\\n var a = b+lambdac\\n update_curvedArrow(a, b, c, posSCALE, 0, source_M, glyph_M_head)\\n break;\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n }\\n \\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_centroid_y(h) {\\n return h/2\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_div_forces(data, div) {\\n switch(data['state'][0]) {\\n case 'IDLE':\\n var str_sec = \\\"No cross section analysed.\\\"\\n break\\n case 'R_SEC':\\n case 'L_SEC':\\n var str_sec = \\\"Cross section at \\\"+Math.round(data['x'][0]10)/10+\\\" m.\\\"\\n break\\n default:\\n console.error(\\\"State \\\"+data['state'][0]+\\\" in state machine not implemented\\\")\\n }\\n const P = data['P'][0]\\n const Rx = data['Rx'][0]\\n const Ry_l = Math.round(data['Ry_l'][0]10)/10\\n const Ry_r = Math.round(data['Ry_r'][0]10)/10\\n const N = Math.abs(data['N'][0])\\n const V = Math.round(Math.abs(data['V'][0])10)/10\\n const M = Math.round(data['M'][0]10)/10\\n \\n div.text = `\\n <p style='font-size:14px'><b>Forces and Moments:</b></p>\\n P = `+P+` kN<br>\\n Rx = `+Rx+` kN<br>\\n Ry (left) = `+Ry_r+` kN<br>\\n Ry (right) = `+Ry_l+` kN<br>\\n `+str_sec+`<br>\\n N = `+N+` kN<br>\\n V = `+V+` kN<br>\\n M = `+M+` kNm\\n \\n ` \\n }\\n \\n \\n function update_NVM_section(data, glyph_N, glyph_V, glyph_M_head, source_M, label_N_section, label_V_section, label_M_section, lambda=0.25, offset_N=1.5, offset_V=2) {\\n const x = 0\\n const y = 0\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const M = data['M'][0]\\n \\n update_arrow(glyph_N, -N, x-N+offset_N, x+offset_N, y, y)\\n update_arrow(glyph_V, -V, x+offset_V, x+offset_V, y-V/2, y+V/2)\\n var b = 6\\n var c = -M/20.8\\n var a = b-lambdac\\n update_curvedArrow(a, b, c, x, y, source_M, glyph_M_head)\\n \\n if (N==0) {\\n label_N_section.glyph.text=''\\n } else {\\n label_N_section.glyph.text='N'\\n }\\n \\n if (V==0) {\\n label_V_section.glyph.text=''\\n } else {\\n label_V_section.glyph.text='V'\\n }\\n \\n if (M==0) {\\n label_M_section.glyph.text=''\\n } else {\\n label_M_section.glyph.text='M'\\n }\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \"},\"id\":\"2066\",\"type\":\"CustomJS\"},{\"attributes\":{\"tools\":[{\"id\":\"1312\"},{\"id\":\"1313\"},{\"id\":\"1314\"},{\"id\":\"1315\"},{\"id\":\"1316\"},{\"id\":\"1317\"},{\"id\":\"1319\"}]},\"id\":\"1320\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"2297\",\"type\":\"Selection\"},{\"attributes\":{\"args\":{\"T_diag\":{\"id\":\"1938\"},\"T_stress_diag\":{\"id\":\"2041\"},\"div_T\":{\"id\":\"1899\"},\"label_T_section\":{\"id\":\"2035\"},\"neutral_axis\":{\"id\":\"1724\"},\"section_T_head\":{\"id\":\"2029\"},\"section_T_line\":{\"id\":\"2023\"},\"section_T_source\":{\"id\":\"2018\"},\"section_torsion_head\":{\"id\":\"1997\"},\"section_torsion_source\":{\"id\":\"1986\"},\"sigma_stress_diag\":{\"id\":\"1712\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve var from the object that uses callback\\n var f = cb_obj.active // checkbox Mt\\n if (f.length==0) f = [1]\\n const db = source.data\\n const L = db['L'][0]\\n const x = db['x'][0]\\n\\n // apply the changes\\n db['Mt'][0] = 100(1-f)\\n db['T'][0] = compute_T(x, db['Mt'][0], L)\\n\\n // update\\n update_torsional_stress(db, T_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n update_T_diagram(db, T_diag)\\n update_T_section(db, section_torsion_head, section_torsion_source, section_T_line, section_T_head, section_T_source, div_T, label_T_section)\\n\\n // emit the changes\\n source.change.emit()\\n\\n // declare functions\\n \\n function update_curvedArrow(a, b, c, pos_x, pos_y, source, arr_head, discr=10, AHF=6) {\\n const data_M = source.data\\n if (c==0) {\\n var a1 = 0\\n var a3 = 0\\n } else {\\n var a1 = b\\n var a3 = (a-b)/c2\\n }\\n const step = 2c / (discr-1);\\n const x = Array.from({length: discr}, (_, i) => -c + step * i);\\n const y = Array.from({length: x.length}, (_, i) => a3 * x[i]*2 + a1)\\n var theta = -Math.atan(2/c(a-b))\\n if (c<0) {\\n theta = theta+Math.PI\\n }\\n data_M['x'] = y.map(y => y+pos_x)\\n data_M['y'] = x.map(x => x+pos_y)\\n \\n arr_head.glyph.size = arrow_growth(2c)AHF\\n arr_head.glyph.angle = theta\\n arr_head.glyph.x = y[y.length-1]+pos_x\\n arr_head.glyph.y = x[x.length-1]+pos_y\\n source.change.emit()\\n }\\n \\n \\n function update_doubleArrow(x_start, x_end, y_start, y_end, source, arr_heads, AHF=6, pixel2unit=10) {\\n // compute the angle of the line\\n const delta_x = x_end-x_start\\n const delta_y = y_end-y_start\\n if (delta_x==0) {\\n if (delta_y > 0) {\\n var theta = Math.PI/2\\n } else {\\n var theta = Math.PI3/2\\n }\\n } else if (delta_x > 0) {\\n var theta = Math.atan(delta_y/delta_x)\\n } else {\\n var theta = Math.atan(delta_y/delta_x)+Math.PI\\n }\\n \\n // head adjust\\n const length_arr = Math.sqrt(delta_x2 + delta_y2)\\n const size_head = arrow_growth(length_arr)AHF\\n const head_x = size_head/pixel2unitMath.cos(theta)\\n const head_y = size_head/pixel2unitMath.sin(theta)\\n \\n // update line\\n const data_line = source.data\\n data_line['x'] = [x_start, x_end]\\n data_line['y'] = [y_start, y_end]\\n source.change.emit()\\n \\n // heads\\n arr_heads.glyph.size = size_head\\n arr_heads.glyph.angle = theta+Math.PI/6\\n //arr_heads.glyph.x = [x_end-head_x/2, x_end-head_x/23]\\n //arr_heads.glyph.y = [y_end-head_y/2, y_end-head_y/23]\\n const source_h = arr_heads.data_source\\n source_h.data['x'] = [x_end-head_x/2, x_end-head_x/23]\\n source_h.data['y'] = [y_end-head_y/2, y_end-head_y/23]\\n source_h.change.emit()\\n }\\n \\n \\n function arrow_growth(variable) {\\n return Math.log(Math.abs(variable)+1)\\n }\\n \\n \\n function update_T_section(data, head_T_curved, source_T_curved, line_T, head_T, source_T, div_T, label_T_section, offset_T=4, pixel2unit=10, scale_T=10) {\\n const Mt = data['Mt'][0]\\n const T = data['T'][0]\\n \\n if (T > 0) {\\n update_doubleArrow(offset_T, offset_T+T/scale_T, 0, 0, source_T, head_T)\\n } else {\\n update_doubleArrow(offset_T-T/scale_T, offset_T, 0, 0, source_T, head_T)\\n }\\n \\n // update visibility\\n if (Mt==0) {\\n div_T.text = \\\"Torsion M<sub>t</sub>=0 kNm (removed)\\\"\\n line_T.glyph.line_alpha = 0 // T\\n head_T.glyph.line_alpha = 0\\n head_T.glyph.fill_alpha = 0\\n // T in cross-section\\n update_curvedArrow(0, 0, 0, 0, 0, source_T_curved, head_T_curved)\\n } else {\\n div_T.text = \\\"Torsion M<sub>t</sub>=\\\"+Mt+\\\" kNm (applied)\\\"\\n line_T.glyph.line_alpha = 1 // T\\n head_T.glyph.line_alpha = 1\\n head_T.glyph.fill_alpha = 1\\n // T in cross-section\\n update_curvedArrow(0, T4/scale_T, Math.abs(T3/scale_T), 0, 0, source_T_curved, head_T_curved)\\n }\\n \\n if (T==0) {\\n label_T_section.glyph.text=''\\n } else {\\n label_T_section.glyph.text='T'\\n }\\n }\\n \\n \\n function compute_T(x, Mt, L) {\\n if (x<L/2) {\\n return Mt/2\\n } else {\\n return -Mt/2\\n }\\n }\\n \\n \\n function update_T_diagram(data, glyph, discr=100) {\\n const L = data['L'][0]\\n const Mt = data['Mt'][0]\\n const x = linspace(0, L, 100)\\n const T_discr = Array.from({length: discr}, (_, i) => compute_T(x[i], Mt, L))\\n update_NVM_diagram(glyph, T_discr)\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function update_NVM_diagram(diagram, y) {\\n const y_ = [...y]\\n const source = diagram.data_source\\n y_.unshift(0)\\n y_.push(0)\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))1000\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_torsion, y_discr)\\n }\\n \\n \"},\"id\":\"2067\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"2194\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2229\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1837\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"callback\":null,\"tooltips\":[[\"Position\",\"@x m\"],[\"Bending moment\",\"@y kNm\"]]},\"id\":\"1351\",\"type\":\"HoverTool\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"1676\"},\"N_stress_diag\":{\"id\":\"1658\"},\"T_stress_diag\":{\"id\":\"2041\"},\"V_stress_diag\":{\"id\":\"1694\"},\"axial_strain_diag\":{\"id\":\"1748\"},\"bending_strain_diag\":{\"id\":\"1768\"},\"centroid\":{\"id\":\"1688\"},\"div\":{\"id\":\"1107\"},\"neutral_axis\":{\"id\":\"1724\"},\"section\":{\"id\":\"1105\"},\"sigma_stress_diag\":{\"id\":\"1712\"},\"source\":{\"id\":\"1007\"},\"tau_stress_diag\":{\"id\":\"1730\"}},\"code\":\"\\n // retrieve data used\\n const db = source.data\\n const t = cb_obj.value // value of the slider\\n const b = db['b'][0]\\n const h = db['h'][0]\\n const A = compute_area(b, h, t)\\n const Iy = compute_inertia_y(b, h, t)\\n const yG = db['yG'][0]\\n const N = db['N'][0]\\n const M = db['M'][0]\\n\\n // apply the changes\\n db['t'][0] = t\\n db['A'][0] = A\\n db['Iy'][0] = Iy\\n db['Iz'][0] = compute_inertia_z(b, h, t)\\n db['y_n_axis'][0] = compute_neutral_axis(N, A, Iy, M, yG)\\n\\n // update\\n update_div_geo(db, div)\\n update_section(db, section)\\n update_axial_stress_strain(db, N_stress_diag, axial_strain_diag)\\n update_bending_stress_strain(db, M_stress_diag, bending_strain_diag, centroid)\\n update_shear_stress(db, V_stress_diag)\\n update_torsional_stress(db, T_stress_diag)\\n update_total_stress(db, sigma_stress_diag, tau_stress_diag, neutral_axis)\\n\\n // emit the changes\\n source.change.emit()\\n\\n \\n function update_div_geo(data, div) {\\n // compute the parameters and dimensions\\n const L = Math.round(data['L'][0]10)/10\\n const b = Math.round(data['b'][0])\\n const h = Math.round(data['h'][0])\\n const t = Math.round(data['t'][0])\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const Iz = data['Iz'][0]\\n // change the div text\\n div.text = `\\n <p style='font-size:14px'><b>Geometrical and mechanical parameters:</b></p>\\n h = `+h+` mm<br>\\n b = `+b+` mm<br>\\n t = `+t+` mm<br>\\n L = `+L+` m<br>\\n A = `+A.toExponential(2)+` mm<sup>2</sup><br>\\n Iy = `+Iy.toExponential(2)+` mm<sup>4</sup><br>\\n Iz = `+Iz.toExponential(2)+` mm<sup>4</sup>` \\n }\\n \\n \\n function update_section(data, glyph_section) {\\n // change the plot of the section\\n const src = glyph_section.data_source\\n const t = data['t'][0]\\n const b = data['b'][0]\\n const h = data['h'][0]\\n src.data.xs = [[[ [b/2, b/2, -b/2, -b/2], [b/2-t, b/2-t, -b/2+t, -b/2+t] ]]]\\n src.data.ys = [[[ [h/2, -h/2, -h/2, h/2], [h/2-t, -h/2+t, -h/2+t, h/2-t] ]]]\\n src.change.emit()\\n }\\n \\n \\n function compute_area(b, h, t) {\\n return bh - (b-t2)(h-2t)\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return bh*3/12 - (b-2t)(h-2t)*3/12\\n }\\n \\n \\n function compute_inertia_z(b, h, t) {\\n return hb*3/12 - (h-2t)(b-2t)*3/12\\n }\\n \\n \\n function compute_neutral_axis(N, A, Iy, M, yG) {\\n if (M == 0) {\\n return yG\\n }\\n else {\\n return yG - N/AIy/M/1000\\n }\\n }\\n \\n \\n function update_axial_stress_strain(data, glyph_stress, glyph_strain, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const A = data['A'][0]\\n const E = data['E'][0]\\n const N = data['N'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_axial = new Array(discr)\\n let strain_axial = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n strain_axial[i] = compute_epsilon_axial(sigma_axial[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_axial, y_discr)\\n update_strain_diagram(glyph_strain, strain_axial, y_discr)\\n }\\n \\n \\n function update_bending_stress_strain(data, glyph_stress, glyph_strain, glyph_centroid, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const E = data['E'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const M = data['M'][0]\\n const y_discr = linspace(0, h, discr)\\n let sigma_bending = new Array(discr)\\n let strain_bending = new Array(discr)\\n const src_centroid = glyph_centroid.data_source\\n \\n // apply the changes\\n src_centroid.data.y = [yG, yG]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n strain_bending[i] = compute_epsilon_bending(sigma_bending[i], E)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, sigma_bending, y_discr)\\n update_strain_diagram(glyph_strain, strain_bending, y_discr)\\n src_centroid.change.emit()\\n }\\n \\n \\n function update_shear_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const yG = data['yG'][0]\\n const Iy = data['Iy'][0]\\n const V = data['V'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_shear = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_shear, y_discr)\\n }\\n \\n \\n function update_total_stress(data, glyph_sigma, glyph_tau, glyph_neutral_axis, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const M = data['M'][0]\\n const N = data['N'][0]\\n const V = data['V'][0]\\n const A = data['A'][0]\\n const Iy = data['Iy'][0]\\n const yG = data['yG'][0]\\n const y_discr = linspace(0, h, discr)\\n const y_n_axis = compute_neutral_axis(N, A, Iy, M, yG)\\n let sigma_bending = new Array(discr)\\n let tau_shear = new Array(discr)\\n let sigma_axial = new Array(discr)\\n let total_sigma = new Array(discr)\\n let total_tau = new Array(discr)\\n const src_n_axis = glyph_neutral_axis.data_source\\n \\n const t = data['t'][0]\\n const T = data['T'][0]\\n let tau_torsion = new Array(discr)\\n \\n \\n // apply the changes\\n db['y_n_axis'][0] = y_n_axis\\n src_n_axis.data.y = [y_n_axis, y_n_axis]\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n // sigma\\n sigma_axial[i] = compute_sigma_axial(N, A)\\n sigma_bending[i] = compute_sigma_bending(y_discr[i], M, Iy, yG)\\n total_sigma[i] = compute_total_sigma(sigma_axial[i], sigma_bending[i])\\n // tau\\n var S = compute_first_moment_of_area_implicit(y_discr[i], data)\\n \\n if (Math.abs(y_discr[i]-yG) >= (h-2data['t'][0])/2) {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, b)\\n } else {\\n tau_shear[i] = compute_tau_shear(V, S, Iy, 2data['t'][0])\\n }\\n \\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n total_tau[i] = compute_total_tau(tau_shear[i], tau_torsion[i])\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_sigma, total_sigma, y_discr)\\n update_stress_diagram(glyph_tau, total_tau, y_discr)\\n src_n_axis.change.emit()\\n }\\n \\n \\n function linspace(start, stop, discr = 100) {\\n const step = (stop - start) / (discr-1);\\n return Array.from({length: discr}, (_, i) => start + step * i);\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N1000/A\\n }\\n \\n \\n function update_stress_diagram(diagram, x, y) {\\n const x_ = [...x]\\n const y_ = [...y]\\n const source = diagram.data_source\\n x_.unshift(0)\\n x_.push(0)\\n y_.unshift(y[0])\\n y_.push(y[y.length-1])\\n source.data.x = x_\\n source.data.y = y_\\n source.change.emit()\\n }\\n \\n \\n function update_strain_diagram(diagram, x, y) {\\n const source = diagram.data_source\\n source.data.x = x\\n source.data.y = y\\n source.change.emit()\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M1e6/Iy(y-yG)\\n }\\n \\n \\n function compute_total_sigma(sigma_axial, sigma_bending) {\\n return sigma_bending+sigma_axial\\n }\\n \\n \\n function compute_total_tau(tau_shear, tau_torsion=0) {\\n return tau_shear + tau_torsion\\n }\\n \\n \\n function compute_first_moment_of_area(y_, b, h, t, yG) {\\n const y = y_-yG\\n const h_ = h-2t\\n if (Math.abs(y) >= h_/2) {\\n return b/2(h2/4-y2)\\n } else {\\n return b/2(h-t)t + t(h_2/4-y2)\\n }\\n }\\n \\n \\n function compute_first_moment_of_area_implicit(y_, data) {\\n return compute_first_moment_of_area(y_, data['b'][0], data['h'][0], data['t'][0], data['yG'][0])\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V1000S/(Iyb_or_t)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2t(b-t)(h-t))*1000\\n }\\n \\n \\n function update_torsional_stress(data, glyph_stress, discr=50) { \\n // define parameters\\n const h = data['h'][0]\\n const b = data['b'][0]\\n const t = data['t'][0]\\n const T = data['T'][0]\\n const y_discr = linspace(0, h, discr)\\n let tau_torsion = new Array(discr)\\n \\n // compute the arrays\\n for (var i = 0; i < discr; i++) {\\n tau_torsion[i] = compute_tau_torsion(T, b, h, t)\\n }\\n \\n // change the diagrams\\n update_stress_diagram(glyph_stress, tau_torsion, y_discr)\\n }\\n \\n 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Application\",\"version\":\"2.4.2\"}};\n",
	- " const render_items = [{\"docid\":\"59ecfd77-c705-4c8c-9c88-28bd01828977\",\"root_ids\":[\"2087\"],\"roots\":{\"2087\":\"272a9d88-57a5-466e-b9b2-cd6e1a1520cb\"}}];\n",
	- " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
	- "\n",
	- " }\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " embed_document(root);\n",
	- " } else {\n",
	- " let attempts = 0;\n",
	- " const timer = setInterval(function(root) {\n",
	- " if (root.Bokeh !== undefined) {\n",
	- " clearInterval(timer);\n",
	- " embed_document(root);\n",
	- " } else {\n",
	- " attempts++;\n",
	- " if (attempts > 100) {\n",
	- " clearInterval(timer);\n",
	- " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
	- " }\n",
	- " }\n",
	- " }, 10, root)\n",
	- " }\n",
	- "})(window);"
	- ],
	- "application/vnd.bokehjs_exec.v0+json": ""
	- },
	- "metadata": {
	- "application/vnd.bokehjs_exec.v0+json": {
	- "id": "2087"
	- }
	- },
	- "output_type": "display_data"
	- }
	- ],
	- "source": [
	- "hidden_code_nb_torsion.main_code(L, h, b, t, A, Iy, Iz, yG, y_n_axis, q, P, Mt, E, N, V, M, T, Rx, Ry_l, Ry_r, discr_NVM, x_discr, N_discr, V_discr, M_discr, T_discr)"
	- ]
	- }
	- ],
	- "metadata": {
	- "interpreter": {
	- "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45"
	- },
	- "kernelspec": {
	- "display_name": "Python 3 (ipykernel)",
	- "language": "python",
	- "name": "python3"
	- },
	- "language_info": {
	- "codemirror_mode": {
	- "name": "ipython",
	- "version": 3
	- },
	- "file_extension": ".py",
	- "mimetype": "text/x-python",
	- "name": "python",
	- "nbconvert_exporter": "python",
	- "pygments_lexer": "ipython3",
	- "version": "3.8.10"
	- }
	- },
	- "nbformat": 4,
	- "nbformat_minor": 4
	-}

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