diff --git a/HiddenCode/hidden_code_nb_actions.py b/HiddenCode/hidden_code_nb_actions.py new file mode 100644 index 0000000..d85c148 --- /dev/null +++ b/HiddenCode/hidden_code_nb_actions.py @@ -0,0 +1,546 @@ +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.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, L*SCALE, L*SCALE], + y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q], + x_fade=[0, 0, L*SCALE, L*SCALE] + ) + + 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_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis + fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2) + models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis + fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=["z"], text_color='gray', text_align='right', text_baseline='middle') + + + ######################################################## + # Define the new figures, widgets and renderers + ######################################################## + # 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, L*SCALE+P, L*SCALE, 0, 0, 'green') + # Reactions (scheme) + scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -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)) + + + + ######################################################## + # 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()} + {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) + 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_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()} + {sb.implement_compute_NJS()} + {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) + 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_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()} + {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_beam, + 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_scheme, + Spacer(height=padding_layout), + div_forces)) + )], + ]) + + show(layout1) \ No newline at end of file diff --git a/HiddenCode/hidden_code_nb_buckling.py b/HiddenCode/hidden_code_nb_buckling.py new file mode 100644 index 0000000..591444f --- /dev/null +++ b/HiddenCode/hidden_code_nb_buckling.py @@ -0,0 +1,508 @@ +import math +import numpy as np +from bokeh.layouts import layout, column, row +from bokeh.models import Div, CustomJS, Slider, Spacer +from bokeh.models.widgets import RadioButtonGroup +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 +from cienpy import buckling + +output_notebook() + + +def main_code(L, h, b, A, Iy, Iz, P, E, N, Rx, discr_NVM, x_discr, n_bracey, n_bracez, Ncrity, Ncritz): + ######################################################## + # Initialisation + ######################################################## + # constants for the visualisation + SCALE = 10 + MAX_B = 3*b + MAX_H = 3*h + MAX_P = 100*P + MAX_L = 10 + + # store the values in a specific format + data_beam = dict( + x=[0, L], + y=[0, 0] + ) + + 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], + P=[P], + x=[initial_position], + y=[0], + Rx=[Rx], + N=[N], + Ncrity=[Ncrity], + Ncritz=[Ncritz], + n_bracey=[n_bracey], + n_bracez=[n_bracez], + xF=[L*SCALE] + ) + + source_beam = ColumnDataSource(data_beam) + 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 + MAX_Q = 5 + OFFSET_Q = 4 + 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(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_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis + fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2) + models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis + fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=["z"], text_color='gray', text_align='right', text_baseline='middle') + + + # 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") + + + ######################################################## + # Define the new figures, widgets and renderers + ######################################################## + # change title in beam (y direction) + fig_beam.title.text = "Simple supported beam: x-y plane" + + + # beam in z direction + fig_beam_z = sb.define_fig_beam(int_x_b, int_y_b, options, + f_h=FIG_H_B, f_b=FIG_B_B) + fig_beam_z.title.text = "Simple supported beam: x-z plane" + (beam_z, support_l_z, support_r_z) = sb.draw_beam(fig_beam_z, source_beam, L, + ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100) + fig_beam_z.x_range = fig_beam.x_range + + + # axial force (beam z direction) + axial_force_z = models.force_vector(fig_beam_z, P, L+P/SCALE, L, 0, 0, 'green') + label_P_force_z = fig_beam_z.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=["P"], text_color="green") + + + # reference system (x-y plane) + axis_arrow_length = 0.8 + axis_arrow_scale = 100 + models.force_vector(fig_beam, axis_arrow_length, -axis_arrow_length-0.1, -0.1, 0, 0, 'gray') + fig_beam.text(x=[-axis_arrow_length], y=[0.1], text=["x axis"], text_color='gray', text_baseline='bottom') + models.force_vector(fig_beam, axis_arrow_length, 0, 0, 0, axis_arrow_length, 'gray') + fig_beam.text(x=[0.1], y=[0.2], text=["y axis"], text_color='gray', text_baseline='bottom') + + + # reference system (x-z plane) + models.force_vector(fig_beam_z, axis_arrow_length, -axis_arrow_length-0.1, -0.1, 0, 0, 'gray') + fig_beam_z.text(x=[-axis_arrow_length], y=[0.1], text=["x axis"], text_color='gray', text_baseline='bottom') + models.force_vector(fig_beam_z, axis_arrow_length, 0, 0, 0, axis_arrow_length, 'gray') + fig_beam_z.text(x=[0.1], y=[0.2], text=["z axis"], text_color='gray', text_baseline='bottom') + + + # slider P + slider_P = Slider( + title="Change the axial force P [kN]", + start=1, + end=MAX_P, + step=1, + value=P + ) + + + # slider L + slider_L = Slider( + title="Change the length of the beam [m]", + start=1, + end=L, + step=0.1, + value=L + ) + + + # bracing options + div_rg_brace_y = Div(text="Number of braces in y direction:") + radiogroup_brace_y = RadioButtonGroup(labels=['No brace', 'One middle brace', 'Two equally spaced braces'], active=n_bracey) + div_rg_brace_z = Div(text="Number of braces in z direction:") + radiogroup_brace_z = RadioButtonGroup(labels=['No brace', 'One middle brace', 'Two equally spaced braces'], active=n_bracez) + + + # figure for buckling + fig_buckling_y = figure(toolbar_location=None, + plot_height=FIG_H_S, + plot_width=FIG_B_S, + title="Beam instability in y direction", + x_axis_label="Position [m]", + x_range = fig_beam.x_range + ) + fig_buckling_y.ygrid.grid_line_alpha = 0 + fig_buckling_y.yaxis.visible = False + fig_buckling_y.line('x', 'y', source=source_beam, line_width=1, color='gray') + mode_shape_y = fig_buckling_y.line(x=[0, L], y=[0, 0], line_width=2, color='black') + + fig_buckling_z = figure(toolbar_location=None, + plot_height=FIG_H_S, + plot_width=FIG_B_S, + title="Beam instability in z direction", + x_axis_label="Position [m]", + x_range = fig_beam.x_range + ) + fig_buckling_z.ygrid.grid_line_alpha = 0 + fig_buckling_z.yaxis.visible = False + fig_buckling_z.line('x', 'y', source=source_beam, line_width=1, color='gray') + mode_shape_z = fig_buckling_z.line(x=[0, L], y=[0, 0], line_width=2, color='black') + + + # show values of forces + div_buckling = Div(width=DIV_B_FORCES, + text=buckling.div_text_buckling(P, Rx, N, "{:.2f}".format(Ncrity), "{:.2f}".format(Ncritz), "No")) + + + # show brace position + point_brace_y = fig_buckling_y.circle(x=[], y=[], size=10, fill_alpha=0.5, fill_color="red", color="red", alpha=0.5) + point_brace_z = fig_buckling_z.circle(x=[], y=[], size=10, fill_alpha=0.5, fill_color="red", color="red", alpha=0.5) + + + + ######################################################## + # Configurethe logics + ######################################################## + args_slider_b_h = dict(source=source, + mode_shape_y=mode_shape_y, + mode_shape_z=mode_shape_z, + div=div_geo, + div_buckling=div_buckling, + section=section) + 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 L = db['L'][0] + const E = db['E'][0] + const n_bracey = db['n_bracey'][0] + const n_bracez = db['n_bracez'][0] + const A = compute_area(b, h) + const Iy = compute_inertia_y(b, h) + const Iz = compute_inertia_z(b, h) + + // apply the changes + db['b'][0] = b + db['A'][0] = A + db['Iy'][0] = Iy + db['Iz'][0] = Iz + db['Ncrity'][0] = compute_N_buckling_y(E, Iy, L, n_bracey) + db['Ncritz'][0] = compute_N_buckling_z(E, Iz, L, n_bracez) + + // update + update_div_geo(db, div) + update_section(db, section) + update_div_buckling(db, div_buckling) + update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z) + + // 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()} + {buckling.implement_update_div_bucklingJS()} + {buckling.implement_compute_N_buckling_yJS()} + {buckling.implement_compute_N_buckling_zJS()} + {buckling.implement_compute_mode_shape_N_bucklingJS()} + {js.implement_linspaceJS()} + {buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)} + """ + update_b = CustomJS(args=args_slider_b_h, code=code_change_b) + + + code_change_h = f""" + // retrieve data used + const db = source.data + const h = cb_obj.value // value of the slider + const b = db['b'][0] + const L = db['L'][0] + const E = db['E'][0] + const n_bracey = db['n_bracey'][0] + const n_bracez = db['n_bracez'][0] + const A = compute_area(b, h) + const Iy = compute_inertia_y(b, h) + const Iz = compute_inertia_z(b, h) + + // apply the changes + db['h'][0] = h + db['A'][0] = A + db['Iy'][0] = Iy + db['Iz'][0] = Iz + db['Ncrity'][0] = compute_N_buckling_y(E, Iy, L, n_bracey) + db['Ncritz'][0] = compute_N_buckling_z(E, Iz, L, n_bracez) + + // update + update_div_geo(db, div) + update_section(db, section) + update_div_buckling(db, div_buckling) + update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z) + + // 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()} + {buckling.implement_update_div_bucklingJS()} + {buckling.implement_compute_N_buckling_yJS()} + {buckling.implement_compute_N_buckling_zJS()} + {buckling.implement_compute_mode_shape_N_bucklingJS()} + {js.implement_linspaceJS()} + {buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)} + """ + update_h = CustomJS(args=args_slider_b_h, code=code_change_h) + + + args_slider_L = dict(source=source, + s_b=source_beam, + support_r_y=support_r, + support_r_z=support_r_z, + axial_force_y=axial_force, + axial_force_z=axial_force_z, + label_P_force_y=label_P_force, + label_P_force_z=label_P_force_z, + point_brace_y=point_brace_y, + point_brace_z=point_brace_z, + mode_shape_y=mode_shape_y, + mode_shape_z=mode_shape_z, + div=div_geo, + div_buckling=div_buckling) + code_change_L = f""" + // retrieve data used + const db = source.data + const data_b = s_b.data + const L = cb_obj.value // value of the slider + const E = db['E'][0] + const Iy = db['Iy'][0] + const Iz = db['Iz'][0] + const n_bracey = db['n_bracey'][0] + const n_bracez = db['n_bracez'][0] + + // apply the changes + data_b['x'][1] = L + db['L'][0] = L + db['Ncrity'][0] = compute_N_buckling_y(E, Iy, L, n_bracey) + db['Ncritz'][0] = compute_N_buckling_z(E, Iz, L, n_bracez) + + // update + update_div_geo(db, div) + update_div_buckling(db, div_buckling) + support_r_y.glyph.x = L + support_r_z.glyph.x = L + axial_force_y.x_start = L+{P/SCALE} + axial_force_y.x_end = L + label_P_force_y.glyph.x = L+{P/SCALE}/2 + axial_force_z.x_start = L+{P/SCALE} + axial_force_z.x_end = L + label_P_force_z.glyph.x = L+{P/SCALE}/2 + update_point_brace(point_brace_y, n_bracey) + update_point_brace(point_brace_z, n_bracez) + update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z) + + // emit the changes + source.change.emit() + s_b.change.emit() + + {beam_section.implement_update_div_geoJS()} + {buckling.implement_update_div_bucklingJS()} + {buckling.implement_compute_N_buckling_yJS()} + {buckling.implement_compute_N_buckling_zJS()} + {buckling.implement_update_point_braceJS()} + {buckling.implement_compute_mode_shape_N_bucklingJS()} + {js.implement_linspaceJS()} + {buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)} + """ + update_L = CustomJS(args=args_slider_L, code=code_change_L) + + + args_slider_P = dict(source=source, + mode_shape_y=mode_shape_y, + mode_shape_z=mode_shape_z, + div_buckling=div_buckling) + code_slider_P = f""" + // retrieve var from the object that uses callback + const db = source.data + const P = cb_obj.value // value of the slider + + // apply the changes + db['P'][0] = P + db['N'][0] = compute_N(P) + db['Rx'][0] = compute_Rx(P) + + // update + update_div_buckling(db, div_buckling) + update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z) + + // emit the changes + source.change.emit() + + // declare functions + {sb.implement_compute_RxJS()} + {sb.implement_compute_NJS()} + {buckling.implement_update_div_bucklingJS()} + {buckling.implement_compute_mode_shape_N_bucklingJS()} + {js.implement_linspaceJS()} + {buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)} + """ + update_P = CustomJS(args=args_slider_P, code=code_slider_P) + + + args_radiogroup_brace_y = dict(source=source, + mode_shape_y=mode_shape_y, + mode_shape_z=mode_shape_z, + div_buckling=div_buckling, + point_brace=point_brace_y) + args_radiogroup_brace_z = dict(source=source, + mode_shape_y=mode_shape_y, + mode_shape_z=mode_shape_z, + div_buckling=div_buckling, + point_brace=point_brace_z) + code_radiogroup_brace = lambda which_axis : f""" + // retrieve data used + const db = source.data + const n_brace = cb_obj.active + const E = db['E'][0] + const L = db['L'][0] + const I = db['I{which_axis}'][0] + + // apply the changes + db['n_brace{which_axis}'][0] = n_brace + db['Ncrit{which_axis}'][0] = compute_N_buckling_{which_axis}(E, I, L, n_brace) + + // update + update_div_buckling(db, div_buckling) + update_point_brace(point_brace, n_brace) + update_mode_shape_N_buckling(db, mode_shape_y, mode_shape_z) + + // emit the changes + source.change.emit() + + {buckling.implement_update_div_bucklingJS()} + {buckling.implement_compute_N_buckling_yJS()} + {buckling.implement_compute_N_buckling_zJS()} + {buckling.implement_update_point_braceJS()} + {buckling.implement_compute_mode_shape_N_bucklingJS()} + {js.implement_linspaceJS()} + {buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)} + """ + update_brace_y = CustomJS(args=args_radiogroup_brace_y, code=code_radiogroup_brace('y')) + update_brace_z = CustomJS(args=args_radiogroup_brace_z, code=code_radiogroup_brace('z')) + + # apply the logics + slider_b.js_on_change('value', update_b) + slider_h.js_on_change('value', update_h) + slider_P.js_on_change('value', update_P) + slider_L.js_on_change('value', update_L) + radiogroup_brace_y.js_on_click(update_brace_y) + radiogroup_brace_z.js_on_click(update_brace_z) + + + ######################################################## + # Build the layout + ######################################################## + padding_layout = 10 + layout1 = layout([ + [column(row(column( + row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout), + slider_b, + slider_h, + slider_P, + slider_L, + row(div_geo, div_buckling), + Spacer(height=padding_layout), + div_rg_brace_y, + radiogroup_brace_y, + div_rg_brace_z, + radiogroup_brace_z))), + column(Spacer(width=padding_layout)), + column(fig_beam, + fig_beam_z, + fig_buckling_y, + fig_buckling_z)) + )], + ]) + + show(layout1) \ No newline at end of file diff --git a/HiddenCode/hidden_code_nb_deflection.py b/HiddenCode/hidden_code_nb_deflection.py new file mode 100644 index 0000000..f9be657 --- /dev/null +++ b/HiddenCode/hidden_code_nb_deflection.py @@ -0,0 +1,1025 @@ +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.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, L*SCALE, L*SCALE], + y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q], + x_fade=[0, 0, L*SCALE, L*SCALE] + ) + + 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*SCALE_DEFL, (MAX_Q+OFFSET_Q)/SCALE*SCALE_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_B*0.8, 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(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_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis + fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2) + models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis + fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], 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*SCALE_DEFL], width=L, height=q/SCALE*SCALE_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, L*SCALE+P, L*SCALE, 0, 0, 'green') + # Reactions (scheme) + scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -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) + V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam) + M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam) + + # 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 + 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) + 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) + 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) + + # 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) + tau_total = tau_V + tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h, + source_section_scheme, scale_x=1) + + # 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) + 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) + + + # 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_N*6], y=[-OFFSET_N*5], 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') + + # 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""" +

+ Ewood = {math.trunc(E_wood/1e3)} GPa; Econcrete = {math.trunc(E_concrete/1e3)} GPa
+ Esteel = {math.trunc(E_steel/1e3)} GPa; Eceramic = {math.trunc(E_ceramic/1e3)} GPa

+ """) + + + ######################################################## + # 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 new file mode 100644 index 0000000..bf32433 --- /dev/null +++ b/HiddenCode/hidden_code_nb_diagrams.py @@ -0,0 +1,599 @@ +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.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, L*SCALE, L*SCALE], + y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q], + x_fade=[0, 0, L*SCALE, L*SCALE] + ) + + 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_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis + fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2) + models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis + fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], 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, L*SCALE+P, L*SCALE, 0, 0, 'green') + # Reactions (scheme) + scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -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) + V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam) + M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam) + + # 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_geo.py b/HiddenCode/hidden_code_nb_geo.py new file mode 100644 index 0000000..ecd1d92 --- /dev/null +++ b/HiddenCode/hidden_code_nb_geo.py @@ -0,0 +1,223 @@ +import math +import numpy as np +from bokeh.layouts import layout, column +from bokeh.models import Div, CustomJS, Slider, Spacer +from bokeh.models.tickers import SingleIntervalTicker +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 + +output_notebook() + + +def main_code(L, h, b, A, Iy, Iz): + ######################################################## + # Initialisation + ######################################################## + # constants for the visualisation + MAX_B = 3*b + MAX_H = 3*h + + # store the values in a specific format + data_beam = dict( + x=[0, L], + y=[0, 0] + ) + + initial_position = L + data = dict( # stores every useful single variable + L=[L], + b=[b], + h=[h], + A=[A], + Iy=[Iy], + Iz=[Iz], + x=[initial_position], + y=[0] + ) + + source_beam = ColumnDataSource(data_beam) + source = ColumnDataSource(data) + + + ######################################################## + # Define figures, widgets and renderers + ######################################################## + FIG_H_B = 200 # height figure beam + FIG_B_B = 700 # width figure beam + FIG_H_SEC = 600 # height figure section + + paddingx = 0.2*L + options = dict( + toolbar_location=None + ) + + fig_beam = figure(**options, + x_axis_label="Position [m]", + plot_height=200, + plot_width=700, + x_range=(0-paddingx, L+paddingx), + y_range=(-1, 1), + title="Simple supported beam" + ) + fig_beam.xgrid.grid_line_alpha = 0 + fig_beam.ygrid.grid_line_alpha = 0 + fig_beam.yaxis.visible = False + + fig_section = figure(**options, + x_axis_label="Width b [mm]", + y_axis_label="Height h [mm]", + plot_height=int(MAX_H*0.9), + plot_width=int(MAX_B), + match_aspect=True, + title="Cross-section of the beam" + ) + fig_section.rect([0], [0], width=MAX_B, height=MAX_H, alpha=0, fill_alpha=0) # transparent rect + fig_section.axis.ticker = SingleIntervalTicker(interval=50, num_minor_ticks=5) + + + # beam + beam = fig_beam.line('x', 'y', source=source_beam, line_width=6, color='black') + b_supp = 0.3 + supp_opt = dict( + fill_color='white', + line_color='black' + ) + support_l = fig_beam.patch([0, b_supp/2, -b_supp/2], + [0, -b_supp/2*math.sqrt(3), -b_supp/2*math.sqrt(3)], + **supp_opt) + support_r = fig_beam.circle([L], [-b_supp/2], radius=b_supp/2, **supp_opt) + + + # section + section = fig_section.rect([0], [0], width=b, height=h, fill_color='white', + color='black', line_width=3, hatch_pattern='/', hatch_color='black') + + + # show mechanical parameters + div_text = lambda h, b, L, A, Iy, Iz : f"""

Geometrical and mechanical parameters

+ h = {round(h)} mm
+ b = {round(b)} mm
+ L = {round(L)} m
+ A = {"{:.2e}".format(A)} mm2
+ Iy = {"{:.2e}".format(Iy)} mm4
+ Iz = {"{:.2e}".format(Iz)} mm4""" + + div = Div( + text=div_text(h, b, L, A, Iy, Iz), + width=300, + height=300 + ) + + + # 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 + ) + slider_L = Slider( + title="Change the length L [m]", + start=1, + end=L+1, + step=0.1, + value=L + ) + + # reference system + axis_arrow_length = 0.8 + axis_arrow_scale = 100 + x_axis_arrow = models.force_vector(fig_beam, axis_arrow_length, L, L+axis_arrow_length, 0, 0, 'gray') + x_axis_label = fig_beam.text(x=[L+axis_arrow_length/2], y=[0.1], text=["x axis"], text_color='gray', text_baseline='bottom') + models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis + fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=["y axis"], text_color='gray', text_baseline='middle', angle=math.pi/2) + models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis + fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=["z axis"], text_color='gray', text_align='right', text_baseline='middle') + + + ######################################################## + # Configurethe logics + ######################################################## + code_slider = lambda var, L_code, b_code, h_code, x_axis_code="" : f""" + // retrieve data used + const data_b = s_b.data + const data_s = s_s.data + // retrieve the var from the object that uses callback + const f = cb_obj.value // value of the slider + // compute the parameters and dimensions + const L = Math.round({L_code}*10)/10 + const b = Math.round({b_code}) + const h = Math.round({h_code}) + const A = b*h + const Iy = Math.round(Math.pow(h, 3)*b/12) + const Iz = Math.round(Math.pow(b, 3)*h/12) + div.text = "

Geometrical and mechanical parameters:

h = "+h+ + " mm
b = "+b+ + " mm
L = "+L+ + " m
A = "+A.toExponential()+ + " mm2
Iy = "+Iy.toExponential()+ + " mm4
Iz = "+Iz.toExponential()+ + " mm4" + // change the plot of the section + section.glyph.width = b + section.glyph.height = h + // change the plot of the beam + data_b['x'][1] = L + support_r.glyph.x = L + {x_axis_code} + // apply the changes + data_s['{var}'] = f + data_s['A'] = A + data_s['Iy'] = Iy + data_s['Iz'] = Iz + s_s.change.emit() + s_b.change.emit() + """ + + x_axis_code = f""" + // change the position of the x axis arrow and text + x_axis_arrow.x_start = L + x_axis_arrow.x_end = L+{axis_arrow_length} + x_axis_label.glyph.x = L+{axis_arrow_length}/2 + """ + + # logic for slider_L + update_L = CustomJS(args=dict(s_b=source_beam, s_s=source, div=div, section=section, support_r=support_r, + x_axis_arrow=x_axis_arrow, x_axis_label=x_axis_label), + code=code_slider("L", "f", "data_s['b']", "data_s['h']", x_axis_code)) + + slider_L.js_on_change('value', update_L) + + # logic for slider_b + update_b = CustomJS(args=dict(s_b=source_beam, s_s=source, div=div, section=section, support_r=support_r), + code=code_slider("b", "data_s['L']", "f", "data_s['h']")) + + slider_b.js_on_change('value', update_b) + + # logic for slider_h + update_h = CustomJS(args=dict(s_b=source_beam, s_s=source, div=div, section=section, support_r=support_r), + code=code_slider("h", "data_s['L']", "data_s['b']", "f")) + + slider_h.js_on_change('value', update_h) + + + ######################################################## + # Build the layout + ######################################################## + layout1 = layout([ + [fig_beam], + [fig_section, Spacer(width=20), column([Spacer(height=50), slider_L, slider_b, slider_h, Spacer(height=50), div])] + ]) + + show(layout1) \ No newline at end of file diff --git a/HiddenCode/hidden_code_nb_mohr.py b/HiddenCode/hidden_code_nb_mohr.py new file mode 100644 index 0000000..b1f5396 --- /dev/null +++ b/HiddenCode/hidden_code_nb_mohr.py @@ -0,0 +1,1700 @@ +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.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, L*SCALE, L*SCALE], + y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q], + x_fade=[0, 0, L*SCALE, L*SCALE] + ) + + 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_H*0.2, MAX_H*1.4) + 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_B*0.8, MAX_H*0.8, 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_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis + fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2) + models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis + fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], 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, L*SCALE+P, L*SCALE, 0, 0, 'green') + # Reactions (scheme) + scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -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) + V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam) + M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam) + + # 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 + 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) + 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) + 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) + + # 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) + tau_total = tau_V + tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h, + source_section_scheme, scale_x=1) + + # 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) + 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) + + + # 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_N*6], y=[-OFFSET_N*5], 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_STATE*0.4], [MAX_DIM_STRESS_STATE*0.4], + 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") + + + ######################################################## + # 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 new file mode 100644 index 0000000..8cf8c6f --- /dev/null +++ b/HiddenCode/hidden_code_nb_plastic.py @@ -0,0 +1,1183 @@ +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.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, L*SCALE, L*SCALE], + y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q], + x_fade=[0, 0, L*SCALE, L*SCALE] + ) + + 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_B*0.8, 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(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_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis + fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2) + models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis + fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], 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, L*SCALE+P, L*SCALE, 0, 0, 'green') + # Reactions (scheme) + scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -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) + V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam) + M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam) + + # 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 + 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) + 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) + 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) + + # 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) + + # 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) + 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) + + + # 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_N*6], y=[-OFFSET_N*5], 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""" +

+ Ewood = {math.trunc(E_wood/1e3)} GPa; Econcrete = {math.trunc(E_concrete/1e3)} GPa
+ Esteel = {math.trunc(E_steel/1e3)} GPa; Eceramic = {math.trunc(E_ceramic/1e3)} GPa

+ """) + + + # 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""" +

+ fy,wood = {math.trunc(fy_wood)} MPa; fy,concrete = {math.trunc(fy_concrete)} MPa
+ fy,steel = {math.trunc(fy_steel)} MPa; fy,glass = {math.trunc(fy_glass)} MPa

+ """) + + + # 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 + (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) + # (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) + + + ######################################################## + # 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 new file mode 100644 index 0000000..8f4675f --- /dev/null +++ b/HiddenCode/hidden_code_nb_stress.py @@ -0,0 +1,923 @@ +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.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, L*SCALE, L*SCALE], + y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q], + x_fade=[0, 0, L*SCALE, L*SCALE] + ) + + 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_B*0.8, 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(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_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis + fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2) + models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis + fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], 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, L*SCALE+P, L*SCALE, 0, 0, 'green') + # Reactions (scheme) + scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -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) + V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam) + M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam) + + # 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 + 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) + 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) + 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) + + # 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) + tau_total = tau_V + tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h, + source_section_scheme, scale_x=1) + + # 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) + 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) + + + # 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_N*6], y=[-OFFSET_N*5], 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 new file mode 100644 index 0000000..b266e65 --- /dev/null +++ b/HiddenCode/hidden_code_nb_torsion.py @@ -0,0 +1,1194 @@ +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.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, L*SCALE, L*SCALE], + y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q], + x_fade=[0, 0, L*SCALE, L*SCALE] + ) + + 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_B*0.8, 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, 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_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis + fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=["y"], text_color='gray', text_baseline='middle', angle=math.pi/2) + models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis + fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], 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, L*SCALE+P, L*SCALE, 0, 0, 'green') + # Reactions (scheme) + scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -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) + V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam) + M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam) + + + # 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 + 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) + 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) + 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) + + + # 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) + tau_total = tau_V + tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h, + source_section_scheme, scale_x=1) + + # 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) + 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) + + + # 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_N*6], y=[-OFFSET_N*5], text=[""], text_color="red", text_baseline='top') + label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[OFFSET_N*4], 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) + + + # 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, T*4/SCALE_T, abs(T*3/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_N*4-T/SCALE_T, OFFSET_N*4, 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) + + # 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_actions.ipynb b/Simple Beam DEMOs/sb_actions.ipynb index f56be60..7a96717 100644 --- a/Simple Beam DEMOs/sb_actions.ipynb +++ b/Simple Beam DEMOs/sb_actions.ipynb @@ -1,697 +1,477 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple beam - Actions\n", "In this second notebook, different actions are applied on the simple supported beam. The internal forces and moments can be visuallized and the N V M graphs are presented. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
\n", + " \n", + " Loading BokehJS ...\n", + "
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*/\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", + " \"
\\n\"+\n", + " \"

\\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", + " \"

\\n\"+\n", + " \"\\n\"+\n", + " \"\\n\"+\n", + " \"from bokeh.resources import INLINE\\n\"+\n", + " \"output_notebook(resources=INLINE)\\n\"+\n", + " \"\\n\"+\n", + " \"
\"}};\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 \"
\\n\"+\n \"

\\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 \"

\\n\"+\n \"\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\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 numpy as np\n", + "import sys\n", + "sys.path.append('../HiddenCode')\n", + "import hidden_code_nb_actions\n", "import math\n", - "from bokeh.layouts import layout, column, row\n", - "from bokeh.models.annotations import Label, Arrow\n", - "from bokeh.models.arrow_heads import VeeHead\n", - "from bokeh.models import Div, CustomJS, Slider, Spacer, Text\n", - "from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup\n", - "from bokeh.plotting import figure, show, ColumnDataSource\n", - "from bokeh.io import output_notebook\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 models\n", - "from cienpy import javascriptcodes as js\n", - "\n", - "# output_notebook()" + "from cienpy import rectangular_section as beam_section" ] }, { "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", "# 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)\n", - "\n", - "\n", - "# constants for the visualisation\n", - "SCALE = 10\n", - "OFFSET_Q = q\n", - "MAX_B = 3*b\n", - "MAX_H = 3*h\n", - "MAX_Q = q/4*5\n", - "\n", - "# store the values in a specific format\n", - "data_beam = dict(\n", - " x=[0, L],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_beam = dict(\n", - " x=[0, L*SCALE],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_q = dict(\n", - " x=[0, 0, L*SCALE, L*SCALE],\n", - " y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],\n", - " x_fade=[0, 0, L*SCALE, L*SCALE]\n", - ")\n", - "\n", - "initial_position = L\n", - "initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC\n", - "initial_FBD = 0 # right=0 left=1\n", - "data = dict( # stores every useful single variable\n", - " state=[initial_state], \n", - " FBD=[initial_FBD],\n", - " SCALE=[SCALE],\n", - " L=[L],\n", - " b=[b],\n", - " h=[h],\n", - " A=[A],\n", - " Iy=[Iy],\n", - " Iz=[Iz],\n", - " P=[P],\n", - " x=[initial_position],\n", - " y=[0],\n", - " q=[q],\n", - " Rx=[Rx],\n", - " Ry_l=[Ry_l],\n", - " Ry_r=[Ry_r],\n", - " N=[N],\n", - " V=[V],\n", - " M=[M],\n", - " xF=[L*SCALE]\n", - ")\n", - "\n", - "source_beam = ColumnDataSource(data_beam)\n", - "source_scheme_beam = ColumnDataSource(data_scheme_beam)\n", - "source_scheme_q = ColumnDataSource(data_scheme_q)\n", - "source = ColumnDataSource(data)" + "Ry_r = sb.compute_Ry_r(q, L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Create the figures, the plots and the widgets (same of Notebook 1 - Geo):" + "Run the complex code for the interactive visualisation:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
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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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
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[m]\",\"value\":6},\"id\":\"1255\",\"type\":\"Slider\"},{\"attributes\":{},\"id\":\"1014\",\"type\":\"LinearScale\"},{\"attributes\":{\"data\":{\"x\":[30.0],\"y\":[0]},\"selected\":{\"id\":\"1325\"},\"selection_policy\":{\"id\":\"1324\"}},\"id\":\"1160\",\"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\":\"1251\",\"type\":\"Scatter\"},{\"attributes\":{\"below\":[{\"id\":\"1018\"}],\"center\":[{\"id\":\"1021\"},{\"id\":\"1025\"},{\"id\":\"1179\"}],\"height\":200,\"left\":[{\"id\":\"1022\"}],\"min_border_left\":0,\"renderers\":[{\"id\":\"1086\"},{\"id\":\"1092\"},{\"id\":\"1098\"},{\"id\":\"1170\"},{\"id\":\"1176\"},{\"id\":\"1185\"},{\"id\":\"1191\"}],\"title\":{\"id\":\"1008\"},\"toolbar\":{\"id\":\"1033\"},\"toolbar_location\":null,\"width\":700,\"x_range\":{\"id\":\"1010\"},\"x_scale\":{\"id\":\"1014\"},\"y_range\":{\"id\":\"1012\"},\"y_scale\":{\"id\":\"1016\"}},\"id\":\"1007\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"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\":{\"coordinates\":null,\"data_source\":{\"id\":\"1094\"},\"glyph\":{\"id\":\"1095\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1097\"},\"nonselection_glyph\":{\"id\":\"1096\"},\"view\":{\"id\":\"1099\"}},\"id\":\"1098\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"1248\"}},\"id\":\"1253\",\"type\":\"CDSView\"},{\"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\":\"1076\",\"type\":\"Rect\"},{\"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\":\"1097\",\"type\":\"Circle\"},{\"attributes\":{\"active\":0,\"js_property_callbacks\":{\"change:active\":[{\"id\":\"1265\"}]},\"labels\":[\"Right-hand\",\"Left-hand\"]},\"id\":\"1257\",\"type\":\"RadioButtonGroup\"},{\"attributes\":{},\"id\":\"1353\",\"type\":\"UnionRenderers\"},{\"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\":\"1102\",\"type\":\"Rect\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1109\"},\"group\":null,\"line_color\":{\"value\":\"gray\"},\"line_width\":{\"value\":2.1972245773362196},\"source\":{\"id\":\"1322\"},\"start\":null,\"x_end\":{\"value\":0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":128.0},\"y_start\":{\"value\":0}},\"id\":\"1110\",\"type\":\"Arrow\"},{\"attributes\":{\"text\":\"Axial force P=10 kN (applied)\"},\"id\":\"1258\",\"type\":\"Div\"},{\"attributes\":{\"text\":\"\\n

Forces and Moments:

\\n P = 10 kN
\\n Rx = 10 kN
\\n Ry (left) = 12.0 kN
\\n Ry (right) = 12.0 kN
\\n No cross section analysed.
\\n N = 0 kN
\\n V = 0 kN
\\n M = 0 kNm\\n \\n \"},\"id\":\"1260\",\"type\":\"Div\"},{\"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\":{\"x\":[0],\"y\":[0]},\"selected\":{\"id\":\"1350\"},\"selection_policy\":{\"id\":\"1349\"}},\"id\":\"1073\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"end\":7.2,\"start\":-1.2000000000000002},\"id\":\"1010\",\"type\":\"Range1d\"},{\"attributes\":{\"fill_color\":{\"value\":\"gray\"},\"line_color\":{\"value\":\"gray\"},\"size\":{\"value\":15.380572041353537}},\"id\":\"1109\",\"type\":\"VeeHead\"},{\"attributes\":{},\"id\":\"1354\",\"type\":\"Selection\"},{\"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\":{\"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\":\"1161\",\"type\":\"Rect\"},{\"attributes\":{\"tools\":[{\"id\":\"1026\"},{\"id\":\"1027\"},{\"id\":\"1028\"},{\"id\":\"1029\"},{\"id\":\"1030\"},{\"id\":\"1031\"}]},\"id\":\"1033\",\"type\":\"Toolbar\"},{\"attributes\":{\"text\":\"\\n

Geometrical and mechanical parameters:

\\n h = 200 mm
\\n b = 100 mm
\\n L = 6 m
\\n A = 2.00e+04 mm2
\\n Iy = 6.67e+07 mm4
\\n Iz = 1.67e+07 mm4\"},\"id\":\"1106\",\"type\":\"Div\"},{\"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\":{\"axis\":{\"id\":\"1018\"},\"coordinates\":null,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1021\",\"type\":\"Grid\"},{\"attributes\":{\"active\":[0],\"js_property_callbacks\":{\"change:active\":[{\"id\":\"1264\"}]},\"labels\":[\"Apply or remove axial force P\"]},\"id\":\"1259\",\"type\":\"CheckboxButtonGroup\"},{\"attributes\":{},\"id\":\"1309\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1030\",\"type\":\"ResetTool\"},{\"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\":{\"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\":{\"axis\":{\"id\":\"1022\"},\"coordinates\":null,\"dimension\":1,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1025\",\"type\":\"Grid\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1121\"},\"glyph\":{\"id\":\"1122\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1124\"},\"nonselection_glyph\":{\"id\":\"1123\"},\"view\":{\"id\":\"1126\"}},\"id\":\"1125\",\"type\":\"GlyphRenderer\"},{\"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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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)/c**2\\n }\\n const step = 2*c / (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(2*c)*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\":\"1261\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1310\",\"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,\"formatter\":{\"id\":\"1282\"},\"group\":null,\"major_label_policy\":{\"id\":\"1283\"},\"ticker\":{\"id\":\"1023\"},\"visible\":false},\"id\":\"1022\",\"type\":\"LinearAxis\"},{\"attributes\":{\"height\":10},\"id\":\"1268\",\"type\":\"Spacer\"},{\"attributes\":{\"end\":300,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1262\"}]},\"start\":10,\"step\":10,\"title\":\"Change the width b [mm]\",\"value\":100},\"id\":\"1107\",\"type\":\"Slider\"},{\"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\":\"1032\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"1016\",\"type\":\"LinearScale\"},{\"attributes\":{\"end\":600,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1263\"}]},\"start\":20,\"step\":20,\"title\":\"Change the height h [mm]\",\"value\":200},\"id\":\"1108\",\"type\":\"Slider\"},{\"attributes\":{\"source\":{\"id\":\"1121\"}},\"id\":\"1126\",\"type\":\"CDSView\"},{\"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 = 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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**3/12\\n }\\n \\n \"},\"id\":\"1263\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1031\",\"type\":\"HelpTool\"},{\"attributes\":{\"source\":{\"id\":\"1112\"}},\"id\":\"1117\",\"type\":\"CDSView\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1122\",\"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\"},\"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_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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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\":\"1264\",\"type\":\"CustomJS\"},{\"attributes\":{\"axis_label\":\"Position [m]\",\"coordinates\":null,\"formatter\":{\"id\":\"1285\"},\"group\":null,\"major_label_policy\":{\"id\":\"1286\"},\"ticker\":{\"id\":\"1019\"}},\"id\":\"1018\",\"type\":\"LinearAxis\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1112\"},\"glyph\":{\"id\":\"1113\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1115\"},\"nonselection_glyph\":{\"id\":\"1114\"},\"view\":{\"id\":\"1117\"}},\"id\":\"1116\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1355\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1023\",\"type\":\"BasicTicker\"},{\"attributes\":{\"data\":{\"text\":[\"z\"],\"x\":[-88.0],\"y\":[0]},\"selected\":{\"id\":\"1356\"},\"selection_policy\":{\"id\":\"1355\"}},\"id\":\"1121\",\"type\":\"ColumnDataSource\"},{\"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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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\":\"1265\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1029\",\"type\":\"SaveTool\"},{\"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\":\"1114\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"1026\",\"type\":\"PanTool\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1113\",\"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\"},\"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_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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/2*(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return q*L/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return q*L/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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\":\"1266\",\"type\":\"CustomJS\"},{\"attributes\":{\"overlay\":{\"id\":\"1032\"}},\"id\":\"1028\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"data\":{\"text\":[\"y\"],\"x\":[0],\"y\":[136.0]},\"selected\":{\"id\":\"1354\"},\"selection_policy\":{\"id\":\"1353\"}},\"id\":\"1112\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1356\",\"type\":\"Selection\"},{\"attributes\":{\"width\":10},\"id\":\"1267\",\"type\":\"Spacer\"},{\"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\":\"1124\",\"type\":\"Text\"},{\"attributes\":{},\"id\":\"1027\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"coordinates\":null,\"end\":{\"id\":\"1118\"},\"group\":null,\"line_color\":{\"value\":\"gray\"},\"line_width\":{\"value\":2.1972245773362196},\"source\":{\"id\":\"1323\"},\"start\":null,\"x_end\":{\"value\":-80.0},\"x_start\":{\"value\":0},\"y_end\":{\"value\":0},\"y_start\":{\"value\":0}},\"id\":\"1119\",\"type\":\"Arrow\"}],\"root_ids\":[\"1278\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n", + " const render_items = [{\"docid\":\"a1bf6f28-4cd4-479a-9950-ff4d2cd2f8ef\",\"root_ids\":[\"1278\"],\"roots\":{\"1278\":\"3c0b4244-f256-4a63-b201-a3e4fbaf4e4c\"}}];\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": "1278" + } + }, + "output_type": "display_data" } ], "source": [ - "FIG_H_B = 200 # height figure beam\n", - "FIG_B_B = 700 # width figure beam\n", - "FIG_H_S = FIG_H_B # height figure scheme\n", - "FIG_B_S = FIG_B_B # width figure scheme\n", - "FIG_H_SEC = 600 # height figure section\n", - "\n", - "options = dict(\n", - " toolbar_location=None\n", - ")\n", - "\n", - "# figure for the beam\n", - "paddingx = 0.2*L\n", - "int_x_b = (0-paddingx, L+paddingx)\n", - "int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)\n", - "fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,\n", - " f_h=FIG_H_B, f_b=FIG_B_B)\n", - "\n", - "\n", - "# figure for the cross-section\n", - "fig_section = sb.define_fig_section(MAX_B, MAX_H*0.8, options, FIG_H_SEC)\n", - "\n", - "\n", - "# beam\n", - "(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,\n", - " ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)\n", - "\n", - "# section\n", - "section = beam_section.draw_section(fig_section, b, h)\n", - "\n", - "\n", - "# show mechanical parameters\n", - "div_geo = Div(text=beam_section.div_text_geo(round(h), round(b), round(L),\n", - " \"{:.2e}\".format(A),\n", - " \"{:.2e}\".format(Iy),\n", - " \"{:.2e}\".format(Iz)))\n", - "\n", - "\n", - "# change geometry\n", - "slider_b = Slider(\n", - " title=\"Change the width b [mm]\",\n", - " start=10,\n", - " end=MAX_B,\n", - " step=10,\n", - " value=b\n", - ")\n", - "slider_h = Slider(\n", - " title=\"Change the height h [mm]\",\n", - " start=20,\n", - " end=MAX_H,\n", - " step=20,\n", - " value=h\n", - ")\n", - "\n", - "# reference system\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis\n", - "fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=[\"y\"], text_color='gray', text_baseline='middle', angle=math.pi/2)\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis\n", - "fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=[\"z\"], text_color='gray', text_align='right', text_baseline='middle')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now define the new figures, renderers and widgets:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# figure for the forces and moments\n", - "fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)\n", - "\n", - "\n", - "# uniform load (beam)\n", - "u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE], width=L, height=q/SCALE,\n", - " fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)\n", - "label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE], text=[\"q\"], text_color=\"blue\")\n", - "\n", - "\n", - "# axial force (beam)\n", - "axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')\n", - "label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=[\"P\"], text_color=\"green\")\n", - "\n", - "\n", - "# position point\n", - "pos_opt = dict(\n", - " source=source,\n", - " size=10,\n", - " fill_alpha=0.5,\n", - " fill_color=\"magenta\",\n", - " color=\"magenta\",\n", - " alpha=0.5\n", - ")\n", - "beam_position = fig_beam.circle('x', 'y', **pos_opt)\n", - "forces_position = fig_scheme.circle('xF', 'y', **pos_opt)\n", - "\n", - "\n", - "# beam (scheme)\n", - "scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')\n", - "scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)\n", - "# uniform load (scheme)\n", - "scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',\n", - " fill_alpha=0.3, alpha=0.3)\n", - "scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',\n", - " color='navy', fill_alpha=0.3, alpha=0.3)\n", - "# axial force (scheme)\n", - "scheme_axial_force = models.force_vector(fig_scheme, P, L*SCALE+P, L*SCALE, 0, 0, 'green')\n", - "# Reactions (scheme)\n", - "scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -Ry_r, 0, 'orange')\n", - "scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')\n", - "scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')\n", - "# force N\n", - "scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# force V\n", - "scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# moment M\n", - "(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)\n", - "\n", - "\n", - "# change the uniform load q\n", - "slider_q = Slider(\n", - " title=\"Change the uniform load q [kN/m]\",\n", - " start=0.1,\n", - " end=MAX_Q,\n", - " step=0.1,\n", - " value=q\n", - ")\n", - "\n", - "\n", - "# choose position of interest\n", - "slider_position = Slider(\n", - " title=\"Change the position x along the beam [m]\",\n", - " start=0,\n", - " end=L,\n", - " step=0.02,\n", - " value=L\n", - ")\n", - "\n", - "\n", - "# choose left or right FBD\n", - "div_rg_FBD = Div(text=\"Free-body diagram (FBD):\")\n", - "radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)\n", - "\n", - "\n", - "# choose axial force or not\n", - "div_cb_P = Div(text=f\"Axial force P={P} kN (applied)\")\n", - "checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])\n", - "\n", - "\n", - "# show values of forces and moments\n", - "div_forces = Div(text=sb.div_text_forces(P, P, Ry_l, Ry_r, \"No cross section analysed.\", 0, 0, 0))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Configure the logics:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "args_slider_pos = dict(source=source,\n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " s_M=source_M,\n", - " arr_head=scheme_M_head)\n", - "code_slider_pos = f\"\"\"\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", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{models.implement_check_stateJS()}\n", - "\"\"\"\n", - "updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)\n", - "\n", - "\n", - "args_slider_b_h = dict(source=source,\n", - " s_b=source_beam,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r)\n", - "code_change_b = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "\"\"\"\n", - "update_b = CustomJS(args=args_slider_b_h, code=code_change_b)\n", - "\n", - "\n", - "code_change_h = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "\"\"\"\n", - "update_h = CustomJS(args=args_slider_b_h, code=code_change_h)\n", - "\n", - "\n", - "args_checkbox_P = dict(source=source,\n", - " s_M=source_M,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force, \n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r, \n", - " fN=scheme_N,\n", - " fV=scheme_V, \n", - " arr_head=scheme_M_head)\n", - "code_checkbox_P = f\"\"\"\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] = {P}*(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", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_compute_RxJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)\n", - "\n", - "\n", - "args_radiogroup_FBD = dict(source=source, \n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M, \n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N, \n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head)\n", - "code_radiogroup_FBD = f\"\"\"\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", - "{models.implement_check_stateJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)\n", - "\n", - "\n", - "args_slider_q = dict(source=source,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M,\n", - " div_f=div_forces,\n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head)\n", - "code_slider_q = f\"\"\"\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", - "{js.implement_update_arrowJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_compute_Ry_lJS()}\n", - "{sb.implement_compute_Ry_rJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_u_loadJS(OFFSET_Q)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)\n", - "\n", - "\n", - "# apply the logics\n", - "slider_b.js_on_change('value', update_b)\n", - "slider_h.js_on_change('value', update_h)\n", - "slider_position.js_on_change('value', updade_slider_pos)\n", - "checkbox_P.js_on_click(update_checkbox_P)\n", - "radiogroup_FBD.js_on_click(update_radiogroup_FBD)\n", - "slider_q.js_on_change('value', update_slider_q)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Build the layout and show the figures. Note that the forces in the scheme are updated after moving the position of the point with the slider.\n", - "Note that the value of the forces and moments shown below represents the intensity, thus is always positive. The direction is given by the vector in the scheme." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "padding_layout = 10\n", - "layout1 = layout([\n", - " [column(row(column(fig_beam,\n", - " row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout),\n", - " slider_b,\n", - " slider_h,\n", - " div_geo,\n", - " Spacer(height=padding_layout),\n", - " slider_position,\n", - " slider_q,\n", - " div_rg_FBD,\n", - " radiogroup_FBD,\n", - " div_cb_P,\n", - " checkbox_P))),\n", - " column(fig_scheme,\n", - " Spacer(height=padding_layout),\n", - " div_forces))\n", - " )],\n", - "])\n", - "\n", - "show(layout1)" + "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)" ] } ], "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": 2 + "nbformat_minor": 4 } diff --git a/Simple Beam DEMOs/sb_buckling.ipynb b/Simple Beam DEMOs/sb_buckling.ipynb index 34341ed..f8111e4 100644 --- a/Simple Beam DEMOs/sb_buckling.ipynb +++ b/Simple Beam DEMOs/sb_buckling.ipynb @@ -1,644 +1,479 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple beam - Buckling\n", - "In this second notebook, the instability of a simple beam under constant axial load is studied. " + "In this last notebook, the instability of a simple beam under constant axial load is studied. " ] }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
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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 \"
\\n\"+\n \"

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\\n\"+\n \"\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\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_buckling\n", "import numpy as np\n", "import math\n", - "from bokeh.layouts import layout, column, row\n", - "from bokeh.models import Div, CustomJS, Slider, Spacer\n", - "from bokeh.models.widgets import RadioButtonGroup\n", - "from bokeh.plotting import figure, show, ColumnDataSource\n", - "from bokeh.io import output_notebook\n", "from cienpy import simplebeam as sb\n", "from cienpy import rectangular_section as beam_section\n", - "from cienpy import models\n", - "from cienpy import javascriptcodes as js\n", - "from cienpy import buckling\n", - "\n", - "# output_notebook()" + "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": 20, + "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)\n", - "\n", - "# constants for the visualisation\n", - "SCALE = 10\n", - "MAX_B = 3*b\n", - "MAX_H = 3*h\n", - "MAX_P = 100*P\n", - "MAX_L = 10\n", - "\n", - "# store the values in a specific format\n", - "data_beam = dict(\n", - " x=[0, L],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "initial_position = L\n", - "initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC\n", - "initial_FBD = 0 # right=0 left=1\n", - "data = dict( # stores every useful single variable\n", - " state=[initial_state], \n", - " FBD=[initial_FBD],\n", - " SCALE=[SCALE],\n", - " L=[L],\n", - " b=[b],\n", - " h=[h],\n", - " E=[E],\n", - " A=[A],\n", - " Iy=[Iy],\n", - " Iz=[Iz],\n", - " P=[P],\n", - " x=[initial_position],\n", - " y=[0],\n", - " Rx=[Rx],\n", - " N=[N],\n", - " Ncrity=[Ncrity],\n", - " Ncritz=[Ncritz],\n", - " n_bracey=[n_bracey],\n", - " n_bracez=[n_bracez],\n", - " xF=[L*SCALE]\n", - ")\n", - "\n", - "source_beam = ColumnDataSource(data_beam)\n", - "source = ColumnDataSource(data)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create the figures, the plots and the widgets (same of Notebook 2 - Actions):" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [], - "source": [ - "FIG_H_B = 200 # height figure beam\n", - "FIG_B_B = 700 # width figure beam\n", - "FIG_H_S = FIG_H_B # height figure scheme\n", - "FIG_B_S = FIG_B_B # width figure scheme\n", - "FIG_H_SEC = 600 # height figure section\n", - "DIV_B_GEO = 170\n", - "DIV_B_FORCES = 170\n", - "\n", - "options = dict(\n", - " toolbar_location=None\n", - ")\n", - "\n", - "# figure for the beam\n", - "MAX_Q = 5\n", - "OFFSET_Q = 4\n", - "paddingx = 0.2*L\n", - "int_x_b = (0-paddingx, L+paddingx)\n", - "int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)\n", - "fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,\n", - " f_h=FIG_H_B, f_b=FIG_B_B)\n", - "\n", - "\n", - "# figure for the cross-section\n", - "fig_section = sb.define_fig_section(MAX_B, MAX_H*0.8, options, FIG_H_SEC)\n", - "\n", - "\n", - "# beam\n", - "(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,\n", - " ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)\n", - "\n", - "# section\n", - "section = beam_section.draw_section(fig_section, b, h)\n", - "\n", - "\n", - "# show mechanical parameters\n", - "div_geo = Div(width= DIV_B_GEO,\n", - " text=beam_section.div_text_geo(round(h), round(b), round(L),\n", - " \"{:.2e}\".format(A),\n", - " \"{:.2e}\".format(Iy),\n", - " \"{:.2e}\".format(Iz)))\n", - "\n", - "\n", - "# change geometry\n", - "slider_b = Slider(\n", - " title=\"Change the width b [mm]\",\n", - " start=10,\n", - " end=MAX_B,\n", - " step=10,\n", - " value=b\n", - ")\n", - "slider_h = Slider(\n", - " title=\"Change the height h [mm]\",\n", - " start=20,\n", - " end=MAX_H,\n", - " step=20,\n", - " value=h\n", - ")\n", - "\n", - "# reference system\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis\n", - "fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=[\"y\"], text_color='gray', text_baseline='middle', angle=math.pi/2)\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis\n", - "fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=[\"z\"], text_color='gray', text_align='right', text_baseline='middle')\n", - "\n", - "\n", - "# axial force (beam)\n", - "axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')\n", - "label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=[\"P\"], text_color=\"green\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now define the new figures, renderers and widgets:" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [], - "source": [ - "# change title in beam (y direction)\n", - "fig_beam.title.text = \"Simple supported beam: x-y plane\"\n", - "\n", - "\n", - "# beam in z direction\n", - "fig_beam_z = sb.define_fig_beam(int_x_b, int_y_b, options,\n", - " f_h=FIG_H_B, f_b=FIG_B_B)\n", - "fig_beam_z.title.text = \"Simple supported beam: x-z plane\"\n", - "(beam_z, support_l_z, support_r_z) = sb.draw_beam(fig_beam_z, source_beam, L,\n", - " ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)\n", - "fig_beam_z.x_range = fig_beam.x_range\n", - "\n", - "\n", - "# axial force (beam z direction)\n", - "axial_force_z = models.force_vector(fig_beam_z, P, L+P/SCALE, L, 0, 0, 'green')\n", - "label_P_force_z = fig_beam_z.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=[\"P\"], text_color=\"green\")\n", - "\n", - "\n", - "# reference system (x-y plane)\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "models.force_vector(fig_beam, axis_arrow_length, -axis_arrow_length-0.1, -0.1, 0, 0, 'gray')\n", - "fig_beam.text(x=[-axis_arrow_length], y=[0.1], text=[\"x axis\"], text_color='gray', text_baseline='bottom')\n", - "models.force_vector(fig_beam, axis_arrow_length, 0, 0, 0, axis_arrow_length, 'gray')\n", - "fig_beam.text(x=[0.1], y=[0.2], text=[\"y axis\"], text_color='gray', text_baseline='bottom')\n", - "\n", - "\n", - "# reference system (x-z plane)\n", - "models.force_vector(fig_beam_z, axis_arrow_length, -axis_arrow_length-0.1, -0.1, 0, 0, 'gray')\n", - "fig_beam_z.text(x=[-axis_arrow_length], y=[0.1], text=[\"x axis\"], text_color='gray', text_baseline='bottom')\n", - "models.force_vector(fig_beam_z, axis_arrow_length, 0, 0, 0, axis_arrow_length, 'gray')\n", - "fig_beam_z.text(x=[0.1], y=[0.2], text=[\"z axis\"], text_color='gray', text_baseline='bottom')\n", - "\n", - "\n", - "# slider P\n", - "slider_P = Slider(\n", - " title=\"Change the axial force P [kN]\",\n", - " start=1,\n", - " end=MAX_P,\n", - " step=1,\n", - " value=P\n", - ")\n", - "\n", - "\n", - "# slider L\n", - "slider_L = Slider(\n", - " title=\"Change the length of the beam [m]\",\n", - " start=1,\n", - " end=L,\n", - " step=0.1,\n", - " value=L\n", - ")\n", - "\n", - "\n", - "# bracing options\n", - "div_rg_brace_y = Div(text=\"Number of braces in y direction:\")\n", - "radiogroup_brace_y = RadioButtonGroup(labels=['No brace', 'One middle brace', 'Two equally spaced braces'], active=n_bracey)\n", - "div_rg_brace_z = Div(text=\"Number of braces in z direction:\")\n", - "radiogroup_brace_z = RadioButtonGroup(labels=['No brace', 'One middle brace', 'Two equally spaced braces'], active=n_bracez)\n", - "\n", - "\n", - "# figure for buckling\n", - "fig_buckling_y = figure(toolbar_location=None,\n", - " plot_height=FIG_H_S,\n", - " plot_width=FIG_B_S,\n", - " title=\"Beam instability in y direction\",\n", - " x_axis_label=\"Position [m]\",\n", - " x_range = fig_beam.x_range\n", - ")\n", - "fig_buckling_y.ygrid.grid_line_alpha = 0\n", - "fig_buckling_y.yaxis.visible = False\n", - "fig_buckling_y.line('x', 'y', source=source_beam, line_width=1, color='gray')\n", - "mode_shape_y = fig_buckling_y.line(x=[0, L], y=[0, 0], line_width=2, color='black')\n", - "\n", - "fig_buckling_z = figure(toolbar_location=None,\n", - " plot_height=FIG_H_S,\n", - " plot_width=FIG_B_S,\n", - " title=\"Beam instability in z direction\",\n", - " x_axis_label=\"Position [m]\",\n", - " x_range = fig_beam.x_range\n", - ")\n", - "fig_buckling_z.ygrid.grid_line_alpha = 0\n", - "fig_buckling_z.yaxis.visible = False\n", - "fig_buckling_z.line('x', 'y', source=source_beam, line_width=1, color='gray')\n", - "mode_shape_z = fig_buckling_z.line(x=[0, L], y=[0, 0], line_width=2, color='black')\n", - "\n", - "\n", - "# show values of forces \n", - "div_buckling = Div(width=DIV_B_FORCES,\n", - " text=buckling.div_text_buckling(P, Rx, N, \"{:.2f}\".format(Ncrity), \"{:.2f}\".format(Ncritz), \"No\"))\n", - "\n", - "\n", - "# show brace position\n", - "point_brace_y = fig_buckling_y.circle(x=[], y=[], size=10, fill_alpha=0.5, fill_color=\"red\", color=\"red\", alpha=0.5)\n", - "point_brace_z = fig_buckling_z.circle(x=[], y=[], size=10, fill_alpha=0.5, fill_color=\"red\", color=\"red\", alpha=0.5)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Configure the logics:" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [], - "source": [ - "args_slider_b_h = dict(source=source,\n", - " mode_shape_y=mode_shape_y,\n", - " mode_shape_z=mode_shape_z,\n", - " div=div_geo, \n", - " div_buckling=div_buckling,\n", - " section=section)\n", - "code_change_b = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{buckling.implement_update_div_bucklingJS()}\n", - "{buckling.implement_compute_N_buckling_yJS()}\n", - "{buckling.implement_compute_N_buckling_zJS()}\n", - "{buckling.implement_compute_mode_shape_N_bucklingJS()}\n", - "{js.implement_linspaceJS()}\n", - "{buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)}\n", - "\"\"\"\n", - "update_b = CustomJS(args=args_slider_b_h, code=code_change_b)\n", - "\n", - "\n", - "code_change_h = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{buckling.implement_update_div_bucklingJS()}\n", - "{buckling.implement_compute_N_buckling_yJS()}\n", - "{buckling.implement_compute_N_buckling_zJS()}\n", - "{buckling.implement_compute_mode_shape_N_bucklingJS()}\n", - "{js.implement_linspaceJS()}\n", - "{buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)}\n", - "\"\"\"\n", - "update_h = CustomJS(args=args_slider_b_h, code=code_change_h)\n", - "\n", - "\n", - "args_slider_L = dict(source=source,\n", - " s_b=source_beam,\n", - " support_r_y=support_r,\n", - " support_r_z=support_r_z,\n", - " axial_force_y=axial_force,\n", - " axial_force_z=axial_force_z,\n", - " label_P_force_y=label_P_force,\n", - " label_P_force_z=label_P_force_z,\n", - " point_brace_y=point_brace_y,\n", - " point_brace_z=point_brace_z,\n", - " mode_shape_y=mode_shape_y,\n", - " mode_shape_z=mode_shape_z,\n", - " div=div_geo,\n", - " div_buckling=div_buckling)\n", - "code_change_L = f\"\"\"\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+{P/SCALE}\n", - "axial_force_y.x_end = L\n", - "label_P_force_y.glyph.x = L+{P/SCALE}/2\n", - "axial_force_z.x_start = L+{P/SCALE}\n", - "axial_force_z.x_end = L\n", - "label_P_force_z.glyph.x = L+{P/SCALE}/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", - "{beam_section.implement_update_div_geoJS()}\n", - "{buckling.implement_update_div_bucklingJS()}\n", - "{buckling.implement_compute_N_buckling_yJS()}\n", - "{buckling.implement_compute_N_buckling_zJS()}\n", - "{buckling.implement_update_point_braceJS()}\n", - "{buckling.implement_compute_mode_shape_N_bucklingJS()}\n", - "{js.implement_linspaceJS()}\n", - "{buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)}\n", - "\"\"\"\n", - "update_L = CustomJS(args=args_slider_L, code=code_change_L)\n", - "\n", - "\n", - "args_slider_P = dict(source=source,\n", - " mode_shape_y=mode_shape_y,\n", - " mode_shape_z=mode_shape_z,\n", - " div_buckling=div_buckling)\n", - "code_slider_P = f\"\"\"\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", - "{sb.implement_compute_RxJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{buckling.implement_update_div_bucklingJS()}\n", - "{buckling.implement_compute_mode_shape_N_bucklingJS()}\n", - "{js.implement_linspaceJS()}\n", - "{buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)}\n", - "\"\"\"\n", - "update_P = CustomJS(args=args_slider_P, code=code_slider_P)\n", - "\n", - "\n", - "args_radiogroup_brace_y = dict(source=source,\n", - " mode_shape_y=mode_shape_y,\n", - " mode_shape_z=mode_shape_z,\n", - " div_buckling=div_buckling,\n", - " point_brace=point_brace_y)\n", - "args_radiogroup_brace_z = dict(source=source,\n", - " mode_shape_y=mode_shape_y,\n", - " mode_shape_z=mode_shape_z,\n", - " div_buckling=div_buckling,\n", - " point_brace=point_brace_z)\n", - "code_radiogroup_brace = lambda which_axis : f\"\"\"\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['I{which_axis}'][0]\n", - "\n", - "// apply the changes\n", - "db['n_brace{which_axis}'][0] = n_brace\n", - "db['Ncrit{which_axis}'][0] = compute_N_buckling_{which_axis}(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", - "{buckling.implement_update_div_bucklingJS()}\n", - "{buckling.implement_compute_N_buckling_yJS()}\n", - "{buckling.implement_compute_N_buckling_zJS()}\n", - "{buckling.implement_update_point_braceJS()}\n", - "{buckling.implement_compute_mode_shape_N_bucklingJS()}\n", - "{js.implement_linspaceJS()}\n", - "{buckling.implement_update_mode_shape_N_bucklingJS(discr_NVM)}\n", - "\"\"\"\n", - "update_brace_y = CustomJS(args=args_radiogroup_brace_y, code=code_radiogroup_brace('y'))\n", - "update_brace_z = CustomJS(args=args_radiogroup_brace_z, code=code_radiogroup_brace('z'))\n", - "\n", - "# apply the logics\n", - "slider_b.js_on_change('value', update_b)\n", - "slider_h.js_on_change('value', update_h)\n", - "slider_P.js_on_change('value', update_P)\n", - "slider_L.js_on_change('value', update_L)\n", - "radiogroup_brace_y.js_on_click(update_brace_y)\n", - "radiogroup_brace_z.js_on_click(update_brace_z)" + "Ncritz = buckling.compute_N_buckling_z(E, Iz, L, n_bracez)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Build the layout and show the figures. Note that the two \"beam instability\" graphs have no y axis (that should show how much the deflection is) because we know only the shape, not the amplitude of the buckling deformation (the constant of integration is set to 1 arbitrarily)." + "Run the complex code for the interactive visualisation:" ] }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 3, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Opening in existing browser session.\n" - ] + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
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Geometrical and mechanical parameters:

\\n h = 100 mm
\\n b = 50 mm
\\n L = 6 m
\\n A = 5.00e+03 mm2
\\n Iy = 4.17e+06 mm4
\\n Iz = 1.04e+06 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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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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 ((-NForces and Instability:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n N = `+N+` kN
\\n V = 0 kN
\\n M = 0 kNm
\\n Ncrit,y = `+Ncrity+` kN
\\n Ncrit,z = `+Ncritz+` kN
\\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)**2*E*Iy/L**2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)*Math.PI)**2*E*Iz/L**2/1e9\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return C*Math.sin((n_brace+1)*Math.PI*x/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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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 ((-NForces and Instability:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n N = `+N+` kN
\\n V = 0 kN
\\n M = 0 kNm
\\n Ncrit,y = `+Ncrity+` kN
\\n Ncrit,z = `+Ncritz+` kN
\\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)**2*E*Iy/L**2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)*Math.PI)**2*E*Iz/L**2/1e9\\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return C*Math.sin((n_brace+1)*Math.PI*x/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

Forces and Instability:

\\n P = 10 kN
\\n Rx = 10 kN
\\n N = -10 kN
\\n V = 0 kN
\\n M = 0 kNm
\\n Ncrit,y = 228.46 kN
\\n Ncrit,z = 57.12 kN
\\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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 ((-NForces and Instability:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n N = `+N+` kN
\\n V = 0 kN
\\n M = 0 kNm
\\n Ncrit,y = `+Ncrity+` kN
\\n Ncrit,z = `+Ncritz+` kN
\\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)**2*E*Iy/L**2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)*Math.PI)**2*E*Iz/L**2/1e9\\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, 2*L/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 C*Math.sin((n_brace+1)*Math.PI*x/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 ((-NForces and Instability:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n N = `+N+` kN
\\n V = 0 kN
\\n M = 0 kNm
\\n Ncrit,y = `+Ncrity+` kN
\\n Ncrit,z = `+Ncritz+` kN
\\n Instability: `+str_insta+`\\n ` \\n }\\n \\n \\n function compute_mode_shape_N_buckling(x, L, n_brace, C=1) {\\n return C*Math.sin((n_brace+1)*Math.PI*x/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 ((-NForces and Instability:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n N = `+N+` kN
\\n V = 0 kN
\\n M = 0 kNm
\\n Ncrit,y = `+Ncrity+` kN
\\n Ncrit,z = `+Ncritz+` kN
\\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)**2*E*Iy/L**2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)*Math.PI)**2*E*Iz/L**2/1e9\\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, 2*L/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 C*Math.sin((n_brace+1)*Math.PI*x/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 ((-NForces and Instability:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n N = `+N+` kN
\\n V = 0 kN
\\n M = 0 kNm
\\n Ncrit,y = `+Ncrity+` kN
\\n Ncrit,z = `+Ncritz+` kN
\\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)**2*E*Iy/L**2/1e9\\n }\\n \\n \\n function compute_N_buckling_z(E, Iz, L, n_bracez) {\\n return ((n_bracez+1)*Math.PI)**2*E*Iz/L**2/1e9\\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, 2*L/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 C*Math.sin((n_brace+1)*Math.PI*x/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 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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": [ - "padding_layout = 10\n", - "layout1 = layout([\n", - " [column(row(column(\n", - " row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout),\n", - " slider_b,\n", - " slider_h,\n", - " slider_P,\n", - " slider_L,\n", - " row(div_geo, div_buckling),\n", - " Spacer(height=padding_layout),\n", - " div_rg_brace_y,\n", - " radiogroup_brace_y,\n", - " div_rg_brace_z,\n", - " radiogroup_brace_z))),\n", - " column(Spacer(width=padding_layout)),\n", - " column(fig_beam,\n", - " fig_beam_z,\n", - " fig_buckling_y,\n", - " fig_buckling_z))\n", - " )],\n", - "])\n", - "\n", - "show(layout1)" + "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": 2 + "nbformat_minor": 4 } diff --git a/Simple Beam DEMOs/sb_deflection.ipynb b/Simple Beam DEMOs/sb_deflection.ipynb index de19ea3..7d0e12f 100644 --- a/Simple Beam DEMOs/sb_deflection.ipynb +++ b/Simple Beam DEMOs/sb_deflection.ipynb @@ -1,1171 +1,486 @@ { "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": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
\n", + " \n", + " Loading BokehJS ...\n", + "
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\\n\"+\n", + " \"
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    • \\n\"+\n", + " \"
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\\n\"+\n \"

\\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 \"

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    • \\n\"+\n \"
  • use INLINE resources instead, as so:
    • \\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\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_deflection\n", "import math\n", - "import numpy as np \n", - "from bokeh.layouts import layout, column, row\n", - "from bokeh.models.annotations import Label, Arrow\n", - "from bokeh.models.arrow_heads import VeeHead\n", - "from bokeh.models import Div, CustomJS, Slider, Spacer, Text\n", - "from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup\n", - "from bokeh.plotting import figure, show, ColumnDataSource\n", - "from bokeh.io import output_notebook\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 models\n", - "from cienpy import javascriptcodes as js\n", - "\n", - "# output_notebook()" + "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)\n", - "\n", - "\n", - "# constants for the visualisation\n", - "SCALE = 10\n", - "OFFSET_Q = q\n", - "MAX_B = 3*b\n", - "MAX_H = 3*h\n", - "MAX_Q = q/4*5\n", - "SCALE_DEFL = 100\n", - "\n", - "\n", - "# store the values in a specific format\n", - "data_beam = dict(\n", - " x=[0, L],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_beam = dict(\n", - " x=[0, L*SCALE],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_q = dict(\n", - " x=[0, 0, L*SCALE, L*SCALE],\n", - " y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],\n", - " x_fade=[0, 0, L*SCALE, L*SCALE]\n", - ")\n", - "\n", - "data_section_scheme = dict(\n", - " x=[0, 0], \n", - " y=[0, h]\n", - ")\n", - "\n", - "initial_position = L\n", - "initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC\n", - "initial_FBD = 0 # right=0 left=1\n", - "data = dict( # stores every useful single variable\n", - " state=[initial_state], \n", - " FBD=[initial_FBD],\n", - " SCALE=[SCALE],\n", - " L=[L],\n", - " b=[b],\n", - " h=[h],\n", - " E=[E],\n", - " A=[A],\n", - " Iy=[Iy],\n", - " Iz=[Iz],\n", - " yG=[yG],\n", - " y_n_axis=[y_n_axis],\n", - " P=[P],\n", - " x=[initial_position],\n", - " y=[0],\n", - " q=[q],\n", - " Rx=[Rx],\n", - " Ry_l=[Ry_l],\n", - " Ry_r=[Ry_r],\n", - " N=[N],\n", - " V=[V],\n", - " M=[M],\n", - " xF=[L*SCALE]\n", - ")\n", - "\n", - "source_beam = ColumnDataSource(data_beam)\n", - "source_scheme_beam = ColumnDataSource(data_scheme_beam)\n", - "source_scheme_q = ColumnDataSource(data_scheme_q)\n", - "source_section_scheme = ColumnDataSource(data_section_scheme)\n", - "source = ColumnDataSource(data)" + "Ry_r = sb.compute_Ry_r(q, L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Create the figures, the plots and the widgets (same of Notebook 3 - Diagrams):" + "Run the complex code for the interactive visualisation:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, - "outputs": [], - "source": [ - "FIG_H_B = 200 # height figure beam\n", - "FIG_B_B = 700 # width figure beam\n", - "FIG_H_S = FIG_H_B # height figure scheme\n", - "FIG_B_S = FIG_B_B # width figure scheme\n", - "FIG_H_SEC = 600 # height figure section\n", - "DIV_B_GEO = 170\n", - "DIV_B_FORCES = 170\n", - "\n", - "options = dict(\n", - " toolbar_location=None\n", - ")\n", - "\n", - "# figure for the beam\n", - "paddingx = 0.2*L\n", - "int_x_b = (0-paddingx, L+paddingx)\n", - "int_y_b = (-OFFSET_Q/SCALE*SCALE_DEFL, (MAX_Q+OFFSET_Q)/SCALE*SCALE_DEFL)\n", - "fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,\n", - " f_h=FIG_H_B, f_b=FIG_B_B)\n", - "\n", - "\n", - "# figure for the cross-section\n", - "fig_section = sb.define_fig_section(MAX_B*0.8, MAX_H*0.8, options, FIG_H_SEC)\n", - "\n", - "\n", - "# beam\n", - "(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,\n", - " ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)\n", - "\n", - "# section\n", - "section = beam_section.draw_section(fig_section, b, h)\n", - "\n", - "\n", - "# show mechanical parameters\n", - "div_geo = Div(width= DIV_B_GEO, \n", - " text=beam_section.div_text_geo(round(h), round(b), round(L),\n", - " \"{:.2e}\".format(A),\n", - " \"{:.2e}\".format(Iy),\n", - " \"{:.2e}\".format(Iz)))\n", - "\n", - "\n", - "# change geometry\n", - "slider_b = Slider(\n", - " title=\"Change the width b [mm]\",\n", - " start=10,\n", - " end=MAX_B,\n", - " step=10,\n", - " value=b\n", - ")\n", - "slider_h = Slider(\n", - " title=\"Change the height h [mm]\",\n", - " start=20,\n", - " end=MAX_H,\n", - " step=20,\n", - " value=h\n", - ")\n", - "\n", - "# reference system\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis\n", - "fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=[\"y\"], text_color='gray', text_baseline='middle', angle=math.pi/2)\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis\n", - "fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=[\"z\"], text_color='gray', text_align='right', text_baseline='middle')\n", - "\n", - "\n", - "# figure for the forces and moments\n", - "fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)\n", - "\n", - "\n", - "# uniform load (beam)\n", - "u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE*SCALE_DEFL], width=L, height=q/SCALE*SCALE_DEFL,\n", - " fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)\n", - "label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE*SCALE_DEFL], text=[\"q\"], text_color=\"blue\")\n", - "\n", - "\n", - "# axial force (beam)\n", - "axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')\n", - "label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2*SCALE_DEFL], text=[\"P\"], text_color=\"green\")\n", - "\n", - "\n", - "# position point\n", - "pos_opt = dict(\n", - " source=source,\n", - " size=10,\n", - " fill_alpha=0.5,\n", - " fill_color=\"magenta\",\n", - " color=\"magenta\",\n", - " alpha=0.5\n", - ")\n", - "# CHAGED: moved below for correct display order of glyphs\n", - "# beam_position = fig_beam.circle('x', 'y', **pos_opt) \n", - "forces_position = fig_scheme.circle('xF', 'y', **pos_opt)\n", - "\n", - "\n", - "# beam (scheme)\n", - "scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')\n", - "scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)\n", - "# uniform load (scheme)\n", - "scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',\n", - " fill_alpha=0.3, alpha=0.3)\n", - "scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',\n", - " color='navy', fill_alpha=0.3, alpha=0.3)\n", - "# axial force (scheme)\n", - "scheme_axial_force = models.force_vector(fig_scheme, P, L*SCALE+P, L*SCALE, 0, 0, 'green')\n", - "# Reactions (scheme)\n", - "scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -Ry_r, 0, 'orange')\n", - "scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')\n", - "scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')\n", - "# force N\n", - "scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# force V\n", - "scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# moment M\n", - "(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)\n", - "\n", - "\n", - "# change the uniform load q\n", - "slider_q = Slider(\n", - " title=\"Change the uniform load q [kN/m]\",\n", - " start=0.1,\n", - " end=MAX_Q,\n", - " step=0.1,\n", - " value=q\n", - ")\n", - "\n", - "\n", - "# choose position of interest\n", - "slider_position = Slider(\n", - " title=\"Change the position x along the beam [m]\",\n", - " start=0,\n", - " end=L,\n", - " step=0.02,\n", - " value=L\n", - ")\n", - "\n", - "\n", - "# choose left or right FBD\n", - "div_rg_FBD = Div(text=\"Free-body diagram (FBD):\")\n", - "radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)\n", - "\n", - "\n", - "# choose axial force or not\n", - "div_cb_P = Div(text=f\"Axial force P={P} kN (applied)\")\n", - "checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])\n", - "\n", - "\n", - "# show values of forces and moments\n", - "div_forces = Div(width=DIV_B_FORCES, \n", - " text=sb.div_text_forces(P, P, Ry_l, Ry_r, \"No cross section analysed.\", 0, 0, 0))\n", - "\n", - "\n", - "# figures for the diagrams\n", - "options_diag = dict(\n", - " toolbar_location=None,\n", - " x_axis_label=\"Position [m]\",\n", - " plot_width=FIG_B_B,\n", - " x_range=fig_beam.x_range\n", - ")\n", - "fig_N = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Axial force\", \"@y kN\")],\n", - " y_axis_label=\"Axial force N [kN]\",\n", - " plot_height=int(FIG_H_B*0.8),\n", - " title=\"N V M Diagrams\")\n", - "fig_V = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Shear force\", \"@y kN\")],\n", - " y_axis_label=\"Shear force V [kN]\",\n", - " plot_height=int(FIG_H_B*0.8))\n", - "fig_M = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Bending moment\", \"@y kNm\")],\n", - " y_axis_label=\"Bending moment M [kNm]\",\n", - " plot_height=FIG_H_B)\n", - "fig_N.xaxis.visible = False\n", - "fig_V.xaxis.visible = False\n", - "\n", - "\n", - "# plot N V M\n", - "N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)\n", - "V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)\n", - "M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)\n", - "\n", - "# point that shows the position that it's analyzed\n", - "N_position = fig_N.circle('x', 'N', **pos_opt)\n", - "V_position = fig_V.circle('x', 'V', **pos_opt)\n", - "M_position = fig_M.circle('x', 'M', **pos_opt)\n", - "\n", - "# figures for the stresses and strains\n", - "FIG_B_ss = 200\n", - "FIG_H_ss = 200\n", - "options_stress_strain = dict(\n", - " toolbar_location=None,\n", - " y_axis_label=\"Height h [mm]\",\n", - " plot_width=FIG_B_ss,\n", - " plot_height=FIG_H_ss\n", - ")\n", - "fig_stress_N = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2099 [MPa]\")\n", - "fig_stress_N.yaxis.visible = False\n", - "fig_axial_strain = figure(**options_stress_strain,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2099 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_axial_strain.yaxis.visible = False\n", - "fig_stress_M = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending stress and centroid\",\n", - " y_range=fig_stress_N.y_range,\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2098 [MPa]\")\n", - "fig_stress_M.yaxis.visible = False\n", - "fig_bending_strain = figure(**options_stress_strain,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2098 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_bending_strain.yaxis.visible = False\n", - "fig_stress_V = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Shear stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU}\\u1d65 [MPa]\")\n", - "fig_stress_V.yaxis.visible = False\n", - "fig_stress_sigma = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress \\N{GREEK SMALL LETTER SIGMA} and neutral axis\",\n", - " y_range=fig_stress_N.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA} [MPa]\")\n", - "fig_stress_tau = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress \\N{GREEK SMALL LETTER TAU}\",\n", - " y_range=fig_stress_V.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU} [MPa]\")\n", - "\n", - "# plot stress N V M\n", - "discr_stress_strain = 10\n", - "scale_x = 25\n", - "y_discr = np.linspace(0, h, discr_stress_strain)\n", - "sigma_N = stst.compute_sigma_axial(y_discr, 0, A)\n", - "N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,\n", - " source_section_scheme, scale_x=scale_x/10)\n", - "sigma_M = stst.compute_sigma_bending(y_discr, 0, Iy, yG)\n", - "(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,\n", - " source_section_scheme, True, yG, scale_x=scale_x)\n", - "S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, yG)\n", - "tau_V = stst.compute_tau_shear(y_discr, 0, S_rect, Iy, b)\n", - "V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)\n", - "\n", - "# plot stress sigma and tau\n", - "sigma_total = sigma_M + sigma_N\n", - "(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,\n", - " source_section_scheme,True, yG, scale_x=scale_x)\n", - "tau_total = tau_V\n", - "tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,\n", - " source_section_scheme, scale_x=1)\n", - "\n", - "# plot strain N M\n", - "strain_axial = stst.compute_epsilon_axial(y_discr, sigma_N, E)\n", - "axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)\n", - "strain_bending = stst.compute_epsilon_bending(y_discr, sigma_M, E)\n", - "bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)\n", - "\n", - "\n", - "# figures for NVM\n", - "fig_NM_section = figure(**options_stress_strain,\n", - " title=\"N and M at position x\",\n", - " match_aspect=True)\n", - "fig_NM_section.axis.visible = False\n", - "fig_NM_section.grid.grid_line_alpha = 0\n", - "\n", - "fig_V_section = figure(**options_stress_strain,\n", - " title=\"V at position x\",\n", - " match_aspect=True)\n", - "fig_V_section.axis.visible = False\n", - "fig_V_section.grid.grid_line_alpha = 0\n", - "\n", - "# section with NVM\n", - "models.section_diagram(fig_NM_section)\n", - "models.section_diagram(fig_V_section)\n", - "\n", - "# NVM in section\n", - "section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')\n", - "section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')\n", - "(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)\n", - "\n", - "# NVM label in section\n", - "OFFSET_N = 1\n", - "label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[\"\"], text_color=\"red\", text_baseline='bottom')\n", - "label_M_section = fig_NM_section.text(x=[OFFSET_N*6], y=[-OFFSET_N*5], text=[\"\"], text_color=\"red\", text_baseline='top')\n", - "label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[0], text=[\"\"], text_color=\"red\", text_baseline='middle')\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now define the new figures, renderers and widgets:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# deflection of the beam\n", - "fig_beam.title.text = \"Simple supported beam with deflection under uniform load\"\n", - "fig_beam.ygrid.grid_line_alpha = 1\n", - "fig_beam.yaxis.visible = True\n", - "fig_beam.yaxis.axis_label = \"Deflection [mm]\"\n", - "\n", - "\n", - "# line 70-76 removed: uniform load (beam) and axial force (beam) in the simple beam\n", - "\n", - "\n", - "# Change the beam in the beam figure to gray and line width smaller and add new line\n", - "beam.glyph.line_width = 1\n", - "beam.glyph.line_color = \"gray\"\n", - "beam_defl = fig_beam.line(x=x_discr,\n", - " y=sb.compute_deflection_uniform_load(x_discr, q, L, Iy, E),\n", - " line_width=6, color='black')\n", - "\n", - "# FROM ABOVE: position point\n", - "beam_position = fig_beam.circle('x', 'y', **pos_opt)\n", - "\n", - "\n", - "# choose different elastic modulus\n", - "E_wood = 8e3 # [MPa]\n", - "E_concrete = 26e3 # [MPa]\n", - "E_ceramic = 300e3 # [MPa]\n", - "slider_elastic = Slider(\n", - " title=\"Change the elastic modulus [MPa]\",\n", - " start=E_wood,\n", - " end=E_ceramic,\n", - " step=1e3,\n", - " value=E,\n", - " margin=(5, 5, 0, 5)\n", - ")\n", - "\n", - "\n", - "# show values of E\n", - "div_E = Div(margin=(0, 5, 0, 5),\n", - " text=f\"\"\"\n", - "

\n", - " Ewood = {math.trunc(E_wood/1e3)} GPa; Econcrete = {math.trunc(E_concrete/1e3)} GPa
\n", - " Esteel = {math.trunc(E_steel/1e3)} GPa; Eceramic = {math.trunc(E_ceramic/1e3)} GPa

\n", - " \"\"\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Configure the logics:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "args_slider_pos = dict(source=source,\n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " s_M=source_M,\n", - " arr_head=scheme_M_head,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_slider_pos = f\"\"\"\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", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{models.implement_check_stateJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "\"\"\"\n", - "updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)\n", - "\n", - "\n", - "args_slider_b = dict(source=source,\n", - " s_b=source_beam,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " beam_defl=beam_defl)\n", - "code_change_b = f\"\"\"\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_deflection_beam(db, beam_defl)\n", - "\n", - "// emit the changes\n", - "source.change.emit()\n", - "\n", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_deflection_beamJS(discr_NVM)}\n", - "{sb.implement_compute_deflection_uniform_loadJS()}\n", - "\"\"\"\n", - "update_b = CustomJS(args=args_slider_b, code=code_change_b)\n", - "\n", - "\n", - "args_slider_h = dict(source=source,\n", - " s_b=source_beam,\n", - " s_ss=source_section_scheme,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " beam_defl=beam_defl)\n", - "code_change_h = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{js.implement_update_deflection_beamJS(discr_NVM)}\n", - "{sb.implement_compute_deflection_uniform_loadJS()}\n", - "\"\"\"\n", - "update_h = CustomJS(args=args_slider_h, code=code_change_h)\n", - "\n", - "\n", - "args_checkbox_P = dict(source=source,\n", - " s_M=source_M,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force, \n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r, \n", - " fN=scheme_N,\n", - " fV=scheme_V, \n", - " arr_head=scheme_M_head,\n", - " N_diag=N_diag,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_checkbox_P = f\"\"\"\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] = {P}*(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", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_compute_RxJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_update_N_diagramJS(discr_NVM)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)\n", - "\n", - "\n", - "args_radiogroup_FBD = dict(source=source, \n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M, \n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N, \n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_radiogroup_FBD = f\"\"\"\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", - "{models.implement_check_stateJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)\n", - "\n", - "\n", - "args_slider_q = dict(source=source,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M,\n", - " div_f=div_forces,\n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " V_diag=V_diag,\n", - " M_diag=M_diag,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section,\n", - " beam_defl=beam_defl)\n", - "code_slider_q = f\"\"\"\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", - "{js.implement_update_arrowJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_compute_Ry_lJS()}\n", - "{sb.implement_compute_Ry_rJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_update_V_diagramJS(discr_NVM)}\n", - "{sb.implement_update_M_diagramJS(discr_NVM)}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_u_loadJS(OFFSET_Q)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_deflection_beamJS(discr_NVM)}\n", - "{sb.implement_compute_deflection_uniform_loadJS()}\n", - "\"\"\"\n", - "update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)\n", - "\n", - "\n", - "args_slider_elastic = dict(source=source,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " centroid=centroid,\n", - " beam_defl=beam_defl)\n", - "# code_slider_elastic = \"\"\n", - "code_slider_elastic = f\"\"\"\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", - "{js.implement_linspaceJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{js.implement_update_deflection_beamJS(discr_NVM)}\n", - "{sb.implement_compute_deflection_uniform_loadJS()}\n", - "\"\"\"\n", - "update_slider_elastic = CustomJS(args=args_slider_elastic, code=code_slider_elastic)\n", - "\n", - "\n", - "# apply the logics\n", - "slider_b.js_on_change('value', update_b)\n", - "slider_h.js_on_change('value', update_h)\n", - "slider_position.js_on_change('value', updade_slider_pos)\n", - "checkbox_P.js_on_click(update_checkbox_P)\n", - "radiogroup_FBD.js_on_click(update_radiogroup_FBD)\n", - "slider_q.js_on_change('value', update_slider_q)\n", - "slider_elastic.js_on_change('value', update_slider_elastic)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Build the layout and show the figures. Note that the forces in the scheme are updated after moving the position of the point with the slider.\n", - "Note that the value of the forces and moments shown below represents the intensity, thus is always positive. The direction is given by the vector in the scheme." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, "outputs": [ { - "name": "stderr", - "output_type": "stream", - "text": [ - "libva error: vaGetDriverNameByIndex() failed with unknown libva error, driver_name = (null)\n" - ] + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n" + ] + }, + "metadata": {}, + "output_type": "display_data" }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "Opening in existing browser session.\n" - ] + "data": { + "application/javascript": [ + "(function(root) {\n", + " function embed_document(root) {\n", + " \n", + " const docs_json = 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\\n Ewood = 8 GPa; Econcrete = 26 GPa
\\n Esteel = 200 GPa; Eceramic = 300 GPa

\\n \"},\"id\":\"1906\",\"type\":\"Div\"},{\"attributes\":{\"data\":{\"x\":[-1.6666666666666667,0,0,-1.6666666666666667],\"y\":[-10,-10,10,10]},\"selected\":{\"id\":\"2113\"},\"selection_policy\":{\"id\":\"2112\"}},\"id\":\"1844\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1595\",\"type\":\"BasicTicker\"},{\"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\":\"1836\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"axis_label\":\"Height h [mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"2075\"},\"group\":null,\"major_label_policy\":{\"id\":\"2076\"},\"ticker\":{\"id\":\"1595\"}},\"id\":\"1594\",\"type\":\"LinearAxis\"},{\"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\"},\"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 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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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/A*Iy/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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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/A*Iy/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 -q*x / (24*E*Iy) * (L**3-2*L*x**2+x**3)*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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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)/c**2\\n }\\n const step = 2*c / (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(2*c)*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*(h**2/4-(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 N*1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/Iy*(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V*1000*S/(Iy*b_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\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/A*Iy/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/2*0.8\\n var a = b-lambda*c\\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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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/A*Iy/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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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 -q*x / (24*E*Iy) * (L**3-2*L*x**2+x**3)*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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/2*0.8\\n var a = b-lambda*c\\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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/2*(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return q*L/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return q*L/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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 -q*x / (24*E*Iy) * (L**3-2*L*x**2+x**3)*1e12\\n }\\n \\n 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\\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/E*100\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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 = 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"display_data" } ], "source": [ - "padding_layout = 10\n", - "layout1 = layout([\n", - " [column(row(column(fig_scheme,\n", - " row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout*3),\n", - " slider_b,\n", - " slider_h,\n", - " slider_position,\n", - " slider_q,\n", - " slider_elastic,\n", - " div_E,\n", - " div_rg_FBD,\n", - " radiogroup_FBD,\n", - " div_cb_P,\n", - " checkbox_P))),\n", - " column(fig_beam,\n", - " Spacer(height=padding_layout),\n", - " fig_N,\n", - " fig_V,\n", - " fig_M)),\n", - " row(column(\n", - " row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_stress_sigma),\n", - " 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),\n", - " ))\n", - " ),\n", - " ],\n", - "])\n", - "\n", - "show(layout1)" + "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)" ] } ], "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": 2 + "nbformat_minor": 4 } diff --git a/Simple Beam DEMOs/sb_diagrams.ipynb b/Simple Beam DEMOs/sb_diagrams.ipynb index da296ea..52caf7f 100644 --- a/Simple Beam DEMOs/sb_diagrams.ipynb +++ b/Simple Beam DEMOs/sb_diagrams.ipynb @@ -1,722 +1,477 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple beam - Diagrams\n", "In this third notebook, the axial N, shear V and bending moment M diagrams are presented. 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\\n\"+\n \"

\\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 \"

\\n\"+\n \"
    \\n\"+\n \"
  • re-rerun `output_notebook()` to attempt to load from CDN again, or
    • \\n\"+\n \"
  • use INLINE resources instead, as so:
    • \\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\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 bokeh.layouts import layout, column, row\n", - "from bokeh.models.annotations import Label, Arrow\n", - "from bokeh.models.arrow_heads import VeeHead\n", - "from bokeh.models import Div, CustomJS, Slider, Spacer, Text\n", - "from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup\n", - "from bokeh.plotting import figure, show, ColumnDataSource\n", - "from bokeh.io import output_notebook\n", "from cienpy import simplebeam as sb\n", - "from cienpy import rectangular_section as beam_section\n", - "from cienpy import models\n", - "from cienpy import javascriptcodes as js\n", - "\n", - "# output_notebook()" + "from cienpy import rectangular_section as beam_section" ] }, { "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": 8, + "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)\n", - "\n", - "\n", - "# constants for the visualisation\n", - "SCALE = 10\n", - "OFFSET_Q = q\n", - "MAX_B = 3*b\n", - "MAX_H = 3*h\n", - "MAX_Q = q/4*5\n", - "\n", - "# store the values in a specific format\n", - "data_beam = dict(\n", - " x=[0, L],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_beam = dict(\n", - " x=[0, L*SCALE],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_q = dict(\n", - " x=[0, 0, L*SCALE, L*SCALE],\n", - " y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],\n", - " x_fade=[0, 0, L*SCALE, L*SCALE]\n", - ")\n", - "\n", - "initial_position = L\n", - "initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC\n", - "initial_FBD = 0 # right=0 left=1\n", - "data = dict( # stores every useful single variable\n", - " state=[initial_state], \n", - " FBD=[initial_FBD],\n", - " SCALE=[SCALE],\n", - " L=[L],\n", - " b=[b],\n", - " h=[h],\n", - " A=[A],\n", - " Iy=[Iy],\n", - " Iz=[Iz],\n", - " P=[P],\n", - " x=[initial_position],\n", - " y=[0],\n", - " q=[q],\n", - " Rx=[Rx],\n", - " Ry_l=[Ry_l],\n", - " Ry_r=[Ry_r],\n", - " N=[N],\n", - " V=[V],\n", - " M=[M],\n", - " xF=[L*SCALE]\n", - ")\n", - "\n", - "source_beam = ColumnDataSource(data_beam)\n", - "source_scheme_beam = ColumnDataSource(data_scheme_beam)\n", - "source_scheme_q = ColumnDataSource(data_scheme_q)\n", - "source = ColumnDataSource(data)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create the figures, the plots and the widgets (same of Notebook 2 - Actions):" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "FIG_H_B = 200 # height figure beam\n", - "FIG_B_B = 700 # width figure beam\n", - "FIG_H_S = FIG_H_B # height figure scheme\n", - "FIG_B_S = FIG_B_B # width figure scheme\n", - "FIG_H_SEC = 600 # height figure section\n", - "\n", - "options = dict(\n", - " toolbar_location=None\n", - ")\n", - "\n", - "# figure for the beam\n", - "paddingx = 0.2*L\n", - "int_x_b = (0-paddingx, L+paddingx)\n", - "int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)\n", - "fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,\n", - " f_h=FIG_H_B, f_b=FIG_B_B)\n", - "\n", - "\n", - "# figure for the cross-section\n", - "fig_section = sb.define_fig_section(MAX_B, MAX_H*0.8, options, FIG_H_SEC)\n", - "\n", - "\n", - "# beam\n", - "(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,\n", - " ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)\n", - "\n", - "\n", - "# section\n", - "section = beam_section.draw_section(fig_section, b, h)\n", - "\n", - "\n", - "# show mechanical parameters\n", - "div_geo = Div(text=beam_section.div_text_geo(round(h), round(b), round(L),\n", - " \"{:.2e}\".format(A),\n", - " \"{:.2e}\".format(Iy),\n", - " \"{:.2e}\".format(Iz)))\n", - "\n", - "\n", - "# change geometry\n", - "slider_b = Slider(\n", - " title=\"Change the width b [mm]\",\n", - " start=10,\n", - " end=MAX_B,\n", - " step=10,\n", - " value=b\n", - ")\n", - "slider_h = Slider(\n", - " title=\"Change the height h [mm]\",\n", - " start=20,\n", - " end=MAX_H,\n", - " step=20,\n", - " value=h\n", - ")\n", - "\n", - "# reference system\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis\n", - "fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=[\"y\"], text_color='gray', text_baseline='middle', angle=math.pi/2)\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis\n", - "fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=[\"z\"], text_color='gray', text_align='right', text_baseline='middle')\n", - "\n", - "\n", - "# figure for the forces and moments\n", - "fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)\n", - "\n", - "\n", - "# uniform load (beam)\n", - "u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE], width=L, height=q/SCALE,\n", - " fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)\n", - "label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE], text=[\"q\"], text_color=\"blue\")\n", - "\n", - "\n", - "# axial force (beam)\n", - "axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')\n", - "label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=[\"P\"], text_color=\"green\")\n", - "\n", - "\n", - "# position point\n", - "pos_opt = dict(\n", - " source=source,\n", - " size=10,\n", - " fill_alpha=0.5,\n", - " fill_color=\"magenta\",\n", - " color=\"magenta\",\n", - " alpha=0.5\n", - ")\n", - "beam_position = fig_beam.circle('x', 'y', **pos_opt)\n", - "forces_position = fig_scheme.circle('xF', 'y', **pos_opt)\n", - "\n", - "\n", - "# beam (scheme)\n", - "scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')\n", - "scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)\n", - "# uniform load (scheme)\n", - "scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',\n", - " fill_alpha=0.3, alpha=0.3)\n", - "scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',\n", - " color='navy', fill_alpha=0.3, alpha=0.3)\n", - "# axial force (scheme)\n", - "scheme_axial_force = models.force_vector(fig_scheme, P, L*SCALE+P, L*SCALE, 0, 0, 'green')\n", - "# Reactions (scheme)\n", - "scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -Ry_r, 0, 'orange')\n", - "scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')\n", - "scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')\n", - "# force N\n", - "scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# force V\n", - "scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# moment M\n", - "(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)\n", - "\n", - "\n", - "# change the uniform load q\n", - "slider_q = Slider(\n", - " title=\"Change the uniform load q [kN/m]\",\n", - " start=0.1,\n", - " end=MAX_Q,\n", - " step=0.1,\n", - " value=q\n", - ")\n", - "\n", - "\n", - "# choose position of interest\n", - "slider_position = Slider(\n", - " title=\"Change the position x along the beam [m]\",\n", - " start=0,\n", - " end=L,\n", - " step=0.02,\n", - " value=L\n", - ")\n", - "\n", - "\n", - "# choose left or right FBD\n", - "div_rg_FBD = Div(text=\"Free-body diagram (FBD):\")\n", - "radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)\n", - "\n", - "\n", - "# choose axial force or not\n", - "div_cb_P = Div(text=f\"Axial force P={P} kN (applied)\")\n", - "checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])\n", - "\n", - "\n", - "# show values of forces and moments\n", - "div_forces = Div(text=sb.div_text_forces(P, P, Ry_l, Ry_r, \"No cross section analysed.\", 0, 0, 0))" + "Ry_r = sb.compute_Ry_r(q, L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now define the new figures, renderers and widgets:" + "Run the complex code for the interactive visualisation:" ] }, { "cell_type": "code", - 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Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
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\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
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h [mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"1503\"},\"group\":null,\"major_label_policy\":{\"id\":\"1504\"},\"ticker\":{\"id\":\"1079\"}},\"id\":\"1055\",\"type\":\"LinearAxis\"},{\"attributes\":{\"source\":{\"id\":\"1003\"}},\"id\":\"1394\",\"type\":\"CDSView\"},{\"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\":{},\"id\":\"1452\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"source\":{\"id\":\"1006\"}},\"id\":\"1400\",\"type\":\"CDSView\"},{\"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\":\"N\"}},\"id\":\"1397\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1453\",\"type\":\"AllLabels\"},{\"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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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)/c**2\\n }\\n const step = 2*c / (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(2*c)*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\":0.2},\"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\":\"N\"}},\"id\":\"1398\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1455\",\"type\":\"BasicTickFormatter\"},{\"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\":{\"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\":{},\"id\":\"1456\",\"type\":\"AllLabels\"},{\"attributes\":{\"source\":{\"id\":\"1006\"}},\"id\":\"1412\",\"type\":\"CDSView\"},{\"attributes\":{\"coordinates\":null,\"group\":null},\"id\":\"1434\",\"type\":\"Title\"},{\"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 = 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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**3/12\\n }\\n \\n \"},\"id\":\"1415\",\"type\":\"CustomJS\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1003\"},\"glyph\":{\"id\":\"1083\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1085\"},\"nonselection_glyph\":{\"id\":\"1084\"},\"view\":{\"id\":\"1087\"}},\"id\":\"1086\",\"type\":\"GlyphRenderer\"},{\"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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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,\"group\":null},\"id\":\"1436\",\"type\":\"Title\"},{\"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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/2*(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return q*L/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return q*L/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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\":{\"data\":{},\"selected\":{\"id\":\"1523\"},\"selection_policy\":{\"id\":\"1522\"}},\"id\":\"1457\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0.1},\"height\":{\"value\":480.0},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":300},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1075\",\"type\":\"Rect\"},{\"attributes\":{\"width\":10},\"id\":\"1419\",\"type\":\"Spacer\"},{\"attributes\":{},\"id\":\"1049\",\"type\":\"LinearScale\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Cross-section of the 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b 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Geometrical and mechanical parameters:

\\n h = 200 mm
\\n b = 100 mm
\\n L = 6 m
\\n A = 2.00e+04 mm2
\\n Iy = 6.67e+07 mm4
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"display_data" + } + ], "source": [ - "# figures for the diagrams\n", - "options_diag = dict(\n", - " toolbar_location=None,\n", - " x_axis_label=\"Position [m]\",\n", - " plot_width=FIG_B_B,\n", - " x_range=fig_beam.x_range\n", - ")\n", - "fig_N = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Axial force\", \"@y kN\")],\n", - " y_axis_label=\"Axial force N [kN]\",\n", - " plot_height=int(FIG_H_B*0.8),\n", - " title=\"N V M Diagrams\")\n", - "fig_V = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Shear force\", \"@y kN\")],\n", - " y_axis_label=\"Shear force V [kN]\",\n", - " plot_height=int(FIG_H_B*0.8))\n", - "fig_M = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Bending moment\", \"@y kNm\")],\n", - " y_axis_label=\"Bending moment M [kNm]\",\n", - " plot_height=FIG_H_B)\n", - "fig_N.xaxis.visible = False\n", - "fig_V.xaxis.visible = False\n", - "\n", - "\n", - "# plot N V M\n", - "N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)\n", - "V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)\n", - "M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)\n", - "\n", - "# point that shows the position that it's analyzed\n", - "N_position = fig_N.circle('x', 'N', **pos_opt)\n", - "V_position = fig_V.circle('x', 'V', **pos_opt)\n", - "M_position = fig_M.circle('x', 'M', **pos_opt)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Configure the logics:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "args_slider_pos = dict(source=source,\n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " s_M=source_M,\n", - " arr_head=scheme_M_head)\n", - "code_slider_pos = f\"\"\"\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", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{models.implement_check_stateJS()}\n", - "\"\"\"\n", - "updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)\n", - "\n", - "\n", - "args_slider_b_h = dict(source=source,\n", - " s_b=source_beam,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r)\n", - "code_change_b = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "\"\"\"\n", - "update_b = CustomJS(args=args_slider_b_h, code=code_change_b)\n", - "\n", - "\n", - "code_change_h = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "\"\"\"\n", - "update_h = CustomJS(args=args_slider_b_h, code=code_change_h)\n", - "\n", - "\n", - "args_checkbox_P = dict(source=source,\n", - " s_M=source_M,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force, \n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r, \n", - " fN=scheme_N,\n", - " fV=scheme_V, \n", - " arr_head=scheme_M_head,\n", - " N_diag=N_diag)\n", - "code_checkbox_P = f\"\"\"\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] = {P}*(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", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_compute_RxJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_update_N_diagramJS(discr_NVM)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)\n", - "\n", - "\n", - "args_radiogroup_FBD = dict(source=source, \n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M, \n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N, \n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head)\n", - "code_radiogroup_FBD = f\"\"\"\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", - "{models.implement_check_stateJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)\n", - "\n", - "\n", - "args_slider_q = dict(source=source,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M,\n", - " div_f=div_forces,\n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " V_diag=V_diag,\n", - " M_diag=M_diag)\n", - "code_slider_q = f\"\"\"\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", - "{js.implement_update_arrowJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_compute_Ry_lJS()}\n", - "{sb.implement_compute_Ry_rJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_update_V_diagramJS(discr_NVM)}\n", - "{sb.implement_update_M_diagramJS(discr_NVM)}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_u_loadJS(OFFSET_Q)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)\n", - "\n", - "\n", - "# apply the logics\n", - "slider_b.js_on_change('value', update_b)\n", - "slider_h.js_on_change('value', update_h)\n", - "slider_position.js_on_change('value', updade_slider_pos)\n", - "checkbox_P.js_on_click(update_checkbox_P)\n", - "radiogroup_FBD.js_on_click(update_radiogroup_FBD)\n", - "slider_q.js_on_change('value', update_slider_q)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Build the layout and show the figures. Note that the forces in the scheme are updated after moving the position of the point with the slider.\n", - "Note that the value of the forces and moments shown below represents the intensity, thus is always positive. The direction is given by the vector in the scheme." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "padding_layout = 10\n", - "layout1 = layout([\n", - " [column(row(column(fig_scheme,\n", - " row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout),\n", - " slider_b,\n", - " slider_h,\n", - " div_geo,\n", - " Spacer(height=padding_layout),\n", - " slider_position,\n", - " slider_q,\n", - " div_rg_FBD,\n", - " radiogroup_FBD,\n", - " div_cb_P,\n", - " checkbox_P))),\n", - " column(fig_beam,\n", - " Spacer(height=padding_layout),\n", - " fig_N,\n", - " fig_V,\n", - " fig_M,\n", - " div_forces))\n", - " )],\n", - "])\n", - "\n", - "show(layout1)" + "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)" ] } ], "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": 2 + "nbformat_minor": 4 } diff --git a/Simple Beam DEMOs/sb_geo.ipynb b/Simple Beam DEMOs/sb_geo.ipynb index b8a0d09..0e9d96b 100644 --- a/Simple Beam DEMOs/sb_geo.ipynb +++ b/Simple Beam DEMOs/sb_geo.ipynb @@ -1,346 +1,460 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple beam - Geometry\n", "In this first notebook, the geometry of a simple beam with rectangular section is explored. The correlated mechanical parameters are also visualized." ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
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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_geo\n", "import math\n", "import numpy as np \n", - "from bokeh.layouts import layout, column\n", - "from bokeh.models import Div, CustomJS, Slider, Spacer\n", - "from bokeh.models.tickers import SingleIntervalTicker\n", - "from bokeh.plotting import figure, show, ColumnDataSource\n", - "from bokeh.io import output_notebook\n", "from cienpy import simplebeam as sb\n", - "from cienpy import rectangular_section as beam_section\n", - "from cienpy import models\n", - "\n", - "# output_notebook()" + "from cienpy import rectangular_section as beam_section" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the geometry:" ] }, { "cell_type": "code", - "execution_count": 7, + "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\n", - "\n", - "# constants for the visualisation\n", - "MAX_B = 3*b\n", - "MAX_H = 3*h\n", - "\n", - "# store the values in a specific format\n", - "data_beam = dict(\n", - " x=[0, L],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "initial_position = L\n", - "data = dict( # stores every useful single variable\n", - " L=[L],\n", - " b=[b],\n", - " h=[h],\n", - " A=[A],\n", - " Iy=[Iy],\n", - " Iz=[Iz],\n", - " x=[initial_position],\n", - " y=[0]\n", - ")\n", - "\n", - "source_beam = ColumnDataSource(data_beam)\n", - "source = ColumnDataSource(data)" + "Iz = beam_section.compute_inertia_z(b, h) # [mm4] weak axis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now define the new figures, renderers and widgets:" + "Run the complex code for the interactive visualisation:" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
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{\"048788ba-8a20-49fa-bd4a-3f0abfb09c19\":{\"defs\":[],\"roots\":{\"references\":[{\"attributes\":{\"children\":[{\"id\":\"1142\"},{\"id\":\"1143\"}]},\"id\":\"1144\",\"type\":\"Column\"},{\"attributes\":{\"children\":[{\"id\":\"1139\"},{\"id\":\"1107\"},{\"id\":\"1105\"},{\"id\":\"1106\"},{\"id\":\"1140\"},{\"id\":\"1104\"}]},\"id\":\"1141\",\"type\":\"Column\"},{\"attributes\":{},\"id\":\"1160\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"children\":[{\"id\":\"1005\"}]},\"id\":\"1142\",\"type\":\"Row\"},{\"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\":{\"data\":{},\"selected\":{\"id\":\"1170\"},\"selection_policy\":{\"id\":\"1169\"}},\"id\":\"1153\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1161\",\"type\":\"Selection\"},{\"attributes\":{\"children\":[{\"id\":\"1038\"},{\"id\":\"1138\"},{\"id\":\"1141\"}]},\"id\":\"1143\",\"type\":\"Row\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.2},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0.2},\"height\":{\"value\":600},\"line_alpha\":{\"value\":0.2},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":300},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1074\",\"type\":\"Rect\"},{\"attributes\":{},\"id\":\"1177\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1014\",\"type\":\"LinearScale\"},{\"attributes\":{\"line_width\":6,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1081\",\"type\":\"Line\"},{\"attributes\":{\"axis\":{\"id\":\"1016\"},\"coordinates\":null,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1019\",\"type\":\"Grid\"},{\"attributes\":{\"interval\":50},\"id\":\"1077\",\"type\":\"SingleIntervalTicker\"},{\"attributes\":{},\"id\":\"1178\",\"type\":\"Selection\"},{\"attributes\":{\"below\":[{\"id\":\"1049\"}],\"center\":[{\"id\":\"1052\"},{\"id\":\"1056\"},{\"id\":\"1118\"},{\"id\":\"1127\"}],\"height\":540,\"left\":[{\"id\":\"1053\"}],\"match_aspect\":true,\"renderers\":[{\"id\":\"1075\"},{\"id\":\"1102\"},{\"id\":\"1124\"},{\"id\":\"1133\"}],\"title\":{\"id\":\"1039\"},\"toolbar\":{\"id\":\"1064\"},\"toolbar_location\":null,\"width\":300,\"x_range\":{\"id\":\"1041\"},\"x_scale\":{\"id\":\"1045\"},\"y_range\":{\"id\":\"1043\"},\"y_scale\":{\"id\":\"1047\"}},\"id\":\"1038\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0.1},\"height\":{\"value\":600},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":300},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1073\",\"type\":\"Rect\"},{\"attributes\":{},\"id\":\"1017\",\"type\":\"BasicTicker\"},{\"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\":{\"source\":{\"id\":\"1071\"}},\"id\":\"1076\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.1,\"line_width\":6,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1082\",\"type\":\"Line\"},{\"attributes\":{\"source\":{\"id\":\"1003\"}},\"id\":\"1085\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1162\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"start\":-1},\"id\":\"1010\",\"type\":\"Range1d\"},{\"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\":\"1163\",\"type\":\"Selection\"},{\"attributes\":{\"data\":{\"A\":[20000],\"Iy\":[66666666.666666664],\"Iz\":[16666666.666666666],\"L\":[6],\"b\":[100],\"h\":[200],\"x\":[6],\"y\":[0]},\"selected\":{\"id\":\"1185\"},\"selection_policy\":{\"id\":\"1184\"}},\"id\":\"1004\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1012\",\"type\":\"LinearScale\"},{\"attributes\":{\"fill_color\":{\"value\":\"white\"},\"radius\":{\"value\":0.15},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1093\",\"type\":\"Circle\"},{\"attributes\":{\"below\":[{\"id\":\"1016\"}],\"center\":[{\"id\":\"1019\"},{\"id\":\"1023\"},{\"id\":\"1109\"}],\"height\":200,\"left\":[{\"id\":\"1020\"}],\"renderers\":[{\"id\":\"1084\"},{\"id\":\"1090\"},{\"id\":\"1096\"},{\"id\":\"1115\"}],\"title\":{\"id\":\"1006\"},\"toolbar\":{\"id\":\"1031\"},\"toolbar_location\":null,\"width\":700,\"x_range\":{\"id\":\"1008\"},\"x_scale\":{\"id\":\"1012\"},\"y_range\":{\"id\":\"1010\"},\"y_scale\":{\"id\":\"1014\"}},\"id\":\"1005\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"angle\":{\"value\":1.5707963267948966},\"text_alpha\":{\"value\":0.2},\"text_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[m]\",\"coordinates\":null,\"formatter\":{\"id\":\"1151\"},\"group\":null,\"major_label_policy\":{\"id\":\"1152\"},\"ticker\":{\"id\":\"1017\"}},\"id\":\"1016\",\"type\":\"LinearAxis\"},{\"attributes\":{\"line_alpha\":0.2,\"line_width\":6,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1083\",\"type\":\"Line\"},{\"attributes\":{\"end\":7.2,\"start\":-1.2000000000000002},\"id\":\"1008\",\"type\":\"Range1d\"},{\"attributes\":{\"source\":{\"id\":\"1098\"}},\"id\":\"1103\",\"type\":\"CDSView\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Simple supported beam\"},\"id\":\"1006\",\"type\":\"Title\"},{\"attributes\":{\"fill_color\":\"white\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1087\",\"type\":\"Patch\"},{\"attributes\":{},\"id\":\"1029\",\"type\":\"HelpTool\"},{\"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\":{},\"id\":\"1021\",\"type\":\"BasicTicker\"},{\"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\":{\"coordinates\":null,\"formatter\":{\"id\":\"1148\"},\"group\":null,\"major_label_policy\":{\"id\":\"1149\"},\"ticker\":{\"id\":\"1021\"},\"visible\":false},\"id\":\"1020\",\"type\":\"LinearAxis\"},{\"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\":{\"axis\":{\"id\":\"1020\"},\"coordinates\":null,\"dimension\":1,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1023\",\"type\":\"Grid\"},{\"attributes\":{\"source\":{\"id\":\"1086\"}},\"id\":\"1091\",\"type\":\"CDSView\"},{\"attributes\":{\"data\":{\"x\":[0],\"y\":[0]},\"selected\":{\"id\":\"1174\"},\"selection_policy\":{\"id\":\"1173\"}},\"id\":\"1098\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1045\",\"type\":\"LinearScale\"},{\"attributes\":{\"data\":{\"x\":[6],\"y\":[-0.15]},\"selected\":{\"id\":\"1165\"},\"selection_policy\":{\"id\":\"1164\"}},\"id\":\"1092\",\"type\":\"ColumnDataSource\"},{\"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\":{\"data\":{\"x\":[0,6],\"y\":[0,0]},\"selected\":{\"id\":\"1161\"},\"selection_policy\":{\"id\":\"1160\"}},\"id\":\"1003\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1047\",\"type\":\"LinearScale\"},{\"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\":{},\"id\":\"1154\",\"type\":\"BasicTickFormatter\"},{\"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\":\"1024\",\"type\":\"PanTool\"},{\"attributes\":{\"overlay\":{\"id\":\"1030\"}},\"id\":\"1026\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"fill_color\":{\"value\":\"gray\"},\"line_color\":{\"value\":\"gray\"},\"size\":{\"value\":4.114506654314834}},\"id\":\"1108\",\"type\":\"VeeHead\"},{\"attributes\":{},\"id\":\"1164\",\"type\":\"UnionRenderers\"},{\"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\":{},\"id\":\"1155\",\"type\":\"AllLabels\"},{\"attributes\":{\"source\":{\"id\":\"1092\"}},\"id\":\"1097\",\"type\":\"CDSView\"},{\"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\":{},\"id\":\"1057\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"1165\",\"type\":\"Selection\"},{\"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\":{},\"id\":\"1156\",\"type\":\"BasicTickFormatter\"},{\"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\":{\"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\":{\"height\":300,\"text\":\"

Geometrical and mechanical parameters

\\n h = 200 mm
\\n b = 100 mm
\\n L = 6 m
\\n A = 2.00e+04 mm2
\\n Iy = 6.67e+07 mm4
\\n Iz = 1.67e+07 mm4\",\"width\":300},\"id\":\"1104\",\"type\":\"Div\"},{\"attributes\":{},\"id\":\"1027\",\"type\":\"SaveTool\"},{\"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\":{},\"id\":\"1028\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1157\",\"type\":\"AllLabels\"},{\"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\":{},\"id\":\"1180\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1025\",\"type\":\"WheelZoomTool\"},{\"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\":\"1181\",\"type\":\"Selection\"},{\"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\":{\"angle\":{\"value\":1.5707963267948966},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1121\",\"type\":\"Text\"},{\"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\":{\"axis\":{\"id\":\"1053\"},\"coordinates\":null,\"dimension\":1,\"group\":null,\"ticker\":null},\"id\":\"1056\",\"type\":\"Grid\"},{\"attributes\":{\"source\":{\"id\":\"1120\"}},\"id\":\"1125\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1182\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"data\":{\"text\":[\"x axis\"],\"x\":[6.4],\"y\":[0.1]},\"selected\":{\"id\":\"1167\"},\"selection_policy\":{\"id\":\"1166\"}},\"id\":\"1111\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1114\",\"type\":\"Text\"},{\"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\":{\"data\":{\"text\":[\"y axis\"],\"x\":[0],\"y\":[136.0]},\"selected\":{\"id\":\"1176\"},\"selection_policy\":{\"id\":\"1175\"}},\"id\":\"1120\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"1181\"},\"selection_policy\":{\"id\":\"1180\"}},\"id\":\"1158\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1183\",\"type\":\"Selection\"},{\"attributes\":{\"source\":{\"id\":\"1129\"}},\"id\":\"1134\",\"type\":\"CDSView\"},{\"attributes\":{\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1112\",\"type\":\"Text\"},{\"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\":{\"data\":{},\"selected\":{\"id\":\"1183\"},\"selection_policy\":{\"id\":\"1182\"}},\"id\":\"1159\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1166\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"text_align\":{\"value\":\"right\"},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1130\",\"type\":\"Text\"},{\"attributes\":{\"fill_color\":{\"value\":\"gray\"},\"line_color\":{\"value\":\"gray\"},\"size\":{\"value\":15.380572041353537}},\"id\":\"1117\",\"type\":\"VeeHead\"},{\"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\":\"1167\",\"type\":\"Selection\"},{\"attributes\":{\"tools\":[{\"id\":\"1024\"},{\"id\":\"1025\"},{\"id\":\"1026\"},{\"id\":\"1027\"},{\"id\":\"1028\"},{\"id\":\"1029\"}]},\"id\":\"1031\",\"type\":\"Toolbar\"},{\"attributes\":{\"height\":50},\"id\":\"1139\",\"type\":\"Spacer\"},{\"attributes\":{},\"id\":\"1148\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"data\":{\"text\":[\"z axis\"],\"x\":[-88.0],\"y\":[0]},\"selected\":{\"id\":\"1178\"},\"selection_policy\":{\"id\":\"1177\"}},\"id\":\"1129\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1041\",\"type\":\"DataRange1d\"},{\"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\":\"1149\",\"type\":\"AllLabels\"},{\"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(f*10)/10\\n const b = Math.round(data_s['b'])\\n const h = Math.round(data_s['h'])\\n const A = b*h\\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 = \\\"

Geometrical and mechanical parameters:

h = \\\"+h+\\n \\\" mm
b = \\\"+b+\\n \\\" mm
L = \\\"+L+\\n \\\" m
A = \\\"+A.toExponential()+\\n \\\" mm2
Iy = \\\"+Iy.toExponential()+\\n \\\" mm4
Iz = \\\"+Iz.toExponential()+\\n \\\" mm4\\\"\\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\":{\"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 = b*h\\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 = \\\"

Geometrical and mechanical parameters:

h = \\\"+h+\\n \\\" mm
b = \\\"+b+\\n \\\" mm
L = \\\"+L+\\n \\\" m
A = \\\"+A.toExponential()+\\n \\\" mm2
Iy = \\\"+Iy.toExponential()+\\n \\\" mm4
Iz = \\\"+Iz.toExponential()+\\n \\\" mm4\\\"\\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\":{\"text_alpha\":{\"value\":0.1},\"text_color\":{\"value\":\"gray\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1113\",\"type\":\"Text\"},{\"attributes\":{\"fill_alpha\":{\"value\":0},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0},\"height\":{\"value\":600},\"line_alpha\":{\"value\":0},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":300},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1072\",\"type\":\"Rect\"},{\"attributes\":{},\"id\":\"1151\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"data\":{\"x\":[0],\"y\":[0]},\"selected\":{\"id\":\"1172\"},\"selection_policy\":{\"id\":\"1171\"}},\"id\":\"1071\",\"type\":\"ColumnDataSource\"},{\"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 = b*h\\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 = \\\"

Geometrical and mechanical parameters:

h = \\\"+h+\\n \\\" mm
b = \\\"+b+\\n \\\" mm
L = \\\"+L+\\n \\\" m
A = \\\"+A.toExponential()+\\n \\\" mm2
Iy = \\\"+Iy.toExponential()+\\n \\\" mm4
Iz = \\\"+Iz.toExponential()+\\n \\\" mm4\\\"\\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\":{},\"id\":\"1152\",\"type\":\"AllLabels\"},{\"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\":{},\"id\":\"1043\",\"type\":\"DataRange1d\"},{\"attributes\":{\"source\":{\"id\":\"1111\"}},\"id\":\"1116\",\"type\":\"CDSView\"},{\"attributes\":{\"height\":50},\"id\":\"1140\",\"type\":\"Spacer\"},{\"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\":{\"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\":{\"overlay\":{\"id\":\"1063\"}},\"id\":\"1059\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1003\"},\"glyph\":{\"id\":\"1081\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1083\"},\"nonselection_glyph\":{\"id\":\"1082\"},\"view\":{\"id\":\"1085\"}},\"id\":\"1084\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"tools\":[{\"id\":\"1057\"},{\"id\":\"1058\"},{\"id\":\"1059\"},{\"id\":\"1060\"},{\"id\":\"1061\"},{\"id\":\"1062\"}]},\"id\":\"1064\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"1058\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1061\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1169\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1170\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1171\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Cross-section of the beam\"},\"id\":\"1039\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"1172\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1060\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1062\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1173\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1174\",\"type\":\"Selection\"},{\"attributes\":{\"axis_label\":\"Width b [mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"1156\"},\"group\":null,\"major_label_policy\":{\"id\":\"1157\"},\"ticker\":{\"id\":\"1077\"}},\"id\":\"1049\",\"type\":\"LinearAxis\"},{\"attributes\":{\"axis\":{\"id\":\"1049\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1052\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1184\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1185\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1175\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1176\",\"type\":\"Selection\"}],\"root_ids\":[\"1144\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n", + " const render_items = [{\"docid\":\"048788ba-8a20-49fa-bd4a-3f0abfb09c19\",\"root_ids\":[\"1144\"],\"roots\":{\"1144\":\"ebc97ded-dd80-4662-9a18-1cf56cf92025\"}}];\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": [ - "FIG_H_B = 200 # height figure beam\n", - "FIG_B_B = 700 # width figure beam\n", - "FIG_H_SEC = 600 # height figure section\n", - "\n", - "paddingx = 0.2*L\n", - "options = dict(\n", - " toolbar_location=None\n", - ")\n", - "\n", - "fig_beam = figure(**options,\n", - " x_axis_label=\"Position [m]\",\n", - " plot_height=200,\n", - " plot_width=700,\n", - " x_range=(0-paddingx, L+paddingx),\n", - " y_range=(-1, 1),\n", - " title=\"Simple supported beam\"\n", - ")\n", - "fig_beam.xgrid.grid_line_alpha = 0\n", - "fig_beam.ygrid.grid_line_alpha = 0\n", - "fig_beam.yaxis.visible = False\n", - "\n", - "fig_section = figure(**options,\n", - " x_axis_label=\"Width b [mm]\",\n", - " y_axis_label=\"Height h [mm]\",\n", - " plot_height=int(MAX_H*0.9),\n", - " plot_width=int(MAX_B),\n", - " match_aspect=True,\n", - " title=\"Cross-section of the beam\"\n", - ")\n", - "fig_section.rect([0], [0], width=MAX_B, height=MAX_H, alpha=0, fill_alpha=0) # transparent rect\n", - "fig_section.axis.ticker = SingleIntervalTicker(interval=50, num_minor_ticks=5)\n", - "\n", - "\n", - "# beam\n", - "beam = fig_beam.line('x', 'y', source=source_beam, line_width=6, color='black')\n", - "b_supp = 0.3\n", - "supp_opt = dict(\n", - " fill_color='white',\n", - " line_color='black'\n", - ")\n", - "support_l = fig_beam.patch([0, b_supp/2, -b_supp/2],\n", - " [0, -b_supp/2*math.sqrt(3), -b_supp/2*math.sqrt(3)],\n", - " **supp_opt)\n", - "support_r = fig_beam.circle([L], [-b_supp/2], radius=b_supp/2, **supp_opt)\n", - "\n", - "\n", - "# section\n", - "section = fig_section.rect([0], [0], width=b, height=h, fill_color='white',\n", - " color='black', line_width=3, hatch_pattern='/', hatch_color='black')\n", - "\n", - "\n", - "# show mechanical parameters\n", - "div_text = lambda h, b, L, A, Iy, Iz : f\"\"\"

Geometrical and mechanical parameters:

\n", - " h = {round(h)} mm
\n", - " b = {round(b)} mm
\n", - " L = {round(L)} m
\n", - " A = {\"{:.2e}\".format(A)} mm2
\n", - " Iy = {\"{:.2e}\".format(Iy)} mm4
\n", - " Iz = {\"{:.2e}\".format(Iz)} mm4\"\"\"\n", - "\n", - "div = Div(\n", - " text=div_text(h, b, L, A, Iy, Iz),\n", - " width=300,\n", - " height=300\n", - ")\n", - "\n", - "\n", - "# change geometry\n", - "slider_b = Slider(\n", - " title=\"Change the width b [mm]\",\n", - " start=10,\n", - " end=MAX_B,\n", - " step=10,\n", - " value=b\n", - ")\n", - "slider_h = Slider(\n", - " title=\"Change the height h [mm]\",\n", - " start=20,\n", - " end=MAX_H,\n", - " step=20,\n", - " value=h\n", - ")\n", - "slider_L = Slider(\n", - " title=\"Change the length L [m]\",\n", - " start=1,\n", - " end=L+1,\n", - " step=0.1,\n", - " value=L\n", - ")\n", - "\n", - "# reference system\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "x_axis_arrow = models.force_vector(fig_beam, axis_arrow_length, L, L+axis_arrow_length, 0, 0, 'gray')\n", - "x_axis_label = fig_beam.text(x=[L+axis_arrow_length/2], y=[0.1], text=[\"x axis\"], text_color='gray', text_baseline='bottom')\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis\n", - "fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=[\"y axis\"], text_color='gray', text_baseline='middle', angle=math.pi/2)\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis\n", - "fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=[\"z axis\"], text_color='gray', text_align='right', text_baseline='middle')\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Configure the logics:" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "code_slider = lambda var, L_code, b_code, h_code, x_axis_code=\"\" : f\"\"\"\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({L_code}*10)/10\n", - " const b = Math.round({b_code})\n", - " const h = Math.round({h_code})\n", - " const A = b*h\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 = \"

Geometrical and mechanical parameters:

h = \"+h+\n", - " \" mm
b = \"+b+\n", - " \" mm
L = \"+L+\n", - " \" m
A = \"+A.toExponential()+\n", - " \" mm2
Iy = \"+Iy.toExponential()+\n", - " \" mm4
Iz = \"+Iz.toExponential()+\n", - " \" mm4\"\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", - " {x_axis_code}\n", - " // apply the changes\n", - " data_s['{var}'] = 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", - "\"\"\"\n", - "\n", - "x_axis_code = f\"\"\"\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+{axis_arrow_length}\n", - "x_axis_label.glyph.x = L+{axis_arrow_length}/2\n", - "\"\"\"\n", - "\n", - "# logic for slider_L\n", - "update_L = CustomJS(args=dict(s_b=source_beam, s_s=source, div=div, section=section, support_r=support_r,\n", - " x_axis_arrow=x_axis_arrow, x_axis_label=x_axis_label),\n", - " code=code_slider(\"L\", \"f\", \"data_s['b']\", \"data_s['h']\", x_axis_code))\n", - "\n", - "slider_L.js_on_change('value', update_L)\n", - "\n", - "# logic for slider_b\n", - "update_b = CustomJS(args=dict(s_b=source_beam, s_s=source, div=div, section=section, support_r=support_r),\n", - " code=code_slider(\"b\", \"data_s['L']\", \"f\", \"data_s['h']\"))\n", - "\n", - "slider_b.js_on_change('value', update_b)\n", - "\n", - "# logic for slider_h\n", - "update_h = CustomJS(args=dict(s_b=source_beam, s_s=source, div=div, section=section, support_r=support_r),\n", - " code=code_slider(\"h\", \"data_s['L']\", \"data_s['b']\", \"f\"))\n", - "\n", - "slider_h.js_on_change('value', update_h)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Build the layout and show the figures:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "layout1 = layout([\n", - " [fig_beam],\n", - " [fig_section, Spacer(width=20), column([Spacer(height=50), slider_L, slider_b, slider_h, Spacer(height=50), div])] \n", - "])\n", - "\n", - "show(layout1)" + "hidden_code_nb_geo.main_code(L, h, b, A, Iy, Iz)" ] } ], "metadata": { "interpreter": { "hash": "f29f3a16a5c47811d2900cf82e6584cc83572ddcd5db25d9cf9bef77823b3d45" }, "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "cienpy venv", "language": "python", - "name": "python3" + "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": 2 + "nbformat_minor": 4 } diff --git a/Simple Beam DEMOs/sb_mohr.ipynb b/Simple Beam DEMOs/sb_mohr.ipynb index 2c37e1a..38281f1 100644 --- a/Simple Beam DEMOs/sb_mohr.ipynb +++ b/Simple Beam DEMOs/sb_mohr.ipynb @@ -1,1861 +1,502 @@ { "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": 18, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
\n", + " \n", + " Loading BokehJS ...\n", + "
" + ] + }, + "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", + " \"
\\n\"+\n", + " \"

\\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", + " \"

\\n\"+\n", + " \"
    \\n\"+\n", + " \"
  • re-rerun `output_notebook()` to attempt to load from CDN again, or
    • \\n\"+\n", + " \"
  • use INLINE resources instead, as so:
    • \\n\"+\n", + " \"
\\n\"+\n", + " \"\\n\"+\n", + " \"from bokeh.resources import INLINE\\n\"+\n", + " \"output_notebook(resources=INLINE)\\n\"+\n", + " \"\\n\"+\n", + " \"
\"}};\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 \"
\\n\"+\n \"

\\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 \"

\\n\"+\n \"
    \\n\"+\n \"
  • re-rerun `output_notebook()` to attempt to load from CDN again, or
    • \\n\"+\n \"
  • use INLINE resources instead, as so:
    • \\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\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 bokeh.layouts import layout, column, row\n", - "from bokeh.models.annotations import Label, Arrow\n", - "from bokeh.models.arrow_heads import VeeHead\n", - "from bokeh.models import Div, CustomJS, Slider, Spacer\n", - "from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup\n", - "from bokeh.plotting import figure, show, ColumnDataSource, output_file, save\n", - "from bokeh.io import output_notebook\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 models\n", - "from cienpy import javascriptcodes as js\n", - "from cienpy import mohrcircle\n", - "\n", - "# output_notebook()" + "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": 19, + "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)\n", - "\n", - "# constants for the visualisation\n", - "SCALE = 10\n", - "OFFSET_Q = q\n", - "MAX_B = 2*b\n", - "MAX_H = 2*h\n", - "MAX_Q = q/4*5\n", - "MAX_STRESS = 60\n", - "MAX_STRESS_MOHR = 10\n", - "MAX_DIM_STRESS_STATE = MAX_STRESS*2.5\n", - "\n", - "# store the values in a specific format\n", - "data_beam = dict(\n", - " x=[0, L],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_beam = dict(\n", - " x=[0, L*SCALE],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_q = dict(\n", - " x=[0, 0, L*SCALE, L*SCALE],\n", - " y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],\n", - " x_fade=[0, 0, L*SCALE, L*SCALE]\n", - ")\n", - "\n", - "data_section_scheme = dict(\n", - " x=[0, 0], \n", - " y=[0, h]\n", - ")\n", - "\n", - "initial_position = L\n", - "initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC\n", - "initial_FBD = 0 # right=0 left=1\n", - "data = dict( # stores every useful single variable\n", - " state=[initial_state], \n", - " FBD=[initial_FBD],\n", - " SCALE=[SCALE],\n", - " L=[L],\n", - " b=[b],\n", - " h=[h],\n", - " E=[E],\n", - " A=[A],\n", - " Iy=[Iy],\n", - " Iz=[Iz],\n", - " yG=[yG],\n", - " y_n_axis=[y_n_axis],\n", - " P=[P],\n", - " x=[initial_position],\n", - " y=[0],\n", - " y_var=[initial_y],\n", - " theta_element=[initial_theta_element], # rad\n", - " theta=[initial_theta], # rad\n", - " sigma_x0=[sigma_x0],\n", - " sigma_y0=[sigma_y0],\n", - " tau_0=[tau_0],\n", - " sigma_average=[sigma_average_mohr],\n", - " r_circle_mohr=[r_circle_mohr],\n", - " sigma_x=[new_state[0]],\n", - " sigma_y=[new_state[1]],\n", - " tau=[new_state[2]],\n", - " q=[q],\n", - " Rx=[Rx],\n", - " Ry_l=[Ry_l],\n", - " Ry_r=[Ry_r],\n", - " N=[N],\n", - " V=[V],\n", - " M=[M],\n", - " xF=[L*SCALE]\n", - ")\n", - "\n", - "source_beam = ColumnDataSource(data_beam)\n", - "source_scheme_beam = ColumnDataSource(data_scheme_beam)\n", - "source_scheme_q = ColumnDataSource(data_scheme_q)\n", - "source_section_scheme = ColumnDataSource(data_section_scheme)\n", - "source = ColumnDataSource(data)\n", - "\n", - "# Constants\n", - "FIG_H_B = 200 # height figure beam\n", - "FIG_B_B = 600 # width figure beam\n", - "FIG_H_S = FIG_H_B # height figure scheme\n", - "FIG_B_S = FIG_B_B # width figure scheme\n", - "FIG_H_SEC = 500 # height figure section\n", - "DIV_B_GEO = 170\n", - "DIV_B_FORCES = 170\n", - "FIG_MOHR = 600\n", - "FIG_STRESS_STATE = 600" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create the figures, the plots and the widgets (same of Notebook 3 - Diagrams):" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [], - "source": [ - "options = dict(\n", - " toolbar_location=None\n", - ")\n", - "\n", - "\n", - "\n", - "######################## Start modifications\n", - "# figure for the beam\n", - "paddingx = 0.2*L\n", - "int_x_b = (0-paddingx, L+paddingx)\n", - "int_y_b = (-MAX_H*0.2, MAX_H*1.4)\n", - "fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,\n", - " f_h=FIG_H_B, f_b=FIG_B_B)\n", - "\n", - "# modify beam \n", - "#TODO: add to cienpy\n", - "def draw_beam_2D(fig, L: float, h: float, b_supp=0.25, ratio = 1.0):\n", - " \"\"\"\n", - " Function that draws the simple beam in a figure.\n", - "\n", - " @param fig (bokeh.plotting.figure.Figure): Figure that will be the canvas for the plot.\n", - " @param src (bokeh.models.sources.ColumnDataSource): Source of the coordinates.\n", - " @param L (float): Length of the beam in m.\n", - " @param x (str): Key for the x values. Defaults to 'x'.\n", - " @param y (str): Key for the y values. Defaults to 'y'.\n", - " @param b_supp (float, optional): Size of the supports in x. Defaults to 0.3.\n", - " @param ratio (float, optional): Ratio of the figure (interval_y/height*100). Defaults to 1.0 (axis equal).\n", - " \n", - " @return tuple: Tuple with the renderers of the beam and supports.\n", - " \"\"\"\n", - " beam = fig.rect([L/2], [h/2], width=L, height=h, \n", - " fill_color='lightgray', color='black', line_width=1)\n", - " supp_opt = dict(\n", - " fill_color='white',\n", - " line_color='black'\n", - " )\n", - " support_l = models.define_pinned(fig, 0, 0, b_supp, ratio, supp_opt)\n", - " support_r = models.define_roller(fig, L, 0, b_supp, ratio, supp_opt)\n", - " \n", - " return (beam, support_l, support_r)\n", - "\n", - "(beam, support_l, support_r) = draw_beam_2D(fig_beam, L, h,\n", - " ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)\n", - "\n", - "# uniform load (beam)\n", - "if q!=0:\n", - " fig_beam.rect([L/2], [(int_y_b[1]+MAX_H)/2], width=L, height=(0.99*(int_y_b[1]-MAX_H)),\n", - " fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)\n", - " fig_beam.text(x=[-0.2], y=[MAX_H], text=[\"q\"], text_color=\"blue\")\n", - "\n", - "####################### End modification\n", - "\n", - "\n", - "\n", - "# figure for the cross-section\n", - "fig_section = sb.define_fig_section(MAX_B*0.8, MAX_H*0.8, options, FIG_H_SEC)\n", - "\n", - "\n", - "# section\n", - "section = beam_section.draw_section(fig_section, b, h)\n", - "\n", - "\n", - "# show mechanical parameters\n", - "div_geo = Div(width= DIV_B_GEO, \n", - " text=beam_section.div_text_geo(round(h), round(b), round(L),\n", - " \"{:.2e}\".format(A),\n", - " \"{:.2e}\".format(Iy),\n", - " \"{:.2e}\".format(Iz)))\n", - "\n", - "\n", - "# change geometry\n", - "slider_b = Slider(\n", - " title=\"Change the width b [mm]\",\n", - " start=10,\n", - " end=MAX_B,\n", - " step=10,\n", - " value=b\n", - ")\n", - "slider_h = Slider(\n", - " title=\"Change the height h [mm]\",\n", - " start=20,\n", - " end=MAX_H,\n", - " step=20,\n", - " value=h\n", - ")\n", - "\n", - "# reference system\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis\n", - "fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=[\"y\"], text_color='gray', text_baseline='middle', angle=math.pi/2)\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis\n", - "fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=[\"z\"], text_color='gray', text_align='right', text_baseline='middle')\n", - "\n", - "\n", - "# figure for the forces and moments\n", - "fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)\n", - "\n", - "\n", - "# axial force (beam)\n", - "axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')\n", - "label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=[\"P\"], text_color=\"green\")\n", - "\n", - "\n", - "# position point\n", - "pos_opt = dict(\n", - " source=source,\n", - " size=10,\n", - " fill_alpha=0.5,\n", - " fill_color=\"magenta\",\n", - " color=\"magenta\",\n", - " alpha=0.5\n", - ")\n", - "forces_position = fig_scheme.circle('xF', 'y', **pos_opt)\n", - "\n", - "\n", - "# beam (scheme)\n", - "scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')\n", - "scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)\n", - "# uniform load (scheme)\n", - "scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',\n", - " fill_alpha=0.3, alpha=0.3)\n", - "scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',\n", - " color='navy', fill_alpha=0.3, alpha=0.3)\n", - "# axial force (scheme)\n", - "scheme_axial_force = models.force_vector(fig_scheme, P, L*SCALE+P, L*SCALE, 0, 0, 'green')\n", - "# Reactions (scheme)\n", - "scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -Ry_r, 0, 'orange')\n", - "scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')\n", - "scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')\n", - "# force N\n", - "scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# force V\n", - "scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# moment M\n", - "(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)\n", - "\n", - "\n", - "# change the uniform load q\n", - "slider_q = Slider(\n", - " title=\"Change the uniform load q [kN/m]\",\n", - " start=0.1,\n", - " end=MAX_Q,\n", - " step=0.1,\n", - " value=q\n", - ")\n", - "\n", - "\n", - "# choose position of interest\n", - "slider_position = Slider(\n", - " title=\"Change the position x along the beam [m]\",\n", - " start=0,\n", - " end=L,\n", - " step=0.02,\n", - " value=L\n", - ")\n", - "\n", - "\n", - "# choose left or right FBD\n", - "div_rg_FBD = Div(text=\"Free-body diagram (FBD):\")\n", - "radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)\n", - "\n", - "\n", - "# choose axial force or not\n", - "div_cb_P = Div(text=f\"Axial force P={P} kN (applied)\")\n", - "checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])\n", - "\n", - "\n", - "# show values of forces and moments\n", - "div_forces = Div(width=DIV_B_FORCES, \n", - " text=sb.div_text_forces(P, P, Ry_l, Ry_r, \"No cross section analysed.\", 0, 0, 0))\n", - "\n", - "\n", - "# figures for the diagrams\n", - "options_diag = dict(\n", - " toolbar_location=None,\n", - " x_axis_label=\"Position [m]\",\n", - " plot_width=FIG_B_B,\n", - " x_range=fig_beam.x_range\n", - ")\n", - "fig_N = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Axial force\", \"@y kN\")],\n", - " y_axis_label=\"Axial force N [kN]\",\n", - " plot_height=int(FIG_H_B*0.8),\n", - " title=\"N V M Diagrams\")\n", - "fig_V = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Shear force\", \"@y kN\")],\n", - " y_axis_label=\"Shear force V [kN]\",\n", - " plot_height=int(FIG_H_B*0.8))\n", - "fig_M = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Bending moment\", \"@y kNm\")],\n", - " y_axis_label=\"Bending moment M [kNm]\",\n", - " plot_height=FIG_H_B)\n", - "fig_N.xaxis.visible = False\n", - "fig_V.xaxis.visible = False\n", - "\n", - "\n", - "# plot N V M\n", - "N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)\n", - "V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)\n", - "M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)\n", - "\n", - "# point that shows the position that it's analyzed\n", - "N_position = fig_N.circle('x', 'N', **pos_opt)\n", - "V_position = fig_V.circle('x', 'V', **pos_opt)\n", - "M_position = fig_M.circle('x', 'M', **pos_opt)\n", - "\n", - "\n", - "# figures for the stresses and strains\n", - "FIG_B_ss = 200\n", - "FIG_H_ss = 200\n", - "options_stress_strain = dict(\n", - " toolbar_location=None,\n", - " y_axis_label=\"Height h [mm]\",\n", - " plot_width=FIG_B_ss,\n", - " plot_height=FIG_H_ss\n", - ")\n", - "fig_stress_N = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2099 [MPa]\")\n", - "fig_stress_N.yaxis.visible = False\n", - "fig_axial_strain = figure(**options_stress_strain,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2099 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_axial_strain.yaxis.visible = False\n", - "fig_stress_M = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending stress and centroid\",\n", - " y_range=fig_stress_N.y_range,\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2098 [MPa]\")\n", - "fig_stress_M.yaxis.visible = False\n", - "fig_bending_strain = figure(**options_stress_strain,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2098 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_bending_strain.yaxis.visible = False\n", - "fig_stress_V = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Shear stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU}\\u1d65 [MPa]\")\n", - "fig_stress_V.yaxis.visible = False\n", - "fig_stress_sigma = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress \\N{GREEK SMALL LETTER SIGMA} and neutral axis\",\n", - " y_range=fig_stress_N.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA} [MPa]\")\n", - "fig_stress_tau = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress \\N{GREEK SMALL LETTER TAU}\",\n", - " y_range=fig_stress_V.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU} [MPa]\")\n", - "\n", - "# plot stress N V M\n", - "discr_stress_strain = 10\n", - "scale_x = 25\n", - "y_discr = np.linspace(0, h, discr_stress_strain)\n", - "sigma_N = stst.compute_sigma_axial(y_discr, 0, A)\n", - "N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,\n", - " source_section_scheme, scale_x=scale_x/10)\n", - "sigma_M = stst.compute_sigma_bending(y_discr, 0, Iy, yG)\n", - "(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,\n", - " source_section_scheme, True, yG, scale_x=scale_x)\n", - "S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, yG)\n", - "tau_V = stst.compute_tau_shear(y_discr, 0, S_rect, Iy, b)\n", - "V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)\n", - "\n", - "# plot stress sigma and tau\n", - "sigma_total = sigma_M + sigma_N\n", - "(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,\n", - " source_section_scheme,True, yG, scale_x=scale_x)\n", - "tau_total = tau_V\n", - "tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,\n", - " source_section_scheme, scale_x=1)\n", - "\n", - "# plot strain N M\n", - "strain_axial = stst.compute_epsilon_axial(y_discr, sigma_N, E)\n", - "axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)\n", - "strain_bending = stst.compute_epsilon_bending(y_discr, sigma_M, E)\n", - "bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)\n", - "\n", - "\n", - "# figures for NVM\n", - "fig_NM_section = figure(**options_stress_strain,\n", - " title=\"N and M at position x\",\n", - " match_aspect=True)\n", - "fig_NM_section.axis.visible = False\n", - "fig_NM_section.grid.grid_line_alpha = 0\n", - "\n", - "fig_V_section = figure(**options_stress_strain,\n", - " title=\"V at position x\",\n", - " match_aspect=True)\n", - "fig_V_section.axis.visible = False\n", - "fig_V_section.grid.grid_line_alpha = 0\n", - "\n", - "# section with NVM\n", - "models.section_diagram(fig_NM_section)\n", - "models.section_diagram(fig_V_section)\n", - "\n", - "# NVM in section\n", - "section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')\n", - "section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')\n", - "(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)\n", - "\n", - "# NVM label in section\n", - "OFFSET_N = 1\n", - "label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[\"\"], text_color=\"red\", text_baseline='bottom')\n", - "label_M_section = fig_NM_section.text(x=[OFFSET_N*6], y=[-OFFSET_N*5], text=[\"\"], text_color=\"red\", text_baseline='top')\n", - "label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[0], text=[\"\"], text_color=\"red\", text_baseline='middle')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now define the new figures, renderers and widgets:" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [], - "source": [ - "SCALE_TAU = 5\n", - "\n", - "# Modify the beam figure and plots (see in the previous code cell)\n", - "\n", - "\n", - "# Modifiy focus point to square in beam\n", - "beam_position = fig_beam.square('x', 'y_var', **pos_opt)\n", - "\n", - "\n", - "# choose height of interest\n", - "slider_y = Slider(\n", - " title=\"Change the height y along the section [mm]\",\n", - " start=0,\n", - " end=h,\n", - " step=1,\n", - " value=initial_y\n", - ")\n", - "\n", - "\n", - "# choose angle theta of interest\n", - "slider_theta_element = Slider(\n", - " title=\"Change the angle \\N{GREEK SMALL LETTER THETA} of the element [°]\",\n", - " start=0,\n", - " end=90,\n", - " step=0.5,\n", - " value=initial_theta_element\n", - ")\n", - "\n", - "\n", - "# figure Mohr circle\n", - "fig_Mohr_circle = figure(toolbar_location=None,\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA} [MPa]\",\n", - " y_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU} [MPa]\",\n", - " plot_height=FIG_MOHR,\n", - " plot_width=FIG_MOHR,\n", - " match_aspect=True,\n", - " # x_range=[-MAX_STRESS_MOHR, MAX_STRESS_MOHR],\n", - " title=\"Mohr circle, x axis: stress \\N{GREEK SMALL LETTER SIGMA} [MPa], y axis: stress \\N{GREEK SMALL LETTER TAU} [MPa]\"\n", - ")\n", - "fig_Mohr_circle.axis.fixed_location = 0\n", - "\n", - "\n", - "# figure stress state element\n", - "fig_stress_state = figure(toolbar_location=None,\n", - " plot_height=FIG_STRESS_STATE,\n", - " plot_width=FIG_STRESS_STATE,\n", - " match_aspect=True,\n", - " title=\"Stress state\"\n", - ")\n", - "fig_stress_state.grid.grid_line_alpha = 0\n", - "fig_stress_state.axis.visible = False\n", - "fig_stress_state.min_border_left = 0\n", - "fig_stress_state.rect([MAX_DIM_STRESS_STATE*0.4], [MAX_DIM_STRESS_STATE*0.4],\n", - " width=MAX_DIM_STRESS_STATE*1.2,\n", - " height=MAX_DIM_STRESS_STATE*1.2,\n", - " alpha=0,\n", - " fill_alpha=0)\n", - "\n", - "\n", - "# stress state (theta 0)\n", - "fig_stress_state.rect([0], [0],\n", - " width=MAX_STRESS/2,\n", - " height=MAX_STRESS/2,\n", - " angle=0,\n", - " fill_alpha=0, color='black', line_width=2)\n", - "fig_stress_state.text([0], [0],\n", - " text=[\"Fixed \\nelement\"],\n", - " text_align=\"center\", text_baseline=\"middle\",\n", - " text_font_size=\"14px\")\n", - "\n", - "\n", - "# stress state variable\n", - "stress_state_theta = fig_stress_state.rect([MAX_STRESS*2], [0],\n", - " width=MAX_STRESS/2,\n", - " height=MAX_STRESS/2,\n", - " angle=initial_theta_element, \n", - " fill_alpha=0, color='black', line_width=2)\n", - "label_stress_state_theta = fig_stress_state.text([MAX_STRESS*2], [0],\n", - " text=[\"Rotating \\nelement\"],\n", - " text_align=\"center\", text_baseline=\"middle\",\n", - " text_font_size=\"14px\")\n", - "\n", - "# rotating axis\n", - "rotating_axis = fig_stress_state.line([0, MAX_DIM_STRESS_STATE], [0, 0],\n", - " line_dash=\"4 4\", line_color=\"black\", line_width=0.5)\n", - "\n", - "\n", - "# arc and label theta in stress state\n", - "arc_theta_element = fig_stress_state.arc(x=[0], y=[0],\n", - " radius=MAX_STRESS, start_angle=0, end_angle=0,\n", - " line_color=\"gray\", line_dash=\"2 5\")\n", - "label_theta_element = fig_stress_state.text([MAX_STRESS], [0],\n", - " text=[\"\"],\n", - " text_baseline=\"middle\", x_offset=5, text_font_size=\"14px\")\n", - "\n", - "# fixed axis\n", - "fig_stress_state.line([0, MAX_DIM_STRESS_STATE], [0, 0],\n", - " line_dash=\"4 4\", line_color=\"black\", line_width=0.5)\n", - "\n", - "\n", - "# stress state arrows\n", - "arrows_stress_state = models.set_arrows_stress_state(fig_stress_state, sigma_x0, sigma_y0, tau_0, MAX_STRESS/2,\n", - " SCALE_TAU)\n", - "\n", - "\n", - "# stress state theta arrows \n", - "arrows_stress_state_theta = models.set_arrows_stress_state(fig_stress_state, sigma_x0, sigma_y0, tau_0, MAX_STRESS/2,\n", - " SCALE_TAU, MAX_STRESS*2)\n", - "\n", - "# Mohr circle\n", - "Mohr_circle = fig_Mohr_circle.circle([sigma_average_mohr], [0],\n", - " radius=r_circle_mohr,\n", - " fill_alpha=0, color=\"gray\")\n", - "\n", - "\n", - "# arc and label theta in Mohr circle\n", - "arc_theta_Mohr = fig_Mohr_circle.arc(x=[sigma_average_mohr], y=[0],\n", - " radius=r_circle_mohr/2, start_angle=0, end_angle=0,\n", - " line_color=\"gray\", line_dash=\"2 5\")\n", - "label_theta_Mohr = fig_Mohr_circle.text([sigma_average_mohr+r_circle_mohr/2], [0],\n", - " text=[\"\"],\n", - " text_baseline=\"middle\", x_offset=5, text_font_size=\"14px\")\n", - "arc_theta_p_Mohr = fig_Mohr_circle.arc(x=[sigma_average_mohr], y=[0],\n", - " radius=r_circle_mohr/2, start_angle=0, end_angle=0,\n", - " line_color=\"gray\", line_dash=\"2 5\")\n", - "label_theta_p_Mohr = fig_Mohr_circle.text([sigma_average_mohr+r_circle_mohr/5*2], [0],\n", - " text=[\"\"],\n", - " text_baseline=\"middle\", x_offset=5, text_font_size=\"14px\")\n", - "\n", - "\n", - "# linking line and two points from current stress state\n", - "mohr_points_opt = dict(\n", - " size=5,\n", - " fill_alpha=0.5,\n", - " alpha=0.5\n", - ")\n", - "line_stress_state = fig_Mohr_circle.line([sigma_x0, tau_0], [sigma_y0, -tau_0],\n", - " line_dash=\"4 4\", line_color=\"blue\", line_width=0.5)\n", - "points_stress_state = fig_Mohr_circle.circle([sigma_x0, tau_0], [sigma_y0, -tau_0],\n", - " **mohr_points_opt, color=\"blue\", fill_color=\"blue\")\n", - "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})\"\n", - "# NB: no subscript of latin y, so use gamma (very similar in the display)\n", - "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})\"\n", - "label_points_stress_state = fig_Mohr_circle.text([sigma_x0, tau_0], [sigma_y0, -tau_0],\n", - " text=[str_label_stress_state1, str_label_stress_state2],\n", - " color=\"blue\", x_offset=5, y_offset=18, text_font_size=\"14px\")\n", - "\n", - "\n", - "# linking line and two points from stress state in function of theta\n", - "line_stress_state_theta = fig_Mohr_circle.line([sigma_x0, tau_0], [sigma_y0, -tau_0],\n", - " line_dash=\"4 4\", line_color=\"red\", line_width=0.5)\n", - "points_stress_state_theta = fig_Mohr_circle.circle([sigma_x0, tau_0], [sigma_y0, -tau_0],\n", - " **mohr_points_opt, color=\"red\", fill_color=\"red\")\n", - "str_label_stress_state_theta1 = \"Rotating element \\n(\\N{GREEK SMALL LETTER SIGMA}\\N{LATIN SUBSCRIPT SMALL LETTER X}, \\N{GREEK SMALL LETTER TAU})\"\n", - "# NB: no subscript of latin y, so use gamma (very similar in the display)\n", - "str_label_stress_state_theta2 = \"Rotating element \\n(\\N{GREEK SMALL LETTER SIGMA}\\N{Greek Subscript Small Letter Gamma}, -\\N{GREEK SMALL LETTER TAU})\"\n", - "label_points_stress_state_theta = fig_Mohr_circle.text([sigma_x0, tau_0], [sigma_y0, -tau_0],\n", - " text=[str_label_stress_state_theta1, str_label_stress_state_theta2],\n", - " text_align=\"right\",\n", - " color=\"red\", x_offset=-5, y_offset=18, text_font_size=\"14px\")" + "new_state = mohrcircle.compute_stress_state_mohr(sigma_average_mohr, r_circle_mohr, initial_theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Configure the logics:" + "Run the complex code for the interactive visualisation:" ] }, { "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [], - "source": [ - "update_circle_mohr = f\"\"\"\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", - "args_slider_pos = dict(source=source,\n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " s_M=source_M,\n", - " arr_head=scheme_M_head,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section,\n", - " Mohr_circle=Mohr_circle,\n", - " line_stress_state=line_stress_state,\n", - " line_stress_state_theta=line_stress_state_theta,\n", - " points_stress_state=points_stress_state,\n", - " points_stress_state_theta=points_stress_state_theta,\n", - " label_points_stress_state=label_points_stress_state,\n", - " label_points_stress_state_theta=label_points_stress_state_theta,\n", - " arc_theta_Mohr=arc_theta_Mohr,\n", - " label_theta_Mohr=label_theta_Mohr,\n", - " arc_theta_p_Mohr=arc_theta_p_Mohr,\n", - " label_theta_p_Mohr=label_theta_p_Mohr,\n", - " arrow_sigma_x1=arrows_stress_state[0], \n", - " arrow_sigma_x2=arrows_stress_state[1], \n", - " arrow_sigma_y1=arrows_stress_state[2], \n", - " arrow_sigma_y2=arrows_stress_state[3], \n", - " arrow_tau_x1=arrows_stress_state[4], \n", - " arrow_tau_x2=arrows_stress_state[5], \n", - " arrow_tau_y1=arrows_stress_state[6], \n", - " arrow_tau_y2=arrows_stress_state[7],\n", - " arrow_sigma_x1_theta=arrows_stress_state_theta[0], \n", - " arrow_sigma_x2_theta=arrows_stress_state_theta[1], \n", - " arrow_sigma_y1_theta=arrows_stress_state_theta[2], \n", - " arrow_sigma_y2_theta=arrows_stress_state_theta[3], \n", - " arrow_tau_x1_theta=arrows_stress_state_theta[4], \n", - " arrow_tau_x2_theta=arrows_stress_state_theta[5], \n", - " arrow_tau_y1_theta=arrows_stress_state_theta[6], \n", - " arrow_tau_y2_theta=arrows_stress_state_theta[7])\n", - "code_slider_pos = f\"\"\"\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", - "{update_circle_mohr}\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", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{models.implement_check_stateJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{mohrcircle.implement_compute_radius_mohrJS()}\n", - "{mohrcircle.implement_compute_sigma_average_mohrJS()}\n", - "{mohrcircle.implement_compute_stress_state_mohrJS()}\n", - "{mohrcircle.implement_compute_principal_theta_mohrJS()}\n", - "{mohrcircle.implement_compute_theta_mohrJS()}\n", - "{mohrcircle.implement_update_circle_mohrJS()}\n", - "{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}\n", - "{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}\n", - "\"\"\"\n", - "updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)\n", - "\n", - "\n", - "args_slider_b = dict(source=source,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " Mohr_circle=Mohr_circle,\n", - " line_stress_state=line_stress_state,\n", - " points_stress_state=points_stress_state,\n", - " points_stress_state_theta=points_stress_state_theta,\n", - " line_stress_state_theta=line_stress_state_theta,\n", - " label_points_stress_state=label_points_stress_state,\n", - " label_points_stress_state_theta=label_points_stress_state_theta,\n", - " arc_theta_Mohr=arc_theta_Mohr,\n", - " label_theta_Mohr=label_theta_Mohr,\n", - " arc_theta_p_Mohr=arc_theta_p_Mohr,\n", - " label_theta_p_Mohr=label_theta_p_Mohr,\n", - " arrow_sigma_x1=arrows_stress_state[0], \n", - " arrow_sigma_x2=arrows_stress_state[1], \n", - " arrow_sigma_y1=arrows_stress_state[2], \n", - " arrow_sigma_y2=arrows_stress_state[3], \n", - " arrow_tau_x1=arrows_stress_state[4], \n", - " arrow_tau_x2=arrows_stress_state[5], \n", - " arrow_tau_y1=arrows_stress_state[6], \n", - " arrow_tau_y2=arrows_stress_state[7],\n", - " arrow_sigma_x1_theta=arrows_stress_state_theta[0], \n", - " arrow_sigma_x2_theta=arrows_stress_state_theta[1], \n", - " arrow_sigma_y1_theta=arrows_stress_state_theta[2], \n", - " arrow_sigma_y2_theta=arrows_stress_state_theta[3], \n", - " arrow_tau_x1_theta=arrows_stress_state_theta[4], \n", - " arrow_tau_x2_theta=arrows_stress_state_theta[5], \n", - " arrow_tau_y1_theta=arrows_stress_state_theta[6], \n", - " arrow_tau_y2_theta=arrows_stress_state_theta[7])\n", - "code_change_b = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{mohrcircle.implement_compute_radius_mohrJS()}\n", - "{mohrcircle.implement_compute_stress_state_mohrJS()}\n", - "{mohrcircle.implement_compute_sigma_average_mohrJS()}\n", - "{mohrcircle.implement_compute_principal_theta_mohrJS()}\n", - "{mohrcircle.implement_compute_theta_mohrJS()}\n", - "{mohrcircle.implement_update_circle_mohrJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}\n", - "{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}\n", - "\"\"\"\n", - "update_b = CustomJS(args=args_slider_b, code=code_change_b)\n", - "\n", - "\n", - "args_slider_h = dict(source=source,\n", - " s_ss=source_section_scheme,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " slider_y=slider_y,\n", - " beam=beam,\n", - " Mohr_circle=Mohr_circle,\n", - " line_stress_state=line_stress_state,\n", - " points_stress_state=points_stress_state,\n", - " points_stress_state_theta=points_stress_state_theta,\n", - " line_stress_state_theta=line_stress_state_theta,\n", - " label_points_stress_state=label_points_stress_state,\n", - " label_points_stress_state_theta=label_points_stress_state_theta,\n", - " arc_theta_Mohr=arc_theta_Mohr,\n", - " label_theta_Mohr=label_theta_Mohr,\n", - " arc_theta_p_Mohr=arc_theta_p_Mohr,\n", - " label_theta_p_Mohr=label_theta_p_Mohr,\n", - " arrow_sigma_x1=arrows_stress_state[0], \n", - " arrow_sigma_x2=arrows_stress_state[1], \n", - " arrow_sigma_y1=arrows_stress_state[2], \n", - " arrow_sigma_y2=arrows_stress_state[3], \n", - " arrow_tau_x1=arrows_stress_state[4], \n", - " arrow_tau_x2=arrows_stress_state[5], \n", - " arrow_tau_y1=arrows_stress_state[6], \n", - " arrow_tau_y2=arrows_stress_state[7],\n", - " arrow_sigma_x1_theta=arrows_stress_state_theta[0], \n", - " arrow_sigma_x2_theta=arrows_stress_state_theta[1], \n", - " arrow_sigma_y1_theta=arrows_stress_state_theta[2], \n", - " arrow_sigma_y2_theta=arrows_stress_state_theta[3], \n", - " arrow_tau_x1_theta=arrows_stress_state_theta[4], \n", - " arrow_tau_x2_theta=arrows_stress_state_theta[5], \n", - " arrow_tau_y1_theta=arrows_stress_state_theta[6], \n", - " arrow_tau_y2_theta=arrows_stress_state_theta[7])\n", - "code_change_h = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{mohrcircle.implement_compute_radius_mohrJS()}\n", - "{mohrcircle.implement_compute_stress_state_mohrJS()}\n", - "{mohrcircle.implement_compute_sigma_average_mohrJS()}\n", - "{mohrcircle.implement_compute_principal_theta_mohrJS()}\n", - "{mohrcircle.implement_compute_theta_mohrJS()}\n", - "{mohrcircle.implement_update_circle_mohrJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}\n", - "{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}\n", - "\"\"\"\n", - "update_h = CustomJS(args=args_slider_h, code=code_change_h)\n", - "\n", - "\n", - "args_checkbox_P = dict(source=source,\n", - " s_M=source_M,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force, \n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r, \n", - " fN=scheme_N,\n", - " fV=scheme_V, \n", - " arr_head=scheme_M_head,\n", - " N_diag=N_diag,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section,\n", - " Mohr_circle=Mohr_circle,\n", - " line_stress_state=line_stress_state,\n", - " points_stress_state=points_stress_state,\n", - " points_stress_state_theta=points_stress_state_theta,\n", - " line_stress_state_theta=line_stress_state_theta,\n", - " label_points_stress_state=label_points_stress_state,\n", - " label_points_stress_state_theta=label_points_stress_state_theta,\n", - " arc_theta_Mohr=arc_theta_Mohr,\n", - " label_theta_Mohr=label_theta_Mohr,\n", - " arc_theta_p_Mohr=arc_theta_p_Mohr,\n", - " label_theta_p_Mohr=label_theta_p_Mohr,\n", - " arrow_sigma_x1=arrows_stress_state[0],\n", - " arrow_sigma_x2=arrows_stress_state[1],\n", - " arrow_sigma_y1=arrows_stress_state[2],\n", - " arrow_sigma_y2=arrows_stress_state[3],\n", - " arrow_sigma_x1_theta=arrows_stress_state_theta[0], \n", - " arrow_sigma_x2_theta=arrows_stress_state_theta[1], \n", - " arrow_sigma_y1_theta=arrows_stress_state_theta[2], \n", - " arrow_sigma_y2_theta=arrows_stress_state_theta[3], \n", - " arrow_tau_x1_theta=arrows_stress_state_theta[4], \n", - " arrow_tau_x2_theta=arrows_stress_state_theta[5], \n", - " arrow_tau_y1_theta=arrows_stress_state_theta[6], \n", - " arrow_tau_y2_theta=arrows_stress_state_theta[7])\n", - "code_checkbox_P = f\"\"\"\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 = {P}*(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", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_compute_RxJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_update_N_diagramJS(discr_NVM)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{mohrcircle.implement_compute_radius_mohrJS()}\n", - "{mohrcircle.implement_compute_stress_state_mohrJS()}\n", - "{mohrcircle.implement_compute_sigma_average_mohrJS()}\n", - "{mohrcircle.implement_compute_principal_theta_mohrJS()}\n", - "{mohrcircle.implement_compute_theta_mohrJS()}\n", - "{mohrcircle.implement_update_circle_mohrJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}\n", - "\"\"\"\n", - "update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)\n", - "\n", - "\n", - "args_radiogroup_FBD = dict(source=source, \n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M, \n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N, \n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_radiogroup_FBD = f\"\"\"\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", - "{models.implement_check_stateJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)\n", - "\n", - "\n", - "args_slider_q = dict(source=source,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M,\n", - " div_f=div_forces,\n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " V_diag=V_diag,\n", - " M_diag=M_diag,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section,\n", - " Mohr_circle=Mohr_circle,\n", - " line_stress_state=line_stress_state,\n", - " points_stress_state=points_stress_state,\n", - " points_stress_state_theta=points_stress_state_theta,\n", - " line_stress_state_theta=line_stress_state_theta,\n", - " label_points_stress_state=label_points_stress_state,\n", - " label_points_stress_state_theta=label_points_stress_state_theta,\n", - " arc_theta_Mohr=arc_theta_Mohr,\n", - " label_theta_Mohr=label_theta_Mohr,\n", - " arc_theta_p_Mohr=arc_theta_p_Mohr,\n", - " label_theta_p_Mohr=label_theta_p_Mohr,\n", - " arrow_sigma_x1=arrows_stress_state[0], \n", - " arrow_sigma_x2=arrows_stress_state[1], \n", - " arrow_sigma_y1=arrows_stress_state[2], \n", - " arrow_sigma_y2=arrows_stress_state[3], \n", - " arrow_tau_x1=arrows_stress_state[4], \n", - " arrow_tau_x2=arrows_stress_state[5], \n", - " arrow_tau_y1=arrows_stress_state[6], \n", - " arrow_tau_y2=arrows_stress_state[7],\n", - " arrow_sigma_x1_theta=arrows_stress_state_theta[0], \n", - " arrow_sigma_x2_theta=arrows_stress_state_theta[1], \n", - " arrow_sigma_y1_theta=arrows_stress_state_theta[2], \n", - " arrow_sigma_y2_theta=arrows_stress_state_theta[3], \n", - " arrow_tau_x1_theta=arrows_stress_state_theta[4], \n", - " arrow_tau_x2_theta=arrows_stress_state_theta[5], \n", - " arrow_tau_y1_theta=arrows_stress_state_theta[6], \n", - " arrow_tau_y2_theta=arrows_stress_state_theta[7])\n", - "code_slider_q = f\"\"\"\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", - "{js.implement_update_arrowJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_compute_Ry_lJS()}\n", - "{sb.implement_compute_Ry_rJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_update_V_diagramJS(discr_NVM)}\n", - "{sb.implement_update_M_diagramJS(discr_NVM)}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_u_loadJS(OFFSET_Q)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{mohrcircle.implement_compute_radius_mohrJS()}\n", - "{mohrcircle.implement_compute_stress_state_mohrJS()}\n", - "{mohrcircle.implement_compute_sigma_average_mohrJS()}\n", - "{mohrcircle.implement_compute_principal_theta_mohrJS()}\n", - "{mohrcircle.implement_compute_theta_mohrJS()}\n", - "{mohrcircle.implement_update_circle_mohrJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}\n", - "{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}\n", - "\"\"\"\n", - "update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)\n", - "\n", - "\n", - "args_slider_theta = dict(source=source,\n", - " Mohr_circle=Mohr_circle,\n", - " line_stress_state=line_stress_state,\n", - " points_stress_state=points_stress_state,\n", - " line_stress_state_theta=line_stress_state_theta,\n", - " points_stress_state_theta=points_stress_state_theta,\n", - " label_points_stress_state=label_points_stress_state,\n", - " label_points_stress_state_theta=label_points_stress_state_theta,\n", - " stress_state_theta=stress_state_theta,\n", - " label_stress_state_theta=label_stress_state_theta,\n", - " arc_theta_element=arc_theta_element,\n", - " label_theta_element= label_theta_element,\n", - " arc_theta_Mohr=arc_theta_Mohr,\n", - " label_theta_Mohr=label_theta_Mohr,\n", - " arc_theta_p_Mohr=arc_theta_p_Mohr,\n", - " label_theta_p_Mohr=label_theta_p_Mohr,\n", - " rotating_axis=rotating_axis,\n", - " beam_position=beam_position,\n", - " arrow_sigma_x1_theta=arrows_stress_state_theta[0], \n", - " arrow_sigma_x2_theta=arrows_stress_state_theta[1], \n", - " arrow_sigma_y1_theta=arrows_stress_state_theta[2], \n", - " arrow_sigma_y2_theta=arrows_stress_state_theta[3], \n", - " arrow_tau_x1_theta=arrows_stress_state_theta[4], \n", - " arrow_tau_x2_theta=arrows_stress_state_theta[5], \n", - " arrow_tau_y1_theta=arrows_stress_state_theta[6], \n", - " arrow_tau_y2_theta=arrows_stress_state_theta[7])\n", - "code_slider_theta = f\"\"\"\n", - "// retrieve data\n", - "const db = source.data\n", - "const theta_element = cb_obj.value/180*Math.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", - "{mohrcircle.implement_update_stress_state_elementsJS(MAX_STRESS, MAX_DIM_STRESS_STATE)}\n", - "{js.implement_arrow_growthJS()}\n", - "{mohrcircle.implement_compute_stress_state_mohrJS()}\n", - "{mohrcircle.implement_compute_principal_theta_mohrJS()}\n", - "{mohrcircle.implement_compute_theta_mohrJS()}\n", - "{mohrcircle.implement_update_circle_mohrJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}\n", - "\"\"\"\n", - "update_slider_theta = CustomJS(args=args_slider_theta, code=code_slider_theta)\n", - "\n", - "\n", - "args_slider_y = dict(source=source,\n", - " Mohr_circle=Mohr_circle,\n", - " line_stress_state=line_stress_state,\n", - " points_stress_state=points_stress_state,\n", - " line_stress_state_theta=line_stress_state_theta,\n", - " points_stress_state_theta=points_stress_state_theta,\n", - " label_points_stress_state=label_points_stress_state,\n", - " label_points_stress_state_theta=label_points_stress_state_theta,\n", - " arc_theta_Mohr=arc_theta_Mohr,\n", - " label_theta_Mohr=label_theta_Mohr,\n", - " arc_theta_p_Mohr=arc_theta_p_Mohr,\n", - " label_theta_p_Mohr=label_theta_p_Mohr,\n", - " beam_position=beam_position,\n", - " arrow_sigma_x1=arrows_stress_state[0], \n", - " arrow_sigma_x2=arrows_stress_state[1], \n", - " arrow_sigma_y1=arrows_stress_state[2], \n", - " arrow_sigma_y2=arrows_stress_state[3], \n", - " arrow_tau_x1=arrows_stress_state[4], \n", - " arrow_tau_x2=arrows_stress_state[5], \n", - " arrow_tau_y1=arrows_stress_state[6], \n", - " arrow_tau_y2=arrows_stress_state[7],\n", - " arrow_sigma_x1_theta=arrows_stress_state_theta[0], \n", - " arrow_sigma_x2_theta=arrows_stress_state_theta[1], \n", - " arrow_sigma_y1_theta=arrows_stress_state_theta[2], \n", - " arrow_sigma_y2_theta=arrows_stress_state_theta[3], \n", - " arrow_tau_x1_theta=arrows_stress_state_theta[4], \n", - " arrow_tau_x2_theta=arrows_stress_state_theta[5], \n", - " arrow_tau_y1_theta=arrows_stress_state_theta[6], \n", - " arrow_tau_y2_theta=arrows_stress_state_theta[7])\n", - "code_slider_y = f\"\"\"\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", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{mohrcircle.implement_compute_radius_mohrJS()}\n", - "{mohrcircle.implement_compute_stress_state_mohrJS()}\n", - "{mohrcircle.implement_compute_sigma_average_mohrJS()}\n", - "{mohrcircle.implement_compute_principal_theta_mohrJS()}\n", - "{mohrcircle.implement_compute_theta_mohrJS()}\n", - "{mohrcircle.implement_update_circle_mohrJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{mohrcircle.implement_update_sigmax_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_sigmay_stateJS(MAX_STRESS/2)}\n", - "{mohrcircle.implement_update_tau_stateJS(MAX_STRESS/2, SCALE_TAU)}\n", - "{mohrcircle.implement_update_sigmax_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_sigmay_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2)}\n", - "{mohrcircle.implement_update_tau_state_thetaJS(MAX_STRESS/2, MAX_STRESS*2, SCALE_TAU)}\n", - "\"\"\"\n", - "update_slider_y = CustomJS(args=args_slider_y, code=code_slider_y)\n", - "\n", - "\n", - "# apply the logics\n", - "slider_b.js_on_change('value', update_b)\n", - "slider_h.js_on_change('value', update_h)\n", - "slider_position.js_on_change('value', updade_slider_pos)\n", - "checkbox_P.js_on_click(update_checkbox_P)\n", - "radiogroup_FBD.js_on_click(update_radiogroup_FBD)\n", - "slider_q.js_on_change('value', update_slider_q)\n", - "slider_theta_element.js_on_change('value', update_slider_theta)\n", - "slider_y.js_on_change('value', update_slider_y)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Build the layout and show the figures. Note that the forces in the scheme are updated after moving the position of the point with the slider.\n", - "Note that the value of the forces and moments shown below represents the intensity, thus is always positive. The direction is given by the vector in the scheme.\n", - "Note that the size of the tau arrows in the stress state elements is 5 times bigger (check the value of the constant SCALE_TAU to change it)." - ] - }, - { - "cell_type": "code", - "execution_count": 23, + "execution_count": 3, "metadata": {}, "outputs": [ { - "name": "stderr", - "output_type": "stream", - "text": [ - "libva error: vaGetDriverNameByIndex() failed with unknown libva error, driver_name = (null)\n" - ] + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n" + ] + }, + "metadata": {}, + "output_type": "display_data" }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "Opening in existing browser session.\n" - ] + "data": { + "application/javascript": [ + "(function(root) {\n", + " function embed_document(root) {\n", + " \n", + " const docs_json = 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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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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)/c**2\\n }\\n const step = 2*c / (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(2*c)*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*(h**2/4-(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 N*1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/Iy*(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V*1000*S/(Iy*b_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\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/A*Iy/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/2*0.8\\n var a = b-lambda*c\\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_0**2 + (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_circle*Math.cos(2*theta)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var tau = -r_circle*Math.sin(2*theta)\\n } else {\\n var sigma_x = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta)\\n var tau = r_circle*Math.sin(2*theta)\\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(2*tau_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 = -2*theta\\n glyph_arc.glyph.end_angle = -2*theta_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_circle*Math.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circle*Math.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/5*2\\n glyph_arc_p.glyph.start_angle = -2*theta_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_circle*Math.cos(theta_p_tmp)/5*2]\\n src_label_theta_p.data.y = [r_circle*Math.sin(-theta_p_tmp)/5*2]\\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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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/A*Iy/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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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/A*Iy/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_0**2 + (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_circle*Math.cos(2*theta)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var tau = -r_circle*Math.sin(2*theta)\\n } else {\\n var sigma_x = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta)\\n var tau = r_circle*Math.sin(2*theta)\\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(2*tau_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 = -2*theta\\n glyph_arc.glyph.end_angle = -2*theta_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_circle*Math.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circle*Math.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/5*2\\n glyph_arc_p.glyph.start_angle = -2*theta_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_circle*Math.cos(theta_p_tmp)/5*2]\\n src_label_theta_p.data.y = [r_circle*Math.sin(-theta_p_tmp)/5*2]\\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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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/A*Iy/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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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_0**2 + (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_circle*Math.cos(2*theta)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var tau = -r_circle*Math.sin(2*theta)\\n } else {\\n var sigma_x = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta)\\n var tau = r_circle*Math.sin(2*theta)\\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(2*tau_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 = -2*theta\\n glyph_arc.glyph.end_angle = -2*theta_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_circle*Math.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circle*Math.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/5*2\\n glyph_arc_p.glyph.start_angle = -2*theta_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_circle*Math.cos(theta_p_tmp)/5*2]\\n src_label_theta_p.data.y = [r_circle*Math.sin(-theta_p_tmp)/5*2]\\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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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*(h**2/4-(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 V*1000*S/(Iy*b_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_0**2 + (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_circle*Math.cos(2*theta)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var tau = -r_circle*Math.sin(2*theta)\\n } else {\\n var sigma_x = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta)\\n var tau = r_circle*Math.sin(2*theta)\\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(2*tau_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 = -2*theta\\n glyph_arc.glyph.end_angle = -2*theta_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_circle*Math.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circle*Math.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/5*2\\n glyph_arc_p.glyph.start_angle = -2*theta_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_circle*Math.cos(theta_p_tmp)/5*2]\\n src_label_theta_p.data.y = [r_circle*Math.sin(-theta_p_tmp)/5*2]\\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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/2*0.8\\n var a = b-lambda*c\\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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/2*(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return q*L/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return q*L/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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_0**2 + (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_circle*Math.cos(2*theta)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var tau = -r_circle*Math.sin(2*theta)\\n } else {\\n var sigma_x = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta)\\n var tau = r_circle*Math.sin(2*theta)\\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(2*tau_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 = -2*theta\\n glyph_arc.glyph.end_angle = -2*theta_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_circle*Math.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circle*Math.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/5*2\\n glyph_arc_p.glyph.start_angle = -2*theta_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_circle*Math.cos(theta_p_tmp)/5*2]\\n src_label_theta_p.data.y = [r_circle*Math.sin(-theta_p_tmp)/5*2]\\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/180*Math.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_stress*Math.cos(theta_element)\\n const y_new = max_stress*Math.sin(theta_element)\\n \\n \\n // update rotating axis\\n const src_axis = glyph_axis.data_source\\n src_axis.data.x = [0, x_new*max_dim/max_stress]\\n src_axis.data.y = [0, y_new*max_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_new*2\\n glyph_stress_state_theta.glyph.y = y_new*2\\n \\n // label element\\n const src_label_element = glyph_label_element_theta.data_source\\n src_label_element.data.x = [x_new*2]\\n src_label_element.data.y = [y_new*2]\\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_stress*Math.cos(theta_element/2)]\\n src_label_theta.data.y = [max_stress*Math.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_circle*Math.cos(2*theta)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var tau = -r_circle*Math.sin(2*theta)\\n } else {\\n var sigma_x = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta)\\n var tau = r_circle*Math.sin(2*theta)\\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(2*tau_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 = -2*theta\\n glyph_arc.glyph.end_angle = -2*theta_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_circle*Math.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circle*Math.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/5*2\\n glyph_arc_p.glyph.start_angle = -2*theta_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_circle*Math.cos(theta_p_tmp)/5*2]\\n src_label_theta_p.data.y = [r_circle*Math.sin(-theta_p_tmp)/5*2]\\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*(h**2/4-(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 N*1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/Iy*(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V*1000*S/(Iy*b_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_0**2 + (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_circle*Math.cos(2*theta)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var tau = -r_circle*Math.sin(2*theta)\\n } else {\\n var sigma_x = sigma_average + r_circle*Math.cos(2*theta-Math.PI)\\n var sigma_y = sigma_average + r_circle*Math.cos(2*theta)\\n var tau = r_circle*Math.sin(2*theta)\\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(2*tau_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 = -2*theta\\n glyph_arc.glyph.end_angle = -2*theta_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_circle*Math.cos(theta+theta_p)/2]\\n src_label_theta.data.y = [r_circle*Math.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/5*2\\n glyph_arc_p.glyph.start_angle = -2*theta_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_circle*Math.cos(theta_p_tmp)/5*2]\\n src_label_theta_p.data.y = [r_circle*Math.sin(-theta_p_tmp)/5*2]\\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

Forces and Moments:

\\n P = 10 kN
\\n Rx = 10 kN
\\n Ry (left) = 12.0 kN
\\n Ry (right) = 12.0 kN
\\n No cross section analysed.
\\n N = 0 kN
\\n V = 0 kN
\\n M = 0 kNm\\n \\n \",\"width\":170},\"id\":\"1255\",\"type\":\"Div\"},{\"attributes\":{},\"id\":\"2485\",\"type\":\"Selection\"},{\"attributes\":{\"axis\":{\"id\":\"1624\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1627\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"2401\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"2240\",\"type\":\"Selection\"},{\"attributes\":{\"tools\":[{\"id\":\"1529\"},{\"id\":\"1530\"},{\"id\":\"1531\"},{\"id\":\"1532\"},{\"id\":\"1533\"},{\"id\":\"1534\"},{\"id\":\"1536\"}]},\"id\":\"1537\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"2419\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1264\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"2441\",\"type\":\"Selection\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2255\"},\"selection_policy\":{\"id\":\"2254\"}},\"id\":\"2183\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"active\":[0],\"js_property_callbacks\":{\"change:active\":[{\"id\":\"2138\"}]},\"labels\":[\"Apply 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

Geometrical and mechanical parameters:

\\n h = 200 mm
\\n b = 100 mm
\\n L = 6 m
\\n A = 2.00e+04 mm2
\\n Iy = 6.67e+07 mm4
\\n Iz = 1.67e+07 mm4\",\"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 [mm]\",\"coordinates\":null,\"formatter\":{\"id\":\"2423\"},\"group\":null,\"major_label_policy\":{\"id\":\"2424\"},\"ticker\":{\"id\":\"1561\"},\"visible\":false},\"id\":\"1560\",\"type\":\"LinearAxis\"},{\"attributes\":{\"axis_label\":\"Axial force N [kN]\",\"coordinates\":null,\"formatter\":{\"id\":\"2295\"},\"group\":null,\"major_label_policy\":{\"id\":\"2296\"},\"ticker\":{\"id\":\"1271\"}},\"id\":\"1270\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"2295\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Shear stress\"},\"id\":\"1546\",\"type\":\"Title\"},{\"attributes\":{\"data\":{},\"selected\":{\"id\":\"2261\"},\"selection_policy\":{\"id\":\"2260\"}},\"id\":\"2186\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"axis\":{\"id\":\"1270\"},\"coordinates\":null,\"dimension\":1,\"group\":null,\"ticker\":null},\"id\":\"1273\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"2351\",\"type\":\"AllLabels\"},{\"attributes\":{},\"id\":\"1271\",\"type\":\"BasicTicker\"},{\"attributes\":{\"axis\":{\"id\":\"1556\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1559\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"2500\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1279\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"2296\",\"type\":\"AllLabels\"},{\"attributes\":{},\"id\":\"1552\",\"type\":\"LinearScale\"},{\"attributes\":{\"end\":200,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"2136\"}]},\"start\":10,\"step\":10,\"title\":\"Change the width b 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"display_data" } ], "source": [ - "padding_layout = 10\n", - "layout1 = layout([\n", - " [column(row(column(fig_scheme,\n", - " row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout),\n", - " slider_b,\n", - " slider_h,\n", - " # row(div_geo, div_forces),\n", - " slider_y,\n", - " slider_theta_element,\n", - " Spacer(height=padding_layout),\n", - " slider_position,\n", - " slider_q,\n", - " div_rg_FBD,\n", - " radiogroup_FBD,\n", - " div_cb_P,\n", - " checkbox_P))),\n", - " column(fig_beam,\n", - " Spacer(height=padding_layout),\n", - " fig_N,\n", - " fig_V,\n", - " fig_M)),\n", - " row(column(\n", - " row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_stress_sigma),\n", - " 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),\n", - " ))\n", - " ),\n", - " column(fig_Mohr_circle, fig_stress_state)\n", - " ],\n", - "])\n", - "\n", - "show(layout1)" + "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)" ] } ], "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": 2 + "nbformat_minor": 4 } diff --git a/Simple Beam DEMOs/sb_plastic.ipynb b/Simple Beam DEMOs/sb_plastic.ipynb index f43e5d2..212d0d9 100644 --- a/Simple Beam DEMOs/sb_plastic.ipynb +++ b/Simple Beam DEMOs/sb_plastic.ipynb @@ -1,1341 +1,487 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple beam - Plastic Analysis\n", "In this first notebook, the plastic analysis is presented." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
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\\n\"+\n \"

\\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 \"

\\n\"+\n \"
    \\n\"+\n \"
  • re-rerun `output_notebook()` to attempt to load from CDN again, or
    • \\n\"+\n \"
  • use INLINE resources instead, as so:
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\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\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 bokeh.layouts import layout, column, row\n", - "from bokeh.models.annotations import Label, Arrow\n", - "from bokeh.models.arrow_heads import VeeHead\n", - "from bokeh.models import Div, CustomJS, Slider, Spacer, Text\n", - "from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup\n", - "from bokeh.plotting import figure, show, ColumnDataSource\n", - "from bokeh.io import output_notebook\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\n", - "from cienpy import models\n", - "from cienpy import javascriptcodes as js\n", - "\n", - "# output_notebook()" + "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", - "# h = 220.6265 # [mm]\n", "b = 100 # [mm]\n", "q = 4; # [kN/m]\n", "P = 10; # [kN]\n", - "# P = 587.418; # [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)\n", - "\n", - "\n", - "# constants for the visualisation\n", - "SCALE = 10\n", - "OFFSET_Q = q\n", - "MAX_B = 3*b\n", - "MAX_H = 3*h\n", - "MAX_Q = q/4*5\n", - "\n", - "# store the values in a specific format\n", - "data_beam = dict(\n", - " x=[0, L],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_beam = dict(\n", - " x=[0, L*SCALE],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_q = dict(\n", - " x=[0, 0, L*SCALE, L*SCALE],\n", - " y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],\n", - " x_fade=[0, 0, L*SCALE, L*SCALE]\n", - ")\n", - "\n", - "data_section_scheme = dict(\n", - " x=[0, 0], \n", - " y=[0, h]\n", - ")\n", - "\n", - "initial_position = L\n", - "initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC\n", - "initial_FBD = 0 # right=0 left=1\n", - "data = dict( # stores every useful single variable\n", - " state=[initial_state], \n", - " FBD=[initial_FBD],\n", - " SCALE=[SCALE],\n", - " L=[L],\n", - " b=[b],\n", - " h=[h],\n", - " E=[E],\n", - " fy=[fy],\n", - " A=[A],\n", - " Iy=[Iy],\n", - " Iz=[Iz],\n", - " yG=[yG],\n", - " y_n_axis=[y_n_axis],\n", - " P=[P],\n", - " x=[initial_position],\n", - " y=[0],\n", - " q=[q],\n", - " Rx=[Rx],\n", - " Ry_l=[Ry_l],\n", - " Ry_r=[Ry_r],\n", - " N=[N],\n", - " V=[V],\n", - " M=[M],\n", - " xF=[L*SCALE]\n", - ")\n", - "\n", - "source_beam = ColumnDataSource(data_beam)\n", - "source_scheme_beam = ColumnDataSource(data_scheme_beam)\n", - "source_scheme_q = ColumnDataSource(data_scheme_q)\n", - "source_section_scheme = ColumnDataSource(data_section_scheme)\n", - "source = ColumnDataSource(data)" + "Ry_r = sb.compute_Ry_r(q, L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Create the figures, the plots and the widgets (same of Notebook 3 - Diagrams):" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "FIG_H_B = 200 # height figure beam\n", - "FIG_B_B = 700 # width figure beam\n", - "FIG_H_S = FIG_H_B # height figure scheme\n", - "FIG_B_S = FIG_B_B # width figure scheme\n", - "FIG_H_SEC = 600 # height figure section\n", - "DIV_B_GEO = 170\n", - "DIV_B_FORCES = 170\n", - "\n", - "options = dict(\n", - " toolbar_location=None\n", - ")\n", - "\n", - "# figure for the beam\n", - "paddingx = 0.2*L\n", - "int_x_b = (0-paddingx, L+paddingx)\n", - "int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)\n", - "fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,\n", - " f_h=FIG_H_B, f_b=FIG_B_B)\n", - "\n", - "\n", - "# figure for the cross-section\n", - "fig_section = sb.define_fig_section(MAX_B*0.8, MAX_H*0.8, options, FIG_H_SEC)\n", - "\n", - "\n", - "# beam\n", - "(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,\n", - " ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)\n", - "\n", - "# section\n", - "section = beam_section.draw_section(fig_section, b, h)\n", - "\n", - "\n", - "# show mechanical parameters\n", - "div_geo = Div(width= DIV_B_GEO, \n", - " text=beam_section.div_text_geo(round(h), round(b), round(L),\n", - " \"{:.2e}\".format(A),\n", - " \"{:.2e}\".format(Iy),\n", - " \"{:.2e}\".format(Iz)))\n", - "\n", - "\n", - "# change geometry\n", - "slider_b = Slider(\n", - " title=\"Change the width b [mm]\",\n", - " start=10,\n", - " end=MAX_B,\n", - " step=10,\n", - " value=b\n", - ")\n", - "slider_h = Slider(\n", - " title=\"Change the height h [mm]\",\n", - " start=20,\n", - " end=MAX_H,\n", - " step=20,\n", - " value=h\n", - ")\n", - "\n", - "# reference system\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis\n", - "fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=[\"y\"], text_color='gray', text_baseline='middle', angle=math.pi/2)\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis\n", - "fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=[\"z\"], text_color='gray', text_align='right', text_baseline='middle')\n", - "\n", - "\n", - "# figure for the forces and moments\n", - "fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)\n", - "\n", - "\n", - "# uniform load (beam)\n", - "u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE], width=L, height=q/SCALE,\n", - " fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)\n", - "label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE], text=[\"q\"], text_color=\"blue\")\n", - "\n", - "\n", - "# axial force (beam)\n", - "axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')\n", - "label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=[\"P\"], text_color=\"green\")\n", - "\n", - "\n", - "# position point\n", - "pos_opt = dict(\n", - " source=source,\n", - " size=10,\n", - " fill_alpha=0.5,\n", - " fill_color=\"magenta\",\n", - " color=\"magenta\",\n", - " alpha=0.5\n", - ")\n", - "beam_position = fig_beam.circle('x', 'y', **pos_opt)\n", - "forces_position = fig_scheme.circle('xF', 'y', **pos_opt)\n", - "\n", - "\n", - "# beam (scheme)\n", - "scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')\n", - "scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)\n", - "# uniform load (scheme)\n", - "scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',\n", - " fill_alpha=0.3, alpha=0.3)\n", - "scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',\n", - " color='navy', fill_alpha=0.3, alpha=0.3)\n", - "# axial force (scheme)\n", - "scheme_axial_force = models.force_vector(fig_scheme, P, L*SCALE+P, L*SCALE, 0, 0, 'green')\n", - "# Reactions (scheme)\n", - "scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -Ry_r, 0, 'orange')\n", - "scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')\n", - "scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')\n", - "# force N\n", - "scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# force V\n", - "scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# moment M\n", - "(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)\n", - "\n", - "\n", - "# change the uniform load q\n", - "slider_q = Slider(\n", - " title=\"Change the uniform load q [kN/m]\",\n", - " start=0.1,\n", - " end=MAX_Q,\n", - " step=0.1,\n", - " value=q\n", - ")\n", - "\n", - "\n", - "# choose position of interest\n", - "slider_position = Slider(\n", - " title=\"Change the position x along the beam [m]\",\n", - " start=0,\n", - " end=L,\n", - " step=0.02,\n", - " value=L\n", - ")\n", - "\n", - "\n", - "# choose left or right FBD\n", - "div_rg_FBD = Div(text=\"Free-body diagram (FBD):\")\n", - "radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)\n", - "\n", - "\n", - "# choose axial force or not\n", - "div_cb_P = Div(text=f\"Axial force P={P} kN (applied)\")\n", - "checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])\n", - "\n", - "\n", - "# show values of forces and moments\n", - "div_forces = Div(width=DIV_B_FORCES, \n", - " text=sb.div_text_forces(P, P, Ry_l, Ry_r, \"No cross section analysed.\", 0, 0, 0))\n", - "\n", - "\n", - "# figures for the diagrams\n", - "options_diag = dict(\n", - " toolbar_location=None,\n", - " x_axis_label=\"Position [m]\",\n", - " plot_width=FIG_B_B,\n", - " x_range=fig_beam.x_range\n", - ")\n", - "fig_N = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Axial force\", \"@y kN\")],\n", - " y_axis_label=\"Axial force N [kN]\",\n", - " plot_height=int(FIG_H_B*0.8),\n", - " title=\"N V M Diagrams\")\n", - "fig_V = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Shear force\", \"@y kN\")],\n", - " y_axis_label=\"Shear force V [kN]\",\n", - " plot_height=int(FIG_H_B*0.8))\n", - "fig_M = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Bending moment\", \"@y kNm\")],\n", - " y_axis_label=\"Bending moment M [kNm]\",\n", - " plot_height=FIG_H_B)\n", - "fig_N.xaxis.visible = False\n", - "fig_V.xaxis.visible = False\n", - "\n", - "\n", - "# plot N V M\n", - "N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)\n", - "V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)\n", - "M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)\n", - "\n", - "# point that shows the position that it's analyzed\n", - "N_position = fig_N.circle('x', 'N', **pos_opt)\n", - "V_position = fig_V.circle('x', 'V', **pos_opt)\n", - "M_position = fig_M.circle('x', 'M', **pos_opt)\n", - "\n", - "\n", - "# figures for the stresses and strains\n", - "FIG_B_ss = 200\n", - "FIG_H_ss = 200\n", - "options_stress_strain = dict(\n", - " toolbar_location=None,\n", - " y_axis_label=\"Height h [mm]\",\n", - " plot_height=FIG_H_ss\n", - ")\n", - "fig_stress_N = figure(**options_stress_strain,\n", - " plot_width=FIG_B_ss,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2099 [MPa]\")\n", - "fig_stress_N.yaxis.visible = False\n", - "fig_axial_strain = figure(**options_stress_strain,\n", - " plot_width=FIG_B_ss,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2099 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_axial_strain.yaxis.visible = False\n", - "fig_stress_M = figure(**options_stress_strain,\n", - " plot_width=FIG_B_ss,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending stress and centroid\",\n", - " y_range=fig_stress_N.y_range,\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2098 [MPa]\")\n", - "fig_stress_M.yaxis.visible = False\n", - "fig_bending_strain = figure(**options_stress_strain,\n", - " plot_width=FIG_B_ss,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2098 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_bending_strain.yaxis.visible = False\n", - "fig_stress_V = figure(**options_stress_strain,\n", - " plot_width=FIG_B_ss,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Shear stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU}\\u1d65 [MPa]\")\n", - "fig_stress_V.yaxis.visible = False\n", - "fig_stress_sigma = figure(**options_stress_strain,\n", - " plot_width=int(FIG_B_ss*1.2),\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress (green=yield) and N.A.\",\n", - " y_range=fig_stress_N.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA} [MPa]\")\n", - "fig_stress_tau = figure(**options_stress_strain,\n", - " plot_width=int(FIG_B_ss*1.2),\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress \\N{GREEK SMALL LETTER TAU}\",\n", - " y_range=fig_stress_V.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU} [MPa]\")\n", - "\n", - "# plot stress N V M\n", - "discr_stress_strain = 10\n", - "scale_x = 25\n", - "y_discr = np.linspace(0, h, discr_stress_strain)\n", - "sigma_N = ststel.compute_sigma_axial(y_discr, 0, A)\n", - "N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,\n", - " source_section_scheme, scale_x=scale_x/10)\n", - "sigma_M = ststel.compute_sigma_bending(y_discr, 0, Iy, yG)\n", - "(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,\n", - " source_section_scheme, True, yG, scale_x=scale_x)\n", - "S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, yG)\n", - "tau_V = ststel.compute_tau_shear(y_discr, 0, S_rect, Iy, b)\n", - "V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)\n", - "\n", - "# plot stress sigma (moved below) and tau\n", - "tau_total = tau_V\n", - "tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,\n", - " source_section_scheme, scale_x=1)\n", - "\n", - "# plot strain N M\n", - "strain_axial = ststel.compute_epsilon_axial(y_discr, sigma_N, E)\n", - "axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)\n", - "strain_bending = ststel.compute_epsilon_bending(y_discr, sigma_M, E)\n", - "bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)\n", - "\n", - "\n", - "# figures for NVM\n", - "fig_NM_section = figure(**options_stress_strain,\n", - " plot_width=FIG_B_ss,\n", - " title=\"N and M at position x\",\n", - " match_aspect=True)\n", - "fig_NM_section.axis.visible = False\n", - "fig_NM_section.grid.grid_line_alpha = 0\n", - "\n", - "fig_V_section = figure(**options_stress_strain,\n", - " plot_width=FIG_B_ss,\n", - " title=\"V at position x\",\n", - " match_aspect=True)\n", - "fig_V_section.axis.visible = False\n", - "fig_V_section.grid.grid_line_alpha = 0\n", - "\n", - "# section with NVM\n", - "models.section_diagram(fig_NM_section)\n", - "models.section_diagram(fig_V_section)\n", - "\n", - "# NVM in section\n", - "section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')\n", - "section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')\n", - "(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)\n", - "\n", - "# NVM label in section\n", - "OFFSET_N = 1\n", - "label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[\"\"], text_color=\"red\", text_baseline='bottom')\n", - "label_M_section = fig_NM_section.text(x=[OFFSET_N*6], y=[-OFFSET_N*5], text=[\"\"], text_color=\"red\", text_baseline='top')\n", - "label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[0], text=[\"\"], text_color=\"red\", text_baseline='middle')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now define the new figures, renderers and widgets:" + "Run the complex code for the interactive visualisation:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, - "outputs": [], - "source": [ - "# choose different elastic modulus\n", - "E_wood = 8e3 # [MPa]\n", - "E_concrete = 26e3 # [MPa]\n", - "E_ceramic = 300e3 # [MPa]\n", - "slider_elastic = Slider(\n", - " title=\"Change the elastic modulus [MPa]\",\n", - " start=E_wood,\n", - " end=E_ceramic,\n", - " step=1e3,\n", - " value=E,\n", - " margin=(5, 5, 0, 5)\n", - ")\n", - "\n", - "\n", - "# show values of E\n", - "div_E = Div(margin=(0, 5, 0, 5),\n", - " text=f\"\"\"\n", - "

\n", - " Ewood = {math.trunc(E_wood/1e3)} GPa; Econcrete = {math.trunc(E_concrete/1e3)} GPa
\n", - " Esteel = {math.trunc(E_steel/1e3)} GPa; Eceramic = {math.trunc(E_ceramic/1e3)} GPa

\n", - " \"\"\")\n", - "\n", - "\n", - "# choose different yield strength\n", - "fy_wood = 16 # [MPa] (bending)\n", - "fy_concrete = 25 # [MPa]\n", - "fy_glass = 1000 # [MPa] (compressive)\n", - "slider_yield = Slider(\n", - " title=\"Change the yield strength [MPa]\",\n", - " start=fy_wood,\n", - " end=fy_glass,\n", - " step=1,\n", - " value=fy,\n", - " margin=(0, 5, 0, 5)\n", - ")\n", - "\n", - "\n", - "# show values of fy\n", - "div_fy = Div(margin=(0, 5, 0, 5),\n", - " text=f\"\"\"\n", - "

\n", - " fy,wood = {math.trunc(fy_wood)} MPa; fy,concrete = {math.trunc(fy_concrete)} MPa
\n", - " fy,steel = {math.trunc(fy_steel)} MPa; fy,glass = {math.trunc(fy_glass)} MPa

\n", - " \"\"\")\n", - "\n", - "\n", - "# add total strain epsilon\n", - "fig_total_strain = figure(**options_stress_strain,\n", - " plot_width=FIG_B_ss,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total strain (green=yield)\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON} [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_total_strain.yaxis.visible = False\n", - "\n", - "\n", - "# add the strain and stress with yield implemented\n", - "# plastic\n", - "discr_pl = 2000\n", - "(stress_pl, strain_pl, y_discr_pl, yNA_pl) = ststpl.compute_total_stress_strain(discr_pl, h, fy, E, N, M, A, Iy, yG)\n", - "tmp_y = np.linspace(0, h, len(stress_pl))\n", - "total_stress_pl_diag = fig_stress_sigma.line([0, *stress_pl, 0], [0, *tmp_y, h], color='green')\n", - "total_strain_pl_diag = fig_total_strain.line(strain_pl*0, y_discr_pl, color='green')\n", - "# elastic\n", - "total_strain = ststel.compute_total_epsilon(strain_axial, strain_bending)\n", - "total_strain_diag = models.strain_diagram(fig_total_strain, total_strain, h, source_section_scheme)\n", - "# (moved from above, total stress sigma elastic)\n", - "sigma_total = sigma_M + sigma_N\n", - "(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,\n", - " source_section_scheme,True, yG, scale_x=scale_x)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Configure the logics:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "args_slider_pos = dict(source=source,\n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " discr_stress=discr_stress_strain,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " s_M=source_M,\n", - " arr_head=scheme_M_head,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section,\n", - " total_strain_diag=total_strain_diag,\n", - " total_stress_pl_diag=total_stress_pl_diag,\n", - " total_strain_pl_diag=total_strain_pl_diag)\n", - "code_slider_pos = f\"\"\"\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", - "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", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{models.implement_check_stateJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{ststel.implement_compute_sigma_axialJS()}\n", - "{ststel.implement_compute_sigma_bendingJS()}\n", - "{ststel.implement_compute_tau_shearJS()}\n", - "{ststel.implement_compute_epsilon_axialJS()}\n", - "{ststel.implement_compute_epsilon_bendingJS()}\n", - "{ststel.implement_compute_total_sigmaJS()}\n", - "{ststel.implement_compute_total_tauJS()}\n", - "{ststel.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_update_plastic_stress_strainJS(discr_pl)}\n", - "{ststpl.implement_compute_NyJS()}\n", - "{ststpl.implement_compute_MyJS()}\n", - "{ststpl.implement_compute_total_stress_strainJS()}\n", - "{ststpl.implement_support_function_plasticJS()}\n", - "{ststel.implement_compute_total_epsilonJS()}\n", - "\"\"\"\n", - "updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)\n", - "\n", - "\n", - "args_slider_b = dict(source=source,\n", - " s_b=source_beam,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " total_strain_diag=total_strain_diag,\n", - " total_stress_pl_diag=total_stress_pl_diag,\n", - " total_strain_pl_diag=total_strain_pl_diag)\n", - "code_change_b = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{ststel.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{ststel.implement_compute_epsilon_axialJS()}\n", - "{ststel.implement_compute_epsilon_bendingJS()}\n", - "{ststel.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{ststel.implement_compute_sigma_bendingJS()}\n", - "{ststel.implement_compute_total_sigmaJS()}\n", - "{ststel.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{ststel.implement_compute_tau_shearJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{ststel.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_plastic_stress_strainJS(discr_pl)}\n", - "{ststpl.implement_compute_NyJS()}\n", - "{ststpl.implement_compute_MyJS()}\n", - "{ststpl.implement_compute_total_stress_strainJS()}\n", - "{ststpl.implement_support_function_plasticJS()}\n", - "{ststel.implement_compute_total_epsilonJS()}\n", - "\"\"\"\n", - "update_b = CustomJS(args=args_slider_b, code=code_change_b)\n", - "\n", - "\n", - "args_slider_h = dict(source=source,\n", - " s_b=source_beam,\n", - " s_ss=source_section_scheme,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " total_strain_diag=total_strain_diag,\n", - " total_stress_pl_diag=total_stress_pl_diag,\n", - " total_strain_pl_diag=total_strain_pl_diag)\n", - "code_change_h = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{ststel.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{ststel.implement_compute_epsilon_axialJS()}\n", - "{ststel.implement_compute_epsilon_bendingJS()}\n", - "{ststel.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{ststel.implement_compute_sigma_bendingJS()}\n", - "{ststel.implement_compute_total_sigmaJS()}\n", - "{ststel.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{ststel.implement_compute_tau_shearJS()}\n", - "{js.implement_update_plastic_stress_strainJS(discr_pl)}\n", - "{ststpl.implement_compute_NyJS()}\n", - "{ststpl.implement_compute_MyJS()}\n", - "{ststpl.implement_compute_total_stress_strainJS()}\n", - "{ststpl.implement_support_function_plasticJS()}\n", - "{ststel.implement_compute_total_epsilonJS()}\n", - "\"\"\"\n", - "update_h = CustomJS(args=args_slider_h, code=code_change_h)\n", - "\n", - "\n", - "args_checkbox_P = dict(source=source,\n", - " s_M=source_M,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force, \n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r, \n", - " fN=scheme_N,\n", - " fV=scheme_V, \n", - " arr_head=scheme_M_head,\n", - " N_diag=N_diag,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section,\n", - " total_strain_diag=total_strain_diag,\n", - " total_stress_pl_diag=total_stress_pl_diag,\n", - " total_strain_pl_diag=total_strain_pl_diag)\n", - "code_checkbox_P = f\"\"\"\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] = {P}*(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", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_compute_RxJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_update_N_diagramJS(discr_NVM)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{ststel.implement_compute_epsilon_axialJS()}\n", - "{ststel.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{ststel.implement_compute_neutral_axisJS()}\n", - "{ststel.implement_compute_sigma_bendingJS()}\n", - "{ststel.implement_compute_total_sigmaJS()}\n", - "{ststel.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{ststel.implement_compute_tau_shearJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_plastic_stress_strainJS(discr_pl)}\n", - "{ststpl.implement_compute_NyJS()}\n", - "{ststpl.implement_compute_MyJS()}\n", - "{ststpl.implement_compute_total_stress_strainJS()}\n", - "{ststpl.implement_support_function_plasticJS()}\n", - "{ststel.implement_compute_total_epsilonJS()}\n", - "{ststel.implement_compute_epsilon_bendingJS()}\n", - "\"\"\"\n", - "update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)\n", - "\n", - "\n", - "args_radiogroup_FBD = dict(source=source, \n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M, \n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N, \n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_radiogroup_FBD = f\"\"\"\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", - "{models.implement_check_stateJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)\n", - "\n", - "\n", - "args_slider_q = dict(source=source,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M,\n", - " div_f=div_forces,\n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " V_diag=V_diag,\n", - " M_diag=M_diag,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section,\n", - " total_strain_diag=total_strain_diag,\n", - " total_stress_pl_diag=total_stress_pl_diag,\n", - " total_strain_pl_diag=total_strain_pl_diag)\n", - "code_slider_q = f\"\"\"\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", - "{js.implement_update_arrowJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_compute_Ry_lJS()}\n", - "{sb.implement_compute_Ry_rJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_update_V_diagramJS(discr_NVM)}\n", - "{sb.implement_update_M_diagramJS(discr_NVM)}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_u_loadJS(OFFSET_Q)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{ststel.implement_compute_epsilon_bendingJS()}\n", - "{ststel.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{ststel.implement_compute_neutral_axisJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{ststel.implement_compute_sigma_bendingJS()}\n", - "{ststel.implement_compute_total_sigmaJS()}\n", - "{ststel.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{ststel.implement_compute_tau_shearJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_plastic_stress_strainJS(discr_pl)}\n", - "{ststpl.implement_compute_NyJS()}\n", - "{ststpl.implement_compute_MyJS()}\n", - "{ststpl.implement_compute_total_stress_strainJS()}\n", - "{ststpl.implement_support_function_plasticJS()}\n", - "{ststel.implement_compute_total_epsilonJS()}\n", - "{ststel.implement_compute_epsilon_axialJS()}\n", - "\"\"\"\n", - "update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)\n", - "\n", - "\n", - "args_slider_yield = dict(source=source,\n", - " total_strain_diag=total_strain_diag,\n", - " total_stress_pl_diag=total_stress_pl_diag,\n", - " total_strain_pl_diag=total_strain_pl_diag)\n", - "code_slider_yield = f\"\"\"\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", - "{js.implement_update_plastic_stress_strainJS(discr_pl)}\n", - "{ststpl.implement_compute_NyJS()}\n", - "{ststpl.implement_compute_MyJS()}\n", - "{ststpl.implement_compute_total_stress_strainJS()}\n", - "{ststpl.implement_support_function_plasticJS()}\n", - "{ststel.implement_compute_total_epsilonJS()}\n", - "{js.implement_linspaceJS()}\n", - "{ststel.implement_compute_epsilon_axialJS()}\n", - "{ststel.implement_compute_epsilon_bendingJS()}\n", - "{ststel.implement_compute_sigma_axialJS()}\n", - "{ststel.implement_compute_sigma_bendingJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "\"\"\"\n", - "update_slider_yield = CustomJS(args=args_slider_yield, code=code_slider_yield)\n", - "\n", - "# for the implementation in the other nbs!!!\n", - "# args_slider_elastic = dict(source=source,\n", - "# N_stress_diag=N_stress_diag,\n", - "# axial_strain_diag=axial_strain_diag,\n", - "# M_stress_diag=M_stress_diag,\n", - "# bending_strain_diag=bending_strain_diag,\n", - "# centroid=centroid)\n", - "# code_slider_elastic = f\"\"\"\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", - "\n", - "# // apply changes\n", - "# source.change.emit()\n", - "\n", - "# // declare functions\n", - "# {js.implement_linspaceJS()}\n", - "# {sb.implement_compute_NJS()}\n", - "# {js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "# {js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "# {ststel.implement_compute_epsilon_bendingJS()}\n", - "# {ststel.implement_compute_epsilon_axialJS()}\n", - "# {ststel.implement_compute_sigma_axialJS()}\n", - "# {js.implement_update_stress_diagramJS()}\n", - "# {js.implement_update_strain_diagramJS()}\n", - "# {ststel.implement_compute_sigma_bendingJS()}\n", - "# \"\"\"\n", - "# update_slider_elastic = CustomJS(args=args_slider_elastic, code=code_slider_elastic)\n", - "\n", - "# slider_elastic.js_on_change('value', update_slider_elastic)\n", - "\n", - "args_slider_elastic = dict(source=source,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " centroid=centroid,\n", - " total_strain_diag=total_strain_diag,\n", - " total_stress_pl_diag=total_stress_pl_diag,\n", - " total_strain_pl_diag=total_strain_pl_diag)\n", - "code_slider_elastic = f\"\"\"\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", - "{js.implement_linspaceJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{ststel.implement_compute_epsilon_bendingJS()}\n", - "{ststel.implement_compute_epsilon_axialJS()}\n", - "{ststel.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{ststel.implement_compute_sigma_bendingJS()}\n", - "{js.implement_update_plastic_stress_strainJS(discr_pl)}\n", - "{ststpl.implement_compute_NyJS()}\n", - "{ststpl.implement_compute_MyJS()}\n", - "{ststpl.implement_compute_total_stress_strainJS()}\n", - "{ststpl.implement_support_function_plasticJS()}\n", - "{ststel.implement_compute_total_epsilonJS()}\n", - "\"\"\"\n", - "update_slider_elastic = CustomJS(args=args_slider_elastic, code=code_slider_elastic)\n", - "\n", - "# apply the logics\n", - "slider_b.js_on_change('value', update_b)\n", - "slider_h.js_on_change('value', update_h)\n", - "slider_position.js_on_change('value', updade_slider_pos)\n", - "checkbox_P.js_on_click(update_checkbox_P)\n", - "radiogroup_FBD.js_on_click(update_radiogroup_FBD)\n", - "slider_q.js_on_change('value', update_slider_q)\n", - "slider_elastic.js_on_change('value', update_slider_elastic)\n", - "slider_yield.js_on_change('value', update_slider_yield)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Build the layout and show the figures. Note that the forces in the scheme are updated after moving the position of the point with the slider.\n", - "Note that the value of the forces and moments shown below represents the intensity, thus is always positive. The direction is given by the vector in the scheme." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Opening in existing browser session.\n" - ] + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n" + ] + }, + "metadata": {}, + "output_type": "display_data" }, { - "name": "stderr", - "output_type": "stream", - "text": [ - "libva error: vaGetDriverNameByIndex() failed with unknown libva error, driver_name = (null)\n" - ] + "data": { + "application/javascript": [ + "(function(root) {\n", + " function embed_document(root) {\n", + " \n", + " const docs_json = {\"cf03a18f-f85a-4414-bd96-45e97dc6b718\":{\"defs\":[],\"roots\":{\"references\":[{\"attributes\":{\"children\":[{\"id\":\"4487\"}]},\"id\":\"4488\",\"type\":\"Column\"},{\"attributes\":{},\"id\":\"4763\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"callback\":null,\"tooltips\":[[\"Position\",\"@x m\"],[\"Shear force\",\"@y kN\"]]},\"id\":\"3812\",\"type\":\"HoverTool\"},{\"attributes\":{\"coordinates\":null,\"group\":null},\"id\":\"4744\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"3806\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"axis_label\":\"Shear force V 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\\n Ewood = 8 GPa; Econcrete = 26 GPa
\\n Esteel = 200 GPa; Eceramic = 300 GPa

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\\n fy,wood = 16 MPa; fy,concrete = 25 MPa
\\n fy,steel = 355 MPa; fy,glass = 1000 MPa

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Geometrical and mechanical parameters:

\\n h = 200 mm
\\n b = 100 mm
\\n L = 6 m
\\n A = 2.00e+04 mm2
\\n Iy = 6.67e+07 mm4
\\n Iz = 1.67e+07 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Forces and Moments:

\\n P = 10 kN
\\n Rx = 10 kN
\\n Ry (left) = 12.0 kN
\\n Ry (right) = 12.0 kN
\\n No cross section analysed.
\\n N = 0 kN
\\n V = 0 kN
\\n M = 0 kNm\\n \\n 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id\":\"4444\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"3499\"},\"glyph\":{\"id\":\"4208\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"4210\"},\"nonselection_glyph\":{\"id\":\"4209\"},\"view\":{\"id\":\"4212\"}},\"id\":\"4211\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"4195\"}},\"id\":\"4200\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"4970\",\"type\":\"Selection\"},{\"attributes\":{\"source\":{\"id\":\"4183\"}},\"id\":\"4188\",\"type\":\"CDSView\"},{\"attributes\":{\"source\":{\"id\":\"3499\"}},\"id\":\"4176\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.2,\"line_dash\":[4,4],\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"4459\",\"type\":\"Line\"},{\"attributes\":{\"args\":{\"M_stress_diag\":{\"id\":\"4169\"},\"N_stress_diag\":{\"id\":\"4151\"},\"V_stress_diag\":{\"id\":\"4187\"},\"arr_head\":{\"id\":\"3746\"},\"axial_strain_diag\":{\"id\":\"4223\"},\"bending_strain_diag\":{\"id\":\"4243\"},\"centroid\":{\"id\":\"4181\"},\"discr_stress\":10,\"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_sb\":{\"id\":\"3497\"},\"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 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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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)/c**2\\n }\\n const step = 2*c / (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(2*c)*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*(h**2/4-(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 N*1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/Iy*(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V*1000*S/(Iy*b_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\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/A*Iy/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/2*0.8\\n var a = b-lambda*c\\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 fy*A/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_fiber*fy/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(discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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, discr*scale_discr_o)\\n for (var i = 1; i < discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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 }\\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 => x*100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3*M_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+2*N_norm+N_norm**2) / (3-3*N_norm**2-2*M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return k*h / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return k*fy/(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 -2*h*(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 -2*h*(1-N_norm)) ) / h**2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3*N_norm*(1-2*h) - 2*k*h**3/(1-h) - (3*k**2-1)/k**2*(1-h)**2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return k*fy/(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-k*Math.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 k*fy/(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-k*h)**3 / (k**2*(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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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/A*Iy/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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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/A*Iy/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 fy*A/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_fiber*fy/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(discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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, discr*scale_discr_o)\\n for (var i = 1; i < discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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 }\\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 => x*100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3*M_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+2*N_norm+N_norm**2) / (3-3*N_norm**2-2*M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return k*h / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return k*fy/(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 -2*h*(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 -2*h*(1-N_norm)) ) / h**2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3*N_norm*(1-2*h) - 2*k*h**3/(1-h) - (3*k**2-1)/k**2*(1-h)**2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return k*fy/(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-k*Math.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 k*fy/(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-k*h)**3 / (k**2*(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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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/A*Iy/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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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 fy*A/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_fiber*fy/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(discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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, discr*scale_discr_o)\\n for (var i = 1; i < discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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 }\\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 => x*100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3*M_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+2*N_norm+N_norm**2) / (3-3*N_norm**2-2*M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return k*h / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return k*fy/(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 -2*h*(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 -2*h*(1-N_norm)) ) / h**2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3*N_norm*(1-2*h) - 2*k*h**3/(1-h) - (3*k**2-1)/k**2*(1-h)**2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return k*fy/(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-k*Math.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 k*fy/(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-k*h)**3 / (k**2*(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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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 fy*A/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_fiber*fy/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(discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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, discr*scale_discr_o)\\n for (var i = 1; i < discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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 }\\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 => x*100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3*M_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+2*N_norm+N_norm**2) / (3-3*N_norm**2-2*M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return k*h / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return k*fy/(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 -2*h*(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 -2*h*(1-N_norm)) ) / h**2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3*N_norm*(1-2*h) - 2*k*h**3/(1-h) - (3*k**2-1)/k**2*(1-h)**2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return k*fy/(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-k*Math.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 k*fy/(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-k*h)**3 / (k**2*(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/E*100\\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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/2*0.8\\n var a = b-lambda*c\\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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/2*(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return q*L/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return q*L/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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 fy*A/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_fiber*fy/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(discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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, discr*scale_discr_o)\\n for (var i = 1; i < discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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 }\\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 => x*100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3*M_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+2*N_norm+N_norm**2) / (3-3*N_norm**2-2*M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return k*h / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return k*fy/(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 -2*h*(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 -2*h*(1-N_norm)) ) / h**2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3*N_norm*(1-2*h) - 2*k*h**3/(1-h) - (3*k**2-1)/k**2*(1-h)**2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return k*fy/(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-k*Math.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 k*fy/(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-k*h)**3 / (k**2*(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/E*100\\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 fy*A/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_fiber*fy/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(discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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, discr*scale_discr_o)\\n for (var i = 1; i < discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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 }\\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 => x*100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3*M_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+2*N_norm+N_norm**2) / (3-3*N_norm**2-2*M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return k*h / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return k*fy/(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 -2*h*(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 -2*h*(1-N_norm)) ) / h**2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3*N_norm*(1-2*h) - 2*k*h**3/(1-h) - (3*k**2-1)/k**2*(1-h)**2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return k*fy/(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-k*Math.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 k*fy/(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-k*h)**3 / (k**2*(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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/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 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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/E*100\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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 fy*A/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_fiber*fy/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(discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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, discr*scale_discr_o)\\n for (var i = 1; i < discr*scale_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 = h*H\\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 => x*100), 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 => x*100), 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 }\\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 => x*100), y_discr, yG]\\n }\\n }\\n \\n \\n function __check_limit(M_norm, N_norm) {\\n const tmp = 2/3*M_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+2*N_norm+N_norm**2) / (3-3*N_norm**2-2*M_norm))\\n }\\n \\n function __compute_k_prime_2Y(k, h){\\n return k*h / (1-h)\\n }\\n\\n function __compute_chi_2Y(k, fy, E, H, yNA){\\n return k*fy/(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 -2*h*(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 -2*h*(1-N_norm)) ) / h**2\\n }\\n\\n function __compute_err_1Y_in(h, k, M_norm, N_norm){\\n return Math.abs(M_norm + 3*N_norm*(1-2*h) - 2*k*h**3/(1-h) - (3*k**2-1)/k**2*(1-h)**2)\\n }\\n \\n function __compute_chi_1Y_in(k, fy, E, H, yNA){\\n // unit: 1/mm\\n return k*fy/(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-k*Math.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 k*fy/(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-k*h)**3 / (k**2*(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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"display_data" } ], "source": [ - "padding_layout = 10\n", - "layout1 = layout([\n", - " [column(row(column(fig_scheme,\n", - " row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout*3),\n", - " slider_b,\n", - " slider_h,\n", - " # row(div_geo, div_forces),\n", - " slider_position,\n", - " slider_q,\n", - " slider_elastic,\n", - " div_E,\n", - " slider_yield,\n", - " div_fy,\n", - " # Spacer(height=padding_layout),\n", - " div_rg_FBD,\n", - " radiogroup_FBD,\n", - " div_cb_P,\n", - " checkbox_P))),\n", - " column(fig_beam,\n", - " Spacer(height=padding_layout),\n", - " fig_N,\n", - " fig_V,\n", - " fig_M)),\n", - " row(column(\n", - " row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_total_strain, fig_stress_sigma),\n", - " 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),\n", - " ))\n", - " ),\n", - " ],\n", - "])\n", - "\n", - "show(layout1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "TODO:\n", - "- add slider E in some NB\n", - "- bigger N and M for plastic\n", - "- change EVERYWHERE neutral_axis with horizontal infinite line?" + "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)" ] } ], "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": 2 + "nbformat_minor": 4 } diff --git a/Simple Beam DEMOs/sb_stress.ipynb b/Simple Beam DEMOs/sb_stress.ipynb index 2c043ba..0d43509 100644 --- a/Simple Beam DEMOs/sb_stress.ipynb +++ b/Simple Beam DEMOs/sb_stress.ipynb @@ -1,1051 +1,483 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple beam - Stress and Strain\n", "In this first notebook, the stresses and strains inside the element are presented." ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
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\\n\"+\n", + " \"
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  • re-rerun `output_notebook()` to attempt to load from CDN again, or
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\\n\"+\n \"

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\\n\"+\n \"
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    • \\n\"+\n \"
  • use INLINE resources instead, as so:
    • \\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\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 bokeh.layouts import layout, column, row\n", - "from bokeh.models.annotations import Label, Arrow\n", - "from bokeh.models.arrow_heads import VeeHead\n", - "from bokeh.models import Div, CustomJS, Slider, Spacer, Text\n", - "from bokeh.models.widgets import RadioButtonGroup, CheckboxButtonGroup\n", - "from bokeh.plotting import figure, show, ColumnDataSource\n", - "from bokeh.io import output_notebook\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 models\n", - "from cienpy import javascriptcodes as js\n", - "\n", - "# output_notebook()" + "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": 8, + "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", - "\n", - "# constants for the visualisation\n", - "SCALE = 10\n", - "OFFSET_Q = q\n", - "MAX_B = 3*b\n", - "MAX_H = 3*h\n", - "MAX_Q = q/4*5\n", - "\n", - "# store the values in a specific format\n", - "data_beam = dict(\n", - " x=[0, L],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_beam = dict(\n", - " x=[0, L*SCALE],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_q = dict(\n", - " x=[0, 0, L*SCALE, L*SCALE],\n", - " y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],\n", - " x_fade=[0, 0, L*SCALE, L*SCALE]\n", - ")\n", - "\n", - "data_section_scheme = dict(\n", - " x=[0, 0], \n", - " y=[0, h]\n", - ")\n", - "\n", - "initial_position = L\n", - "initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC\n", - "initial_FBD = 0 # right=0 left=1\n", - "data = dict( # stores every useful single variable\n", - " state=[initial_state], \n", - " FBD=[initial_FBD],\n", - " SCALE=[SCALE],\n", - " L=[L],\n", - " b=[b],\n", - " h=[h],\n", - " E=[E],\n", - " A=[A],\n", - " Iy=[Iy],\n", - " Iz=[Iz],\n", - " yG=[yG],\n", - " y_n_axis=[y_n_axis],\n", - " P=[P],\n", - " x=[initial_position],\n", - " y=[0],\n", - " q=[q],\n", - " Rx=[Rx],\n", - " Ry_l=[Ry_l],\n", - " Ry_r=[Ry_r],\n", - " N=[N],\n", - " V=[V],\n", - " M=[M],\n", - " xF=[L*SCALE]\n", - ")\n", - "\n", - "source_beam = ColumnDataSource(data_beam)\n", - "source_scheme_beam = ColumnDataSource(data_scheme_beam)\n", - "source_scheme_q = ColumnDataSource(data_scheme_q)\n", - "source_section_scheme = ColumnDataSource(data_section_scheme)\n", - "source = ColumnDataSource(data)" + "Ry_r = sb.compute_Ry_r(q, L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Create the figures, the plots and the widgets (same of Notebook 3 - Diagrams):" + "Run the complex code for the interactive visualisation:" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/javascript": [ + "(function(root) {\n", + " function embed_document(root) {\n", + " \n", + " const docs_json = {\"2176674f-1649-400e-926b-89abf8d8156a\":{\"defs\":[],\"roots\":{\"references\":[{\"attributes\":{\"children\":[{\"id\":\"1923\"}]},\"id\":\"1924\",\"type\":\"Column\"},{\"attributes\":{\"axis\":{\"id\":\"1799\"},\"coordinates\":null,\"dimension\":1,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1802\",\"type\":\"Grid\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"N and M at position x\"},\"id\":\"1785\",\"type\":\"Title\"},{\"attributes\":{\"axis_label\":\"Height h 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Forces and Moments:

\\n P = 10 kN
\\n Rx = 10 kN
\\n Ry (left) = 12.0 kN
\\n Ry (right) = 12.0 kN
\\n No cross section analysed.
\\n N = 0 kN
\\n V = 0 kN
\\n M = 0 kNm\\n \\n \",\"width\":170},\"id\":\"1261\",\"type\":\"Div\"},{\"attributes\":{\"axis_label\":\"Stress \\u03c3\\u2098 [MPa]\",\"coordinates\":null,\"formatter\":{\"id\":\"2063\"},\"group\":null,\"major_label_policy\":{\"id\":\"2064\"},\"ticker\":{\"id\":\"1494\"}},\"id\":\"1493\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1491\",\"type\":\"LinearScale\"},{\"attributes\":{\"callback\":null,\"tooltips\":[[\"Position\",\"@x m\"],[\"Axial force\",\"@y kN\"]]},\"id\":\"1287\",\"type\":\"HoverTool\"},{\"attributes\":{\"active\":[0],\"js_property_callbacks\":{\"change:active\":[{\"id\":\"1902\"}]},\"labels\":[\"Apply or remove axial force 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Geometrical and mechanical parameters:

\\n h = 200 mm
\\n b = 100 mm
\\n L = 6 m
\\n A = 2.00e+04 mm2
\\n Iy = 6.67e+07 mm4
\\n Iz = 1.67e+07 mm4\",\"width\":170},\"id\":\"1107\",\"type\":\"Div\"},{\"attributes\":{\"data\":{\"x\":{\"__ndarray__\":\"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA=\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[10]},\"y\":{\"__ndarray__\":\"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA=\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[10]}},\"selected\":{\"id\":\"2106\"},\"selection_policy\":{\"id\":\"2105\"}},\"id\":\"1868\",\"type\":\"ColumnDataSource\"},{\"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\":{\"data\":{\"x\":[0.0],\"y\":[0.0]},\"selected\":{\"id\":\"2108\"},\"selection_policy\":{\"id\":\"2107\"}},\"id\":\"1875\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_color\":{\"value\":\"gray\"},\"line_color\":{\"value\":\"gray\"},\"size\":{\"value\":15.380572041353537}},\"id\":\"1110\",\"type\":\"VeeHead\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1101\"},\"glyph\":{\"id\":\"1102\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1104\"},\"nonselection_glyph\":{\"id\":\"1103\"},\"view\":{\"id\":\"1106\"}},\"id\":\"1105\",\"type\":\"GlyphRenderer\"},{\"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\":\"1877\",\"type\":\"Scatter\"},{\"attributes\":{\"source\":{\"id\":\"1101\"}},\"id\":\"1106\",\"type\":\"CDSView\"},{\"attributes\":{\"end\":600,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1901\"}]},\"start\":20,\"step\":20,\"title\":\"Change the height h 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d\":\"1162\",\"type\":\"Rect\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1881\"},\"glyph\":{\"id\":\"1882\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1884\"},\"nonselection_glyph\":{\"id\":\"1883\"},\"view\":{\"id\":\"1886\"}},\"id\":\"1885\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1887\"},\"glyph\":{\"id\":\"1888\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1890\"},\"nonselection_glyph\":{\"id\":\"1889\"},\"view\":{\"id\":\"1892\"}},\"id\":\"1891\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"data\":{\"text\":[\"z\"],\"x\":[-88.0],\"y\":[0]},\"selected\":{\"id\":\"2097\"},\"selection_policy\":{\"id\":\"2096\"}},\"id\":\"1122\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"data\":{\"x\":[30.0],\"y\":[0]},\"selected\":{\"id\":\"1980\"},\"selection_policy\":{\"id\":\"1979\"}},\"id\":\"1161\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_color\":{\"value\":\"red\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1884\",\"type\":\"Text\"},{\"attributes\":{\"source\":{\"id\":\"1122\"}},\"id\":\"1127\",\"type\":\"CDSView\"},{\"attributes\":{\"data\":{\"text\":[\"\"],\"x\":[6],\"y\":[-5]},\"selected\":{\"id\":\"2112\"},\"selection_policy\":{\"id\":\"2111\"}},\"id\":\"1887\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"hatch_alpha\":{\"value\":0.1},\"height\":{\"value\":18.0},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"width\":{\"value\":72.0},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1163\",\"type\":\"Rect\"},{\"attributes\":{\"below\":[{\"id\":\"1139\"}],\"center\":[{\"id\":\"1142\"},{\"id\":\"1146\"},{\"id\":\"1225\"},{\"id\":\"1228\"},{\"id\":\"1231\"},{\"id\":\"1234\"},{\"id\":\"1237\"},{\"id\":\"1240\"}],\"height\":200,\"left\":[{\"id\":\"1143\"}],\"match_aspect\":true,\"renderers\":[{\"id\":\"1165\"},{\"id\":\"1198\"},{\"id\":\"1204\"},{\"id\":\"1210\"},{\"id\":\"1216\"},{\"id\":\"1222\"},{\"id\":\"1247\"},{\"id\":\"1253\"}],\"title\":{\"id\":\"1129\"},\"toolbar\":{\"id\":\"1154\"},\"toolbar_location\":null,\"width\":700,\"x_range\":{\"id\":\"1131\"},\"x_scale\":{\"id\":\"1135\"},\"y_range\":{\"id\":\"1133\"},\"y_scale\":{\"id\":\"1137\"}},\"id\":\"1128\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"source\":{\"id\":\"1881\"}},\"id\":\"1886\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1133\",\"type\":\"DataRange1d\"},{\"attributes\":{\"source\":{\"id\":\"1887\"}},\"id\":\"1892\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1135\",\"type\":\"LinearScale\"},{\"attributes\":{\"text_alpha\":{\"value\":0.1},\"text_baseline\":{\"value\":\"top\"},\"text_color\":{\"value\":\"red\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1889\",\"type\":\"Text\"},{\"attributes\":{\"coordinates\":null,\"formatter\":{\"id\":\"1936\"},\"group\":null,\"major_label_policy\":{\"id\":\"1937\"},\"ticker\":{\"id\":\"1140\"},\"visible\":false},\"id\":\"1139\",\"type\":\"LinearAxis\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1893\"},\"glyph\":{\"id\":\"1894\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1896\"},\"nonselection_glyph\":{\"id\":\"1895\"},\"view\":{\"id\":\"1898\"}},\"id\":\"1897\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"coordinates\":null,\"formatter\":{\"id\":\"1933\"},\"group\":null,\"major_label_policy\":{\"id\":\"1934\"},\"ticker\":{\"id\":\"1144\"},\"visible\":false},\"id\":\"1143\",\"type\":\"LinearAxis\"},{\"attributes\":{\"text_alpha\":{\"value\":0.2},\"text_baseline\":{\"value\":\"top\"},\"text_color\":{\"value\":\"red\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1890\",\"type\":\"Text\"},{\"attributes\":{\"data\":{\"text\":[\"\"],\"x\":[5],\"y\":[0]},\"selected\":{\"id\":\"2146\"},\"selection_policy\":{\"id\":\"2145\"}},\"id\":\"1893\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"text_alpha\":{\"value\":0.1},\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"red\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1895\",\"type\":\"Text\"},{\"attributes\":{\"axis\":{\"id\":\"1139\"},\"coordinates\":null,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1142\",\"type\":\"Grid\"},{\"attributes\":{\"source\":{\"id\":\"1893\"}},\"id\":\"1898\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1137\",\"type\":\"LinearScale\"},{\"attributes\":{\"coordinates\":null,\"group\":null,\"text\":\"Forces and Moments Scheme\"},\"id\":\"1129\",\"type\":\"Title\"},{\"attributes\":{\"text_baseline\":{\"value\":\"middle\"},\"text_color\":{\"value\":\"red\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1894\",\"type\":\"Text\"},{\"attributes\":{\"axis\":{\"id\":\"1143\"},\"coordinates\":null,\"dimension\":1,\"grid_line_alpha\":0,\"group\":null,\"ticker\":null},\"id\":\"1146\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1152\",\"type\":\"HelpTool\"},{\"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\":\"1140\",\"type\":\"BasicTicker\"},{\"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\"},\"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 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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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/A*Iy/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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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/A*Iy/M/1000\\n }\\n }\\n \\n \"},\"id\":\"1900\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1144\",\"type\":\"BasicTicker\"},{\"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\":\"1164\",\"type\":\"Rect\"},{\"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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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)/c**2\\n }\\n const step = 2*c / (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(2*c)*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*(h**2/4-(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 N*1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/Iy*(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V*1000*S/(Iy*b_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\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/A*Iy/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/2*0.8\\n var a = b-lambda*c\\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\":{},\"id\":\"1148\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1147\",\"type\":\"PanTool\"},{\"attributes\":{\"overlay\":{\"id\":\"1153\"}},\"id\":\"1149\",\"type\":\"BoxZoomTool\"},{\"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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h) {\\n return h*b**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/A*Iy/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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_or_t)\\n }\\n \\n \"},\"id\":\"1901\",\"type\":\"CustomJS\"},{\"attributes\":{},\"id\":\"1150\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1151\",\"type\":\"ResetTool\"},{\"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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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\":{\"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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/2*0.8\\n var a = b-lambda*c\\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\":{\"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\":\"1153\",\"type\":\"BoxAnnotation\"},{\"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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/2*(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return q*L/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return q*L/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/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 M*1e6/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*(h**2/4-(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 V*1000*S/(Iy*b_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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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 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"display_data" + } + ], "source": [ - "FIG_H_B = 200 # height figure beam\n", - "FIG_B_B = 700 # width figure beam\n", - "FIG_H_S = FIG_H_B # height figure scheme\n", - "FIG_B_S = FIG_B_B # width figure scheme\n", - "FIG_H_SEC = 600 # height figure section\n", - "DIV_B_GEO = 170\n", - "DIV_B_FORCES = 170\n", - "\n", - "options = dict(\n", - " toolbar_location=None\n", - ")\n", - "\n", - "# figure for the beam\n", - "paddingx = 0.2*L\n", - "int_x_b = (0-paddingx, L+paddingx)\n", - "int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)\n", - "fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,\n", - " f_h=FIG_H_B, f_b=FIG_B_B)\n", - "\n", - "\n", - "# figure for the cross-section\n", - "fig_section = sb.define_fig_section(MAX_B*0.8, MAX_H*0.8, options, FIG_H_SEC)\n", - "\n", - "\n", - "# beam\n", - "(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,\n", - " ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)\n", - "\n", - "# section\n", - "section = beam_section.draw_section(fig_section, b, h)\n", - "\n", - "\n", - "# show mechanical parameters\n", - "div_geo = Div(width= DIV_B_GEO, \n", - " text=beam_section.div_text_geo(round(h), round(b), round(L),\n", - " \"{:.2e}\".format(A),\n", - " \"{:.2e}\".format(Iy),\n", - " \"{:.2e}\".format(Iz)))\n", - "\n", - "\n", - "# change geometry\n", - "slider_b = Slider(\n", - " title=\"Change the width b [mm]\",\n", - " start=10,\n", - " end=MAX_B,\n", - " step=10,\n", - " value=b\n", - ")\n", - "slider_h = Slider(\n", - " title=\"Change the height h [mm]\",\n", - " start=20,\n", - " end=MAX_H,\n", - " step=20,\n", - " value=h\n", - ")\n", - "\n", - "# reference system\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis\n", - "fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=[\"y\"], text_color='gray', text_baseline='middle', angle=math.pi/2)\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis\n", - "fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=[\"z\"], text_color='gray', text_align='right', text_baseline='middle')\n", - "\n", - "\n", - "# figure for the forces and moments\n", - "fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)\n", - "\n", - "\n", - "# uniform load (beam)\n", - "u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE], width=L, height=q/SCALE,\n", - " fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)\n", - "label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE], text=[\"q\"], text_color=\"blue\")\n", - "\n", - "\n", - "# axial force (beam)\n", - "axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')\n", - "label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/2], text=[\"P\"], text_color=\"green\")\n", - "\n", - "\n", - "# position point\n", - "pos_opt = dict(\n", - " source=source,\n", - " size=10,\n", - " fill_alpha=0.5,\n", - " fill_color=\"magenta\",\n", - " color=\"magenta\",\n", - " alpha=0.5\n", - ")\n", - "beam_position = fig_beam.circle('x', 'y', **pos_opt)\n", - "forces_position = fig_scheme.circle('xF', 'y', **pos_opt)\n", - "\n", - "\n", - "# beam (scheme)\n", - "scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')\n", - "scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)\n", - "# uniform load (scheme)\n", - "scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',\n", - " fill_alpha=0.3, alpha=0.3)\n", - "scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',\n", - " color='navy', fill_alpha=0.3, alpha=0.3)\n", - "# axial force (scheme)\n", - "scheme_axial_force = models.force_vector(fig_scheme, P, L*SCALE+P, L*SCALE, 0, 0, 'green')\n", - "# Reactions (scheme)\n", - "scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -Ry_r, 0, 'orange')\n", - "scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')\n", - "scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')\n", - "# force N\n", - "scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# force V\n", - "scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# moment M\n", - "(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)\n", - "\n", - "\n", - "# change the uniform load q\n", - "slider_q = Slider(\n", - " title=\"Change the uniform load q [kN/m]\",\n", - " start=0.1,\n", - " end=MAX_Q,\n", - " step=0.1,\n", - " value=q\n", - ")\n", - "\n", - "\n", - "# choose position of interest\n", - "slider_position = Slider(\n", - " title=\"Change the position x along the beam [m]\",\n", - " start=0,\n", - " end=L,\n", - " step=0.02,\n", - " value=L\n", - ")\n", - "\n", - "\n", - "# choose left or right FBD\n", - "div_rg_FBD = Div(text=\"Free-body diagram (FBD):\")\n", - "radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)\n", - "\n", - "\n", - "# choose axial force or not\n", - "div_cb_P = Div(text=f\"Axial force P={P} kN (applied)\")\n", - "checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])\n", - "\n", - "\n", - "# show values of forces and moments\n", - "div_forces = Div(width=DIV_B_FORCES, \n", - " text=sb.div_text_forces(P, P, Ry_l, Ry_r, \"No cross section analysed.\", 0, 0, 0))\n", - "\n", - "\n", - "# figures for the diagrams\n", - "options_diag = dict(\n", - " toolbar_location=None,\n", - " x_axis_label=\"Position [m]\",\n", - " plot_width=FIG_B_B,\n", - " x_range=fig_beam.x_range\n", - ")\n", - "fig_N = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Axial force\", \"@y kN\")],\n", - " y_axis_label=\"Axial force N [kN]\",\n", - " plot_height=int(FIG_H_B*0.8),\n", - " title=\"N V M Diagrams\")\n", - "fig_V = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Shear force\", \"@y kN\")],\n", - " y_axis_label=\"Shear force V [kN]\",\n", - " plot_height=int(FIG_H_B*0.8))\n", - "fig_M = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Bending moment\", \"@y kNm\")],\n", - " y_axis_label=\"Bending moment M [kNm]\",\n", - " plot_height=FIG_H_B)\n", - "fig_N.xaxis.visible = False\n", - "fig_V.xaxis.visible = False\n", - "\n", - "\n", - "# plot N V M\n", - "N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)\n", - "V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)\n", - "M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)\n", - "\n", - "# point that shows the position that it's analyzed\n", - "N_position = fig_N.circle('x', 'N', **pos_opt)\n", - "V_position = fig_V.circle('x', 'V', **pos_opt)\n", - "M_position = fig_M.circle('x', 'M', **pos_opt)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now define the new figures, renderers and widgets:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "# figures for the stresses and strains\n", - "FIG_B_ss = 200\n", - "FIG_H_ss = 200\n", - "options_stress_strain = dict(\n", - " toolbar_location=None,\n", - " y_axis_label=\"Height h [mm]\",\n", - " plot_width=FIG_B_ss,\n", - " plot_height=FIG_H_ss\n", - ")\n", - "fig_stress_N = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2099 [MPa]\")\n", - "fig_stress_N.yaxis.visible = False\n", - "fig_axial_strain = figure(**options_stress_strain,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2099 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_axial_strain.yaxis.visible = False\n", - "fig_stress_M = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending stress and centroid\",\n", - " y_range=fig_stress_N.y_range,\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2098 [MPa]\")\n", - "fig_stress_M.yaxis.visible = False\n", - "fig_bending_strain = figure(**options_stress_strain,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2098 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_bending_strain.yaxis.visible = False\n", - "fig_stress_V = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Shear stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU}\\u1d65 [MPa]\")\n", - "fig_stress_V.yaxis.visible = False\n", - "fig_stress_sigma = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress \\N{GREEK SMALL LETTER SIGMA} and neutral axis\",\n", - " y_range=fig_stress_N.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA} [MPa]\")\n", - "fig_stress_tau = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress \\N{GREEK SMALL LETTER TAU}\",\n", - " y_range=fig_stress_V.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU} [MPa]\")\n", - "\n", - "# plot stress N V M\n", - "discr_stress_strain = 10\n", - "scale_x = 25\n", - "y_discr = np.linspace(0, h, discr_stress_strain)\n", - "sigma_N = stst.compute_sigma_axial(y_discr, 0, A)\n", - "N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,\n", - " source_section_scheme, scale_x=scale_x/10)\n", - "sigma_M = stst.compute_sigma_bending(y_discr, 0, Iy, yG)\n", - "(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,\n", - " source_section_scheme, True, yG, scale_x=scale_x)\n", - "S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, yG)\n", - "tau_V = stst.compute_tau_shear(y_discr, 0, S_rect, Iy, b)\n", - "V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)\n", - "\n", - "# plot stress sigma and tau\n", - "sigma_total = sigma_M + sigma_N\n", - "(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,\n", - " source_section_scheme,True, yG, scale_x=scale_x)\n", - "tau_total = tau_V\n", - "tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,\n", - " source_section_scheme, scale_x=1)\n", - "\n", - "# plot strain N M\n", - "strain_axial = stst.compute_epsilon_axial(y_discr, sigma_N, E)\n", - "axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)\n", - "strain_bending = stst.compute_epsilon_bending(y_discr, sigma_M, E)\n", - "bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)\n", - "\n", - "\n", - "# figures for NVM\n", - "fig_NM_section = figure(**options_stress_strain,\n", - " title=\"N and M at position x\",\n", - " match_aspect=True)\n", - "fig_NM_section.axis.visible = False\n", - "fig_NM_section.grid.grid_line_alpha = 0\n", - "\n", - "fig_V_section = figure(**options_stress_strain,\n", - " title=\"V at position x\",\n", - " match_aspect=True)\n", - "fig_V_section.axis.visible = False\n", - "fig_V_section.grid.grid_line_alpha = 0\n", - "\n", - "# section with NVM\n", - "models.section_diagram(fig_NM_section)\n", - "models.section_diagram(fig_V_section)\n", - "\n", - "# NVM in section\n", - "section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')\n", - "section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')\n", - "(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)\n", - "\n", - "# NVM label in section\n", - "OFFSET_N = 1\n", - "label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[\"\"], text_color=\"red\", text_baseline='bottom')\n", - "label_M_section = fig_NM_section.text(x=[OFFSET_N*6], y=[-OFFSET_N*5], text=[\"\"], text_color=\"red\", text_baseline='top')\n", - "label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[0], text=[\"\"], text_color=\"red\", text_baseline='middle')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Configure the logics:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "args_slider_pos = dict(source=source,\n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " s_M=source_M,\n", - " arr_head=scheme_M_head,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_slider_pos = f\"\"\"\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", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{models.implement_check_stateJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "\"\"\"\n", - "updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)\n", - "\n", - "\n", - "args_slider_b = dict(source=source,\n", - " s_b=source_beam,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag)\n", - "code_change_b = f\"\"\"\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", - "\n", - "// emit the changes\n", - "source.change.emit()\n", - "\n", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "\"\"\"\n", - "update_b = CustomJS(args=args_slider_b, code=code_change_b)\n", - "\n", - "\n", - "args_slider_h = dict(source=source,\n", - " s_b=source_beam,\n", - " s_ss=source_section_scheme,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag)\n", - "code_change_h = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "\"\"\"\n", - "update_h = CustomJS(args=args_slider_h, code=code_change_h)\n", - "\n", - "\n", - "args_checkbox_P = dict(source=source,\n", - " s_M=source_M,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force, \n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r, \n", - " fN=scheme_N,\n", - " fV=scheme_V, \n", - " arr_head=scheme_M_head,\n", - " N_diag=N_diag,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_checkbox_P = f\"\"\"\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] = {P}*(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", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_compute_RxJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_update_N_diagramJS(discr_NVM)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)\n", - "\n", - "\n", - "args_radiogroup_FBD = dict(source=source, \n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M, \n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N, \n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_radiogroup_FBD = f\"\"\"\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", - "{models.implement_check_stateJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)\n", - "\n", - "\n", - "args_slider_q = dict(source=source,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M,\n", - " div_f=div_forces,\n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " V_diag=V_diag,\n", - " M_diag=M_diag,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_slider_q = f\"\"\"\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", - "{js.implement_update_arrowJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_compute_Ry_lJS()}\n", - "{sb.implement_compute_Ry_rJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_update_V_diagramJS(discr_NVM)}\n", - "{sb.implement_update_M_diagramJS(discr_NVM)}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_u_loadJS(OFFSET_Q)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain)}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)\n", - "\n", - "# apply the logics\n", - "slider_b.js_on_change('value', update_b)\n", - "slider_h.js_on_change('value', update_h)\n", - "slider_position.js_on_change('value', updade_slider_pos)\n", - "checkbox_P.js_on_click(update_checkbox_P)\n", - "radiogroup_FBD.js_on_click(update_radiogroup_FBD)\n", - "slider_q.js_on_change('value', update_slider_q)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Build the layout and show the figures. Note that the forces in the scheme are updated after moving the position of the point with the slider.\n", - "Note that the value of the forces and moments shown below represents the intensity, thus is always positive. The direction is given by the vector in the scheme." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "padding_layout = 10\n", - "layout1 = layout([\n", - " [column(row(column(fig_scheme,\n", - " row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout),\n", - " slider_b,\n", - " slider_h,\n", - " row(div_geo, div_forces),\n", - " Spacer(height=padding_layout),\n", - " slider_position,\n", - " slider_q,\n", - " div_rg_FBD,\n", - " radiogroup_FBD,\n", - " div_cb_P,\n", - " checkbox_P))),\n", - " column(fig_beam,\n", - " Spacer(height=padding_layout),\n", - " fig_N,\n", - " fig_V,\n", - " fig_M)),\n", - " row(column(\n", - " row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_stress_sigma),\n", - " 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),\n", - " ))\n", - " )],\n", - "])\n", - "\n", - "show(layout1)" + "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)" ] } ], "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": 2 + "nbformat_minor": 4 } diff --git a/Simple Beam DEMOs/sb_torsion.ipynb b/Simple Beam DEMOs/sb_torsion.ipynb index fd90504..e136c34 100644 --- a/Simple Beam DEMOs/sb_torsion.ipynb +++ b/Simple Beam DEMOs/sb_torsion.ipynb @@ -1,1353 +1,488 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "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." ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
\n", + " \n", + " Loading BokehJS ...\n", + "
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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": 8, + "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)\n", - "\n", - "# constants for the visualisation\n", - "SCALE = 10\n", - "SCALE_T = 10\n", - "OFFSET_Q = q\n", - "MAX_B = 3*b\n", - "MAX_H = 3*h\n", - "MAX_T = 2*t\n", - "MAX_Q = q/4*5\n", - "\n", - "# store the values in a specific format\n", - "data_beam = dict(\n", - " x=[0, L],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_beam = dict(\n", - " x=[0, L*SCALE],\n", - " y=[0, 0]\n", - ")\n", - "\n", - "data_scheme_q = dict(\n", - " x=[0, 0, L*SCALE, L*SCALE],\n", - " y=[OFFSET_Q, OFFSET_Q+q, OFFSET_Q+q, OFFSET_Q],\n", - " x_fade=[0, 0, L*SCALE, L*SCALE]\n", - ")\n", - "\n", - "data_section_scheme = dict(\n", - " x=[0, 0], \n", - " y=[0, h]\n", - ")\n", - "\n", - "initial_position = L\n", - "initial_state = 'IDLE' # possible cases: IDLE, R_SEC, L_SEC\n", - "initial_FBD = 0 # right=0 left=1\n", - "data = dict( # stores every useful single variable\n", - " state=[initial_state], \n", - " FBD=[initial_FBD],\n", - " SCALE=[SCALE],\n", - " L=[L],\n", - " b=[b],\n", - " h=[h],\n", - " t=[t],\n", - " E=[E],\n", - " A=[A],\n", - " Iy=[Iy],\n", - " Iz=[Iz],\n", - " yG=[yG],\n", - " y_n_axis=[y_n_axis],\n", - " P=[P],\n", - " x=[initial_position],\n", - " y=[0],\n", - " q=[q],\n", - " Mt=[Mt],\n", - " Rx=[Rx],\n", - " Ry_l=[Ry_l],\n", - " Ry_r=[Ry_r],\n", - " N=[N],\n", - " V=[V],\n", - " M=[M],\n", - " T=[T],\n", - " xF=[L*SCALE]\n", - ")\n", - "\n", - "source_beam = ColumnDataSource(data_beam)\n", - "source_scheme_beam = ColumnDataSource(data_scheme_beam)\n", - "source_scheme_q = ColumnDataSource(data_scheme_q)\n", - "source_section_scheme = ColumnDataSource(data_section_scheme)\n", - "source = ColumnDataSource(data)\n", - "\n", - "# Constants\n", - "FIG_H_B = 200 # height figure beam\n", - "FIG_B_B = 700 # width figure beam\n", - "FIG_H_S = FIG_H_B # height figure scheme\n", - "FIG_B_S = FIG_B_B # width figure scheme\n", - "FIG_H_SEC = 600 # height figure section\n", - "DIV_B_GEO = 170\n", - "DIV_B_FORCES = 170" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create the figures, the plots and the widgets (same of Notebook 4 - Stresses and Strains):" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "options = dict(\n", - " toolbar_location=None\n", - ")\n", - "\n", - "# figure for the beam\n", - "paddingx = 0.2*L\n", - "int_x_b = (0-paddingx, L+paddingx)\n", - "int_y_b = (-OFFSET_Q/SCALE, (MAX_Q+OFFSET_Q)/SCALE)\n", - "fig_beam = sb.define_fig_beam(int_x_b, int_y_b, options,\n", - " f_h=FIG_H_B, f_b=FIG_B_B)\n", - "\n", - "\n", - "# figure for the cross-section\n", - "fig_section = sb.define_fig_section(MAX_B*0.8, MAX_H*0.8, options, FIG_H_SEC)\n", - "\n", - "# Doge for scale (if not visualized, remove this part because the browser don't support it correctly)\n", - "h_img = 350 # mm\n", - "fig_section.image_url(url=['https://img-10.stickers.cloud/packs/9a805d22-5d64-42f0-ae3c-bf58e080a463/webp/71246027-2154-494f-adcc-eeb814c11dad.webp'], x=-h_img/2, y=-MAX_H/2*1.01, h=h_img, w=h_img)\n", - "fig_section.text(x=[0], y=[-MAX_H/2-h_img*1.05], text_align=\"center\", text=[f\"Doge for scale (h={h_img} mm)\"], text_font_size=\"10px\")\n", - "\n", - "\n", - "# beam\n", - "(beam, support_l, support_r) = sb.draw_beam(fig_beam, source_beam, L,\n", - " ratio = (int_y_b[1]-int_y_b[0])/FIG_H_B*100)\n", - "\n", - "# section\n", - "section = beam_section.draw_section(fig_section, b, h, t)\n", - "\n", - "\n", - "# show mechanical parameters\n", - "div_geo = Div(width= DIV_B_GEO, \n", - " text=beam_section.div_text_geo(round(h), round(b), round(t), round(L),\n", - " \"{:.2e}\".format(A),\n", - " \"{:.2e}\".format(Iy),\n", - " \"{:.2e}\".format(Iz)))\n", - "\n", - "\n", - "# change geometry\n", - "slider_b = Slider(\n", - " title=\"Change the width b [mm]\",\n", - " start=MAX_T*2+10,\n", - " end=MAX_B,\n", - " step=10,\n", - " value=b\n", - ")\n", - "slider_h = Slider(\n", - " title=\"Change the height h [mm]\",\n", - " start=MAX_T*2+10,\n", - " end=MAX_H,\n", - " step=10,\n", - " value=h\n", - ")\n", - "\n", - "# reference system\n", - "axis_arrow_length = 0.8\n", - "axis_arrow_scale = 100\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, 0, 0, axis_arrow_length*axis_arrow_scale*1.6, 'gray') # y axis\n", - "fig_section.text(x=[0], y=[axis_arrow_length*axis_arrow_scale*1.7], text=[\"y\"], text_color='gray', text_baseline='middle', angle=math.pi/2)\n", - "models.force_vector(fig_section, axis_arrow_length*10, 0, -axis_arrow_length*axis_arrow_scale, 0, 0, 'gray') # z axis\n", - "fig_section.text(x=[-axis_arrow_length*axis_arrow_scale*1.1], y=[0], text=[\"z\"], text_color='gray', text_align='right', text_baseline='middle')\n", - "\n", - "\n", - "# figure for the forces and moments\n", - "fig_scheme = sb.define_figure_scheme(L, SCALE, MAX_Q, OFFSET_Q, options, FIG_H_S, FIG_B_S)\n", - "\n", - "\n", - "# uniform load (beam)\n", - "u_load = fig_beam.rect([L/2], [(q/2+OFFSET_Q)/SCALE], width=L, height=q/SCALE,\n", - " fill_color='blue', color='navy', fill_alpha=0.6, alpha=0.6)\n", - "label_u_load = fig_beam.text(x=[-0.2], y=[OFFSET_Q/SCALE], text=[\"q\"], text_color=\"blue\")\n", - "\n", - "\n", - "# axial force (beam)\n", - "axial_force = models.force_vector(fig_beam, P, L+P/SCALE, L, 0, 0, 'green')\n", - "label_P_force = fig_beam.text(x=[L+P/2/SCALE], y=[OFFSET_Q/SCALE/4], text=[\"P\"], text_color=\"green\")\n", - "\n", - "\n", - "# position point\n", - "pos_opt = dict(\n", - " source=source,\n", - " size=10,\n", - " fill_alpha=0.5,\n", - " fill_color=\"magenta\",\n", - " color=\"magenta\",\n", - " alpha=0.5\n", - ")\n", - "beam_position = fig_beam.circle('x', 'y', **pos_opt)\n", - "forces_position = fig_scheme.circle('xF', 'y', **pos_opt)\n", - "\n", - "\n", - "# beam (scheme)\n", - "scheme_beam = fig_scheme.line('x', 'y', source=source_scheme_beam, line_width=2, color='black')\n", - "scheme_fade_beam = fig_scheme.line(x=[0, L*SCALE], y=[0, 0], line_width=2, color='black', alpha=0.2)\n", - "# uniform load (scheme)\n", - "scheme_u_load = fig_scheme.patch('x', 'y', source=source_scheme_q, fill_color='blue', color='navy',\n", - " fill_alpha=0.3, alpha=0.3)\n", - "scheme_fade_u_load = fig_scheme.patch('x_fade', 'y', source=source_scheme_q, fill_color='blue',\n", - " color='navy', fill_alpha=0.3, alpha=0.3)\n", - "# axial force (scheme)\n", - "scheme_axial_force = models.force_vector(fig_scheme, P, L*SCALE+P, L*SCALE, 0, 0, 'green')\n", - "# Reactions (scheme)\n", - "scheme_Ry_r = models.force_vector(fig_scheme, Ry_r, L*SCALE, L*SCALE, -Ry_r, 0, 'orange')\n", - "scheme_Ry_l = models.force_vector(fig_scheme, Ry_l, 0, 0, -Ry_l, 0, 'orange')\n", - "scheme_Rx_l = models.force_vector(fig_scheme, Rx, -Rx, 0, 0, 0, 'orange')\n", - "# force N\n", - "scheme_N = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# force V\n", - "scheme_V = models.force_vector(fig_scheme, 0, 0, 0, 0, 0, 'red')\n", - "# moment M\n", - "(scheme_M_line, scheme_M_head, source_M) = models.define_curvedArrow(fig_scheme, 0, 0, 0, size_head=0)\n", - "\n", - "\n", - "# change the uniform load q\n", - "slider_q = Slider(\n", - " title=\"Change the uniform load q [kN/m]\",\n", - " start=0.1,\n", - " end=MAX_Q,\n", - " step=0.1,\n", - " value=q\n", - ")\n", - "\n", - "\n", - "# choose position of interest\n", - "slider_position = Slider(\n", - " title=\"Change the position x along the beam [m]\",\n", - " start=0,\n", - " end=L,\n", - " step=0.02,\n", - " value=L\n", - ")\n", - "\n", - "\n", - "# choose left or right FBD\n", - "div_rg_FBD = Div(text=\"Free-body diagram (FBD):\")\n", - "radiogroup_FBD = RadioButtonGroup(labels=['Right-hand', 'Left-hand'], active=initial_FBD)\n", - "\n", - "\n", - "# choose axial force or not\n", - "div_cb_P = Div(text=f\"Axial force P={P} kN (applied)\")\n", - "checkbox_P = CheckboxButtonGroup(labels=['Apply or remove axial force P'], active=[0])\n", - "\n", - "\n", - "# show values of forces and moments\n", - "div_forces = Div(width=DIV_B_FORCES, \n", - " text=sb.div_text_forces(P, P, Ry_l, Ry_r, \"No cross section analysed.\", 0, 0, 0))\n", - "\n", - "\n", - "# figures for the diagrams\n", - "options_diag = dict(\n", - " toolbar_location=None,\n", - " x_axis_label=\"Position [m]\",\n", - " plot_width=FIG_B_B,\n", - " x_range=fig_beam.x_range\n", - ")\n", - "fig_N = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Axial force\", \"@y kN\")],\n", - " y_axis_label=\"Axial force N [kN]\",\n", - " plot_height=int(FIG_H_B*0.8),\n", - " title=\"N V M Diagrams\")\n", - "fig_V = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Shear force\", \"@y kN\")],\n", - " y_axis_label=\"Shear force V [kN]\",\n", - " plot_height=int(FIG_H_B*0.8))\n", - "fig_M = figure(**options_diag,\n", - " tooltips= [(\"Position\", \"@x m\"),\n", - " (\"Bending moment\", \"@y kNm\")],\n", - " y_axis_label=\"Bending moment M [kNm]\",\n", - " plot_height=FIG_H_B)\n", - "fig_N.xaxis.visible = False\n", - "fig_V.xaxis.visible = False\n", - "\n", - "\n", - "# plot N V M\n", - "N_diag = models.NVM_diagram(fig_N, x_discr, N_discr, L, source_beam)\n", - "V_diag = models.NVM_diagram(fig_V, x_discr, V_discr, L, source_beam)\n", - "M_diag = models.NVM_diagram(fig_M, x_discr, M_discr, L, source_beam)\n", - "\n", - "\n", - "# point that shows the position that it's analyzed\n", - "N_position = fig_N.circle('x', 'N', **pos_opt)\n", - "V_position = fig_V.circle('x', 'V', **pos_opt)\n", - "M_position = fig_M.circle('x', 'M', **pos_opt)\n", - "\n", - "\n", - "# figures for the stresses and strains\n", - "FIG_B_ss = 200\n", - "FIG_H_ss = 200\n", - "options_stress_strain = dict(\n", - " toolbar_location=None,\n", - " y_axis_label=\"Height h [mm]\",\n", - " plot_width=FIG_B_ss,\n", - " plot_height=FIG_H_ss,\n", - ")\n", - "fig_stress_N = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2099 [MPa]\")\n", - "fig_stress_N.yaxis.visible = False\n", - "fig_axial_strain = figure(**options_stress_strain,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Axial strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2099 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_axial_strain.yaxis.visible = False\n", - "fig_stress_M = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending stress and centroid\",\n", - " y_range=fig_stress_N.y_range,\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA}\\u2098 [MPa]\")\n", - "fig_stress_M.yaxis.visible = False\n", - "fig_bending_strain = figure(**options_stress_strain,\n", - " tooltips= [(\"Strain\", \"@x %\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Bending strain\",\n", - " x_axis_label=\"Strain \\N{GREEK SMALL LETTER EPSILON}\\u2098 [%]\",\n", - " y_range=fig_stress_N.y_range)\n", - "fig_bending_strain.yaxis.visible = False\n", - "fig_stress_V = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Shear stress\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU}\\u1d65 [MPa]\")\n", - "fig_stress_V.yaxis.visible = False\n", - "fig_stress_sigma = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress \\N{GREEK SMALL LETTER SIGMA} and neutral axis\",\n", - " y_range=fig_stress_N.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER SIGMA} [MPa]\")\n", - "fig_stress_tau = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Total stress \\N{GREEK SMALL LETTER TAU}\",\n", - " y_range=fig_stress_V.y_range,\n", - " y_axis_location=\"right\",\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU} [MPa]\")\n", - "\n", - "\n", - "# plot stress N V M\n", - "discr_stress_strain = 50\n", - "scale_x = 25\n", - "y_discr = np.linspace(0, h, discr_stress_strain)\n", - "sigma_N = stst.compute_sigma_axial(y_discr, N, A)\n", - "N_stress_diag = models.stress_diagram(fig_stress_N, sigma_N, h,\n", - " source_section_scheme, scale_x=scale_x/10)\n", - "sigma_M = stst.compute_sigma_bending(y_discr, 0, Iy, yG)\n", - "(M_stress_diag, centroid) = models.stress_diagram(fig_stress_M, sigma_M, h,\n", - " source_section_scheme, True, yG, scale_x=scale_x)\n", - "S_rect = beam_section.compute_first_moment_of_area(y_discr, b, h, t, yG)\n", - "tau_V = stst.compute_tau_shear(y_discr, 0, S_rect, Iy, b)\n", - "V_stress_diag = models.stress_diagram(fig_stress_V, tau_V, h, source_section_scheme, scale_x=1)\n", - "\n", - "\n", - "# plot stress sigma and tau\n", - "sigma_total = sigma_M + sigma_N\n", - "(sigma_stress_diag, neutral_axis) = models.stress_diagram(fig_stress_sigma, sigma_total, h,\n", - " source_section_scheme,True, yG, scale_x=scale_x)\n", - "tau_total = tau_V\n", - "tau_stress_diag = models.stress_diagram(fig_stress_tau, tau_total, h,\n", - " source_section_scheme, scale_x=1)\n", - "\n", - "# plot strain N M\n", - "strain_axial = stst.compute_epsilon_axial(y_discr, sigma_N, E)\n", - "axial_strain_diag = models.strain_diagram(fig_axial_strain, strain_axial, h, source_section_scheme)\n", - "strain_bending = stst.compute_epsilon_bending(y_discr, sigma_M, E)\n", - "bending_strain_diag = models.strain_diagram(fig_bending_strain, strain_bending, h, source_section_scheme)\n", - "\n", - "\n", - "# figures for NVM\n", - "fig_NM_section = figure(**options_stress_strain,\n", - " title=\"N and M at position x\",\n", - " match_aspect=True)\n", - "fig_NM_section.axis.visible = False\n", - "fig_NM_section.grid.grid_line_alpha = 0\n", - "\n", - "fig_V_section = figure(**options_stress_strain,\n", - " title=\"V at position x\",\n", - " match_aspect=True)\n", - "fig_V_section.axis.visible = False\n", - "fig_V_section.grid.grid_line_alpha = 0\n", - "\n", - "\n", - "# section with NVM\n", - "models.section_diagram(fig_NM_section)\n", - "models.section_diagram(fig_V_section)\n", - "\n", - "\n", - "# NVM in section\n", - "section_N = models.force_vector(fig_NM_section, 0, 0, 0, 0, 0, 'red')\n", - "section_V = models.force_vector(fig_V_section, 0, 0, 0, 0, 0, 'red')\n", - "(section_M_line, section_M_head, source_section_M) = models.define_curvedArrow(fig_NM_section, 0, 0, 0, size_head=0)\n", - "\n", - "\n", - "# NVM label in section\n", - "OFFSET_N = 1\n", - "label_N_section = fig_NM_section.text(x=[P*1.1], y=[OFFSET_N], text=[\"\"], text_color=\"red\", text_baseline='bottom')\n", - "label_M_section = fig_NM_section.text(x=[OFFSET_N*6], y=[-OFFSET_N*5], text=[\"\"], text_color=\"red\", text_baseline='top')\n", - "label_V_section = fig_V_section.text(x=[OFFSET_N*5], y=[OFFSET_N*4], text=[\"\"], text_color=\"red\", text_baseline='middle')" + "Ry_r = sb.compute_Ry_r(q, L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now define the new figures, renderers and widgets:" + "Run the complex code for the interactive visualisation:" ] }, { "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "# applied torsion Mt\n", - "str_Mt = \"M\\N{LATIN SUBSCRIPT SMALL LETTER T}\"\n", - "div_cb_T = Div(text=f\"Torsion {str_Mt}={Mt} kNm (applied)\")\n", - "checkbox_T = CheckboxButtonGroup(labels=[f'Apply or remove torsion {str_Mt}'], active=[0])\n", - "\n", - "\n", - "# torsion diagram\n", - "fig_M.plot_height = int(FIG_H_B*0.8)\n", - "fig_M.xaxis.visible = False\n", - "fig_T = figure(**options_diag,\n", - " tooltips= [(\"Position:\", \"@x m\"),\n", - " (\"Torsion:\", \"@y kNm\")],\n", - " y_axis_label=\"Torsion T [kNm]\",\n", - " plot_height=FIG_H_B)\n", - "\n", - "\n", - "# change geometry (thickness)\n", - "slider_t = Slider(\n", - " title=\"Change the thicknes t [mm]\",\n", - " start=2,\n", - " end=MAX_T,\n", - " step=1,\n", - " value=t\n", - ")\n", - "\n", - "\n", - "# plot T\n", - "T_diag = models.NVM_diagram(fig_T, x_discr, T_discr, L, source_beam)\n", - "\n", - "\n", - "# point that shows the position that it's analyzed\n", - "T_position = fig_T.circle('x', 'T', **pos_opt)\n", - "\n", - "\n", - "# figure for the stress tau_T\n", - "fig_stress_T = figure(**options_stress_strain,\n", - " tooltips= [(\"Stress\", \"@x MPa\"),\n", - " (\"Height\", \"@y mm\")],\n", - " title=\"Torsional stress\",\n", - " y_range=fig_stress_V.y_range,\n", - " x_axis_label=\"Stress \\N{GREEK SMALL LETTER TAU}\\N{LATIN SUBSCRIPT SMALL LETTER T} [MPa]\")\n", - "fig_stress_T.yaxis.visible = False\n", - "\n", - "\n", - "# torsion in the section\n", - "(section_torsion_line, section_torsion_head, section_torsion_source) = models.define_curvedArrow(fig_section, 0, T*4/SCALE_T, abs(T*3/SCALE_T), size_head=20)\n", - "\n", - "\n", - "# moment Mt in beam\n", - "PIXEL2UNIT_BEAM = 100\n", - "(beam_torsion_line, beam_torsion_head, source_beam_torsion) = models.define_doubleArrow(fig_beam, L/2, L/2+Mt/SCALE/10, 0, 0,\n", - " arrow_color=\"green\", pixel2unit=PIXEL2UNIT_BEAM)\n", - "# label\n", - "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\")\n", - "\n", - "\n", - "# add torsion in section stress\n", - "T_DOUBLE_HEAD_SIZE = 10\n", - "(section_T_line, section_T_head, section_T_source) = models.define_doubleArrow(fig_V_section, OFFSET_N*4-T/SCALE_T, OFFSET_N*4, 0, 0, size_head=T_DOUBLE_HEAD_SIZE)\n", - "# label\n", - "label_T_section = fig_V_section.text(x=[Mt*1.1/SCALE_T], y=[OFFSET_N], text=[\"T\"], text_color=\"red\", text_baseline='bottom')\n", - "\n", - "\n", - "# tau stress torsion\n", - "tau_T = beam_section.compute_tau_torsion(y_discr, T, b, h, t)\n", - "T_stress_diag = models.stress_diagram(fig_stress_T, tau_T, h, source_section_scheme, scale_x=1)\n", - "\n", - "# Easter egg\n", - "EasterEgg1 = fig_N.text(x=[2], y=[-4], text=\"\", text_color=\"purple\", text_font_size=\"10px\", angle=math.pi/10)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Configure the logics:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "args_slider_pos = dict(source=source,\n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " s_M=source_M,\n", - " arr_head=scheme_M_head,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section,\n", - " section_T_line=section_T_line,\n", - " section_T_head=section_T_head,\n", - " section_T_source=section_T_source,\n", - " section_torsion_head=section_torsion_head,\n", - " section_torsion_source=section_torsion_source,\n", - " label_T_section=label_T_section,\n", - " div_T=div_cb_T,\n", - " T_stress_diag=T_stress_diag)\n", - "code_slider_pos = f\"\"\"\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", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{models.implement_check_stateJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{sb.implement_update_T_sectionJS(scale_T=SCALE_T)}\n", - "{js.implement_update_doubleArrowJS()}\n", - "{sb.implement_compute_TJS()}\n", - "{beam_section.implement_compute_tau_torsionJS()}\n", - "{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}\n", - "\"\"\"\n", - "updade_slider_pos = CustomJS(args=args_slider_pos, code=code_slider_pos)\n", - "\n", - "\n", - "args_slider_b = dict(source=source,\n", - " s_b=source_beam,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " T_stress_diag=T_stress_diag,\n", - " div_P=div_cb_P)\n", - "code_change_b = f\"\"\"\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 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 == {MAX_B}) {{\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{beam_section.implement_compute_tau_torsionJS()}\n", - "{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}\n", - "\"\"\"\n", - "update_b = CustomJS(args=args_slider_b, code=code_change_b)\n", - "\n", - "\n", - "args_slider_h = dict(source=source,\n", - " s_b=source_beam,\n", - " s_ss=source_section_scheme,\n", - " div=div_geo, \n", - " section=section,\n", - " support_r=support_r,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " T_stress_diag=T_stress_diag,\n", - " div_T=div_cb_T,\n", - " EE1=EasterEgg1)\n", - "code_change_h = f\"\"\"\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 == {MAX_H}) {{\n", - " div_T.text = str_tmp+str_Doge\n", - "}} else {{\n", - " div_T.text = str_tmp.replace(str_Doge, '')\n", - "}}*/\n", - "if (h == {MAX_H}) {{\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{beam_section.implement_compute_tau_torsionJS()}\n", - "{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}\n", - "\"\"\"\n", - "update_h = CustomJS(args=args_slider_h, code=code_change_h)\n", - "\n", - "\n", - "args_checkbox_P = dict(source=source,\n", - " s_M=source_M,\n", - " div_P=div_cb_P,\n", - " div_f=div_forces,\n", - " fP=scheme_axial_force, \n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r, \n", - " fN=scheme_N,\n", - " fV=scheme_V, \n", - " arr_head=scheme_M_head,\n", - " N_diag=N_diag,\n", - " neutral_axis=neutral_axis,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_checkbox_P = f\"\"\"\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] = {P}*(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", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_compute_RxJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_compute_NJS()}\n", - "{sb.implement_update_N_diagramJS(discr_NVM)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{beam_section.implement_compute_tau_torsionJS()}\n", - "\"\"\"\n", - "update_checkbox_P = CustomJS(args=args_checkbox_P, code=code_checkbox_P)\n", - "\n", - "\n", - "args_radiogroup_FBD = dict(source=source, \n", - " s_sb=source_scheme_beam,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M, \n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N, \n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " tau_stress_diag=tau_stress_diag)\n", - "code_radiogroup_FBD = f\"\"\"\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", - "{models.implement_check_stateJS()}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{sb.implement_update_scheme_positionJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "\"\"\"\n", - "update_radiogroup_FBD = CustomJS(args=args_radiogroup_FBD, code=code_radiogroup_FBD)\n", - "\n", - "\n", - "args_slider_q = dict(source=source,\n", - " s_q=source_scheme_q,\n", - " s_M=source_M,\n", - " div_f=div_forces,\n", - " div_P=div_cb_P,\n", - " fP=scheme_axial_force,\n", - " fRx=scheme_Rx_l,\n", - " fRyl=scheme_Ry_l,\n", - " fRyr=scheme_Ry_r,\n", - " fN=scheme_N,\n", - " fV=scheme_V,\n", - " arr_head=scheme_M_head,\n", - " V_diag=V_diag,\n", - " M_diag=M_diag,\n", - " centroid=centroid,\n", - " neutral_axis=neutral_axis,\n", - " V_stress_diag=V_stress_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " section_N=section_N,\n", - " section_V=section_V,\n", - " section_M_head=section_M_head,\n", - " s_section_M=source_section_M,\n", - " label_N_section=label_N_section,\n", - " label_V_section=label_V_section,\n", - " label_M_section=label_M_section)\n", - "code_slider_q = f\"\"\"\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", - "{js.implement_update_arrowJS()}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_parabolaJS()}\n", - "{js.implement_arrow_alphaJS()}\n", - "{js.implement_update_arrowJS()}\n", - "{sb.implement_compute_VJS()}\n", - "{sb.implement_compute_MJS()}\n", - "{sb.implement_compute_Ry_lJS()}\n", - "{sb.implement_compute_Ry_rJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{sb.implement_update_V_diagramJS(discr_NVM)}\n", - "{sb.implement_update_M_diagramJS(discr_NVM)}\n", - "{sb.implement_update_reactionsJS()}\n", - "{sb.implement_update_external_forcesJS()}\n", - "{sb.implement_update_u_loadJS(OFFSET_Q)}\n", - "{sb.implement_update_internal_forcesJS()}\n", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{beam_section.implement_compute_centroid_yJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{sb.implement_update_div_forcesJS()}\n", - "{js.implement_update_NVM_sectionJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{beam_section.implement_compute_tau_torsionJS()}\n", - "\"\"\"\n", - "update_slider_q = CustomJS(args=args_slider_q, code=code_slider_q)\n", - "\n", - "\n", - "args_checkbox_T = dict(source=source,\n", - " T_diag=T_diag,\n", - " div_T=div_cb_T,\n", - " label_T_section=label_T_section,\n", - " section_T_line=section_T_line,\n", - " section_T_head=section_T_head,\n", - " section_T_source=section_T_source,\n", - " section_torsion_head=section_torsion_head,\n", - " section_torsion_source=section_torsion_source,\n", - " neutral_axis=neutral_axis,\n", - " sigma_stress_diag=sigma_stress_diag,\n", - " tau_stress_diag=tau_stress_diag,\n", - " T_stress_diag=T_stress_diag)\n", - "code_checkbox_T = f\"\"\"\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] = {Mt}*(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", - "{js.implement_update_curvedArrowJS()}\n", - "{js.implement_update_doubleArrowJS()}\n", - "{js.implement_arrow_growthJS()}\n", - "{sb.implement_update_T_sectionJS(scale_T=SCALE_T)}\n", - "{sb.implement_compute_TJS()}\n", - "{sb.implement_update_T_diagramJS(discr_NVM)}\n", - "{js.implement_linspaceJS()}\n", - "{js.implement_update_NVM_diagramJS()}\n", - "{beam_section.implement_compute_tau_torsionJS()}\n", - "{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}\n", - "\"\"\"\n", - "update_checkbox_T = CustomJS(args=args_checkbox_T, code=code_checkbox_T)\n", - "\n", - "\n", - "args_slider_t = dict(source=source,\n", - " div=div_geo,\n", - " section=section,\n", - " N_stress_diag=N_stress_diag,\n", - " axial_strain_diag=axial_strain_diag,\n", - " M_stress_diag=M_stress_diag,\n", - " bending_strain_diag=bending_strain_diag,\n", - " centroid=centroid,\n", - " V_stress_diag=V_stress_diag,\n", - " sigma_stress_diag=sigma_stress_diag, \n", - " tau_stress_diag=tau_stress_diag,\n", - " neutral_axis=neutral_axis,\n", - " T_stress_diag=T_stress_diag)\n", - "code_change_t = f\"\"\"\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", - "{beam_section.implement_update_div_geoJS()}\n", - "{beam_section.implement_update_sectionJS()}\n", - "{beam_section.implement_compute_areaJS()}\n", - "{beam_section.implement_compute_inertia_yJS()}\n", - "{beam_section.implement_compute_inertia_zJS()}\n", - "{stst.implement_compute_neutral_axisJS()}\n", - "{js.implement_update_axial_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_bending_stress_strainJS(discr_stress_strain)}\n", - "{js.implement_update_shear_stressJS(discr_stress_strain, hollow_rectangular_section=True)}\n", - "{js.implement_update_total_stressJS(discr_stress_strain, T_opt=True, hollow_rectangular_section=True)}\n", - "{js.implement_linspaceJS()}\n", - "{stst.implement_compute_epsilon_axialJS()}\n", - "{stst.implement_compute_epsilon_bendingJS()}\n", - "{stst.implement_compute_sigma_axialJS()}\n", - "{js.implement_update_stress_diagramJS()}\n", - "{js.implement_update_strain_diagramJS()}\n", - "{stst.implement_compute_sigma_bendingJS()}\n", - "{stst.implement_compute_total_sigmaJS()}\n", - "{stst.implement_compute_total_tauJS()}\n", - "{beam_section.implement_compute_first_moment_of_areaJS()}\n", - "{beam_section.implement_compute_first_moment_of_area_implicitJS()}\n", - "{stst.implement_compute_tau_shearJS()}\n", - "{beam_section.implement_compute_tau_torsionJS()}\n", - "{beam_section.implement_update_torsional_stressJS(discr_stress_strain)}\n", - "\"\"\"\n", - "update_t = CustomJS(args=args_slider_t, code=code_change_t)\n", - "\n", - "\n", - "\n", - "# apply the logics\n", - "slider_b.js_on_change('value', update_b)\n", - "slider_h.js_on_change('value', update_h)\n", - "slider_position.js_on_change('value', updade_slider_pos)\n", - "checkbox_P.js_on_click(update_checkbox_P)\n", - "radiogroup_FBD.js_on_click(update_radiogroup_FBD)\n", - "slider_q.js_on_change('value', update_slider_q)\n", - "slider_t.js_on_change('value', update_t)\n", - "checkbox_T.js_on_click(update_checkbox_T)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Build the layout and show the figures. Note that the forces in the scheme are updated after moving the position of the point with the slider.\n", - "Note that the value of the forces and moments shown below represents the intensity, thus is always positive. The direction is given by the vector in the scheme." - ] - }, - { - "cell_type": "code", - "execution_count": 12, + "execution_count": 3, "metadata": {}, "outputs": [ { - "name": "stderr", - "output_type": "stream", - "text": [ - "ERROR:bokeh.core.validation.check:E-1001 (BAD_COLUMN_NAME): Glyph refers to nonexistent column name. This could either be due to a misspelling or typo, or due to an expected column being missing. : key \"text\" value \"\" [renderer: GlyphRenderer(id='6528', ...)]\n" - ] + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n" + ] + }, + "metadata": {}, + "output_type": "display_data" }, { - "name": "stderr", - "output_type": "stream", - "text": [ - "libva error: vaGetDriverNameByIndex() failed with unknown libva error, driver_name = (null)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Opening in existing browser session.\n" - ] + "data": { + "application/javascript": [ + "(function(root) {\n", + " function embed_document(root) {\n", + " \n", + " const docs_json = {\"59ecfd77-c705-4c8c-9c88-28bd01828977\":{\"defs\":[],\"roots\":{\"references\":[{\"attributes\":{\"children\":[{\"id\":\"2086\"}]},\"id\":\"2087\",\"type\":\"Column\"},{\"attributes\":{\"callback\":null,\"tooltips\":[[\"Position:\",\"@x m\"],[\"Torsion:\",\"@y 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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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n t = `+t+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h - (b-t*2)*(h-2*t)\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12 - (b-2*t)*(h-2*t)**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h, t) {\\n return h*b**3/12 - (h-2*t)*(b-2*t)**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/A*Iy/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-2*data['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, 2*data['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-2*data['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, 2*data['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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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-2*t\\n if (Math.abs(y) >= h_/2) {\\n return b/2*(h**2/4-y**2)\\n } else {\\n return b/2*(h-t)*t + t*(h_**2/4-y**2)\\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 V*1000*S/(Iy*b_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/A*Iy/M/1000\\n }\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2*t*(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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// 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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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)/c**2\\n }\\n const step = 2*c / (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(2*c)*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-2*t\\n if (Math.abs(y) >= h_/2) {\\n return b/2*(h**2/4-y**2)\\n } else {\\n return b/2*(h-t)*t + t*(h_**2/4-y**2)\\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 N*1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/Iy*(y-yG)\\n }\\n \\n \\n function compute_tau_shear(V, S, Iy, b_or_t) {\\n return V*1000*S/(Iy*b_or_t)\\n }\\n \\n \\n function compute_epsilon_axial(sigma_axial, E) {\\n return sigma_axial/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\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/A*Iy/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-2*data['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, 2*data['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-2*data['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, 2*data['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/2*0.8\\n var a = b-lambda*c\\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 Mt=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 Mt=\\\"+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, T*4/scale_T, Math.abs(T*3/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.PI*3/2\\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_x**2 + delta_y**2)\\n const size_head = arrow_growth(length_arr)*AHF\\n const head_x = size_head/pixel2unit*Math.cos(theta)\\n const head_y = size_head/pixel2unit*Math.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/2*3]\\n //arr_heads.glyph.y = [y_end-head_y/2, y_end-head_y/2*3]\\n const source_h = arr_heads.data_source\\n source_h.data['x'] = [x_end-head_x/2, x_end-head_x/2*3]\\n source_h.data['y'] = [y_end-head_y/2, y_end-head_y/2*3]\\n source_h.change.emit()\\n }\\n \\n \\n function compute_T(x, Mt, L) {\\n if (xGeometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n t = `+t+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h - (b-t*2)*(h-2*t)\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12 - (b-2*t)*(h-2*t)**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h, t) {\\n return h*b**3/12 - (h-2*t)*(b-2*t)**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/A*Iy/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-2*data['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, 2*data['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-2*data['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, 2*data['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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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-2*t\\n if (Math.abs(y) >= h_/2) {\\n return b/2*(h**2/4-y**2)\\n } else {\\n return b/2*(h-t)*t + t*(h_**2/4-y**2)\\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 V*1000*S/(Iy*b_or_t)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2*t*(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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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-2*data['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, 2*data['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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/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-2*t\\n if (Math.abs(y) >= h_/2) {\\n return b/2*(h**2/4-y**2)\\n } else {\\n return b/2*(h-t)*t + t*(h_**2/4-y**2)\\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 V*1000*S/(Iy*b_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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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/(2*t*(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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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/2*0.8\\n var a = b-lambda*c\\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 q*x-q*L/2\\n }\\n \\n \\n function compute_M(x, q, L) {\\n return q*x/2*(x-L)\\n }\\n \\n \\n function compute_Ry_l(q, L) {\\n return q*L/2\\n }\\n \\n \\n function compute_Ry_r(q, L) {\\n return q*L/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, pos*SCALE-N+offset_N, pos*SCALE+offset_N, 0, 0)\\n update_arrow(glyph_V, -V, pos*SCALE+offset_V, pos*SCALE+offset_V, -V/2, V/2)\\n var b = 6\\n var c = -M/2*0.8\\n var a = b-lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 0, source_M, glyph_M_head)\\n break;\\n case 'L_SEC':\\n // internal forces\\n update_arrow(glyph_N, N, pos*SCALE+N-offset_N, pos*SCALE-offset_N, 0, 0)\\n update_arrow(glyph_V, V, pos*SCALE-offset_V, pos*SCALE-offset_V, V/2, -V/2)\\n var b = -6\\n var c = -M/2*0.8\\n var a = b+lambda*c\\n update_curvedArrow(a, b, c, pos*SCALE, 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 = 2*c / (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(2*c)*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-2*data['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, 2*data['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-2*data['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, 2*data['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/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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/A*Iy/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 M*1e6/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-2*t\\n if (Math.abs(y) >= h_/2) {\\n return b/2*(h**2/4-y**2)\\n } else {\\n return b/2*(h-t)*t + t*(h_**2/4-y**2)\\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 V*1000*S/(Iy*b_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

Forces and Moments:

\\n P = `+P+` kN
\\n Rx = `+Rx+` kN
\\n Ry (left) = `+Ry_r+` kN
\\n Ry (right) = `+Ry_l+` kN
\\n `+str_sec+`
\\n N = `+N+` kN
\\n V = `+V+` kN
\\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/2*0.8\\n var a = b-lambda*c\\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/(2*t*(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)/c**2\\n }\\n const step = 2*c / (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(2*c)*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.PI*3/2\\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_x**2 + delta_y**2)\\n const size_head = arrow_growth(length_arr)*AHF\\n const head_x = size_head/pixel2unit*Math.cos(theta)\\n const head_y = size_head/pixel2unit*Math.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/2*3]\\n //arr_heads.glyph.y = [y_end-head_y/2, y_end-head_y/2*3]\\n const source_h = arr_heads.data_source\\n source_h.data['x'] = [x_end-head_x/2, x_end-head_x/2*3]\\n source_h.data['y'] = [y_end-head_y/2, y_end-head_y/2*3]\\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 Mt=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 Mt=\\\"+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, T*4/scale_T, Math.abs(T*3/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 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/(2*t*(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-2*data['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, 2*data['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/A*Iy/M/1000\\n }\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/A\\n }\\n \\n \\n function compute_sigma_bending(y, M, Iy, yG) {\\n return M*1e6/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-2*t\\n if (Math.abs(y) >= h_/2) {\\n return b/2*(h**2/4-y**2)\\n } else {\\n return b/2*(h-t)*t + t*(h_**2/4-y**2)\\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 V*1000*S/(Iy*b_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

Geometrical and mechanical parameters:

\\n h = `+h+` mm
\\n b = `+b+` mm
\\n t = `+t+` mm
\\n L = `+L+` m
\\n A = `+A.toExponential(2)+` mm2
\\n Iy = `+Iy.toExponential(2)+` mm4
\\n Iz = `+Iz.toExponential(2)+` mm4` \\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 b*h - (b-t*2)*(h-2*t)\\n }\\n \\n \\n function compute_inertia_y(b, h) {\\n return b*h**3/12 - (b-2*t)*(h-2*t)**3/12\\n }\\n \\n \\n function compute_inertia_z(b, h, t) {\\n return h*b**3/12 - (h-2*t)*(b-2*t)**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/A*Iy/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-2*data['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, 2*data['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-2*data['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, 2*data['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/E*100\\n }\\n \\n \\n function compute_epsilon_bending(sigma_bending, E) {\\n return sigma_bending/E*100\\n }\\n \\n \\n function compute_sigma_axial(N, A) {\\n return N*1000/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 M*1e6/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-2*t\\n if (Math.abs(y) >= h_/2) {\\n return b/2*(h**2/4-y**2)\\n } else {\\n return b/2*(h-t)*t + t*(h_**2/4-y**2)\\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 V*1000*S/(Iy*b_or_t)\\n }\\n \\n \\n function compute_tau_torsion(T, b, h, t) {\\n return -T/(2*t*(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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Geometrical and mechanical parameters:

\\n h = 200 mm
\\n b = 100 mm
\\n t = 10 mm
\\n L = 6 m
\\n A = 5.60e+03 mm2
\\n Iy = 2.78e+07 mm4
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Forces and Moments:

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\\n Rx = 10 kN
\\n Ry (left) = 12.0 kN
\\n Ry (right) = 12.0 kN
\\n No cross section analysed.
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\\n V = 0 kN
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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": [ - "padding_layout = 10\n", - "layout1 = layout([\n", - " [column(row(column(fig_scheme,\n", - " row(fig_section, Spacer(width=padding_layout), column(Spacer(height=padding_layout*3),\n", - " slider_b,\n", - " slider_h,\n", - " slider_t,\n", - " # row(div_geo, div_forces),\n", - " slider_position,\n", - " slider_q,\n", - " Spacer(height=padding_layout*3),\n", - " div_rg_FBD,\n", - " radiogroup_FBD,\n", - " div_cb_P,\n", - " checkbox_P,\n", - " Spacer(height=padding_layout*3),\n", - " div_cb_T,\n", - " checkbox_T))),\n", - " column(fig_beam,\n", - " Spacer(height=padding_layout),\n", - " fig_N,\n", - " fig_V,\n", - " fig_M,\n", - " fig_T)),\n", - " row(column(\n", - " row(fig_NM_section, fig_axial_strain, fig_stress_N, fig_bending_strain, fig_stress_M, fig_stress_sigma),\n", - " row(fig_V_section, Spacer(width=FIG_B_ss), fig_stress_V, Spacer(width=FIG_B_ss), fig_stress_T, fig_stress_tau),\n", - " ))\n", - " ),\n", - " ],\n", - "])\n", - "\n", - 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