Influence line support reaction A

Click –> Live Code on the top right corner of this screen to investigate some influence lines!

import micropip
await micropip.install("ipympl")

import numpy as np
import sympy as sym
import matplotlib.pylab as plt
from ipywidgets import widgets, interact
from matplotlib.patches import Arc,StepPatch

%matplotlib widget

EI, x = sym.symbols('EI, x',real=True)

Av, Bv = sym.symbols('Av, Bv',real=True)
a, L= sym.symbols('a, L ',positive=True,real=True)
C1, C2, C3, C4 = sym.symbols('C1, C2, C3, C4')

q = -Bv * sym.SingularityFunction(x,L,-1) - Av * sym.SingularityFunction(x,0,-1) + 1 * sym.SingularityFunction(x,a,-1)
V = -sym.integrate(q,x)+C1
M = sym.integrate(V,x)+C2
kappa = M / EI
phi = sym.integrate(kappa,x)+C3
w = - sym.integrate(phi,x)+C4
eq1 = sym.Eq(w.subs(x,0),0)
eq2 = sym.Eq(w.subs(x,L),0)
eq3 = sym.Eq(M.subs(x,0),0)
eq4 = sym.Eq(M.subs(x,L),0)
eq5 = sym.Eq(V.subs(x,-1),0)
eq6 = sym.Eq(V.subs(x,L+1),0)
sol = sym.solve([eq1,eq2,eq3,eq4,eq5,eq6],[C1,C2,C3,C4,Av,Bv])
V_sol = V.subs(sol)
V_subs = V_sol.subs([(L,5),(a,2),(EI,5000)])
V_numpy = sym.lambdify([L,a,EI,x],V_sol.rewrite(sym.Piecewise))
M_sol = M.subs(sol)
M_subs = M_sol.subs([(L,5),(a,2),(EI,5000)])
M_numpy = sym.lambdify([L,a,EI,x],M_sol.rewrite(sym.Piecewise))
Av_sol = sol[Av].rewrite(sym.Piecewise)
Av_numpy = sym.lambdify([L,a,EI],Av_sol)
Bv_sol = sol[Bv].rewrite(sym.Piecewise)
Bv_numpy = sym.lambdify([L,a,EI],Bv_sol)

fig, axs = plt.subplots(2, 1, figsize=(7, 6))
x = np.linspace(0,5,2)
def func(b):
    axs[0].clear()  # Clear the existing plot
    axs[1].clear()
    
    axs[0].plot([0,5],[0,0],color='black',linewidth=2)
    #axs[0].grid()
    axs[0].annotate(text='', xy=(0,0), xytext=(0,Av_numpy(5,b,5000)), arrowprops=dict(arrowstyle='simple'))
    axs[0].annotate('%.2f kN' % Av_numpy(5,b,5000),xy = [0.2,Av_numpy(5,b,5000)])
    axs[0].annotate(text='', xy=(5,0), xytext=(5,Bv_numpy(5,b,5000)), arrowprops=dict(arrowstyle='simple'))
    #axs[0].annotate('%.2f kN' % Bv_numpy(5,b,5000),xy = [4.3,0.5])
    axs[0].annotate(text='', xy=(b,0), xytext=(b,-1), arrowprops=dict(arrowstyle='simple'))
    axs[0].set_ylim([-1,1])
    axs[0].invert_yaxis()
    axs[0].axis('off')
    title0 = 'Free body diagram for unit load at $x_F = '+str(b)+'$'
    axs[0].set_title(title0)
    axs[1].plot([0,5],[0,0],color='black',linewidth=2)
    axs[1].grid()
    axs[1].axis('equal')
    axs[1].plot(x,Av_numpy(5,x,5000),color='blue')
    axs[1].plot(b,Av_numpy(5,b,5000),marker='o')
    axs[1].annotate('%.2f kN' % Av_numpy(5,b,5000),xy = [b,Av_numpy(5,b,5000)+0.2])
    axs[1].invert_yaxis()
    title1 = 'Influence line for support reaction at A'
    axs[1].set_title(title1)

    axs[1].spines['right'].set_color('none')
    axs[1].spines['top'].set_color('none')
    axs[1].spines['bottom'].set_position('zero')
    axs[1].spines['left'].set_position('zero')
    plt.draw()  

    
interact(func, b = widgets.FloatSlider(min=0, max=5, value=2, step=0.1, description="Location unit load x_F = ... (m)",readout_format='.1f',style= {'description_width': '200px'},layout = {'width': '400px'}) );