import matplotlib
if not hasattr(matplotlib.RcParams, "_get"):
matplotlib.RcParams._get = dict.get
Voorbeeld vaste hoekverdraaiing#
%pip install git+https://github.com/twrijsdijk/sympy
from sympy.physics.continuum_mechanics import Beam
from sympy import symbols
#Omschrijving van de balk
r0,m0 = symbols(['r0', 'm0'])
b = Beam(6, 500, 10)
b.apply_load(r0, 0, -1)
b.apply_load(m0, 0, -2)
b.apply_load(-250, 6, -1)
b.bc_deflection = [(0,0)]
b.bc_slope = [(0,2)]
#berekeningen
b.solve_for_reaction_loads(r0, m0)
print('belasting', b.load)
print('Dwarskrachten', b.shear_force())
print('Reactiekrachten', b.reaction_loads)
print('Moment',b.bending_moment())
print('Hoeverdraaiing',b.slope())
print('Doorbuiging',b.deflection())
#plots
axes = b.plot_loading_results()
belasting -1500*SingularityFunction(x, 0, -2) + 250*SingularityFunction(x, 0, -1) - 250*SingularityFunction(x, 6, -1)
Dwarskrachten 1500*SingularityFunction(x, 0, -1) - 250*SingularityFunction(x, 0, 0) + 250*SingularityFunction(x, 6, 0)
Reactiekrachten {m0: -1500, r0: 250}
Moment 1500*SingularityFunction(x, 0, 0) - 250*SingularityFunction(x, 0, 1) + 250*SingularityFunction(x, 6, 1)
Hoeverdraaiing -3*SingularityFunction(x, 0, 1)/10 + SingularityFunction(x, 0, 2)/40 - SingularityFunction(x, 6, 2)/40 + 2
Doorbuiging 2*x - 3*SingularityFunction(x, 0, 2)/20 + SingularityFunction(x, 0, 3)/120 - SingularityFunction(x, 6, 3)/120
