import matplotlib
if not hasattr(matplotlib.RcParams, "_get"):
matplotlib.RcParams._get = dict.get
Voorbeeld rotatieveer midden oplegging#
%pip install git+https://github.com/twrijsdijk/sympy
from sympy.physics.continuum_mechanics import Beam
from sympy import symbols
#Omschrijving van de balk
b = Beam(6, 500, 10)
r0 = b.apply_support(0,'pin')
r3 = b.apply_support(3,'pin')
r6 = b.apply_support(6,'pin')
b.apply_load(100, 2, -1)
b.apply_load(100, 4, -1)
b.apply_rotation_spring(3, 1000)
#berekeningen
b.solve_for_reaction_loads(r3)
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()
d = b.draw()
d.show()
belasting -5300*SingularityFunction(x, 0, -1)/189 + 100*SingularityFunction(x, 2, -1) + 5000*SingularityFunction(x, 3, -3)/63 - 27200*SingularityFunction(x, 3, -1)/189 + 100*SingularityFunction(x, 4, -1) - 5300*SingularityFunction(x, 6, -1)/189
Dwarskrachten 5300*SingularityFunction(x, 0, 0)/189 - 100*SingularityFunction(x, 2, 0) - 5000*SingularityFunction(x, 3, -2)/63 + 27200*SingularityFunction(x, 3, 0)/189 - 100*SingularityFunction(x, 4, 0) + 5300*SingularityFunction(x, 6, 0)/189
Reactiekrachten {R_0: -5300/189, R_6: -5300/189, R_3: -27200/189}
Moment 5300*SingularityFunction(x, 0, 1)/189 - 100*SingularityFunction(x, 2, 1) - 5000*SingularityFunction(x, 3, -1)/63 + 27200*SingularityFunction(x, 3, 1)/189 - 100*SingularityFunction(x, 4, 1) + 5300*SingularityFunction(x, 6, 1)/189
Hoeverdraaiing -53*SingularityFunction(x, 0, 2)/18900 + SingularityFunction(x, 2, 2)/100 + SingularityFunction(x, 3, 0)/63 - 68*SingularityFunction(x, 3, 2)/4725 + SingularityFunction(x, 4, 2)/100 - 53*SingularityFunction(x, 6, 2)/18900 + 23/3150
Doorbuiging 23*x/3150 - 53*SingularityFunction(x, 0, 3)/56700 + SingularityFunction(x, 2, 3)/300 + SingularityFunction(x, 3, 1)/63 - 68*SingularityFunction(x, 3, 3)/14175 + SingularityFunction(x, 4, 3)/300 - 53*SingularityFunction(x, 6, 3)/56700
c:\Users\tomvanwoudenbe\AppData\Local\tudelft-conda\envs\tinus\Lib\site-packages\sympy\physics\continuum_mechanics\beam.py:2915: UserWarning: Please, note that this schematic view might not be in agreement with the sign convention used by the Beam class for load-related computations, because it was not possible to determine the sign (hence, the direction) of the following loads:
* Moment -S_3 located at 3
* Moment S_3 located at 3
warnings.warn(warning_head + warning_body)
