While solving different beam problems I found that currently only
determinate beams can be solved (simply supported, cantilever,
overhanging).
However it is unable to solve indeterminate beams (fixed, propped
cantilever and continuous beams).
For fixed beam
>>> from sympy.physics.continuum_mechanics.beam import Beam
>>> from sympy import symbols, Piecewise
>>> E, I = symbols('E, I')
>>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
>>> b = Beam(4, E, I)
>>> b.apply_load(R1, 0, -1)
>>> b.apply_load(R2, 0, -2)
>>> b.apply_load(R3, 4, -1)
>>> b.apply_load(R4, 4, -2)
>>> b.apply_load(6, 2, -1)
>>> b.bc_deflection = [(0, 0), (4, 0)]
>>> b.bc_slope = [(0,0), (4,0)]
>>> b.solve_for_reaction_loads(R1,R2,R3,R4)
>>>b.shear_force()
R3*SingularityFunction(x, 4, 0) + R4*SingularityFunction(x, 4, -1) + (-R3 -
6)*SingularityFunction(x, 0, 0) + (4*R3 - R4 + 12)*SingularityFunction(x, 0,
-1) + 6*SingularityFunction(x, 2, 0)
>>> b.bending_moment()
R3*SingularityFunction(x, 4, 1) + R4*SingularityFunction(x, 4, 0) + (-R3 - 6
)*SingularityFunction(x, 0, 1) + (4*R3 - R4 + 12)*SingularityFunction(x, 0,
0) + 6*SingularityFunction(x, 2, 1)
Currently it reduces from 4 reactions to 2 reactions .
However these type of problem can easily be solved using various methods
for indeterminate analysis for example - three moment theorem .
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