参考資料

Statically indeterminate beams＜

WolframAlpha

勉強中

単純梁（中心荷重）

単純梁（等分布荷重）

自乗の表示が間違っています。sympy

単純梁（中心荷重）

PartialScript.py

def _main():
    from sympy.core import symbols
    from sympy.plotting import plot

    l = symbols('l', positive=True, real=True)
    RA, RB = symbols('R_A, R_B')
    P = symbols('P')
    E, I = symbols('E, I')
    x = symbols('x')
    loads = [
        (-RA, 0, -1),
        (-RB, l, -1),
        (P, 0.5*l, -1),
        (0, 0, -2),
        (0, l, -2)
    ]

    b = Beam(l, E, I)
    for load in loads:
        b.apply_load(*load)
    b.bc_deflection = [
        (0, 0),
        (l, 0)
    ]

    b.solve_for_reaction_loads(RA, RB )
    print(b.reaction_loads)
    print("v(x)=",b.deflection())
    print("v(l/2)=",b.deflection().subs({x: 0.5*l}))
    print("  1/48=",1/48)

    # こことんでもなく雑な数字
    constants = {l: 1, P: 1, E: 1, I: 1}
    plot(
        # b.shear_force().subs(constants),
        b.bending_moment().subs(constants),
        # b.slope().subs(constants),
        # b.deflection().subs(constants),
        (b.variable, 0, b.length.subs(constants))
    )

if __name__ == '__main__':
    _main()
# {R_A: 0.5*P, R_B: 0.5*P}
# v(x)= (0.0625*P*l**2*x - 0.0833333333333333*P*SingularityFunction(x, 0, 3) + P*SingularityFunction(x, 0.5*l, 3)/6 - 0.0833333333333333*P*SingularityFunction(x, l, 3))/(E*I)
# v(l/2)= 0.0208333333333333*P*l**3/(E*I)
#   1/48= 0.020833333333333332

単純梁（等分布荷重）

PartialScript.py

def _main():
    from sympy.core import symbols
    from sympy.plotting import plot

    l = symbols('l', positive=True, real=True)
    RA, RB = symbols('R_A, R_B')
    E, I = symbols('E, I')
    x = symbols('x')
    w = symbols('w')

    loads = [
        (-RA, 0, -1),
        (-w, 0, 0, l),
        (-RB, l, -1),
        (0, 0, -2),
        (0, l, -2)
    ]

    b = Beam(l, E, I)
    for load in loads:
        b.apply_load(*load)
    b.bc_deflection = [
        (0, 0),
        (l, 0)
    ]

    b.solve_for_reaction_loads(RA, RB )
    print(b.reaction_loads)
    print("v(x)=",b.deflection())
    print("v(l/2)=",b.deflection().subs({x: 0.5*l}))
    print("-5/384=",-5/384)

    # こことんでもなく雑な数字
    constants = {l: 1, w: 1, E: 1, I: 1}
    plot(
        # b.shear_force().subs(constants),
        b.bending_moment().subs(constants),
        # b.slope().subs(constants),
        # b.deflection().subs(constants),
        (b.variable, 0, b.length.subs(constants))
    )

if __name__ == '__main__':
    _main()
# {R_A: -l*w/2, R_B: -l*w/2}
# v(x)= (-l**3*w*x/24 + l*w*SingularityFunction(x, 0, 3)/12 + l*w*SingularityFunction(x, l, 3)/12 - w*SingularityFunction(x, 0, 4)/24 + w*SingularityFunction(x, l, 4)/24)/(E*I)
# v(l/2)= -0.0130208333333333*l**4*w/(E*I)
# -5/384= -0.013020833333333334