Equations 1

import sympy as sm
from sympy.physics.continuum_mechanics.beam import Beam

E = sm.Symbol('E')
I = sm.Symbol('I')
b = Beam(10, E, I)
r0 = b.apply_support(0, type="pin")
r10 = b.apply_support(10, type="pin")
b.solve_for_ild_reactions(-1, r0, r10)

b.ild_reactions

{R_0: SingularityFunction(a, 0, 0) - SingularityFunction(a, 0, 1)/10 + SingularityFunction(a, 10, 1)/10,
 R_10: SingularityFunction(a, 0, 1)/10 - SingularityFunction(a, 10, 0) - SingularityFunction(a, 10, 1)/10}

b.ild_reactions[r0]

\[\displaystyle {\left\langle a \right\rangle}^{0} - \frac{{\left\langle a \right\rangle}^{1}}{10} + \frac{{\left\langle a - 10 \right\rangle}^{1}}{10}\]

b.ild_reactions[r10]

\[\displaystyle \frac{{\left\langle a \right\rangle}^{1}}{10} - {\left\langle a - 10 \right\rangle}^{0} - \frac{{\left\langle a - 10 \right\rangle}^{1}}{10}\]