Problem 6-5

Figure

Figure

import sympy
sympy.init_printing()


def intmM(L,m0,m1,M0,M1,w=0,EI=1.):
    return (L/24.)*(m0*(w*L*L + 8.*M0 + 4.*M1) + m1*(w*L*L + 4.*M0 + 8.*M1))/EI

Part 1 - Determine horizontal displacement of member end d

Figure

sympy.var('w L EI')
\[\left ( w, \quad L, \quad EI\right )\] 
intmM(3*L,L,L,0,0,w,2*EI)
\[\frac{1.125 L^{4} w}{EI}\]

Part 2 - Determine the rotation of member end d

Figure

intmM(3*L,0,1,0,0,w,2*EI)
\[\frac{0.5625 L^{3} w}{EI}\]