PROBLEM:
The elastic cantilever beam ABC is fixed at A and supported at B by a vertical elastic member BD. The beam is subjected to a linearly distributed load over half of its length. The beam ABC has flexural rigidity El and length L, and the rod has Young's modulus E, cross-sectional area A, and length L/2.
Using Castigliano's theorem, determine the deflection of point C on the beam. Specifically:
a) Show the free body diagram of the structure.
b) Indicate whether dummy load(s) and redundant/internal load(s) are needed. Notice that the structure is statically indeterminate.
c) Determine the strain energy of the entire structure, i.e., of beam ABC and rod BD. Ignore the effects of shear energy in your analysis.
d) Clearly state how Castigliano's second theorem is applied to determine the deflection of point C on the beam.
e) Determine the deflection of point C on the beam. Express your result in terms of wo, E, L, I and A
