The angled beam ABC in the figure is composed of segments AB and BC joined at B at a 90˚ angle. Both segments have length L and uniform section stiffness EI. The beam is fixed at C and loaded by a downward concentrated force, P, applied at its free end A.
You will use Castiglano's theorem to determine the vertical downward deflection vA of the free end A and the horizontal deflection uB of section B (towards A) as indicated in the figure below.
1.
Use Castigliano's theorem to obtain a symbolic expression for the downward vertical deflection vA of the free end A, in terms of P, L, and EI ( enter this as EI without the multiplication sign).
2.
Use Castigliano's theorem to obtain a symbolic expressions for the horizontal deflection uB of section B (towards A) in terms of P, L, and EI ( enter this as EI without the multiplication sign). Hint: You will have to introduce a dummy load that is work-conjugate to the desired deflection uB