$5.$ Using Castigliano's method, find the slope at the mid$-$length C of a straight, beam due to the applied moment Mo$,$ as shown.

$($a$)$ Write a FBD showing all the support reactions, $($b$)$ Show that the problem is statically indeterminate, $($c$)$ Write equations for bending moment for segments BC and CA with B as the origin, $($d$)$ Write expressions for strain energy stored in BC and CA$,($e$)$ Identify the additional boundary condition at B to solve for R$.$ Assume flexural rigidity of the beam EI to be a known quantity.