Problem $2(12$ points$)-$ The rigid bar is pinned at A and is supported by two identical deformable rods at E and C$.$ A force $F$ is applied at B$.$ The rods have a modulus of elasticity of $E_r$ and a cross$-$sectional area of $A_r.$ Follow the steps below to algebraically express the displacement of point B in terms of the given variables.

$($a$)$ Draw the FBD of the rigid bar. $(3$ points$)$

$($b$)$ Express the equilibrium equations for the rigid bar. Hint: take moment about a point that simplifies your system of linear equations. $(3$ points$)$

$($c$)$ Express the compatibility equation of rods EF and CD $.(2$ points$)$

$($d$)$ Express the deformation of point $B,{}_B,$ in terms of the given variables $E_r,A_r,F,$ and $a.(4$ points$)$