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 $\backslash (\backslash$mathbf$\{$F$\}\backslash )$ is applied at B$.$ The rods have a modulus of elasticity of $\backslash (\backslash$mathbf$\{$E$\}\_\{\backslash$mathbf$\{$r$\}\}\backslash )$ and a cross$-$sectional area of $\backslash (\backslash$mathbf$\{$A$\}\_\{\backslash$mathbf$\{$r$\}\}\backslash ).$ 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 $\backslash (\backslash$mathrm$\{$B$\},\backslash$boldsymbol$\{\backslash$delta$\}\_\{\backslash$mathbf$\{$B$\}\}\backslash ),$ in terms of the given variables $\backslash (\backslash$mathbf$\{$E$\}\_\{\backslash$mathbf$\{$r$\}\},\backslash$mathbf$\{$A$\}\_\{\backslash$mathbf$\{$r$\}\},\backslash$mathbf$\{$F$\}\backslash ),$ and $\backslash (\backslash$mathbf$\{$a$\}\backslash ).(4$ points$)$