$($textbook$,$ problem $4-86,$ use the materials properties in the table below$)$

The figure shows a rectangular member $OB,$ made from $\frac{1}{4}-$in$-$thick aluminum plate, pinned to the ground at one end, and supported by a $\frac{1}{2}-$in$-$diameter round steel rod that is formed into an are and pinned to the ground at $C.$ A load of $100$ lbf is applied at $B.$ Use Castigliano's theorem to determine the vertical deflection at point $B.$ Justify any choices to neglect any components of strain energy.

$|$ Physical Constants of Materials

$\backslash$table$[[$Material$,$Modulus of Elasticity E$,$Modulus of Rigidity $G,\backslash$table$[[$Poisson$\text{'}$s$],[$Ratio

$u$