Problem $3.($Midterm Exam, Fall $2015$ & Spring $2017)$ For the truss shown below: $($a$)$ Compute the

horizontal deflection at joint $D$ under the given loading, $($b$)$ Compute the horizontal deflection at joint $D$

under the given loading and a temperature increase of $50C$ for member $BD$ only. Assume a coefficient of

thermal expansion, $a=12\mathrm{.}0{10}^{-6}\frac{m}{mC}.,$ Note: E$.$A$.$ is constant for all bars., and $($c$)$ If the horizontal

displacement at Joint $D$ is not to exceed $5\mathrm{.}0$ cm $,$ what is the minimum required value of $E.A.$ for part $($a$)$ and

part $($b$).$ Note: A and $C$ are pinned and roller supports, respectively.