Problem $4(15$ points$)$: For the truss in the figure, use the method of virtual work to obtain the vertical displacement of joint E if member AE is fabricated $0\mathrm{.}5$ in too long, member BE is fabricated $0\mathrm{.}3$ in too short, member BD is fabricated $0\mathrm{.}6$ in too long and members $CD,AB,DE$ and BC is subjected to a change in temperature of $200F.$ The material of the truss has the following properties: thermal expansion coefficient $=6\mathrm{.}60\frac{{10}^{-6}}{}F.$

Note: show all the steps in order and FBD$\text{'}$s necessary