$(7$ pts $)$ Thermal Effects. An ASTM A$36$ W$12$x$40$ structural steel beam $12$ ft long with a cross$-$section area of $11\mathrm{.}7in.{?}^2$ is placed between two rigid supports when the temperature is $35F($no stress$).(1)$ Compute the stress developed in the beam if the temperature rises to $110F$ when two rigid supports do not yield at all, and $(2)$ Compute the stress developed in the beam if the temperature rises to $110F$ when two rigid supports actually yield $($move$)$ a total distance of $0\mathrm{.}03$ in $.$ Refer to Appendix G for necessary mechanical properties. Assume that the proportional limit is $34,000$ psi $-$ Hint: useful example $11\mathrm{.}6$ and $11\mathrm{.}7$

$(8$ pts$)$ Shear force and bending moment. For the beam shown, $(1)$ draw free$-$body diagrams, and $(2)$ calculate the shear and bending moment at $4$ ft and $14$ ft from the left end of the beams. $-$ Hint: useful example $13\mathrm{.}4.$