$(20$ points$)$ A simply supported beam spans $40$ feet and supports the factored loads shown in the figure $($shear force diagram is provided$).$ The top flange is braced at the supports and the point loads only. Assume A$992$ Grade $50$ steel.

a$.$ Complete the bending moment diagram, and determine the $M_{\text{m}\text{a}\text{x}}$ when you calculate Cb for section AB $($end$-$span$).$

b$.$ Use $=1150k-ft.$ Assuming $Cb=1\mathrm{.}0$ for section BC $,$ select the lightest wide flange section that will support the given loads for section BC$.$

$($Partial Answers: potential beam selections are W$30$x$99$ and W$30$x$108)$

a$)$ Draw the factored shear force and bending moment diagrams in the spaces provided.