$2.$ Consider a simply$-$supported beam with lateral support at both ends only $($i$.$e$.,$ laterally unsupported beam$).$ Find the factored moment carrying capacity $\backslash (\backslash$left$(\backslash$mathrm$\{$M$\}\_\{\backslash$mathrm$\{$r$\}\}\backslash$right$)\backslash )$ of this beam under uniformly distributed load. The beam has a length of $5\mathrm{.}5$ m $,$ where the section is W$31052.$

a$.$ Compare Mr of the same beam when it is laterally supported at both of its supports and mid$-$point.

b$.$ Compare Mr of the same beam when it is laterally supported throughout the compression flange.