Part $($a$)$: A steel beam $($A$572$ Grade $50)$ is loaded at mid$-$span as shown. Using a deflection criteria of L$/360$ under live load, and a depth restriction of $14"$ nominal, select the most economical W$14$ cross section, which also satisfies the AISC compactness criteria, that can support the load for flexure, shear and deflection criteria. Neglect the beam self weight.

Part $($b$)$: If the compressive top flange of the beam is adequately braced against lateral$-$torsional buckling, then find the moment capacity, Mn$,$ of the wide flange cross section chosen in Part $($a$).(30$ points$)$

Assume:

$Fb=30$ksi

$FV=20$ksi

$E=30,000$ksi