A simply supported beam spanning $30$ft$.$ is to support the service loads. The top flange of the

beam has continuous lateral support $($no lateral torsional buckling$).$ Answer the following

questions. Use A$992$ Grade $50$ steel and ignore the self$-$weight of the beam. $(30$ points$)$

a$.$ Assuming the maximum factored moment is Mu$=500$k$-$ft$,$ select the most economical wide

flange section to carry the moment. $($Do not consider shear or deflection$).$

b$.$ Check the local plate buckling criteria for the selected section.

c$.$ If the architect requires a maximum beam size of W$18,$ which beam would you choose.

Answer: Zx $=133$in$^3$