Problem $1(20$ pts$.)$

A simply supported steel beam over a $22-$ft span carries a uniformly distributed dead load of $2\mathrm{.}5\frac{k}{f}t,$ including an allowance for self$-$weight, and a live load of $3\mathrm{.}5\frac{k}{f}t.$ The steel is A$992,$ Grade $50.$ The beam has full lateral support. Determine the most economical beam section that could be safely used. Design for bending only using LRFD$.$

Problem $2(10$ pts$.)$

A simply supported steel beam carries a factored concentrated load of $55$ kips at the center of its $36-ft$ span. The beam has lateral support at the center of the span and at both ends