Problem $1(50$ points$)$:

A composite floor system consists of ASTM A$992$ W$18\backslash$times $55$ steel beams supporting a formed steel deck and concrete slab. The deck ribs are oriented perpendicular to the longitudinal axis of the beams. The deck geometry is shown below. The total depth from bottom of deck to top of slab is $7^{\text{'}\text{'}}.$ Normal weight concrete $($unit weight $=145$ pcf $)$ is used, with a $28-$day compressive strength of $5$ ksi $.$ The beams are simply supported over a span of $48$ feet, and are spaced at $12$ feet on center. One $\frac{3}{4}"$x$5"$ stud anchor is welded to the top flange of the beams in each rib.

a$)$ Calculate the design moment strength of the composite beam

b$)$ Calculate the lower bound moment of inertia of the composite beam

c$)$ Obtain the values requested in parts a$)$ and b$)$ by using design tables in the AISC Manual