Determine the demand capacity ratio $($DCR $=$ Mu $/\backslash$phi Mn$)$ for a W$21$x$44($Fy $=50$ ksi$)$ with a simple span of $40$ ft$.$ The spacing to adjacent beams is $12$ ft on each side of the W$21$x$44.$ The slab is composed of a $3"$ deep steel deck with $4"$ of lightweight concrete $($f$\text{'}$c $=4,000$ psi; w $=110$ pcf$)$ over the top of the deck $($total thickness $=3"+4"=7").$ The deck is oriented perpendicular to the beam. The ribs in the deck are spaced at $12"$ centers. There are two $3/4"$ diameter studs in each rib for a total of $80$ studs over the entire beam length. The service loading is Wd $=0\mathrm{.}865$ k$/$ft including beam weight and WL $=1\mathrm{.}200$ k$/$ft$.$ Consider unshored construction. a$.$ Use either the AISC design aids or the detailed equilibrium equations b$.$ Verify that the section is adequate for the initial non$-$composite conditions assuming self$-$weight loading $($WSW$)$ is $0\mathrm{.}649$ k$/$ft and a construction live load $($WCLL$)$ is $0\mathrm{.}240$ k$/$ft$.$ c$.$ Determine a recommended camber for the beam