Problem $1.$ Fig A shows a floor system with main girders and floor beams. The following data are given: Slab thickness $=6$ in$.$ Columns $=18$ in $18$ in$.$ Total girder depth $($including the slab$)=24$ in$.$ Web width of girders $=12in.$ Super$-$imposed live load $=60$ psf$.$ Superimposed dead load $=20$ psf$.$

$($a$)$ Calculate the tributary area for the exterior span $AB.$

$($b$)$ Calculate the factored dead load and factored live load for the exterior span $AB.$ Use the live load reduction factor, if applicable.

$($c$)$ Calculate the ultimate moment at the midspan of $AB.$ Use the most critical combination of the loads.

Problem $2.$ Fig B shows a T$-$beam cross section. Assume $f_c^{\text{'}}=4000,f_y=60$ksi.

$($a$)$ Calculate the factored nominal resistance moment.

$($b$)$ Check whether the code requirement for the minimum reinforcement is satisfied or not.

$($c$)$ Check whether the failure mode of the beam is tension controlled or not.

Fig A

Fig B