Show all calculations and steps clearly. Do not skip any step. The symbols have their usual meaning. Use ACI$-318.$

Problem $1.$ Fig A shows a floor system with main girders and floor beams. The following data are given: Slab thickness $=6$ in$.$ Columns $=18in18in.$ Total girder depth $($including the slab$)=24$ in$.$ Web width of girders $=12in.$ Super$-$imposed live load $=60psf.$ Superimposed dead load $=20psf.$

$($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.