Q$1)$ A simply supported beam $($B$-2)$ supports a uniformly distributed load and is braced at six foot intervals in addition to a composite slab that is secured to the compression flange of the beam via shear studs. Assume that the beam is made of ASTM A$992$ grade with $Fy=50$ksi. Select the lightest $W$ shape to safely support the following loads:

$($Safely support means design a beam for bending and shear!$)$

$DL=100$ psf; LL $=75$ psf

Beams are spaced at $12$ feet o$.$c$.$ so $($using tributary are concept$)$

${}_{DL}=100\frac{\text{\#}}{f}{t}^2{12}^{\text{'}}=1,200\frac{\text{\#}}{f}t.$

${}_{LL}=75\frac{\text{\#}}{f}{t}^2{12}^{\text{'}}=900\frac{\text{\#}}{f}t.$