$($Note $-$ Use $f^{\text{'}}c=4,000,fy=60,000$ and concrete unit weight $150l\frac{b}{c}$uft unless otherwise noted. All answers require units where applicable. Show all work.$)$

Determine the ultimate design load $w_u(\frac{k}{f}t)$ for the rectangular concrete beam B $1$ in the floor system sketched $($in section$)$ below. The slab is $8^{\text{'}\text{'}}$ thick and the stem of the beam below the slab is $24$ in deep $x18$ in wide. The beam is part of a floor system with beams spaced at $15$ ft on center. Superimposed dead load is $50$ psf and live load is $100$ psf $($both unfactored$).$