The interior floor system shown in the figure has W$24$ x $55$ sections spaced $8ft\mathrm{.}6$ in$.$ on center and is supporting a floor dead load of $52$ psf$.$

and a live floor load of $83$ psf$.$ Determine the governing load in $lb./ft.$ that each beam must support.

Area of $s||$ supporter foot of lei by W $24x$

Area supp by one $blon($shaded$)$