In a slab$-$beam system, the effective flange width was determined to be $48$ in$.,$ the web width was $16$in$.$ and the slab thickness was $4$in$.$ If the effective depth is chosen as $23$ in$.,$ calculate the area of steel for this given T$-$section to resist an external factored moment of M$\_$u$=820$ K$-$ft$.$ Given f$\text{'}\_$c$=4,000$ psi; normal weight of concrete and f$\_$y$=60,000$ psi $(25$ points$)$