Problem $2[50$ Points$].$ The following reinforced concrete beam has a span length of $20$ ft and is simply supported at both ends. It is subjected to a uniformly distributed dead load of $w_D=3\mathrm{.}5ki\frac{p}{f}t($including the self$-$weight$)$ and a concentrated live load of $P_1=30$kip as shown in the following figure.

For this beam, design the cross section by assuming that ${}_s=0\mathrm{.}01425,f_c=4$ksi, and $f_y=60$ksi.