Chapter $5.$ Design of T$-$Beams

Problem $1.$ Determine the amount of reinforcing steel required for the T$-$beam shown if $f_y=60,000$ psi, $f_c^{\text{'}}=4,000,$ simple span length $=20ft,M_D=200k-ft($includes member weight$),$ and $M_L=500k-ft.$ Try at least two iterations to check the convergence of the $z.(35pts)$