A rectangular beam should be designed as a doubly reinforced to resist a factored moment $360$ kip$-$ft $(400$ kip$-$ft nominal$).$ For architectural reasons the cross section is limited to width b$=12$ in and total height h$=24$ in$.$ The project specifies normal weight concrete with $28$ day compressive strength $f_c\text{'}=3,000$ psi and $f_y=40,000$ psi steel yielding. For simplicity use d$=20\mathrm{.}5$ in and d$\text{'}=2\mathrm{.}5$ in$.$