Design a singly reinforced rectangular section to resist a factored moment of $232$ Kft $(320$ kN$-$m$)$ if f$\_\{$c$\}\text{'}=4(28$ MPa$),$ f$\_\{$y$\}=60$ ksi $(420$ MPa$),$ and b $=10$in $(250$ mm$)$ using $($a$)$ Pmax, $($b$)$ rho $=0\mathrm{.}016$ and $($c$)$ rho $=0\mathrm{.}012$