Problem $2$: $(30$ Points$)$

Design the reinforced concrete beam $($normal weight concrete$)$ ABC shown in Fig. $1,$ for which you have calculated the moment in problem $1.$ Use Strength Design Method to design the beam. Given that,

$($a$)$ From architectural considerations, width $\backslash (\backslash$mathrm$\{$b$\}\backslash$leq $\backslash$mathbf$\{12\}\backslash )".$

$($b$)\backslash ($ f$\_\{$c$\}^\{\backslash$prime$\}=5,000\backslash$mathrm$\{$psi$\},$ f$\_\{$y$\}=60,000\backslash$mathrm$\{$psi$\}\backslash )$

Design the reinforced concrete beam AB i$.$e$.$

$1.$ Determine the required reinforcement $($As$)$ in the tension and compression sides $($if any$).$ Also select number and appropriate steel size.

$2.$ Draw sketches of longitudinal detail $(1$ detail$)$ and cross$-$sectional details $($at least $2$ details$)$ showing the placement of the reinforcements for all possible flexural moments.

Note: Use your engineering judgment for answering the questions.

Fig. $1$