For the cross section shown below, the material and sectional properties are given as follows:

$f_c^{\text{'}}=4$ksi,$f_y=60$ksi,$b=30in,d=20in,$ concrete cover depth $1\mathrm{.}5in.$

$E_s$:$=29000000*,E_c=57000\sqrt[\phantom{2}]{f_c^{\text{'}}},{}_y=0\mathrm{.}002$

$($a$)$ Determine the maximum steel area $A_s$ that can lead to tension driven failure. One can use

Table A$.4$ in the textbook to easily calculate design parameters.

$($b$)$ To ensure under$-$reinforcement, the steel area is to be decided as a value between $90\%$ and

$95\%$ of $A_s$ estimated in P$1($a$).$ Determine the reinforcing bars $($i$.$e$.,$ bar size, and the number of

bars$)$ to meet the required steel area. It is assumed that a single type of rebar is chosen $($i$.$e$.,$

rebars of different sizes shall not be combined$).$

$($c$)$ Given the decided steel area, calculate the nominal and the design moment capacity. One

cannot use the design aids.