Question $2.(60$ Points$)$:

A rectangular concrete beam has the dimensions of $b=12in,h=36in,$

$d=33\mathrm{.}5$ in$,$ and is reinforced with two No$.10$ steel rebars. The concrete

compressive strength is ${}_c=5$ksi, and the yield point of the steel rebar

is $f_y=60$ksi.

a$.$ Using the universal procedure covered in the class, determine the

nominal flexural strength, $($moment $M_n)$ at which this beam fails

$($i$.$e$.,$ Stage $3).$

b$.$ Using the equivalent rectangular stress distribution $($a$.$k$.$a$.,$ Whitney

Stress Block$)$ determine the nominal flexural strength, $($moment

$M_n)$ of this beam. How different is the result than what you found in

Part $($a$)$ of this Question?

c$.$ Determine the magnitude of the reduction factor $$ based on the ACI

provisions and calculate the design flexural$/$moment capacity $(M_n).$

d$.$ Does this RC beam have the minimum reinforcement area $(A_{s,\text{m}\text{i}\text{n}})$ needed for flexure per

ACI $318,$ Article $9\mathrm{.}6\mathrm{.}1\mathrm{.}2?$