Problem $2(25\%)$

The rectangular beam shown in the figure is reinforced with $3-$#$10$ Grade $60$ reinforcing bars. Considering the cross$-$section area of one #$10$ reinforcing bar is $1\mathrm{.}27i{n}^3$ and the following material properties:

$,$ Yield strength of steel, $f_y=60$ksi.

$,$ Compressive strength of concrete $f_c^{\text{'}}=4,000$

Do the following:

$($a$)$ Calculate the amount of reinforcement required for a balanced strain condition

$($b$)$ Calculate the nominal flexural moment capacity of the section, $M_n,$ using the equivalent rectangular stress distribution method.

$($c$)$ Determine the strength reduction factor $.$ Is the section tension$-$controlled, compressioncontrolled or in the transition zone?

$($d$)$ Calculate the minimum reinforcement ratio allowed by the ACI $318$ code for this section

$($e$)$ Calculate the factored moment capacity of this section, $M_n.$