Considering the beam section shown below, and the following parameters:

$h=36in.$

$d=32\mathrm{.}5in.$

$b=12in.$

$d^{\text{'}}=3\mathrm{.}5in.$

Assume there is a #$3$ stirrup in place. Assume $f_c^{\text{'}}=4,000$ psi and $f_y=60,000.$ Determine the following:

a$)$ Does the compression steel yield? $(20$ pts$.)$

b$)$ If the beam is loaded with a live load of $3\mathrm{.}0$kip$\frac{s}{f}t.,$ a superimposed dead load of $1\mathrm{.}0ki\frac{p}{f}t.,$ and the self$-$weight of the beam, calculate the short$-$term deflection due to the live load. The span length is $18-$feet. Remember all loads are service loads. Assume all loads have been applied in calculating the deflection and that there has been no other loading in place. Ignore the compression steel when calculating the moment$($s$)$ of inertia. Use the deflection equation below. $(30$ pts$.)$

$=\frac{5w{L}^4}{384EI}$