A beam with the cross$-$section shown below is $25$ feet long. The beam is simply supported and loaded with uniform

dead load of $1ki\frac{p}{f}t($including the self$-$weight$)$ and a uniform live load of $2\mathrm{.}3$kip$\frac{s}{f}t.$

For uniformly distributed loads, ${}_{\text{m}\text{a}\text{x}}=\frac{5w{l}^4}{384EI}$

$A_s=6$#$8$ bars of Grade $60$ steel

$f_c^{\text{'}}=4000$ psi normal weight concrete

a$.$ Where is the cracked neutral axis for the beam?

b$.$ What is the cracked moment of inertia?

c$.$ What is the anticipated immediate deflection due to live loading?

d$.$ How does the deflection you computed in part c compare to the code limits for the immediate deflection due to live

load on a floor, assuming the beam will not support or be attached to nonstructural elements sensitive to large

deflections?