A beam with the cross$-$section shown below is $32$ 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, ${}_{\text{m}\text{a}\text{x}}=\frac{5w{l}^4}{384EI}$

$A_s=()2$

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? See Table $24\mathrm{.}2\mathrm{.}2.$

e$.$ If $25\%$ of the live load is expected to be sustained, compute the additional long$-$term deflection caused by the sustained live load after $3$ years. $($This question is not asking for the whole deflection after partitions calculation I did in the videos for this week. This question is intended to be simpler, so plea'se read it carefully.$)$