A simply supported beam with cross$-$section shown in the following

figure has a span of $28$ ft and supports a dead load of $1\mathrm{.}5$ kip$/$ft$,$ including

its own self$-$weight plus a live load of $1\mathrm{.}5$ kip$/$ft$.$ The concrete strength is

$4500$ psi. Compute:

$($a$)$ the immediate dead$-$load deflection

$($b$)$ the immediate dead$-$plus$-$live load deflection

$($c$)$ the defection occurring after partitions are installed. Assume that the

partitions are installed one year after the concrete is cast and assume that

$20$ percent of the live load is sustained.

Hint: Find the NA of the gross concrete section $($using two rectangles$).$

Then find the gross Moment of Inertia. For finding Mcr$,$ you can use the

distance $($yt$)$ from the NA to the tension side. You can then find the cracked

section NA by using two rectangles with unknown NA depth, and then the

cracked section Moment of Inertia. If you wish to use the compression

steel in finding the long$-$term deflection multiplier, please use $2-$#$3$ hanger

rebars.

Can someone solve this for me$.$ Thanks.