$1.$ A $24$ long concrete beam with a uniform dead load of $1\mathrm{.}0$k$/$ft and a uniform live load of $2\mathrm{.}0$k$/$ft

$$ f$$c $=3,000$psi

$$ fy $=60,000$psi

a$.$ Calculate the maximum factor uniform load on the beam $(7$ pts$)$

b$.$ Per ACI moment coefficients, calculate the maximum positive and negative beam moments, Mu $(8$ pts$)$

c$.$ If the beam width is $10$ in and the maximum positive beam moment is $180$ k$-$ft$,$ calculate estimated beam depth and width $(5$ pts$)$

d$.$ If the estimated beam depth is $17$ in & the beam width is $12$ in$,$ determine the required area of reinforcement & select bars $(7$ pts$)$

e$.$ If the area of reinforcing is $2\mathrm{.}70$ in$2,$ calculate the tension force in the reinforcing, T $(3$ pts$)$

$2.$ A concrete beam with a rectangular cross section has f$$c $=3,000$psi & steel with fy $=40$ ksi. Select the beam dimensions and reinforcement for a balanced section if the beam sustains a moment due to dead load of $60$ kip$-$ft and a moment due to live load of $90$ kip$-$ft$.(20$ pts$)$

$3.$ Find the area of steel reinforcement required and select the bars for a beam if the section dimensions are b $=14$ in$.$ and d $=25$ in$.(20$ pts$)$

$$ f$$c $=4,000$psi

$$ fy $=60$ ksi

$$ A moment due to dead load of $36$ kip$-$ft

$$ A moment due to live load of $65$ kip$-$ft