$1.$ A rectangular beam of width b $=15$ in$.,$ effective depth d $=21\mathrm{.}5$ in$.,$ and total depth h $=24$ in$.$

spans $18\mathrm{.}5$ ft between simple supports. It will carry a dead load of $1\mathrm{.}08$ kips$/$ft including self$-$

weight, plus a service live load of $4\mathrm{.}00$ kips$/$ft$.$ Reinforcement consists of four evenly spaced No$.$

$7($No$.22)$ bars in one row. The clear cover on the sides is $2$ in$.$ Material strengths are fy $=80,000$ psi and

Confirm the suitability of the proposed design based on Eq$.(7\mathrm{.}3).$ Fs can be estimated from Fy without a strict calculation.

$2.$ For the beam addressed in Problem $1,$ calculate the effective moment of inertia. The service

load coming from the combination of the dead load of $1\mathrm{.}80$ kips$/$ft and the live load $4\mathrm{.}00$ kips$/$ft

shall be considered. The corresponding bending moment shall be calculated as WL$^2/8.$