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

spans $18\mathrm{.}5$ ft between simple supports. It will carry a dead load of $1\mathrm{.}08$kip$\frac{s}{f}t$ 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 $f_x=80,000$

psi and $f_c^{\text{'}}=4000$ psi.

Confirm the suitability of the proposed design based on Eq$.(7\mathrm{.}3).f_s$ can be estimated from $f_y$

without a strict calculation.

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 $1\mathrm{.}80$kip$\frac{s}{f}t$ and the live load $4\mathrm{.}00$kip$\frac{s}{f}t$

shall be considered. The corresponding bending moment shall be calculated as $\frac{w{L}^2}{8}.$