$D_{**}$ Prob. $6\mathrm{.}5-20.$ The cross section of a steel$-$reinforced concrete beam of width $b$ is shown in Fig. P$6\mathrm{.}5-20$a$.$ The allowable compressive stress in the concrete is ${}_c,$ and the allowable tensile stress in the steel is ${}_s.$ The diameter of each of the three steel bars is $d,$ and the ratio of the moduli of elasticity is $\frac{E_s}{E_c}.$ Assume that the area of the steel bars is concentrated along a horizontal line at a distance of $h$ from the top of the beam, and assume that the concrete is only effective in compression. That is$,$ tension is carried solely by the steel bars. Calculate the maximum allowable bending moment for the beam. Let $b=12$ in$.,h=16$ in$.,d=0\mathrm{.}875$ in$.({}_{\text{a}\text{l}\text{l}\text{o}\text{w}}{)}_c=1\mathrm{.}5$ksi,$({}_{\text{a}\text{l}\text{l}\text{o}\text{w}}{)}_s=18$ksi, and $\frac{E_s}{E_c}=10.$