A rectangular beam made using concrete with $f_c^{\text{'}}=4000$ and steel with $f_y=60,000$ has width $b=10in.,$ total depth $h=18in.,$ and effective depth $d=15\mathrm{.}5in,$ Fig. $3.$ The concrete modulus of rupture is $f_r=475.$ The elastic moduli of steel and concrete are $29,000$ksi and $3,600$ksi. The tensile steel area is made of five #$11$ bars.

$($a$)$ Find the maximum service load moment that can be resisted without stressing the concrete higher than $0\mathrm{.}45f_c^{\text{'}}$ or the steel above $0\mathrm{.}40f_y.$

$($b$)$ Determine the nominal flexural strength of the beam section $(M_n),$ and calculate the ratio of nominal flexural strength to service load moment.

$($c$)$ Determine whether this beam will show flexural cracking before reaching the service load calculated in part $($a$).$

Figure $3$: Concrete beam section in Problem $7.$