$8-7$ A rectangular beam with cross section $b=14$ in$.,h=24$ in$.,$ and $d=21\mathrm{.}5$ in$.$ supports a total factored load of $3\mathrm{.}9$kip$\frac{s}{f}t,$ including its own dead load. The beam is simply supportec with a $22-$ft span. It is reinforced with five No$.7$ Grade$-60$ bars, two of which are cut off between midspan and the support and three of which extend $10in.$ past the centers of the supports. $f_c^{\text{'}}=4000$ psi. $($normal weight$).$ The beam has Grade $60$ No$.3$ stirrups satisfying ACI Code Sections $9\mathrm{.}7\mathrm{.}6\mathrm{.}2\mathrm{.}2$ and $9\mathrm{.}6\mathrm{.}3\mathrm{.}4.$

a$.$ Plot to scale the factored moment diagram. $M=wl\frac{x}{2}-w\frac{x^2}{2},$ where $x$ is the distance from the support and $l$ is the span.

b$.$ Plot the moment$-$strength diagram and locate the cutoff points for the two cutoff bars such that the moment strength diagram stays above the factored moment.