Consider the beam shown below with a uniformly distributed dead load $($not including the self$-$weight$)$ w subscript D$=5\mathrm{.}2$ k$/$ft and a concentrated live load P subscript L$=37$ k acting in the middle of the beam. f subscript y$=60$ ksi and f to the power of apostrophe subscript c$=4000$ psi.

Beam length L$=16$ ft$.$

$($a$)$ Design the beam cross$-$section for maximum bending moment.

$($b$)$ Considering the entire beam, determine the bar cut$-$off points. Ensure that the beam has sufficient strength along the length of the beam.

$($c$)$ Design the shear reinforcement for the beam.