Consider the cantilever beam below, which supports a distributed dead load of $1\mathrm{.}5$ kip$/$ft plus a concentrated live load of $12$ kips as shown. Considering the LRFD load combination $1\mathrm{.}2$ DL $+1\mathrm{.}6$ LL and ignoring the beam self$-$weight, do the following:

A$.$ Determine beam dimensions and required reinforcement. Assume a beam depth $H=\frac{L}{4\mathrm{.}5}$ and $\frac{B}{H}$ ratio between $1\mathrm{.}5$ and $4.$

B$.$ Select beam dimensions and rebar arrangement. Calculate the factored moment capacity of the section.

C$.$ Sketch the beam cross$-$section, including bar spacing, clear cover, etc. Assume #$4$ stirrups are in use.

For your calculations assume the following material properties: $=4000$ and $=60$ ksi.

Live Load, $P_L=12$ kips

$w_0=1\mathrm{.}5ki\frac{p}{f}t$