Problem $1(44$ pts$)$:

Design a beam to withstand the concentrated live load shown in the figure below as well as a $1\frac{k}{f}t$ distributed dead load $($assume that this dead load includes an estimate for beam weight$).$ Live load deflections must be $\frac{L}{360}.$ Verify the shear and moment capacity of your member with hand$-$calculations. Bracing against lateral torsional buckling is provided at the support and live load location. You may assume the load case $1\mathrm{.}2$D $+1\mathrm{.}6$L governs.

$P_r=Rl$

$F_y=50$ksi

$w_D=1\frac{k}{f}t$