$(30\%)$ Problem $3$ :

Design a Southern Pine No$.1$ beam to carry the loads shown $($roof beam, no plaster$).$ Assume the beam is supported at each end by an eight$-$inch block wall. Consider bending, shear and deflection. The allowable deflection is $(\frac{1}{240})$ of the span length for total load.

$Fb=1,550$;$Fv=110$;$E=1\mathrm{.}6{10}^6$