Problem $3$:

Given: The beam shown below has a compression side of the member suppoited laterally at the ends and mid$-$span only. The span length is $L=25ft.$

The member is a $\frac{31}{8}18$ DF glulam Stress Class $24F-1\mathrm{.}8E.$ The load combination is D $+L($ASD$).$

Assume $C{M}_M=1\mathrm{.}0,C{D}_D=1\mathrm{.}0$ and $C{t}_t=1\mathrm{.}0.$ Show all work to calculate $C_v$ and $C{L}_L.$

Find: The maximum allowable bending moment in $k-ft$ and the corresponding maximum allowable load $P$ in kip that would cause maximum allowable bending moment.

$(20$ points$)$