Question $4($a:$15$ points, b: $20$ points$)$

Consider the roof plan of the single$-$story single$-$family house in Question $3$ with the same loading.

$($a$)$ Compute the maximum moment of girder G$1$ using only the ASD load combinations D $+$ LR and $\backslash (0\mathrm{.}6\backslash$mathrm$\{$D$\}\backslash$pm $0\mathrm{.}6\backslash$mathrm$\{$~W$\}\backslash ).$ Assume that the girder is simply supported and report the maximum moment in each of the three load combinations and whether it is positive or negative.

$($b$)$ Using a glulam beam size of $5-1/2\backslash (\backslash$times $18\backslash )$ with Douglas Fir$-$Larch species group and Stress Class of $16$F$1\mathrm{.}3$ E for girder G$1,$ determine if the girder is adequate to support the loading given with the load combinations in part $($a$).$

$\backslash (>\backslash )$ Consider only bending. Note that the design requirement should be satisfied individually in each of the three load combinations.

$\backslash (>\backslash )$ Consider dry$-$service and normal temperature conditions, and no lateral$-$torsional buckling.

$\backslash (>\backslash )$ The high$-$quality tension lams should be placed at the bottom or top of the beam based on the positive and negative moments in part $($a$).$