$(10$ points, Shear Strength Calculation$)$ Determine the available strength of a WT$5$x$22\mathrm{.}5,$

A$992$ steel, with the flanges welded to a $\frac{1}{2}$ in$.$ gusset plate with unequal length longitudinal

welds $-$ a $6$ in$.$ weld and a $12$ in$.$ weld, as shown in the figure below. Considering yielding and

net area rupture, determine the LRFD design strength of the WT$5$x$22\mathrm{.}5.$