Problem $2(25$ points$).$ A steel bar of thickness $\backslash ($ h $\backslash ),$ to be used as a beam, is welded to vertical support by two fillet welds as shown in the figure. Dimensions are provided below.

$($a$)$ Find the safe bending force $\backslash ($ F $\backslash )$ if the allowable shear stress in the welds is $\backslash (\backslash$tau$\_\{\backslash$text $\{$allow $\}\}\backslash ).$

$($b$)$ In part a$,$ you found a simple expression for F in terms of the allowable shear stress. Find the allowable load if the electrode is E$7010,$ the bar is $1020$ HR$,$ and the support is $1015$ HR$.$