$18-3.$ Use LRFD method for the following welded shape: The flanges are $7/8$ in $12$ in$,$ the web

is $3/8$ in $46$ in$,$ and the member is simply supported, uniformly loaded, and has continuous lateral support of the compression flange.

$($a$)$ Determine the design flexural strength if A$572$ Grade $50$ steel is used. $($Ans$.$Mn

$2383\mathrm{.}7$ ft$-$k$,$ LRFD$)$

$($b$)$ If the span is $40$ ft and supports the loads wD $4\mathrm{.}6$ k$/$ft $($not including the beam weight$)$

and wL $3\mathrm{.}7$ k$/$ft$,$ verify the moment capacity and select transverse stiffeners as needed.

$($Ans$.$ Mu $2320$ ft$-$k $<$Mn $2383\mathrm{.}7$ ft$-$k; $1$st stiffener panel, a $57$ in