Select the lightest $W10$ shape for column $AB$ of the pinned$-$base unbraced$-$moment frame

shown in the figure. Assume all members are made of A$992$ steel. All members are

oriented such that bending is about the strong $(x-x)$ axis, and $K_y$ perpendicular to the

plane of the frame is $1\mathrm{.}0.$ Bracing in the $y-$direction is provided at the one$-$third points of

the column height

using pinned$-$end

connections at $5-ft$ on

center as shown in the

figure. The loads on

each column are $P{D}_D=$

$80-$kip and $P_L=90-$kip.