Prob # $4$: A column is required to support a service dead load of $150$ kips and a service live load of $165$ kips.

Assume that the overall length of column is $19$ ft $.$ For $x-$axis buckling it has pin supports. For $y-$axis buckling

it is braced at mid height and has pir$-$fix supports at the two ends. $($i$)$ design the column by choosing a suitable

W$-$shape for it$.$ Employ the $(KL$ concept in your solution and $($ii$)$ check if the chosen section satisfies the

local buckling criterion

$(16+4)pts.$