Question $4$:

A long, slender structural steel $E=29,000$ksi HSS $84\frac{1}{4}$ shape $,I_y=14\mathrm{.}4i{n}^4)$ is used as a $32-$ft$-$long column. The column is supported in the $x$ direction at base A and pinned at ends A and $C$ against translation in the $y$ and $z$ directions. Lateral support is provided to the column so that deflection in the $x-z$ plane is restrained at midheight $B$; however, the column is free to deflect in the $x-y$ plane at $B.$ Determine the maximum compressive load that the column can support if a factor of safety of $1\mathrm{.}92$ is required. In your analysis, consider the possibility that buckling could occur about either the strong axis $($i$.$e$.,$ the $z$ axis$)$ or the weak axis $($i$.$e$.,$ the $y$ axis$)$ of the steel column.