A pin$-$ended column has length L$,$ as shown. The cross$-$section of the column is

rectangular, with side lengths t and $3$t$.$ The total length is L$.$ A load is applied, parallel to the

long$-$axis of the column, as shown. This load causes the column it to buckle. The column can

buckle either in the plane of the page, or out of the plane of the page

$($A$)$ Find the expression for Iz if the column buckles in plane

$($B$)$ Find the expression for the critical buckling force for in plane buckling.

$($C$)$ Find the expression for Iz if the column buckles out of plane.

$($D$)$ Find the expression for the critical buckling force for out of plane buckling.

Problem $5.$ A pin$-$ended column has length $\backslash (\backslash$mathbf$\{$L$\}\backslash ),$ as shown. The cross$-$section of the column is rectangular, with side lengths $\backslash (\backslash$mathbf$\{$t$\}\backslash )$ and $\backslash (3\backslash$mathbf$\{$t$\}\backslash ).$ The total length is L $.$ A load is applied, parallel to the long$-$axis of the column, as shown. This load causes the column it to buckle. The column can buckle either in the plane of the page, or out of the plane of the page.

$($A$)$ Find the expression for $\backslash (\backslash$mathbf$\{$l z$\}\backslash )$ if the column buckles in plane

$($B$)$ Find the expression for the critical buckling force for in plane buckling.

$($C$)$ Find the expression for $\backslash (\backslash$mathbf$\{$l z$\}\backslash )$ if the column buckles out of plane.

$($D$)$ Find the expression for the critical buckling force for out of plane buckling.