send to expert $5-$ A pin$-$ended column of height $2\mathrm{.}2$ m has a circular cross$-$section with an external diameter of $55$ mm $,$ and a wall thickness of $2\mathrm{.}0$ mm and is converted to an open section by a narrow longitudinal slit. If the ends of the column are free to warp and the column is made from materials with $\backslash (\backslash$mathrm$\{$E$\}=50\backslash$mathrm$\{$GPa$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$G$\}=15\backslash$mathrm$\{$GPa$\}\backslash ),$ determine the values of axial load which would cause the column to buckle in:

a$)$ pure bending mode

b$)$ pure torsion mode