$11\mathrm{.}2$

A $10-$meter steel column $(E=200$GPa $)$ has the shown crosssection at right. Find the elastic buckling load for each of the following cases:

i $-$ both ends are hinged.

ii $-$ both ends are fixed.

iii $-$ both ends are hinged and the column is braced in the $x-x$ direction at its mid$-$height.

iv $-$ both ends are fixed and the column is supported in the $x-$x direction at its mid$-$height.

$v-$ both ends are hinged for the $x-$direction and hingedfixed for the $y-$direction

Assume: $A=14\mathrm{.}910{10}^{3}m{m}^2$;$I_x=25\mathrm{.}170{10}^{6}m{m}^4$;$I_y=8\mathrm{.}563{10}^{6}m{m}^4$