A long, slender column ABC is pin$-$supported at the ends and compressed by an axial load $P($Fig$.11-15).$ Lateral support is provided at the midpoint $B$ in the plane of the figure. However, lateral support perpendicular to the plane of the figure is provided only at the ends.

The column is constructed of a standard steel shape $($IPN $220)$ having modulus of ehasticity $E=200$GPa and proportional limit ${}_{pl}=300$MPa. The total length of the column is $L=8m.$

Determine the allowable load $P_{\text{a}\text{l}\text{l}\text{o}\text{w}}$ using a factor of safety $n=2\mathrm{.}5$ with respect to Euler buckling of the column.

$I_1=3060c{m}^4,I_2=162c{m}^4,A=39\mathrm{.}5c{m}^2$