A long slender column ABC is pinned at ends A and $C$ and compressed by an

axial force $P,$ as shown in Figure $4.$ At the midpoint $B,$ lateral supports are

provided to prevent deflection in the plane of the figure. The steel column is

a $250UC72\mathrm{.}9$ section. The distance between lateral supports is $L=6m.$

Calculate the allowable load $P$ using a factor of safety of $2\mathrm{.}5,$ and taking into

account the possibility of Euler buckling about either of the principal

centroidal axes.

Section details of $250UC72\mathrm{.}9$ column:$-$

$I_{11}=114{10}^{5}m{m}^4$

$I_{22}=38\mathrm{.}8{10}^{5}m{m}^4$

Section $x-x$

Figure $4$ : Axially loaded column