Q$3.$ Column $AD$ having a symmetrical I$-$shaped cross section is subjected to an axial compressive load $P$ as illustrated in Figure $3.$ The column is unrestrained about its major axis for the whole span length, except at its both supports. About its minor axis, the column is additionally retrained at every one third point of the span length $($i$.$e$.$ at $B$ and $C).$ The Young's modulus of the column is $E=40$GPa, Poisson ratio is $0\mathrm{.}3.$ Calculate the maximum critical load $P$ that can be resisted by the column. Consider both in$-$plane buckling and out$-$of$-$plane buckling.

$(20$ marks$)$

All dimensions in $mm.$

Figure $3.$ Column problem