An I beam column with fixed ends $($at x$=0$ and x$=12$ m$)$ is braced at midpoint C as shown below and loaded in compression by a force P$.$ Buckling can potentially occur in either xy plane or xz plane $($out of the page$).$ The bracing acts as a simple support $($i$.$e$.$ pinned support$)$ in the xy plane, and there is no such midspan support for buckling in the xz plane.

Which plane is more likely to buckle and why? Include relevant calculations to support your choice.

Given your answer to part a$,$ find the allowable axial force P assuming a safety factor of $2.$

Material Properties: E$=200$ GPa; Sy$=280$ MPa

Important properties of the cross$-$section:

A $=27\mathrm{.}5\backslash$times $103$ mm$2$

Iyy $=712\backslash$times $106$ mm$4$

Izz $=282\backslash$times $106$ mm$4$