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Column ABC has a uniform rectangular cross section with $b=13mm$ and $d=23mm.$ The column is braced in the $xz$ plane

at its midpoint $C$ and carries a centric load $P$ of magnitude $3\mathrm{.}6kN.$ Knowing that a factor of safety of $3\mathrm{.}4$ is required,

determine the largest allowable length L$.$ Assume the bracing prevents motion only along the $xz$ plane and use $E=200$

GPa.

MOI of cross$-$section about the $x-$axis

Moment of inertia about the $x-$axis is given as $I_x=b\frac{d^3}{12}=13\mathrm{.}181{10}^{-9}(m^4)$

MOI of cross$-$section about the $y-$axis

Moment of inertia about the $y-$axis is given as $l_y=,{10}^{-9}(m^4)$ SOLVE THE ENTIRE PROBLEM