Column ABC carries a centric load $P=5kN$ and has a uniform rectangular cross$-$section $bd.$

Points A and $B$ are supported by pin connections and the column is braced against the

displacement in $x-$direction in the $xz$ plane at its midpoint $C.$ The modulus of elasticity of the

column is $E=70$GPa and the allowable stress is $70$MPa.

Determine the values of $b$ and $d$ so that the factor of safety corresponding to buckling in the $xz$

and $yz$ planes is the same at $2\mathrm{.}5.$ Given that $L=1m.$