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Column $AB$ carries a centric load $P$ of magnitude $17$ kips. Cables $BC$ and $BD$ are taut and prevent motion only of point $B$ in

the $xz$ plane. Using Euler's formula and a factor safety of $2\mathrm{.}2$ and neglecting the tension in the cables, determine the

allowable length $L.$ Use $E=30{10}^6.$

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

Using Appendix $E,$ moment of inertia about the $x-$axis is given as $I_x=118($in ${?}^4)$

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

Using appendix $E,$ moment of inertia about the $y-$axis is given as $I_y=11\mathrm{.}4($in ${?}^4)$

Effective length in the $yz$ plane

Beam $AB$ is fixed$-$free and therefore $L_e=2L$

Effective length in the $xz$ plane

Beam $AB$ is fixed$-$pinned and therefore $L_e=0\mathrm{.}7L$

Critical buckling load

The critical buckling load for the beam is given as $Pcr=FSP=37\mathrm{.}4$ kip

Allowable length for motion in the yz plane

To prevent buckling in the $yz$ plane, the allowable length is

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