Column AB carries a centric load P of magnitude 16 kips. Cables BC and BD are taut and prevent motion only of point B in

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Column AB carries a centric
load P of magnitude 16 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 2.4 and neglecting the tension in the cables, determine
the allowable length L. Use E = 31
× 106 psi.
MOI of cross-section about the x-axis
Using Appendix E, moment of inertia about the x-axis is given as
Ix=118 (in4)
MOI of cross-section about the y-axis
Using appendix E, moment of inertia about the y-axis is given as
Iy=11.4 (in4)
Effective length in the yz plane
Beam AB is fixed-free and therefore Le=2L
Effective length in the xz plane
Beam AB is fixed-pinned and therefore
Le=0.7L
Critical buckling load
The critical buckling load for the beam is given as
Pcr=FSxP=38.4 kip
Allowable length for motion in the yz plane
For motion in the yz plane,
Pcr<π2EIx/(2L)2→L<40.401
(ft)
Allowable length for motion in the xz plane
To prevent buckling in the xz plane, the allowable length is
__________ (ft)