Approximate Derivation of Critical Buckling Load
Publication: Journal of Architectural Engineering
Volume 15, Issue 4
Abstract
This paper proposes an approximate derivation for the critical buckling load of a column, based on the application of a uniformly loaded beam's midspan moment and deflection to the buckled column's rotational equilibrium. The curvature of a pin-ended member, when it buckles under axial load, is similar to the curvature assumed by the same member when it deflects under a uniformly distributed load applied transversely along its entire length. Euler's famous equation for critical buckling load is based, of course, on the former assumption, in which the deflected column assumes the shape of a sine curve. However, dividing a uniformly loaded beam's midspan moment by its deflection provides a conservative result for the critical buckling load, within 3% of Euler's value, that can be derived solely on the basis of these commonly used beam equations.
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References
Timoshenko, S. P. (1958). Strength of materials, Part I, Van Nostrand Reinhold, New York.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, McGraw-Hill, New York.
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© 2009 ASCE.
History
Received: Apr 21, 2008
Accepted: Feb 20, 2009
Published online: Nov 13, 2009
Published in print: Dec 2009
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Jonathan Ochshorn
Associate Professor, Dept. of Architecture, College of Architecture, Art and Planning, Cornell Univ., 143 East Sibley Hall, Ithaca, NY 14853.
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