Critical Compressive Stress of a Beam-Column to a Second Order

[+] Author and Article Information
D. Chattoraj

Department of Mathematics, Hooghly Mohasin College, Hooghly, India

S. K. Bose

Department of Mathematics, Regional Engineering College, Durgapur, India

J. Appl. Mech 48(4), 978-980 (Dec 01, 1981) (3 pages) doi:10.1115/1.3157771 History: Received October 01, 1980; Revised February 01, 1981; Online July 21, 2009


Buckling of a beam-column under axial loads at the ends is considered as a three-dimensional stability problem. Displacement and stress fields are written in terms of Neuber-Papkovich potentials. These are then approximated to forms containing one more higher-order term than those corresponding to the Euler-Bernoulli equations. These expressions yield a modified formula for the bending moment. The energy method applied to the equations yield a modified form of Euler critical load and Shanley tangent modulus formula. The effect of the second-order modification is to decrease the critical load. For mild steel this decrease exceeds 5 percent for the slenderness ratio less than 25.

Copyright © 1981 by ASME
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