Flexural-Torsional Buckling of Cantilever Strip Beam-Columns with Linearly Varying Depth
Publication: Journal of Engineering Mechanics
Volume 136, Issue 6
Abstract
In this paper, one investigates the elastic flexural-torsional buckling of linearly tapered cantilever strip beam-columns acted by axial and transversal point loads applied at the tip. For prismatic and wedge-shaped members, the governing differential equation is integrated in closed form by means of confluent hypergeometric functions. For general tapered members , the solution to the boundary value problem is obtained in the form of a Frobenius’ series, which is shown to converge in the interior of the domain and at the boundary if and only if . Therefore, for the Frobenius’ series solution cannot be used to establish the characteristic equation for the cantilever beam-columns; the problem is then solved numerically by means of a collocation procedure. Some of the analytical solutions (buckling loads) were compared with the results of shell finite-element analyses and an excellent agreement was found in all cases, thus validating the mathematical model and confirming the correctness of the analytical results. The paper closes with a discussion on the convexity of the stability domain (in the load parameter space) and the accuracy of approximations based on Dunkerley-type theorems.
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Acknowledgments
The second writer gratefully acknowledges the financial support of FCT (Portuguese Foundation for Science and Technology) through the Doctoral Grant No. UNSPECIFIEDSFRH/BD/39115/2007.
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Published In
Journal of Engineering Mechanics
Volume 136 • Issue 6 • June 2010
Pages: 787 - 800
Copyright
© 2010 ASCE.
History
Received: Sep 18, 2009
Accepted: Nov 16, 2009
Published online: Nov 21, 2009
Published in print: Jun 2010
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