Piecewise Linear Warping Theory for Multilayered Elastic Beams
Publication: Journal of Engineering Mechanics
Volume 124, Issue 4
Abstract
Warping due to transverse shear in multilayered elastic beams is studied in this paper. The Bernoulli-Kirchhoff hypothesis that plane sections remain plane after deformations, with independent rotations, is assumed for each lamina to account for the out-of-plane deformation of the composite cross section. The effects of shear are included by taking the rotations independent of the transverse deflection, as in Timoshenko beam theory. The result is a simple piecewise linear warping theory for layered composite beams. The solution to the governing equations is presented in terms of the eigenvalues and eigenvectors of a generalized matrix eigenvalue problem associated with the coefficient matrices that appear in the governing equations. The problem of a two-layered cantilever beam subjected to a uniformly distributed loading is solved in detail to show the effects of different elastic moduli on the interfacial shear stress. Compared with a finite-element solution, the current theory yields significant improvement over elementary beam theory (excluding warping) in predicting the interface shear stress.
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Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 124 • Issue 4 • April 1998
Pages: 377 - 384
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Apr 1, 1998
Published in print: Apr 1998
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