Unified Formulations of the Shear Coefficients in Timoshenko Beam Theory
Publication: Journal of Engineering Mechanics
Volume 143, Issue 9
Abstract
Two elastostatic approaches are presented in order provide a simple, but technically effective, assessment of shear coefficients in Timoshenko beam theory. First the elasticity solution of Saint-Venant’s flexure problem is used to set forth a unified formulation of Cowper’s formula for shear coefficients. Afterward a novel elasticity-based displacement field for a Timoshenko beam is introduced and an energy-consistent variational scheme is developed using the Reissner principle. The new variational framework is then applied to elliptical, circular, and rectangular cross sections. Validation of the results is given by numerical comparison with the other shear deformation factors over an extended range of Poisson’s and aspect ratios. Unlike previous treatments, the proposed shear coefficients for shallow cross sections do not result in numerical instability.
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Acknowledgments
The author would like to acknowledge Professor Raffaele Barretta for his valuable and constructive suggestions which were greatly beneficial in the improvement of the manuscript. The author would also like to thank the anonymous reviewers for their detailed and insightful comments to the manuscript.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 9 • September 2017
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©2017 American Society of Civil Engineers.
History
Received: Oct 21, 2016
Accepted: Feb 28, 2017
Published online: May 16, 2017
Published in print: Sep 1, 2017
Discussion open until: Oct 16, 2017
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