It was recently shown that the shear coefficient for a rectangular Timoshenko beam is highly dependent on the aspect ratio of the beam. This research investigates the reasons for that behavior by comparison of the Timoshenko beam solution with a new three-dimensional solution for a simply supported beam. The new solution is a series solution that converges to any desired accuracy. Comparisons are also made to both elementary and Mindlin plates. The Mindlin plate solution is in excellent agreement with the three-dimensional solution for the simply supported case, and is used as a basis of comparison for a free-free beam. It is found that a shear coefficient which would cause matching of the three-dimensional and Mindlin solutions would have to be a function of the wave length as well as the aspect ratio. Physical explanations are given for the high dependence on aspect ratio and for the dependence on wave length.
On Timoshenko Beams of Rectangular Cross-Section
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, August 6, 2002; final revision, August 6, 2003. Associate Editor: R. C. Benson. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Hutchinson, J. R. (June 22, 2004). "On Timoshenko Beams of Rectangular Cross-Section ." ASME. J. Appl. Mech. May 2004; 71(3): 359–367. https://doi.org/10.1115/1.1751186
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