Timoshenko Beam Theory Is Not Always More Accurate Than Elementary Beam Theory

[+] Author and Article Information
J. W. Nicholson, J. G. Simmonds

Department of Applied Mathematics and Computer Science, University of Virginia, Charlottesville, Va.

J. Appl. Mech 44(2), 337-338 (Jun 01, 1977) (2 pages) doi:10.1115/1.3424048 History: Received October 01, 1976; Revised January 01, 1977; Online July 12, 2010


A counterexample involving a homogeneous, elastically isotropic beam of narrow rectangular cross section supports the assertion in the title. Specifically, a class of two-dimensional displacement fields is considered that represent exact plane stress solutions for a built-in cantilevered beam subject to “reasonable” loads. The one-dimensional vertical displacement V predicted by Timoshenko beam theory for these loads can be regarded as an approximation to either the exact vertical displacement v at the center line, or a weighted average of v over the cross section, or a quantity defined to make the virtual work of beam theory equal to that of plane stress theory. Regardless of the interpretation of V and despite the presence of an adjustable shear factor, Timoshenko beam theory for this class of problems is never more accurate than elementary beam theory.

Copyright © 1977 by ASME
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