On the Accuracy of the Bernoulli-Euler Theory for Beams of Variable Section

[+] Author and Article Information
Bruno A. Boley

Institute of Flight Structures, Columbia University, New York, N. Y.

J. Appl. Mech 30(3), 373-378 (Sep 01, 1963) (6 pages) doi:10.1115/1.3636564 History: Received October 22, 1962; Online September 16, 2011


The stresses and deflections of thin rectangular beams of arbitrary variable depth, in pure bending, according to the theory of plane stress, are considered. They are obtained in the form of series; the first term of each series is identical with the strength-of-materials solution and the others represent the necessary correction to that theory. This form of the solution is chosen because of its convenience in the study of the relationship between the Bernoulli-Euler and the exact solution. The former is found to be quite accurate for thin beams and, when certain conditions are satisfied by the ordinates (and their spanwise derivatives) of the upper and lower edges of the beam. The Bernoulli-Euler theory is ambiguous in prescribing the position of the axis of a beam of variable cross section; admissible choices for the axis are presented.

Copyright © 1963 by ASME
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