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.
Skip Nav Destination
On the Accuracy of the Bernoulli-Euler Theory for Beams of Variable Section
Bruno A. Boley
Institute of Flight Structures, Columbia University, New York, N. Y.
- Views Icon Views
- Share Icon Share
- Search Site
Boley, B. A. (September 1, 1963). "On the Accuracy of the Bernoulli-Euler Theory for Beams of Variable Section." ASME. J. Appl. Mech. September 1963; 30(3): 373–378. https://doi.org/10.1115/1.3636564
Download citation file:
Get Email Alerts
2021 Timoshenko Medal Acceptance Speech: Presented at the AMD Awards Event on November 3, 2021.
J. Appl. Mech (February 2022)