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Pure bending of beams having initial curvature

Published online by Cambridge University Press:  04 July 2016

M. Holland
M. Holland*
Affiliation:
Department of Mechanical Engineering, Liverpool Polytechnic
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Extract

Three theories of bending are available to the designer for the determination of bending stresses in curved beams. (1) The Euler-Bernoulli hypothesis (often referred to as the simple theory of bending), which assumes a linear distribution of bending stress, having a zero stress value at the mid-plane, i.e. the centroidal and neutral axes are coincident. (2) The Winkler theory, which predicts a depression of the neutral axis away from the centroidal axis and towards the centre of curvature. This theory produces a hyperbolic distribution of bending stress across the section, having a maximum amplitude at the fibre nearest the centre of curvature. (3) The Golovin theory, which is exact.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 78 , Issue 768 , December 1974 , pp. 570 - 573
Copyright
Copyright © Royal Aeronautical Society 1974 

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References

1. Winkler, E. Zivilingenieur, Vol 4, p 232, 1858.Google Scholar
2. Golovin, H. Trans. Inst. Tech., St Petersburg, 1881.Google Scholar
3. Timoshenko, S. and Goodier, J. N. Theory of Elasticity (Second edition, pp 61–65). McGraw-Hill, New York, 1951.Google Scholar
4. Ford, H. Advanced mechanics of materials (First edition, pp 257–258). Longmans, London, 1963.Google Scholar