Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-23T20:57:34.104Z Has data issue: false hasContentIssue false

The Flexural Centre or Centre of Shear

Published online by Cambridge University Press:  28 July 2016

W. J. Duncan*
Affiliation:
University of Glasgow

Extract

This paper reviews work on the flexural centre of elastic cantilever beams and contains a number of hitherto unpublished results, including a formula giving the position of the flexural centre in terms of the Prandtl torsional stress function.

The appearance of the note by Jacobs has prompted the preparation of a review of this subject which is all the more desirable as several of the investigations made shortly before the 1939-45 War were never published and others, although published, seem to be in danger of being overlooked. The present paper contains a number of hitherto unpublished results. The question of nomenclature is worthy of mention since general agreement is lacking. Some of the names used are flexural centre, centre of flexure, elastic centrum and centre of shear but a complete search of the literature would probably lead to the discovery of yet other names. The terms “centre of shear” and “elastic centrum” seem vague and fail to indicate that the point referred to has any special relation to flexure. We shall here use the name “flexural centre” exclusively.

Type
Technical Notes
Copyright
Copyright © Royal Aeronautical Society 1953

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Jacobs, J. A. (1953). The Centre of Shear of Aerofoil Sections. Journal of the Royal Aeronautical Society, April 1953.Google Scholar
2. de Saint-Venant, B. (1856). Journal de Mathematiques (Liouville), Sér. 2, t. 1 (1856).Google Scholar
3. Love, A. E. H. (1906). A Treatise on the Mathematical Theory of Elasticity, Chap. XV. Cambridge, 2nd edition, 1906.Google Scholar
4. Griffith, A. A., and Taylor, G. I. (1917). The Problem of Flexure and its Solution by the Soap-Film Method. R. & M. 399, 1917.Google Scholar
5. McKinnon Wood, R. and Perring, W. G. A. (1929). Stresses and Strains in Airscrews with Particular Reference to Twist. R. & M. 1274, 1929.Google Scholar
6. Duncan, W. J. (1932). Torsion and Flexure of Cylinders and Tubes, Chap. IV. R. & M. 1444, 1932.Google Scholar
7. Fisher, H. R. (1934). The Definition of the Flexural Centre of a Cylinder in Terms of St. Venant's Solutions for Flexure and Torsion. A.R.C. 1162, 1934 (unpublished).Google Scholar
8. Williams, D. (1935). Some Features of the Behaviour in Bending of Thin-walled Tubes and Channels. R. & M. 1669, 1935.Google Scholar
9. Stevenson, A. C. (1939). Flexure with Shear and Associated Torsion in Prisms of Uni-axial and Asymmetric Cross-Sections. Phil. Trans. Roy. Soc. A, Vol. 237, p. 161, 1939.Google Scholar
10. Stevenson, A. C. (1939). Ibid., Corrigenda et Addenda. Phil. Trans. Roy. Soc. A, Vol. 237, p. 566, 1939.Google Scholar
11. Stevenson, A. C. (1938). On the Definition and Determination of the Centre of Flexure and the Centre of Least Strain. A.R.C. 3478, 1938 (unpublished).Google Scholar
12. Duncan, W. J. (1938). Note on the Flexural Centre of a Cylinder whose Section Possesses an Axis of Symmetry. A.R.C. 3596, 1938 (unpublished).Google Scholar
13. Duncan, W. J. (1932). On the Torsion of Cylinders of Symmetrical Section. Proc. Roy. Soc. A, Vol. 136, p. 95, 1932.Google Scholar
14. Duncan, W. J., Ellis, D. L. and Scruton, C. (1933). The Flexural Centre and the Centre of Twist of an Elastic Cylinder. Phil. Mag., Ser. 7, Vol. XVI, p. 201, 1933.CrossRefGoogle Scholar