Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-02T20:03:24.868Z Has data issue: false hasContentIssue false

The General Theory of Cylindrical and Conical Tubes Under Torsion and Bending Loads

Single and Many Cell Tubes of Arbitrary Cross-Section with Rigid Diaphragms

Published online by Cambridge University Press:  28 July 2016

Extract

This paper presents a rational method of stressing single or many cell tubes particularly of the type encountered in wing structures. The theory has been developed for conical or cylindrical tubes of arbitrary cross-section the shape of which is maintained by a closely spaced system of diaphragms rigid in their own planes and parallel to the root section. Within the limits of the assumptions the theory is exact for right cylindrical tubes, and is applicable with adequate accuracy to cylindrical or conical tubes in which the inclination of any generator to the normal to the root plane does not exceed 10°.

The analysis given unifies the theories of bending and torsion and shows that the commonly used method of separating the bending and torsion loads by means of a shear centre is in general incorrect.

The formulae have been developed in such forms that attention is concentrated on the necessary corrections to the stresses as indicated by the ordinary engineers' theory. These correction terms include all effects of shear lag, diffusion, and end effects hitherto taken into account only in some very special cases.

Particularly important for practical applications is the structure consisting of a number of direct stress carrying members (booms) connected by walls effective only in shear. The simplest structure of the latter type is the four-boom tube with or without nose and trailing cells, and in this case explicit formulae are given which are immediately applicable to practical calculations. Formulae are also given for the more complex case of a six-boom tube in which the two extra booms are introduced to represent more accurately the direct stress carrying capacity of the top and bottom panels between the two spars.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1947

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. Reissner, H.. Neuere Probleme aus der Flugzeugstatik. Z.F.M., Vol. 17, No. 18, September 1926.Google Scholar
2. Ebner, H.. Die Beanspruchung duennwandiger Kastentraeger auf Drillung bei behinderter Querschnittswoelbung. Z.F.M., Vol. 24, Nos. 23, 24, Dec. 1933.Google Scholar
3. Williams, D.. Torsion of a Rectangular Tube with Axial Constraints. R. & M. 1619, May 1934.Google Scholar
4. Williams, D.. The Stresses in Certain Tubes of Rectangular Cross Section under Torque. R. & M. 1761, May 1936.Google Scholar
5. Cox, H. L.. On the Stressing of Polygonal Tubes with Particular Reference to the Torsion of Tapered Tubes of Trapezoidal Section. R. & M. 1908, December 1942.Google Scholar
6. Fine, M.. The Torsion of Stiffened Cylindrical and Conical Shells of Doubly Symmetrical Rectangular Section. R.A.E. Report No. S.M.E. 3252, May 1943.Google Scholar
7. Kuhn, P.. A Method of Calculating Bending Stresses Due to Torsion. A.R.C. Report 6640, April 1943, reprinted from N.A.C.A. Advance Restricted Report, December 1942.Google Scholar
8. Williams, D. and Fine, M.. The Effect of End-Constraint on Thin Walled Cylinders Subject to Torque. S.M.E. Report No. 3321, May 1945.Google Scholar
9. Schnadel, G.. Die mittragende Breite in Kastentraegern und im Doppelboden. Werft. Reed. Hafen. Vol. 9, No. 5, 1928.Google Scholar
10. Ebner, H. and Koeller, H.. Zur Berechnung des Kraftverlaufes in versteiften Zylinderschalen. Luftfahrtforschung, Vol. 14, No. 12, December 1937.Google Scholar
11. Williams, D. and Fine, M.. Stress Distribution in Reinforced Flat Sheet, Cylindrical Shells and Cambered Box Beams under Bending Actions. R.A.E. Report No. A.D. 3140 September 1940.Google Scholar
12. Hemp, W. S.. The Monocoque Wing I. “Exact” Theory for a Uniform Symmetrical Wing with an Infinite Number of Rigid Ribs. A.R.C. Report No. 6995, Strut 715, 1943.Google Scholar
13. Dunne, P. C.. A Method of Stressing the Singly Symmetrical Trapezoidal Tube (Unpublished). Boulton Paul Aircraft Ltd., Technical Note No. 23, Feb. 1945.Google Scholar
14. Hildebrand, F. B.. The Exact Solution of Shear Lag. Problems in Flat Panels and Box Beams assumed Rigid in the Transverse Direction. N.A.C.A., Technical Note No. 894, 1943.Google Scholar
15. Hadji-Argyris, J. and Cox, H. L.. Diffusion of Loads into Flat Stiffened Panels of Varying Section. R. & M. 1969, May 1944.Google Scholar
16. Hadji-Argyris, J.. Diffusion of Symmetrical Loads into Stiffened Parallel Panels with Constant Area Edge Members. R. & M. 2038, November 1944.Google Scholar
17. Hadji-Argyris, J.. Diffusion of Anti-Symmetrical Loads and Theory of Bending of Parallel Panels. A.R.C. Report, February 1946.Google Scholar
18. Southwell, R. V.. On the Torsion of Conical Shells. Proc. Roy. Soc. Series A. Vol. 163, p. 337, 1937.Google Scholar