Cantilevered and Linearly Tapered Thin‐Walled Members
Publication: Journal of Engineering Mechanics
Volume 116, Issue 4
Abstract
In order to design a new power‐transmission tower built with a cantilevered and tapered thin‐walled steel member instead of the usual angle steel or pipe, the governing equations for a doubly symmetric and linearly tapered thin‐walled member are presented in a general way by means of Hamilton's principle. Closed‐form solutions are indicated for the static problems. Next, the exactness of the proposed elastic solutions is proven using numerical calculations for a cantilevered and linearly tapered thin‐walled member with a circular, octagonal, or rectangular transverse cross section. It is shown that the mechanical behavior of the cantilevered and linearly tapered thin‐walled members is remarkably different from that of the cantilevered thin‐walled member with uniform cross section and that the difference arises even for fairly small tapering angles. The effect of the transverse shear deformation for the current problem is shown to be negligible.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Boley, B. A. (1963). “On the accuracy of the Bernoulli‐Euler theory for beams of variable section.” J. Appl. Mech., 30, 373–378.
2.
Chong, K. P., Swanson, W. D., and Matlock, R. B. (1977). “Shear analysis of tapered beams.” J. Struct. Div., ASCE, 102(9), 1781–1788.
3.
Culver, C. G., and Preg, S. M. (1968). “Elastic stability of tapered beam‐columns.” J. Struct. Div., ASCE, 94(2), 455–470.
4.
Cowper, G. R. (1966). “The shear coefficient in Timoshenko's beam theory.” J. Appl. Mech., 33, 335–340.
5.
Fogel, C. M., and Ketter, R. L. (1962). “Elastic strength of tapered columns.” J. Struct. Div., ASCE, 88(5), 67–106.
6.
Gere, J. M., and Carter, W. O. (1962). “Critical buckling loads for tapered columns.” J. Struct. Div., ASCE, 88(1), 1–11.
7.
Isoda, K., and Oono, U. (eds.) (1971). Handbook of numerical calculation by Fortran (in Japanese). Oome‐sha, Japan, 149.
8.
Johnston, B. G. (1976). Guide to stability design criteria for metal structures, Chap. 11. Tapered structural members, 3rd Ed., John Wiley & Sons, Inc., New York, N.Y., 330–358.
9.
Lee, L. H. N. (1959). “On the lateral buckling of a tapered narrow rectangular beam.” J. Appl. Mech., 26, 457–458.
10.
Lee, G. C., and Szabo, B. A. (1967). “Torsional response of tapered I‐girders.” J. Struct. Div., ASCE, 93(5), 233–252.
11.
Schreyer, H. L. (1978). “Elementary theory for linearly tapered beams.” J. Engrg. Mech. Div., ASCE, 104(3), 515–527.
12.
Takabatake, H., and Matsuoka, O. (1983). “The elastic theory of thin‐walled open cross sections with local deformations.” Int. J. Solids Struct., 19(12), 1065–1088.
13.
Takabatake, H., and Matsuoka, O. (1983). “Experimental studies to restoring force characteristics of cantilevered cylinders.” (in Japanese). J. Struct. Const. Engrg., 353, 62–71.
14.
Takabatake, H. (1986). “Elastic analyses of tapered thin‐walled members.” (in Japanese). J. Struct. Const. Engrg., 364, 68–79.
15.
Takabatake, H., and Matsuoka, O. (1987). “Elastic analyses of circular cylindrical shells by rod theory including distortion of cross section.” Int. J. Solids Struct., 23(6), 797–817.
16.
Verma, M. K., and Murty, A. V. K. (1973). “Non‐linear bending of beams of variable cross‐section.” Int. J. Mech. Sci., 15, 183–187.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 116 • Issue 4 • April 1990
Pages: 733 - 750
Copyright
Copyright © 1990 ASCE.
History
Published online: Apr 1, 1990
Published in print: Apr 1990
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.