Thin‐Walled Curved Beams. I: Formulation of Nonlinear Equations
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of Engineering Mechanics
Volume 120, Issue 10
Abstract
An extensive investigation on the buckling and large displacement behavior of thin‐walled circular beams has been conducted theoretically. Equilibrium equations governing the linear, the bifurcation buckling, and the large displacement behavior have been derived using the principle of minimum total potential energy. An explicit and clear approximation of the curvature effect is made in the derivation process. The paper concludes with a series of fundamental nonlinear equations that describe the elastic behavior of thin‐walled curved beams. A companion paper examines closed‐form solutions for arch‐buckling problems based on the formulations presented in this paper and demonstrates the rigor and the validity of the present formulation.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bleich, F. (1962). Buckling strength of metal structures. McGraw‐Hill, New York, N.Y.
2.
Dabrowski, R. (1968). Curved thin‐walled girders, theory and analysis. Cement and Concrete Association, London, England.
3.
Fukumoto, Y., and Nishada, S. (1981). “Ultimate load behavior of curved I‐beam.” J. Engrg. Mech., ASCE, 107(2), 367–385.
4.
Guide specifications for horizontally curved highway bridges, as revised in 1981, 1982, 1984, and 1986. (1980). American Association of State Highway and Transportation Officials, Washington, D.C.
5.
Highway structure design handbook. (1965). Vol. 1, ADUSS, U.S. Steel Corp., Pittsburg, Pa., 88–2222.
6.
Kang, Y. J. (1992). “Nonlinear theory of thin‐walled curved beams and finite element formulation,” PhD thesis, Auburn University, Auburn, Alab.
7.
Kang, Y. J., and Yoo, C. H. (1990). “Flexural stress of curved bridge girders.” Proc. 1990 Annual Tech. Session, Structural Stability Research Council, St. Louis, Mo., Apr.
8.
Kang, Y. J., and Yoo, C. H. (1994). “Thin‐walled curved beams. II: analytical solutions for buckling of arches.” J. Engrg. Mech., ASCE, 120(10), 2102–2125.
9.
Kitipornchai, S., and Chan, S. L. (1990). “Stability and nonlinear finite element analysis of thin‐walled structures.” Finite element applications to thin‐walled structures, J. W. Bull, ed., Elsevier Applied Science, New York, N.Y. 89–130.
10.
Kuo, S. R., and Yang, Y. B. (1991). “New theory on buckling of curved beams.” J. Engrg. Mech., ASCE, 117(8), 1698–1717.
11.
Love, A. E. H. (1927). A treatise on the mathematical theory of elasticity. 4th Ed., Dover, New York, N.Y.
12.
McManus, P. F., Nasir, G. A., and Culver, C. G. (1969). “Horizontally curved girders—state of the art.” J. Struct. Div., ASCE, 95(5), 853–870.
13.
Morris, D. L. (1968). “Curved beam stiffness coefficients.” J. Struct. Div., ASCE, 94(5), 1164–1174.
14.
Nakai, H., and Yoo, C. H. (1988). Analysis and design of curved steel bridges, McGraw‐Hill, New York, N.Y.
15.
Palani, G. S., and Rajasekaran, S. (1992). “Finite element analysis of thin‐walled curved beams made of composites.” J. Struct. Engrg., ASCE, 118(8), 2039–2062.
16.
Papangelis, T. P., and Trahair, N. S. (1987a). “Flexural‐torsional buckling of arches.” J. Struct. Engrg., ASCE, 113(4), 889–906.
17.
Papangelis, T. P., and Trahair, N. S. (1987b). “Flexural‐torsional buckling tests on arches.” J. Struct. Engrg., ASCE, 113(7), 1433–1443.
18.
Rajasekaran, S., and Padmanabhan, S. (1989). “Equations of curved beams.” J. Engrg. Mech., ASCE, 115(5), 1094–1111.
19.
Rajasekaran, S., and Ramm, E. (1984). “Discussion of ‘Flexural‐torsional stability of curved beams.’ by C. H. Yoo.” J. Engrg. Mech., ASCE, 110(1), 144–148.
20.
Rasjasekaran, S., Sundararajan, T., and Rao, K. S. (1988). “Discussion of ‘Static stability of curved thin‐walled beams.’ by Y. B. Yang and S. R. Kuo.” J. Engrg. Mech., ASCE, 114(5), 915–918.
21.
Suros, O., and Chu, H. Y. (1991). “Reducing airport congestion.” Mod. Steel Constr., June, 21–25.
22.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, 2d Ed., McGraw‐Hill, New York, N.Y.
23.
Usami, T., and Koh, S. Y. (1980). “Large displacement theory of thin‐walled curved members and its application to lateral‐torsional buckling analysis of circular arches.” J. Solids Struct., 16, 71–95.
24.
Vlasov, V. Z. (1961). Thin walled elastic beams. 2d Ed., National Science Foundation, Washington, D.C.
25.
Washizu, K. (1975). Variational methods in elasticity and plasticity. 2d Ed., Pergamon Press, New York, N.Y.
26.
Yang, Y. B., and Kuo, S. R. (1986). “Static stability of curved thin‐walled beams.” J. Engrg. Mech., ASCE, 112(8), 821–841.
27.
Yang, Y. B., and Kuo, S. R. (1987). “Effect of curvature on stability of curved beams.” J. Struct. Engrg., ASCE, 113(6), 1185–1202.
28.
Yang, Y. B., Kuo, S. R., and Cherng, Y. D. (1989). “Curved beam element for nonlinear analysis.” J. Engrg. Mech., ASCE, 115(4), 840–855.
29.
Yang, Y. B., Kuo, S. R., and Yau, J. D. (1991). “Use of straight‐beam approach to study buckling of curved beams.” J. Struct. Engrg., ASCE, 117(7), 1963–1978.
30.
Yoo, C. H. (1979). “Matrix formulation of curved girders.” J. Engrg. Mech. Div., ASCE, 105(6), 971–988.
31.
Yoo, C. H. (1982). “Flexural‐torsional stability of curved beams.” J. Engrg. Mech. Div., ASCE, 108(6), 1351–1369.
32.
Yoo, C. H., and Pfeiffer, P. A. (1983). “Elastic stability of curved members.” J. Struct. Engrg., ASCE, 109(12), 2922–2940.
33.
Yoo, C. H., and Pfeiffer, P. A. (1984). “Buckling of curved beams with in‐plane deformation.” J. Struct. Engrg., ASCE, 100(2), 291–300.
34.
Yoshida, H., and Imoto, Y. (1973). “Inelastic lateral buckling of restrained beams.” J. Engrg. Mech. Div., ASCE, 99(2), 343–336.
35.
Yoshida, H., and Maegawa, K. (1983). “Ultimate strength analysis of curved I‐beams.” J. Engrg. Mech., ASCE, 109(1), 192–214.
36.
Yoshida, H., and Maegawa, K. (1984). “Lateral instability of I‐beams with imperfections.” J. Struct. Engrg., ASCE, 110(8), 1875–1892.
Information & Authors
Information
Published In
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Feb 25, 1993
Published online: Oct 1, 1994
Published in print: Oct 1994
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.