Elastic Stability of Curved Members
Publication: Journal of Structural Engineering
Volume 109, Issue 12
Abstract
A general solution method of a system of coupled differential equations governing the elastic buckling of thin‐walled curved members is presented. The finite element displacement method is formulated based on a variational principle. The stiffness and stability properties of the finite elements are consistent and are obtained within the bounds of linearized displacement theories. Included are the warping contributions to the buckling loads and the effects of antisymmetry of the cross section which were found to be significant. Examination of a convergence test indicated an extremely fast converging upper bound solutions as expected due to the utilization of the variational procedure. Critical loads were obtained using a computer program (CVSTB) developed for a few combinations of loading and boundary conditions and design charts were prepared. Comparative studies were made with a few existing solutions and possible sources of discrepancies were traced.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bleich, F., Buckling Strength of Metal Structures, McGraw‐Hill Book Co., New York, N.Y., 1964.
2.
Chaudhuri, S. K., and Shore, S., “Dynamic Analysis of Horizontally Curved I‐Girder Bridges,” Journal of the Structural Division, ASCE, Vol. 103, No. ST8, Proc. Paper 13121, Aug., 1977, pp. 1589–1604.
3.
Cheney, J. A., “Bending and Buckling of Thin‐Walled Open‐Section Rings,” Journal of the Engineering Mechanics Division, ASCE, Vol. 89, No. EM5, Oct., 1963, pp. 17–44.
4.
Culver, C. G., “Instability of Horizontally Curved Members,” Research report submitted to Commonwealth of Pennsylvania, Department of Highways, 1971.
5.
Dabrowski, R., “Equations of Bending and Torsion of Curved Thin‐Walled Bars with Asymmetric Cross Section,” Archiwum Mechaniki Stosowanej, Vol. 12, No. 5–6, 1960, pp. 789–799.
6.
Engel, S., “Structural Analysis of Circular Curved Beams,” Journal of the Structural Division, ASCE, Vol. 93, No. ST1, Proc. Paper 5099, Feb., 1967, pp. 221–234.
7.
Fehrenbach, J. P., “Natural Frequencies of Horizontally Curved Beams,” thesis presented to Marquette University, at Milwaukee, Wisc., in 1979, in partial fulfillment of the requirements for the Degree of Master of Science.
8.
Goldberg, J. E., and Bogdanoff, J. L., “Out‐of‐Plane Buckling of I‐Section Rings,” International Association of Bridge and Structural Engineer, Vol. 22, 1962, pp. 73–92.
9.
Gupta, K. K., “Engenproblem Solution by a Combined Strum Sequence and Inverse Iteration Technique,” International Journal of Numerical Methods in Engineering, Vol. 7, 1973, pp. 17–42.
10.
Krajcinovic, D., “A Consistent Discrete Elements Technique for Thin‐Walled Assemblages,” International Journal of Solids and Structures, Vol. 5, 1969, pp. 639–662.
11.
Lavelle, F. H., “Analysis of Curved Steel Girder Bridges,” Engineering Journal, AISC, Vol. 3, No. 3, July, 1966.
12.
McManus, P. F., Nasir, G. A., and Culver, C. G., “Horizontally Curved Girders—State of the Art,” Journal of the Structural Division, ASCE, Vol. 95, No. ST5, Proc. Paper 6546, May, 1969, pp. 853–870.
13.
Ojalvo, M., Demuts, E., and Tokarz, F., “Out‐Of‐Plane Buckling of Curved Members,” Journal of the Structural Division, ASCE, Vol. 95, No. ST10, Oct., 1969, pp. 2305–2316.
14.
Pfeiffer, P. A., “Elastic Stability of Curved Beams,” thesis presented to Marquette University, at Milwaukee, Wis., in 1979, in partial fulfillment of the requirements for the Degree of Master of Science.
15.
Reddy, M. N., and Tuma, J. J., “Analysis of Laterally Loaded Continuous Curved Beams,” Journal of the Structural Division, ASCE, Vol. 93, No. ST1, Proc. Paper 5118, Feb., 1967, pp. 495–513.
16.
Saint‐Venant, B., “Memoire sur le calcul de la resistant et de la flexion des pieces solides a simple on a double courbure, en prenant simultanement en consideration les divers efforts auxquels eiles peuvent entre soumises dans tous les sens,” Comptes‐Rendus l'Academie des Sciences de Paris, Vol. XVII, 1843, pp. 942 and 1020–1031.
17.
Schulz, M., and Chedraui, M., “Tables for Circularly Curved Horizontal Beams with Symmetric Uniform Load,” Journal of American Concrete Institute, Vol. 53, No. 53–58, May, 1957, pp. 1033–1040.
18.
Simitses, G. L., An Introduction to the Elastic Stability of Structures, Prentice‐Hall, Englewood Cliffs, N.J., 1976.
19.
Timoshenko, S., and Gere, J. M., Theory of Elastic Stability, 2nd Edition, McGraw‐Hill, New York, N.Y., 1961.
20.
Vacharajittiphan, P., and Trahair, N. S., “Flexural‐Torsional Buckling of Curved Members,” Journal of the Structural Division, ASCE, Vol. 101, No. ST6, Proc. Paper 11350, June, 1975, pp. 1223–1238.
21.
Vlasov, V. Z., Thin‐Walled Elastic Beams, 2nd Edition, National Science Foundation, Washington, D.C., 1961.
22.
Yoo, C. H., “Bioment Contribution to Stability of Thin‐Walled Assemblages,” Computers & Structures, Vol. 11, No. 5, May, 1980, pp. 465–471.
23.
Yoo, C. H., “Matrix Formulation of Curved Girders,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM6, Proc. Paper 15078, Dec., 1979, pp. 971–988.
24.
Yoo, C. H., and Fhrenbach, J. P., “Natural Frequencies of Curved Girders,” Journal of the Engineering Mechanics Division, ASCE, Vol. 107, No. EM2, Apr., 1981, pp. 339–354.
25.
Yoo, C. H., and Heins, C. P., “Plastic Collapse of Horizontally Curved Bridge Girders,” Journal of the Structural Division, ASCE, Vol. 98, No. ST4, Proc. Paper 8848, Apr., 1972, pp. 889–914.
26.
Yoo, C., “Flexural‐Torsional Stability of Curved Beams,” Journal of the Engineering Mechanics Division, ASCE, Vol. 108, No. EM6, Dec., 1982, pp. 1351–1369.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 109 • Issue 12 • December 1983
Pages: 2922 - 2940
Copyright
Copyright © 1983 ASCE.
History
Published online: Dec 1, 1983
Published in print: Dec 1983
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.