In-Plane Elastic Stability of Arches under a Central Concentrated Load
Publication: Journal of Engineering Mechanics
Volume 128, Issue 7
Abstract
This paper is concerned with the in-plane elastic stability of arches with a symmetric cross section and subjected to a central concentrated load. The classical methods of predicting elastic buckling loads consider bifurcation from a prebuckling equilibrium path to an orthogonal buckling path. The prebuckling equilibrium path of an arch involves both axial and transverse deformations and so the arch is subjected to both axial compression and bending in the prebuckling stage. In addition, the prebuckling behavior of an arch may become nonlinear. The bending and nonlinearity are not considered in prebuckling analysis of classical methods. A virtual work formulation is used to establish both the nonlinear equilibrium conditions and the buckling equilibrium equations for shallow arches. Analytical solutions for antisymmetric bifurcation buckling and symmetric snap-through buckling loads of shallow arches subjected to this loading regime are obtained. Approximations for the symmetric buckling load of shallow arches and nonshallow fixed arches and for the antisymmetric buckling load of nonshallow pin-ended arches, and criteria that delineate shallow and nonshallow arches are proposed. Comparisons with finite element results demonstrate that the solutions and approximations are accurate. It is found that the existence of antisymmetric bifurcation buckling loads is not a sufficient condition for antisymmetric bifurcation buckling to take place.
Get full access to this article
View all available purchase options and get full access to this article.
Reference
ABAQUS Standard User’s Manual version 5.8. (1998). Hibbit, Karlsson and Sorensen Inc., Abaqus, Pawtucket, R.I.
Bradford, M. A., Uy, B., and Pi, Y.-L. (2000). “In-plane stability of arches under a central concentrated load.” UNICIV Rep. No. 396, the School of Civil and Environmental Engineering, Univ. of New South Wales, Sydney, Australia.
Calhoun, P. R., and DaDeppo, D. A.(1983). “Nonlinear finite element analysis of clamped arches.” J. Struct. Eng., 109(3), 599–612.
Column Research Committee of Japan, ed. (1971). Handbook of structural stability, Tokyo.
Dickie, J. F., and Broughton, P.(1971). “Stability criteria for shallow arches.” J. Eng. Mech. Div., 97(EM3), 951–965.
Elias, Z. M., and Chen, K. L.(1988). “Nonlinear shallow curved-beam finite element.” J. Eng. Mech., 114(6), 1076–1087.
Galambas, T. V., ed. (1988). Guide to stability design criteria for metal structures, 4th Ed., Wiley, New York.
Gjelsvik, A., and Bodner, S. R.(1962). “Energy criterion and snap-through buckling of arches.” J. Eng. Mech. Div., 88(EM5), 87–134.
Johnston, B. G., ed. (1976). Guide to stability design criteria for metal structures, 3rd Ed., Wiley, New York.
Kang, Y. J., and Yoo, C. H.(1994). “Thin-walled curved beams. II: Analytical solutions for buckling of arches.” J. Eng. Mech., 120(10), 2102–2125.
Noor, A. K., and Peters, J. M.(1981). “Mixed model and reduced/selective integration displacement model for nonlinear analysis of curved beams.” Int. J. Numer. Methods Eng., 17(4), 615–631.
Papangelis, J. P., Hancock, G. J., and Trahair, N. S. (1998). PRFSA, version 3.0. Centre for Advanced Structural Engineering, Univ. of Sydney, Sydney, Australia.
Pi, Y.-L., and Bradford, M. A.(2002). “In-plane stability of arches.” Int. J. Solids Struct., 39(1), 105–125.
Pi, Y.-L., and Trahair, N. S.(1998). “Non-linear buckling and postbuckling of elastic arches.” Eng. Struct., 20(7), 571–579.
Rajasekaran, S., and Padmanabhan, S.(1989). “Equations of curved beams.” J. Eng. Mech., 115(5), 1094–1111.
Schreyer, H. L., and Masur, E. F.(1966). “Bucklnig of shallow arches.” J. Eng. Mech. Div., 92(EM4), 1–17.
Simitses, G. J. (1976). An introduction to the elastic stability of structures, Prentice-Hall, Englewood Cliffs, N.J.
Stolarski, H., and Belytschko, T.(1982). “Membrane locking and reduced integration for curved elements.” ASME Trans. J. Appl. Mech., 49(1), 172–176.
Timoshenko, S., and Gere, J. M. (1961). Theory of elastic stability, McGraw-Hill, New York.
Trahair, N. S., and Bradford, M. A. (1998). The behavior and design of steel structures to AS4100, 3rd Ed., Australian, E&FN Spon, London.
Vlasov, V. Z. (1961). Thin-walled elastic beams, 2nd Ed., Israel Program for Scientific Translation, Jerusalem, Israel.
Wen, R. K., and Suhendro, B.(1991). “Nonlinear curved-beam element for arch structures.” J. Struct. Eng., 117(11), 3496–3515.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 128 • Issue 7 • July 2002
Pages: 710 - 719
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Dec 13, 2000
Accepted: Sep 18, 2001
Published online: Jun 14, 2002
Published in print: Jul 2002
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.