Nonlinear Elastic Behavior of I-Beams Curved in Plan
Publication: Journal of Structural Engineering
Volume 123, Issue 9
Abstract
The vertical deflections perpendicular to the plane of a horizontal beam curved in plan are coupled with its twist rotations, and its axial deflections are coupled with its horizontal radial deflections. Because of the first of these couplings, a horizontally curved beam subjected to vertical loading has both primary bending and torsion actions. In the nonlinear range, second-order couplings between the vertical and horizontal deflections and the twist rotations are developed, and the nonlinear behavior of the curved beam becomes more complicated. This paper studies the linear, neutral, and nonlinear equilibrium of elastic horizontally curved I-beams under vertical loading and develops a curved finite-element model for their analysis. It is found that when the included angle of a curved beam is small, the primary coupling is also small and bending is the major action. In this case, the nonlinear behavior is similar to the elastic flexural-torsional buckling of a straight beam. However, if the included angle of the curved beam is not small, the primary coupling becomes significant and both torsion and bending are major actions. In this case, nonlinear behavior develops very early and is quite different from the flexural-torsional buckling behavior of a straight beam.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Akhtar, M. N.(1987). “Element stiffness of circular member.”J. Struct. Engrg., ASCE, 113(4), 867–872.
2.
Arici, M.(1989). “Reciprocal conjugate method for space curved bars.”J. Struct. Engrg., ASCE, 115(3), 560–575.
3.
Baron, F.(1961). “Matrix analysis of structures curved in space.”J. Struct. Div., ASCE, 87(3), 2779–2788.
4.
Bathe, K., and Bolourchi, S.(1979). “Large displacement analysis of three-dimensional beam structures.”Int. J. Numer. Methods in Engrg., 14(7), 961–986.
5.
Becker, G. (1965). “Ein beitrag zur statischen berechnung beliebig gelagerter ebner gekrümmter stäbe mit einfach symmetrichen dünnwandigen offenen profilen von in stabachse veränderlichem querschnitt unter berücksichtigung der wöbkrafttorsion.”Der Stahlbau, Berlin, Germany, Heft 11, 334–346; Heft 12, 368–377 (in German).
6.
Brookhart, G. C.(1967). “Circular-arc I-type girders.”J. Struct. Div., ASCE, 93(6), 133–159.
7.
Crisfield, M. A.(1981). “A fast incremental/iterative solution procedure that handles snap-through.”Comp. and Struct., 13(1), 55–62.
8.
Dabrowski, R. (1968). Curved thin-walled girders, theory and analysis. Springer-Verlag New York, Inc., New York, N.Y.
9.
El-Amin, F. M., and Brotton, D. M.(1976). “Horizontally curved beam finite element including warping.”Int. J. Numer. Methods in Engrg., 10(6), 1397–1428.
10.
El-Amin, F. M., and Kasem, M. A.(1978). “High order horizontally curved beam finite element including warping for steel bridges.”Int. J. Numer. Methods in Engrg., 12(1), 159–167.
11.
Fukumoto, Y., and Nishida, S.(1981). “Ultimate load behavior of curved I-beams.”J. Engrg. Mech. Div., ASCE, 107(2), 367–385.
12.
Heins, C. P., and Spates, K. R.(1970). “Behaviour of single horizontally curved girder.”J. Struct Div., ASCE, 96(7), 1511–1523.
13.
Hsu, T. T., Fu, C. C., and Schelling, D. R.(1990). “An improved horizontally-curved beam element.”Comp. and Struct., 34(2), 313–318.
14.
Kang, Y. J., and Yoo, C. H.(1993). “Thin-walled curved beams. I: Formulation of nonlinear equations.”J. Engrg. Mech., ASCE, 120(10), 2072–2101.
15.
Krenk, S.(1994). “A general format for curved and non-homogeneous beam element.”Comp. and Struct., 50(4), 449–454.
16.
Liew, J. Y. R., Thevendran, V., Shanmugam, N. E., and Tan, L. O.(1995). “Behaviour and design of horizontally curved steel beams.”J. Constr. Steel Res., 32(1), 37–67.
17.
Love, A. E. H. (1944). A treatise on the mathematical theory of elasticity, 4th Ed., Dover Publications, Inc., New York, N.Y.
18.
Nakai, H., and Yoo, C. H. (1988). Analysis and design of curved steel bridges. McGraw-Hill, Inc., New York, N.Y.
19.
Pantazopoulou, S. J.(1992). “Low-order interpolation functions for curved beams.”J. Engrg. Mech., ASCE, 118(2), 329–350.
20.
Papangelis, J. P., and Trahair, N. S.(1987a). “Flexural-torsional buckling of arches.”J. Struct. Engrg., ASCE, 113(4), 889–906.
21.
Papangelis, J. P., and Trahair, N. S. (1987b). “Finite element analysis of arch lateral buckling.”Civ. Engrg. Trans., Inst. of Engrs., Australia, CE29(1), 34–39, Canberra, Australia.
22.
Pi, Y.-L., and Trahair, N. S.(1994). “Nonlinear inelastic analysis of steel beam-columns. I: Theory.”J. Struct. Engrg., ASCE, 120(7), 2041–2061.
23.
Pi, Y.-L., and Trahair, N. S.(1996a). “Three-dimensional nonlinear analysis of elastic arches.”Engrg. Struct., 18(1), 49–63.
24.
Pi, Y.-L., and Trahair, N. S. (1996b). “Nonlinear elastic behaviour of I-beams curved in plan.”Res. Rep. No. 734, Dept. of Civ. Engrg., University of Sydney, Sydney, Australia.
25.
Pi, Y.-L., Papangelis, J. P., and Trahair, N. S.(1995). “Prebuckling deformations and flexural-torsional buckling of arches.”J. Struct. Engrg., ASCE, 121(9), 1313–1322.
26.
Pippard, A. J. S., and Baker, J. F. (1968). The analysis of engineering structures, 4th Ed., Edward Arnold, Ltd., London, U.K.
27.
Rajasekaran, S., and Padmanabhan, S.(1989). “Equations of curved beams.”J. Engrg. Mech., ASCE, 115(5), 1094–1111.
28.
Saleeb, A. F., and Gendy, A. S.(1991). “Shear-flexible models for spatial buckling of thin-walled curved beams.”Int. J. Numer. Methods in Engrg., 31(4), 729–757.
29.
Sawko, F.(1968). “Computer analysis of grillages curved in plan.”Proc., Int. Assn. for Bridge and Struct. Engrg., 8, 151–170.
30.
Simo, J. C., and Vu-Quoc, L.(1986). “A three-dimensional finite strain rod model. Part II: Computational aspects.”Comp. Methods in Appl. Mech. Engrg., 56(1), 79–116.
31.
Tan, L. O., Thevendran, V., Liew, J. Y. R., and Shanmugam, N. E.(1992). “Analysis and design of I-beams curved in plan.”J. Singapore Struct. Steel Soc., Steel Struct., 3(1), 39–45.
32.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, 2nd Ed., McGraw-Hill, Inc., New York, N.Y.
33.
Trahair, N. S. (1993). Flexural-torsional buckling of structures. E&FN Spon, London, U.K.
34.
Vlasov, V. Z. (1961). Thin-walled elastic beams, 2nd Ed., National Science Foundation, Washington, D.C.
35.
Wagner, H. (1936). “Verdrehung und knicknung von offenen profilen (torsion and buckling of open sections).”NACA Tech. Memo. No. 807, NACA, Washington, D.C. (in German).
36.
Wen, R. K., and Suhendro, B.(1991). “Nonlinear curved-beam element for arch structures.”J. Struct. Engrg., ASCE, 117(11), 3496–3515.
37.
Yang, Y-B., and Kuo, S.-R.(1987). “Effect of curvature on stability of curved beams.”J. Struct. Engrg., ASCE, 113(6), 1185–1202.
38.
Yoo, C. H.(1979). “Matrix formulation of curved girders.”J. Engrg. Mech. Div., ASCE, 105(6), 971–988.
39.
Yoo, C. H.(1982). “Flexural-torsional stability of curved beams.”J. Engrg. Mech. Div., ASCE, 108(6), 1351–1369.
40.
Yoo, C. H., Kang, Y. J., and Davidson, J. S.(1996). “Buckling analysis of curved beams by finite-element discretization.”J. Engrg. Mech., ASCE, 122(8), 762–770.
41.
Yoshida, H., and Maegawa, K.(1983). “Ultimate strength analysis of curved I-beams.”J. Engrg. Mech. Div., ASCE, 109(1), 192–214.
Information & Authors
Information
Published In
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Sep 1, 1997
Published in print: Sep 1997
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.