Lateral Postbuckling Analysis of Beam Columns
Publication: Journal of Engineering Mechanics
Volume 120, Issue 4
Abstract
The elastic lateral postbuckling response of geometrically perfect beams, under simultaneously uniform bending and axial compression, is examined in the vicinity of the critical bifurcational state. The field equations, which include the warping effect of the cross section, are highly nonlinear due to the nonlinear bending‐moment‐curvature relationship. The stability of the critical state associated with a stable bifurcation point is analytically established using a comprehensive approach. Therefore, these beam columns are not sensitive to initial imperfections, exhibiting postbuckling strength. However, the postbuckling equilibrium path is quite shallow (becoming more shallow with the increase of the axial force), so the load‐carrying capacity of such beam columns above the critical state is rather limited. The analysis is supplemented by illustrative examples for I‐beam columns for which the effect of various parameters on the initial postbuckling path is also discussed.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bradford, M., Cuk, P., Gizejowski, M., and Trahair, N. (1987). “Inelastic lateral buckling of beam‐columns.” J. Struct. Engrg., ASCE, 113(11), 2259–2277.
2.
Cheng, J., Yura, J., and Johnson, P. (1988). “Lateral buckling of coped steel beams.” J. Struct. Engrg., ASCE, 114(1), 1–15.
3.
Dym, C. L., and Shames, J. N. (1973). Solid mechanics: A variational approach. McGraw‐Hill, New York, N.Y., 489.
4.
Hjelmstad, K., and Lee, S. (1989). “Lateral buckling of beams in eccentrically braced frames.” J. Constr. Steel Res., 14(4), 251–272.
5.
Koiter, W. T. (1945). “On the stability of elastic equilibrium,” PhD dissertation, Polytechnic Institute of Delft, at Delft, The Netherlands (in Dutch).
6.
Kounadis, A. N. (1988). “Efficiency and accuracy of linearized post‐buckling analyses of frames based on elastica.” Int. J. Solids and Struct., 24(11), 1097–1112.
7.
Kounadis, A. N. (1989). “An efficient and simple approximate technique for solving nonlinear initial‐value problems.” Proc., Academy of Athens, Athens, Greece, 64, 237–252.
8.
Kounadis, A. N. (1992). “An efficient and simple approximate technique for solving nonlinear initial and boundary‐value problems.” Comput. Mech., 9, 221–231.
9.
Kounadis, A. N., and Mallis, J. (1987). “Two efficient approaches for the elastica problem of nonlinear elastic bars.” J. Engrg. Mech., ASCE, 113(5), 766–799.
10.
Kounadis, A. N., and Mallis, J. (1988a). “Dynamic stability of initially crooked columns under a time‐dependent axial displacement of their support.” J. Mech. and Appl. Math., 44(4), 579–596.
11.
Kounadis, A. N., and Mallis, J. (1988b). “An efficient approximate technique for large‐deflection analysis of circular plates.” J. Industrial Math. Soc., 38, 49–69.
12.
Kounadis, A. N., and Mallis, J. (1989). “On the accuracy of various large axial displacement formulae for crooked columns.” Comput. Mech., 4, 47–58.
13.
Milisavlijevic, B. M. (1988). “Lateral buckling of a cantilever beam with imperfections.” Acta Mechanica, 74, 123–137.
14.
Nakashima, M., Nakamura, T., and Wakabayashi, M. (1983). “Post‐buckling instability of steel beam‐columns.” J. Struct. Engrg., ASCE, 109, 1414–1430.
15.
Ojalvo, I., and Newman, M. (1968). “Buckling of naturally curved and twisted beams.” J. Engrg. Mech. Div., ASCE, 94(5), 1067–1087.
16.
Simitses, G. J., and Kounadis, A. N. (1978). “Buckling of imperfect rigid jointed frames.” J. Engrg. Mech. Div., ASCE, 104(5), 569–586.
17.
Soltis, L., and Christiano, P. (1972). “Finite deformation of biaxially loaded columns.” J. Struct. Div., ASCE, 98(12), 2647–2662.
18.
Takabatake, H. (1988). “Lateral buckling of I‐beams with web stiffeners and batten plates.” Int. J. Solids and Struct., 24(10), 1003–1020.
19.
Thomson, G. M. T., and Hunt, G. V. (1973). General theory of elastic stability. John Wiley & Sons, London, England, 28.
20.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability. McGraw‐Hill, New York, N.Y.
21.
Trahair, N. S. (1977). The behavior and design of steel structures. Chapman and Hall, London, England.
22.
Wang, Y., El‐khentas, M., and Nethercot, D. (1987). “Lateral‐torsional buckling of end‐restrained beams.” J. Constr. Steel Res., 7(5), 335–362.
23.
Yang, Y., and Yau, I. (1987). “Stability of beams with tapered I sections.” J. Engrg. Mech., ASCE, 113(9), 1337–1357.
Information & Authors
Information
Published In
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Dec 16, 1991
Published online: Apr 1, 1994
Published in print: Apr 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.