Buckling Mode Interaction in Fixed-End Column with Central Brace
Publication: Journal of Engineering Mechanics
Volume 125, Issue 3
Abstract
The postbuckling behavior of an elastic fixed-end column with an elastic brace at the center is investigated. Attention is focused on those of brace stiffness near its threshold value at which, under axial load, the column becomes critical with respect to two buckling modes simultaneously. We show that, for the brace stiffness greater than the threshold value, there are precisely two secondary bifurcation points on each primary postbuckling path bifurcating from one of the least two classical buckling loads, and the corresponding secondary postbuckling paths connect all of these secondary bifurcation points in a loop. For the brace stiffness less than the threshold value, no secondary bifurcation occurs. The asymptotic expansions of the primary and secondary postbuckling paths are constructed. The stability analysis indicates that, when the brace stiffness goes beyond its threshold value, the primary postbuckling path with a node in the center becomes unstable from stable by means of the secondary bifurcation (i.e., secondary buckling occurs).
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bauer, L., Keller, H. B., and Reiss, E. L. ( 1975). “Multiple eigenvalues lead to secondary bifurcation.” SIAM Rev., 17, 101–122.
2.
Bresler, B., and Gilbert, P. H. ( 1961). “Tie requirement for reinforced concrete columns.” ACI J., 58, 559–569.
3.
DeWolf J. T., and Pelliccione, J. F. (1979). “Cross-brace design.”J. Struct. Div., ASCE, 105, 1379–1391.
4.
Golubitsky, M., and Schaeffer, D. G. ( 1985). Singularities and groups in bifurcation theory. Vol. 1, Springer, New York.
5.
Koiter, W. T. ( 1945). “On the stability of elastic equilibrium,” Dissertation, Delft, The Netherlands (English translation: NASA Tech. Trans., F10, 833, 1967).
6.
Mau, S. T. (1989). “Buckling and post-buckling analyses of columns with discrete supports.”J. Engrg. Mech., ASCE, 115, 721–739.
7.
Potier-Ferry, M. ( 1978). “Bifurcation et stabilité pour des systèmes dérivant d'un potentiel.” J. Mécanique, Paris, 17, 579–608.
8.
Shearer, M. ( 1980). “Secondary bifurcation near a double eigenvalue.” SIAM J. Math. Anal., 11, 365–389.
9.
Timoshenko, S. P., and Gere, J. M. ( 1961). Theory of elastic stability, 2nd Ed., McGraw-Hill, New York.
10.
Triantafyllidis, N., and Peek, R. ( 1992). “On stability and the worst imperfection shape in solids with nearly simultaneous eigenmodes.” Int. J. Solids Struct., 29, 2281–2299.
11.
Wu, B. ( 1993). “Secondary buckling of an elastic strut on an elastic foundation under axial compression.” Acta Mechanica Sinica, 25, 443–451 (in Chinese).
12.
Wu, B. ( 1995). “Secondary buckling of an elastic strut under axial compression.” Z. angew. Math. Mech., 75, 741–751.
Information & Authors
Information
Published In
History
Received: May 5, 1997
Published online: Mar 1, 1999
Published in print: Mar 1999
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.