Buckling of Variable Section Columns under Axial Loading
Publication: Journal of Engineering Mechanics
Volume 136, Issue 4
Abstract
In this paper, the static stability of the variable cross section columns, subjected to distributed axial force, is considered. The presented solution is based on the singular perturbation method of Wentzel-Kramers-Brillouin and the column is modeled using Euler-Bernoulli beam theory. Closed-form solutions are obtained for calculation of buckling loads and the corresponding mode shapes. The obtained results are compared with the results in the literature to verify the present approach. Using numerous examples, it is shown that the represented solution has a very good convergence and accuracy for determination of the instability condition.
Get full access to this article
View all available purchase options and get full access to this article.
References
Au, F. T. K., Zheng, D. Y., and Cheung, Y. K. (1999). “Vibration and stability of non-uniform beams with abrupt changes of cross-section by using modified beam vibration functions.” Appl. Math. Model., 23, 19–34.
Eisenberger, M. (1991). “Buckling loads for variable cross-section members with variable axial forces.” Int. J. Solids Struct., 27(2), 135–143.
Eisenberger, M., and Reich, Y. (1989). “Static, vibration and stability analysis of non-uniform beams.” Comput. Struct., 31(4), 567–573.
Elfelsoufi, Z., and Azrar, L. (2005). “Buckling, flutter and vibration analyses of beams by integral equation formulations.” Comput. Struct., 83, 2632–2649.
Elishakoff, I. (1999). “New closed-form solutions for buckling of a variable stiffness column by MATHEMATICA.” J. Sound Vib., 224(1), 172–182.
Ermopoulos, J. Ch. (1997). “Equivalent buckling length of non-uniform members.” Constructional Steel Research, 42(2), 141–158.
Frisch-Fay, R. (1966). “On the stability of a strut under uniformly distributed axial forces.” Int. J. Solids Struct., 2, 361–369.
Iremonger, M. J. (1980). “Finite difference buckling analysis of non-uniform columns.” Comput. Struct., 12, 741–748.
Karabalis, D. L., and Beskos, D. E. (1983). “Static, dynamic and stability analysis of structures composed of tapered beams.” Comput. Struct., 16(6), 731–748.
Lee, B. K., Carr, A. J., Lee, T. E., and Kim, I. J. (2006). “Buckling loads of columns with constant volume.” J. Sound Vib., 294, 381–387.
O’Rourke, M., and Zebrowski, T. (1977). “Buckling load for non-uniform columns.” Comput. Struct., 7, 717–720.
Rahai, A. R., and Kazemi, S. (2008). “Buckling analysis of non-prismatic columns based on modified vibration modes.” Commun. Nonlinear Sci. Numer. Simul., 13(8), 1721–1735.
Smith, W. G. (1988). “Analytic solutions for tapered column buckling.” Comput. Struct., 28(5), 677–681.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, 2nd Ed., McGraw-Hill, New York.
Totry, E. M., Altus, E., and Proskura, A. (2007). “Buckling of non-uniform beams by a direct functional perturbation method.” Probab. Eng. Mech., 22, 88–99.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 136 • Issue 4 • April 2010
Pages: 472 - 476
Copyright
© 2010 ASCE.
History
Received: Oct 7, 2008
Accepted: Sep 26, 2009
Published online: Mar 15, 2010
Published in print: Apr 2010
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.