Buckling of Restrained Columns with Shear Deformation and Axial Shortening
Publication: Journal of Engineering Mechanics
Volume 117, Issue 9
Abstract
There are two well‐known approaches proposed for incorporating shear deformation in the analysis of column buckling. Engesser's approach assumes that the shear component acts perpendicularly to the total slope while Haringx's approach assumes that it acts perpendicularly to the bending slope. It appears that discussions are still going on as to which of the approaches is more accurate. It is doubtful if the problem can be resolved through mechanics, as Reissner had pointed out that the approaches depend on the form of the assumed, one‐dimensional, stress‐strain relations. This paper will use Engesser's approach for the shearflexural buckling analysis of continuously restrained columns. The effect of axial shortening is also considered. A derivation is presented for the total potential energy functional, which forms the basis of the finite element method for solution. A parametric study is carried out to investigate sensitivity to various design parameters.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ang, K. K., and Wang, C. M. (1990). “Shear‐flexural buckling of columns.” J. Engrg. Mech., ASCE, 116(6), 1220–1241.
2.
Bathe, K. J. (1982). Finite element procedures in engineering analysis. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
3.
Cheng, F. Y., and Pantelides, C. P. (1988a). “Dynamic Timoshenko beam‐columns on elastic media.” J. Struct. Engrg., ASCE, 114(7), 1524–1550.
4.
Cheng, F. Y., and Pantelides, C. P. (1988b). “Static Timoshenko beam‐columns on elastic media.” J. Struct. Engrg., ASCE, 114(5), 1152–1172.
5.
Derham, C. J., and Thomas, A. G. (1981). “The design of seismic isolation bearings.” Control of seismic response of piping systems and other structures by base isolation, J. M. Kelly, ed., Univ. of California, Berkeley, Calif., 21–36.
6.
Elsgolc, L. E. (1961). Calculus of variations. Pergamon Press, Oxford, England.
7.
Engesser, F. (1891). “Die knickfestigkeit gerader stabe.” Zentralbl. Bauverwaltung, 11, 483–486 (in German).
8.
Gent, A. N. (1964). “Elastic stability of rubber compression springs.” J. Mech. Engrg. Sci., 6(4), 318–326.
9.
Gjelsvik, A. (1990). “Buckling of built‐up columns with or without stay plates.” J. Engrg. Mech., ASCE, 116(5), 1142–1159.
10.
Haringx, J. A. (1948). “On highly compressible helical springs and robber rods, and their application for vibration‐free mountings, I‐III.” Reports R 94, 101, 109 Philips research reports, Eindhoven, 1–97.
11.
Koh, C. G., and Kelly, J. M. (1989). “Viscoelastic stability model for elastomeric isolation bearings.” J. Struct. Engrg., ASCE, 115(2), 285–302.
12.
Langhaar, H. L. (1962). Energy methods in applied mechanics. John‐Wiley, New York, N.Y.
13.
Lin, F. J., Glauser, E. C., and Johnston, B. G. (1970). “Behavior of laced and battened structural members.” J. Struct. Div., ASCE, 96(7), 1377–1401.
14.
Nanni, J. (1971). “Das Eulersche knickproblem unter berucksichtigung der querkrafte.” Z. Angew. Math. Phys., 22, 156–185 (in German).
15.
Reissner, E. (1982). “Some remarks on the problem of column buckling.” Ingenieur‐Archiv, 52, 115–119.
16.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability. McGraw‐Hill, New York, N.Y.
17.
Wang, C. M., Kitipornchai, S., and Al‐Bermani, F. G. A. (1991). “Buckling of columns: Allowance for axial shortening,” submitted to Int. J. Mech. Sci., in press.
18.
Williams, F. W. (1990). Discussion on “Dynamic Timoshenko beam‐columns on elastic media,” by Journal of Structural Engineering, ASCE, 116(2), 558–561.
19.
Ziegler, H. (1982). “Arguments for and against Engesser's buckling formulas.” Ingenieur‐Archiv, 52, 105–113.
Information & Authors
Information
Published In
Copyright
Copyright © 1991 ASCE.
History
Published online: Sep 1, 1991
Published in print: Sep 1991
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.