Optimal Designs of I‐Beams against Lateral Buckling
Publication: Journal of Engineering Mechanics
Volume 116, Issue 9
Abstract
This paper concerns the optimal distribution of a given volume of material in I‐beams so as to maximize the elastic flexural‐torsional buckling capacities. The material distribution has been restricted to different top‐to‐bottom flange‐width ratios, linear tapering of flange width, or linear tapering of web depth. Based on the Rayleigh‐Timoshenko energy method, a canonical form of the Ray‐leigh quotient is derived for the three types of design considered. For the maximum buckling capacity, the quotient is first minimized with respect to the displacement function and then maximized with respect to the design parameter. To avoid inelastic behavior and a small cross‐sectional area in the optimal beam designs, a maximum permissible normal‐stress constraint is imposed. Optimal designs of simply supported I‐beams under general moment gradient are presented. A comparison study is made to determine which of the three design types is the most effective way of distributing material for maximum buckling capacities.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anderson, J. M., and Trahair, N. S. (1972). “Stability of monosymmetric beams and cantilevers.” J. Struct. Div., ASCE, 98(1), 269–285.
2.
Bradford, M. A. (1988). “Elastic buckling of tapered monosymmetric I‐beams.” J. Struct. Engrg., ASCE, 114(5), 977–996.
3.
Elizarov, A. F. (1968). “On the problem of design of minimal weight structures.” Trudy Tomsk. Inzh Stroit Inst., Vol. 14, pp. 7–20.
4.
Gopak, K. N. (1970). “Optimal beam under a lateral stability constraint.” Gidroaeromekhanika i Teoria Uprugosti, 11, 113–120 (in Russian).
5.
Kitipomchai, S. V., and Trahair, N. S. (1972). “Elastic stability of tapered I‐beams.” J. Struct. Div., ASCE, 98(3), 713–728.
6.
Kitipomchai, S., Wang, C. M., and Trahair, N. S. (1986). “Buckling of monosymmetric I‐beams under moment gradient.” J. Struct. Engrg., ASCE, 113(6), 1391–1395.
7.
Popelar, C. H. (1976). “Optimal design of beams against buckling: A potential energy approach.” J. Struct. Mech., 4(2), 181–196.
8.
Popelar, C. H. (1977). “Optimal design of structures against buckling: A complementary energy approach.” J. Struct. Mech., 5(1), 45–66.
9.
Reklaitis, G. V., Ravindran, A., and Ragsdell, K. M. (1983). Engineering optimization methods and applications. Wiley‐Interscience, New York, N.Y.
10.
Roberts, T. M., and Burt, C. A. (1985). “Instability of monosymmetric I‐beams and cantilevers.” Int. J. Mech. Sci., 27(5), 313–324.
11.
Sofronov, Y. D. (1974). “Minimum weight design of beams with respect to lateral buckling.” Trudy Kazanskogo Avyatsyonnogo Instituta, Vol. 168, pp. 34–43 (in Russian).
12.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability. McGraw‐Hill Book Co., Inc., New York, N.Y.
13.
Timoshenko, S. P., and Goodier, J. N. (1970). Theory of elasticity, 3rd Ed., McGraw‐Hill Book Co., Inc., New York, N.Y.
14.
Wang, C. M., et al. (1986). “Optimal design of tapered beams for maximum buckling strength.” Engrg. Struct., Vol. 8(4), 276–284.
15.
Zyczkowski, M., and Gajewski, A. (1983). “Optimal structural design under stability constraints.” Collapse, J. M. T. Thompson and G. W. Hunt, eds., Cambridge University Press, Cambridge, England, 299–332.
Information & Authors
Information
Published In
Copyright
Copyright © 1990 ASCE.
History
Published online: Sep 1, 1990
Published in print: Sep 1990
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.