Nonlinear EI Equation for Slender Composite Columns Bending about the Minor Axis
Publication: Journal of Structural Engineering
Volume 132, Issue 10
Abstract
The moment magnifier method was introduced into design practice to eliminate the need for extensive calculations, based on the solution to a differential equation, for the second-order moments in slender columns. This method is strongly influenced by the effective flexural stiffness , which varies due to the nonlinearity of the concrete stress–strain curve and the cracking along the column length among other factors. The equations given in the ACI building code are approximate when compared to the EI values computed from the axial load–bending moment–curvature relationships. This study was undertaken to determine the influence of a full range of variables on used for the design of slender, tied, composite columns in which the bending moment was applied about the minor axis of the steel shape encased in concrete, and also to examine the existing ACI equations. Approximately 12,000 isolated square composite columns, each with a different combination of specified properties of variables, were simulated and used to generate the stiffness data. The columns studied were subjected to short-term ultimate loads and equal and opposite end moments causing symmetrical single curvature bending. A new nonlinear equation for was then developed for use in design of slender composite columns subjected to minor axis bending and is proposed as an alternative to the existing ACI equations.
Get full access to this article
View all available purchase options and get full access to this article.
References
ACI Committee 318. (2002). Building code requirements for structural concrete (ACI 318–02) and Commentary (ACI 318R-02), American Concrete Institute, Farmington Hills, Mich.
Anslijn, R., and Janss, J. (1974). “Le calcul des charges ultimes des colonnes métalliques enrobées de béton.” Rapport MT 89, C. R. I. F., Bruxelles, Belgium.
Bondale, S. (1966a). “Column theory with special reference to composite columns.” The Consulting Engineer, July, 72–77.
Bondale, S. (1966b). “Column theory with special reference to composite columns.” The Consulting Engineer, August, 43–48.
Bondale, S. (1966c). “Column theory with special reference to composite columns.” The Consulting Engineer, September, 68–70.
Chen, W. F., and Lui, E. M. (1987). Structural stability—Theory and implementation, Elsevier Science, New York.
Galambos, T. V. (1963). “Inelastic lateral buckling of beams.” J. Struct. Div., 89(5), 217–242.
Johnson, R. P., and May, I. M. (1978). “Tests on restrained composite columns.” Struct. Eng., 56B(2), 21–27.
MacGregor, J. G. (1976). “Safety and limit states design for reinforced concrete.” Can. J. Civ. Eng., 3(4), 484–513.
MacGregor, J. G., Breen, J. B., and Pfrang, E. O. (1970). “Design of slender concrete columns.” ACI J., 67(1), 6–28.
Mirza, S. A. (1989). “Parametric study of composite column strength variability.” J. Constr. Steel Res., 14, 121–137.
Mirza, S. A. (1990). “Flexural stiffness of rectangular reinforced concrete columns.” ACI Struct. J., 87(4), 425–435.
Mirza, S. A., Lee, P. M., and Morgan, D. L. (1987). “ACI stability resistance factor for reinforced concrete columns.” J. Struct. Eng., 113(9), 1963–1976.
Mirza, S. A., and MacGregor, J. G. (1982). “Probabilistic study of strength of reinforced concrete members.” Can. J. Civ. Eng., 9(3), 431–448.
Mirza, S. A., and Skrabek, B. W. (1991). “Reliability of short composite beam–column strength interaction.” J. Struct. Eng., 117(8), 2320–2239.
Mirza, S. A., and Skrabek, B. W. (1992). “Statistical analysis of slender composite beam-column strength.” J. Struct. Eng., 118(5), 1312–1332.
Mirza, S. A., and Tikka, T. K. (1999a). “Flexural stiffness of composite columns subjected to major axis bending.” ACI Struct. J., 96(1)19–28.
Mirza, S. A., and Tikka T. K. (1999b). “Flexural stiffness of composite columns subjected to bending about the minor axis of structural steel section core.” ACI Struct. J., 96(5), 748–756.
Morino, S., Matsui, C., and Watanabe, H. (1985). “Strength of biaxially loaded SRC columns.” Proc., Composite and Mixed Construction, ASCE, Reston, Va., 185–194.
Newmark, N. M. (1943). “Numerical procedure for computing deflections, moments, and buckling loads.” Trans. Am. Soc. Civ. Eng., 108, 1161–1234.
Park, R., Priestly, M. J. N., and Gill, W. D. (1982). “Ductility of square-confined concrete columns.” J. Struct. Div., 108(4), 929–950.
Procter, A. N. (1967). “Full size tests facilitate derivation of reliable design methods.” The Consulting Engineer, 31(8), 54–60.
Roderick, J. W., and Loke, Y. O. (1974). “Pin-ended composite columns bent about the minor axis.” Rep. R-254 Civil Engineering Labs, Sydney Univ., Sydney, Australia.
Roik, K., and Mangerig, I. (1987). “Experimentelle Untersuchungen der Tragfähigkeit von einbetonierten Stahlprofilstützen unter besonderer Berücksichtigung des Langzeit Verhaltens von Beton.” Bericht zu P102, Studiengesellschaft für Anwendungstechnik von Eisen und Stahl e. V., Düsseldorf, Germany.
Roik, K. H., and Schwalbenhofer K., (1988). “Experimentelle Untersuchungen zum plastischen Verhalten von Verbundstützen.” Bericht zu P125, Studiengesellschaft für Anwendungstechnik von Eisen und Stahl e. V., Düsseldorf, Germany.
Suzuki, T., Takiguchi, K., Ichinose, T., and Okamoto, T. (1984). “Effects of Hoop Reinforcement in Steel and Reinforced Concrete Composite Sections.” Proc., 3rd South Pacific Regional Conference on Earthquake Engineering, Wellington, New Zealand, 198–214.
Tikka, T. K., and Mirza, S. A. (2005). “Nonlinear EI equation for slender reinforced concrete columns.” ACI Struct. J., 102(6), 839–848.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of Elastic Stability, 2nd Ed., McGraw-Hill, New York.
Young, B. W., (1971). “Residual stresses in hot rolled sections.” Rep. CUED/C-Struct/TR.8, Dept. of Engineering, Univ. of Cambridge, London.
Information & Authors
Information
Published In
Copyright
© 2006 ASCE.
History
Received: Jul 27, 2005
Accepted: Oct 17, 2005
Published online: Oct 1, 2006
Published in print: Oct 2006
Notes
Note. Associate Editor: Enrico Spacone
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.