Refined Second-Order Analysis of Frames with Members under Lateral and Axial Loads
Publication: Journal of Structural Engineering
Volume 122, Issue 5
Abstract
Loads such as those caused by wind, snow, and dead weight act along members in a frame structure. This type of member loads is extremely common in the practical design and analysis of structures. However, most research studies on the second-order and nonlinear analysis of frames idealize all loads as nodal forces and moments. Unlike in a linear analysis, the stress due to the nodal moments and forces in a second-order analysis cannot be simply superimposed on the stress created by the loads along members to obtain the final bending moment and force diagrams, because they affect the nonlinear element stiffness. Without careful consideration of the interactive and nonlinear response of the element with member and nodal loads, the accuracy of a nonlinear analysis for realistic problems is questionable. This paper presents the formulation of a proficient element for the second-order analysis of frames accounting for the nonlinear interaction between the element stiffness, the nodal load, and the member load. The degree of accuracy satisfies the requirement for practical applications, while the simplicity allows the approach to be easily coded in a computer program for the practical analysis of steel frames.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
AlBermani, F. G. A., and Kitipornchai, S.(1990). “Nonlinear analysis of thin-walled structures using least element/member.”J. Struct. Engrg., ASCE, 116(1), 215–234.
2.
AS4100-1990, steel structures. (1990). Standards Assoc. of Australia, Sydney, Australia.
3.
Chan, S. L. (1988). “Geometric and material nonlinear analysis of beam-columns and frames using the minimum residual displacement method.”Int. J. Numer. Methods in Engrg., Vol. 26, 2657–2669.
4.
Chan, S. L., and Zhou, Z. H.(1994). “A pointwise equilibrium polynomial (PEP) element for nonlinear analysis of frames.”J. Struct. Engrg., ASCE, 120(6), 1703–1717.
5.
Chen, W. F., and Lui, E. M. (1987). “Effect of joint flexibility on the behavior of steel frames.”Comp. and Struct., Vol. 26, 719–732.
6.
Connor, J. J., Logcher, R. D., and Chan, S. C.(1968). “Nonlinear analysis of elastic framed structures.”J. Struct. Div., ASCE, 94(6), 1525–1547.
7.
“GMNAF: Geometric and material nonlinear analysis of frames.”User's reference manual, 9303-03, Dept. of Civ. and Struct. Engrg., Hong Kong Polytech. Univ., Hung Hom, Kow Loon, Hong Kong.
8.
Izzuddin, B. A., and Elnashai, A. S.(1993). “Adaptive space frame analysis. Part II: A distributed plasticity approach.”Struct. and Build., J., 99(3), 317–326.
9.
Jennings, A.(1968). “Frame analysis including change of geometry.”J. Struct. Div., ASCE, 94(3), 627–637.
10.
Kondoh, K. and Atluri, S. N. (1986). “A simplified finite element method for large deformation, post-bucking analysis of large frame structures, using explicitly derived tangent stiffness matrices.”Int. J. Numer. Methods in Engrg., Vol. 23, 69–90.
11.
Meek, J. L., and Tan, H. S. (1984). “Geometrially nonlinear analysis of space frames by an incremental iterative technique.”Comp. Methods in Appl. Mech. and Engrg., Vol. 47, 261–282.
12.
Oran, C.(1973). “Tangent stiffness in plane frames.”J. Struct. Div., ASCE, 99(6), 191–212.
13.
Saafan, S. A.(1963). “Nonlinear behaviour of structural plane frames.”J. Struct. Div., ASCE, 89(4), 557–579.
14.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, 2nd Ed., McGraw-Hill Book Co., Inc., New York, N.Y.
15.
Zienkiewics, O. C., and Wood, R. D.(1977). “Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells.”Comp. and Struct., 7(6), 725–735.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 122 • Issue 5 • May 1996
Pages: 548 - 554
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: May 1, 1996
Published in print: May 1996
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.