Nonlinear Finite Element Analysis of Angle and Tee Beam‐Columns
Publication: Journal of Structural Engineering
Volume 113, Issue 4
Abstract
Asymmetric thin‐walled open sections such as angles are used widely in trusses and transmission towers. Such members have relatively low torsional and bending stiffnesses and are connected eccentrically. The geometrical nonlinear second order analysis of frames comprising this type of member is not generally available. This paper derives the element geometric stiffness matrix for angle and tee beam‐columns. The total potential energy of a general thin‐walled beam‐column element is formulated, incorporating member geometrical nonlinearity. The validity and accuracy of the formulation are demonstrated on different problems, for which the buckling loads and the load‐deformation relationships are derived. The latter is obtained by formulating the incremental and the total force‐deformation equilibrium equations and using the numerical arc‐length method to trace the load‐deformation path. The influence of the prebuckling deformations is incorporated in the analysis by modifying the structural tangent stiffness continuously for geometry updates.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Akay, H. U., Johnson, C. P., and Will, K. M., “Lateral and Local Buckling of Beams and Frames,” Journal of the Structural Division, ASCE, Vol. 103, No. ST9, Sept., 1977, pp. 1821–1832.
2.
Attard, M., Somervaille, I. J., and Kabiala, A. P., “Stability Theory and Analysis of Thin‐Walled Open Beams,” Uniciv Report No. R‐200, The University of New South Wales, Sydney, Australia, 1981.
3.
Barsoum, R. S., and Gallagher, R. H., “Finite Element Analysis of Torsional and Torsional‐Flexural Stability Problem,” International Journal of Numerical Method in Engineering, Vol. 2, 1970, pp. 335–352.
4.
Bathe, K. J., and Wilson, E. L., Numerical Methods in Finite Element Analysis, Prentice‐Hall, Inc., New York, N.Y., 1976.
5.
Batoz, J. L., and Dhatt, G., “Incremental Displacement Algorithms for Nonlinear Problems,” International Journal of Numerical Method in Engineering, Vol. 14, 1979, pp. 1262–1266.
6.
Bergan, P. G., Hottigmoe, G., Krakeland, B., and Soreide, T. H., “Solution Techniques for Nonlinear Finite Element Problems,” International Journal of Numerical Method in Engineering, Vol. 12, 1978, pp. 1677–1696.
7.
Chajes, A., Principles of Structural Stability Theory, Civil Engineering and Engineering Mechanics Series, Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1974.
8.
Chen, W. F., and Atsuta, T., Theory of Beam‐Columns, Volume 2: Space Behavior and Design, McGraw‐Hill, Inc., New York, N.Y., 1977.
9.
Connor, Jr.J., Logcher, R. D., and Chan, S. C., “Nonlinear Analysis of Elastic Framed Structures,” Journal of the Structural Division, ASCE, Vol. 94, No. ST6, June, 1968, pp. 1525–1547.
10.
Crisfield, M. A., “A Fast Incremental/Iterative Solution Procedure that Handles Snap‐Through,” Computers and Structures, Vol. 13, 1981, pp. 55–62.
11.
Galambos, T. V., Structural Members and Frames, Prentice Hall, Inc., Englewood Cliffs, N.J., 1968.
12.
Gere, J. M., and Weaver, W. J., Analysis of Framed Structures, Van Nostrand Reinhold, New York, N.Y., 1965.
13.
Hu, X. R., Shen, Z. Y., and Lu, L. W., “Inelastic Stability Analysis of Biaxially Loaded Beam‐Columns by Finite Element Methods,” Proceedings, International Conference on Finite Element Method, Shanghai, China, 1982, pp. 52–57.
14.
Johnson, C. P., and Will, K. M., “Beam Buckling by Finite Element Procedure,” Journal of the Structural Division, ASCE, Vol. 100, No. ST3, Mar., 1974, pp. 669–685.
15.
Kitipornchai, S., “Torsional‐Flexural Buckling of Angles: A Parametric Study,” Journal of Constructional Steel Research, Vol. 3, No. 3, 1983, pp. 27–31.
16.
Kitipornchai, S., and Lee, H. W., “Inelastic Buckling of Single Angle, Tee and Double Angle Struts,” Journal of Constructional Steel Research, Vol. 6, No. 1, 1986, pp. 3–20.
17.
Kitipornchai, S., and Wang, C. M., “Lateral Buckling of Tee Beams Under Moment Gradient,” Computers and Structures, Vol. 23, No. 1, 1986, pp. 69–76.
18.
Krajcinovic, D., “A Consistent Discrete Elements Technique for Thin‐Walled Assemblages,” International Journal of Solids and Structures, Vol. 5, 1969, pp. 639–662.
19.
Meek, J. L., and Tan, H. S., “Large Deflection and Post‐Buckling Analysis of Two and Three Dimensional Elastic Spatial Frames,” Research Report, No. CE49, Department of Civil Engineering, University of Queensland, Brisbane, Australia, 1983.
20.
Oran, C., “Tangent Stiffness in Space Frames,” Journal of the Structural Division, ASCE, Vol. 99, No. ST6, June, 1983, pp. 987–1001.
21.
Powell, G., and Klingner, R., “Elastic Lateral Buckling of Steel Beams,” Journal of the Structural Division, ASCE, Vol. 96, No. ST9, Sept., 1970, pp. 1919–1932.
22.
Przemieniecki, J. S., Theory of Matrix Structural Analysis, McGraw‐Hill, Inc., New York, N.Y., 1968.
23.
Ramm, E., “Strategies for Tracing the Nonlinear Response Near Limit Points,” Nonlinear Finite Element Analysis in Structural Mechanics, W. Wunderlich, E. Stein, and K. J. Bathe, eds., Springer‐Verlag, Berlin; Germany, 1981, pp. 63–89.
24.
Roberts, T. M., and Azizian, Z. G., “Instability of Thin‐Walled Bars,” Journal of Engineering Mechanics, ASCE, Vol. 109, No. 3, Mar., 1983, pp. 781–794.
25.
Santathadaporn, S., and Chen, W. F., “Analysis of Biaxial Loaded H‐Columns,” Journal of the Structural Division, ASCE, Vol. 99, No. ST3, Mar., 1973, pp. 491–509.
26.
Timoshenko, S. P., and Gere, J. M., Theory of Elastic Stability, 2nd ed., McGraw‐Hill, Inc., New York, N.Y., 1961.
27.
Trahair, N. S., The Behaviour and Design of Steel Structures, Chapman and Hall, London, England, 1977.
28.
Trahair, N. S., “Restrained Elastic Beam‐Columns,” Journal of the Structural Division, ASCE, Vol. 95, No. ST12, Dec., 1969, pp. 2641–2663.
29.
Vinnakota, S., and Aysto, P., “Inelastic Spatial Stability of Restrained Beam‐Columns,” Journal of the Structural Division, ASCE, Vol. 100, No. ST11, Nov., 1974, pp. 2235–2254.
30.
Woolcock, S. T., and Kitipornchai, S., “Design of Single Angle Struts,” Steel Construction, Australian Institute of Steel Construction, Vol. 14, No. 4, 1980, pp. 2–23.
31.
Woolcock, S. T., and Kitipornchai, S., “Design of Single Angle Web Struts in Trusses,” Journal of Structural Engineering, ASCE, Vol. 112, No. 6, June, 1986, pp. 1327–1345.
32.
Yang, Y. B., “Linear and Nonlinear Analysis of Space Frames with Non‐Uniform Torsion Using Interactive Computer Graphics,” thesis presented to Cornell University, at Ithaca, N.Y., in 1984, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 113 • Issue 4 • April 1987
Pages: 721 - 739
Copyright
Copyright © 1987 ASCE.
History
Published online: Apr 1, 1987
Published in print: Apr 1987
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.