Self-Equilibrating Element for Second-Order Analysis of Semirigid Jointed Frames
Publication: Journal of Engineering Mechanics
Volume 121, Issue 8
Abstract
An accurate pointwise equilibrating polynomial element with springs connected to its ends to model semirigid connections is derived. The formulated element and coded computer program for second-order nonlinear analysis of flexibly jointed steel frames is employed to study a variety of problems using one element per member, which is not possible by the conventional cubic Hermitian function and most of the currently available elements. When incorporated into a nonlinear-analysis computer program, the versatility of the program is greatly improved as the convergence rate is increased, and the modeling effort for accurate solution is reduced considerably because the element stiffness remains accurate under high axial load. The capability of the proposed element in handling a harsh benchmark problem is also verified in one of the examples.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Chan, S. L.(1988). “Geometric and material nonlinear analysis of beam-columns and frames using the minimum residual displacement method.”Int. J. for Numerical Methods in Engrg., 26, 2657–2669.
2.
Chan, S. L.(1992). “Large deflection kinematic formulations for three dimensional framed structures.”Comp. Methods in Appl. Mech. and Engrg., 95, 17–36.
3.
Chan, S. L., and Ho, G. W. M. (1990). “A comparative study on the nonlinear numerical algorithms.”Proc., 3rd Int.Conf. on Adv. in Numerical Methods in Engrg. Theory and Applications, Univ. Coll. Swansea, Swansea, U.K., 552–565.
4.
Chan, S. L., and Yau, C. Y. (1992). “Nonlinear analysis of roof truss composed of pinned, rigid and semi-rigid jointed members.”Proc., Int. Congr. on Innovative Long Span Struct., Toronto, Canada, 175–185.
5.
Chan, S. L., and Zhou, Z. W.(1994). “A pointwise equilibrium polynomial (PEP) element for nonlinear analysis of frames.”J. Struct. Engrg., ASCE, 120(6), 1703–1717.
6.
Chen, W. F., and Chan, S. L.(1995). “Second-order inelastic analysis of steel frames using element with mid-span and end springs.”J. Struct. Engrg., ASCE, 121(3), 530–541.
7.
Chen, W. F., and Lui, E. M.(1987). “Effect of joint flexibility on the behavior of steel frames.”Comp. and Struct., 26, 719–732.
8.
El-Sheikh, A. I. (1993). “Numerical analysis of space trusses with flexible member-end joints.”Space Struct. 8(3), 189–197.
9.
Frye, M. J., and Morris, G. A.(1975). “Analysis of flexibly connected steel frames.”Can. J. Civ. Engrs,, 2, 280–291.
10.
Ho, W. M. G., and Chan, S. L.(1991a). “Semi-bifurcation and bifurcation analysis of flexibly connected steel frames.”J. Struct. Engrg., ASCE, 117(8), 2299–2319.
11.
Ho, W. M. G., and Chan, S. L. (1991b). “Numerical study on the post-buckling analysis of steel arches.”Proc., 6th Int. Conf. in Australia on Finite Element Methods, Univ. of Sydney, New South Wales, Australia, 421–428.
12.
Ho, W. M. G., and Chan, S. L.(1993). “An accurate and efficient method for large deflection analysis of frames with semi-rigid connections.”J. Constr. Steel Res., 26, 171–191.
13.
Kishi, N., and Chen, W. F.(1990). “Moment-rotation relations of semi-rigid connections with angles.”J. Struct. Engrg., ASCE, 116(7), 1813–1834.
14.
Koon, C. M. (1993). “Design and ultimate analysis of trusses with semi-rigid connections,” MSCE dissertation, Hong Kong Polytechnic Univ., Hung Hom, Kowloon, Hong Kong.
15.
Lui, E. M., and Chen, W. F.(1988). “Behavior of braced and unbraced semi-rigid frames.”Int. J. Solids and Struct., 24(9), 893–913.
16.
Nonlinear benchmarks. (1989). Nat. Agency for Finite Element Methods and Standards (NAFEMS), Dept. of Trade and Industry, Nat. Engrg. Lab., East Kilbride, Glasgow, U.K.
17.
NAF. (1992). Geometric and material nonlinear analysis of frames: Computer program reference manual, 9207-2, Dept. of Civ. and Struct. Engrg., Hong Kong Polytechnic Univ., Hung Hom, Kowloon, Hong Kong.
18.
Nethercot, D. A. (1985). “Steel beam-to-column connections—a review of test data and its applicability to the evaluation of joint behavior in the performance of steel frames.” CIRIA project study.
19.
Pecknold, D. A., Ghaboussi, J., and Healey, T. J.(1985). “Snap-through and bifurcation in a simple structure.”J. Engrg. Mech., ASCE, 111(7), 909–922.
20.
Ramberg, W., and Osgood, W. R. (1943). “Description of stress-strain curves by three parameters.”NACA Tech. Rep. No. 902, Nat. Advisory Committee for Aeronautics, Washington, D.C.
21.
So, K. W. A., and Chan, S. L.(1991). “Buckling analysis of frames using 1 element/member.”J. Constr. Steel Res., 20, 271–289.
22.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, 2nd Ed., McGraw-Hill Book Co., New York, N.Y.
23.
Toader, I. H. I.(1993). “Stability function for members with semi-rigid joint connections.”J. Struct. Engrg., ASCE, 119(2), 505–521.
24.
White, D. W., Liew, R. J. Y., and Chen, W. F. (1993). “Toward advanced analysis in LRFD.”Plastic hinge based methods for advanced analysis and design of steel frames—an assessment of the state-of-the-art, D. W. White and W. F. Chen, eds., Struct. Stability Res. Council, Chicago, Ill., 95–174.
25.
Yang, Y. B., and Chiou, H. T.(1987). “Rigid body motion test for nonlinear analysis with beam elements.”J. Engrg. Mech., ASCE, 113(9), 1404–1419.
26.
Zienkiewicz, 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 Engineering Mechanics
Volume 121 • Issue 8 • August 1995
Pages: 896 - 902
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Aug 1, 1995
Published in print: Aug 1995
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.