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Stiffness Matrices for Linear and Buckling Analyses of Composite Beams with Partial Shear Connection

Published online by Cambridge University Press:  05 May 2011

L.-J. Leu  and
C.-W. Huang
L.-J. Leu*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
C.-W. Huang*
Affiliation:
Department of Civil Engineering, Chung Yuan Christian University, Chung Li, Taiwan 32023, R.O.C.
*
* Professor
** Assistant Professor
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Abstract

This paper is concerned with linear and buckling analyses of composite beams with partial shear connection (partial composite beams) using the finite element method. Two elements derived from different types of shape functions are proposed in this study. The first element, referred to as exact, is based on the exact shape functions obtained by solving the differential equations governing the transverse displacement and the slip of the shear connector layer of a partial composite beam. The second element, referred to as approximate, is based on the conventional linear and cubic shape functions used in conventional axial and beam elements. By making use of these two types of shape functions, the elastic and geometric stiffness matrices can be derived explicitly from the strain energy and the load potential, respectively. Both types of elements can be used to carry out linear static and buckling analyses. As expected, the exact element is more accurate than the approximate element if the same discretization is adopted. However, the approximate element has the advantage of easy implementation since the expressions of its elastic and geometric stiffness matrices are very simple. Also, the solutions obtained from the approximate element converge very fast; with reasonable discretization, say 8 elements per member, very accurate solutions can be obtained.

Keywords

Partial composite beamsPartial shear connectionExact shape functionsStiffness matricesLinear analysisBuckling analysis
Type
Articles
Information
Journal of Mechanics , Volume 22 , Issue 4 , December 2006 , pp. 299 - 309
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

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References

1.Plum, D. R. and Horne, M. R.,“The Analysis of Continuous Composite Beams with Partial Interaction,” Proc. Inst. Civ. Eng., Part 2, 59, pp. 625–643 (1975).Google Scholar
2.Gjelsvik, A., “Analog-Beam Method for Determining Shear -Lag Effects,”.J. Eng. Mech., 117, pp. 1575–1594 (1991).Google Scholar
3.Betti, R. and Gjelsvik, A., “Elastic Composite Beams,” Comput. Struct., 59, pp. 437–451 (1996).CrossRefGoogle Scholar
4.Jasim, N. A., “Computation of Deflections for Continuous Composite Beams with Partial Interaction,” Proc. Inst. Civ. Eng., Structs. & Bldgs., 122, pp. 347–354 (1997).CrossRefGoogle Scholar
5.Jasim, N. A.and Ali, A. A. M., “Deflections of Composite Beams with Partial Shear Connection,” Struct. Eng. 75(4), pp. 58–61 (1997).Google Scholar
6.Oehlers, D. J., Seracino, R and Yeo, M. F., “Effect of Friction on Shear Connection in Composite Bridge Beams,” J. Bridge. Eng., 5, pp. 91–98 (2000).CrossRefGoogle Scholar
7.Sebastian, W. M. and McConnel, R. E. , R. E., “Nonlinear FE Analysis of Steel-Concrete Composite Structures,” J. Struct. Eng., 126, pp. 662–674 (2000).CrossRefGoogle Scholar
8.Salari, M. R., Spacone, E., Shing, P. B. and Frangopol, D. M., “Nonlinear Analysis of Composite Beams with Deformable Shear Connectors,” J. Struct. Eng., 124, pp. 1148–1158(1998).CrossRefGoogle Scholar
9.Fabbrocino, G., Manfredi, G. and Cosenza, E. , E., “Modeling of Continuous Steel-Concrete Composite Beams: Computational Aspects,” Comput. Struct., 80, pp. 2241–2251 (2002).CrossRefGoogle Scholar
10.Ayoub., A. and Filippou, F. C., “Mixed Formulation of Nonlinear Steel-Concrete Composite Beam Element,” J. Struct. Eng., 126, pp. 371–381 (2000).CrossRefGoogle Scholar
11.Girhammar, U. A. and Gopu, V. K. A., “Composite Beam-Columns with Interlayer Slip: Exact Analysis,” J. Struct. Eng., 119, pp. 1265–1282 (1993).CrossRefGoogle Scholar
12.McGuire, W., Gallagher, R. H. and Ziemian, R. D., Matrix Structural Analysis, 2nd Ed., John Wiley & Sons, New York (2000).Google Scholar
13.Chajes, A., Principles of Structural Stability Theory, Prentice-Hall, New York (1974).Google Scholar
14.Chen, W. F. and Lui, E. M., Structural Stability: Theory and Implementation, Elsevier, New York (1987).Google Scholar
15.Bathe, K. J., Finite Element Procedures, Prentice-Hall, New York (1996).Google Scholar