Shear-Flexible Steel-Concrete Composite Beams in Partial Interaction: Closed-Form “Exact” Expression of the Stiffness Matrix
Publication: Journal of Engineering Mechanics
Volume 138, Issue 2
Abstract
This paper presents a theoretical model for analyzing shear-flexible steel-concrete composite beams in partial interaction. Both concrete slab and steel beam are modeled according to Timoshenko’s theory, and a continuous linear-behaving shear connection is considered between the two connected members. Simplified kinematic assumptions have been considered for the displacement fields of the two connected members to derive a model, which is at one time rather general, but even simple enough to be easily handled and actually solved in closed-form. The analytical formulation of both stiffness matrix and vector of equivalent nodal forces is the key achievement of the present paper. They completely define an “exact” finite element for the mentioned model and can be easily employed for carrying out computationally efficient analyses of steel-concrete composite beams looking after the effect of both shear flexibility of the structural members and slips occurring at the interface between the two connected members. Simple applications are finally proposed for demonstrating that the present “exact” finite element can be employed for analyzing shear-flexible steel-concrete composite beams by using just one element-per-member. Thus, it is more efficient than both alternative numerical solutions already available in the scientific literature and commercial finite element packages.
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References
Abdel-Aziz, K. (1986). “Numerical modeling and experimental study of composite beams with partial or spaced shear connection.” Ph.D. thesis. No. D 86-3, INSA Rennes, Rennes, France.
Adekola, A. O. (1968). “Partial interaction between elastically connected elements of a composite beam.” Int. J. Solid Struct., 4(11), 1125–1135.
Aribert, J. M., and Labib, A. G. (1982). “Modéle de calcul élasto-plastique de poutres mixtes à connection partielle.” Construction Métallique, 4, 3–51 (in French).
Ayoub, A., and Filippou, F. C. (2000). “Mixed formulation of nonlinear steel-concrete composite beam element.” J. Struct. Eng., 126(3), 371–381.
Dezi, L., Gara, F., and Leoni, G. (2007). “A shear deformable steel-concrete composite beam model.” Proc. 6th Int. Conf. on Steel & Aluminium Struct. (ICSAS ’07), R. Beale, ed., Oxford Brookes University, Oxford, UK, 457–464.
Faella, C., Martinelli, E., and Nigro, E. (2002). “Steel and concrete composite beams: “Exact” expression of the stiffness matrix and applications.” Comput. Struct., 80(11), 1001–1009.
Faella, C., Martinelli, E., and Nigro, E. (2003a). “Shear connection nonlinearity and deflections of steel—concrete composite beams: A simplified method.” J. Struct. Eng., 129(1), 12–20.
Faella, C., Martinelli, E., and Nigro, E. (2003b). “Non-linear-behaviour of steel concrete composite frames with partial shear connection.” Proc. ASSCCA’03, A. A. Balkema, Lisse, The Netherlands, 555–561.
Faella, C., Martinelli, E., and Nigro, E. (2008). “Analysis of steel-concrete composite PR-frames in partial shear interaction: A numerical model and some applications.” Eng. Struct., 30(4), 1178–1186.
Faella, C., Martinelli, E., and Nigro, E. (2010). “Steel-concrete composite beams in partial interaction: Closed-form “exact” expression of the stiffness matrix and the vector of equivalent nodal forces.” Eng. Struct., 32(12), 3866–3878.
Newmark, N. M., Siess, C. P., and Viest, I. M. (1951). “Tests and analysis of composite beams with incomplete interaction.” Proc. Soc. Exp. Stress Anal., 9(1), 75–92.
Nguyen, Q.-H., Martinelli, E., and Hjiaj, M. (2011). “Derivation of the exact stiffness matrix for a two-layer Timoshenko beam element with partial interaction.” Eng. Struct., 33(2), 298–307.
Ranzi, G., Bradford, M. A., and Uy, B. (2004). “A direct stiffness analysis of a composite beam with partial interaction.” Int. J. Numer. Meth. Eng., 61(5), 657–672.
Ranzi, G., and Zona, A. (2007). “A steel-concrete composite beam model with partial interaction including the shear deformability of the steel component.” Eng. Struct., 29(11), 3026–3041.
Salari, M. R., and Spacone, E. (2001). “Analysis of steel-concrete composite frames with bond-slip.” J. Struct. Eng., 127(11), 1243–1250.
SAP2000, v.11 [Computer software]. Computers and Structures, Inc., Berkeley, CA.
Schnabl, S., Saje, M., Turk, G., and Planinc, I. (2007). “Analytical solution of two-layer beam taking into account interlayer slip and shear deformation.” J. Struct. Eng., 133(6), 886–894.
Timoshenko, S. P. (1925). “Analysis of bi-metal thermostats.” J. Opt. Soc. Am., 11(3), 233–255.
Xu, R., and Wu, Y. (2007). “Static, dynamic, and buckling analysis of partial interaction composite members using Timoshenko’s beam theory.” Int. J. Mech. Sci., 49(10), 1139–1155.
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© 2012 American Society of Civil Engineers.
History
Received: Feb 23, 2010
Accepted: Aug 1, 2011
Published online: Aug 3, 2011
Published in print: Feb 1, 2012
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