Dynamic Response of Composite Beams with Partial Shear Interaction Using a Higher-Order Beam Theory
Publication: Journal of Structural Engineering
Volume 139, Issue 1
Abstract
Dynamic response of composite beams with partial interaction is presented using a one-dimensional finite-element model based on a higher-order beam theory. The proposed model takes into account the effect of partial shear interaction between the adjacent layers, as well as the transverse shear deformation of the beam. A third order variation of the axial displacement of the fibers over the beam depth is taken to have a parabolic variation of shear stress, which vanishes at both the top and bottom fibers of the transverse composite surface, as clearly derived on the free and tangentially unloaded surface of the continua. In the proposed finite-element model, there is no need to incorporate any shear correction factor, and the model is free from the shear locking problem. The proposed numerical model is validated by comparing the results with those available in the literature. Many new results are presented, because there are no published results on vibration and buckling of composite beams based on higher-order beam theory.
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References
Arzumi, Y., Hamada, S., and Kajita, T. (1981). “Elasto-plastic analysis of composite beams with incomplete interaction by finite element method.” Comput. Struct., 14(5–6), 453–462.
Ayoub, A., and Filippou, F. C. (2000). “Mixed formulation for nonlinear steel-concrete composite beam element.” J. Struct. Div., 126(3), 371–381.
Bathe, K. J. (1996). Finite element procedures, Prentice Hall, Upper Saddle River, NJ.
Berczyński, S., and Wróblewski, T. (2005). “Vibration of steel–concrete composite beams using the Timoshenko beam model.” J. Vibrat. Cont., 11(6), 829–848.
Chakrabarti, A., Sheikh, A. H., Griffith, M., and Oehlers, D. J. (2011). “Analysis of composite beams with partial shear interaction using a higher order beam theory.” Eng. Struct., 36(1), 283-291.
Cook, R. D., Malkus, D. S., Plsha, M. E., and Witt, R. J. (2002). Concepts and applications of finite element analysis, Wiley, New York.
Dall’Asta, A., and Zona, A. (2002). “Nonlinear analysis of composite beams by a displacement approach.” Comput. Struct., 80(27–30), 2217–2228.
Faella, C., Martinelli, E., and Nigro, E. (2002). “Steel and concrete composite beams with flexible shear connection: Exact analytical expression of the stiffness matrix and applications.” Comput. Struct., 80(11), 1001–1009.
Girhammar, U. A., and Pan, D. (1993). “Dynamic analysis of composite members with interlayer slip.” J. Solids Struct., 30(6), 797–823.
Goodman, J. R., and Popov, E. P. (1968). “Layered beam systems with interlayer slip.” J. Struct. Div., 94(11), 2535–2547.
Huang, C. W., and Su, Y. H. (2008). “Dynamic characteristics of partial composite beams.” Int. J. Struct. Stab. Dyn., 8(4), 665–685.
Jasim, N. A. (1997). “Computation of deflections for continuous composite beams with partial interaction.” Proc., Inst. Civil Eng. Struct. Build., 122(3), 347–354.
Kant, T. (1982). “Numerical analysis of thick plates.” Comput. Methods Appl. Mech. Eng., 31(1), 1–18.
Newmark, N. M., Siess, C. P., and Viest, I. M. (1951). “Test and analysis of composite beams with incomplete interaction.” Proc., Soc. Exp. Stress Anal., 9(1), 75–92.
Nguyen, Q. H., Hjiaj, M., and Guezouli, S. (2011a). “Exact finite element model for shear-deformable two-layer beams with discrete shear connection.” Finite Elem. Anal. Des., 47(7), 718–727.
Nguyen, Q. H., Hjiaj, M., and Uy, B. (2010). “Time-dependent analysis of composite beams with partial interaction based on time-discrete exact stiffness matrix.” Eng. Struct., 32(9), 2902–2911.
Nguyen, Q. H., Martinelli, E., and Hjiaj, M. (2011b). “Derivation of the exact stiffness matrix for a two layer Timoshenko beam element with partial interaction.” Eng. Struct., 33(2), 298–307.
Oehlers, D. J., and Bradford, M. A. (1995). Composite steel and concrete structural members: Fundamental behaviour, Pergamon Press, Oxford, U.K.
Ranzi, G. (2008). “Locking problems in the partial interaction analysis of multi-layered composite beams.” Eng. Struct., 30(10), 2900–2911.
Ranzi, G., Bradford, M. A., and Uy, B. (2004). “A direct stiffness analysis of a composite beam with partial interaction.” Int. J. Numer. Methods Eng., 61(5), 657–672.
Ranzi, G., Dall’Asta, A., Ragni, L., and Zona, A. (2010). “A geometric nonlinear model for composite beams with partial interaction.” Eng. Struct., 32(5), 1384–1396.
Ranzi, G., Gara, F., Leoni, G. and Bradford, M. A. (2006). “Analysis of composite beams with partial shear interaction using available modelling techniques: A comparative study.” Comput. Struct., 84(13–14), 939–941.
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.
Reddy, J. N. (1984). “A simple higher-order theory for laminated composite plates.” J. Appl. Mech., 51(4), 745–752.
Salari, M. R., Spacone, E., Shing, P. B., and Frangopol, D. M. (1998). “Nonlinear analysis of composite beams with deformable shear connectors.” J. Struct. Div., 124(10), 1148–1186.
Schnabl, S., Planinc, I., Saje, M., Cas, B., and Turk, G. (2006). “An analytical model of layered continuous beams with partial interaction.” Struct. Eng. Mech., 22(3), 263–278.
Schnabl, S., Saje, M., Turk, G., and Planinc, I. (2007). “Locking-free two-layer Timoshenko beam element with interlayer slip.” Finite Elem. Anal. Des., 43(9), 705–714.
Vinayaka, R. U., Prathap, G., and Naganarayana, B. P. (1996). “Beam elements based on higher order theory-I: Formulation and analysis of performance.” Comput. Struct., 58(4), 775–789.
Whitney, J. M. (1973). “Shear correction factors for orthotropic laminates under static load.” J. Appl. Mech., 40(1), 302–304.
Wu, Y. F., Oehlers, D. J., and Griffith, M. C. (2002). “Partial-interaction analysis of composite beam/column members.” Mech. Struct. Mach., 30(3), 309–332.
Xu, R., and Wu, Y. F. (2007a). “Static, dynamic, and buckling analysis of partial interaction composite members using Timoshenko’s beam theory.” Int. J. Mech. Sci., 49(10), 1139–1155.
Xu, R., and Wu, Y. F. (2007b). “Two dimensional analytical solutions of simply supported composite beams with interlayer slips.” Int. J. Solids Struct., 44(1), 165–175.
Xu, R., and Wu, Y. F. (2008). “Free vibration and buckling of composite beams with interlayer slip by two-dimensional theory.” J. Sound Vibrat., 313(3–5), 875–890.
Zona, A., and Ranzi, G. (2011). “Finite element models for non-linear analysis of steel concrete composite beams with partial interaction in combined bending and shear.” Finite Elem. Anal. Des., 47(2), 98–118.
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Information
Published In
Journal of Structural Engineering
Volume 139 • Issue 1 • January 2013
Pages: 47 - 56
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Aug 5, 2011
Accepted: Mar 2, 2012
Published online: Mar 6, 2012
Published in print: Jan 1, 2013
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