Finite-Element Formulations for the Spatial Static Response of Steel Beams Bonded to a GFRP Plate
Publication: Journal of Engineering Mechanics
Volume 141, Issue 4
Abstract
This study develops four finite elements (FEs) for the analysis of wide-flange steel beams reinforced with a glass fiber–reinforced polymer (GFRP) plate bonded together via an adhesive layer. The formulations treat each of the steel beams and GFRP plates as Vlasov-Gjelsvik thin-walled beams. Two elements are based on shear-deformable kinematics, whereas the other two are based on non-shear-deformable kinematics. The formulations capture the longitudinal-flexural and lateral-torsional responses of the system. Results are then compared with three-dimensional FE analysis solutions based on a current computer program, and the importance of incorporating shear-deformation effects is illustrated, particularly when predicting predominantly torsional responses. The formulation is used to investigate the interaction effect of the shear modulus of the adhesive layer and the length of the GFRP plate.
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Acknowledgments
The authors gratefully acknowledge financial support from the Vietnamese government through a full scholarship to the first author. Additional support from the Natural Sciences and Engineering Council (NSERC) of Canada to the second author is gratefully acknowledged.
References
ABAQUS 6.12-3 [Computer software]. Providence, RI, Dassault Systèmes Simulia.
Ayoub, A. (2001). “A two-field mixed variational principle for partially connected composite beams.” Finite Elem. Anal. Des., 37(11), 929–959.
Ayoub, A. (2005). “A force-based model for composite steel-concrete beams with partial interaction.” J. Constr. Steel Res., 61(3), 387–414.
Back, S. Y., and Will, K. M. (1998). “A shear-flexible element with warping for thin-walled open beams.” Int. J. Numer. Meth. Eng., 43(7), 1173–1191.
Back, S. Y., and Will, K. M. (2008). “Shear-flexible thin-walled element for composite I-beams.” Eng. Struct., 30(5), 1447–1458.
Challamel, N., Bernard, F., and Casandjian, C. (2010). “Out-of-plane behaviour of partially composite or sandwich beams by exact and finite element methods.” Thin-Walled Struct., 48(8), 561–580.
Dall’Asta, A. D., and Zona, A. (2004). “Comparison and validation of displacement and mixed elements for the non-linear analysis of continuous composite beams.” Comput. Struct., 82(23-26), 2117–2130.
El Damatty, A. A., and Abushagur, M. (2003). “Testing and modeling of shear and peel behavior for bonded steel/FRP connections.” Thin-Walled Struct., 41(11), 987–1003.
El Damatty, A. A., Korol, R. M., and Mirza, F. A. (1997). “Large displacement extension of consistent shell element for static and dynamic analysis.” Comput. Struct., 62(6), 943–960.
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(9), 2744–2754.
Frostig, Y., and Baruch, M. (1993). “High-order buckling analysis of sandwich beams with transversely flexible core.” J. Eng. Mech., 476–495.
Frostig, Y., Baruch, M., Vilnay, O., and Sheinman, I. (1992). “High-order theory for sandwich-beam behavior with transversely flexible core.” J. Eng. Mech., 1026–1043.
Ganapathi, M., Patel, B. P., Polit, O., and Touratier, M. (1999). “A C1 finite element including transverse shear and torsion warping for rectangular sandwich beams.” Int. J. Numer. Meth. Eng., 45(1), 47–75.
Girhammar, U. A., and Pan, D. H. (2007). “Exact static analysis of partially composite beams and beam-columns.” Int. J. Mech. Sci., 49(2), 239–255.
Gjelsvik, A. (1981). The theory of thin walled bars, 1st Ed., Wiley, New York.
Gunnlaugsson, G. A., and Pedersen, P. T. (1982). “A finite element formulation for beams with thin walled cross-sections.” Comput. Struct., 15(6), 691–699.
Kim, N. I., and Shin, D. K. (2008). “Coupled deflection analysis of thin walled Timoshenko laminated composite beams.” Comput. Mech., 43(4), 493–514.
Koziey, B. L., and Mirza, F. A. (1997). “Consistent thick shell element.” Comput. Struct., 65(4), 531–549.
Lee, J., Kim, S.-E., and Hong, K. (2002). “Lateral buckling of I-section composite beams.” Eng. Struct., 24(7), 955–964.
Lee, J., and Lee, S.-H. (2004). “Flexural–torsional behavior of thin-walled composite beams.” Thin-Walled Struct., 42(9), 1293–1305.
Martinelli, E., Faella, C., and di Palma, G. (2012). “Shear-flexural steel-concrete composite beams in partial interaction: Closed-form ‘exact’ expression of the stiffness matrix.” J. Eng. Mech., 151–163.
MATLAB R2011b [Computer software]. Natick, MA, MathWorks.
Nguyen, Q.-H., Martinelli, E., and Hiiaj, M. (2011). “Derivation of the exact stiffness matrix for a two-layer Timoshenko beam element with partial interaction.” Eng. Struct., 33(2), 298–307.
Nowzartash, F., and Mohareb, M. (2005). “Planar bending of sandwich beams with transverse loads off the centroidal axis.” J. Eng. Mech., 131(4), 385–396.
Pai, P. F. (2007). Highly flexible structures: Modelling, computation, and experimentation, American Institute of Aeronautics and Astronautics (AIAA), Reston, VA.
Perel, V. Y., and Palazotto, A. N. (2001). “Finite element formulation for cylindrical bending of a transversely compressible sandwich plate, based on assumed transverse strains.” Int. J. Solids Struct., 38(30–31), 5373–5409.
Pham, V. P. (2013). “Stress-deformation theories for the analysis of steel beams reinforced with GFRP plates.” M.Sc. thesis, Dept. of Civil Engineering, Univ. of Ottawa, Ottawa.
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., Gara, F., and Ansourian, P. (2006). “General method of analysis for composite beams with longitudinal and transverse partial interaction.” Comput. Struct., 84(31–32), 2373–2384.
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., Spacone, E., Shing, P. B., and Frangopol, D. M. (1998). “Nonlinear analysis of composite beams with deformable shear connectors.” J. Struct. Eng., 1148–1158.
Siddique, M. A. A., and El Damatty, A. A. (2012). “Enhancement of buckling capacity of steel plates strengthened with GFRP plates.” Thin-Walled Struct., 60(16), 154–162.
Siddique, M. A. A., and El Damatty, A. A. (2013). “Improvement of local buckling behaviour of steel beams through bonding GFRP plates.” Compos. Struct., 96(Feb), 44–56.
Sousa, J. B. M., Jr. (2013). “Exact finite elements for multilayered composite beam-columns with partial interaction.” Comput. Struct., 123(Jul), 48–57.
Vlasov, V. Z. (1961). Thin-walled elastic beams, 2nd Ed., Israel Program for Scientific Translations, Jerusalem.
Vo, T. P., and Lee, J. (2009). “Flexural–torsional coupled vibration and buckling of thin-walled open section composite beams using shear-deformable beam theory.” Int. J. Mech. Sci., 51(9–10), 631–641.
Vo, T. P., and Lee, J. (2013). “Vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under axial loads and end moments.” Mech. Adv. Mater. Struct., 20(8), 652–665.
Wu, L., and Mohareb, M. (2011). “Finite element formulation for shear deformable thin-walled beams.” Can. J. Civ. Eng., 38(4), 383–392.
Zona, A., and Ranzi, G. (2011). “Finite element models for nonlinear 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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© 2014 American Society of Civil Engineers.
History
Received: Jan 21, 2014
Accepted: Aug 8, 2014
Published online: Sep 10, 2014
Published in print: Apr 1, 2015
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