Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear analysis of composite beams with partial shear interaction by means of the direct stiffness method

  • Ranzi, G. (The University of Sydney) ;
  • Bradford, M.A. (The University of Sydney, UNSW)
  • Received : 2006.10.24
  • Accepted : 2008.12.17
  • Published : 2009.03.25
⟨ Previous Next ⟩

Abstract

This paper presents a modelling technique for the nonlinear analysis of composite steel-concrete beams with partial shear interaction. It extends the applicability of two stiffness elements previously derived by the authors using the direct stiffness method, i.e. the 6DOF and the 8DOF elements, to account for material nonlinearities. The freedoms are the vertical displacement, the rotation and the slip at both ends for the 6DOF stiffness element, as well as the axial displacement at the level of the reference axis for the 8DOF stiffness element. The solution iterative scheme is based on the secant method, with the convergence criteria relying on the ratios of the Euclidean norms of both forces and displacements. The advantage of the approach is that the displacement and force fields of the stiffness elements are extremely rich as they correspond to those required by the analytical solution of the elastic partial interaction problem, thereby producing a robust numerical technique. Experimental results available in the literature are used to validate the finite element proposed in the paper. For this purpose, those reported by Chapman and Balakrishnan (1964), Fabbrocino et al. (1998, 1999) and Ansourian (1981) are utilised; these consist of six simply supported beams with a point load applied at mid-span inducing positive bending moment in the beams, three simply supported beams with a point load applied at mid-span inducing negative bending moment in the beams, and six two-span continuous composite beams respectively. Based on these comparisons, a preferred degree of discretisation suitable for the proposed modelling technique expressed as a function of the ratio between the element length and depth is proposed, as is the number of Gauss stations needed. This allows for accurate prediction of the nonlinear response of composite beams.

Keywords

References

  1. ABAQUS (2003), ABAQUS Standard User's Manual, Version 6.4, Hibbitt, Karlsson and Sorensen Inc., Pawtucket, RI, USA.
  2. Ansourian, P. (1981), "Experiments on continuous composite beams", Proc. Ins. Civil Eng., London, Part 2, 71, 25-51.
  3. Ansys (2003), Ansys Multiphysics 8.0, Ansys Inc., Canonsburg, Pa, USA.
  4. CEB-FIB (Comite Euro-International du Beton - Federation International de la Precontrainte) (1993), Model Code 1990: Design Code, Thomas Telford, London, UK.
  5. CEB-FIB (Comite Euro-International du Beton - Federation International de la Precontrainte) (1998), CEB Bulletin d'information n. 242: Ductility of reinforced concrete structures, FIB Federation International du Beton, Paris, France, 112-113.
  6. Chapman, J.C. and Balakrishnan, S. (1964), "Experiments on composite beams", The Structural Engineer, 42(11), 369-383.
  7. 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, 1001-1009. https://doi.org/10.1016/S0045-7949(02)00038-X
  8. Faella, C., Martinelli, E. and Nigro, E. (2003), "Shear connection nonlinearity and deflections of steel-concrete composite beams: A simplified method", J. Struct. Eng., ASCE, 129(1), 12-20. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:1(12)
  9. Fabbrocino, G., Manfredi, G., Pecce, M. and Cosenza, E. (1998), "Nonlinear behaviour of composite beams in the hogging moment region: numerical study", Proc. III Italian Workshop on Composite Construction, Ancona, Italy, October 1998 (In Italian).
  10. Fabbrocino, G., Manfredi, G., Cosenza, E. and Pecce, M. (1999), "Nonlinear behaviour of composite beams under negative moment: an experimental-theoretical comparison", Proc. of the 2nd European Conf. Steel Structures EUROSTEEL '99, Prague, Czech Republic, May 1999.
  11. Girhammar, U.A. and Pan, D. (1993), "Dynamic analysis of composite members with interlayer slip", Int. J. Solids Struct., 30(6), 797-823. https://doi.org/10.1016/0020-7683(93)90041-5
  12. Leon, R.T. and Viest, I.M. (1996), "Theories of incomplete interaction in composite beams", Proc. Conf. Comp. Constr. Steel. Con. III, Irsee, Germany, June, 858-870.
  13. May, I.M., Morley, C.T. and Chen, Y.Y. (2003), "Benchmarking of non-linear finite element analyses for reinforced concrete deep beams", Proc. EURO-C 2003 Conf. Computational Modelling of Concrete Structures, St. Johann im Pongau, Austria, 751-756.
  14. Newmark, N.M., Siess, C.P. and Viest, I.M. (1951), "Tests and analysis of composite beams with incomplete interaction", Proc. Society Experimental Stress Analysis, 9(1), 75-92.
  15. Pi, Y. L., Bradford, M.A. and Uy, B. (2005a), "Second-order nonlinear inelastic analysis of composite steel-concrete composite members. I: Theory", J. Struct. Eng., ASCE, 132(5), 751-761. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:5(751)
  16. Pi, Y. L., Bradford, M.A. and Uy, B. (2005b), "Second-order nonlinear inelastic analysis of composite steelconcrete composite members. II: Applications", J. Struct. Eng., ASCE, 132(5), 762-771. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:5(762)
  17. Ranzi, G. and Bradford, M.A. (2007), "Direct stiffness analysis of a composite beam-column element with partial interaction", Comput. Struct. (accepted for publication).
  18. Ranzi, G., Bradford, M.A. and Uy, B. (2003), "A general method of analysis of composite beams with partial interaction", Steel Composite Struct., 3(3), 169-184. https://doi.org/10.12989/scs.2003.3.3.169
  19. 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, 657-672. https://doi.org/10.1002/nme.1091
  20. Reddy, J.N. (2004), An Introduction to Nonlinear Finite Element Analysis, Oxford University Press, Oxford, UK.
  21. Spacone, E. and El-Tawil, S. (2004), "Nonlinear analysis of steel-concrete composite structures: state of the art", J. Struct. Eng., ASCE, 130(2), 159-168. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:2(159)
  22. Sun, C.H., Bradford, M.A. and Gilbert, R.I. (1993), "Numerical analysis for concrete framed structures using the finite element method", Comput. Struct., 48(1), 73-79. https://doi.org/10.1016/0045-7949(93)90459-Q
  23. Weaver, W. and Gere, J.M. (1990), Matrix Analysis of Framed Structures, 3rd edn., Chapman and Hall, London, 1990.
  24. Yam, L.C.P. and Chapman, J.C. (1968), "The inelastic behaviour of simply supported composite beams of steel and concrete", Proc. of the Institution of Civil Engineers, London, Part 2, 41, 651-683.
  25. Zhang, Y.X., Bradford, M.A. and Gilbert, R.I. (2006), "A new triangular layered plate element for the nonlinear analysis of reinforced concrete slabs", Commun. Numer. Meth. Eng., 22(7), 677-709. https://doi.org/10.1002/cnm.839
  26. Zona, A. (2003), "Finite Element Modelling of Composite Beams", PhD Thesis, University of Ancona, Italy.

Cited by

  1. Generalised Beam Theory for composite beams with longitudinal and transverse partial interaction vol.22, pp.10, 2017, https://doi.org/10.1177/1081286516653799
  2. Increasing the flexural capacity of RC beams using partially HPFRCC layers vol.16, pp.4, 2015, https://doi.org/10.12989/cac.2015.16.4.545
  3. Evaluation on structural behaviors of prestressed composite beams using external prestressing member vol.34, pp.2, 2010, https://doi.org/10.12989/sem.2010.34.2.247
  4. Mechanical behaviour research of long span prestressed steel–concrete composite beam vol.18, pp.sup2, 2014, https://doi.org/10.1179/1432891714Z.000000000468
  5. Practical nonlinear inelastic analysis method of composite steel-concrete beams with partial composite action vol.134, 2017, https://doi.org/10.1016/j.engstruct.2016.12.017
  6. A higher order steel–concrete composite beam model vol.80, 2014, https://doi.org/10.1016/j.engstruct.2014.09.002
  7. A GBT Model for the Analysis of Composite Steel–Concrete Beams with Partial Shear Interaction vol.4, 2015, https://doi.org/10.1016/j.istruc.2015.10.002
  8. Generalised Beam Theory (GBT) for composite beams with partial shear interaction vol.99, 2015, https://doi.org/10.1016/j.engstruct.2015.05.025
  9. Finite Elements for Higher Order Steel-Concrete Composite Beams vol.11, pp.2, 2021, https://doi.org/10.3390/app11020568