DOI QR코드

DOI QR Code

A finite element yield line model for the analysis of reinforced concrete plates

  • Rasmussen, L.J. (Ramboll) ;
  • Baker, G. (Department of Civil Engineering, The University of Queensland)
  • Published : 1998.06.25

Abstract

This paper concerns the development and implementation of an orthotropic, stress resultant elasto-plastic finite element model for the collapse load analysis of reinforced concrete plates. The model implements yield line plasticity theory for reinforced concrete. The behaviour of the yield functions are studied, and modifications introduced to ensure a robust finite element model of cases involving bending and twisting stress resultants ($M_x$, $M_y$, $M_{xy}$). Onset of plasticity is always governed by the general yield-line-model (YLM), but in some cases a switch to the stress resultant form of the von Mises function is used to ensure the proper evolution of plastic strains. Case studies are presented, involving isotropic and orthotropic plates, to assess the behaviour of the yield line approach. The YLM function is shown to perform extremely well, in predicting both the collapse loads and failure mechanisms.

Keywords

References

  1. Baker, G. (1991), "Optimum pointwise reinforcement requirements in plastic fracturing continua", Int. Jnl. Solids and Struct., 28(1), 87-104. https://doi.org/10.1016/0020-7683(91)90049-L
  2. de Borst, R. and Feenstra, P.H. (1990), "Studies in anisotropic plasticity with reference to the Hill criterion", Int. Jnl. Numer. Meths. Engrg., 29, 315-336. https://doi.org/10.1002/nme.1620290208
  3. de Borst, R., Muhlhaus, H.B. (1992), "Gradient dependent plasticity: formulation and algorithmic aspects", Int. Jnl. Numer. Meths. Engrg., 35, 521-539. https://doi.org/10.1002/nme.1620350307
  4. Braestrup, M. (1970), "Yield line theory and limit analysis of plates and slabs", Mag. Conc. Res., 22(71), 99-100. https://doi.org/10.1680/macr.1970.22.71.99
  5. Braestrup, M. and Morley, C.T. (1980), "Dome effects in RC slabs: elastic-plastic analysis", Jnl. Struct. Div., ASCE, 106(ST6), 1255-1262.
  6. Gilbert, R.I. and Warner, R.F. (1978), "Tension stiffening in reinforced concrete slabs", ASCE Jnl. Struct. Div., 104, 1885-1900.
  7. Ghoneim, M.G. and McGregor, J.G. (1994), "Test of reinforced concrete plates under combined inplane and lateral loads", ACI Struct. Jnl., 91(1), 19-30.
  8. Hand, F.R., Pecknold, D.A. and Schnobrich, W.C. (1973), "Nonlinear layered analysis of RC plates and shells", ASCE Jnl. Struct. Div., 99(ST7), 1491-1505.
  9. Lin, C.-S. and Scordelis, A.C. (1975), "Nonlinear analysis of RC shells of general form", Jnl. Struct. Div. ASCE, 101(ST3), 523-538.
  10. LUSAS (1991), Finite Element Analysis System, Version 11. FEA Ltd.: London.
  11. Meek, J.L. and Tan, H.S. (1986), "A faceted shell element with loof nodes", Int. Jnl. Numer. Meths. Engrg., 23, 49-67. https://doi.org/10.1002/nme.1620230106
  12. Morley, C.T. (1966), "On the yield criterion of an orthtropic reinforced concrete slab element", Jnl. Mech. Phys. Solids, 14, 33-47. https://doi.org/10.1016/0022-5096(66)90018-4
  13. Munro, J. and da Fonseca, A.M.A (1978), "Yield line method by finite elements and linear programming", Struct. Engr., 58B(2), 37-44.
  14. Nielsen, M.P. (1984), Limit Analysis and Concrete Plasticity, Prentice Hall: Englewood Cliffs, NJ.
  15. Owen, D.R.J. and Figuerias, J.A. (1983), "Elasto-plastic analysis of anisotropic plates and shells by the semi-Ioof element", It. Jnl. Numer. Meths. Engrg., 19, 521-539. https://doi.org/10.1002/nme.1620190406
  16. Prager, W. (1952), "The general theory of limit design", Proc. 8th Int. Congr. Theor. and Appl. Mechs., Istanbul, Vol. II, 65-72.
  17. Rajendam, S. and Morley, C.T. (1974), "A general yield criterion for reinforced concrete slab elements", Mag. Conc. Res., 26(89), 212-270. https://doi.org/10.1680/macr.1974.26.89.212
  18. Ristic, S., Baker, G. and Meek, J.L. (1993), "Plastic analysis of shells using a macro DKL+LST element", In Proceedings of the 13th Australasian Conf. Mechs. Struct. and Mater., L.C. Schmidt (ed)., University of Wollongong, 2, 737-744.
  19. Ueda, Y. and Tetsuya, Y. (1982), "The plastic node method: a new method of plastic analysis", Comp. Meths. Appl. Mechs. Engrg., 34, 1089-1103. https://doi.org/10.1016/0045-7825(82)90103-7
  20. Ueda, Y. and Fujikubo, M. (1991), "Generalization of the plastic node method", Comp. Meths. Appl. Mechs. Engrg., 92, 33-53. https://doi.org/10.1016/0045-7825(91)90196-D
  21. Wood, R. (1955), "Studies in composite construction, Part II", National Building Studies, Research Paper No. 22, London.
  22. Zienkiewicz, O.C., Valliappan, S. and King, I.P (1969), "Elasto-plastic solutions of engineering problems by 'Initial Stress' finite element approach", Int. Jnl. Numer. Meths. Engrg., 1, 75-100. https://doi.org/10.1002/nme.1620010107

Cited by

  1. Finite element linear and nonlinear, static and dynamic analysis of structural elements – an addendum – A bibliography (1996‐1999) vol.17, pp.3, 2000, https://doi.org/10.1108/02644400010324893
  2. Global Constitutive Model for Reinforced Concrete Plates vol.133, pp.3, 2007, https://doi.org/10.1061/(ASCE)0733-9399(2007)133:3(257)
  3. Finite element modelling of double skin composite slabs vol.38, pp.7, 2002, https://doi.org/10.1016/S0168-874X(01)00093-2