Structural Engineering and Mechanics

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The role of softening in the numerical analysis of R.C. framed structures

  • Published : 1997.11.25
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Abstract

Reinforced Concrete beams with tension and compression softening material constitutive laws are studied. Energy-based and non-local regularisation techniques are presented and applied to a R.C. element. The element characteristics (sectional tangent stiffness matrix, element tangent stiffness matrix restoring forces) are directly derived from their symbolic expressions through numerical integration. In this way the same spatial grid allows us to obtain a non-local strain estimate and also to sample the contributions to the element stiffness matrix. Three examples show the spurious behaviors due to the strain localization and the stabilization effects given by the regularisation techniques, both in the case of tension and compression softening. The possibility to overestimate the ultimate load level when the non-local strain measure is applied to a non softening material is shown.

Keywords

References

  1. Bazant, Z.P. and Ta-Peng Chan, (1984), "Instability of non-local continuum and strain averaging", J. of Eng. Mech. ASCE, 110(10), 1441-1450. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:10(1441)
  2. Bazant, Z.P., Pan, J. and Pijaudier-Cabot, G. (1987), "Softening in reinforced concrete beams and frames", J. of Eng. Mech. ASCE, 113(12), 2333-2347.
  3. Bontempi, F., Malerba, P.G. and Romano, L., (1995), "A direct secant formulation for the reinforced and prestressed concrete frame analysis", Studi e Ricerche, 16, Scuola di Specializzazione in Costruzioni in C.A., Politecnico di Milano (in Italian).
  4. Carmeliet, J. and de Borst, R., (1995), "Stochastic approaches for damage evolution in standard and non standard continua", Int. J. of Solids and Structures, 32(8/9), 1149-1160. https://doi.org/10.1016/0020-7683(94)00182-V
  5. Crisfield, M.A., (1982), "Local instabilities in the non-linear analysis of reinforced concrete beams and slabs", Proc. Instn. Civ. Engrs, Part 2, 73, 135-145. https://doi.org/10.1680/iicep.1982.1876
  6. de Borst, R., (1987), "Computation of post-bifurcation and post-failure behaviour of strain-softening solids", Computers & Structures, 25(2), 211-224. https://doi.org/10.1016/0045-7949(87)90144-1
  7. de Borst, R., Carmeliet, J., Pamin, J. and Sluys, L.J., (1994), "New horizons in computer analysis of damage and fracture in quasi-brittle solids", Fracture and Damage in Quasibrittle Structures, edited by Z.P. Bazant, M. Jirasek and J. Mazars, E&FN.
  8. Feenstra, P.H. and de Borst, R., (1993), "Aspects of robust computational modeling for plain and reinforced concrete", HERON, 38(4).
  9. Ghosh, S.K. and Cohn, M.Z. (1972), "Non-linear analysis of strain softening structures", Inelasticity and Non-Linearity in Structural Concrete, University of Waterloo Press.
  10. Gilbert, R.I. and Warner, R.F. (1978), "Tension stiffening in reinforced concrete slabs", J. of Struct. Eng. ASCE, 104(ST12), 1885-1900.
  11. Kim, J.K. and Lee, T.G. (1992), "Non-linear analysis of reinforced concrete beams with softening", Computers & Structures, 44(3), 567-573. https://doi.org/10.1016/0045-7949(92)90389-H
  12. Malerba, P.G. and Bontempi, F., (1990), "Material and geometrical non-linear analysis of reinforced concrete frames", EPMESC III, Int. Conf. on Education, Practice and Promotion of Comput. Methods in Engineering using Small Computers, Macao, August, Vol. I, 121-132.
  13. Ottosen, N.S., (1986), "Thermodynamic consequences of strain softening in tension", J. of Eng. Mech. ASCE, 112(11), 1152-1164. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:11(1152)
  14. Planas, J., Elices, M. and Guinea, G.V., (1993), "Cohesive cracks versus non-local models:closing the gap", Int. J. of Fracture, No.63, 173-187.
  15. Ramm, E., (1981), "Strategies for tracing the non-linear response near limit points", Non-linear Finite Element Analysis in Structural Mechanics, W. Wunderlich, E. Stein, K.J. Bathe Edirots, Springer Verlag, Berlin.
  16. Seydel, R. (1984), "A continuation algorithm with step control", International Series of Numerical Mathematics, 70, Birkhauser Verlag Basel.
  17. Seydel, R. (1988), From Equilibrium to Chaos: Practical bifurcation and stability analysis, Elsevier Science Publishing Co. Inc., N.Y.
  18. Troger, H. and Steindl, A. (1991), Non-linear Stability and Bifurcation Theory, Springer-Verlag, Wien.
  19. Wagner, W. and Wriggers, P. (1988), "A simple method for the calculation of postcritical branches", Eng. Computations, 5, June, 103-109. https://doi.org/10.1108/eb023727

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