Computers and Concrete

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Closed form ultimate strength of multi-rectangle reinforced concrete sections under axial load and biaxial bending

  • da Silva, V. Dias (Department of Civil Engineering, University of Coimbra, Polo II-Pinhal de Marrocos) ;
  • Barros, M.H.F.M. (Department of Civil Engineering, University of Coimbra, Polo II-Pinhal de Marrocos) ;
  • Julio, E.N.B.S. (Department of Civil Engineering, University of Coimbra, Polo II-Pinhal de Marrocos) ;
  • Ferreira, C.C. (Department of Civil Engineering, University of Coimbra, Polo II-Pinhal de Marrocos)
  • Received : 2006.03.22
  • Accepted : 2009.11.24
  • Published : 2009.12.25
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Abstract

The analysis of prismatic members made of reinforced concrete under inclined bending, especially the computation of ultimate loads, is a pronounced non-linear problem which is frequently solved by discretizing the stress distribution in the cross-section using interpolation functions. In the approach described in the present contribution the exact analytical stress distribution is used instead. The obtained expressions are integrated by means of a symbolic manipulation package and automatically converted to optimized Fortran code. The direct problem-computation of ultimate internal forces given the position of the neutral axis-is first described. Subsequently, two kinds of inverse problem are treated: the computation of rupture envelops and the dimensioning of reinforcement, given design internal forces. An iterative Newton-Raphson procedure is used. Examples are presented.

Keywords

References

  1. Alfano, G., Marmo, F. and Rosati, L. (2007), "An unconditionally convergent algorithm for the evaluation of the ultimate limit state of rc sections subject to axial force and biaxial bending", Int. J. Numer. Meth. Eng., 72(8), 924-963. https://doi.org/10.1002/nme.2033
  2. Alfano, G., Marmo, F. and Rosati, L. (2008), "Enhanced solution strategies for the ultimate strength analysis of composite steel-concrete sections subject to axial force and biaxial bending", Comput. Method. Appl. M., 197(9-12), 1033-1055. https://doi.org/10.1016/j.cma.2007.10.001
  3. Bonet, J.L., Romero, M.L., Miguel, P.F. and Fernandez, M.A. (2004), "A fast stress integration algorithm for reinforced concrete sections with axial loads and biaxial bending", Comput. Struct., 82(2-3), 213-225. https://doi.org/10.1016/j.compstruc.2003.10.009
  4. Brondum, T. (1987), "Ultimate flexural capacity of cracked polygonal concrete sections with circular holes under biaxial bending", ACI Concrete Int., 84(3), 212-215.
  5. Charalampakisa, A.E. and Koumousis, V.K. (2008), "Ultimate strength analysis of composite sections under biaxial bending and axial load", Comput. Method. Appl. M., 39(11), 923-936.
  6. Comite Euro-internacional du beton (1991), "CEB-FIB Model Code 1990", C. E. B. Bulletin No. 203-204, y205.
  7. De Vivo, L. and Rosati, L. (1998). "Ultimate strength analysis of reinforced concrete sections subject to axial force and biaxial bending", Comput. Method. Appl. M., 166, 261-287. https://doi.org/10.1016/S0045-7825(98)00091-7
  8. European Committee for Standardization: Eurocode 2 (2004), "Design of concrete structures-Part 1: General rules and rules for buildings", EN 1992-1-1, Brussels, December.
  9. Fafitis, A. (2001), "Interaction surfaces of reinforced-concrete sections in biaxial bending", J. Struct. Eng-ASCE, 127(7), 840-846. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:7(840)
  10. Julio, E.S., Branco, F. and Silva, V.D. (2005), "RC Jacketing interface inuence on monotonic loading response", ACI Struct. J., 102(2), 252-257.
  11. Maple 8, http://www.maplesoft.com
  12. Barros, M.H.F.M., Barros, A.F.M. and Ferreira, C.C. (2004), "Closed form solution of optimal design of rectangular reinforced concrete sections", Eng. Computation, 21(7), 761-776. https://doi.org/10.1108/02644400410565298
  13. Barros, M.H.F.M., Ferreira, C.C. and Barros, A.F.M. (2005), "Closed form interaction surfaces for nonlinear design codes of reinforced concrete columns with model code 90", Comput. Concrete, 2(1), 55-77. https://doi.org/10.12989/cac.2005.2.1.055
  14. Rodriguez, J.A. and Aristizabal-Ochoa, J.D. (1999), "Biaxial Interaction Diagrams for Short RC Columns of Any Cross Section", J. Struct. Eng-ASCE, 125(6), 672-683. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:6(672)
  15. Sfakianakis, M.G. (2002), "Biaxial bending with axial force of reinforced, composite and repaired concrete sections of arbitrary shape by fiber model and computer graphics", Adv. Eng. Softw., 33(4), 227-242. https://doi.org/10.1016/S0965-9978(02)00002-9
  16. Yen, J.R. (1991), "Quasi-Newton method for reinforced concrete column analysis and design", J. Struct. Eng-ASCE, 117(3), 657-666. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:3(657)
  17. Zupan, D. and Saje, M. (2005) "Analytical integration of stress field and tangent material moduli over concrete cross-sections", Comput. Struct. 83(28-30), 2368-2380. https://doi.org/10.1016/j.compstruc.2005.03.030

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