KSCE Journal of Civil Engineering

, Volume 15, Issue 1, pp 131–144 | Cite as

Curvature ductility of RC sections based on eurocode: Analytical procedure

  • Srinivasan Chandrasekaran
  • Luciano Nunziante
  • Giorgio Serino
  • Federico Carannante
Article
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Accepted:

Abstract

Correct estimate of curvature ductility of reinforced concrete members has always been an attractive subject of study as it engenders a reliable estimate of capacity of buildings under seismic loads. The majority of the building stock needs structural assessment to certify their safety under revised seismic loads by new codes. Structural assessment of existing buildings, by employing nonlinear analyses tools like pushover, needs an accurate input of moment-curvature relationship for reliable results. In the present study, nonlinear characteristics of constitutive materials are mathematically modelled according to Eurocode, currently in prevalence and analytical predictions of curvature ductility of reinforced concrete sections are presented. Relationships, in explicit form, to estimate the moment-curvature response are proposed, leading to closed form solutions after their verification with those obtained from numerical procedures. The purpose is to estimate curvature ductility under service loads in a simpler closed form manner. The influence of longitudinal tensile and compression steel reinforcement ratios on curvature ductility is also examined and discussed. The spread sheet program used to estimate the moment-curvature relationship, after simplifying the complexities involved in such estimate, predicts in good agreement with the proposed analytical expressions. Avoiding somewhat tedious hand calculations and approximations required in conventional iterative design procedures, the proposed estimate of curvature ductility avoids errors and potentially unsafe design.

Keywords

analytical solutions concrete curvature ductility elasto plastic reinforced concrete seismic structures yield 
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References

  1. Agarwal, P. and Shrikhande, M. (2006). Earthquake resistant design of structures, Prentice Hall of India Pvt. Ltd, New Delhi. IndiaGoogle Scholar
  2. Akkar, S. and Metin, A. (2007). “Assessment of improved nonlinear static procedures in FEMA 440.” J. Struct. Engrg., ASCE, Vol. 133, No. 9, pp. 1237–1246.CrossRefGoogle Scholar
  3. ATC (2005). Improvements of nonlinear static seismic analysis procedures, Report No. FEMA 440, Washington, D.C.Google Scholar
  4. Building Seismic Safety Council (BSSC) (2003). NEHRP recommended provisions for seismic regulations for new buildings and other structures, Report. No. FEMA 450, Washington, D.C.Google Scholar
  5. Carreira, D. and Chu, K. H. (1986). “The moment-curvature relationship of RC members.” ACI. J., Vol. 83, pp. 191–198.Google Scholar
  6. Challamel, N. and Hjiaj, M. (2005). “Non-local behaviour of plastic softening beams.” J. Acta Mechanics, Vol. 178, pp. 125–146.MATHCrossRefGoogle Scholar
  7. Chandrasekaran, S. and Anubhab, R. (2006). “Seismic evaluation of multi storey RC frames using modal push over analysis.” J. Nonlinear Dyn, Vol. 43, No. 4, pp. 329–342.MATHCrossRefGoogle Scholar
  8. Chen, W. F. (1994a). Constitutive equations for engineering materials, Vol.1: Elasticity and modelling, Elsevier Publications.Google Scholar
  9. Chen, W. F. (1994b). Constitutive equations for engineering materials, Vol.2: Plasticity and modelling, Elsevier Publications.Google Scholar
  10. D.M.9 gennaio 1996 (1996). Norme tecniche per il calcolo, L’esecuzione ed il Collaudo Delle Strutture in Cemento Armato, Normale e Pre-Compresso e Per le Strutture Metalliche (in Italian).Google Scholar
  11. Fan, S.-C. and Wang, F. (2002). “A new strength criterion for concrete.” ACI. J. Struct., Vol. 99, pp. 317–326.Google Scholar
  12. Huang, C. H., Tuan, Y. A., and Hsu, R. Y. (2006). “Nonlinear pushover analysis of in-filled concrete frames.” J. Eq. Engrg. & Engrg. Vib, Vol. 5, No. 2, pp. 245–255.CrossRefGoogle Scholar
  13. IS:456-2000 (2000). Plain and reinforced concrete — Code of Practice, Fourth revision. Bureau of Indian Standards, New Delhi, India.Google Scholar
  14. IS:13920-2003 (2003). Ductile detailing for reinforced concrete structures subjected to seismic forces, Bureau of Indian Standards, New Delhi, India.Google Scholar
  15. Jirasek, M. and Bazant, Z. P. (2002). Inelastic analysis of structures, Wiley, New York.Google Scholar
  16. Ko, M. Y., Kim, S. W., and Kim, J. K. (2001). “Experimental study on the plastic rotation capacity of reinforced high strength beams.” J. Mat. & Struct., Vol. 34, No. 5, pp. 302–311.CrossRefGoogle Scholar
  17. Lopes, M. R. and Bernardo, L. F. A. (2003). “Plastic rotation capacity of high-strength concrete beams.” J. Mat. & Struct., Vol. 36, No. 1, pp. 22–31.CrossRefGoogle Scholar
  18. Luciano Nunziante and Raffaele Ocone (1988). Limit design of frames subjected to seismic loads, CUEN Publications (Cooperativa Universitaria Editrice Napoletana), Italy.Google Scholar
  19. Mo, Y. L. (1992). “Investigation of reinforced concrete frame behaviour: Theory and tests.” Mag. of Concrete Research, Vol. 44, No. 160, pp. 163–173.CrossRefGoogle Scholar
  20. Norme Tecniche per le Costruzioni — D.M. 14 settembre, 2005 (in Italian).Google Scholar
  21. Nunziante, L., Gambarotta, L., and Tralli, A. (2007). Scienza della Costruzioni, McGraw-Hill (in italian).Google Scholar
  22. Ordinanza del Presidente del Consiglio dei Ministri del 20 Marzo (2003). Primi elementi in materia di criteri generali per la classificazione sismica del territorio nazionale e di normative tecniche per le costruzioni in zona sismica (in Italian).Google Scholar
  23. Ordinanza 3316: Correzioni e Modifiche All’ordinanza 3274 (2005). Modifiche ed integrazioni all’ordinanza del Presidente del Consiglio dei Ministri n. 3274 del 20 Marzo 2003 (in Italian).Google Scholar
  24. Park, R. and Paulay, T. (1975). Reinforced concrete structures, John Wiley & Sons, Inc.Google Scholar
  25. Paulay, T. and Priestley, M. J. N. (1992). Seismic design of RC and masonry buildings, John Wiley & Sons, NY, USA.CrossRefGoogle Scholar
  26. Pfrang, E. O., Siess, C. P., and Sozen, M. A. (1964). “Load-momentcurvature characteristics of RC cross-sections.” ACI J., Vol. 61, No. 7, pp. 763–778.Google Scholar
  27. Pisanty, A. and Regan, P. E. (1998). “Ductility requirements for redistribution of moments in RC elements and a possible size effect.” J. Mat. & Struct., Vol. 31, No. 8, pp. 530–535.CrossRefGoogle Scholar
  28. Pisanty, A. and Regan, P. E. (1993). “Redistribution of moments and the possible demand for ductility.” CEB Bulletin d’ Information, Vol. 218, pp. 149–162.Google Scholar
  29. Sankarasubramanian, G. and Rajasekaran, S. (1996). “Constitutive modelling of concrete using a new failure criterion.” J. Comp. & Struct., Vol. 58, pp. 1003–1014.MATHCrossRefGoogle Scholar
  30. UNI ENV 1991-1. Eurocodice 1 (1991a) Basi di calcolo ed azioni sulle strutture, Parte 1: Basi di Calcolo (in Italian).Google Scholar
  31. UNI ENV 1991-2-1. Eurocodice 1 (1991b) Basi di calcolo ed azioni sulle strutture, Parte 2-1: Azioni Sulle Strutture — Massa Volumica, Pesi Propri e Carichi Imposti (in Italian).Google Scholar
  32. Wood, R. H. (1968). “Some controversial and curious developments in plastic theory of structures.” In: Engg Plasticity, Heyman, J., Leckie, F. A. (eds.), Cambridge University Press, Cambridge, pp. 665–691.Google Scholar

Copyright information

© Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Srinivasan Chandrasekaran
    • 1
  • Luciano Nunziante
    • 2
  • Giorgio Serino
    • 2
  • Federico Carannante
    • 2
  1. 1.Dept. of Ocean EngineeringIndian Institute of Technology MadrasChennaiIndia
  2. 2.Dept. of Structural EngineeringUniversity of Naples Federico IINaplesItaly

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