Seismic damage analysis including inelastic shear–flexure interaction

  • Panagiotis E. Mergos
  • Andreas J. Kappos
Original Research Paper


The paper focusses on seismic damage analysis of reinforced concrete (R/C) members, accounting for shear–flexure interaction in the inelastic range. A finite element of the beam-column type recently proposed by the writers for the seismic analysis of R/C structures is first briefly described. The analytical model consists of two distributed flexibility sub-elements which interact throughout the analysis to simulate inelastic flexural and shear response. The finite element accounts for shear strength degradation with inelastic curvature demand, as well as coupling between inelastic flexural and shear deformations after flexural yielding. Based on this model, a seismic damage index is proposed taking into account both inelastic flexural and shear deformations, as well as their interaction. The finite element and the seismic damage index are used to analyse the response of R/C columns tested under cyclic loading and failing either in shear or in flexure. It is shown that the analytical model and damage index can predict and describe well the hysteretic response of R/C columns with different types of failure.


Reinforced concrete members Distributed flexibility models Shear–flexure interaction Damage indices 


  1. Aboutaha R, Engelhardt D, Jirsa J, Kreger E (1999) Rehabilitation of shear critical concrete columns by use of rectangular steel jackets. ACI Struct J 96(1): 68–77Google Scholar
  2. Cosenza E, Manfredi G, Verderame GA (2006) Fibre model for pushover analysis of underdesigned R/C frames. Comput Struct 84: 904–916CrossRefGoogle Scholar
  3. D’Ambrisi A, Filippou FC (1997) Correlation studies on an R/C frame shaking-table specimen. Earthq Eng Struct Dyn 26: 1021–1040CrossRefGoogle Scholar
  4. Elwood K, Moehle JP (2003) Shake table tests and analytical studies on the gravity load collapse of R/C frames. PEER Report No. 2003/01. University of California, BerkeleyGoogle Scholar
  5. Garstka B, Krätzig W, Stangenberg F (1993) Damage assessment in cyclically loaded reinforced concrete members. Proc Eurodyn 1: 121–128Google Scholar
  6. Kappos AJ (1997) Seismic damage indices for R/C buildings. Prog Struct Eng Mater 1(1): 78–87CrossRefGoogle Scholar
  7. Kappos AJ, Xenos A (1996) A reassessment of ductility and energy-based seismic damage indices for reinforced concrete structures. Proc Eurodyn 2: 965–970Google Scholar
  8. Kowalsky MJ, Priestley MJN (1995) Shear behaviour of lightweight concrete columns under seismic conditions. Report No. SSRP-95/10. University of San Diego, CaliforniaGoogle Scholar
  9. Lee DH, Elnashai AS (2001) Seismic analysis of R/C bridge columns with flexure-shear interaction. J Struct Eng 127(5): 546–553CrossRefGoogle Scholar
  10. Lehman D, Moehle JP (1998) Seismic performance of well confined concrete bridge columns. PEER Report 1998/01. University of California, BerkeleyGoogle Scholar
  11. Lynn A, Moehle JP, Mahin S, Holmes W (1996) Seismic evaluation of existing reinforced concrete building columns. Earthq Spectra 12(4): 715–739CrossRefGoogle Scholar
  12. Marini A, Spacone E (2006) Analysis of reinforced concrete elements including shear effects. ACI Struct J 103(5): 645–655Google Scholar
  13. Mergos PE, Kappos AJ (2008) A distributed shear and flexural flexibility model with shear–flexure interaction for R/C members subjected to seismic loading. Earthq Eng Struct Dyn, published on-line April 4, 2008Google Scholar
  14. Meyer I, Krätzig W, Stangenberg F (1988) Damage prediction in reinforced concrete frames under seismic actions. Eur Earthq Eng 3(1): 9–15Google Scholar
  15. Oesterle RG, Fiorato AE, Aristizabal-Ochoa JD, Corley WG (1980) Hysteretic response of reinforced concrete structural walls. Proceeding of ACISP-63: reinforced concrete structures subjected to wind and earthquake forces, DetroitGoogle Scholar
  16. Ozcebe G, Saatcioglu M (1989) Hysteretic shear model for reinforced concrete members. J Struct Eng 115(1): 132–148CrossRefGoogle Scholar
  17. Papia M, Russo G (1989) Compressive concrete strain at buckling of longitudinal reinforcement. J Struct Eng 115(2): 382–397CrossRefGoogle Scholar
  18. Park R, Paulay T (1975) Reinforced concrete structures. Wiley, New YorkCrossRefGoogle Scholar
  19. Park YJ, Reinhorn AM, Kunnath SK (1987) Inelastic damage analysis of reinforced concrete frame-shear wall structures. Technical Report NCEER 87-0008, State University of New York at BuffaloGoogle Scholar
  20. Petrangeli M, Pinto P, Ciampi V (1999) Fiber element for cyclic bending and shear of R/C structures. I: theory. J Eng Mech 125(9): 994–1001CrossRefGoogle Scholar
  21. Pincheira J, Dotiwala F, Souza J (1999) Seismic analysis of older reinforced Concrete columns. Earthq Spectra 1999(15(2): 245–272CrossRefGoogle Scholar
  22. Priestley MJN, Seible F, Calvi GM (1996) Seismic design and retrofit of bridges. Wiley, New YorkCrossRefGoogle Scholar
  23. Priestley MJN, Verma R, Xiao Y (1994) Seismic shear strength of reinforced concrete columns. J Struct Eng 120(8): 2310–2329CrossRefGoogle Scholar
  24. Ricles JM, Yang YS, Priestley MJN (1998) Modelling nonductile R/C columns for seismic analysis of bridges. J Struct Eng 124(4): 415–425CrossRefGoogle Scholar
  25. Saatcioglu M, Ozcebe G (1989) Response of reinforced concrete columns to simulated seismic loading. ACI Struct J 86(1): 3–12Google Scholar
  26. Sezen H, Moehle JP (2004) Shear strength model for lightly reinforced concrete columns. J Struct Eng 130(11): 1692–1703CrossRefGoogle Scholar
  27. Sivaselvan MV, Reinhorn AM (1999) Hysteretic models for cyclic behaviour of deteriorating inelastic structures. Technical Report MCEER-99-0018, University at Buffalo, State University of New YorkGoogle Scholar
  28. Takayanagi T, Derecho AT, Gorley WG (1979) Analysis of inelastic shear deformation effects in reinforced concrete structural wall systems. Proceeding of nonlinear design of concrete structures, CSCE-ASCE-ACI-CEB international symposium, University of Waterloo, ON, CanadaGoogle Scholar
  29. Thom CV (1983) The Effects of inelastic shear on the seismic response of structures. PhD Thesis, University of Auckland, New ZealandGoogle Scholar
  30. Valles RE, Reinhorn AM, Kunnath SK, Li C, Madan A (1996) IDAR/C2D Version 4.0: a program for the inelastic damage analysis of buildings. Technical Report NCEER-96-0010, University at Buffalo, State University of New YorkGoogle Scholar
  31. Williams M, Villemure I, Sexsmith R (1997) Evaluation of seismic damage indices for concrete elements loaded in combined shear and flexure. ACI Struct J 94(3): 315–322Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Laboratory of Concrete and Masonry Structures, Department of Civil EngineeringAristotle University of ThessalonikiThessalonikiGreece

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