Materials and Structures

, Volume 49, Issue 6, pp 2223–2236 | Cite as

End cover separation in RC beams strengthened in flexure with bonded FRP reinforcement: simplified finite element approach

Original Article


The flexural performance of RC beams can be improved using externally bonded (EB) or near-surface mounted (NSM) fiber-reinforced polymer (FRP) reinforcement. One of the commonly observed failure modes of such FRP-strengthened RC beams is the end cover separation failure mode which involves the detachment of the bonded FRP reinforcement together with the cover concrete along the level of the longitudinal steel reinforcement. This paper presents a simplified 2-D (plane stress) nonlinear finite element (FE) approach for end cover separation failure in RC beams strengthened in flexure with either EB or NSM FRP reinforcement. In this simplified FE approach, only the part of the RC beam between the two cracks near the critical end of the FRP reinforcement is considered. This approach leads to the determination of the FRP debonding strain at the cracked section in the strengthened region adjacent to the crack at the end of the FRP reinforcement, which can then be used to determine the moment acting on this cracked section at debonding failure through conventional section analysis. The validity of the proposed simplified FE approach is demonstrated through comparisons with results from the full 2-D (plane stress) nonlinear FE approach and laboratory tests.


FRP Strengthening Bonded FRP reinforcement RC beams Finite element (FE) analysis Cover separation 



The authors are grateful for the financial support received from the Research Grants Council of the Hong Kong Special Administrative Region (Project No. PolyU 5315/09E) and the National Natural Science Foundation of China (Project No. 51308483). The authors would like to thank Prof Jian-Fei Chen at Queen’s University Belfast for his helpful comments on this work.


  1. 1.
    Teng JG, Chen JF, Smith ST, Lam L (2002) FRP-strengthened RC structures. Wiley, West SussexGoogle Scholar
  2. 2.
    Hollaway LC, Teng JG (eds) (2008) Strengthening and rehabilitation of civil infrastructures using FRP composites. Woodhead, CambridgeGoogle Scholar
  3. 3.
    De Lorenzis L, Teng JG (2007) Near-surface mounted FRP reinforcement: an emerging technique for strengthening structures. Composites B 38(2):119–143CrossRefGoogle Scholar
  4. 4.
    Zhang SS, Teng JG, Yu T (2014) Bond strength model for CFRP strips near-surface mounted to concrete. ASCE J Compos Constr 18(3):A4014003Google Scholar
  5. 5.
    Teng JG, Chen JF (2009) Mechanics of debonding in FRP-plated RC beams. Proc Inst Civil Eng Struct Build 162(5):335–345CrossRefGoogle Scholar
  6. 6.
    Smith ST, Teng JG (2001) Interfacial stresses in plated beams. Eng Struct 23(7):857–871CrossRefGoogle Scholar
  7. 7.
    Zhang SS, Teng JG (2013) Interaction forces in RC beams strengthened with near-surface mounted rectangular bars and strips. Composites B 45(1):697–709CrossRefGoogle Scholar
  8. 8.
    Zhang SS, Teng JG (2014) Finite element analysis of end cover separation in RC beams strengthened in flexure with FRP. Eng Struct 75:550–560CrossRefGoogle Scholar
  9. 9.
    Teng JG, De Lorenzis L, Wang B, Rong L, Wong TN, Lam L (2006) Debonding failures of RC beams strengthened with near-surface mounted CFRP strips. ASCE J Compos Constr 10(2):92–105CrossRefGoogle Scholar
  10. 10.
    Barros JAO, Dias SJE, Lima JLT (2007) Efficacy of CFRP-based techniques for the flexural and shear strengthening of concrete beams. Cem Concr Compos 29(3):203–217CrossRefGoogle Scholar
  11. 11.
    Zhang S, Raoof M, Wood LA (1995) Prediction of peeling failure of reinforced concrete beams with externally bonded steel plates. Proc Inst Civil Eng Struct Build 110(3):257–268CrossRefGoogle Scholar
  12. 12.
    Raoof M, Zhang S (1997) An insight into the structural behaviour of reinforced concrete beams with externally bonded plates. Proc Inst Civil Eng Struct Build 122(4):477–492CrossRefGoogle Scholar
  13. 13.
    Wang CY, Ling FS (1998) Prediction model for the debonding failure of cracked RC beams with externally bonded FRP sheets. Proceedings of 2nd international conference of composites in infrastructure (ICCI). Department of Civil Engineering and Engineering Mechanics, University of Arizona, Arizona, pp 548–562Google Scholar
  14. 14.
    Raoof M, Hassanen MAH (2000) Peeling failure of reinforced concrete beams with fibre-reinforced plastic or steel plates glued to their soffits. Proc Inst Civil Eng Struct Build 140(3):291–305CrossRefGoogle Scholar
  15. 15.
    Gao B, Leung CKY, Kim JK (2005) Prediction of concrete cover separation failure for RC beams strengthened with CFRP strips. Eng Struct 27(2):177–189CrossRefGoogle Scholar
  16. 16.
    De Lorenzis L, Nanni A (2003) Proposed design procedure of NSM FRP reinforcement for strengthening of RC beams. Proceedings of 6th international symposium on FRP reinforcement for concrete structures. World Scientific, New Jersey, pp 1455–1464CrossRefGoogle Scholar
  17. 17.
    Al-Mahmoud F, Castel A, Francois R, Tourneur C (2010) RC beams strengthened with NSM CFRP rods and modeling of peeling-off failure. Compos Struct 92(8):1920–1930CrossRefGoogle Scholar
  18. 18.
    Smith ST, Teng JG (2002) FRP-strengthened RC beams. II: assessment of debonding strength models. Eng Struct 24(4):397–417CrossRefGoogle Scholar
  19. 19.
    Arduini M, Tommaso AD, Nanni A (1997) Brittle failure in FRP plate and sheet bonded beams. ACI Struct J 94(4):363–370Google Scholar
  20. 20.
    Rahimi H, Hutchinson A (2001) Concrete beams strengthened with externally bonded FRP plates. ASCE J Compos Constr 5(1):44–56CrossRefGoogle Scholar
  21. 21.
    Yang ZJ, Chen JF, Proverbs D (2003) Finite element modelling of concrete cover separation failure in FRP plated RC beams. Constr Build Mater 17(1):3–13CrossRefGoogle Scholar
  22. 22.
    Camata G, Spacone E, Zarnic R (2007) Experimental and nonlinear finite element studies of RC beams strengthened with FRP plates. Composites B 38(2):277–288CrossRefGoogle Scholar
  23. 23.
    MSC.MARC (2005) User’s manual. MSC. Software Corporation, Santa AnaGoogle Scholar
  24. 24.
    Bazant ZP, Oh BH (1983) Crack band theory for fracture of concrete. Mater Struct 16(93):155–177Google Scholar
  25. 25.
    CEB-FIP (1993) CEB-FIP Model Code 1990. Thomas Telford, LondonGoogle Scholar
  26. 26.
    Hordijk DA (1991) Local approach to fatigue of concrete. PhD thesis, Delft University of TechnologyGoogle Scholar
  27. 27.
    Okamura H, Maekawa K (1991) Nonlinear analysis and constitutive models of reinforced concrete. Gihodo-Shuppan, TokyoGoogle Scholar
  28. 28.
    Teng JG, Zhang SS, Dai JG, Chen JF (2013) Three-dimensional meso-scale finite element modeling of bonded joints between a near-surface mounted FRP strip and concrete. Comput Struct 117:105–117CrossRefGoogle Scholar
  29. 29.
    Buyukozturk O (1977) Nonlinear analysis of reinforced concrete structures. Comput Struct 7:149–156CrossRefGoogle Scholar
  30. 30.
    Elwi AA, Murray DW (1979) A 3D hypoelastic concrete constitutive relationship. ASCE J Eng Mech 105(4):623–641Google Scholar
  31. 31.
    Saenz LP (1964) Discussion of equation for the stress–strain curve of concrete, by Desayi and Krishnan. J Am Concr Inst 61:1229–1235Google Scholar
  32. 32.
    Lu XZ, Teng JG, Ye LP, Jiang JJ (2005) Bond–slip models for FRP sheets/plates bonded to concrete. Eng Struct 27(6):920–937CrossRefGoogle Scholar
  33. 33.
    Zhang SS, Teng JG, Yu T (2013) Bond–slip model for CFRP strips near-surface mounted to concrete. Eng Struct 56:945–953CrossRefGoogle Scholar
  34. 34.
    Ahmed O, van Gemert D, Vanderwalle L (2001) Improved model for plate end shear of CFRP strengthened RC beams. Cem Concr Compos 23(1):3–19CrossRefGoogle Scholar
  35. 35.
    Maalej M, Bian Y (2001) Interfacial shear stress concentration in FRP-strengthened beams. Compos Struct 54(4):417–426CrossRefGoogle Scholar
  36. 36.
    Smith ST, Teng JG (2003) Shear-bending interaction in debonding failures of FRP-plated RC beams. Adv Struct Eng 6(3):183–199CrossRefGoogle Scholar
  37. 37.
    Yao J, Teng JG (2007) Plate end debonding in FRP-plated RC beams—I: experiments. Eng Struct 29(10):2457–2471CrossRefGoogle Scholar
  38. 38.
    BS 8110 (1997) Structural use of concrete—part 1: code of practice for design and construction. British Standards Institute, LondonGoogle Scholar

Copyright information

© RILEM 2015

Authors and Affiliations

  1. 1.School of Civil, Mining & Environmental Engineering, Faculty of Engineering & Information SciencesUniversity of WollongongWollongongAustralia
  2. 2.Department of Civil and Environmental EngineeringThe Hong Kong Polytechnic UniversityHong KongChina

Personalised recommendations