Materials and Structures

, Volume 43, Supplement 1, pp 73–90 | Cite as

Deflections of concrete beams reinforced with FRP bars

Original Article


The aim of this study is to experimentally and theoretically investigate the flexural behavior of concrete beams reinforced with fiber reinforced polymer (FRP) bars. In this research, three types of experiments were made. First, the tensile properties of FRP and steel bars were tested, then the bond-slip behavior between bars and concrete was tested on standard specimens and, in the end, three series of concrete beams reinforced with GFRP, CFRP and steel bars were tested up to failure. The theoretical model for calculating deflections was developed, which included bond-slip behavior of FRP bars. The theoretical results were compared to the test results of beam deflections, as well to deflection results obtained by theoretical models developed by other authors.


Concrete beams FRP bars Bond-slip behavior Cracks Deflections 

List of symbols


Curvature of concrete part of cross section


Curvature of cross section due to FRP reinforcement


Area of tensile FRP reinforcement


Width of concrete beam


Effective depth of the cross section


Distance between tensile reinforcement and tensile edge of the cross section


Modulus of elasticity of FRP reinforcement


Compressive force in concrete


Tensile force in concrete


Tensile force in FRP reinforcement


Compressive force in FRP reinforcement (if applicable)


Depth of the concrete beam


Cracking moment of the concrete member cross section


Design value of the bending moment for which deflection is being calculated (EC2)


Bending moment in cross section at the distance x from beam support


Distance between the neutral axis and the lower edge of cross section in stress state I


Distance between the neutral axis and the upper edge of cross section in stress state I


Lever arm


Distance between tensile reinforcement and compressive force in cross section


Tensile strain of concrete at the reinforcement level


Tensile strain of concrete at the tensile edge of cross section


Tensile strain of concrete at the compressive edge of cross section


Tensile strain of FRP reinforcement


Strain of steel bar at failure


Maximum strain of steel bar


Strain at lower yielding stress


Strain at upper yielding stress


FRP reinforcement ratio (tensile reinforcement)


FRP reinforcement ratio producing balanced strain conditions


Stress of the steel bars with permanent strain of 0.2%


Tensile stress in concrete at tensile edge of cross section


Tensile stress of FRP reinforcement


Stress of steel bar at failure


Maximum stress of steel bar


Lower yielding stress


Upper yielding stress



Special thanks to companies “Armirac” and “Viadukt” for making reinforcement and concrete specimens, to Civil Engineering Institute—Zagreb and the Department for Technical Mechanics of Civil Engineering Faculty at the University of Zagreb for specimens testing. The investigations described herein have been done within the frame of the research project No. 0082203 “Application of non-metal materials in concrete structures” which has been supported by a grant from the Ministry of Science, Education and Sport of the Republic of Croatia. All supports have been gratefully acknowledged.


  1. 1.
    ACI Committee 440 (2006) Guide for the design and construction of concrete reinforced with FRP Bars. 440.1R-06, American Concrete Institute, Farmington Hills, MIGoogle Scholar
  2. 2.
    Benmokrane B, Chaallal O, Masmoudi R (1996) Flexural response of concrete beams reinforced with FRP reinforcing bars. ACI Struct J 93(1):46–55 January–FebruaryGoogle Scholar
  3. 3.
    Faza SS, Ganga Rao HVS (1992) Pre-and post-cracking deflection behavior of concrete beams reinforced with Fibre-reinforced plastic rebars. In: Neale KW, Labossiere P (eds) Proceedings of the first international conference on the use of advanced composite materials in bridges and structures, ACMBS I. Canadian Society for Civil Engineering, Montreal, pp 151–160Google Scholar
  4. 4.
    Alsayed SH, Al-Salloum YA, Almusallam TH (2000) Performance of glass fiber reinforced plastic bars as a reinforcing material for concrete structures. Composites: B 31:555–567CrossRefGoogle Scholar
  5. 5.
    Hall T, Ghali A (2000) Long-term deflection prediction of concrete members reinforced with glass fibre reinforced polymer bars. Can J Civil Eng 27:890–898CrossRefGoogle Scholar
  6. 6.
    Razaqpur AG, Isgor OB (2000) Methods for calculating deflections of FRP reinforced concrete structures. In: Proceeding of the 3rd international conference on advanced composite materials in bridges and structures, August 2000. Ottawa, Canada, pp 371–378Google Scholar
  7. 7.
    Favre R, Charif H (1994) Basic model and simplified calculations of deformations according to the CEB-FIP model code 1990. ACI Struct J 91(2):169–177Google Scholar
  8. 8.
    Branson DE (1968) Design procedures for computing deflections. ACI J 65:730–742 SeptemberGoogle Scholar
  9. 9.
    Hall TS (2000) Deflections of concrete members reinforced with fibre reinforced polymer (FRP) bars. A thesis submitted to the Faculty of Graduate Studies in partial fulfillment of the requirements for the degree of Master of Science, Department of Civil Engineering, Calgary, Alberta, Canada, JanuaryGoogle Scholar
  10. 10.
    Benmokrane B, Zhang B, Laoubi K, Tighiouart B, Lord I (2001) Mechanical and bond properties of new generation of isorod CFRP reinforcing bars for concrete structures. Technical Progress Report, NSERC Research Chair in FRP Reinforcement for Concrete Structures, CanadaGoogle Scholar
  11. 11.
    Castro P, Carino NJ (1998) Tensile and nondestructive testing of FRP bars. J Compos Constr 2(1):17–27CrossRefGoogle Scholar
  12. 12.
    Fib bulletin 10 (2000) Bond of reinforcement in concrete, August, 2000Google Scholar
  13. 13.
    ENV 1992-1-1 (1991) Eurocode 2—design of concrete structures; part 1: general rules and rules for buildings, revised final draft, BrusselsGoogle Scholar
  14. 14.
    Damjanic FB (1983) Reinforced concrete failure prediction under both static and transient conditions. Ph.D. Thesis, Department of Civil Engineering, University College of Swansea, UKGoogle Scholar
  15. 15.
    Tepfers R (1980) Bond and stress along lapped reinforcing bars. Mag Concr Res 32(112):135–142CrossRefGoogle Scholar
  16. 16.
    Soric Z (1987) Bond and bond slip in reinforced masonry structures. Ph.D. Thesis, University of Colorado, Department of Civil, Environmental and Architectural Engineering, Boulder, Colorado, USAGoogle Scholar
  17. 17.
    Manfredi G, Pecce M (1998) A refined R.C. beam element including bond–slip relationship for the analysis of continuous beams. Comput Struct 69(1):53–62MATHCrossRefGoogle Scholar

Copyright information

© RILEM 2010

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringUniversity of ZagrebZagrebCroatia

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