Skip to main content
SpringerLink
Log in

Comparison of numerical behaviors of FRP reinforced concrete beams using three smeared crack models

  • Original Article
  • Published:
Materials and Structures Aims and scope Submit manuscript

Abstract

The numerical behaviors of fiber reinforced polymer (FRP) bar reinforced concrete beams using three non-linear finite element models are compared with the recorded data. First approach is based on strain decomposition into elastic and crack strain and is capable of simulating multiple non-orthogonal cracks. The remaining two approaches are based on the total strain crack model and include a rotating crack model (RCM) and an orthogonal fixed crack model (FCM). The analysis is carried out with the help of 2D-isoparametric plane-stress elements. Compression softening and tension stiffening effects of cracked concrete are considered. Tension reinforcement consists of either steel or FRP bars. The accuracy of the models has been discussed with reference to the authors’ tests as well as various studies reported in the literature. Both RCM and orthogonal FCM models showed good agreement with the recorded data which was also found consistent with every type of FRP bar.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Abbreviations

A f :

Area of FRP bars

b :

Width of section

h :

Height of section

E cr :

Crack normal stiffness

f c :

Ultimate compressive strength

f ct :

Concrete tensile strength

f cu :

Cube compressive strength

σ:

Stress corresponding to strain ε

εcon :

Elastic concrete strain

εcr :

Crack strain

εt :

Ultimate tensile strain corresponding to f ct

εo :

Ultimate compressive strain corresponding to f c

μ:

Factor to take tension stiffening of concrete into account. It gradually decreases from 1 to 0 as a function of crack normal strain (ε cr n ) [Fig. 2]

References

  1. American Concrete Institute (ACI) (2006) Guide for the design and construction of concrete reinforced with FRP bars (ACI 440.1R-06), Detroit, Michigan

  2. Canadian Standards Association (CSA) (2002) Design and construction of building components with fiber reinforced polymers, Toronto, Ontario

  3. Japan Society of Civil Engineers (JSCE) (1997) Recommendation for design and construction for reinforced concrete structures using continuous fiber reinforcing materials, Concrete Engineering Series 23, Tokyo

  4. Fanning P (2001) Nonlinear models of reinforced and post-tensioned concrete beams. Electron J Struct Eng 2:111–119

    Google Scholar 

  5. Al-Sunna RAS (2006). Deflection behaviour of FRP reinforced concrete flexural members. PhD thesis, University of Sheffield, UK

  6. Rafi MM, Nadjai A (2009) Evaluation of ACI deflection model for FRP reinforced concrete beams and suggested modification. ACI Struct J 106(6):762–771

    Google Scholar 

  7. Rafi MM, Nadjai A (2011) A suggested model for European code to calculate deflection of FRP reinforced concrete beams. Mag Concr Res 63(1). doi:10.1680/macr.2011.63.1.1

  8. TNO Building and Construction Research (2005) DIANA finite element analysis, User’s Manual release 9, Delft

  9. Rafi MM, Nadjai A, Ali F, Talamona D (2008) Aspects of behaviour of CFRP reinforced concrete beams in bending. Constr Build Mater 22(3):277–285

    Article  Google Scholar 

  10. Rashid YR (1698) Analysis of prestressed concrete pressure vessels. Nucl Eng Des 7:334–344

    Article  Google Scholar 

  11. de Borst R, Nauta P (1985) Non-orthogonal cracks in a smeared finite element model. Eng Comput 2:35–46

    Article  Google Scholar 

  12. de Borst R (1986) Computational aspects of smeared crack analysis. In: Hinton E, Owen R (Eds) Computational modelling of reinforced concrete structures, Swansea. Pineridge Press Publishers, pp 44–83

  13. Vecchio FJ, Collins MP (1991) The modified compression-field theory for reinforced concrete elements subjected to shear. ACI Struct J 83(22):219–231

    Google Scholar 

  14. Rafi MM (2010) Fire performance of FRP reinforced concrete beams: experimental and theoretical studies. Lambert Academic Publishing, Germany

  15. Achillides Z, Pilakoutas K, Waldron P (1997) Modelling of FRP rebar bond behaviour. In: Proceedings of the 3rd international symposium on non-metallic (FRP) reinforcement for concrete structures, Sapporo, Japan, pp 423–430

  16. Achillides Z, Pilakoutas K (2002) Analytical approach to the bond behaviour of FRP bars in concrete. In: Proceedings of the 3rd international symposium on bond in concrete—from research to standards, Budapest, pp 700–707

  17. Achillides Z, Pilakoutas K (2006) FE modelling of bond interaction of FRP bars to concrete. Struct Concr 7(1):7–16

    Article  Google Scholar 

  18. Adam JM, Ivorra S, Pallarés FJ, Giménez E, Calderón PA (2008) Column-joint assembly in RC columns strengthened by steel caging. Proc ICE Struct Build 161(6):337–348

    Google Scholar 

  19. Irannejad HR, Khoei AR (2004) FE analysis of bond for smooth FRP rods embedded in concrete. In: Proceedings of the XXI International Congress of Theoretical and Applied Mechanics, Warsaw, Poland

  20. Kawakami M, Ito T (2003) Nonlinear finite element analysis of prestressed concrete members using ADINA. Comput Struct 81:727–734

    Article  Google Scholar 

  21. Kaewunruen S, Remennikov AM (2006) Nonlinear finite element modelling of railway prestressed concrete sleeper. In: Proceedings of the Tenth East Asia-pacific Conference on Structural Engineering & Construction (EASEC-10), Bangkok, Thailand, 2006

  22. Kotsovos M, Perry S (1986) Behaviour of concrete subjected to passive confinement. Materiaux et Construction 19(112):259–264

    Google Scholar 

  23. Rericha P (1991) Layer model of bending-shear failure in RC plates and beams. J Compos Constr ASCE 117(10):2865–2883

    Google Scholar 

  24. Wolanski AJ (2004) Flexural behaviour of reinforced and prestressed concrete beams using finite element analysis. Faculty of the Graduate School, Marquette University, Milwaukee, Thesis for the Degree of Master of Science

  25. Adam JM, Ivorra S, Pallarés FJ, Giménez E, Calderón PA (2009) Axially loaded RC columns strengthened by steel caging: finite element modelling. Construct Build Mater 23(6):2265–2276

    Article  Google Scholar 

  26. Adam JM, Ivorra S, Pallarés FJ, Giménez E, Calderón PA (2009b) Axially loaded RC columns strengthened by steel caging. Proc ICE Struct Build 162(3):199–208

    Google Scholar 

  27. Ferreira AJM, Camanho PP, Marques AT, Fernandes AA (2001) Modelling of concrete beams reinforced with FRP re-bars. Compos Struct 53:107–116

    Article  Google Scholar 

  28. Polak MA, Vecchio FJ (1993) Nonlinear analysis of reinforced-concrete shells. J Struct Eng ASCE 119(12):3439–3462

    Article  Google Scholar 

  29. Polak MA (1998) Modeling punching shear of reinforced concrete slabs using layered finite elements. ACI Struct J 95(1):71–80

    MathSciNet  Google Scholar 

  30. Barbosa AF, Ribeiro GO (1998) Analysis of reinforced concrete structures using ANSYS nonlinear concrete model. In: Idelshon S, Onate E, Dvorkin E (eds) Computational mechanics: new trends and applications. CIMNE, Barcelona, Spain

    Google Scholar 

  31. Erduran E, Yakut A (2004) Drift based damage functions for reinforced concrete columns. Comput Struct 82:121–130

    Article  Google Scholar 

  32. Vecchio FJ, Selby RG (1991) Toward compression-field analysis of reinforced concrete solids. J Struct Eng ASCE 117(6):1740–1758

    Article  Google Scholar 

  33. Cornelissen HAW, Hordijk DA, Reinhardt HW (1986) Experimental determination of crack softening characteristics of normal-weight and lightweight concrete. Heron 31(2):45–56

    Google Scholar 

  34. Thorenfeldt E, Tomaszewicz A, Jensen JJ (1987) Mechanical properties of high-strength concrete and application in design. In: Proceedings of the Symposium on Utilization of High-Strength Concrete, Tapir, Trondheim, pp 149–159

  35. British Standards Institution (CP110) (1972) Code of practice for structure use of use of concrete, London

  36. Eurocode 2 (1992) Design of concrete structures, Part1-1: general rules and rules for building, Brussels

  37. American Concrete Institute (ACI) (2002) Building code requirements for structural concrete (ACI 318R-02), Detroit, Michigan

  38. Wittmann FH (2002) Crack formation and fracture energy of normal and high strength concrete. Sadhana 27(4):413–423

    Article  Google Scholar 

  39. Zhao W, Pilakoutas K, Waldron P (1997) FRP reinforced concrete: calculations for deflections. In: Proceedings of the 3rd international symposium on non-metallic (FRP) reinforcement for concrete structures, Sapporo, Japan, pp 511–518

  40. Powasusorn S, Bracci MB (2006) Behavior of reinforced concrete members prone to shear deformations: part I—effect of confinement. ACI Struct J 103(5):736–746

    Google Scholar 

  41. Powasusorn S, Bracci MB (2006) Behavior of reinforced concrete members prone to shear deformations: part II—effect of interfacial bond stress-slip. ACI Struct J 103(5):747–753

    Google Scholar 

  42. Pecce G, Manfredi G, Cosenza E (2000) Experimental response and code models of GFRP RC beams in bending. J Compos Constr ASCE 4(4):182–190

    Google Scholar 

  43. Maji A, Orozco AL (2005) Prediction of bond failure and deflection of carbon fiber-reinforced plastic concrete beams. Exp Mech 45(1):35–41

    Article  Google Scholar 

  44. Rashid MA, Mansur MA, Paramasivam P (2005) Behavior of aramid fiber-reinforced polymer reinforced high strength concrete beams under bending. J Compos Constr ASCE 9(2):117–127

    Google Scholar 

Download references

Acknowledgment

The authors wish to acknowledge the support provided for this research by the School of Built Environment, University of Ulster.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, NED University of Engineering & Technology, Karachi, 75270, Pakistan

    Muhammad Masood Rafi

  2. FireSERT, University of Ulster at Jordanstown, Shore Road, Newtownabbey, BT37 0QB, UK

    Ali Nadjai

Authors
  1. Muhammad Masood Rafi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Nadjai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Masood Rafi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rafi, M.M., Nadjai, A. Comparison of numerical behaviors of FRP reinforced concrete beams using three smeared crack models. Mater Struct 45, 93–106 (2012). https://doi.org/10.1617/s11527-011-9753-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1617/s11527-011-9753-6

Keywords

Search

Navigation