Materials and Structures

, Volume 45, Issue 4, pp 623–636 | Cite as

Design of SFRC structural elements: flexural behaviour prediction

  • Renaud de Montaignac
  • Bruno Massicotte
  • Jean-Philippe Charron
Original Article


Practical steel fibre reinforced concrete (SFRC) applications in load-carrying structural members have yet to gain wide acceptance in design codes. This is partly explained by the lack of a unified design philosophy adapted to this material. A model based on simple and widely accepted assumptions is proposed for the analysis and the design of SFRC members subjected to bending moments. In order to evaluate the accuracy of the analytical model predictions, an extensive experimental program was conducted on 21 rectangular and T-beams of various sizes produced with five different types of SFRC. The contribution of fibres at different loading phases in bending is described in detail. The analytical model accuracy to predict maximum crack opening applicable in service conditions and at the ultimate flexural strength are compared to experimental measurements. Discrepancies observed are related to the dispersion of the material properties and the difference of fibre orientation in beams and characterization specimens. Finally, the proposed design approach is applied to the design of a realistic T-beam subjected to positive and negative bending moments.


Steel fibre reinforced concrete Flexural behaviour Analytical model Characteristic length Fibre orientation Design 

List of symbols


Young modulus


Height of the specimen


Length between support


Reference length (geometric parameter)


Bending moment


Experimental bending moment


Model bending moment


Normal force


Normal load


Compression normal force


Tensile normal force due to FRC


Tensile normal force due to conventional steel reinforcement


Tensile normal force due elastic behaviour of concrete




Crack width


Maximum crack opening for design


Distance between neutral axis and the extreme tensile side of the cross section


Crack depth






Strain at face in compression


Elastic strain


Strain at face in tension


Strain equivalent to a crack opening


Reinforcement strength reduction factor


SFRC strength reduction factor


Crack angle


Reliability coefficient






Post-cracking stress



This project has been financially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Center for Research on Concrete Infrastructures of Quebec (FQRNT—CRIB). Materials were graciously provided by Bekaert, Holcim and Euclid.


  1. 1.
    European Committee for Standardization (2004) Eurocode 2: design of concrete structures—part 1-1: general rules and rules for buildingsGoogle Scholar
  2. 2.
    ACI Committee 318 (2008) Building code and commentary, report ACI 318-08/318R-08. American Concrete Institute, Farmington HillsGoogle Scholar
  3. 3.
    CSA A23.3-04 (2005) Design of concrete structures. Canadian Standard Association, TorontoGoogle Scholar
  4. 4.
    FIB (2010) “Model code 2010” First complete draft. International Federation for Structural Concrete, LausanneGoogle Scholar
  5. 5.
    ACI Committee 544 (2002) Design considerations for steel fiber reinforced concrete, ACI 544.1R-96. American Concrete Institute (ACI), Farmington HillsGoogle Scholar
  6. 6.
    Massicotte B, Filiatrault A, Mossor B, Tremblay S (1999) Compressive strength and ductility of steel fiber reinforced concrete columns. ACI special publication SP-182: structural applications of fiber reinforced concrete, pp 163–180Google Scholar
  7. 7.
    Moffatt K, Massicotte B (2004) Design of continuous SFRC bridge decks for serviceability criteria. In: Proceeding of the sixth RILEM symposium of fibre-reinforced concrete, Varrena, Italia, September 20–22, pp 1173–1182Google Scholar
  8. 8.
    Tran VNG, Bernard ES, Beasley AJ (2005) Constitutive modeling of fiber reinforced shotcrete panels. J Eng Mech 131(5):512–521CrossRefGoogle Scholar
  9. 9.
    RILEM (2002) RILEM TC 162-TDF—tests and design methods for steel fibre reinforced concrete: design of steel fibre reinforced concrete using the σ–w method: principles and applications. Mater Struct 35:262–278CrossRefGoogle Scholar
  10. 10.
    ASTM C 1550 (2008) Standard test method for flexural toughness of fiber-reinforced concrete (using centrally-loaded round panel). ASTM, West ConshohockenGoogle Scholar
  11. 11.
    EN 14651 (2004) Test method for metallic fibre concrete—measuring the flexural tensile strength (limit of proportionality, residual). Varenna, ItalyGoogle Scholar
  12. 12.
    RILEM (2001) RILEM TC 162-TDF—tests and design methods for steel fibre reinforced concrete: uni-axial tension test for steel fibre reinforced concrete. Mater Struct 34:3–6CrossRefGoogle Scholar
  13. 13.
    De Montaignac R, Massicotte B, Charron J-P, Nour A (2011) Design of SFRC structural elements: post-cracking tensile strength measurement. Mater Struct. doi: 10.1617/s11527-011-9784-z
  14. 14.
    Casanova P, Rossi P (1997) Analysis and design of SFRC beams. ACI Struct J 94(5):595–624Google Scholar
  15. 15.
    Zhang J, Stang H (1998) Application of stress crack width relationship in predicting the flexural behavior of fibre-reinforced concrete. J Cem Concr Res 28(3):439–452CrossRefGoogle Scholar
  16. 16.
    Massicotte B (2004) Implementing SFRC design into North American codes: application to a building floor. Invited paper to the International workshop on the advanced in fibre reinforced concrete, Bergamo, Italia, September 24–25, pp 73–80Google Scholar
  17. 17.
    AFGC-SETRA (2002) Ultra high performance fibre-reinforced concretes, interim recommendations. AFGC Publication, FranceGoogle Scholar
  18. 18.
    RILEM (2003) RILEM TC 162-TDF—tests and design methods for steel fibre reinforced concrete: σ–ε design method—final recommendation. Mater Struct 36:560–567CrossRefGoogle Scholar
  19. 19.
    Ultkjaer JP, Krenk S, Brincker R (1995) Analytical model for fictitious crack propagation in concrete beams. ASCE J Eng Mech 121(1):7–15CrossRefGoogle Scholar
  20. 20.
    UNI 11188 (2004) Design, production and control of steel fibre reinforced structural elements. Italian Board of Standardization, MilanGoogle Scholar
  21. 21.
    Kooiman AG (2000) Modelling SFRC for structural design. PhD thesis, University of Delft, Delft, Netherlands. ISBN: 90-70235-60-XGoogle Scholar
  22. 22.
    Habel K (2004) Structural behaviour of elements combining UHPFRC and reinforced. PhD thesis, École Polytechnique Fédérale de LausannGoogle Scholar
  23. 23.
    Soranakom C, Mobasher B (2009) Flexural design of fiber-reinforced concrete. ACI Mater J 106(5):461–469Google Scholar
  24. 24.
    Di Prisco M, Plizzari G, Vandevalle L (2009) Fibre reinforced concrete: new design perspectives. Mater Struct 42:1261–1281CrossRefGoogle Scholar
  25. 25.
    Rossi P (1988) Les bétons de fibres métalliques. Presses de l’ENPC, ParisGoogle Scholar
  26. 26.
    CNR-DT 204 (2006) Guidelines for design, construction and production control of fiber reinforced concrete structures. National Research Council of Italy, RomeGoogle Scholar
  27. 27.
    Iyengar SRKT, Raviraj S, Ravikumar P (1998) Analysis study of fictitious crack propagation in concrete beams using a bi-linear σ–w relation. In: 3th International conference on fracture mechanics of concrete and structure (FRAMCOS III), Japan, pp 315–324Google Scholar
  28. 28.
    Pedersen C (1996) New production processes, materials and calculation techniques for fiber reinforced concrete pipes. PhD thesis, Department of Structural Engineering and Materials, Technical, University of Denmark, Series R, no. 14Google Scholar
  29. 29.
    Strack M (2008) Modelling of crack opening of SFRC under tension and bending, In: 7th International Rilem symposium on FRC: design and application, pp 323–332Google Scholar

Copyright information

© RILEM 2011

Authors and Affiliations

  • Renaud de Montaignac
    • 1
  • Bruno Massicotte
    • 1
  • Jean-Philippe Charron
    • 1
  1. 1.Department of Civil, Geological and Mining EngineeringEcole Polytechnique of MontréalMontrealCanada

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