An improved strut-and-tie model to predict the ultimate strength of steel fiber-reinforced concrete corbels

  • T. S. MustafaEmail author
  • F. B. A. Beshara
  • A. A. Mahmoud
  • M. M. A. Khalil
Original Article


In this paper, a strut-and-tie model is proposed for predicting the ultimate shear capacity of steel fiber reinforced concrete corbels. The proposed strut-and-tie model accounts for the effect of concrete strength, fiber volume, fiber aspect ratio, ratio of main steel and horizontal stirrups ratio, horizontal load ratio and shear span-to-depth ratio. The ultimate shear predictions of the proposed model are validated with 146 test results from the literature. The comparison shows that the proposed model performs well in predicting the ultimate shear capacity of steel fiber reinforced concrete corbels. The overall average value of the ratio between the experimental and the predicted strengths is 1.1 and the standard deviation is 0.105. Compared with the existing testing results, the strut-and-tie model predictions of the American and the British standard are more conservative than the improved strut-and-tie model. Also, comparative studies between the proposed model and the strut-and-tie models provided by other researchers in the literature are presented. Finally, sensitivity studies are performed for fiber parameters. The ratio between the ultimate shear strength for steel fiber reinforced concrete corbels and the ultimate shear strength for non-fibrous corbels are studied versus the steel fiber parameters considering shape of fiber and shear span-to-depth ratio. The studied fiber parameters are fiber volume content and fiber aspect ratio.


Corbels Horizontal stirrups Fiber aspect ratio Steel fibers Strut and tie Ultimate shear capacity Vertical load 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    McCormac JC, Brown R (2014) Design of reinforced concrete handbook, Ninth edn. ACI, Farmington Hills, pp 675–682Google Scholar
  2. 2.
    Bungale S, Taranath A (2012) Reinforced concrete design of tall buildings handbook. Concrete Reinforcing Steel Institute, Schaumburg, pp 85–90Google Scholar
  3. 3.
    Fattuhi NI (1990) Strength of SFRC corbels subjected to vertical load. J Struct Eng ASCE 116(3):701–718CrossRefGoogle Scholar
  4. 4.
    Fattuhi NI (1994) Strength of FRC corbels in flexure. J Struct Eng 120(2):360–377CrossRefGoogle Scholar
  5. 5.
    Fattuhi NI (1989) Ductility of reinforced concrete corbels containing either steel fibers or stirrups. ACI Struct J 86(6):644–651Google Scholar
  6. 6.
    Fattuhi NI (1994) Reinforced concrete corbel made with plain and fibrous concretes. ACI Struct J 91(5):530–536Google Scholar
  7. 7.
    Fattuhi NI (1990) Column-load effect on reinforced concrete corbels. J Struct Eng 116(1):188–197CrossRefGoogle Scholar
  8. 8.
    Fattuhi NI, Hughes P (1990) Reinforced steel fiber concrete corbels with various shear span-to-depth ratio. ACI Struct J 86(6):590–596Google Scholar
  9. 9.
    Campione G, LaMendola L, Papia M (2005) Flexural behavior of concrete corbels containing steel fibers or wrapped with FRP sheets. J Mater Struct 38(6):617–625CrossRefGoogle Scholar
  10. 10.
    Salman M, Al-Shaarbaf I (2014) Experimental study on the behavior of normal and high strength self-compacting reinforced concrete corbels. J Eng Dev 18(6):17–35Google Scholar
  11. 11.
    Alameer M (2004) Effects of fibers and headed bars on the response of concrete corbels. M.Sc. thesis, Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada, May 2004Google Scholar
  12. 12.
    Hafez M, Ahmed M, Diab H (2012) Shear behavior of high strength fiber reinforced concrete corbels. J Eng Sci Assiut Univ 5:696–987Google Scholar
  13. 13.
    Kriz L, Raths B (1965) Connections in precast concrete structures—strength of corbels. PCI J 10(1):16–47CrossRefGoogle Scholar
  14. 14.
    Khalil M (2018) Analytical studies on steel fiber reinforced concrete corbels. M.Sc. thesis, Benha University, Faculty of Engineering, Shoubra, Egypt, May 2018Google Scholar
  15. 15.
    ACI Committee 318 (2014) Building code requirements for structural concrete, ACI-318-14Google Scholar
  16. 16.
    British Standard (1997) Code of practice for design and construction, BS-8110-1-1997Google Scholar
  17. 17.
    Russo G, Venir R, Pauletta M, Somma G (2006) Reinforced concrete corbels-shear strength model and design formula. ACI Struct J 103(1):3–10Google Scholar
  18. 18.
    Solanki H, Sabnis GM (1987) Reinforced concrete corbels simplified. ACI Struct J 84(5):428–432Google Scholar
  19. 19.
    Campione G, LaMendola L, Papia M (2007) Steel fiber-reinforced concrete corbels: experimental behavior and shear strength prediction. ACI Struct J 104(5):570–597Google Scholar
  20. 20.
    Beaudin J (1990) Handbook of fiber reinforced concrete: principles, properties, developments and applications. Noyes Publications, Park RidgeGoogle Scholar
  21. 21.
    Abdul-Razzak A, Ali AM (2011) Modelling and numerical simulation of high strength fiber reinforced concrete corbels. J Appl Math Model 35(35):2901–2915CrossRefGoogle Scholar
  22. 22.
    Mustafa TS (2007) Behavior of high strength fiber reinforced concrete beams. M.Sc. thesis, Benha University, Faculty of Engineering, Shoubra, Egypt, May 2007Google Scholar
  23. 23.
    Demeke A, Tegos I (1994) Steel fiber reinforced concrete in biaxial stress tension compression conditions. ACI Struct J 91(5):579–584Google Scholar
  24. 24.
    Foster SJ, Malik AR (2002) Evaluation of efficiency factor models in strut and tie modeling of non-flexural members. ASCE J Struct Eng 128(5):569–577CrossRefGoogle Scholar

Copyright information

© RILEM 2019

Authors and Affiliations

  • T. S. Mustafa
    • 1
    Email author
  • F. B. A. Beshara
    • 1
  • A. A. Mahmoud
    • 1
    • 2
  • M. M. A. Khalil
    • 1
  1. 1.Civil Engineering Department, Faculty of Engineering, ShoubraBenha UniversityCairoEgypt
  2. 2.Higher Institute of Engineering15 MayEgypt

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