Strengths of Struts and Nodal Zones for Strut-and-Tie Model Design of Reinforced Concrete Corbels

Young Mook Yun, Youjong Lee


The strut-and-tie model (STM) method is useful for the limit state design of reinforced concrete (RC) corbels. However, for the rational design of RC corbels, designers must accurately determine the strengths of concrete struts and nodal zones to check the strength conditions of a selected STM and the anchorage of reinforcing bars in nodal zones. In this study, the authors suggested a numerical process for determining the strengths of concrete struts and nodal zones in RC corbel STMs. The technique incorporates the state of two-dimensional (2-D) stresses at the strut and nodal zone locations, 2-D failure envelope of concrete, deviation angle between the strut orientation and compressive principal stress trajectory, and the effect of concrete confinement by reinforcing bars. The authors also proposed the strength equations of struts and nodal zones that apply to the typical determinate and indeterminate STMs of RC corbels. The authors considered the effects of the shear span-to-effective depth ratio, the horizontal-to-vertical load ratio, and the primary tensile and horizontal shear reinforcement ratios in developing the strength equations. The authors predicted the failure strengths of 391 RC corbels tested to examine the appropriateness of the proposed numerical process and strength equations. The predicted failure strength compares very well with experimental results, proving that the rational analysis and design of RC corbels are possible by using the present study's strut and nodal zone strengths.


Doi: 10.28991/cej-2021-03091725

Full Text: PDF


Reinforce Concrete Corbel; Strut-and-Tie Model; Concrete Strut; Nodal Zone.


FIB, CEP-FIP Model Code 2010, Comité Euro-International du Bé ton, International Federation for Structural Concrete, Lausanne, Switzerland, (2010). doi:10.1002/9783433604090.

AASHTO, AASHTO LRFD Bridge Design Specifications, 8th Edition, American Association of State Highway and Transportation Officials, Washington DC, (2018).

ACI, Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19), American Concrete Institute, Farmington Hills, MI, 2019. doi:10.14359/51716937.

B. Thulimann, Shear Strength of Reinforced and Prestressed Concrete - CEB Approach, SP 59-6, American Concrete Institute, Farmington Hills, MI, 1976. doi:10.14359/17767.

M. P. Nielsen, M. W. Braestrup, B. C. Jensen, and F. Bach, Concrete Plasticity, Beam Shear - Shear in Joints - Punching Shear, Special Publication, Danish Society for Structural Science and Engineering, Lyngby, Denmark, (1978).

J. A. Ramirez and J. E. Breen, Proposed Design Procedure for Shear and Torsion in Reinforced and Prestressed Concrete, Research Report 248-4F, Center for Transportation Research, University of Texas at Austin, TX, (1983).

P. Marti, “Basic Tools of Reinforced Concrete Beam Design,” American Concrete Institute, 82(1), 46-56, 1985. doi:10.14359/10314.

Schlaich, Jorg, Kurt Schafer, and Mattias Jennewein. “Toward a Consistent Design of Structural Concrete.” PCI Journal 32, no. 3 (May 1, 1987): 74–150. doi:10.15554/pcij.05011987.74.150.

A. Alshegeir, Analysis and Design of Disturbed Regions with Strut-tie Models, Ph.D. Dissertation, School of Civil Engineering, Purdue University, IN, (1992).

K. Bergmeister, J. E. Breen, J. O. Jirsa, and M. E. Kreger, Detailing in Structural Concrete, Research Report 1127-3F, University of Texas at Austin, TX, (1993).

Yun, Young Mook, and Julio A. Ramirez. “Strength of Struts and Nodes in Strut-Tie Model.” Journal of Structural Engineering 122, no. 1 (January 1996): 20–29. doi:10.1061/(asce)0733-9445(1996)122:1(20).

J. G. MacGregor, Reinforced Concrete - Mechanics and Design, 3rd Edition, Prentice Hall, Englewood Cliffs, NJ, (1997).

European Committee for Standardization, Eurocode 2: Design of Concrete Structures, Brussels, Belgium, (2004). doi:10.3403/02214914.

Canadian Standards Association, Design of concrete structures (CSA A23.3-14), Rexdale, ON, Canada, (2014).

Building and Civil Engineering Standards Committee, Plain, Reinforced and Prestressed Concrete Structures - Part 1: Design and Construction (DIN 1045-1), Deutsches Institut Fur Normung E.V., Berlin, (2008).

Yun, Y. M., and J. A. Ramirez. “Strength of Concrete Struts in Three-Dimensional Strut-Tie Models.” Journal of Structural Engineering 142, no. 11 (November 2016): 04016117. doi:10.1061/(asce)st.1943-541x.0001584.

ACI Subcommittee 445, Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP-208, American Concrete Institute, Farmington Hills, MI, (2002).

Yun, Young Mook, and Hyun Soo Chae. “An Optimum Indeterminate Strut-and-Tie Model for Reinforced Concrete Corbels.” Advances in Structural Engineering 22, no. 12 (May 8, 2019): 2557–2571. doi:10.1177/1369433219845689.

KCI, Examples of Strut-Tie Model Design of Structural Concretes, Kimoondang, Korean Concrete Institute, Seoul, Korea, (2013).

M. P. Collins and D. Mitchell, Prestressed Concrete Structures, Prentice Hall, Englewood Cliffs, NJ, (1997).

E. G. Nawy, Prestressed Concrete: A Fundamental Approach, 5th Edition, Pearson Prentice Hall, Upper Saddle River, NJ, (2009).

J. K. Wight, Reinforced Concrete: Mechanics and Design, 7th Edition, Pearson Prentice Hall, Upper Saddle River, NJ, (2016).

Kriz, L. B., and C. H. Raths. “Connections in Precast Concrete Structures—Strength of Corbels.” PCI Journal 10, no. 1 (February 1, 1965): 16–61. doi:10.15554/pcij.02011965.16.61.

B. R. Hermansen and J. Cowan, “Modified Shear-Friction Theory for Bracket Design.” ACI Journal Proceedings 71, no. 2 (1974): 55-60. doi:10.14359/11169.

Mattock, Alan H., K. C. Chen, and K. Soongswang. “The Behavior of Reinforced Concrete Corbels.” PCI Journal 21, no. 2 (March 1, 1976): 52–77. doi:10.15554/pcij.03011976.52.77.

N. I. Fattuhi and B. P. Hughes, “Ductility of Reinforced Concrete Corbels Containing Either Steel Fibers or Stirrups.” ACI Structural Journal 86, no. 6 (1989): 644-651. doi:10.14359/2660.

N. I. Fattuhi and B. P. Hughes, “Reinforced Steel Fiber Concrete Corbels With Various Shear Span-to-Depth Ratios.” ACI Materials Journal 86, no. 6 (1989). doi:10.14359/2243.

Yong, Yook‐Kong, and P. Balaguru. “Behavior of Reinforced High‐Strength‐Concrete Corbels.” Journal of Structural Engineering 120, no. 4 (April 1994): 1182-1201. doi:10.1061/(asce)0733-9445(1994)120:4(1182).

Fattuhi, N. I. “Strength of SFRC Corbels Subjected to Vertical Load.” Journal of Structural Engineering 116, no. 3 (March 1990): 701–718. doi:10.1061/(asce)0733-9445(1990)116:3(701).

N. I. Fattuhi, “Reinforced Corbels Made with Plain and Fibrous Concretes.” ACI Structural Journal 91, no. 5 (1994): 530-536. doi:10.14359/4166.

N. I. Fattuhi, “Reinforced Corbels Made With High-Strength Concrete and Various Secondary Reinforcements.” ACI Structural Journal 91, no. 4 (1994): 376-383. doi:10.14359/4142

S. J. Foster, R. E. Powell, and H. S. Selim, “Performance of High-Strength Concrete Corbels.” ACI Structural Journal 93, no. 5 (1996): 555-563. doi:10.14359/9714.

M. Bourget, Y. Delmas, and F. Toutlemonde, “Experimental Study of the Behavior of Reinforced High-Strength Concrete Short Corbels.” Materials and Structures 34, no. 237 (November 8, 2005): 155–162. doi:10.1617/13620.

G. Campione, L. L. Mendola, and M. Papia, “Flexural Behaviour of Concrete Corbels Containing Steel Fibers or Wrapped with FRP Sheets.” Materials and Structures 38, no. 280 (January 21, 2005): 617–625. doi:10.1617/14210.

G. Campione, L. L. Mendola, and M. L. Mangiavillano, “Steel Fiber-Reinforced Concrete Corbels: Experimental Behavior and Shear Strength Prediction.” ACI Structural Journal 104, no. 5 (2007): 570-579. doi:10.14359/18859.

Yang, Jun-Mo, Joo-Ha Lee, Young-Soo Yoon, William D. Cook, and Denis Mitchell. “Influence of Steel Fibers and Headed Bars on the Serviceability of High-Strength Concrete Corbels.” Journal of Structural Engineering 138, no. 1 (January 2012): 123–129. doi:10.1061/(asce)st.1943-541x.0000427.

Urban, Tadeusz, and Łukasz Krawczyk. “Strengthening Corbels Using Post-Installed Threaded Rods.” Structural Concrete 18, no. 2 (April 2017): 303–315. doi:10.1002/suco.201500215.

Khosravikia, Farid, Hyun su Kim, Yousun Yi, Heather Wilson, Hossein Yousefpour, Trevor Hrynyk, and Oguzhan Bayrak. “Experimental and Numerical Assessment of Corbels Designed Based on Strut-and-Tie Provisions.” Journal of Structural Engineering 144, no. 9 (September 2018): 04018138. doi:10.1061/(asce)st.1943-541x.0002137.

Wilson, Heather R., Hossein Yousefpour, Michael D. Brown, and Oguzhan Bayrak. “Investigation of Corbels Designed According to Strut-and-Tie and Empirical Methods.” ACI Structural Journal 115, no. 3 (May 2018). doi:10.14359/51701917.

Abdul-Razzaq, Khattab Saleem, and Asala Asaad Dawood. “Corbel Strut and Tie Modeling – Experimental Verification.” Structures 26 (August 2020): 327–339. doi:10.1016/j.istruc.2020.04.021.

Ivanova, Ivelina, Jules Assih, and Dimitar Dontchev. “Influence of Anchorage Length of Composite Fabrics and Bonded Surface on the Strengthened Short Reinforced Concrete Corbel by Bonding CFRF.” European Journal of Environmental and Civil Engineering 24, no. 12 (September 27, 2018): 1993–2009. doi:10.1080/19648189.2018.1498395.

A. J. Abdulridha, H. K. Risan, and Z. M. Taki, “Numerical Analysis of Reinforced Concrete Corbel Strengthening by CFRP under Monotonic Loading,” International Journal of Civil Engineering and Technology, 9(10), (2018): 1554-1565.

Romanichen, R. M., and R. A. Souza. “Reinforced Concrete Corbels Strengthened with External Prestressing.” Revista IBRACON de Estruturas e Materiais 12, no. 4 (August 2019): 812–831. doi:10.1590/s1983-41952019000400006.

F. J., Al-Talqany, and Alhussainy A. M. “Stractural Behavior of Reinforced Concrete Corbel Using High-Strength Materials under Monotonic and Repeated Loads.” International Journal of Applied Science 2, no. 2 (April 17, 2019): p1. doi:10.30560/ijas.v2n2p1.

Shakir, Qasim M. “Response of Innovative High Strength Reinforced Concrete Encased-Composite Corbels.” Structures 25 (June 2020): 798–809. doi:10.1016/j.istruc.2020.03.056.

ACI-ASCE Subcommittee 445, Further Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP-273, American Concrete Institute, Farmington Hills, MI, (2010).

Lee, Seong-Cheol, Jae-Yeol Cho, and Frank J. Vecchio. “Model for Post-Yield Tension Stiffening and Rebar Rupture in Concrete Members.” Engineering Structures 33, no. 5 (May 2011): 1723–1733. doi:10.1016/j.engstruct.2011.02.009.

Full Text: PDF

DOI: 10.28991/cej-2021-03091725


  • There are currently no refbacks.

Copyright (c) 2021 Young Mook Yun, Youjong Lee

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.