A Semi-Empirical Equation based on the Strut-and-Tie Model for the Shear Strength Prediction of Deep Beams with Multiple Large Web Openings


  • L. T. Hussein Department of Civil Engineering, College of Engineering, University of Baghdad, Iraq
  • R. M. Abbas Department of Civil Engineering, College of Engineering, University of Baghdad, Iraq


The behavior and shear strength of full-scale (T-section) reinforced concrete deep beams, designed according to the strut-and-tie approach of ACI Code-19 specifications, with various large web openings were investigated in this paper. A total of 7 deep beam specimens with identical shear span-to-depth ratios have been tested under mid-span concentrated load applied monotonically until beam failure. The main variables studied were the effects of width and depth of the web openings on deep beam performance. Experimental data results were calibrated with the strut-and-tie approach, adopted by ACI 318-19 code for the design of deep beams. The provided strut-and-tie design model in ACI 318-19 code provision was assessed and found to be unsatisfactory for deep beams with large web openings. A simplified empirical equation to estimate the shear strength for deep T-beams with large web openings based on the strut-and-tie model was proposed and verified with numerical analysis. The numerical study considered three-dimensional finite element models, in ABAQUS software, that have been developed to simulate and predict the performance of deep beams. The results of numerical simulations were in good agreement and exhibited close correlation with the experimental data. The test results showed that the enlargement in the size of web openings substantially reduces the elements' shear capacity. The experiments revealed that increasing the width of the openings has more effect than the depth at reducing the load-carrying capacity.


deep beams, reinforced concrete, T-beams, web opening, strut-and-tie model, finite element analysis, shear strength


Download data is not yet available.


K. H. Tan and H. Y. Lu, "Shear Behavior of Large Reinforced Concrete Deep Beams and Code Comparisons," Structural Journal, vol. 96, no. 5, pp. 836–846, Sep. 1999. DOI: https://doi.org/10.14359/738

M. P. Collins, E. C. Bentz, and E. G. Sherwood, "Where is Shear Reinforcement Required? Review of Research Results and Design Procedures," Structural Journal, vol. 105, no. 5, pp. 590–600, Sep. 2008. DOI: https://doi.org/10.14359/19942

K. S. Ismail, M. Guadagnini, and K. Pilakoutas, "Strut-and-Tie Modeling of Reinforced Concrete Deep Beams," Journal of Structural Engineering, vol. 144, no. 2, Feb. 2018, Art. no. 04017216. DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0001974

L. D. Lorenzis and A. Nanni, "Shear Strengthening of Reinforced Concrete Beams with Near-Surface Mounted Fiber-Reinforced Polymer Rods," Structural Journal, vol. 98, no. 1, pp. 60–68, Jan. 2001. DOI: https://doi.org/10.14359/10147

G. Zhang et al., "Reinforced concrete deep beam shear strength capacity modelling using an integrative bio-inspired algorithm with an artificial intelligence model," Engineering with Computers, Dec. 2020. DOI: https://doi.org/10.1007/s00366-020-01137-1

J. Wight, Reinforced Concrete: Mechanics and Design, 3rd ed. Upper Saddle River, NJ, USA: Prentice Hall, 1997.

S. T. Mau and T. S. T. C. Hsu, "Formula for the Shear Strength of Deep Beams," Structural Journal, vol. 86, no. 5, pp. 516–523, Sep. 1989. DOI: https://doi.org/10.14359/3008

K. N. Smith and A. S. Vantsiotis, "Shear Strength of Deep Beams," Journal Proceedings, vol. 79, no. 3, pp. 201–213, May 1982. DOI: https://doi.org/10.14359/10899

W. A. Jasim, Y. B. A. Tahnat, and A. M. Halahla, "Behavior of reinforced concrete deep beam with web openings strengthened with (CFRP) sheet," Structures, vol. 26, pp. 785–800, May 2020. DOI: https://doi.org/10.1016/j.istruc.2020.05.003

O. E. Hu and K. H. Tan, "Large reinforced-concrete deep beams with web openings: test and strut-and-tie results," Magazine of Concrete Research, vol. 59, no. 6, pp. 423–434, May 2007. DOI: https://doi.org/10.1680/macr.2007.59.6.423

D. B. Birrcher, "Design of reinforced concrete deep beams for strength and serviceability," Ph.D. dissertation, University of Texas at Austin, Austin TX, USA, 2009.

ACI-ASCE Committee 445, 445R-99: Recent Approaches to Shear Design of Structural Concrete (Reapproved 2009). ACI, 2009.

M. F. Andermatt and A. S. Lubell, "Behavior of Concrete Deep Beams Reinforced with Internal Fiber-Reinforced Polymer—Experimental Study," Structural Journal, vol. 110, no. 4, pp. 585–594, Jul. 2013. DOI: https://doi.org/10.14359/51685744

J. Schlaich, K. Schafer, and M. Jennewein, "Toward a Consistent Design of Structural Concrete," PCI Journal, vol. 32, no. 3, pp. 74–150, May 1987. DOI: https://doi.org/10.15554/pcij.05011987.74.150

S. P. Ray and C. S. Reddy, "Strength of reinforced deep beams with and without opening in the web," The Indian Concrete Journal, vol. 53, no. 9, pp. 242–246, Sep. 1987.

A. Y. Pranata, D. Tjitradi, and I. Prasetia, "Horizontal Web Reinforcement Configuration Analysis of Deep Beam Capacity and Behavior using Finite Element Modeling," Engineering, Technology & Applied Science Research, vol. 10, no. 1, pp. 5242–5246, Feb. 2020. DOI: https://doi.org/10.48084/etasr.3256

M. A. J. Hassan and A. F. Izzet, "Serviceability of Reinforced Concrete Gable Roof Beams with Openings under Static Loads," Engineering, Technology & Applied Science Research, vol. 9, no. 5, pp. 4813–4817, Oct. 2019. DOI: https://doi.org/10.48084/etasr.3110

N. H. Saksena and P. G. Patel, "Effects of the circular openings on the behavior of concrete beams without additional reinforcement in opening region using fem method," International Journal of Advanced Engineering Technology, vol. 4, no. 2, 2013.

A. Shubbar, H. Alwan, E. Y. Phur, J. McLoughlin, and A. Al-khaykan, "Studying the Structural Behaviour of RC Beams with Circular Openings of Different Sizes and Locations Using FE Method," International Journal of Structural and Construction Engineering, vol. 11, no. 7, pp. 916–919, 2017.

M. A. J. Hassan and A. F. Izzet, "Experimental and Numerical Comparison of Reinforced Concrete Gable Roof Beams with Openings of Different Configurations," Engineering, Technology & Applied Science Research, vol. 9, no. 6, pp. 5066–5073, Dec. 2019. DOI: https://doi.org/10.48084/etasr.3188

K. Mohamed, A. S. Farghaly, and B. Benmokrane, "Strut Efficiency-Based Design for Concrete Deep Beams Reinforced with Fiber-Reinforced Polymer Bars," Structural Journal, vol. 113, no. 4, pp. 791–800, Jul. 2016. DOI: https://doi.org/10.14359/51688476

ACI-ASCE Committee 318, ACI CODE-318-19: Building Code Requirements for Structural Concrete and Commentary. ACI, 2019.

N. Rezaei, G. Klein, and D. B. Garber, "Effect of Development and Geometry on Behavior of Concrete Deep Beams," Structural Journal, vol. 116, no. 3, pp. 171–181, May 2019. DOI: https://doi.org/10.14359/51713308

"Abaqus Analysis User’s Guide (6.14)." (accessed Feb. 08, 2022).


How to Cite

L. T. Hussein and R. M. Abbas, “A Semi-Empirical Equation based on the Strut-and-Tie Model for the Shear Strength Prediction of Deep Beams with Multiple Large Web Openings”, Eng. Technol. Appl. Sci. Res., vol. 12, no. 2, pp. 8289–8295, Apr. 2022.


Abstract Views: 205
PDF Downloads: 131

Metrics Information
Bookmark and Share

Most read articles by the same author(s)