Experimental Study to Evaluate Antisymmetric Reinforced Concrete Deep Beams with Openings under Concentrated Loading Using Strut and Tie Model

Document Type : Original Article


Civil Engineering Department, University of Technology – Iraq, Baghdad, Iraq


The Strut-and-Tie modeling (STM) technique represents an applicable and valuable method for structural engineers to design disturbed regions (D-regions) of reinforced concrete structures where the assumption of plane sections remaining plane after loading is inapplicable. The most important aspect to guarantee the suitable structural and economic performance of the design is finding a suitable truss-analogy model, leading to the use of a more efficient model in structural buildings. The evaluation of the antisymmetric Strut-and-Tie models (STM) with openings under different concentrated external loads has not been comprehensively investigated in the literature. So, to address this gap, the goal of this paper is to achieve the most efficient reinforcement layout design in antisymmetric reinforced concrete deep beams with openings under concentrated loading using the strut and tie model.  The experimental work was conducted and included (3) antisymmetric reinforced concrete deep beams with openings that were tested under different concentrated loadings (25, 35, and 16 kips for Specimens 1, 2, and 3, respectively) using the strut and tie model. The ANSYS FEM software is used for the initial strut and tie analysis, and the RISA-3D structural analysis program is used to find the internal forces for all members under concentrated external loads in each specimen. The findings of this paper show that Specimen 1 had the highest efficiency of 1.67, while Specimen 3 had the lowest efficiency of 1.31. It can be concluded that the efficient reinforcement layout of the strut and tie model leads to the highest efficiency of the model, regardless of the value of the externally applied load.

Graphical Abstract

Experimental Study to Evaluate Antisymmetric Reinforced Concrete Deep Beams with Openings under Concentrated Loading Using Strut and Tie Model


Main Subjects

  1. Shear, A.-A.C.o. and Torsion, "Recent approaches to shear design of structural concrete", Journal of Structural Engineering, Vol. 124, No. 12, (1998), 1375-1417, https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1375)
  2. "American association of state highway officials and transportation (aashto), “lrfd bridge design specifications. 7th edition ed.”", in AASHTO, Washington, DC, (2014 of Conference).
  3. Committee, A., "Building code requirements for structural concrete (aci 318-08) and commentary, American Concrete Institute. (2008).
  4. Association, C.S., "Design of concrete structures (csa a23. 3-04)", CSA, Rexdale, Ontario, (2004).
  5. Institution, B.S., "Eurocode 2: Design of concrete structures: Part 1-1: General rules and rules for buildings, British Standards Institution, (2004).
  6. Taerwe, L. and Matthys, S., Fib model code for concrete structures 2010. 2013, Ernst & Sohn, Wiley.
  7. Ritter, W., "The hennebique design method (die bauweise hennebique)", Schweizerische Bauzeitung (Zurich), Vol. 33, No. 7, (1899), 59-61.
  8. Mörsch, E., "Concrete-steel construction:(der eisenbetonbau), Engineering news publishing Company, (1909).
  9. Schlaich, J., Schäfer, K. and Jennewein, M., "Toward a consistent design of structural concrete", PCI journal, Vol. 32, No. 3, (1987), 74-150.
  10. Schlaich, J. and Schafer, K., "Design and detailing of structural concrete using strut-and-tie models", Structural Engineer, Vol. 69, No. 6, (1991), 113-125.
  11. Xie, Y.M. and Steven, G.P., "A simple evolutionary procedure for structural optimization", Computers & Structures, Vol. 49, No. 5, (1993), 885-896, https://doi.org/10.1016/0045-7949(93)90035-C.
  12. Yang, X.Y., Xie, Y.M., Steven, G.P. and Querin, O., "Bidirectional evolutionary method for stiffness optimization", AIAA Journal, Vol. 37, No. 11, (1999), 1483-1488, https://doi.org/10.2514/2.626
  13. Liang, Q.Q., Xie, Y.M. and Steven, G.P., "Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure", Structural Journal, Vol. 97, No. 2, (2000), 322-330.
  14. Liang, Q.Q., Xie, Y.M. and Steven, G.P., "Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization", ACI Structural Journal, Vol. 98, No. 2, (2001), 226-232.
  15. Cai, C.S., "Three-dimensional strut-and-tie analysis for footing rehabilitation", Practice Periodical on Structural Design and Construction, Vol. 7, No. 1, (2002), 14-25, https://doi.org/10.1061/(ASCE)1084-0680(2002)7:1(14)
  16. Leu, L.-J., Huang, C.-W., Chen, C.-S. and Liao, Y.-P., "Strut-and-tie design methodology for three-dimensional reinforced concrete structures", Journal of Structural Engineering, Vol. 132, No. 6, (2006), 929-938, https://doi.org/10.1061/(ASCE)0733-9445(2006)132:6(929)
  17. Nagarajan, P. and Pillai, T.M., "Development of strut and tie models for simply supported deep beams using topology optimization", Sonklanakarin Journal of Science and Technology, Vol. 30, No. 5, (2008), 641.
  18. Bruggi, M., "Generating strut-and-tie patterns for reinforced concrete structures using topology optimization", Computers & Structures, Vol. 87, No. 23-24, (2009), 1483-1495, https://doi.org/10.1016/j.compstruc.2009.06.003
  19. Guest, J.K., "Imposing maximum length scale in topology optimization", Structural and Multidisciplinary Optimization, Vol. 37, (2009), 463-473, https://doi.org/10.1007/s00158-008-0250-7
  20. Guest, J.K. and Moen, C.D., "Reinforced concrete design with topology optimization", in Structures Congress 2010: 19th Analysis and Computation Specialty Conference. (2010), 445-454. https://doi.org/10.1061/41131(370)39
  21. Herranz, J.P., Santa María, H., Gutierrez, S. and Riddell, R., "Optimal strut-and-tie models using full homogenization optimization method", ACI Structural Journal, Vol. 109, No. 5, (2012), 605.
  22. Almeida, V.S., Simonetti, H.L. and Neto, L.O., "Comparative analysis of strut-and-tie models using smooth evolutionary structural optimization", Engineering Structures, Vol. 56, (2013), 1665-1675, https://doi.org/10.1016/j.engstruct.2013.07.007
  23. Palmisano, F. and Elia, A., "Shape optimization of strut-and-tie models in masonry buildings subjected to landslide-induced settlements", Engineering Structures, Vol. 84, (2015), 223-232, https://doi.org/10.1016/j.engstruct.2014.11.030
  24. Palmisano, F., Alicino, G. and Vitone, A., "Nonlinear analysis of rc discontinuity regions by using the bi-directional evolutionary structural optimization method", in Proc. of the OPT-I, An International Conference on Engineering and Applied Sciences Optimization. (2014), 749-758.
  25. Bruggi, M., "A numerical method to generate optimal load paths in plain and reinforced concrete structures", Computers & Structures, Vol. 170, (2016), 26-36, https://doi.org/10.1016/j.compstruc.2016.03.012
  26. El-Metwally, S. and Chen, W.-F., "Structural concrete: Strut-and-tie models for unified design, CRC Press, (2017).
  27. Chen, H., Yi, W.-J. and Hwang, H.-J., "Cracking strut-and-tie model for shear strength evaluation of reinforced concrete deep beams", Engineering Structures, Vol. 163, (2018), 396-408, https://doi.org/10.1016/j.engstruct.2018.02.077
  28. Geevar, I. and Menon, D., "Strength of reinforced concrete pier caps-experimental validation of strut-and-tie method", ACI Structural Journal, Vol. 116, No. 1, (2019).
  29. Al-Ameri, A., Jawad, F. and Fattah, M., "Vertical and lateral displacement response of foundation to earthquake loading", International Journal of Engineering, Transactions A: Basics, Vol. 33, No. 10, (2020), 1864-1871, doi: 10.5829/IJE.2020.33.10A.05.
  30. Hussein, A., Al-Neami, M. and Rahil, F., "Effect of hydrodynamic pressure on saturated sand supporting liquid storage tank during the earthquake", International Journal of Engineering, Transactions B: Applications, Vol. 34, No. 5, (2021), 1176-1183, doi: 10.5829/IJE.2021.34.05B.11.
  31. Xia, Y., Langelaar, M. and Hendriks, M.A., "Automated optimization-based generation and quantitative evaluation of strut-and-tie models", Computers & Structures, Vol. 238, (2020), 106297, https://doi.org/10.1016/j.compstruc.2020.106297
  32. Xia, Y., Langelaar, M. and Hendriks, M.A., "Optimization‐based three‐dimensional strut‐and‐tie model generation for reinforced concrete", Computer‐Aided Civil and Infrastructure Engineering, Vol. 36, No. 5, (2021), 526-543, https://doi.org/10.1111/mice.12614
  33. Xia, Y., Langelaar, M. and Hendriks, M.A., "Optimization-based strut-and-tie model generation for reinforced concrete structures under multiple load conditions", Engineering Structures, Vol. 266, (2022), 114501, https://doi.org/10.1016/j.engstruct.2022.114501
  34. Kassem, M.M., Nazri, F.M., Farsangi, E.N. and Ozturk, B., "Improved vulnerability index methodology to quantify seismic risk and loss assessment in reinforced concrete buildings", Journal of Earthquake Engineering, Vol. 26, No. 12, (2022), 6172-6207, https://doi.org/10.1080/13632469.2021.1911888
  35. Kassem, M.M., Nazri, F.M., Farsangi, E.N. and Ozturk, B., "Development of a uniform seismic vulnerability index framework for reinforced concrete building typology", Journal of Building Engineering, Vol. 47, (2022), 103838, https://doi.org/10.1016/j.jobe.2021.103838
  36. Jabbar, A.M., Mohammed, D.H. and Hasan, Q.A., "A numerical study to investigate shear behavior of high-strength concrete beams externally retrofitted with carbon fiber reinforced polymer sheets", International Journal of Engineering, Transactions B: Applications,, Vol. 36, No. 11, (2023), 2112-2123, doi: 10.5829/IJE.2023.36.11B.15.
  37. Mohammed, A., Al-Zuheriy, A. and Abdulkareem, B., "An experimental study to predict a new formula for calculating the deflection in wide concrete beams reinforced with shear steel plates", International Journal of Engineering, Transactions B: Applications, Vol. 36, No. 2, (2023), 360-371, doi: 10.5829/IJE.2023.36.02B.15.
  38. Chaudhari, A.D. and Suryawanshi, S., "Development and calibration of an efficiency factor model for recycled aggregate concrete struts", International Journal of Engineering, Transactions B: Applications, Vol. 36, No. 8, (2023), 1449-1458, doi: 10.5829/IJE.2023.36.08B.05.