Strut-and-tie model for shear strength prediction of RC exterior beam–column joints under seismic loading

  • Panatchai ChetchotisakEmail author
  • Eakkawit Arjsri
  • Jaruek Teerawong
Original Research


Based on the Kupfer failure envelope of concrete, an analytical model called the “interactive strut-and-tie model” (ISTM) for predicting the joint shear capacity of exterior beam–column joints (EBCJs) was formulated and is presented in this study. The ISTM consists of the interaction of the strengths of concrete struts and tension ties, and the strength contributions from shear reinforcements consisting of column ties, intermediate column vertical bars and crossed inclined bars are taken into account. The proposed approach was calibrated and validated using a large dataset of 328 EBCJ test results, covering a broad range of important parameters such as the aspect ratio, axial load ratio, beam reinforcement ratio and horizontal joint reinforcement ratio. Finally, the joint shear strengths computed by the ISTM were also compared against those obtained from state-of-the-art models and were found to have resulted in much more precision and uniformity.


Exterior beam–column joint Earthquake Shear strength Strut-and-tie Reinforced concrete 



The authors gratefully acknowledge the financial support from Rajamangala University of Technology Isan, Thailand.


  1. ACI Committee 318 (2014) Building code requirements for structural concrete (ACI 318-14) and commentary. American Concrete Institute, Detroit, USAGoogle Scholar
  2. Alaee P, Li B (2017) High-strength concrete exterior beam–column joints with high-yield strength steel reinforcements. Eng Struct 145:305–321. CrossRefGoogle Scholar
  3. Al-Osta MA, Khan U, Baluch MH, Rahman MK (2018) Effects of variation of axial load on seismic performance of shear deficient RC exterior BCJs. Int J Concr Struct Mater. CrossRefGoogle Scholar
  4. Alva GMS, El Debs ALH, El Debs MK (2007) An experimental study on cyclic behavior of reinforced Concrete connections. Can J Civ Eng 34(4):565–575. CrossRefGoogle Scholar
  5. Antonopoulos CP, Triantafillou TC (2003) Experimental investigation of FRP-strengthened RC beam–column joints. J Compos Constr ASCE 7(1):39–49. CrossRefGoogle Scholar
  6. Architectural Institute of Japan (AIJ) (2010) AIJ standard for structural calculation of reinforced concrete structures (Japanese). Maruzen, TokyoGoogle Scholar
  7. Bakir PG (2003) Seismic resistance and mechanical behaviour of exterior beam–column joints with crossed inclined bars. Stuct Eng Mech 16(4):493–517. CrossRefGoogle Scholar
  8. Beydokhti EZ, Shariatmadar H (2016) Strengthening and rehabilitation of exterior RC beam–column joints using carbon-FRP jacketing. Mater Struct 49:5067–5083. CrossRefGoogle Scholar
  9. Bindhu KR, Jaya KP (2008) Performance of exterior beam column joints with crossed inclined bars under seismic type loading. J Eng Appl Sci 3(7):591–597Google Scholar
  10. Chalioris CE, Bantilas KE (2017) Shear strength of reinforced concrete beam–column joints with crossed inclined bars. Eng Struct 140:241–255. CrossRefGoogle Scholar
  11. Chalioris CE, Favvata MJ, Karayannis CG (2008) Reinforced concrete beam–column joints with crossed inclined bars under cyclic deformations. J Earthq Eng Struct Dyn 37(6):881–897CrossRefGoogle Scholar
  12. Chetchotisak P, Teerawong J, Yindeesuk S, Song J (2014) New strut-and-tie-models for shear strength prediction and design of RC deep beams. Comput Concr 14(1):19–40. CrossRefGoogle Scholar
  13. Chetchotisak P, Yindeesuk S, Teerawong J (2017) Interactive strut-and-tie-model for shear strength prediction of RC pile caps. Comput Concr 20(3):339–348. CrossRefGoogle Scholar
  14. Chun SC, Kim DY (2004) Evaluation of mechanical anchorage of reinforcement by exterior beam–column joint experiments. In: 13th world conference on earthquake engineering, paper no. 0326, Vancouver, BC, CanadaGoogle Scholar
  15. Chun SC, Shin YS (2014) Cyclic testing of exterior beam–column joints with varying joint aspect ratio. ACI Struct J 111(3):693–704CrossRefGoogle Scholar
  16. Chutarat N, Aboutaha RS (2003) Cyclic response of exterior reinforcement concrete beam–column joints reinforcement with headed bars-experimental investigation. ACI Struct J 100(2):259–264Google Scholar
  17. Clyde C, Pantelides CP, Reaveley LD (2000) Performance-based evaluation of exterior reinforced concrete building joints for seismic excitation. Pacific earthquake eng research center, PEER report 2000/05, University of California, BerkeleyGoogle Scholar
  18. CSA A23.3-04 (2004) Design of concrete structures. Canadian Standards Association, RexdaleGoogle Scholar
  19. De Risi MT, Ricci P, Verderame GM, Manfredi G (2016) Experimental assessment of unreinforced exterior beam–column joints with deformed bars. Eng Struct 112:215–232. CrossRefGoogle Scholar
  20. Durrani AJ, Zerbe HE (1987) Seismic resistance of RC exterior connections with floor slab. J Struct Eng ASCE 113(8):1850–1864CrossRefGoogle Scholar
  21. Ehsani MR, Alameddine F (1991) Design recommendations for type 2 high-strength reinforced concrete connections. ACI Struct J 88(3):277–291Google Scholar
  22. Ehsani MR, Wight JK (1985) Exterior reinforced concrete beam-to-column connections subjected to earthquake-type loading. ACI Struct J 82(4):492–499Google Scholar
  23. Ehsani MR, Moussa AE, Vallenilla CR (1987) Comparison of inelastic behavior of reinforced ordinary- and high-strength concrete frames. ACI Struct J 84(2):161–169Google Scholar
  24. El-Amoury T, Ghobarah A (2002) Seismic rehabilitation of beam–column joint using GFRP sheets. Eng Struct 24:1397–1407CrossRefGoogle Scholar
  25. Engindeniz M, Kahn LF, Zureick AH (2008) Performance of an RC corner beam–column joint severely damaged under bidirectional loading and rehabilitated with FRP composites. ACI SP 258:19–36Google Scholar
  26. Eurocode 8 (2004) Design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. BSI British Standards, LondonGoogle Scholar
  27. Fisher MJ, Sezen H (2011) Behavior of exterior reinforced concrete beam–column joints including a new reinforcement. Struct Eng Mech 40(6):867–883CrossRefGoogle Scholar
  28. Fujii S, Morita S (1991) Comparison between interior and exterior RC beam–column joint behavior, design of beam–column joints for seismic resistance. ACI J 132:145–166Google Scholar
  29. Ghobarah A, El-Amoury T (2005) Seismic rehabilitation of deficient exterior concrete frame joints. J Compos Constr ASCE 9(1):408–416CrossRefGoogle Scholar
  30. Ghobarah A, Said AM (2002) Shear strengthening of beam–column joints. Eng Struct 24(7):881–888CrossRefGoogle Scholar
  31. Haach VG, El Debs A, El Debs MK (2008) Evaluation of the influence of the column axial load on the behavior of monotonically loaded R/C exterior beam–column joints through numerical simulations. Eng Struct 30(4):965–975. CrossRefGoogle Scholar
  32. Hakuto S, Park R, Tanaka H (2000) Seismic load tests on interior and exterior beam–column joints with substandard reinforcing details. ACI Struct J 97(1):11–25Google Scholar
  33. Hamil SJ (2000) Reinforced concrete beam–column connection behavior. Ph.D. Dissertation, University of Durham, United KingdomGoogle Scholar
  34. Hanson NW, Connor HW (1967) Seismic resistance of reinforced concrete beam–column joints. J Struct Div ASCE 93:533–559Google Scholar
  35. Hassan WM, Moehle JP (2018) Shear strength of exterior and corner beam–column joints without transverse reinforcement. ACI Struct J 115(6):1719–1728CrossRefGoogle Scholar
  36. Hwang SJ, Lee HJ (1999) Analytical model for predicting shear strengths of exterior reinforced concrete beam–column joints for seismic resistance. ACI Struct J 96(5):846–857Google Scholar
  37. Hwang SJ, Fang WH, Lee HJ, Yu HW (2001) Analytical model for predicting shear strength of squat walls. J Struct Eng ASCE 127(1):43–50. CrossRefGoogle Scholar
  38. Hwang SJ, Lee HJ, Wang KC (2004) Seismic design and detailing of exterior reinforced concrete beam–column joints. In: 13th world conference on earthquake engineering, Vancouver, BC, Canada, paper no. 397Google Scholar
  39. Hwang SJ, Lee HJ, Liao TF, Wang KC, Tsai HH (2005) Role of hoops on shear strength of reinforced concrete beam–column joints. ACI Struct J 102(3):445–453Google Scholar
  40. Hwang HJ, Park HG, Choi WS, Chung L, Kim JK (2014) Cyclic loading test for beam–column connections with 600 MPa (87 ksi) beam flexural reinforcing bars. ACI Struct J 111(4):913–924CrossRefGoogle Scholar
  41. Hwang SJ, Tsai RJ, Lam WK, Moehle JP (2017) Simplification of softened strut-and-tie model for strength prediction of discontinuity regions. ACI Struct J 114(5):1239–1248Google Scholar
  42. Idayani BS (2007) The influence of concrete strength on the behaviour of external beam–column joints. Master Thesis, University of MalaysiaGoogle Scholar
  43. IS 13920 (2016) Ductile design and detailing of reinforced concrete structures subjected to seismic forces—code of practice, IndiaGoogle Scholar
  44. Jeon JS, Shafieezadeh A, DesRoches R (2014) Statistical models for shear strength of RC beam–column joints using machine-learning techniques. Earthq Eng Struct Dyn 43:2075–2095. CrossRefGoogle Scholar
  45. Kaku T, Asakusa H (1991) Ductility estimation of exterior beam–column subassemblages in reinforced concrete frames. ACI SP 123:167–185Google Scholar
  46. Kanada K, Kondon G, Fujii S, Morita S (1984) Relation between beam bar anchorage and shear resistance at exterior beam–column joints. Trans Jpn Concr Inst 6:433–440Google Scholar
  47. Karayannis CG, Chalioris CE, Sideris KK (1998) Effectiveness of RC beam–column connection repairing using epoxy resin injections. J Earthq Eng 2(2):217–240Google Scholar
  48. Karayannis CG, Chalioris CE, Sirkelis GM (2008) Local retrofit of exterior RC beam–column joints using thin RC jackets-An experimental study. J Earthq Eng Struct Dyn 37:727–746CrossRefGoogle Scholar
  49. Kassem W (2015) Strut-and-tie modelling for the analysis and design of RC beam–column joints. Mater Struct. CrossRefGoogle Scholar
  50. Kim J, LaFave JM, Song J (2009) Joint shear behavior of reinforced concrete beam–column connections. Mag Concr Res 61(2):119–132CrossRefGoogle Scholar
  51. Kotsovou G (2012) Behavior of reinforced concrete beam–column joints under cyclic loading. PhD Thesis. School of Civil Engineering, National Technical University of Athens (in Greek) Google Scholar
  52. Kotsovou G, Mouzakis H (2012) Seismic design of RC external beam–column joints. Bull Earthq Eng 10(2):645–677. CrossRefGoogle Scholar
  53. Kuang JS, Wong HF (2006) Effects of beam bar anchorage on beam–column joint behavior. Struct Build 159(2):115–124CrossRefGoogle Scholar
  54. Kuang JS, Wong HF (2011) Effectiveness of horizontal stirrups in joint core for exterior beam–column joints with nonseismic design. Procedia Eng 14:3301–3307. CrossRefGoogle Scholar
  55. Kupfer H, Gerstle KH (1973) Behavior of concrete under biaxial stress. J Eng Mech Div ASCE 99(4):853–866Google Scholar
  56. Kusuhara FH, Shiohara H (2008) Tests of R/C beam–column joint with variant boundary conditions and irregular details on anchorage of beam bars. In: The 14th world conference on earthquake engineering, Beijing, ChinaGoogle Scholar
  57. Lee HJ, Chang CJ (2017) High-strength reinforcement in exterior beam–column joints under cyclic loading. ACI Struct J 114(5):1325–1338Google Scholar
  58. Lee HJ, Yu SY (2009) Cyclic response of exterior beam–column joints with different anchorage methods. ACI Struct J 106(3):329–339Google Scholar
  59. Le-Trung K, Lee K, Lee J, Lee DH, Woo S (2010) Experimental study of RC beam–column joints strengthened using CFRP composites. Compos Part B 41:76–85. CrossRefGoogle Scholar
  60. Lima C, Martinelli E, Faella C (2012a) Capacity models for shear strength of exterior joints in RC frames: state-of-the-art and synoptic examination. Bull Earthq Eng 10:967–983. CrossRefGoogle Scholar
  61. Lima C, Martinelli E, Faella C (2012b) Capacity models for shear strength of exterior joints in RC frames: experimental assessment and recalibration. Bull Earthq Eng 10:985–1007. CrossRefGoogle Scholar
  62. Liu C (2006) Seismic behaviour of beam–column joint subassemblies reinforced with steel fibres. Master Thesis, University of Canterbury, New ZealandGoogle Scholar
  63. Mangalathu S, Jeon JS (2018) Classification of failure mode and prediction of shear strength for reinforced concrete beam–column joints using machine learning techniques. Eng Struct 160:85–94. CrossRefGoogle Scholar
  64. Masi A, Santarsiero G, Verderame GM et al (2009) Capacity models of beam–column joints: provisions of European and Italian seismic codes and possible improvements. Eurocode 8 Perspectives from the Italian Standpoint Workshop, Napoli, Italy, Italian, pp 145–158Google Scholar
  65. Megget LM (1974) Cyclic behaviour of exterior reinforced concrete beam–column Joints. Bull N Z Nat Soc Earthq Eng 7(1):22–47Google Scholar
  66. Megget LM, Park R (1971) Reinforced concrete exterior beam–column joints under seismic loading. N Z Eng 26(11):341–353Google Scholar
  67. Mitra N, Lowes LN (2007) Evaluation, calibration, and verification of a reinforced concrete beam–column joint model. J Struct Eng ASCE 133(1):105–120. CrossRefGoogle Scholar
  68. Murty CVR, Rai DC, Bajpai KK, Jain SK (2003) Effectiveness of reinforcement details in exterior reinforced concrete beam–column joints for earthquake resistance. ACI Struct J 100(2):149–156Google Scholar
  69. NZS 3101 (2006) Concrete structures standard: part 1—the design of concrete structures. New Zealand Standards, Wellington, New ZealandGoogle Scholar
  70. Ortiz IR (1993) Strut-and-tie modeling of reinforced concrete short beams and beam–column joints. PhD dissertation, University of Westminster, London, UKGoogle Scholar
  71. Pampanin S, Calvi GM, Moratti M (2002) Seismic behavior of R.C. beam–column joints design for gravity loads. 12th European conference on earthquake engineering, LondonGoogle Scholar
  72. Pantelides CP, Clyde C, Reaveley LD (2002) Performance-based evaluation of reinforced concrete building exterior joints for seismic excitation. Earthq Spectra 18(3):449–480CrossRefGoogle Scholar
  73. Paratea K, Kumar R (2016) Investigation of shear strength models for exterior RC beam–column joint. Struct Eng Mech 58(3):475–514CrossRefGoogle Scholar
  74. Paratea K, Kumar R (2019) Shear strength criteria for design of RC beam–column joints in building codes. Bull Earthq Eng. CrossRefGoogle Scholar
  75. Park S, Mosalam KM (2012) Parameters for shear strength prediction of exterior beam column joints without transverse reinforcement. Eng Struct 36:198–209. CrossRefGoogle Scholar
  76. Park, R, Paulay, T (1973) Behaviour of reinforced concrete external beam–column joints under cyclic loading. In: Proceeding of 5th world conference on earthquake engineering, Rome, pp 772–781Google Scholar
  77. Parker DE, Bullman PJM (1997) Shear strength within reinforced concrete beam–column joints. Struct Eng 75(4):53–57Google Scholar
  78. Paulay T, Priestley MJN (1992) Seismic design of reinforced concrete and masonry buildings. Wiley, HobokenCrossRefGoogle Scholar
  79. Paulay T, Scarpas A (1981) Behavior of exterior beam–column joints. Bull New Zealand Nat Soc Earthq Eng 14(3):131–144Google Scholar
  80. Pauletta M, Di Luca D, Russo G (2015) Exterior beam column joints—shear strength model and design formula. Eng Struct 94:70–81. CrossRefGoogle Scholar
  81. Ricci P, De Risi MT, Verderame GM, Manfredi G (2016) Experimental tests of unreinforced exterior beam–column joints with plain bars. Eng Struct 118:178–194. CrossRefGoogle Scholar
  82. Santarsiero G, Masi A (2015) Seismic performance of RC beam–column joints retrofitted with steel dissipation jackets. Eng Struct 106:85–95. CrossRefGoogle Scholar
  83. Scott RH (1996) Intrinsic mechanisms in reinforced concrete beam–column connection behavior. ACI Struct J 93(3):1–11Google Scholar
  84. Shafaei J, Hosseini A, Marefat SM, Ingham JM (2017) Rehabilitation of earthquake damaged external RC beam–column joints by joint enlargement using prestressed steel angles. Earthq Eng Struct Dyn 46:291–316. CrossRefGoogle Scholar
  85. Shrestha R, Smith ST, Samali B (2009) Strengthening RC beam–column connections with FRP strips. Struct Build 162(5):23–334. CrossRefGoogle Scholar
  86. Standards Association of New Zealand (2006) The design of concrete structures. NZS 3101:2006, New Zealand Standards Authority, Wellington, New ZealandGoogle Scholar
  87. Tasuji ME, Slate FO, Nilson AH (1978) Stress–strain response and fracture of concrete in biaxial loading. ACI J 75(7):306–312Google Scholar
  88. The MathWorks Inc. (2011) MATLAB version 7.12.0 ed. Natick, MA, USAGoogle Scholar
  89. Tran TM, Hadi MNS (2017) Shear strength model of reinforced-concrete exterior joint under cyclic loading. Struct Build 170:603–617. CrossRefGoogle Scholar
  90. Tsonos AG (1999) Lateral load response of strengthened reinforced concrete beam-to-column joints. ACI Struct J 96(1):46–56Google Scholar
  91. Tsonos AG (2004) Improvement of the earthquake resistance of R/C beam–column joints under the influence of P-D effect and axial force variations using inclined bars. Struct Eng Mech 18(4):389–410CrossRefGoogle Scholar
  92. Tsonos AG (2007) Cyclic load behavior of reinforced concrete beam–column subassemblages of modern structures. ACI Struct J 104(4):468–478Google Scholar
  93. Tsonos AG, Tegos IA, Penelis GG (1992) Seismic resistance of type 2 exterior beam–column joints reinforced with inclined bars. ACI Struct J 89(1):3–12Google Scholar
  94. Uzumeri SM (1977) Strength and ductility of cast-in-place beam–column joints. ACI J 53:293–350Google Scholar
  95. Vatani-Oskouei A (2010) Repairing of seismically damaged RC exterior beam–column connection using CFRP. J Reinf Plast Compos 29:3257–3274CrossRefGoogle Scholar
  96. Vollum RL, Newman JB (1999) The design of reinforced concrete external beam–column joints. Struct Eng 77(23–24):21–27Google Scholar
  97. Wallace JW, McConnel SW, Gupta P, Cote PA (1998) Use of headed reinforcement in beam–column joints subjected to earthquake loads. ACI Struct J 95(5):590–606Google Scholar
  98. Wang GL, Meng SP (2008) Modified strut-and-tie model for prestressed concrete deep beams. Eng Struct 30(4):3489–3496. CrossRefGoogle Scholar
  99. Wang GL, Dai JG, Teng JG (2012) Shear strength model for RC beam–column joints under seismic loading. Eng Struct 40:350–360. CrossRefGoogle Scholar
  100. Wong HF (2005) Shear strength and seismic performance of non-seismically designed reinforced concrete beam–column joints. Ph.D. Thesis, Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong KongGoogle Scholar
  101. Wong HF, Kuang JS (2008) Effects of beam–column depth ratio on joint seismic behavior. Struct Build 161(2):91–101CrossRefGoogle Scholar
  102. Zhang N, Tan KH (2007) Direct strut-and-tie model for single span and continuous deep beams. Eng Struct 29:2987–3001. CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Civil EngineeringRajamangala University of Technology IsanKhon KaenThailand
  2. 2.Department of Civil EngineeringKhon Kaen UniversityKhon KaenThailand

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