Bulletin of Earthquake Engineering

, Volume 17, Issue 2, pp 803–844 | Cite as

A simplified numerical model to simulate RC beam–column joints collapse

  • Javad Shayanfar
  • Ali Hemmati
  • Habib Akbarzadeh BengarEmail author
Original Research


Post-earthquake reconnaissance confirmed that the high vulnerability of non-seismically detailed RC frame structures could be related to shear failure in the core of the beam–column joints which might cause the collapse of the structure. The main focus was given on developing a simplified numerical model to simulate RC beam–column joints collapse based on theoretical formulations and experimental observations. For this, a joint model has been proposed so that nonlinearities in the joint core were considered by two diagonal axial springs. According to the principal stress approach, a more refined calibration of principle tensile stress versus joint rotation relation was developed to calculate the characteristics of these springs. In the model, the effects of the main factors influencing the mechanical behavior of RC joints i.e. column intermediate bars, joint aspect ratio, joint shear reinforcements, type of beam bar anchorage, etc. were considered. To verify the simplified numerical model, it was vastly applied to experimental specimens available in the literature. Results revealed that the model was capable of estimating inelastic response of RC joints with reasonable precision. Furthermore, assuming the joint core to behave as a rigid body, even for joints reinforced by shear reinforcements might bring about non-conservative predictions in terms of strength and ductility capacities. Based on a parametric study, it was also concluded that the effectiveness of the influential factors of RC beam–column joints is noticeably a function of the level of the axial load applied on the column. Using experimentally computed factors and simple procedure to calculate joint characteristics could make the model properly suitable for practical applications.


Beam–column joint Nonlinear analysis Principal tensile stress Simplified numerical model 


  1. ACI 352R-02 (2002) Recommendations for design of beam–column-joints in monolithic reinforced concrete structures. American Concrete Institute, ACI ASCE, Committee 352, DetroitGoogle Scholar
  2. Akguzel U, Pampanin S (2010) Effects of variation of axial load and bi-directional loading on seismic performance of GFRP retrofitted reinforced concrete exterior beam–column joints. J Compos Constr 14(1):94–104Google Scholar
  3. Akguzel U, Pampanin S (2012) Assessment and design procedure for the seismic retrofit of reinforced concrete beam–column joints using FRP composite materials. J Compos Constr 16:21–34Google Scholar
  4. Alva GMS, De Cresce El Debs ALH, El Debs MK (2007) An experimental study on cyclic behaviour of reinforced concrete connections. Can J Civ Eng 34(4):565–575Google Scholar
  5. Antonopoulos CP, Triantafillou TC (2003) Experimental investigation of FRP strengthened RC beam column joints. J Compos Constr 7:39–49Google Scholar
  6. Biddah MSA (1997) Seismic behaviour of existing and rehabilitated reinforced concrete frame connections. Ph.D. dissertation, McMaster University, OntarioGoogle Scholar
  7. Campione G, Cavaleri L, Failla A (2016) Flexural behavior of external beam–column reinforced concrete assemblages externally strengthened with steel cages. ACI Struct J 113(5):883Google Scholar
  8. Chalioris CE, Favvata M, Karayannis CG (2008) Reinforced concrete beam–column joints with crossed inclined bars under cyclic deformations. J Earthq Eng Struct Dyn 37:881–897Google Scholar
  9. Chun SC, Lee SH, Kang TH, Oh B, Wallace JW (2007) Mechanical anchorage in exterior beam–column joints subjected to cyclic loading. ACI Struct J 104(1):102Google Scholar
  10. Chun SC, Kim, DY (2004) Evaluation of mechanical anchorage of reinforcement by exterior beam–column joint experiments. In: Proceedings of 13th world conference on earthquake engineering (No. 0326)Google Scholar
  11. Clyde C, Pantelides CP, Reaveley LD (2000) Performance-based evaluation of exterior reinforced concrete building joints for seismic excitation. Report PEER 2000/05. Pacific Earthquake Engineering Research CenterGoogle Scholar
  12. Computer and Structures Inc (2008) SAP2000 analysis references. Computer and Structures Inc, BerkeleyGoogle Scholar
  13. De Risi MT, Verderame GM (2017) Experimental assessment and numerical modelling of exterior non-conforming beam–column joints with plain bars. Eng Struct 150:115–134Google Scholar
  14. De Risi MT, Ricci P, Verderame GM, Manfredi G (2016a) Experimental assessment of unreinforced exterior beam–column joints with deformed bars. Eng Struct 112:215–232Google Scholar
  15. De Risi MT, Ricci P, Verderame GM (2016b) Modelling exterior unreinforced beam–column joints in seismic analysis of non-ductile RC frames. J Earthq Eng Struct Dyn 46(6):899–923Google Scholar
  16. Del Vecchio C, Di Ludovico M, Balsamo A, Prota A, Manfredi G, Dolce M (2014) Experimental investigation of exterior RC beam–column joints retrofitted with FRP systems. J Compos Constr 18:1–13Google Scholar
  17. Del Vecchio C, Di Ludovico M, Prota A, Manfredi G (2016) Modelling beam–column joints and FRP strengthening in the seismic performance assessment of RC existing frames. Compos Struct 142:107–116Google Scholar
  18. Del Vecchio C, Gentile ER, Pampanin S (2017) The simplified lateral mechanism analysis (SLaMa) for the seismic performance assessment of a case study building damaged in the 2011 Christchurch earthquake. Research Report 2016-02 Civil and Natural Resources EngineeringGoogle Scholar
  19. Dhake PD, Patil HS, Patil YD (2015) Anchorage behaviour and development length of headed bars in exterior beam–column joints. Mag Concr Res 67(2):53–62Google Scholar
  20. Di Ludovico M, Balsamo A, Prota A, Verderame GM, Dolce M, Manfredi G (2012) Preliminary results of an experimental investigation on RC beam–column joints. International Institute for FRP in Construction, Rome, pp 1–9Google Scholar
  21. Ehsani MR, Moussa AE, Valenilla CR (1987) Comparison of inelastic behavior of reinforced ordinary-and high-strength concrete frames. ACI Struct J 84(2):161–169Google Scholar
  22. El-Amoury T (2003) Seismic rehabilitation of concrete frame beam–column joints. Ph.D. dissertation, McMaster University, OntarioGoogle Scholar
  23. Elwood K (2002) Shake table tests and analytical studies on the gravity load collapse of reinforced concrete frames. Ph.D. Dissertation. University of California, Berkeley, CaliforniaGoogle Scholar
  24. Favvata MJ, Izzuddin BA, Karayannis CG (2008) Modelling exterior beam–column joints for seismic analysis of RC frame structures. J Earthq Eng Struct Dyn 37(13):1527–1548Google Scholar
  25. Garcia R, Jemaa Y, Helal Y, Maurizio G, Pilakoutas K (2013) Seismic strengthening of severely damaged beam–column RC joints using CFRP. J Comps Constr 18(2):04013048Google Scholar
  26. Genesio G (2012) Seismic assessment of RC exterior beam–column joints and retrofit with haunches using post-installed anchors. Ph.D. Dissertation. University of Stuttgart, StuttgartGoogle Scholar
  27. Genesio G, Sharma A (2010) Seismic retrofit solution for reinforced concrete exterior beam–column joints using a fully fastened haunch: Part 2-1—as-built joints. IWB, University of Stuttgart, Stuttgart, Test Report No. WS 221/07-10/01Google Scholar
  28. Gergely BJ, Pantelides CP, Reaveley LD (2000) Shear strengthening RCT-joints using CFRP composites. J Compos Constr 4:56–64Google Scholar
  29. Ghobarah A, Said A (2001) Seismic rehabilitation of beam–column joints using FRP laminates. J Earthq Eng 5(1):113–129Google Scholar
  30. Ha GJ, Cho CG, Kang HW, Feo L (2013) Seismic improvement of RC beam–column joints using hexagonal CFRP bars combined with CFRP sheets. Compos Struct 95:464–470Google Scholar
  31. Hadi MN, Tran TM (2016) Seismic rehabilitation of reinforced concrete beam–column joints by bonding with concrete covers and wrapping with FRP composites. Mater Struct 49(1–2):467–485Google 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 Behaviour. Ph.D. dissertation, Durham University, DurhamGoogle Scholar
  34. Hassan WM (2011) Analytical and experimental assessment of seismic vulnerability of beam–column joints without transverse reinforcement in concrete buildings. Ph.D. Dissertation. University of California, Berkeley, CaliforniaGoogle Scholar
  35. Helal Y (2012) Seismic strengthening of deficient exterior RC beam–column sub-assemblages using posttensioned metal strips. Ph.D. dissertation, University of Sheffield, SheffieldGoogle Scholar
  36. Hertanto E (2005) Seismic assessment of pre-1970s reinforced concrete structures. Master Thesis. University of Canterbury, ChristchurchGoogle Scholar
  37. 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
  38. Jeon JS, Lowes LN, DesRoches R, Brilakis I (2015) Fragility curves for non-ductile reinforced concrete frames that exhibit different component response mechanisms. Eng Struct 85:127–143Google Scholar
  39. Kaku T, Asakusa H (1991) Ductility estimation of exterior beam–column subassemblages in reinforced concrete frames. ACI Special Publication, Design of Beam–column Joints for Seismic Resistance, ACI, Farmington Hills, pp 167–186Google Scholar
  40. Kam WY (2010) Selective Weakening and Post-tensioning for the Seismic Retrofit of Non-Ductile RC Frames. Ph.D. Dissertation. University of Canterbury, ChristchurchGoogle Scholar
  41. Kang TH, Ha SS, Choi DU (2010) Bar pullout tests and seismic tests of small-headed bars in beam–column joints. ACI Struct J 107(1):32Google Scholar
  42. Karayannis CG, Sirkelis G (2008) Strengthening and rehabilitation of RC beam–column joints using carbon-FRP jacketing and epoxy resin injection. J Earthq Eng Struct Dyn 37(5):769–790Google Scholar
  43. Karayannis CG, Chalioris CE, Sideris KK (1998) Effectiveness of RC beam–column connection repair using epoxy resin injections. J Earthq Eng 2(2):217–240Google Scholar
  44. Karayannis CG, Chalioris CE, Sirkelis GM (2008) Local retrofit of external RC beam column joints using thin RC jackets: an experimental study. J Earthq Eng Struct Dyn 37(5):727–746Google Scholar
  45. Kaya O, Yalcin C, Parvin A, Altay S (2008) Repairing of shear-damaged RC joint panel zone using chemical epoxy injection methodology. In: Proceedings of 14th world conference on earthquake engineering, BeijingGoogle Scholar
  46. Kim CG, Eom TS, Park HG, Kim TW (2016) Seismic performance of lightly reinforced concrete beam–column connections for low-rise buildings. J Arch Inst Korea Struct Constr 32(3):19–30Google Scholar
  47. Kuang JS, Wong HF (2013) Horizontal hoops in non-seismically designed beam–column joints. HKIE Trans 20(3):164–171Google Scholar
  48. Laterza M, D’Amato M, Gigliotti R (2017) Modelling of gravity-designed RC sub-assemblages subjected to lateral loads. Eng Struct 130:242–260Google Scholar
  49. 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 Eng 41(1):76–85Google Scholar
  50. Liu C (2006) Seismic behaviour of beam–column joint subassemblies reinforced with steel fibers. Master Thesis. University of Canterbury, ChristchurchGoogle Scholar
  51. Lowes LN, Altoontash A (2003) Modelling reinforced-concrete beam–column joints subjected to cyclic loading. J Struct Eng 129:1686–1697Google Scholar
  52. Lynn AC (2001) Seismic evaluation of existing reinforced concrete building columns. Ph.D. Dissertation. University of California, Berkeley, CaliforniaGoogle Scholar
  53. Melo J, Varum H, Rossetto T, Costa A (2012) Cyclic response of RC beam–column joints reinforced with plain bars: an experimental testing campaign. In: Proceedings of 15th world conference on earthquake engineering, Lisbon, PortugalGoogle Scholar
  54. Murty CVR, Rai D, 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
  55. Niroomandi A, Maheri A, Maheri MR, Mahini SS (2010) Seismic performance of ordinary RC frames retrofitted at joints by FRP sheets. Eng Struct 32:2326–2336Google Scholar
  56. Niroomandi A, Najafgholipour MA, Ronagh HR (2014) Numerical investigation of the affecting parameters on the shear failure of nonductile RC exterior joints. Eng Failure Anal 46:62–67Google Scholar
  57. NZS 3101 (1995) Design of concrete structures, vols 1, 2. Standards Association of New Zealand, WellingtonGoogle Scholar
  58. Pampanin S, Calvi GM, Moratti M (2002) Seismic behavior of RC beam–column joints designed for gravity only. In:‏ Proceeding, 12th European conference on earthquake engineering (ECEE), LondonGoogle Scholar
  59. Pampanin S, Magenes G, Carr A (2003) Modelling of shear hinge mechanism in poorly detailed RC beam–column joints. In: Fib symposium on concrete structures in seismic regions, Athens, GreeceGoogle Scholar
  60. Pampanin S, Bolognini D, Pavese A (2007) Performance-based seismic retrofit strategy for existing RC frame systems using FRP composites. J Compos Constr 11(2):211–226Google Scholar
  61. Pantelides CP, Hansen J, Nadauld J, Reaveley LD (2002) Assessment of reinforced concrete building exterior joints with substandard details. Report no. PEER 2002/18. Pacific Earthquake Engineering Research CenterGoogle Scholar
  62. Park S, Mosalam KM (2012) Parameters for shear strength prediction of exterior beam–column joints without transverse reinforcement. Eng Struct 36:198–209Google Scholar
  63. Parvin A, Altay S, Yalcin C, Kaya O (2010) CFRP Rehabilitation of concrete frame joints with inadequate shear and anchorage details. J Compos Constr 14(1):72–82Google Scholar
  64. Priestley MJN (1997) Displacement based seismic assessment of reinforced concrete buildings. J Earthq Eng 1(1):157–192Google Scholar
  65. Priestley MJN, Seible F, Calvi GM (1996) Seismic design and retrofit of bridge structures. Wiley, New YorkGoogle Scholar
  66. Realfonzo R, Napoli A, Pinilla JGR (2014) Cyclic behavior of RC beam–column joints strengthened with FRP systems. Constr Build Mater 54:282–297Google Scholar
  67. Ricci P, De Risi MT, Verderame GM, Manfredi G (2016) Experimental tests of unreinforced exterior beam–column joints with plain bars. Eng Struct 118:178–194Google Scholar
  68. Santarsiero G, Masi A (2015) Seismic performance of RC beam–column joints retrofitted with steel dissipation jackets. Eng Struct 85:95–106Google Scholar
  69. Sasmal S (2009) Performance evaluation and strengthening of deficient beam–column sub-assemblages under cyclic loading.‏ Ph.D. Dissertation. University of Stuttgart, StuttgartGoogle Scholar
  70. Sezen H (2002) Seismic behavior and Modelling of reinforced concrete building columns. Ph.D. Dissertation. University of California, Berkeley, CaliforniaGoogle Scholar
  71. Shafaei J, Zareian MS, Hosseini Marefat MS (2014) Effects of joint flexibility on lateral response of reinforced concrete frames. Eng Struct 81:412–431Google Scholar
  72. Sharma A (2013) Seismic behavior and retrofitting of RC frame structures with emphasis on beam–column joints: experiments and numerical Modelling. Ph.D. Dissertation. University of Stuttgart, StuttgartGoogle Scholar
  73. Sharma A, Eligehausen R, Reddy GR (2011) A new model to simulate joint shear behavior of poorly detailed beam–column connections in RC structures under seismic loads, part I: exterior joints. Eng Struct 33:1034–1035Google Scholar
  74. Shayanfar J, Akbarzadeh BH (2016) Numerical model to simulate shear behaviour of RC joints and columns. Comput Concrete 18(4):877–901Google Scholar
  75. Shayanfar J, Akbarzadeh BH (2017) Nonlinear analysis of RC frames considering shear behaviour of members under varying axial load. Bull Earthq Eng 15(5):2055–2078Google Scholar
  76. Shayanfar J, Akbarzadeh BH (2018) A practical model for simulating nonlinear behaviour of FRP strengthened RC beam–column joints. Steel Compos Struct 27(1):49–74Google Scholar
  77. Shayanfar J, Akbarzadeh BH, Niroomandi A (2016) A proposed model for predicting nonlinear behavior of RC joints under seismic loads. Mater Des 95:563–579Google Scholar
  78. Shayanfar J, Shamkhali MH, Akbarzadeh BH, Hemmati A, Mirani SS (2017) Simulation of nonlinear behaviour of RC joints with 180°-hook under varying axial load. In: The international conference on recent progresses in civil engineering, AmolGoogle Scholar
  79. Shayanfar J, Akbarzadeh BH, Parvin A (2018) Analytical prediction of seismic behavior of RC joints and columns under varying axial load. Eng Struct 174:792–813Google Scholar
  80. Shrestha R, Smith ST, Samali B (2009) Strengthening RC beam–column connections with FRP strips. Proc Inst Civil Eng Struct Build 162(5):323–334Google Scholar
  81. Tsonos AG (2002) Seismic repair of exterior R/C beam-to-column joints using two sided jackets. Struct Eng Mech 13(1):17–34Google Scholar
  82. Tsonos AG (2007) Cyclic load behavior of reinforced concrete beam–column subassemblages of modern structures. ACI Struct J 104(4):468Google Scholar
  83. Tsonos AG (2014) An innovative solution for strengthening old R/C structures and for improving the FRP strengthening method. Struct Monit Maint Int J 1(3):323–338Google Scholar
  84. Tsonos AG, Papanikolaou KV (2003) Post-earthquake repair and strengthening of reinforced concrete beam–column connections (theoretical & experimental investigation). Bull N Z Soc Earthq Eng 36(2):73–93Google Scholar
  85. 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
  86. Unal M, Burak B (2013) Development and analytical verification of an inelastic reinforced concrete joint model. Eng Struct 52:284–294Google Scholar
  87. Wong HF (2005). Shear strength and seismic performance of non-seismically designed reinforced concrete beam–column joints. Ph.D. dissertation, Hong Kong Univ of Science and Technology, Kwoloon, Hong KongGoogle Scholar
  88. Wong HF, Kuang JS (2008) Effects of beam: column depth ratio on joint seismic behaviour. Proc Inst Civil Eng Struct Build 161(2):91–101Google Scholar
  89. Yurdakul O, Avsar O (2016) Strengthening of substandard reinforced concrete beam–column joints by external post-tension rods. Eng Struct 107:9–22Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of MazandaranBabolsarIran

Personalised recommendations