Skip to main content
SpringerLink
Log in

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

  • Original Research
  • Published:
Bulletin of Earthquake Engineering Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • ACI Committee 318 (2014) Building code requirements for structural concrete (ACI 318-14) and commentary. American Concrete Institute, Detroit, USA

  • Alaee P, Li B (2017) High-strength concrete exterior beam–column joints with high-yield strength steel reinforcements. Eng Struct 145:305–321. https://doi.org/10.1016/j.engstruct.2017.05.024

    Article  Google Scholar 

  • 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. https://doi.org/10.1186/s40069-018-0303-2

    Article  Google Scholar 

  • 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. https://doi.org/10.1139/l06-164

    Article  Google Scholar 

  • Antonopoulos CP, Triantafillou TC (2003) Experimental investigation of FRP-strengthened RC beam–column joints. J Compos Constr ASCE 7(1):39–49. https://doi.org/10.1061/(asce)1090-0268(2003)7:1(39)

    Article  Google Scholar 

  • Architectural Institute of Japan (AIJ) (2010) AIJ standard for structural calculation of reinforced concrete structures (Japanese). Maruzen, Tokyo

    Google Scholar 

  • Bakir PG (2003) Seismic resistance and mechanical behaviour of exterior beam–column joints with crossed inclined bars. Stuct Eng Mech 16(4):493–517. https://doi.org/10.12989/sem.2003.16.4.493

    Article  Google Scholar 

  • Beydokhti EZ, Shariatmadar H (2016) Strengthening and rehabilitation of exterior RC beam–column joints using carbon-FRP jacketing. Mater Struct 49:5067–5083. https://doi.org/10.1617/s11527-016-0844-2

    Article  Google Scholar 

  • 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):591–597

    Google Scholar 

  • Chalioris CE, Bantilas KE (2017) Shear strength of reinforced concrete beam–column joints with crossed inclined bars. Eng Struct 140:241–255. https://doi.org/10.1016/j.engstruct.2017.02.072

    Article  Google Scholar 

  • 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):881–897

    Google Scholar 

  • 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. https://doi.org/10.12989/cac.2014.14.1.019

    Article  Google Scholar 

  • 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. https://doi.org/10.12989/cac.2017.20.3.329

    Article  Google Scholar 

  • 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, Canada

  • Chun SC, Shin YS (2014) Cyclic testing of exterior beam–column joints with varying joint aspect ratio. ACI Struct J 111(3):693–704

    Google Scholar 

  • 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):259–264

    Google Scholar 

  • 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, Berkeley

  • CSA A23.3-04 (2004) Design of concrete structures. Canadian Standards Association, Rexdale

  • 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. https://doi.org/10.1016/j.engstruct.2016.01.016

    Article  Google Scholar 

  • Durrani AJ, Zerbe HE (1987) Seismic resistance of RC exterior connections with floor slab. J Struct Eng ASCE 113(8):1850–1864

    Google Scholar 

  • Ehsani MR, Alameddine F (1991) Design recommendations for type 2 high-strength reinforced concrete connections. ACI Struct J 88(3):277–291

    Google Scholar 

  • Ehsani MR, Wight JK (1985) Exterior reinforced concrete beam-to-column connections subjected to earthquake-type loading. ACI Struct J 82(4):492–499

    Google Scholar 

  • Ehsani MR, Moussa AE, Vallenilla CR (1987) Comparison of inelastic behavior of reinforced ordinary- and high-strength concrete frames. ACI Struct J 84(2):161–169

    Google Scholar 

  • El-Amoury T, Ghobarah A (2002) Seismic rehabilitation of beam–column joint using GFRP sheets. Eng Struct 24:1397–1407

    Google Scholar 

  • 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 258:19–36

    Google Scholar 

  • Eurocode 8 (2004) Design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. BSI British Standards, London

  • Fisher MJ, Sezen H (2011) Behavior of exterior reinforced concrete beam–column joints including a new reinforcement. Struct Eng Mech 40(6):867–883

    Google Scholar 

  • 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 132:145–166

    Google Scholar 

  • Ghobarah A, El-Amoury T (2005) Seismic rehabilitation of deficient exterior concrete frame joints. J Compos Constr ASCE 9(1):408–416

    Google Scholar 

  • Ghobarah A, Said AM (2002) Shear strengthening of beam–column joints. Eng Struct 24(7):881–888

    Google Scholar 

  • 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. https://doi.org/10.1016/j.engstruct.2007.06.005

    Article  Google Scholar 

  • 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):11–25

    Google Scholar 

  • Hamil SJ (2000) Reinforced concrete beam–column connection behavior. Ph.D. Dissertation, University of Durham, United Kingdom

  • Hanson NW, Connor HW (1967) Seismic resistance of reinforced concrete beam–column joints. J Struct Div ASCE 93:533–559

    Google Scholar 

  • Hassan WM, Moehle JP (2018) Shear strength of exterior and corner beam–column joints without transverse reinforcement. ACI Struct J 115(6):1719–1728

    Google Scholar 

  • 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):846–857

    Google Scholar 

  • 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. https://doi.org/10.1061/(ASCE)0733-445(2001)127:1(43)

    Article  Google Scholar 

  • 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. 397

  • 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):445–453

    Google Scholar 

  • 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):913–924

    Google Scholar 

  • 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):1239–1248

    Google Scholar 

  • Idayani BS (2007) The influence of concrete strength on the behaviour of external beam–column joints. Master Thesis, University of Malaysia

  • IS 13920 (2016) Ductile design and detailing of reinforced concrete structures subjected to seismic forces—code of practice, India

  • 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. https://doi.org/10.1002/eqe.2437

    Article  Google Scholar 

  • Kaku T, Asakusa H (1991) Ductility estimation of exterior beam–column subassemblages in reinforced concrete frames. ACI SP 123:167–185

    Google Scholar 

  • 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 6:433–440

    Google Scholar 

  • Karayannis CG, Chalioris CE, Sideris KK (1998) Effectiveness of RC beam–column connection repairing using epoxy resin injections. J Earthq Eng 2(2):217–240

    Google Scholar 

  • 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 37:727–746

    Google Scholar 

  • Kassem W (2015) Strut-and-tie modelling for the analysis and design of RC beam–column joints. Mater Struct. https://doi.org/10.1617/s11527-015-0732-1

    Article  Google Scholar 

  • Kim J, LaFave JM, Song J (2009) Joint shear behavior of reinforced concrete beam–column connections. Mag Concr Res 61(2):119–132

    Google Scholar 

  • 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)

  • Kotsovou G, Mouzakis H (2012) Seismic design of RC external beam–column joints. Bull Earthq Eng 10(2):645–677. https://doi.org/10.1007/s10518-011-9303-1

    Article  Google Scholar 

  • Kuang JS, Wong HF (2006) Effects of beam bar anchorage on beam–column joint behavior. Struct Build 159(2):115–124

    Google Scholar 

  • 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. https://doi.org/10.1016/j.proeng.2011.07.417

    Article  Google Scholar 

  • Kupfer H, Gerstle KH (1973) Behavior of concrete under biaxial stress. J Eng Mech Div ASCE 99(4):853–866

    Google Scholar 

  • 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, China

  • Lee HJ, Chang CJ (2017) High-strength reinforcement in exterior beam–column joints under cyclic loading. ACI Struct J 114(5):1325–1338

    Google Scholar 

  • Lee HJ, Yu SY (2009) Cyclic response of exterior beam–column joints with different anchorage methods. ACI Struct J 106(3):329–339

    Google Scholar 

  • 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. https://doi.org/10.1016/j.compositesb.2009.06.005

    Article  Google Scholar 

  • 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. https://doi.org/10.1007/s10518-012-9340-4

    Article  Google Scholar 

  • 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. https://doi.org/10.1007/s10518-012-9342-2

    Article  Google Scholar 

  • Liu C (2006) Seismic behaviour of beam–column joint subassemblies reinforced with steel fibres. Master Thesis, University of Canterbury, New Zealand

  • 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. https://doi.org/10.1016/j.engstruct.2018.01.008

    Article  Google Scholar 

  • 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 145–158

  • Megget LM (1974) Cyclic behaviour of exterior reinforced concrete beam–column Joints. Bull N Z Nat Soc Earthq Eng 7(1):22–47

    Google Scholar 

  • Megget LM, Park R (1971) Reinforced concrete exterior beam–column joints under seismic loading. N Z Eng 26(11):341–353

    Google Scholar 

  • 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. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:1(105)

    Article  Google Scholar 

  • 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):149–156

    Google Scholar 

  • NZS 3101 (2006) Concrete structures standard: part 1—the design of concrete structures. New Zealand Standards, Wellington, New Zealand

  • Ortiz IR (1993) Strut-and-tie modeling of reinforced concrete short beams and beam–column joints. PhD dissertation, University of Westminster, London, UK

  • 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, London

  • Pantelides CP, Clyde C, Reaveley LD (2002) Performance-based evaluation of reinforced concrete building exterior joints for seismic excitation. Earthq Spectra 18(3):449–480

    Google Scholar 

  • Paratea K, Kumar R (2016) Investigation of shear strength models for exterior RC beam–column joint. Struct Eng Mech 58(3):475–514

    Google Scholar 

  • Paratea K, Kumar R (2019) Shear strength criteria for design of RC beam–column joints in building codes. Bull Earthq Eng. https://doi.org/10.1007/s10518-018-0492-8

    Article  Google Scholar 

  • Park S, Mosalam KM (2012) Parameters for shear strength prediction of exterior beam column joints without transverse reinforcement. Eng Struct 36:198–209. https://doi.org/10.1016/j.engstruct.2011.11.017

    Article  Google Scholar 

  • 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 772–781

  • Parker DE, Bullman PJM (1997) Shear strength within reinforced concrete beam–column joints. Struct Eng 75(4):53–57

    Google Scholar 

  • Paulay T, Priestley MJN (1992) Seismic design of reinforced concrete and masonry buildings. Wiley, Hoboken

    Google Scholar 

  • Paulay T, Scarpas A (1981) Behavior of exterior beam–column joints. Bull New Zealand Nat Soc Earthq Eng 14(3):131–144

    Google Scholar 

  • Pauletta M, Di Luca D, Russo G (2015) Exterior beam column joints—shear strength model and design formula. Eng Struct 94:70–81. https://doi.org/10.1016/j.engstruct.2015.03.040

    Article  Google Scholar 

  • 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. https://doi.org/10.1016/j.engstruct.2016.03.033

    Article  Google Scholar 

  • Santarsiero G, Masi A (2015) Seismic performance of RC beam–column joints retrofitted with steel dissipation jackets. Eng Struct 106:85–95. https://doi.org/10.1016/j.engstruct.2014.12.013

    Article  Google Scholar 

  • Scott RH (1996) Intrinsic mechanisms in reinforced concrete beam–column connection behavior. ACI Struct J 93(3):1–11

    Google Scholar 

  • 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. https://doi.org/10.1002/eqe.2794

    Article  Google Scholar 

  • Shrestha R, Smith ST, Samali B (2009) Strengthening RC beam–column connections with FRP strips. Struct Build 162(5):23–334. https://doi.org/10.1680/stbu.2009.162.5.323

    Article  Google Scholar 

  • Standards Association of New Zealand (2006) The design of concrete structures. NZS 3101:2006, New Zealand Standards Authority, Wellington, New Zealand

  • Tasuji ME, Slate FO, Nilson AH (1978) Stress–strain response and fracture of concrete in biaxial loading. ACI J 75(7):306–312

    Google Scholar 

  • The MathWorks Inc. (2011) MATLAB version 7.12.0 ed. Natick, MA, USA

  • Tran TM, Hadi MNS (2017) Shear strength model of reinforced-concrete exterior joint under cyclic loading. Struct Build 170:603–617. https://doi.org/10.1680/jstbu.15.00022

    Article  Google Scholar 

  • Tsonos AG (1999) Lateral load response of strengthened reinforced concrete beam-to-column joints. ACI Struct J 96(1):46–56

    Google Scholar 

  • 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):389–410

    Google Scholar 

  • Tsonos AG (2007) Cyclic load behavior of reinforced concrete beam–column subassemblages of modern structures. ACI Struct J 104(4):468–478

    Google Scholar 

  • 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):3–12

    Google Scholar 

  • Uzumeri SM (1977) Strength and ductility of cast-in-place beam–column joints. ACI J 53:293–350

    Google Scholar 

  • Vatani-Oskouei A (2010) Repairing of seismically damaged RC exterior beam–column connection using CFRP. J Reinf Plast Compos 29:3257–3274

    Google Scholar 

  • Vollum RL, Newman JB (1999) The design of reinforced concrete external beam–column joints. Struct Eng 77(23–24):21–27

    Google Scholar 

  • 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):590–606

    Google Scholar 

  • Wang GL, Meng SP (2008) Modified strut-and-tie model for prestressed concrete deep beams. Eng Struct 30(4):3489–3496. https://doi.org/10.1016/j.engstruct.2008.05.020

    Article  Google Scholar 

  • Wang GL, Dai JG, Teng JG (2012) Shear strength model for RC beam–column joints under seismic loading. Eng Struct 40:350–360. https://doi.org/10.1016/j.engstruct.2012.02.038

    Article  Google Scholar 

  • 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 Kong

  • Wong HF, Kuang JS (2008) Effects of beam–column depth ratio on joint seismic behavior. Struct Build 161(2):91–101

    Google Scholar 

  • Zhang N, Tan KH (2007) Direct strut-and-tie model for single span and continuous deep beams. Eng Struct 29:2987–3001. https://doi.org/10.1016/j.engstruct.2007.02.004

    Article  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen, 40000, Thailand

    Panatchai Chetchotisak & Eakkawit Arjsri

  2. Department of Civil Engineering, Khon Kaen University, Khon Kaen, 40002, Thailand

    Jaruek Teerawong

Authors
  1. Panatchai Chetchotisak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eakkawit Arjsri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jaruek Teerawong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Panatchai Chetchotisak.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chetchotisak, P., Arjsri, E. & Teerawong, J. Strut-and-tie model for shear strength prediction of RC exterior beam–column joints under seismic loading. Bull Earthquake Eng 18, 1525–1546 (2020). https://doi.org/10.1007/s10518-019-00756-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-019-00756-4

Keywords

Search

Navigation