A Strain Based Non-linear Finite Element Analysis of the Exterior Beam Column Joint

  • Shivaji T. BidgarEmail author
  • Partha Bhattacharya
Conference paper


The aim of the present work is to study the behavior of an exterior RC beam-column sub assemblage in a building frame. A nonlinear analysis is carried out up to the yielding of the reinforcement both in compression and tension zone subjected to monotonic loading. The analysis up to the failure of the exterior beam-column joint is carried out using a FE based numerical model. A strain based nonlinear finite element analysis program is developed using 2D plane stress formulation, modified compression field theory, concept of equivalent principal strains, smeared rotating crack approach and secant stiffness formulation in MATLAB environment. The concrete is modeled as four node isoparametric plane stress element and the reinforcement as two node bar element with two degrees of freedom at each node. A perfect bond is assumed at the interface between the concrete and the reinforcement. The load-deformation behavior of lower column, upper column and the beam is measured and compared with the linear ANSYS model and are in well agreement. Subsequently the variation in stresses and strains in the beam column joint are obtained for nonlinear zone and are presented and discussed.


Reinforced concrete Nonlinear analysis Secant stiffness Plastic hinge Finite element method Exterior beam column joint Monotonic load 



The present work described in this paper was supported by All India Council of Technical Education (AICTE) New Delhi, under the scheme of Quality improvement programme (QIP)—Polytechnic and Higher and Technical Education Government of Maharashtra Mumbai and Department of Civil Engineering, Jadavpur University Kolkata. All are gratefully acknowledged.


  1. 1.
    Kumar S (2004) Cyclic behavior of lightly reinforced beam-to-column joints. In: Proceeding of 13th world conference on earthquake engineering, Vancouver, BC, Canada, 1–6 Aug 2004, paper no 1907Google Scholar
  2. 2.
    Wong HF, Kuang JS (2008) Effect of beam-column depth ratio on joint seismic behavior. Proc Inst Civil Eng Struct Build 161:91–101CrossRefGoogle Scholar
  3. 3.
    Scott RH, Hamil SJ, Baglin PS (1999) Behavior of high strength concrete beam-column connections. In: Proceedings of 2nd international conference on high-performance concrete, performance and quality of concrete structures, Gramado, pp 699–713Google Scholar
  4. 4.
    Hamil SJ, Scott RH (2000) Developments in high strength concrete beam-column connection design. University of Durham, UK (ACI Special Publication, web details)Google Scholar
  5. 5.
    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 33:1034–1051Google Scholar
  6. 6.
    Vecchio FJ, Collins MP (1986) The modified compression field theory for reinforced concrete elements subjected to shear. J ACI 83(22):219–231Google Scholar
  7. 7.
    Darwin D, Pecknold DA (1977) Nonlinear biaxial stress-strain law for concrete. J Eng Mech 103(EM2):229–241Google Scholar
  8. 8.
    He W, Wu YF, Liew KM et al (2006) A 2D total strain based constitutive model for predicting the behavior of concrete structures. Int J Eng Sci 44:1280–1303CrossRefGoogle Scholar
  9. 9.
    Vonk RA (1992) Softening of concrete loaded in compression. PhD thesis, Eindhoven University of Technology, Einthoven, The NetherlandsGoogle Scholar
  10. 10.
    Bidgar ST, Bhattacharya PA (2014) Strain based nonlinear finite element analysis of reinforced concrete beam analysis using secant stiffness approach. J Struct Eng CSIR-SERC Chennai India 41(2):169–182Google Scholar
  11. 11.
    Wong PS, Vecchio FJ (2002) Vector 2 and formworks user manualGoogle Scholar
  12. 12.
    Bidgar ST, Bhattacharya P (2014) Nonlinear finite element analysis of reinforced concrete exterior beam column joint subjected to monotonic loading. RTCET STM J 4(2):1–10 (accepted for online publication)Google Scholar
  13. 13.
    Bazant ZP, Oh BH (1983) Crack band theory for fracture of concrete. RILEM Mater Struct 16(93):155–177Google Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Department of Civil EngineeringJadavpur UniversityKolkataIndia
  2. 2.Applied Mechanics DepartmentGovernment Polytechnic, OsmanabadOsmanabadIndia

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