Materials and Structures

, Volume 48, Issue 8, pp 2521–2544 | Cite as

Element mesh, section discretization and material hysteretic laws for fiber beam–column elements of composite structural members

  • Mu-Xuan Tao
  • Jian-Guo Nie
Original Article


A fiber beam–column element for nonlinear analysis of composite structural members is developed in this paper. The programing of complex material uniaxial constitutive laws and the implementation of the developed element into a general commercial standard finite-element package are discussed. Intensive parametric studies on the modeling strategies of element mesh, section discretization and material hysteretic laws are carried out to develop fiber element with sufficient accuracy, efficiency, stability and practicality for composite structural members. Rational element mesh scheme is recommended to capture the sharp jump of the curvature value at the plastic hinge region and to effectively overcome the numerical difficulty of pathological mesh-sensitivity brought about by the strain softening effect. Efficient section discretization schemes are proposed to give results of sufficient accuracy for the hysteretic behavior of composite members under complex cyclic load histories. The Bauschinger effect of the steel is found to be the most significant factor dominating the accuracy, and the hysteretic law of the concrete can be simplified by ignoring the complex strength and stiffness degradation effects with little influence on the accuracy. Finally, the developed program COMPONA-MARC and the recommended modeling strategies are validated by extensive experimental results of composite structural members.


Fiber beam–column element Composite beam Concrete filled steel tube Nonlinear analysis Element mesh Section discretization Material hysteretic laws Programing 



The writers gratefully acknowledge the financial support provided by the National Science Fund of China (Grand Number 51378291), and Twelfth Five-Year plan major projects supported by National Science and Technology (Grant Number 2011BAJ09B01).


  1. 1.
    Zhou F, Mosalam KM, Nakashima M (2007) Finite-element analysis of a composite frame under large lateral cyclic loading. ASCE J Struct Eng 133(7):1018–1026CrossRefGoogle Scholar
  2. 2.
    Nie JG, Tao MX, Cai CS, Chen G (2011) Modeling and investigation of elasto-plastic behavior of steel–concrete composite frame systems. J Constr Steel Res 67(12):1973–1984CrossRefGoogle Scholar
  3. 3.
    Spacone E, EI-Tawil S (2004) Nonlinear analysis of steel–concrete composite structures: state of the art. ASCE J Struct Eng 130(2):159–168CrossRefGoogle Scholar
  4. 4.
    Kostic SM, Filippou FC (2012) Section discretization of fiber beam–column elements for cyclic inelastic response. ASCE J Struct Eng 138(5):592–601CrossRefGoogle Scholar
  5. 5.
    Taucer FF, Spacone E, Filippou FC (1991) A fiber beam–column element for seismic response analysis of reinforced concrete structures (EERC report 91/17). Earthquake Engineering Research Center, University of California, BerkeleyGoogle Scholar
  6. 6.
    Neuenhofer A, Filippou FC (1997) Evaluation of nonlinear frame finite-element models. ASCE J Struct Eng 123(7):958–966CrossRefGoogle Scholar
  7. 7.
    Belytschko T, Bazant ZP, Hyun YW, Chang TP (1986) Strain-softening materials and finite-element solutions. Comput Struct 23(2):163–180CrossRefGoogle Scholar
  8. 8.
    Campbell SD (1994) Nonlinear elements for three dimensional frame analysis. Ph.D. thesis, University of California, BerkeleyGoogle Scholar
  9. 9.
    Berry MP (2006) Performance modeling strategies for modern reinforced concrete bridge columns. Ph.D. thesis, University of Washington, SeattleGoogle Scholar
  10. 10.
    Mander JB, Priestley MJN, Park R (1988) Theoretical stress–strain model for confined concrete. ASCE J Struct Eng 114(8):1804–1826CrossRefGoogle Scholar
  11. 11.
    Martinez-Rueda JE, Elnashai AS (1997) Confined concrete model under cyclic load. Mater Struct 30(4):139–147CrossRefGoogle Scholar
  12. 12.
    Esmaeily A, Xiao Y (2005) Behavior of reinforced concrete columns under variable axial loads: analysis. ACI Struct J 102(5):736–744Google Scholar
  13. 13.
    Légeron F, Paultre P, Mazars J (2005) Damage mechanics modeling of nonlinear seismic behavior of concrete structures. ASCE J Struct Eng 131(6):946–955CrossRefGoogle Scholar
  14. 14.
    Sima JF, Roca P, Molins C (2008) Cyclic constitutive model for concrete. Eng Struct 30(3):695–706CrossRefGoogle Scholar
  15. 15.
    Sakai J, Kawashima K (2006) Unloading and reloading stress–strain model for confined concrete. ASCE J Struct Eng 132(1):112–122CrossRefGoogle Scholar
  16. 16.
    Spacone E, Filippou FC, Taucer FF (1996) Fibre beam–column model for non-linear analysis of R/C frames: part I. Formulation. Earthq Eng Struct Dyn 25(7):711–725CrossRefGoogle Scholar
  17. 17.
    Scott MH, Fenves GL, McKenna F, Filippou FC (2008) Software patterns for nonlinear beam–column models. ASCE J Struct Eng 134(4):562–571CrossRefGoogle Scholar
  18. 18.
    MSC.MARC Version 2007r1 [Computer software]. MSC.Software Corp., Santa AnaGoogle Scholar
  19. 19.
    Zona A, Barbato M, Conte JP (2008) Nonlinear seismic response analysis of steel–concrete composite frames. ASCE J Struct Eng 134(6):986–997CrossRefGoogle Scholar
  20. 20.
    Nie JG, Tao MX (2012) Slab spatial composite effect in composite frame systems. I: effective width for ultimate loading capacity. Eng Struct 38(5):171–184CrossRefGoogle Scholar
  21. 21.
    Salari MR, Spacone E (2001) Analysis of steel–concrete composite frames with bond-slip. ASCE J Struct Eng 127(11):1243–1250CrossRefGoogle Scholar
  22. 22.
    Amadio C, Fragiacomo M (1993) A finite element model for the study of creep and shrinkage effects in composite beams with deformable shear connections. Costruzioni Matalliche 4:213–228Google Scholar
  23. 23.
    Han LH, Zhao XL, Tao Z (2001) Tests and mechanics model of concrete-filled SHS stub columns, columns and beam–columns. Steel Comput Struct Int J 1(1):51–74CrossRefGoogle Scholar
  24. 24.
    Chen ZY, Zhu JQ, Wu PG (1992) High strength concrete and its application, vol 1. Tsinghua University Press, Beijing, p 218 (in Chinese)Google Scholar
  25. 25.
    Comité Euro-International du Béton-Fédération International de la Précontrainte (CEB-FIP) (1993) CEB-FIB model code 1990, design code. Thomas Telford, LondonGoogle Scholar
  26. 26.
    Chen SM, Gu P (2005) Load carrying capacity of composite beams prestressed with external tendons under positive moment. J Constr Steel Res 61(4):515–530CrossRefGoogle Scholar
  27. 27.
    Jia YL, Chen SM, Wang XD (2009) Study of the plastic hinge length of steel and concrete composite beams with external tendons under negative bending. J Zhengzhou Univ (Eng Sci) 30(3):5–8 (in Chinese)Google Scholar
  28. 28.
    Tao MX, Nie JG (2014) Fiber beam–column model considering slab spatial composite effect for nonlinear analysis of composite frame systems. ASCE J Struct Eng 140(1):04013039CrossRefGoogle Scholar
  29. 29.
    Xue WC, Li K, Li L, Zheng RG (2009) Seismic behavior of steel–concrete composite beams. Proc Inst Civil Eng Struct Build 162(SB6):419–427CrossRefGoogle Scholar
  30. 30.
    Fujinaga T, Matsui C, Tsuda K, Yamaji Y (1998) Limiting axial compressive force and structural performance of concrete filled steel circular tubular beam–columns. In: Proceedings of the fifth pacific structural steel conference, Seoul, pp 979–984Google Scholar
  31. 31.
    Zhang MH (1995) Experimental research on the behavior of negative moment regions of composite steel–concrete beams. Master thesis, Tsinghua University, Beijing (in Chinese)Google Scholar
  32. 32.
    Nie JG, Li FX, Fan JS, Zhang XG, Diao S (2011) Experimental study on flexural behavior of composite beams with different concrete flange construction. J Highw Transp Res Dev 5(1):30–35Google Scholar
  33. 33.
    Nie JG, Fan JS, Cai CS (2008) Experimental study of partially shear-connected composite beams with profiled sheeting. Eng Struct 30(1):1–12CrossRefGoogle Scholar
  34. 34.
    Tomii M, Yoshimaro K, Morishita Y (1977) Experimental studies on concrete filled steel tubular stub column under concentric loading. In: Proceedings of the international colloquium on stability of structures under static and dynamic loads, Washington: SSRC/ASCE, pp 718–741Google Scholar
  35. 35.
    Prion HGL, Boehme J (1994) Beam–column behaviour of steel tubes filled with high strength concrete. Can J Civ Eng 21:207–218CrossRefGoogle Scholar
  36. 36.
    Uy B (2000) Strength of concrete filled steel box columns incorporating local buckling. ASCE J Struct Eng 126(3):341–352CrossRefGoogle Scholar
  37. 37.
    Shakir-Khalil H, Zeghiche J (1989) Experimental behaviour of concrete filled rolled rectangular hollow-section column. Struct Eng 67(19):346–353Google Scholar
  38. 38.
    Bridge RQ (1976) Concrete filled steel tubular column. Report No.R283, School of Civil Engineering, University of Sydney, SydneyGoogle Scholar
  39. 39.
    O’Brien AD, Rangan BV (1993) Test on slender tubular steel columns filled with high strength concrete. Aust Civ Eng Transp CE 35(4):287–292Google Scholar

Copyright information

© RILEM 2014

Authors and Affiliations

  1. 1.Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil EngineeringTsinghua UniversityBeijingChina

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