Skip to main content
SpringerLink
Log in

Fiber beam–column element model considering reinforcement anchorage slip in the footing

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

Abstract

A simple and computationally efficient fiber beam–column element model is developed to consider reinforcement anchorage slip in the footing, which may cause the fixed-end rotation and greatly influence the seismic response of a reinforced concrete column. First, on the basis of an effective macro model for calculating anchorage slip and a classical uniaxial stress–strain relationship of rebar, the reinforcement anchorage slip in the footing is formulated. The macro model assumed a stepped bond stress to deal with the bond–slip relationship, and the slip is derived by integrating the strain over the development length. Then, the derived anchorage slip is introduced into the framework of the conventional fiber element model. By considering the rebar fiber strain in the footing fiber element as the sum of the rebar deformation and the anchorage slip, the stress–strain skeleton curve and the hysteretic law of rebar are modified. After that, the developed fiber model is validated by simulating two quasi-static tests of reinforced concrete columns. The developed model shows good accuracy in simulating the moment capacity and column stiffness, whereas the conventional fiber model may significantly overestimate the column initial and unloading stiffness. Finally, the shake-table test of a full-scale flexure-dominated bridge column is simulated to further validate the developed model. Comparisons indicate the considerably improved accuracy of the developed model in simulating the column displacement time-histories, base moment–column displacement responses, and base moment–base curvature responses. In addition, the rebar anchorage slip and the lateral displacement ratio owing to this slip effect are well predicted by the developed model. Therefore, the model is validated at structural, sectional, and micro levels.

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
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28

Similar content being viewed by others

References

  • Alsiwat JM, Saatcioglu M (1992) Reinforcement anchorage slip under monotonic loading. ASCE J Struct Eng 118(9):2421–2438

    Article  Google Scholar 

  • Bažant ZP, Oh BH (1983) Crack band theory for fracture of concrete. Mater Struct 16(3):155–177

    Google Scholar 

  • Coleman J, Spacone E (2001) Localization issues in force-based frame elements. ASCE J Struct Eng 127(11):1257–1265

    Article  Google Scholar 

  • Comité Euro-International du Béton-Fédération International de la Précontrainte (CEB-FIP) (1993) CEB-FIP model code 1990, design code. Thomas Telford, London

    Book  Google Scholar 

  • Ding R, Tao MX, Nie JG, Mo YL (2016) Shear deformation and sliding-based fiber beam–column model for seismic analysis of reinforced concrete coupling beams. ASCE J Struct Eng 142(7):04016032

    Article  Google Scholar 

  • Eligehausen R, Popov EP, Bertero VV (1983) Local bond stress–slip relationships of deformed bars under generalized excitations. Report UCB/EERC 83/23. Earthquake Engineering Research Center, University of California, Berkeley, CA

    Google Scholar 

  • Esmaeily A, Xiao Y (2005) Behavior of reinforced concrete columns under variable axial loads: analysis. ACI Strut J 102(5):736–744

    Google Scholar 

  • Feng Y, Kowalsky MJ, Nau JM (2015) Finite-element method to predict reinforcing bar buckling in RC structures. ASCE J Struct Eng 141(5):04014147

    Article  Google Scholar 

  • Filippou FC, Popov EP, Bertero VV (1983) Effects of bond deterioration on hysteretic behavior of reinforced concrete joints. Report UCB/EERC 83/19. Earthquake Engineering Research Center, University of California, Berkeley, CA

    Google Scholar 

  • Filippou FC, D’Ambrisi A, Issa A (1999) Effects of reinforcement slip on hysteretic behavior of reinforced concrete frame members. ACI Strut J 96(3):327–335

    Google Scholar 

  • Hognestad E, Hanson NW, McHenry D (1955) Concrete stress distribution in ultimate strength design. ACI J Proc 52(12):455–480

    Google Scholar 

  • Hose YD, Seible F, Priestley MJN (1997) Strategic relocation of plastic hinges in bridge columns. Report SSRP 97/05. Earthquake Engineering Research Center, University of California, San Diego, CA

    Google Scholar 

  • Kawashima K, Watanabe G, Hayakawa R (2003) Seismic performance of RC bridge columns subjected to bilateral excitation. In: Proceedings of 35th joint meeting, panel on wind and seismic effects, Tsukuba Science City, Japan

  • Kostic SM, Filippou FC (2012) Section discretization of fiber beam–column elements for cyclic inelastic response. ASCE J Struct Eng 138(5):592–601

    Article  Google Scholar 

  • Lara O, Ventura CE, Suarez VA (2012) Cumulative damage study for the 2010 “blind prediction contest” of a reinforced concrete bridge column. In: Proceedings of 15th world conference on earthquake engineering, Lisbon, Portugal

  • Légeron F, Paultre P, Mazars J (2005) Damage mechanics modeling of nonlinear seismic behavior of concrete structures. ASCE J Struct Eng 131(6):946–955

    Article  Google Scholar 

  • Mander JB, Priestley MJN, Park R (1988) Theoretical stress–strain model for confined concrete. ASCE J Struct Eng 114(8):1804–1826

    Article  Google Scholar 

  • Monti G, Nuti C (1992) Nonlinear cyclic behavior of reinforcing bars including buckling. ASCE J Struct Eng 118(12):3268–3284

    Article  Google Scholar 

  • Monti G, Spacone E (2000) Reinforced concrete fiber beam element with bond–slip. ASCE J Struct Eng 126(6):654–661

    Article  Google Scholar 

  • Monti G, Filippou FC, Spacone E (1997) Finite element for anchored bars under cyclic load reversals. ASCE J Struct Eng 123(5):614–623

    Article  Google Scholar 

  • MSC.Software Corporation (2012) MSC.Marc 2012 volume A: theory and user information, Santa Ana, CA

  • Nie J, Tao M, Cai CS, Chen G (2011) Modeling and investigation of elasto-plastic behavior of steel–concrete composite frame systems. J Constr Steel Res 67(12):1973–1984

    Article  Google Scholar 

  • Otani S (1974) Inelastic analysis of R/C frame structures. ASCE J Struct Div 100(7):1433–1449

    Google Scholar 

  • Pacific Earthquake Engineering Research Center (PEER) (2016) Concrete column blind prediction contest 2010. http://nisee2.berkeley.edu/peer/prediction_contest. 10 Jan 2016

  • Petrangeli M (1999) Fiber element for cyclic bending and shear of RC structures. II: verification. ASCE. J Eng Mech 125(9):1002–1009

    Article  Google Scholar 

  • Priestley MJN, Park R (1987) Strength and ductility of concrete bridge columns under seismic loading. ACI Strut J 84(1):61–76

    Google Scholar 

  • Saatcioglu M, Alsiwat JM, Ozcebe G (1992) Hysteretic behavior of anchorage slip in R/C members. ASCE J Struct Eng 118(9):2439–2458

    Article  Google Scholar 

  • Sakai J, Kawashima K (2006) Unloading and reloading stress–strain model for confined concrete. ASCE J Struct Eng 132(1):112–122

    Article  Google Scholar 

  • Schoettler MJ, Restrepo JI, Guerrini G, Duck DE, Carrea F (2015) A full-scale, single-column bridge bent tested by shake-table excitation. PEER report 2015/02. Pacific Earthquake Engineering Research Center (PEER), University of California, Berkeley, CA

    Google Scholar 

  • Sezen H, Chowdhury T (2009) Hysteretic model for reinforced concrete columns including the effect of shear and axial load failure. ASCE J Struct Eng 135(2):139–146

    Article  Google Scholar 

  • Sezen H, Moehle JP (2006) Seismic tests of concrete columns with light transverse reinforcement. ACI Strut J 103(6):842–849

    Google Scholar 

  • Sezen H, Setzler EJ (2008) Reinforcement slip in reinforced concrete columns. ACI Strut J 105(3):280–289

    Google Scholar 

  • 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):711–725

    Article  Google Scholar 

  • 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):04013039

    Article  Google Scholar 

  • Tao MX, Nie JG (2015) Element mesh, section discretization and material hysteretic laws for fiber beam–column elements of composite structural members. Mater Struct 48(8):2521–2544

    Article  Google Scholar 

  • Taucer F, Spacone E, Filippou FC (1991) A fiber beam–column element for seismic response analysis of reinforced concrete structures. Report UCB/EERC 91/17. Earthquake Engineering Research Center, University of California, Berkeley, CA

    Google Scholar 

  • Terzic V, Schoettler MJ, Restrepo JI, Mahin SA (2015) Concrete column blind prediction contest 2010: Outcomes and observations. PEER report 2015/01. Pacific Earthquake Engineering Research Center (PEER), University of California, Berkeley, CA

    Google Scholar 

  • Tirasit P, Kawashima K (2007) Seismic performance of square reinforced concrete columns under combined cyclic flexural and torsional loadings. J Earthq Eng 11(3):425–452

    Article  Google Scholar 

  • Zahn FA (1985) Design of reinforced concrete bridge columns for strength and ductility. Ph.D. thesis. University of Canterbury, Christchurch, New Zealand

  • Zhang J, Stang H, Li VC (2000) Experimental study on crack bridging in FRC under uniaxial fatigue tension. J Mater Civil Eng 12(1):66–73

    Article  Google Scholar 

  • Zhang J, Stang H, Li VC (2001) Crack bridging model for fibre reinforced concrete under fatigue tension. Int J Fatigue 23(8):655–670

    Article  Google Scholar 

  • Zhao J, Sritharan S (2007) Modeling of strain penetration effects in fiber-based analysis of reinforced concrete structures. ACI Strut J 104(2):133–141

    Google Scholar 

  • Zhao J, Sritharan S (2016) OpenSees Wiki: Bond SP01—strain penetration model for fully anchored steel reinforcing bars. http://opensees.berkeley.edu/wiki/index.php/Bond_SP01_-_-_Strain_Penetration_Model_for_Fully_Anchored_Steel_Reinforcing_Bars. 10 Jan 2016

Download references

Acknowledgments

The writers gratefully acknowledge the financial support provided by the Beijing Natural Science Foundation (Grand Number 8162023) and the National Natural Science Foundation of China (grant number 51229801 and 51138007). The authors also express their sincere appreciation to the reviewers of this paper for their constructive comments and suggestions.

Author information

Authors and Affiliations

  1. Key Laboratory of Civil Engineering Safe and Durability of China Education Ministry, Department of Civil Engineering, Tsinghua University, Beijing, 100084, China

    Wen-Hao Pan & Mu-Xuan Tao

  2. Beijing Engineering Research Center of Steel and Concrete Composite Structures, Department of Civil Engineering, Tsinghua University, Beijing, 100084, China

    Jian-Guo Nie

Authors
  1. Wen-Hao Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mu-Xuan Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jian-Guo Nie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mu-Xuan Tao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pan, WH., Tao, MX. & Nie, JG. Fiber beam–column element model considering reinforcement anchorage slip in the footing. Bull Earthquake Eng 15, 991–1018 (2017). https://doi.org/10.1007/s10518-016-9987-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-016-9987-3

Keywords

Search

Navigation