Skip to main content
SpringerLink
Log in

An efficient fiber beam-column element considering flexure–shear interaction and anchorage bond-slip effect for cyclic analysis of RC structures

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

Abstract

In this paper, a fiber beam-column element considering flexure–shear interaction and bond-slip effect is developed for cyclic analysis of reinforced concrete (RC) structures. The element is based on conventional displacement-based Timoshenko beam theory, where the transverse shear deformation is included, and adopts the fiber model to describe the section force–deformation behavior. In the fiber model, shear deformation is assumed to be uniformly distributed along the section and is only resisted by concrete, thus the multi-dimensional concrete damage model is used for concrete fibers and therefore flexure–shear interaction is reflected naturally at the material level. Meanwhile, to account for the significant bond-slip effect at critical regions, the anchorage slip of bars at these regions is analytically derived. Then it is used to modify the uniaxial stress–strain model for steel fibers by assuming that the total strain can be treated as the sum of the bar deformation and anchorage slip, therefore the bond-slip effect is implicitly but simply represented. To validate the proposed element, a series of RC member and structure tests under cyclic loading are simulated. The results indicate that the proposed element can predict cyclic responses of RC structures, and can be used as a reliable tool for analysis of RC structures.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  • Adibi M, Marefat MS, Arani KK, Zare H (2017a) External retrofit of beam-column joints in old fashioned rc structures. Earthq Struct 12(2):237–250

    Article  Google Scholar 

  • Adibi M, Marefat MS, Esmaeily A, Arani KK, Esmaeily A (2017b) Seismic retrofit of external concrete beam-column joints reinforced by plain bars using steel angles prestressed by cross ties. Eng Struct 148:813–828

    Article  Google Scholar 

  • Alemdar BN, White DW (2005) Displacement, flexibility, and mixed beam-column finite element formulations for distributed plasticity analysis. J Struct Eng 131(12):1811–1819

    Article  Google Scholar 

  • Almeida JP, Das S, Pinho R (2012) Adaptive force-based frame element for regularized softening response. Comput Struct 102:1–13

    Article  Google Scholar 

  • Almeida JP, Correia AA, Rui P (2015) Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: applications. Eng Struct 89:218–235

    Article  Google Scholar 

  • Almeida JP, Tarquini D, Beyer K (2016) Modelling approaches for inelastic behaviour of rc walls: multi-level assessment and dependability of results. Arch Comput Methods Eng 23(1):69–100

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Armero F, Ehrlich D (2006) Numerical modeling of softening hinges in thin Euler–Bernoulli beams. Comput Struct 84(10):641–656

    Article  Google Scholar 

  • Ayoub A, Filippou FC (1999) Mixed formulation of bond-slip problems under cyclic loads. J Struct Eng 125(6):661–671

    Article  Google Scholar 

  • Bae S, Bayrak O (2008) Plastic hinge length of reinforced concrete columns. ACI Struct J 105(3):290–300

    Google Scholar 

  • Belytschko T, Hsieh B (1973) Non-linear transient finite element analysis with convected co-ordinates. Int J Numer Meth Eng 7(3):255–271

    Article  Google Scholar 

  • Bui N, Ngo M, Nikolic M, Brancherie D, Ibrahimbegovic A (2014) Enriched timoshenko beam finite element for modeling bending and shear failure of reinforced concrete frames. Comput Struct 143:9–18

    Article  Google Scholar 

  • Building Research Institute BRI (1978) Aseismic analysis of building structural members: a list of experimental results on deformation ability of reinforced concrete columns under large deflection (No. 3). Ministry of Construction, Japan

    Google Scholar 

  • Ceresa P, Petrini L, Rui P (2007) Flexure–shear fiber beam-column elements for modeling frame structures under seismic loading—state of the art. J Earthq Eng 11(sup1):46–88

    Article  Google Scholar 

  • Ceresa P, Petrini L, Rui P, Sousa R (2009) A fibre flexure–shear model for seismic analysis of RC-framed structures. Earthq Eng Struct Dyn 38(5):565–586

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Correia AA, Almeida JP, Rui P (2015) Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part I: theory. Eng Struct 89:204–217

    Article  Google Scholar 

  • Crisfield MA, Remmers JJ, Verhoosel CV et al (2012) Nonlinear finite element analysis of solids and structures. Wiley, New York

    Google Scholar 

  • D’Ambrisi A, Filippou FC (1999) Modeling of cyclic shear behavior in RC members. J Struct Eng 125(10):1143–1150

    Article  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. J Struct Eng 142(7):04016,032

    Article  Google Scholar 

  • Faria R, Oliver J, Cervera M (1998) A strain-based plastic viscous-damage model for massive concrete structures. Int J Solids Struct 35(14):1533–1558

    Article  Google Scholar 

  • Feng DC, Li J (2015) Stochastic nonlinear behavior of reinforced concrete frames. II: numerical simulation. J Struct Eng 142(3):04015,163

    Article  Google Scholar 

  • Feng DC, Ren XD (2017) Enriched force-based frame element with evolutionary plastic hinge. Journal of Structural Engineering 143(10):06017,005

    Article  Google Scholar 

  • Feng DC, Kolay C, Ricles JM, Li J (2016a) Collapse simulation of reinforced concrete frame structures. Struct Des Tall Spec Build 25(12):578–601

    Article  Google Scholar 

  • Feng DC, Ren XD, Li J (2016b) Implicit gradient delocalization method for force-based frame element. J Struct Eng 142(2):04015,122

    Article  Google Scholar 

  • Feng DC, Wu G, Sun ZY, Xu JG (2017) A flexure–shear timoshenko fiber beam element based on softened damage-plasticity model. Eng Struct 140:483–497

    Article  Google Scholar 

  • Feng DC, Ren XD, Li J (2018) Softened damage-plasticity model for analysis of cracked reinforced concrete structures. J Struct Eng 144(6):04018,044

    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 

  • Hibbitt, Karlsson, Sorensen (2001) ABAQUS/standard user’s manual, vol 1. Hibbitt, Karlsson & Sorensen, Pawtucket

    Google Scholar 

  • Hsu TTC (1988) Softened truss model theory for shear and torsion. ACI Struct J 85(6):624–635

    Google Scholar 

  • Ju JW (1989) On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int J Solids Struct 25(7):803–833

    Article  Google Scholar 

  • Kagermanov A, Ceresa P (2017) Fiber-section model with an exact shear strain profile for two-dimensional rc frame structures. J Struct Eng 143(10):04017,132

    Article  Google Scholar 

  • Koutromanos I, Bowers J (2016) Enhanced strain beam formulation resolving several issues of displacement-based elements for nonlinear analysis. J Eng Mech 142(9):04016,059

    Article  Google Scholar 

  • Kwak HG, Kim JK (2006) Implementation of bond-slip effect in analyses of RC frames under cyclic loads using layered section method. Eng Struct 28(12):1715–1727

    Article  Google Scholar 

  • Lee J, Fenves GL (1998) Plastic-damage model for cyclic loading of concrete structures. J Eng Mech 124(8):892–900

    Article  Google Scholar 

  • Lee CL, Filippou FC (2015) Frame element with mixed formulations for composite and RC members with bond slip. I: theory and fixed-end rotation. J Struct Eng 141(11):04015,039

    Article  Google Scholar 

  • Li J, Ren XD (2009) Stochastic damage model for concrete based on energy equivalent strain. Int J Solids Struct 46(11):2407–2419

    Article  Google Scholar 

  • Li ZX, Gao Y, Zhao Q (2016) A 3D flexure–shear fiber element for modeling the seismic behavior of reinforced concrete columns. Eng Struct 117:372–383

    Article  Google Scholar 

  • Limkatanyu S, Spacone E (2002) Reinforced concrete frame element with bond interfaces. I: displacement-based, force-based, and mixed formulations. J Struct Eng 128(3):346–355

    Article  Google Scholar 

  • Lodhi MS, Sezen H (2012) Estimation of monotonic behavior of reinforced concrete columns considering shear-flexure-axial load interaction. Earthq Eng Struct Dyn 41(41):2159–2175

    Google Scholar 

  • Lowes LN, Mitra N, Altoontash A (2003) A beam-column joint model for simulating the earthquake response of reinforced concrete frames. Pacific Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley

    Google Scholar 

  • Lynn AC, Moehle JP, Mahin SA, Holmes WT (1996) Seismic evaluation of existing reinforced concrete building columns. Earthq Spectra 12(4):715–739

    Article  Google Scholar 

  • Menegotto M (1973) Method of analysis for cyclically loaded RC plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending. In: Proceedings of IABSE symposium on resistance and ultimate deformability of structures acted on by well defined repeated loads, pp 15–22

  • Mergos PE, Kappos AJ (2008) A distributed shear and flexural flexibility model with shear-flexure interaction for RC members subjected to seismic loading. Earthq Eng Struct Dyn 37(12):1349–1370

    Article  Google Scholar 

  • Mergos PE, Kappos AJ (2010) Seismic damage analysis including inelastic shear-flexure interaction. Bull Earthq Eng 8(1):27–46

    Article  Google Scholar 

  • Mergos PE, Kappos AJ (2012) A gradual spread inelasticity model for RC beam-columns, accounting for flexure, shear and anchorage slip. Eng Struct 44(6):94–106

    Article  Google Scholar 

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

    Google Scholar 

  • Mohr S, Bairán JM, Mar AR (2010) A frame element model for the analysis of reinforced concrete structures under shear and bending. Eng Struct 32(12):3936–3954

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mullapudi TRS, Ayoub AS (2013) Analysis of reinforced concrete columns subjected to combined axial, flexure, shear and torsional loads. J Struct Eng 139(4):561–573

    Article  Google Scholar 

  • Neuenhofer A, Filippou FC (1998) Geometrically nonlinear flexibility-based frame finite element. J Struct Eng 124(6):704–711

    Article  Google Scholar 

  • Pan WH, Tao MX, Nie JG (2017) Fiber beam-column element model considering reinforcement anchorage slip in the footing. Bull Earthq Eng 15(3):991–1018

    Article  Google Scholar 

  • Petrangeli M, Pinto PE, Ciampi V (1999) Fiber element for cyclic bending and shear of RC structures. I: theory. J Eng Mech 125(9):994–1001

    Article  Google Scholar 

  • Saatcioglu M, Grira M (1999) Confinement of reinforced concrete columns with welded reinforcement grids. ACI Struct J 96(1):29–39

    Google Scholar 

  • Saritas A (2006) Mixed formulation frame element for shear critical steel and reinforced concrete structural members. Ph.D. Thesis, University of California, Berkeley, CA, USA

  • Saritas A, Filippou FC (2009) Inelastic axial-flexure–shear coupling in a mixed formulation beam finite element. Int J Non-linear Mech 44(8):913–922

    Article  Google Scholar 

  • Schoettler M, Restrepo J, Guerrini G, Duck D, Carrea F (2012) A full-scale, single-column bridge bent tested by shake-table excitation. Center for Civil Engineering Earthquake Research, Department of Civil Engineering, University of Nevada, Reno

    Google Scholar 

  • Scott MH, Jafari Azad V (2017) Response sensitivity of material and geometric nonlinear force-based timoshenko frame elements. Int J Numer Meth Eng 111(5):474–492

    Article  Google Scholar 

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

    Google Scholar 

  • Spacone E, Marini A (2006) Analysis of reinforced concrete elements including shear effects. ACI Struct J 103(5):645–655

    Google Scholar 

  • Spacone E, Filippou FC, Taucer FF (1996) Fibre beam-column model for non-linear analysis of RC frames: part I. Formulation. Earthq Eng Struct Dyn 25(7):711–726

    Article  Google Scholar 

  • Stramandinoli RSB, Rovere HLL (2012) FE model for nonlinear analysis of reinforced concrete beams considering shear deformation. Eng Struct 35:244–253

    Article  Google Scholar 

  • Tarquini D, Almeida JP, Beyer K (2017) Axially equilibrated displacement-based beam element for simulating the cyclic inelastic behaviour of rc members. Earthq Eng Struct Dyn 46(9):1471–1492

    Article  Google Scholar 

  • Terzic V, Schoettler MJ, Restrepo JI, Mahin SA (2015) Concrete column blind prediction contest 2010: outcomes and observations. PEER Report 1

  • Tesser L, Filippou F, Talledo D, Scotta R, Vitaliani R (2011) Nonlinear analysis of RC panels by a two parameter concrete damage model. In: III ECCOMAS thematic conference on computational methods in structural dynamics and earthquake engineering, pp 25–28

  • Toprak AE, Bal IE, Glay FG (2015) Review on the macro-modeling alternatives and a proposal for modeling coupling beams in tall buildings. Bull Earthq Eng 13(8):2309–2326

    Article  Google Scholar 

  • Ueda T, Lin I, Hawkins NM (1986) Beam bar anchorages in exterior column beam connections. ACI J Proc 83(3):412–422

    Google Scholar 

  • Vecchio FJ, Collins MP (1986) The modified compression-field theory for reinforced concrete elements subjected to shear. ACI J Proc 83(2):219–231

    Google Scholar 

  • Vecchio FJ, Collins MP (1988) Predicting the response of reinforced concrete beams subjected to shear using modified compression field theory. ACI Struct J 85(3):258–268

    Google Scholar 

  • Wu JY (2004) Damage energy release rate-based elastoplastic damage constitutive model for concrete and its application to nonlinear analysis of structures. Ph.D. Thesis, Tongji University, Shanghai

  • Wu JY (2013) New enriched finite elements with softening plastic hinges for the modeling of localized failure in beams. Comput Struct 128:203–218

    Article  Google Scholar 

  • Wu JY (2017) A unified phase-field theory for the mechanics of damage and quasi-brittle failure. J Mech Phys Solids 103:72–99

    Article  Google Scholar 

  • Wu JY (2018) A geometrically regularized gradient-damage model with energetic equivalence. Comput Methods Appl Mech Eng 328:612–637

    Article  Google Scholar 

  • Wu JY, Li J, Faria R (2006) An energy release rate-based plastic-damage model for concrete. Int J Solids Struct 43(3):583–612

    Article  Google Scholar 

  • Xu SY, Zhang J (2011) Hysteretic shear-flexure interaction model of reinforced concrete columns for seismic response assessment of bridges. Earthq Eng Struct Dyn 40(3):315–337

    Article  Google Scholar 

  • Yu J, Tan KH (2014) Numerical analysis with joint model on RC assemblages subjected to progressive collapse. Mag Concrete Res 66(23):1201–1218

    Article  Google Scholar 

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

    Google Scholar 

Download references

Acknowledgements

Financial supports from the National Natural Science Foundation of China (Grant Nos. 51708106, 51778130), the Natural Science Foundation of Jiangsu Province (Grant No. BK20170680), and the Fundamental Research Funds for the Central Universities are greatly appreciated.

Author information

Authors and Affiliations

  1. Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing, 210096, China

    De-Cheng Feng

  2. College of Civil Engineering, Hunan University, Changsha, 410082, China

    Jun Xu

Authors
  1. De-Cheng Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Xu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Feng, DC., Xu, J. An efficient fiber beam-column element considering flexure–shear interaction and anchorage bond-slip effect for cyclic analysis of RC structures. Bull Earthquake Eng 16, 5425–5452 (2018). https://doi.org/10.1007/s10518-018-0392-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-018-0392-y

Keywords

Search

Navigation