A 3D finite element model for reinforced concrete structures analysis

Bono, G. F. F.; Campos Filho, A.; Pacheco, A. R.

doi:10.1590/S1983-41952011000400002

Abstracts

This work presents a numerical model for 3D analyses through the finite element method of reinforced concrete structures subjected to monotonic loads. The proposed model for concrete is orthotropic and uses the equivalent uniaxial strain concept. The equivalent uniaxial stress-strain relation is generalized to take into account the triaxial stress conditions. The parameters used in the equivalent uniaxial stress-strain curve are determined from the failure surface defined in the principal stress space. The implementation in finite elements is based on the consideration of smeared cracks with cracks rotating according to the directions of the principal stresses. Also, an embedded reinforcement model was implemented to represent existent reinforcing bars. Finally, some results are compared with experimental data from the literature to demonstrate the validity of the numerical model developed.

reinforced concrete; finite element method; constitutive models; orthotropic model

Este trabalho apresenta um modelo numérico para análise tridimensional de estruturas de concreto armado submetidas a cargas monótonas. O modelo proposto para o concreto é um modelo ortotrópico e utiliza o conceito de deformação uniaxial equivalente. A relação tensão-deformação uniaxial equivalente é generalizada para levar em consideração as condições triaxiais de tensão. Os parâmetros usados na curva tensão-deformação uniaxial equivalente são determinados a partir da superfície de ruptura definida no espaço de tensões principais. Também, implementouse um modelo de armadura incorporada para representar as barras de armadura. Por fim, apresentam-se resultados comparativos com ensaios experimentais e analíticos para demonstrar a validade do modelo numérico.

concreto armado; método dos elementos finitos; modelos constitutivos; modelo ortotrópico

A 3D finite element model for reinforced concrete structures analysis

Modelo 3D de elementos finitos para análise de estruturas de concreto armado

G. F. F. Bono^I; A. Campos Filho^II; A. R. Pacheco^II

^IGraduate Program in Civil and Environmental Engineering, Federal University of Pernambuco, giuliana.franca@gmail.com, BR 104, Km 59, S/N, Nova Caruaru, 55002-970, Caruaru, Pernambuco, Brazil

^IIGraduate Program in Civil Engineering, Federal University of Rio Grande do Sul, americo@ufrgs.br, apacheco@ufrgs.br, Av. Osvaldo Aranha - 99, 3¼ andar, 90035-190, Porto Alegre, Rio Grande do Sul, Brazil

RESUMO

Este trabalho apresenta um modelo numérico para análise tridimensional de estruturas de concreto armado submetidas a cargas monótonas. O modelo proposto para o concreto é um modelo ortotrópico e utiliza o conceito de deformação uniaxial equivalente. A relação tensão-deformação uniaxial equivalente é generalizada para levar em consideração as condições triaxiais de tensão. Os parâmetros usados na curva tensão-deformação uniaxial equivalente são determinados a partir da superfície de ruptura definida no espaço de tensões principais. Também, implementouse um modelo de armadura incorporada para representar as barras de armadura. Por fim, apresentam-se resultados comparativos com ensaios experimentais e analíticos para demonstrar a validade do modelo numérico.

Palavras-chave: concreto armado; método dos elementos finitos; modelos constitutivos; modelo ortotrópico.

ABSTRACT

This work presents a numerical model for 3D analyses through the finite element method of reinforced concrete structures subjected to monotonic loads. The proposed model for concrete is orthotropic and uses the equivalent uniaxial strain concept. The equivalent uniaxial stress-strain relation is generalized to take into account the triaxial stress conditions. The parameters used in the equivalent uniaxial stress-strain curve are determined from the failure surface defined in the principal stress space. The implementation in finite elements is based on the consideration of smeared cracks with cracks rotating according to the directions of the principal stresses. Also, an embedded reinforcement model was implemented to represent existent reinforcing bars. Finally, some results are compared with experimental data from the literature to demonstrate the validity of the numerical model developed.

Keywords: reinforced concrete; finite element method; constitutive models; orthotropic model.

Texto completo disponivel apenas em PDF.

Full text avaliable only in PDF

Received: 07 Feb 2011

Accepted: 03 Jun 2011

Available Online: 07 Oct 2011

01 Patrick, M.D. and Sharon Huo, X. Finite element modeling of slab-on-beam concrete bridge superstructures. Computers and Concrete, v.1, n.3, p.355-369, 2004.
02 Kim, S.H. and Aboutaha, R.S. Finite element analysis of carbon fiber-reinforced polymer (CFRP) strengthened reinforced concrete beams. Computers and Concrete, v.1, n.4, p.401-416, 2004.
03 Park, S. and Aboutaha, R. Finite element modeling methodologies for FRP strengthened RC members. Computers and Concrete, v.2, n.5, p.389-409, 2005.
04 Hoque, M., Rattanawangcharoen, N. and Shah, A.H. 3D nonlinear mixed finite-element analysis of RC beams and plates with and without FRP reinforcement. Computers and Concrete, v.4, n.2, p.135-156, 2007.
05 Smadi, M.M. and Belakhdar, K.A. Nonlinear finite element analysis of high strength concrete slabs. Computers and Concrete, v.4, n.3, p.187-206, 2007.
06 Souza, R.A., Kuchma, D.A., Park, J.W. and Bittencourt, T.N. Nonlinear finite element analysis of four-pile caps supporting columns subjected to generic loading. Computers and Concrete, v.4, n.5, p.363-376, 2007.
07 Shayanfar, M.A. and Safiey, A. Hypoelastic modeling of reinforced concrete walls. Computers and Concrete, v.5, n.3, p.195-216, 2008.
08 Manzoli, O.L., Oliver, J., Huespe, A.E. and Diaz, G. A mixture theory based method for three-dimensional modeling of reinforced concrete members with embedded crack finite elements. Computers and Concrete, v.5, n.4, p.401-416, 2008.
09 Bono, G.F.F. Constitutive models for tridimensional analysis or reinforced concrete structures through the Finite Element Method. PhD Dissertation, Federal University of Rio Grande do Sul, Brazil, 2008.
10 Elwi, A.E. and Hrudey, M. Finite element model for curved embedded reinforcement. ASCE J. Eng. Mech., v.115, n.4, p.740-754, 1989.
11 Darwin, D. and Pecknold D.A. Nonlinear biaxial stress–strain law for concrete. ASCE J. Eng. Mech., v.103, n.2, p.229–241, 1977.
12 Elwi, A.A. and Murray D.W. A 3D hypoelastic concrete constitutive relationship. ASCE J. Eng. Mech. Div., v.105(EM4), p.623-641, 1979.
13 Balan, T.A., Filippou, F.C. and Popov E.P. Constitutive model for 3D cyclic analysis of concrete structures. ASCE J. Eng. Mech., v.123, n.2, p.143-153, 1997.
14 Balan, T.A., Spacone, E. and Kwon, M. A 3D hypoplastic model for cyclic analysis of concrete structures. Eng. Struct., v. 23, n.4, p.333–342, 2001.
15 Kwon, M. Three dimensional finite element analysis for reinforced concrete members. PhD dissertation, Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, 2000.
16 Kwon, M. and Spacone, E. Three-dimensional finite element analyses of reinforced concrete columns. Computers and Structures, v.80, p.199-212, 2002.
17 Saenz I. P. Discussion of equation for the stress–strain curve of concrete by P. Desay and S. Krishnan. ACI J., v.61, n.9, p.1229–1235, 1964.
18 Popovics, S. Numerical approach to the complete stress–strain relation for concrete. Cement Concr. Res., v.3, n.5, p.583–599, 1973.
19 Comitê Euro-International du Béton. CEB-FIP Model code 1990. Thomas Telford Services Ltda, 1993.
20 Chen, W.F. and Han, D.J. Plasticity for Structural Engineers, Springer-Verlag New York Inc., New York, 1988.
21 Menetrey, P. and Willam, K.J. Triaxial failure criterion for concrete and its generalization. ACI Struct. J., v. 92, n.3, p.311–318, 1995.
22 Ottosen, N.S. A failure criterion for concrete. ASCE J. Eng. Mech. Div., v.103(EM4), p.527-627, 1977.
23 Willam, K.J and Warnke, E.P. Constitute models for the triaxial behavior of concrete. Int. Assoc. Bridge Struct. Proc., v.19, p.1–30, 1974.
24 Kupfer, H.B., Hilsdorf H.K. and Rusch, H. Behavior of concrete under biaxial stress. ACI J., v.66, n.8, p.656-666, 1969.
25 IMSL Fortran 90 MP Library. Fortran 90 Subroutines and Functions, Ed. 6.5, 2000.
26 Bouzaiene, A. and Massicotte, B. Hypoelastic tridimensional model for nonproportional loading of plain concrete", ASCE J. Eng. Mech., v.123, n.11, p.1111-1120, 1997.
27 Smith, S.S., Willam, K.J., Gerstle, K.H. and Sture, S. Concrete over the top, or: is there life after peak?. ACI J., v.86, n.5, p.491–497, 1989.
28 Bresler, B. and Scordelis, A.C. Shear strength of reinforced concrete beams. ACI J., v.60, n.1, p.51-72, 1963.
29 Hinton, E. Numerical Methods and Software for Dynamic Analysis of Plates and Shells, Swansea: Pineridge Press, 1988.

Publication Dates

Publication in this collection
21 Aug 2014
Date of issue
Oct 2011

History

Received
07 Feb 2011
Accepted
03 June 2011

This work is licensed under a Creative Commons Attribution 4.0 International License.

[1] 01 Patrick, M.D. and Sharon Huo, X. Finite element modeling of slab-on-beam concrete bridge superstructures. Computers and Concrete, v.1, n.3, p.355-369, 2004.

[2] 02 Kim, S.H. and Aboutaha, R.S. Finite element analysis of carbon fiber-reinforced polymer (CFRP) strengthened reinforced concrete beams. Computers and Concrete, v.1, n.4, p.401-416, 2004.

[3] 03 Park, S. and Aboutaha, R. Finite element modeling methodologies for FRP strengthened RC members. Computers and Concrete, v.2, n.5, p.389-409, 2005.

[4] 04 Hoque, M., Rattanawangcharoen, N. and Shah, A.H. 3D nonlinear mixed finite-element analysis of RC beams and plates with and without FRP reinforcement. Computers and Concrete, v.4, n.2, p.135-156, 2007.

[5] 05 Smadi, M.M. and Belakhdar, K.A. Nonlinear finite element analysis of high strength concrete slabs. Computers and Concrete, v.4, n.3, p.187-206, 2007.

[6] 06 Souza, R.A., Kuchma, D.A., Park, J.W. and Bittencourt, T.N. Nonlinear finite element analysis of four-pile caps supporting columns subjected to generic loading. Computers and Concrete, v.4, n.5, p.363-376, 2007.

[7] 07 Shayanfar, M.A. and Safiey, A. Hypoelastic modeling of reinforced concrete walls. Computers and Concrete, v.5, n.3, p.195-216, 2008.

[8] 08 Manzoli, O.L., Oliver, J., Huespe, A.E. and Diaz, G. A mixture theory based method for three-dimensional modeling of reinforced concrete members with embedded crack finite elements. Computers and Concrete, v.5, n.4, p.401-416, 2008.

[9] 09 Bono, G.F.F. Constitutive models for tridimensional analysis or reinforced concrete structures through the Finite Element Method. PhD Dissertation, Federal University of Rio Grande do Sul, Brazil, 2008.

[10] 10 Elwi, A.E. and Hrudey, M. Finite element model for curved embedded reinforcement. ASCE J. Eng. Mech., v.115, n.4, p.740-754, 1989.

[11] 11 Darwin, D. and Pecknold D.A. Nonlinear biaxial stress–strain law for concrete. ASCE J. Eng. Mech., v.103, n.2, p.229–241, 1977.

[12] 12 Elwi, A.A. and Murray D.W. A 3D hypoelastic concrete constitutive relationship. ASCE J. Eng. Mech. Div., v.105(EM4), p.623-641, 1979.

[13] 13 Balan, T.A., Filippou, F.C. and Popov E.P. Constitutive model for 3D cyclic analysis of concrete structures. ASCE J. Eng. Mech., v.123, n.2, p.143-153, 1997.

[14] 14 Balan, T.A., Spacone, E. and Kwon, M. A 3D hypoplastic model for cyclic analysis of concrete structures. Eng. Struct., v. 23, n.4, p.333–342, 2001.

[15] 15 Kwon, M. Three dimensional finite element analysis for reinforced concrete members. PhD dissertation, Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, 2000.

[16] 16 Kwon, M. and Spacone, E. Three-dimensional finite element analyses of reinforced concrete columns. Computers and Structures, v.80, p.199-212, 2002.

[17] 17 Saenz I. P. Discussion of equation for the stress–strain curve of concrete by P. Desay and S. Krishnan. ACI J., v.61, n.9, p.1229–1235, 1964.

[18] 18 Popovics, S. Numerical approach to the complete stress–strain relation for concrete. Cement Concr. Res., v.3, n.5, p.583–599, 1973.

[19] 19 Comitê Euro-International du Béton. CEB-FIP Model code 1990. Thomas Telford Services Ltda, 1993.

[20] 20 Chen, W.F. and Han, D.J. Plasticity for Structural Engineers, Springer-Verlag New York Inc., New York, 1988.

[21] 21 Menetrey, P. and Willam, K.J. Triaxial failure criterion for concrete and its generalization. ACI Struct. J., v. 92, n.3, p.311–318, 1995.

[22] 22 Ottosen, N.S. A failure criterion for concrete. ASCE J. Eng. Mech. Div., v.103(EM4), p.527-627, 1977.

[23] 23 Willam, K.J and Warnke, E.P. Constitute models for the triaxial behavior of concrete. Int. Assoc. Bridge Struct. Proc., v.19, p.1–30, 1974.

[24] 24 Kupfer, H.B., Hilsdorf H.K. and Rusch, H. Behavior of concrete under biaxial stress. ACI J., v.66, n.8, p.656-666, 1969.

[25] 25 IMSL Fortran 90 MP Library. Fortran 90 Subroutines and Functions, Ed. 6.5, 2000.

[26] 26 Bouzaiene, A. and Massicotte, B. Hypoelastic tridimensional model for nonproportional loading of plain concrete", ASCE J. Eng. Mech., v.123, n.11, p.1111-1120, 1997.

[27] 27 Smith, S.S., Willam, K.J., Gerstle, K.H. and Sture, S. Concrete over the top, or: is there life after peak?. ACI J., v.86, n.5, p.491–497, 1989.

[28] 28 Bresler, B. and Scordelis, A.C. Shear strength of reinforced concrete beams. ACI J., v.60, n.1, p.51-72, 1963.

[29] 29 Hinton, E. Numerical Methods and Software for Dynamic Analysis of Plates and Shells, Swansea: Pineridge Press, 1988.

Brasil

Brasil

A 3D finite element model for reinforced concrete structures analysis

Modelo 3D de elementos finitos para análise de estruturas de concreto armado

Abstracts

Publication Dates

History