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Keywords: reinforced, beams, concrete, carbon fibre reinforced polymer, finite element modelling.

Summary

Carbon fibre reinforced polymer (CFRP) strengthening of reinforced concrete beams is becoming a popular approach of retrofitting reinforced beams. In order to analyse and predict where and how the CFRP strengthening should be applied, it is advantageous to numerically model the structure and then apply the appropriate CFRP strengthening techniques.

The ADINA [1] finite element software provides a dedicated two-dimensional eight noded isoparametric element to model the nonlinear response of brittle materials based on a constitutive model for the triaxial behaviour of concrete after Williams and Warnke [2]. The element includes a smeared crack analogy for cracking in tension zones and a plasticity algorithm to account for the possibility of concrete crushing in compression zones. Each element has eight integration points at which cracking and crushing checks are performed. The model is capable of predicting both cracking and crushing failure modes of concrete. Cracking occurs when the principle tensile stress exceeds the ultimate in any direction. Crushing occurs when all the existing stresses are compressive and lie outside the failure surface. After crushing, the elastic modulus is set to zero in all directions and the element effectively disappears. A summary of model features are:

Nonlinear elastic model
Based on uniaxial stress strain response
Includes tensile strength
Small strain assumptions
Constant Poisson's ratio

Results [3] of ultimate load tests on ordinarily reinforced and CFRP strengthened reinforced concrete beams were used to assess the suitability of the reinforced concrete model implemented in ADINA in predicting the ultimate response of six reinforced concrete beams. The numerical models of the reinforced beams were consistent with the test results in all cases studied. However, the model shows slightly more stiffness since the bond slip between concrete and steel reinforcement or CFRP materials is excluded in the finite element model. Also, the crack patterns at the final loads from the finite element models correspond well with the observed failure modes of the experimental beams. Finally, upon comparing the ultimate loads at failure, the obtained differences are within tolerable limits.

References

1: ADINA (Automatic Dynamic Incremental Nonlinear Analysis), Watertown, MA, USA, 2002.
2: William K.J., Warnke E.D., "Constitutive Model for the Triaxial Behaviour of Concrete", Proceedings of the International Association for Bridge and Structural Engineering, 19, p.174, ISMES, Bergamo, Italy, 1975.
3: Issa C.A., Abou Jouadeh A., "Experimental Study of CFRP Strengthening of Reinforced Concrete Beams", Journal of Architectural Engineering, ASCE, pp. 121-125, December 2004. doi:10.1061/(ASCE)1076-0431(2004)10:4(121)

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 292 Finite Element Simulation of Reinforced Concrete Beams Strengthened with Externally Bonded Carbon Fibre Reinforced Polymer C.A. Issa¹ and G.A. Saad² ¹Civil Engineering Department, Lebanese American University, Byblos, Lebanon ²University of Southern California, Los Angeles CA, United States of America doi:10.4203/ccp.88.292 purchase the full-text of this paper Full Bibliographic Reference for this paper C.A. Issa, G.A. Saad, "Finite Element Simulation of Reinforced Concrete Beams Strengthened with Externally Bonded Carbon Fibre Reinforced Polymer", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 292, 2008. doi:10.4203/ccp.88.292 Keywords: reinforced, beams, concrete, carbon fibre reinforced polymer, finite element modelling. Summary Carbon fibre reinforced polymer (CFRP) strengthening of reinforced concrete beams is becoming a popular approach of retrofitting reinforced beams. In order to analyse and predict where and how the CFRP strengthening should be applied, it is advantageous to numerically model the structure and then apply the appropriate CFRP strengthening techniques. The ADINA [1] finite element software provides a dedicated two-dimensional eight noded isoparametric element to model the nonlinear response of brittle materials based on a constitutive model for the triaxial behaviour of concrete after Williams and Warnke [2]. The element includes a smeared crack analogy for cracking in tension zones and a plasticity algorithm to account for the possibility of concrete crushing in compression zones. Each element has eight integration points at which cracking and crushing checks are performed. The model is capable of predicting both cracking and crushing failure modes of concrete. Cracking occurs when the principle tensile stress exceeds the ultimate in any direction. Crushing occurs when all the existing stresses are compressive and lie outside the failure surface. After crushing, the elastic modulus is set to zero in all directions and the element effectively disappears. A summary of model features are: Nonlinear elastic model Based on uniaxial stress strain response Includes tensile strength Small strain assumptions Constant Poisson's ratio Results [3] of ultimate load tests on ordinarily reinforced and CFRP strengthened reinforced concrete beams were used to assess the suitability of the reinforced concrete model implemented in ADINA in predicting the ultimate response of six reinforced concrete beams. The numerical models of the reinforced beams were consistent with the test results in all cases studied. However, the model shows slightly more stiffness since the bond slip between concrete and steel reinforcement or CFRP materials is excluded in the finite element model. Also, the crack patterns at the final loads from the finite element models correspond well with the observed failure modes of the experimental beams. Finally, upon comparing the ultimate loads at failure, the obtained differences are within tolerable limits. References 1 ADINA (Automatic Dynamic Incremental Nonlinear Analysis), Watertown, MA, USA, 2002. 2 William K.J., Warnke E.D., "Constitutive Model for the Triaxial Behaviour of Concrete", Proceedings of the International Association for Bridge and Structural Engineering, 19, p.174, ISMES, Bergamo, Italy, 1975. 3 Issa C.A., Abou Jouadeh A., "Experimental Study of CFRP Strengthening of Reinforced Concrete Beams", Journal of Architectural Engineering, ASCE, pp. 121-125, December 2004. doi:10.1061/(ASCE)1076-0431(2004)10:4(121) purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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