New Model for the Analysis of Size-Scale Effects on the Ductility of Reinforced Concrete Elements in Bending
Publication: Journal of Engineering Mechanics
Volume 135, Issue 3
Abstract
The well-known cohesive crack model describes strain localization with a softening stress variation in concrete members subjected to tension. An analogous behavior is also observed in compression, when strain localization takes place in a damaged zone and the stress reaches the compression strength with surface energy dissipation. In the present paper, we propose the new concept of overlapping crack model, which is analogous to the cohesive one and permits us to simulate material interpenetration due to crushing. The two aforementioned elementary models are merged into a more complex algorithm able to describe both cracking and crushing growths during loading processes in reinforced concrete members. A numerical procedure based on elastic coefficients is developed, taking into account the proposed constitutive laws in tension and compression. With this algorithm, it is possible to effectively capture the flexural behavior of reinforced concrete beams by varying the reinforcement percentage and/or the beam depth.
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Acknowledgments
The financial support provided by the European UnionEU to the Leonardo da Vinci Project “Innovative Learning and Training on Fracture” (ILTOF) is gratefully acknowledged.
References
Barbosa, A. F. and Ribeiro, G. O., and (1998). “Analysis of reinforced concrete structures using ANSYS nonlinear concrete model.” Computational Mechanics: New trends and applications, S. Idelsohn, E. Onate, and E. Dvorkin, eds., CIMNE, Barcelona, Spain, 1–7.
Bazant, Z. P., and Kim, J. K. (1984). “Size effect in shear failure of longitudinally reinforced beams.” ACI J., 81(5), 456–468.
Bigaj, A. J., and Walraven, J. C. (1993). “Size effect on rotational capacity of plastic hinges in reinforced concrete beams.” CEB Bulletin d’Information No. 218, Lausanne, Switzerland, 7-23.
Bosco, C., and Carpinteri, A. (1992). “Softening and snap-through behavior of reinforced elements.” J. Eng. Mech., 118(8), 1564–1577.
Bosco, C., Carpinteri, A., and Debernardi, P. G. (1990). “Minimum reinforcement in high strength concrete.” J. Struct. Eng., 116(2), 427–437.
Bosco, C., and Debernardi, P. G. (1992). “Experimental investigation on the ultimate rotational capacity of RC beams.” Rep. No. 36, Atti del Dipartimento, Politecnico di Torino, Ingegneria Strutturale.
Carpinteri, A. (1981). “A fracture mechanics model for reinforced concrete collapse.” Proc., IABSE Colloquium, Delft University Press, Delft, The Netherlands, 17–30.
Carpinteri, A. (1984). “Stability of fracturing process in RC beam.” J. Struct. Eng., 110(3), 544–558.
Carpinteri, A. (1985). “Interpretation of the Griffith instability as a bifurcation of the global equilibrium.” Proc., NATO Advanced Research Workshop on Application of Fracture Mechanics to Cementitious Composites, S. P. Shah, ed., Martinus Nijhoff Publishers, Dordrecht, The Netherlands, 287–316.
Carpinteri, A. (1989). “Size effects on strength, toughness, and ductility.” J. Eng. Mech., 115(7), 1375–1392.
Carpinteri, A., ed. (1999). Minimum reinforcement in concrete members, Elsevier Science Ltd., Oxford, U.K., VIII +203.
Carpinteri, A., Di Tommaso, A., and Fanelli, M. (1986). “Influence of material parameters and geometry on cohesive crack propagation.” Fracture toughness and fracture energy of concrete, F. H. Wittmann, ed., Elsevier, Amsterdam, The Netherlands, 117–135.
Carpinteri, A., Ferro, G., and Ventura, G. (2005). “Scale-independent constitutive law for concrete in compression.” Proc., 11th Int. Conf. on Fracture (ICF) (CD-ROM), A. Carpinteri, ed., Trading, Torino, Italy, Paper No. 5556.
Carpinteri, A., Ventura, G., and Carmona, J. R. (2007). “Flexural to shear and crushing failure transitions in RC beams by the bridged crack model.” Proc., 6th Int. FraMCoS Conf., Vol. 2, A. Carpinteri, P. Gambarova, G. Ferro, and G. Plizzari, eds., Taylor & Francis, Catania, Italy, 677–684.
Cela, J. J. L. (2002). “Material identification procedure for elastoplastic Drucker-Prager model.” J. Eng. Mech., 128(5), 586–591.
Comité Euro–International du Béton. (1993). CEB-FIP Model Code 1990, Thomas Telford, Ltd., Lausanne, Switzerland.
Corley, W. G. (1966). “Rotational capacity of reinforced concrete beams.” J. Struct. Div., 92(ST5), 121–146.
Dahl, H., and Brincker, R. (1989) “Fracture energy of high-strength concrete in compression.” Proc., Int. Conf. on Recent Developments in the Fracture of Concrete and Rock, S. P. Shah, S. E. Swartz, and B. Barr, eds., Elsevier Applied Science, Cardiff, U.K., 523–536.
Eligehausen, R., and Langer, P. (1987). “Rotation capacity of plastic hinges and allowable degree of moment redistribution.” CEB Bulletin d’Information No. 175, Lausanne, Switzerland, 93-102.
EN. (1992). “Eurocode 2: Design of concrete structures—Part 1-1: General rules and rules for buildings.” EN 1992-1-1, 5.6.3, Rotation Capacity, Brussels.
Fantilli, A. P., Iori, I., and Vallini, P. (2007). “Size effect of compressed concrete in four point bending RC beams.” Eng. Fract. Mech., 74(1–2), 97–108.
Gustafsson, P. J., and Hillerborg, A. (1988). “Sensitivity in shear strength of longitudinally reinforced concrete beams energy of concrete.” ACI Struct. J., 85(3), 286–294.
Hillerborg, A. (1990). “Fracture mechanics concepts applied to moment capacity and rotational capacity of reinforced concrete beams.” Eng. Fract. Mech., 35(1/2/3), 233–240.
Hillerborg, A., Modeer, M., and Petersson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res., 6(6), 773–782.
Jansen, C. D., and Shah, S. P. (1997). “Effect of length on compressive strain softening of concrete.” J. Eng. Mech., 123(1), 25–35.
Jenq, Y. S., and Shah, S. P. (1989). “Shear resistance of reinforced concrete beams—a fracture mechanics approach.” Fracture mechanics: Application to concrete, V. C. Li and Z. P. Bazant, eds., American Concrete Institute, Detroit, 327–358.
Macchi, G. (1969). “Limit-states design of statically indeterminate structures composed of linear members.” Costruzioni in Cemento Armato, Studi e Rendinconti, 6, 151–190.
Suzuki, M., Akiyama, M., Matsuzaki, H., and Dang, T. H. (2006). “Concentric loading test of RC columns with normal- and high-strength materials and averaged stress-strain model for confined concrete considering compressive fracture energy.” Proc., 2nd fib Int. Conf. (CD-ROM), Doppiavoce, Napoli, Italy, ID 3–13.
van Vliet, M., and van Mier, J. (1996). “Experimental investigation of concrete fracture under uniaxial compression.” Mech. Cohesive-Frict. Mater., 1(1), 115–127.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 3 • March 2009
Pages: 221 - 229
Copyright
© 2009 ASCE.
History
Received: Aug 2, 2007
Accepted: Oct 15, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
Notes
Note. Associate Editor: George Z. Voyiadjis
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