Element Size and Other Restrictions in Finite-Element Modeling of Reinforced Concrete at Elevated Temperatures
Publication: Journal of Engineering Mechanics
Volume 139, Issue 10
Abstract
One of the accepted approaches for postpeak finite-element modeling of RC comprises combining plain concrete, reinforcement, and interaction behaviors. In these, the postpeak strain–softening behavior of plain concrete is incorporated by the use of fracture energy concepts. This study attempts to extend this approach for RC at elevated temperatures. Prior to the extension, the approach is investigated for associated modeling issues and a set of limits of application are formulated. The available models of the behavior of plain concrete at elevated temperatures were used to derive inherent fracture energy variation with temperature. It is found that the currently used tensile elevated temperature model assumes that the fracture energy decays with temperature. The existing models in compression also show significant decay of fracture energy at higher temperatures () and a considerable variation in values. Application of the evaluated fracture energy values shows that these impose severe element size and reinforcement ratio limits. The effect of the limits is illustrated for a RC specimen.
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Acknowledgments
The authors thank William Kingston of the BRE Centre for Fire Safety Engineering for stimulating discussions.
References
Anderberg, Y., and Thelandersson, S. (1976). “Stress and deformation characteristics of concrete at high temperatures. 2. Experimental investigation and material behaviour model.” Rep. No. 34, Div. of Structural Mechanics and Concrete Construction, Lund Institute of Technology, Lund, Sweden.
Bažant, Z. P., and Lin, F.-B. (1988). “Nonlocal smeared cracking model for concrete fracture.” J. Struct. Eng., 114(11), 2493–2510.
Bažant, Z. P., and Oh, B. H. (1983). “Crack band theory for fracture of concrete.” Mat. Struct., RILEM, Paris, 16(93), 155–177.
British Standards Institution (BSI). (2004). “Eurocode 2: Design of concrete structures. Part 1-2: General rules—Structural fire design.” BS EN 1992-1-2:2004, London.
Cervenka, V., Pukl, R., and Eligehausen, R. (1990). “Computer simulation of anchoring technique in reinforced concrete beams.” Computer aided analysis and design of concrete structures, N. Bicanic et al., eds., Pineridge Press, Swansea, U.K., 1–21.
de Borst, R., Remmers, J. J. C., Needleman, A., and Abellan, M.-A. (2004). “Discrete vs. smeared crack models for concrete fracture: Bridging the gap.” Int. J. Numer. Anal. Met., 28(7–8), 583–607.
Fédération International de la Précontrainte (CEB-FIP). (1993). Bulletin d’Information, Model code No. 1990, Swiss Federal Institute of Technology, Lausanne, Switzerland (in French).
Feenstra, P. H., and de Borst, R. (1995). “Constitutive model for reinforced concrete.” J. Eng. Mech., 121(5), 587–595.
Fletcher, I., Welch, S., Torero, J., Carvel, R., and Usmani, A. (2007). “Behaviour of concrete structures in fire.” Thermal Sci., 11(2), 37–52.
Gopalaratnam, V. S., and Shah, S. P. (1985). “Softening response of plain concrete in direct tension.” ACI J., 82(3), 310–323.
Gupta, A. K., and Maestrini, S. R. (1990). “Tension-stiffness model for reinforced concrete bars.” J. Struct. Eng., 116(3), 769–790.
He, W., Wu, Y.-F., and Liew, K. M. (2008). “A fracture energy based constitutive model for analysis of reinforced concrete structures under cyclic loading.” Comput. Methods Appl. Mech. Eng., 197(51–52), 4745–4762.
Hertz, K. (2005). “Concrete strength for fire safety design.” Mag. Concr. Res., 57(8), 445–453.
Hertz, K. (2004). “Reinforcement data for fire safety design.” Mag. Concr. Res., 56(8), 453–459.
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.” Cement Concr. Res., 6(6), 773–782.
Hofstetter, G., and Mang, H. A. (1996). “Computational plasticity of reinforced and prestressed concrete structures.” Comput. Mech., 17(4), 242–254.
Law, A., and Gillie, M. (2008). “Load induced thermal strain: Implications for structural behaviour.” Proc., Int. Conf. on Structures in Fire, K. H. Tan et. al., eds., SiF'08, Singapore, 448–496.
Li, L.-Y., and Purkiss, J. (2005). “Strain-stress constitutive equations of concrete material at elevated temperatures.” Fire Saf. J., 40(7), 669–689.
Lie, T., and Lin, T. (1985). “Fire performance of reinforced concrete columns.” Fire Safety: Science and Engineering, ASTM STP No. 882, ASTM, West Conshohocken, PA, 176–205.
Maier, G., and Hueckel, T. (1979). “Nonassociated and coupled flow rules of elastoplasticity for rock-like materials.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 16(2), 77–92.
Nakamura, H., and Higai, T. (2001). “Compressive fracture energy and fracture zone length of concrete.” Modeling of inelastic behavior of RC structures under seismic loads, P. Shing, et al., eds., ASCE, New York, 471–487.
Pankaj, P. (1990). “Finite element analysis in strain softening and localisation problems.” Ph.D. thesis, Univ. of Wales, Swansea, U.K.
Pramono, E., and Willam, K. (1989). “Fracture energy-based plasticity formulation of plain concrete.” J. Eng. Mech., 115(6), 1183–1204.
Stramandinoli, R., and La Rovere, H. (2008). “An efficient tension-stiffening model for nonlinear analysis of reinforced concrete members.” Eng. Struct., 30(7), 2069–2080.
Syroka, E., Bobiński, J., and Tejchman, J. (2011). “FE analysis of reinforced concrete corbels with enhanced continuum models.” J. FE Anal. Des., 47(9), 1066–1078.
Terro, M. (1998). “Numerical modeling of the behavior of concrete structures in fire.” ACI Struct. J., 95(2), 183–193.
van Mier, J. (1984). “Strain-softening of concrete under multiaxial loading conditions.” Ph.D. thesis, Eindhoven Univ. of Technology, Eindhoven, Netherlands.
Vonk, R. (1992). “Softening of concrete loaded in compression.” Ph.D. thesis, Eindhoven Univ. of Technology, Eindhoven, Netherlands.
Willam, K., et al. (1987). Constitutive driver for triaxial response behavior of plain concrete, Structural Research Series No. 87-08, Univ. of Colorado, Boulder, CO.
Youssef, M., and Moftah, M. (2007). “General stress-strain relationship for concrete at elevated temperatures.” Eng. Struct., 29(10), 2618–2634.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 139 • Issue 10 • October 2013
Pages: 1325 - 1333
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Sep 2, 2011
Accepted: Dec 11, 2012
Published online: Dec 13, 2012
Published in print: Oct 1, 2013
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