General Stress-Strain Model for Steel- and FRP-Confined Concrete
Publication: Journal of Composites for Construction
Volume 19, Issue 4
Abstract
A new and general stress-strain model for concrete confined by steel or fiber reinforced polymer (FRP) is developed in this work. One additional variable and one constant are added to the well-known Popovics model to control the type and the shape of the stress-strain curve. The proposed model has one simple, continuous, and explicit expression and can exhibit either hardening or softening types of responses. This general model provides a unified platform for modeling stress-strain of concrete confined by different materials, such as steel or FRP, and help to overcome inconsistency or complexity. The parameters of the stress-strain model are determined by analytical study and data regression using a large and up-to-date test database. The proposed stress-strain model is validated with experimental results and compared with existing models; it shows good performance and superior flexibility and versatility of the model.
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Acknowledgments
The work that is described in this paper was fully supported by the grants from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 124113] and the National Natural Science Foundation of China (No. 51208262).
References
Ahmad, S. H., and Shah, S. P. (1982). “Stress-strain curves of concrete confined by spiral reinforcement.” ACI J., 79(6), 484–490.
Aire, C., Gettu, R., Casas, J. R., Marqués, S., and Marques, D. (2010). “Concrete laterally confined with fibre-reinforced polymers (FRP): Experimental study and theoretical model.” Materiales de Construcción, 60(297), 19–31.
Almusallam, T. H. (2007). “Behavior of normal and high-strength concrete cylinders confined with E-glass/epoxy composite laminates.” Compos. Part B, 38(5), 629–639.
American Concrete Institute (ACI). (1999). “Building code requirements for structural concrete and commentary.”, Farmington Hills, MI.
Assa, B., Nishiyama, M., and Watanabe, F. (2001). “New approach for modeling confined concrete. I: Circular columns.” J. Struct. Eng., 743–750.
Benzaid, R., Chikh, N. E., and Mesbah, H. (2009). “Study of the compressive behavior of short concrete columns confined by fiber reinforced composite.” Arabian J. Sci. Eng., 34(1B), 15–26.
Benzaid, R., Mesbah, H., and Chikh, N. E. (2010). “FRP-confined concrete cylinders: axial compression experiments and strength model.” J. Reinf. Plast. Comp., 29(16), 2469–2488.
Berthet, J., Ferrier, E., and Hamelin, P. (2005). “Compressive behavior of concrete externally confined by composite jackets. Part A: Experimental study.” Constr. Build. Mater., 19(3), 223–232.
Bullo, S. (2003). “Experimental study of the effects of the ultimate strain of fiber reinforced plastic jackets on the behavior of confined concrete.” Proc., Int. Conf. Composites in Constructions, D. Bruno, G. Spadea, and R. N. Swamy, eds., Univ. of Calabria, Cosenza, Italy, 465–470.
Chaallal, O., Shahawy, M., and Hassan, M. (2003). “Performance of axially loaded short rectangular columns strengthened with carbon fiber-reinforced polymer wrapping.” J. Compos. Constr., 200–208.
Cui, C., and Sheikh, S. A. (2010). “ Experimental study of normal- and high-strength concrete confined with fiber-reinforced polymers.” J. Compos. Constr., 553–561.
Dai, J. G., Bai, Y. L., and Teng, J. G. (2011). “Behavior and modeling of concrete confined with FRP composites of large deformability.” J. Compos. Constr., 963–973.
De Lorenzis, L., Micelli, F., and La Tegola, A. (2002). “ Influence of specimen size and resin type on the behavior of FRP-confined concrete cylinders.” Proc., 1st Int. Conf. Advanced Polymer Composites for Structural Applications in Construction, Thomas Telford, London, U.K., 231–239.
Demer, M., and Neale, K. W. (1994). “Strengthening of concrete columns with unidirectional composite sheets.” Proc., Developments in Short and Medium Span Bridge Engineering, A. A. Mufti, B. Bakht, and L. G. Jaeger, eds., Canadian Society for Civil Engineering, Montreal, QC, Canada, 895–905.
Elsanadedy, H. M., Al-Salloum, Y. A., Alsayed, S. H., and Iqbal, R. A. (2012). “Experimental and numerical investigation of size effects in FRP-wrapped concrete columns.” Constr. Build. Mater., 29(4), 56–72.
European Committee for Standardization. (1991). “Eurocode 2: Design of concrete structures—Part 1: General rules and rules for buildings.”, Brussels, Belgium.
Fahmy, M. F., and Wu, Z. (2010). “Evaluating and proposing models of circular concrete columns confined with different FRP composites.” Compos. Part B Eng., 41(3), 199–213.
Fardis, M. N., and Khalili, H. H. (1982). “FRP-encased concrete as a structural material.” Mag. Concrete Res., 34(121), 191–202.
Harries, K. A., and Kharel, G. (2002). “Behavior and modeling of concrete subject to variable confining pressure.” ACI Mater. J., 99(2), 180–189.
Hognestad, E. (1951). “A study of combined bending and axial load in reinforced concrete members.”, Engineering Experiment Station, Univ. of Illinois, Urbana, IL.
Hoshikuma, J., Kawashima, K., Nagaya, K., and Taylor, A. W. (1997). “Stress-strain model for confined reinforced concrete in bridge piers.” J. Struct. Eng., 624–633.
Howie, I., and Karbhari, V. M. (1994). “Effect of materials architecture on strengthening: Efficiency of composite wraps for deteriorating columns in the North-East.” Proc., 3rd Materials Engineering Conf., K. D. Basham, ed., ASCE, Reston, VA, 199–206.
Ilki, A., and Kumbasa, N. (2003). “Compressive behaviour of carbon fibre composite jacketed concrete with circular and non-circular cross-sections.” J. Earthquake Eng., 7(3), 381–406.
Ilki, A., and Kumbasar, N. (2002). “Behavior of damaged and undamaged concrete strengthened by carbon fiber composite sheets.” Struct. Eng. Mech., 13(1), 75–90.
Ilki, A., Kumbasar, N., and Koc, V. (2004). “Low strength concrete members externally confined with FRP sheets.” Struct. Eng. Mech., 18(2), 167–194.
Issa, C., and Karam, G. (2004). “Compressive strength of concrete cylinders with variable widths CFRP wraps.” Proc., 4th Int. Conf. on Advanced Composite Materials in Bridges and Structures, Canadian Society for Civil Engineering, Calgary, AB, Canada.
Jiang, J. F., and Wu, Y. F. (2012). “Identification of material parameters for Drucker-Prager plasticity model for FRP confined circular concrete columns.” Int. J. Solids. Struct., 49(3–4), 445–456.
Jiang, T., and Teng, J. G. (2007). “Analysis-oriented stress-strain models for FRP-confined concrete.” Eng. Struct., 29(11), 2968–2986.
Karabinis, A. I., and Rousakis, T. C. (2002). “Concrete confined by FRP material: a plasticity approach.” Eng. Struct., 24(7), 923–932.
Karbhari, V. M., and Gao, Y. Q. (1997). “Composite jacketed concrete under uniaxial compression—Verification of simple design equations.” J. Mater. Civ. Eng., 185–193.
Kono, S. I. M., and Kaku, T. (1998). “Evaluation of confining effects of CFRP sheets on reinforced concrete members.” Proc., 2nd Int. Conf. on Composites in Infrastructures, H. Saadatmanesh and M. R. Ehsani, eds., Univ. of Arizona, Tucson, AZ, 343–355.
Lam, L., and Teng, J. G. (2003). “Design-oriented stress-strain model for FRP-confined concrete.” Constr. Build. Mater., 17(6–7), 471–489.
Lam, L., and Teng, J. G. (2004). “Ultimate condition of fiber reinforced polymer-confined concrete.” J. Compos. Constr., 539–548.
Lam, L., Teng, J. G., Cheung, C. H., and Xiao, Y. (2006). “FRP-confined concrete under axial cyclic compression.” Cem. Concr. Compos., 28(10), 949–958.
Lee, J. Y., Yi, C. K., Jeong, H. S., Kim, S. W., and Kim, J. K. (2010). “Compressive response of concrete confined with steel spirals and FRP composites.” J. Compos. Mater., 44(4), 481–504.
Liang, M., Wu, Z. M., Ueda, T., Zheng, J. J., and Akogbe, R. (2012). “Experiment and modeling on axial behavior of carbon fiber reinforced polymer confined concrete cylinders with different sizes.” J. Reinf. Plast. Comp., 31(6), 389–403.
Lin, C. T., and Li, Y. F. (2003). “An effective peak stress formula for concrete confined with carbon fibre reinforced plastics.” Can. J. Civ. Eng., 30(5), 882–889.
Lin, H. J., and Chen, C. T. (2001). “Strength of concrete cylinder confined by composite materials.” J. Reinf. Plast. Comp., 20(18), 1577–1600.
Mandal, S., Hoskin, A., and Fam, A. (2005). “Influence of concrete strength on confinement effectiveness of fiber-reinforced polymer circular jackets.” ACI Struct. J., 102(3), 383–392.
Mander, J. B., Priestley, M. J. N., and Park, R. (1988a). “Theoretical stress-strain model for confined concrete.” J. Struct. Eng., 1804–1826.
Mander, J. B., Priestley, M. J. N., and Park, R. (1988b). “Observed stress-strain behavior of confined concrete.” J. Struct. Eng., 1827–1849.
Micelli, F., and Modarelli, R. (2013). “Experimental and analytical study on properties affecting the behaviour of FRP-confined concrete.” Compos. Part B, 45(1), 1420–1431.
Miyauchi, K., Inoue, S., Kuroda, T., and Kobayashi, A. (1999). “Strengthening effects with carbon fiber sheet for concrete column.” Trans. Jpn. Concr. Inst., 21(3), 143–150.
Miyauchi, K., Nishibayashi, S., and Inoue, S. (1997). “Estimation of strengthening effects with carbon fiber sheet for concrete column.” Proc., 3rd Int. Symp. of Non-metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3), Japan Concrete Institute, Sapporo, Japan, 217–224.
Moran, D. A., and Pantelides, C. P. (2002). “Stress-strain model for fiber-reinforced polymer-confined concrete.” J. Compos. Constr., 233–240.
Ozbakkaloglu, T., and Akin, E. (2012). “Behavior of FRP-confined normal- and high-strength concrete under cyclic axial compression.” J. Compos. Constr., 451–463.
Ozbakkaloglu, T., and Lim, J. C. (2013). “Axial compressive behavior of FRP-confined concrete: Experimental test database and a new design-oriented model.” Compos. Part B, 55(12), 607–634.
Ozbakkaloglu, T., Lim, J. C., and Vincent, T. (2013). “FRP-confined concrete in circular sections: Review and assessment of stress-strain models.” Eng. Struct., 49(4), 1068–1088.
Popovics, S. (1973). “A numerical approach to the complete stress-strain curve of concrete.” Cem. Concr. Res., 3(5), 583–599.
Priestley, M. J. N., and Seible, F. (1995). “Design of seismic retrofit measures for concrete and masonry structures.” Constr. Build. Mater., 9(6), 365–377.
Richard, R. M., and Abbott, B. J. (1975). “Versatile elastic-plastic stress-strain formula.” J. Eng. Mech. Div., 101(4), 511–515.
Rochette, P., and Labossiere, P. (2000). “Axial testing of rectangular column models confined with composites.” J. Compos. Constr., 129–136.
Rousakis, T. (2001). “Experimental investigation of concrete cylinders confined by carbon FRP sheets under monotonic and cyclic axial compressive load.”, Division of Building Technology, Chalmers University of Technology, Göteborg, Sweden.
Rousakis, T., You, C., De Lorenzis, L., and Tamuzs, V. (2003). “Concrete cylinders confined by carbon FRP sheets subjected to monotonic and cyclic axial compressive loads.” Proc., 6th Int. Symp. on FRP Reinforcement for Concrete Structures, K. H. Tan, ed., Singapore, 571–580.
Saadatmanesh, H., Ehsani, M. R., and Li, M. W. (1994). “Strength and ductility of concrete columns externally reinforced with fiber-composite Straps.” ACI Struct. J., 91(4), 434–447.
Saafi, M., Toutanji, H. A., and Li, Z. J. (1999). “Behavior of concrete columns confined with fiber reinforced polymer tubes.” ACI Mater. J., 96(4), 500–509.
Saatcioglu, M., and Razvi, S. R. (1992). “Strength and ductility of confined concrete.” J Struct. Eng., 1590–1607.
Saenz, N., and Pantelides, C. P. (2006). “Short and medium term durability evaluation of FRP-confined circular concrete.” J. Compos. Constr., 244–253.
Samaan, M., Mirmiran, A., and Shahawy, M. (1998). “Model of concrete confined by fiber composites.” J. Struct. Eng., 1025–1031.
Sargin, M. (1971). “Stress-strain relationships for concrete and the analysis of structural concrete sections.”, Solid Mechanics Division, Univ. of Waterloo, Ontario, Canada.
Shah, S. P., Fafitis, A., and Arnold, R. (1983). “Cyclic loading of spirally reinforced-concrete.” J. Struct. Eng., 1695–1710.
Shahawy, M., Mirmiran, A., and Beitelman, T. (2000). “Tests and modeling of carbon-wrapped concrete columns.” Compos. Part B Eng., 31(6), 471–480.
Shehata, I. A. E. M., Carneiro, L. A. V., and Shehata, L. C. D. (2002). “Strength of short concrete columns confined with CFRP sheets.” Mater. Struct., 35(245), 50–58.
Shehata, I. A. E. M., Carneiro, L. A. V., and Shehata, L. C. D. (2007). “Strength of confined short concrete columns.” Proc., 8th Int. Symp. on Fiber Reinforced Polymer Reinforcement for Concrete Structures, Dept. of Civil Engineering, Univ. of Patras, Patras, Greece, 1–10.
Silva, M. A., and Rodrigues, C. C. (2006). “Size and relative stiffness effects on compressive failure of concrete columns wrapped with glass FRP.” J. Mater. Civ. Eng., 334–342.
Smith, S. T., Kim, S. J., and Zhang, H. (2010). “Behavior and effectiveness of FRP wrap in the confinement of large concrete cylinders.” J. Compos. Constr., 573–582.
Song, X. B., Gu, X. L., Li, Y. P., Chen, T., and Zhang, W. P. (2013). “Mechanical behavior of FRP-strengthened concrete columns subjected to concentric and eccentric compression loading.” J. Compos. Constr., 336–346.
Suter, R., and Pinzelli, R. (2001). “Confinement of concrete columns with FRP sheets.” Proc., 5th Symp. on Fibre Reinforced Plastic Reinforcement for Concrete Structures, C. Burgoyne, ed., Cambridge, U.K., 791–802.
Teng, J. G., Jiang, T., Lam, L., and Luo, Y. Z. (2009). “Refinement of a design-oriented stress-strain model for FRP-confined concrete.” J. Compos. Constr., 269–278.
Teng, J. G., Yu, T., Wong, Y. L., and Dong, S. L. (2007). “Hybrid FRP-concrete-steel tubular columns: Concept and behaviour.” Constr. Build. Mater., 21(4), 846–854.
Theriault, M., Neale, K. W., and Claude, S. (2004). “Fiber-reinforced polymer-confined circular concrete columns: Investigation of size and slenderness effects.” J. Compos. Constr., 323–331.
Toutanji, H. A. (1999). “Stress-strain characteristics of concrete columns externally confined with advanced fiber composite sheets.” ACI Mater. J., 96(3), 397–404.
Vincent, T., and Ozbakkaloglu, T. (2013a). “Influence of concrete strength and confinement method on axial compressive behavior of FRP confined high- and ultra high-strength concrete.” Compos. Part B, 50(7), 413–428.
Vincent, T., and Ozbakkaloglu, T. (2013b). “Influence of fiber orientation and specimen end condition on axial compressive behavior of FRP-confined concrete.” Constr. Build. Mater., 47(10), 814–826.
Wang, L. M., and Wu, Y. F. (2008). “Effect of corner radius on the performance of CFRP-confined square concrete columns: Test.” Eng. Struct., 30(2), 493–505.
Watanable, K., et al. (1997). “Confinement effect of FRP sheet on strength and ductility of concrete cylinders under uniaxial compression.” Proc., 3rd Int. Symp. of Non-metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3), Japan Concrete Institute, Sapporo, Japan, 233–240.
Wei, Y., and Wu, Y. F. (2014). “Compression behavior of concrete columns confined by high strength steel wire.” Constr. Build. Mater., 54, 443–453.
Wei, Y. Y., and Wu, Y. F. (2012). “Unified stress-strain model of concrete for FRP-confined columns.” Constr. Build. Mater., 26(1), 381–392.
Wong, Y. L., Yu, T., Teng, J. G., and Dong, S. L. (2008). “Behavior of FRP-confined concrete in annular section columns.” Compos. Part B-Eng., 39(3), 451–466.
Wu, G., Lü, Z., and Wu, Z. (2006a). “Strength and ductility of concrete cylinders confined with FRP composites.” Constr. Build. Mater., 20(3), 134–148.
Wu, G., Wu, Z., Lu, Z., and Ando, Y. (2008). “Structural performance of concrete confined with hybrid FRP composites.” J. Reinf. Plast. Comp., 27(12), 1323–1348.
Wu, Y. F., and Jiang, C. (2013a). “Effect of load eccentricity on the stress-strain relationship of FRP-confined concrete columns.” Compos. Struct., 98, 228–241.
Wu, Y. F., and Jiang, J. F. (2013b). “Effective strain of FRP for confined circular concrete columns.” Compos. Struct., 95, 479–491.
Wu, Y. F., Liu, T., and Oehlers, D. J. (2006b). “Fundamental principles that govern retrofitting of reinforced concrete columns by steel and FRP jacketing.” Adv. Struct. Eng., 9(4), 507–533.
Wu, Y. F., and Wang, L. M. (2009). “Unified strength model for square and circular concrete columns confined by external jacket.” J. Struct. Eng., 253–261.
Wu, Y. F., and Wei, Y. Y. (2010). “Effect of cross-sectional aspect ratio on the strength of CFRP-confined rectangular concrete columns.” Eng. Struct., 32(1), 32–45.
Wu, Y. F., and Zhou, Y. W. (2010). “Unified strength model based on Hoek-Brown failure criterion for circular and square concrete columns confined by FRP.” J. Compos. Constr., 175–184.
Xiao, Y., and Wu, H. (2000). “Compressive behavior of concrete confined by carbon fiber composite jackets.” J. Mater. Civ. Eng., 139–146.
Xiao, Y., and Wu, H. (2003). “Compressive behavior of concrete confined by various types of FRP composite jackets.” J. Reinf. Plast. Comp., 22(13), 1187–1201.
Youssef, M. N., Feng, M. Q., and Mosallam, A. S. (2007). “Stress–strain model for concrete confined by FRP composites.” Compos. Part B: Eng., 38(5), 614–628.
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Journal of Composites for Construction
Volume 19 • Issue 4 • August 2015
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© 2014 American Society of Civil Engineers.
History
Received: Apr 9, 2014
Accepted: Jun 25, 2014
Published online: Oct 2, 2014
Discussion open until: Mar 2, 2015
Published in print: Aug 1, 2015
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