Equivalent Moment of Inertia Based on Integration of Curvature
Publication: Journal of Composites for Construction
Volume 15, Issue 3
Abstract
This paper evaluates the benefits of computing deflection with an equivalent moment of inertia based on integration of curvature to account for changes in member stiffness along the span. Results are evaluated for steel and fiber-reinforced polymer reinforced (FRP-reinforced) concrete flexural members with different loading arrangements and support conditions. Closed-form solutions of integrated expressions for deflection are expressed in terms of an equivalent moment of inertia and compared to deflection computed with an effective moment of inertia based on the stiffness at the critical section. Results from this comparison are validated with measured deflections from an experimental database for FRP-reinforced concrete. Current code-related approaches are also compared to the experimental database. It is shown herein that the use of an integration-based expression for the moment of inertia can lead to improved prediction of deflection, though the use of an effective moment of inertia based on member stiffness at the critical section gives a reasonably conservative estimate of deflection in many cases. The benefits of taking account of changes in stiffness along the member span are more evident when low reinforcing ratios are used in combination with FRP reinforcement, and use of the integration-based expression may be warranted when deflection control is critical in such cases.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work presented in this paper is part of an ongoing investigation looking at serviceability issues related to deflection and cracking in steel- and FRP-reinforced concrete. Funding was provided by the Natural Sciences and Engineering Research Council of Canada together with support from the University of New Brunswick. This support is gratefully acknowledged.
References
Al-Sunna, R. A. S. (2006). “Deflection behaviour of FRP-reinforced concrete flexural members.” Ph.D. dissertation, University of Sheffield, Sheffield, England, 318.
Al-Zaid, R. Z., Al-Shaikh, A. H., and Abu-Hussein, M. H. (1991). “Effect of loading type on the effective moment of inertia of reinforced concrete beams.” ACI Struct. J., 88(2), 184–190.
American Concrete Institute (ACI) Committee 318. (1971). “Building code requirements for reinforced concrete.” ACI 318-71, ACI, Farmington Hills, MI, 78.
American Concrete Institute (ACI) Committee 318. (2008). “Building code requirements for structural concrete and commentary.” ACI 318-08, ACI, Farmington Hills, MI, 465.
American Concrete Institute (ACI) Committee 435. (1995). “Control of deflection in concrete structures.” ACI 435R-95, ACI, Farmington Hills, MI, 88.
American Concrete Institute (ACI) Committee 440. (1996). “State-of-the-art report on fiber reinforced plastic (FRP) reinforcement for concrete structures.” ACI 440R-96, ACI, Farmington Hills, MI, 68.
American Concrete Institute (ACI) Committee 440. (2003). “Guide for the design and construction of concrete reinforced with FRP bars.” ACI 440.1R-03, ACI, Farmington Hills, MI, 42.
American Concrete Institute (ACI) Committee 440. (2006). “Guide for the design and construction of concrete reinforced with FRP bars.” ACI 440.1R-06, ACI, Farmington Hills, MI, 44.
Benmokrane, B., Chaallal, O., and Masmoudi, R. (1996). “Flexural response of concrete beams reinforced with FRP reinforcing bars.” ACI Struct. J., 91(2), 46–55.
Bischoff, P. H. (2005). “Reevaluation of deflection prediction for concrete beams reinforced with steel and fibre reinforced polymer (FRP) bars.” J. Struct. Eng., 131(5), 752–767.
Bischoff, P. H. (2006). “Discussion of ‘Behavior of aramid fiber-reinforced polymer reinforced high strength concrete beams under bending’ by M. A. Rashid, M. A. Mansur, and P. Paramasivam,” J. Compos. Constr., 10(4), 367–368.
Bischoff, P. H. (2007a). “Deflection calculations of FRP-reinforced concrete beams based on modifications to the existing Branson equation.” J. Compos. Constr., 11(1), 4–14.
Bischoff, P. H. (2007b). “Rational model for calculating deflection of reinforced concrete beams and slabs.” Can. J. Civ. Eng., 34(8), 992–1002.
Bischoff, P. H., and Johnson, R. D. (2007). “Effect of shrinkage on short-term deflection of reinforced concrete beams and slabs.” Structural Implications of Shrinkage and Creep of Concrete, ACI SP 246-10, N. J. Gardner and M. A. Chiorino, eds., American Concrete Institute, Farmington Hills, MI, 167–180.
Bischoff, P. H., and Paixao, R. (2004). “Tension stiffening and cracking of concrete reinforced with glass fiber-reinforced polymer (GFRP) bars.” Can. J. Civ. Eng., 31(4), 579–588.
Bischoff, P. H., and Scanlon, A. (2007). “Effective moment of inertia for calculating deflections of concrete members containing steel reinforcement and FRP reinforcement.” ACI Struct. J., 104(1), 68–75.
Branson, D. E. (1965). “Instantaneous and time-dependent deflections of simple and continuous reinforced concrete beams.” HPR Report No. 7, Part 1, Alabama Highway Department, Bureau of Public Roads, Montgomery, AL, 78.
Canadian Standards Association (CSA). (2002). “Design and construction of building components with fibre-reinforced polymers.” CSA Standard S806-02, Rexdale (Toronto), Ontario, 177.
Comité Euro-International du Béton (CEB-FIP). (1993). “CEB-FIP Model Code (MC-90).” Thomas Telford, London, 437.
European Committee for Standardization (CEN). (2004). “Design of concrete structures—Part 1-1: General rules and rules for buildings.” Eurocode 2, European Standard BS EN 1992-1-1: 2004. Brussels, 230.
Faza, S. S. (1991). “Bending and bond behavior and design of concrete beams reinforced with fiber reinforced plastic rebars.” Ph.D. dissertation, West Virginia University, Morgantown, WV, 200.
Ghali, A. (1993). “Deflection of reinforced concrete members: A critical review.” ACI Struct. J., 90(4), 364–373.
Gross, S. P., Dinehart, D. W., Yost, J. R., and Theisz, P. (2004). “Experimental tests of high-strength concrete beams reinforced with CFRP bars.” Proc. of the 4th Intl. Conf. on Advanced Composite Materials in Bridges and Structures, Calgary, Canada, Paper No. 153, 1–8.
International Conf. of Building Officials (ICBO). (1997). “Structural engineering design provisions.” 1997 Uniform Building Code (UBC), Vol. 2. International Conference of Building Officials, Whittier, California.
Int. Federation for Structural Concrete (FIB). (2007). “FRP reinforcement in RC structures.” Bulletin 40, Lausanne, Switzerland, 147.
Kakizawa, T., Ohno, S., and Yonezawa, T. (1993). “Flexural behavior and energy absorption of carbon FRP-reinforced concrete beams,” Fiber Reinforced Plastic Reinforcement for Concrete Structures, ACI SP-138, American Concrete Institute, Farmington Hills, MI, 585–598.
Kassem, C., El-Salakawy, E., and Benmokrane, B. (2003). “Deflection behaviour of concrete beams reinforced with carbon FRP composite bars.” Deflection Control for the Future, ACI SP-210. N. J. Gardner, ed., American Concrete Institute, Farmington Hills, MI, 173–190.
Malhas, F. A., and Rahman, A. (2003). “A comparison of the ACI and EC2 code provisions for flexural deflections.” Deflection Control for the Future, ACI SP-210, N. J. Gardner, ed., American Concrete Institute, Farmington Hills, MI, 93–114.
Masmoudi, R., Theriault, M., and Benmokrane, B. (1998). “Flexural behavior of concrete beams reinforced with deformed fiber reinforced plastic reinforcing rods.” ACI Struct. J., 95(6), 665–675.
Mota, C., Alminar, S., and Svecova, D. (2006). “Critical review of deflection formulas for FRP-RC members.” J. Compos. Constr., 10(3), 183–194.
Nakano, K., Matsuzaki, Y., Fukuyama, H., and Teshigawara, M. (1993). “Flexural performance of concrete beams reinforced with continuous fiber bars.” Fiber Reinforced Plastic Reinforcement for Concrete Structures, ACI SP-138, American Concrete Institute, Farmington Hills, MI, 743–766.
Rasheed, H. A., Nayal, R., and Melhem, H. (2004). “Response prediction of concrete beams reinforced with FRP bars.” Compos. Struct., 65(2), 193–204.
Razaqpur, A. G., Svecova, D., and Cheung, M. S. (2000). “Rational method for calculating deflection of fiber-reinforced polymer reinforced beams.” ACI Struct. J., 97(1), 175–185.
Scanlon, A., and Bischoff, P. H. (2008). “Shrinkage restraint and loading history effects on deflection of flexural members.” ACI Struct. J., 105(4), 498–506.
Theriault, M., and Benmokrane, B. (1998). “Effects of FRP reinforcement ratio and concrete strength on flexural behavior of concrete beams.” J. Compos. Constr., 2(1), 7–16.
Toutanji, H., and Saafi, M. (2000). “Flexural behavior of concrete beams reinforced with glass fiber-reinforced polymer bars.” ACI Struct. J., 97(5), 712–719.
Yost, J. R., Gross, S. P., and Dinehart, D. W. (2003). “Effective moment of inertia for glass fiber-reinforced polymer-reinforced concrete beams.” ACI Struct. J., 100(6), 732–739.
Information & Authors
Information
Published In
Journal of Composites for Construction
Volume 15 • Issue 3 • June 2011
Pages: 263 - 273
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Apr 29, 2010
Accepted: Aug 11, 2010
Published online: Aug 20, 2010
Published in print: Jun 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.