Proposed Development Length Equations for GFRP Bars in Flexural Reinforced Concrete Members
Publication: Journal of Composites for Construction
Volume 27, Issue 1
Abstract
The bond at the interface between concrete and the surface of a glass fiber–reinforced polymer (GFRP) bar is the most critical parameter to ensure that the strains between the GFRP bar and the surrounding concrete are compatible. To prevent bond failure, an adequate development length should be provided. This study evaluated the current recommended equations for the development length using an approach based on the regression analysis of an experimental database of results from 431 recent tests of beam bonding reported in the literature. The main objective of this work is to optimize the development length equation through a comprehensive assessment of the influencing parameters. The parameters studied in this investigation are the concrete compressive strength, concrete cover, confinement effect, bar diameter, bar location, bar surface profile, and bar tensile stress. The proposed equations were compared with the equations in current design codes.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and codes generated or used during the study appear in the published article.
Acknowledgments
The authors would like to acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and MST Rebar Inc. (formerly B&B FRP Manufacturing Inc.).
Notation
The following symbols are used in this paper:
- Ab
- cross-sectional area of the bar (mm2);
- Atr
- area of transverse reinforcement (mm2);
- a
- shear span length (mm);
- c
- concrete cover to the center of the bar (mm);
- db
- diameter of reinforcing bars (mm);
- dc
- bottom concrete cover thickness (mm);
- dcs
- concrete cover thickness measured to the center of reinforcement (mm);
- dc,side
- side concrete cover thickness (mm);
- EFRP
- elastic modulus of GFRP bars (MPa);
- Es
- elastic modulus of steel bars (MPa);
- F
- applied load from the actuator (N);
- concrete compressive strength (MPa);
- fcr
- concrete cracking strength (MPa);
- ff
- design stress in GFRP reinforcement in tension (MPa);
- ffr
- developed stress in the GFRP bars (MPa);
- ffrpu
- ultimate stress of the bar (MPa);
- ffu
- design tensile strength of FRP reinforcement (MPa);
- fy
- specified yield strength of steel reinforcing bars (MPa);
- square root of the specified compressive strength of concrete;
- j
- lever arm from the center of the compression block to the center of tension reinforcement (mm);
- Ktr
- transverse reinforcement index;
- k1
- bar location factor;
- k2
- concrete density factor;
- k3
- bar size factor;
- k4
- bar fiber factor;
- k5
- bar surface profile factor;
- ld
- development length (mm);
- le
- embedded length of the reinforcing bar (mm);
- le−exp.
- experimental embedded length of the reinforcing bar and the same as le (mm);
- le−theo.
- theoretical embedded length that corresponds to the maximum experimental stress in the GFRP bar at failure (mm);
- n
- number of bars developed or spliced along the potential splitting failure plane;
- s
- spacing of transverse reinforcing bars (mm);
- T
- failure load monitored in beams at bond failure (N);
- u
- average bond stress (MPa);
- α
- coefficient accounts for the bar location; and
- τ
- average bond stress (MPa).
References
Achillides, Z. 1998. “Bond behaviour of FRP bars in concrete.” Ph.D. thesis, Dept. of Civil and Structural Engineering, The Univ. of Sheffield.
ACI (American Concrete Institute). 2015. Guide for the design and construction of concrete reinforced with fiber-reinforced polymer bars. ACI 440.1R-15. Farmington Hills, MI: ACI.
Alves, J., A. El-Ragaby, and E. El-Salakawy. 2011. “Durability of GFRP bars” bond to concrete under different loading and environmental conditions.” J. Compos. Constr. 15 (3): 249–262. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000161.
Aly, R. 2005. “Experimental and analytical studies on bond behaviour of tensile lap spliced FRP reinforcing bars in concrete.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Sherbrooke.
Aly, R., B. Benmokrane, and U. Ebead. 2006. “Tensile lap splicing of fiber-reinforced polymer reinforcing bars in concrete.” ACI Struct. J. 103 (6): 857–864.
Asadian, A., A. Eslami, A. S. Farghaly, and B. Benmokrane. 2019a. “Splice strength of staggered and non-staggered bundled glass fiber-reinforced polymer reinforcing bars in concrete.” ACI Struct. J. 116 (4): 129–142. https://doi.org/10.14359/51714482.
Asadian, A., A. Eslami, A. S. Farghaly, and B. Benmokrane. 2019b. “Lap-splice length of bundled glass fiber-reinforced polymer bars in unconfined concrete.” ACI Struct. J. 116 (5): 287–299. https://doi.org/10.14359/51716775.
Baena, M., L. Torres, A. Turon, and C. Barris. 2009. “Experimental study of bond behaviour between concrete and FRP bars using a pullout test.” Composites, Part B 40 (8): 784–797. https://doi.org/10.1016/j.compositesb.2009.07.003.
Basaran, B., and I. Kalkan. 2020. “Development length and bond strength equations for FRP bars embedded in concrete.” Compos. Struct. 251 (June): 112662. https://doi.org/10.1016/j.compstruct.2020.112662.
Benmokrane, B., B. Tighiouart, and O. Chaallal. 1996. “Bond strength and load distribution of GFRP reinforcing bars in concrete.” ACI Mater. J. 93 (3): 246–253.
Choi, D.-U., S.-C. Chun, and S.-S. Ha. 2012. “Bond strength of glass fibre-reinforced polymer bars in unconfined concrete.” Eng. Struct. 34: 303–313. https://doi.org/10.1016/j.engstruct.2011.08.033.
Cosenza, E., G. Manfredi, and R. Realfonzo. 1997. “Behavior and modeling of bond of FRP rebars to concrete.” J. Compos. Constr. 1 (2): 40–51. https://doi.org/10.1061/(ASCE)1090-0268(1997)1:2(40).
CSA (Canadian Standard Association). 1994. Design of concrete structures. CAN/CSA A23.3-94. Mississauga, ON, Canada: CSA.
CSA (Canadian Standard Association). 2002. Design and construction of building structures with fiber reinforced polymers. CAN/CSA S806-02. Mississauga, ON, Canada: CSA.
CSA (Canadian Standard Association). 2012. Design and construction of building structures with fiber reinforced polymers. CAN/CSA S806-12. Mississauga, ON, Canada: CSA.
CSA (Canadian Standard Association). 2014. Canadian highway bridge design. CAN/CSA S6-14. Mississauga, ON, Canada: CSA.
CSA (Canadian Standard Association). 2019. Design of concrete structures. CAN/CSA A23.3-19. Mississauga, ON, Canada: CSA.
DeFreese, J. M., and C. L. Roberts-Wollmann. 2002. Glass fiber reinforced polymer bars as Top Mat reinforcement for bridge decks. Rep. No. VTRC 03-CR6. Charlottesville, VA: Virginia Transportation Research Council.
Ehsani, M. R., H. Saadatmanesh, and S. Tao. 1996. “Design recommendations for bond of GFRP rebars to concrete.” J. Struct. Eng. 122 (3): 247–254. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:3(247).
Esfahani, M. R., M. Rakhshanimehr, and S. R. Mousavi. 2013. “Bond strength of lap-spliced GFRP bars in concrete beams.” J. Compos. Constr. 17 (3): 314–323. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000359.
Hao, Q., Y. Wang, Z. He, and J. Ou. 2009. “Bond strength of glass fiber reinforced polymer ribbed rebars in normal strength concrete.” Constr. Build. Mater. 23 (2): 865–871. https://doi.org/10.1016/j.conbuildmat.2008.04.011.
Harajli, M., and M. Abouniaj. 2010. “Bond performance of GFRP bars in tension: Experimental evaluation and assessment of ACI 440 guidelines.” J. Compos. Constr. 14 (6): 659–668. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000139.
Hossain, K. M. A. 2018. “Bond strength of GFRP bars embedded in engineered cementitious composite using RILEM beam testing.” Int. J. Concr. Struct. Mater. 12 (1): 6. https://doi.org/10.1186/s40069-018-0240-0.
Issa, M. S., I. M. Metwally, and S. M. Elzeiny. 2011. “Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP rebars.” Eng. Struct. 33 (5): 1754–1763. https://doi.org/10.1016/j.engstruct.2011.02.014.
Kotynia, R., D. Szczech, and M. Kaszubska. 2017. “Bond behavior of GRFP bars to concrete in beam test.” Procedia Eng. 193: 401–408. https://doi.org/10.1016/j.proeng.2017.06.230.
Makhmalbaf, E., and A. G. Razaqpur. 2022. “Development length of glass fibre reinforced polymer (GFRP) rebar based on non-uniform bond stress.” Can. J. Civ. Eng. 49 (3): 420–431. https://doi.org/10.1139/cjce-2020-0400.
Mosley, C. P., A. K. Tureyen, and R. J. Frosch. 2008. “Bond strength of nonmetallic reinforcing bars.” ACI Struct. J. 105 (5): 634–642.
Okelo, R. 2007. “Realistic bond strength of FRP rebars in NSC from beam specimens.” J. Aerosp. Eng. 20 (3): 133–140. https://doi.org/10.1061/(ASCE)0893-1321(2007)20:3(133).
Orangun, C. O., J. O. Jirsa, and J. E. Breen. 1975. The strength of anchor bars: A Re-evaluation of test data on development length and splices. Research Report 154-3F. Austin, TX: Center for Highway Research, the University of Texas.
Pay, A. C., E. Canbay, and R. J. Frosch. 2014. “Bond strength of spliced fiber-reinforced polymer reinforcement.” ACI Struct J. 111 (2): 257–266.
Pecce, M., G. Manfredi, R. Realfonzo, and E. Cosenza. 2001. “Experimental and analytical evaluation of bond properties of GFRP bars.” J. Mater. Civ. Eng. 13 (4): 282–290. https://doi.org/10.1061/(ASCE)0899-1561(2001)13:4(282).
Saleh, N., A. Ashour, D. Lam, and T. Sheehan. 2019. “Experimental investigation of bond behaviour of two common GFRP bar types in high—Strength concrete.” Constr. Build. Mater. 201: 610–622. https://doi.org/10.1016/j.conbuildmat.2018.12.175.
Shield, C., C. French, and J. Hanus. 1999. “Bond of GFRP rebar for consideration in bridge decks.” In Proc., 4th Int. Symp. on Fiber Reinforced Polymer Reinforcement for Reinforced Concrete Structures, edited by C. W. Dolan, S. H. Rizkalla, and A. Nanni, 393–406. Farmington Hills, MI: American Concrete Institute.
Shield, C. K., C. French, and A. Retika. 1997. “Thermal and mechanical fatigue effects on GFRP rebar-concrete bond.” In Proc., 3rd Int. Symp. on Non-Metallic Reinforcement for Concrete Structures, 381–388. Tokyo, Japan: Japan Concrete Institute.
Sólyom, S., G. L. Balázs, and A. Borosnyói. 2016. “Material characteristics and bond tests for FRP rebars.” Concr. Struct. 16: 38–44.
Tepfers, R. 1973. “A theory of bond applied to overlapped tensile reinforcement splices for deformed bars.” Ph.D. thesis, Dept. of Architecture and Civil Engineering, Chalmers Univ. of Technology.
Tighiouart, B., B. Benmokrane, and D. Gao. 1998. “Investigation of bond in concrete member with Fibre Reinforced Polymer (FRP) bars.” Constr. Build. Mater. 12 (8): 453–462. https://doi.org/10.1016/S0950-0618(98)00027-0.
Tighiouart, B., B. Benmokrane, and P. Mukhopadhyaya. 1999. “Bond strength of glass FRP rebar splices in beams under static loading.” Constr. Build. Mater. 13 (7): 383–392. https://doi.org/10.1016/S0950-0618(99)00037-9.
Wambeke, B. W., and C. K. Shield. 2006. “Development length of glass fiber-reinforced polymer bars in concrete.” ACI Struct. J. 103 (1): 11–17.
Xue, W., Q. Zheng, and Y. Yang. 2014. “Bond behavior of sand-coated deformed glass fiber reinforced polymer rebars.” J. Reinf. Plast. Compos. 83: 283–298.
Yan, F., Z. Lin, and M. Yang. 2016. “Bond mechanism and bond strength of GFRP bars to concrete: A review.” Composites, Part B 98: 56–69. https://doi.org/10.1016/j.compositesb.2016.04.068.
Zemour, N., A. Asadian, E. A. Ahmed, K. H. Khayat, and B. Benmokrane. 2018. “Experimental study on the bond behavior of GFRP bars in normal and self-consolidating concrete.” Constr. Build. Mater. 189: 869–881. https://doi.org/10.1016/j.conbuildmat.2018.09.045.
Information & Authors
Information
Published In
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jun 21, 2021
Accepted: Aug 3, 2022
Published online: Nov 7, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 7, 2023
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.