Crack-Based Evaluation of Internally FRP-Reinforced Concrete Deep Beams without Shear Reinforcement
Publication: Journal of Composites for Construction
Volume 27, Issue 5
Abstract
The maintenance or replacement of critical infrastructure exposed to aggressive environments is a major problem in many countries. To address this issue, alternative noncorrosive materials, such as fiber-reinforced polymers (FRPs), have been proposed to substitute conventional steel bars. However, large-scale tests of beams with small shear-span-to-depth ratios (deep beams) and FRP bars have shown a significant reduction of shear strength compared to similar beams with steel reinforcement. Therefore, the main objective of this paper is to model and explain the mechanisms that govern the reduction in strength. Twelve test specimens from the literature are analyzed based on a crack-based assessment framework for steel-reinforced concrete members, which is extended to account for FRP bars. The crack-based approach shows that large strains in the flexural FRP reinforcement diminish the aggregate interlock resistance and cause premature shear-induced flexural failures in members without shear reinforcement. It is also shown that the model adequately captures local and global deformations, as well as the effects of beam slenderness, longitudinal reinforcement axial stiffness, concrete strength, and crack geometry on the shear response of internally FRP-reinforced concrete deep beams without shear reinforcement.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors would like to express their gratitude to Matthias Andermatt and Dr. Adam Lubell for providing photographs from their test campaign on 12 deep beams with GFRP reinforcement. The photographs were used in this study to measure the crack geometry (in Appendix III) and use it as an input for the crack-based 2PKT simulations.
Notation
The following symbols are used in this paper:
- Ar
- area of longitudinal bars on the flexural tension side;
- a
- shear span (from center of load to center of support);
- ag
- maximum aggregate size;
- b
- beam width;
- C
- force in the reduced compression zone above the critical crack;
- c
- compression zone depth in pure bending;
- d
- effective depth;
- db
- diameter of bottom longitudinal bars;
- dCLZ
- depth of critical loading zone;
- dcz
- depth of reduced compression zone;
- Ec
- modulus of elasticity of concrete;
- Er
- modulus of elasticity of GFRP;
- fc
- compressive strength of concrete;
- fc,eff
- effective concrete plastic strength that accounts for concrete brittleness in compression;
- fct
- tensile strength of concrete;
- fu
- tensile strength of GFRP;
- h
- beam depth;
- Icr
- moment of inertia of cracked section;
- lb1
- loading plate width;
- lb1e
- effective width of the loading plate;
- lb2
- bearing plate width;
- lCLZ
- horizontal projection of critical loading zone;
- lf
- length of pure flexure region;
- lk
- length of the bottom reinforcement whose elongation contributes to the crack opening;
- ltr
- length necessary to transfer (anchor) the force from the FRP bars to the support region;
- nci
- predicted normal aggregate interlock stress;
- nci,max
- predicted maximum normal aggregate interlock stress;
- P
- applied point load;
- s
- crack slip;
- scr
- crack spacing along the flexural reinforcement;
- T
- tensile force in the bottom reinforcement;
- V
- shear force;
- VCLZ
- predicted shear resisted by critical loading zone;
- Vci
- predicted shear resisted by aggregate interlock;
- Vci,max
- predicted maximum shear resisted by aggregate interlock;
- Vcr,fl
- predicted shear corresponding to flexural cracking;
- Vcr,sh
- predicted shear corresponding to the formation of inclined cracks;
- Vcz
- predicted shear strength using the shear-induced flexural crushing model;
- Veq
- shear derived from the moment equilibrium of the shear span;
- Vexp
- measured shear strength;
- Vd
- predicted shear resisted by dowel action;
- Vpred(A)
- predicted shear strength using the simplified 2PKT;
- Vpred(B)
- predicted shear strength using the crack-based 2PKT;
- Vs
- predicted shear resisted by stirrups;
- Vsect
- sectional shear strength;
- V2PKT(A)
- predicted shear strength using the simplified 2PKT;
- V2PKT(B)
- predicted shear strength using the crack-based 2PKT;
- vci
- predicted tangential aggregate interlock stress;
- vci,max
- predicted maximum tangential aggregate interlock stress;
- w
- crack width;
- wexp
- measured maximum crack width;
- wpred
- predicted maximum crack width;
- wh
- predicted horizontal crack displacement;
- wv
- predicted vertical crack displacement;
- x
- coordinate along x-axis;
- y
- coordinate along y-axis;
- z
- lever arm of the internal longitudinal forces;
- α
- angle of line extending from the inner edge of support plate to the far edge of the tributary area of the loading plate;
- αCLZ
- local inclination of critical crack in critical loading zone;
- α1
- global angle of critical crack (angle of critical diagonal crack in the original 2PKT);
- ɛt,avg
- average strain along bottom longitudinal reinforcement;
- Δ
- beam midspan deflection;
- Δc
- vertical displacement of critical loading zone (shear distortion of CLZ);
- ρ
- ratio of longitudinal bars on the flexural tension side; and
- φ
- curvature in pure flexure region.
References
ACI (American Concrete Institute). 2015. Guide for the design and construction of structural concrete reinforced with fiber-reinforced polymer (FRP) bars. ACI 440.1R-15. Farmington Hills, MI: ACI.
Alam, M. S. 2021. “Assessment of shear capacity of fiber-reinforced polymer deep beams using different methods.” ACI Struct. J. 118 (6): 237–250.
Andermatt, M. F., and A. S. Lubell. 2010. Concrete deep beams reinforced with internal FRP. Structural Engineering Rep. No. 291. Edmonton, AB, Canada: Dept. of Civil and Environmental Engineering, Univ. of Alberta.
Andermatt, M. F., and A. S. Lubell. 2013a. “Strength modeling of concrete deep beams reinforced with internal fiber-reinforced polymer.” ACI Struct. J. 110 (4): 595–605.
Andermatt, M. F., and A. S. Lubell. 2013b. “Behavior of concrete deep beams reinforced with internal fiber-reinforced polymer-experimental study.” ACI Struct. J. 110 (4): 585–594.
Baena, M., L. Torres, A. Turon, and C. Barris. 2009. “Experimental study of bond behaviour between concrete and FRP bars using a pull-out test.” Composites, Part B 40 (8): 784–797. https://doi.org/10.1016/j.compositesb.2009.07.003.
Bediwy, A., K. Mahmoud, and E. El-Salakawy. 2021. “Structural behavior of FRCC layered deep beams reinforced with GFRP headed-end bars.” Eng. Struct. 243: 112648. https://doi.org/10.1016/j.engstruct.2021.112648.
CSA (Canadian Standards Association). 2019. Design of concrete structures. CSA A23.3:2019. Mississauga, ON, Canada: CSA.
CSA (Canadian Standards Association). 2021. Design and construction of building structures with fibre-reinforced polymers. S806-12 (R2021). Mississauga, ON, Canada: CSA.
El-Sayed, A. K., E. F. El-Salakawy, and B. Benmokrane. 2012. “Shear strength of fibre-reinforced polymer reinforced concrete deep beams without web reinforcemen.” Can. J. Civ. Eng. 39 (5): 546–555. https://doi.org/10.1139/l2012-034.
Farghaly, A. S., and B. Benmokrane. 2013. “Shear behavior of FRP-reinforced concrete deep beams without web reinforcement.” J. Compos. Constr. 17 (6): 04013015. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000385.
fib (International Federation for Structural Concrete). 2007. FRP reinforcement in RC structures. fib Bulletin 40. Lausanne, Switzerland: fib.
fib (International Federation for Structural Concrete). 2013. Fib model code for concrete structures 2010. Berlin: Ernst & Sohn.
Garay-Moran, J., and A. S. Lubell. 2008. Behaviour of concrete deep beams reinforced with high strength reinforcement. Structural Engineering Rep. No. 277. Edmonton, AB, Canada: Dept. of Civil and Environmental Engineering, Univ. of Alberta.
JSCE (Japan Society of Civil Engineers). 1997. Recommendation for design and construction of concrete structures using continuous fiber reinforcing materials. Concrete Engineering Series 23. Tokyo: JSCE.
Leonhardt, F., and R. Walther. 1964. The Stuttgart shear tests 1961: Contributions to the treatment of the problems of shear in reinforced concrete construction. C&CA Translation No. 111. London: Cement and Concrete Association.
Li, B., K. Maekawa, and H. Okamura. 1989. “Contact density model for stress transfer across cracks in concrete.” J. Fac. Eng. Univ. Tokyo 40 (1): 9–52.
Mihaylov, B. I. 2015. “Five-spring model for complete shear behaviour of deep beams.” Struct. Concr. 16: 71–83. https://doi.org/10.1002/suco.201400044.
Mihaylov, B. I. 2017. “Two-parameter kinematic approach for shear strength of deep concrete beams with internal FRP reinforcement.” J. Compos. Constr. 21 (2): 04016094. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000747.
Mihaylov, B. I., E. C. Bentz, and M. P. Collins. 2010. “Behavior of large deep beams subjected to monotonic and reversed cyclic shear.” ACI Struct. J. 107 (6): 726–734.
Mihaylov, B. I., E. C. Bentz, and M. P. Collins. 2013. “Two-parameter kinematic theory for shear behavior of deep beams.” ACI Struct. J. 110 (3): 447–456.
Mihaylov, B. I., and R. Franssen. 2017. “Shear–flexure interaction in the critical sections of short coupling beams.” Eng. Struct. 152: 370–380. https://doi.org/10.1016/j.engstruct.2017.09.024.
Mohamed, A. M., K. Mahmoud, and E. F. El-Salakawy. 2020. “Behavior of simply supported and continuous concrete deep beams reinforced with GFRP bars.” J. Compos. Constr. 24 (4): 04020032. https://doi.org/10.1061/(ASCE)CC.1943-5614.0001039.
Mohamed, K., A. S. Farghaly, and B. Benmokrane. 2016. “Strut efficiency-based design for concrete deep beams reinforced with fiber-reinforced polymer bars.” ACI Struct. J. 113 (4): 791–800. https://doi.org/10.14359/51688476.
Mohamed, K., A. S. Farghaly, and B. Benmokrane. 2017. “Effect of vertical and horizontal web reinforcement on the strength and deformation of concrete deep beams reinforced with GFRP bars.” J. Struct. Eng. 143 (8): 04017079. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001786.
Muttoni, A., J. Schwartz, and B. Thürlimann. 1996. Design of concrete structures with stress fields. Basel, Switzerland: Birkhäuser Verlag Basel.
Okelo, R., and R. L. Yuan. 2005. “Bond strength of fiber reinforced polymer rebars in normal strength concrete.” J. Compos. Constr. 9 (3): 203–213. https://doi.org/10.1061/(ASCE)1090-0268(2005)9:3(203).
Rogowsky, D. M., J. G. MacGregor, and S. Y. Ong. 1986. “Tests of reinforced concrete deep beams.” ACI Struct. J. 83 (4): 614–623.
Sigrist, V. 1995. “On the deformation capacity of reinforced concrete girders.” [In German.] Ph.D. thesis, Institute for Structural Analysis and Construction (IBK), ETH Zürich.
Trandafir, A. N., D. K. Palipana, G. T. Proestos, and B. I. Mihaylov. 2022a. “Framework for crack-based assessment of existing lightly reinforced concrete deep members.” ACI Struct. J. 119 (1): 255–266.
Trandafir, A. N., G. T. Proestos, and B. I. Mihaylov. 2022b. “Detailed crack-based assessment of a 4-m deep beam test specimen.” Struct. Concr. 24 (1): 756–770. https://doi.org/10.1002/suco.202200149.
Zhang, N., and K.-H. Tan. 2007. “Size effect in RC deep beams: Experimental investigation and STM verification.” Eng. Struct. 29 (12): 3241–3254. https://doi.org/10.1016/j.engstruct.2007.10.005.
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Published In
Journal of Composites for Construction
Volume 27 • Issue 5 • October 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Nov 23, 2022
Accepted: Jun 6, 2023
Published online: Jul 26, 2023
Published in print: Oct 1, 2023
Discussion open until: Dec 26, 2023
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