A New Analytical Model for Deflection of Concrete Beams Reinforced by BFRP Bars and Steel Fibres under Cyclic Loading
Abstract
:1. Introduction
2. Materials and Methods
2.1. Material Properties
2.2. Test Beams
2.3. Experiment Setup and Procedure
3. Results and Discussion
3.1. Failure Modes, Service Load Moment, and Ultimate Moment Capacity
3.2. Load-Deflection Curve and Envelope Curve
3.2.1. Number of Unloading–Reloading Cycles
3.2.2. BFRP Reinforcement Ratio
3.2.3. Steel Fiber Volume Fraction and Shape
3.2.4. Concrete Strength
3.3. Residual Deflection
3.4. Stiffness Degradation
4. Experimental Results versus Model Prediction
4.1. Theoretical Calculation of Deflection of FRP-RC Beams
- (1)
- A beam section is homogeneous before concrete cracking, and the contribution of the BFRP bars to the total moment of inertia of a beam section is neglected. Therefore, the total moment of inertia (Ig) can be obtained by the following equation.
- (2)
- After a crack is initiated in concrete, the contribution of the concrete in the tension zone is neglected. Therefore, the moment of inertia (Icr) of the cracked beam section can be obtained by the following equation.
4.2. A New Model for the Deflection of the BFRP-RC Beams with Steel Fibers
5. Conclusions
- The service load moment of the BFRP-RC beams with 1.5% by volume steel fibers was 103.3% higher than that of the beams without fibers, and the deflection and the residual deflection of the beams were reduced by 48.18% and 30.36% at the applied load of 100kN. Moreover, increasing the steel-fiber volume fraction can significantly enhance the stiffness of the BFRP-RC beams after cracking.
- Increasing the number of unloading–reloading cycles reduced the peak load and increased the residual deflection of the BFRP-RC beams under the same deflection. The deflection of the beams increased by 11% after the first stage of three loading and unloading cycles, while the deflection increased by only 8% after three unloading and reloading cycles in the second and third stages of loading.
- The BFRP reinforcement ratio had the greatest influence on the load-deflection curves, load-residual deflection curves, and stiffness–displacement curves of the BFRP-RC beams. Higher-strength concrete was beneficial in improving the stiffness of the beams and reducing their deflection. A higher BFRP reinforcement ratio was beneficial to improving the serviceability of the BFRP-RC beams, which is the controlling limit state for the structural design of the BFRP-RC beams with steel fibers.
- Combined with the influences of cyclic loading on the deflection, a new analytical method for evaluating the deflection of the BFRP-RC beams with steel fibers under cyclic loading was proposed in this research, which gives better results than any other available model in literature and design codes when compared with experimental results.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Siddika, A.; Al Mamun, A.; Alyousef, R.; Amran, Y.M. Strengthening of reinforced concrete beams by using fiber-reinforced polymer composites: A review. J. Build. Eng. 2019, 25, 100798. [Google Scholar] [CrossRef]
- Kadhim, M.M.; Jawdhari, A.R.; Altaee, M.J.; Adheem, A.H. Finite element modelling and parametric analysis of FRP strengthened RC beams under impact load. J. Build. Eng. 2020, 32, 101526. [Google Scholar] [CrossRef]
- Sun, Z.; Fu, L.; Feng, D.-C.; Vatuloka, A.R.; Wei, Y.; Wu, G. Experimental study on the flexural behavior of concrete beams reinforced with bundled hybrid steel/FRP bars. Eng. Struct. 2019, 197, 109443. [Google Scholar] [CrossRef]
- Mehany, S.; Mohamed, H.M.; Benmokrane, B. Contribution of lightweight self-consolidated concrete (LWSCC) to shear strength of beams reinforced with basalt FRP bars. Eng. Struct. 2021, 231, 111758. [Google Scholar] [CrossRef]
- Tran, T.T.; Pham, T.M.; Hao, H. Effect of hybrid fibers on shear behaviour of geopolymer concrete beams reinforced by basalt fiber reinforced polymer (BFRP) bars without stirrups. Compos. Struct. 2020, 243, 112236. [Google Scholar] [CrossRef]
- Barris, C.; Torres, L.; Vilanova, I.; Miàs, C.; Llorens, M. Experimental study on crack width and crack spacing for Glass-FRP reinforced concrete beams. Eng. Struct. 2017, 131, 231–242. [Google Scholar] [CrossRef]
- Saleh, Z.; Goldston, M.; Remennikov, A.M.; Sheikh, M.N. Flexural design of GFRP bar reinforced concrete beams: An appraisal of code recommendations. J. Build. Eng. 2019, 25, 100794. [Google Scholar] [CrossRef]
- Han, S.; Zhou, A.; Ou, J. Relationships between interfacial behavior and flexural performance of hybrid steel-FRP composite bars reinforced seawater sea-sand concrete beams. Compos. Struct. 2021, 277, 114672. [Google Scholar] [CrossRef]
- Xiao, S.-H.; Lin, J.-X.; Li, L.-J.; Guo, Y.-C.; Zeng, J.-J.; Xie, Z.-H.; Wei, F.-F.; Li, M. Experimental study on flexural behavior of concrete beam reinforced with GFRP and steel-fiber composite bars. J. Build. Eng. 2021, 2, 103087. [Google Scholar] [CrossRef]
- Khorasani, A.M.; Esfahani, M.R.; Sabzi, J. The effect of transverse and flexural reinforcement on deflection and cracking of GFRP bar reinforced concrete beams. Compos. Part B Eng. 2019, 161, 530–546. [Google Scholar] [CrossRef]
- Dong, H.-L.; Zhou, W.; Wang, Z. Flexural performance of concrete beams reinforced with FRP bars grouted in corrugated sleeves. Compos. Struct. 2019, 215, 49–59. [Google Scholar] [CrossRef]
- Zeng, W.; Ding, Y.; Zhang, Y.; Dehn, F. Effect of steel fiber on the crack permeability evolution and crack surface topography of concrete subjected to freeze-thaw damage. Cem. Concr. Res. 2020, 138, 106230. [Google Scholar] [CrossRef]
- Jabbour, R.; Assaad, J.J.; Hamad, B. Cost-to-performance assessment of polyvinyl alcohol fibers in concrete structures. Mech. Adv. Mater. Struct. 2021, 1–20. [Google Scholar] [CrossRef]
- Chellapandian, M.; Mani, A.; Prakash, S.S. Effect of macro-synthetic structural fibers on the flexural behavior of concrete beams reinforced with different ratios of GFRP bars. Compos. Struct. 2020, 254, 112790. [Google Scholar] [CrossRef]
- de Sá, F.R.; Silva, F.D.A.; Cardoso, D.C. Tensile and flexural performance of concrete members reinforced with polypropylene fibers and GFRP bars. Compos. Struct. 2020, 253, 112784. [Google Scholar] [CrossRef]
- Liu, X.; Sun, Y.; Wu, T.; Liu, Y. Flexural cracks in steel fiber-reinforced lightweight aggregate concrete beams reinforced with FRP bars. Compos. Struct. 2020, 253, 112752. [Google Scholar] [CrossRef]
- Abed, F.; AlHafiz, A.R. Effect of basalt fibers on the flexural behavior of concrete beams reinforced with BFRP bars. Compos. Struct. 2019, 215, 23–34. [Google Scholar] [CrossRef]
- Ibrahim, S.S.; Kandasamy, S.; Pradeepkumar, S.; Bose, R.S.C. Effect of discrete steel fibres on strength and ductility of FRP laminated RC beams. Ain Shams Eng. J. 2020, 12, 1329–1337. [Google Scholar] [CrossRef]
- Issa, M.S.; Metwally, I.M.; Elzeiny, S.M. Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP rebars. Eng. Struct. 2011, 33, 1754–1763. [Google Scholar] [CrossRef]
- Hosseini, S.-A.; Nematzadeh, M.; Chastre, C. Prediction of shear behavior of steel fiber-reinforced rubberized concrete beams reinforced with glass fiber-reinforced polymer (GFRP) bars. Compos. Struct. 2021, 256, 113010. [Google Scholar] [CrossRef]
- Dev, A.; Chellapandian, M.; Prakash, S.S.; Kawasaki, Y. Failure-mode analysis of macro-synthetic and hybrid fibre-reinforced concrete beams with GFRP bars using acoustic emission technique. Constr. Build. Mater. 2020, 249, 118737. [Google Scholar] [CrossRef]
- Nie, X.; Fu, B.; Teng, J.; Bank, L.; Tian, Y. Shear Behavior of Reinforced Concrete Beams with GFRP Needles as Coarse Aggregate Partial Replacement: Full-Scale Experiments. In Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications; CRC Press: Boca Raton, FL, USA, 2019; pp. 1548–1553. [Google Scholar] [CrossRef]
- Junaid, M.T.; Elbana, A.; Altoubat, S.; Al-Sadoon, Z. Experimental study on the effect of matrix on the flexural behavior of beams reinforced with Glass Fiber Reinforced Polymer (GFRP) bars. Compos. Struct. 2019, 222, 110930. [Google Scholar] [CrossRef]
- Zhu, H.; Cheng, S.; Gao, D.; Neaz, S.M.; Li, C. Flexural behavior of partially fiber-reinforced high-strength concrete beams reinforced with FRP bars. Constr. Build. Mater. 2018, 161, 587–597. [Google Scholar] [CrossRef]
- Ge, W.; Song, W.; Ashour, A.; Lu, W.; Cao, D. Flexural performance of FRP/steel hybrid reinforced engineered cementitious composite beams. J. Build. Eng. 2020, 31, 101329. [Google Scholar] [CrossRef]
- Al-Saawani, M.A.; El-Sayed, A.K.; Al-Negheimish, A.I. Effect of shear-span/depth ratio on debonding failures of FRP-strengthened RC beams. J. Build. Eng. 2020, 32, 101771. [Google Scholar] [CrossRef]
- Zhu, H.; Li, Z.; Wen, C.; Cheng, S.; Wei, Y. Prediction model for the flexural strength of steel fiber reinforced concrete beams with fiber-reinforced polymer bars under repeated loading. Compos. Struct. 2020, 250, 112609. [Google Scholar] [CrossRef]
- Li, Z.; Zhu, H.; Du, C.; Gao, D.; Yuan, J.; Wen, C. Experimental study on cracking behavior of steel fiber-reinforced concrete beams with BFRP bars under repeated loading. Compos. Struct. 2021, 267, 113878. [Google Scholar] [CrossRef]
- Li, Z.; Zhu, H.; Zhen, X.; Wen, C.; Chen, G. Effects of steel fiber on the flexural behavior and ductility of concrete beams reinforced with BFRP rebars under repeated loading. Compos. Struct. 2021, 270, 114072. [Google Scholar] [CrossRef]
- Cheng, L. Flexural fatigue analysis of a CFRP form reinforced concrete bridge deck. Compos. Struct. 2011, 93, 2895–2902. [Google Scholar] [CrossRef]
- GB/T 30022-2013; The Method for Basic Mechanical Properties of Fiber Reinforced Polymer Bar. China National Standard: Beijing, China, 2013.
- JG/T 472-2015; Steel Fiber Reinforced Concrete. China National Standard: Beijing, China, 2015.
- GB175-2007; Common Portland Cement. China National Standard: Beijing, China, 2007.
- ACI 440. 1R-15; Guide for the Design and Construction of Concrete Reinforced with FRP Bars. American Concrete Institute: Farmington Hills, MI, USA, 2015.
- CAN, CSA S806–12; Canadian Standard, Design and Construction of Building Structures with Fiber-Reinforced Polymers. Canadian Standards Association: Toronto, ON, Canada, 2012.
- Gao, D.; Gu, Z.; Wei, C.; Wu, C.; Pang, Y. Effects of fiber clustering on fatigue behavior ofs steel fiber reinforced concrete beams. Constr. Build. Mater. 2021, 301, 124070. [Google Scholar] [CrossRef]
- JGJ/T 101-2015; Specification for Seismic Test of Building. China National Standard: Beijing, China, 2015.
- Bischoff, P.H. Reevaluation of Deflection Prediction for Concrete Beams Reinforced with Steel and Fiber Reinforced Polymer Bars. J. Struct. Eng. 2005, 131, 752–767. [Google Scholar] [CrossRef]
- Bischoff, P.H. Deflection Calculation of FRP Reinforced Concrete Beams Based on Modifications to the Existing Branson Equation. J. Compos. Constr. 2007, 11, 4–14. [Google Scholar] [CrossRef]
- Benmokrane, B.; Chaallal, O.; Masmoudi, R. Flexural response of concrete beams reinforced with FRP reinforcing bars. ACI Struct. J. 1996, 93, 46–55. [Google Scholar]
- Alsayed, S.; Al-Salloum, Y.; Almusallam, T. Performance of glass fiber reinforced plastic bars as a reinforcing material for concrete structures. Compos. Part B Eng. 2000, 31, 555–567. [Google Scholar] [CrossRef]
- ISIS Canada Research Network. Reinforcing Concrete Structures with Fibre Reinforced Polymers; Design Manual No. 3; Canadian Standards Association: Toronto, ON, Canada, 2007. [Google Scholar]
Types | lsf (mm) | dsf (mm) | lsf/dsf | ft,sf (MPa) | Esf (GPa) | Number of Hook-Ends |
---|---|---|---|---|---|---|
3D | 35 | 0.55 | 65 | 1345 | 200 | 1 |
4D | 60 | 0.90 | 65 | 1600 | 200 | 1.5 |
5D | 60 | 0.90 | 65 | 2300 | 200 | 2 |
Types | Diameter (mm) | Tensile Strength (ffu) (MPa) | Young Modulus (Ef) (GPa) | Yield Strength |
---|---|---|---|---|
BFRP | 12 | 1080 | 47.0 | — |
BFRP | 14 | 1060 | 46.5 | — |
Beams | Water | Cement | Sand | Steel Fiber | Coarse Aggregate | Polycarboxylate Superplasticizer |
---|---|---|---|---|---|---|
B0.56C60V1.0S3 | 172 | 521.2 | 669.3 | 78.5 (3D) | 1013.5 | 5.212 |
B0.77C60V1.0S3 | 172 | 521.2 | 669.3 | 78.5 (3D) | 1013.5 | 5.212 |
B1.15C60V1.0S3 | 172 | 521.2 | 669.3 | 78.5 (3D) | 1013.5 | 5.212 |
B1.65C60V1.0S3 | 172 | 521.2 | 669.3 | 78.5 (3D) | 1013.5 | 5.212 |
B1.15C60 | 172 | 521.2 | 648.6 | — | 1058.2 | 2.606 |
B1.15C60V0.5S3 | 172 | 521.2 | 658.9 | 39.3 (3D) | 1035.9 | 4.170 |
B1.15C60V1.5S3 | 172 | 521.2 | 679.6 | 117.8 (3D) | 991.1 | 7.297 |
B1.15C60V1.0S4 | 172 | 521.2 | 669.3 | 78.5 (4D) | 1013.5 | 5.212 |
B1.15C60V1.0S5 | 172 | 521.2 | 669.3 | 78.5 (5D) | 1013.5 | 5.212 |
B1.15C30V1.0S3 | 215 | 330.8 | 706.2 | 78.5 (3D) | 1124.0 | 0 |
Aggregate | Specific Gravity | Water Absorption | Fineness Modulus | Free Moisture Content | Graded Zone |
---|---|---|---|---|---|
Fine aggregate | 2.60 | 1.01% | 2.78 | 2% | II |
Coarse aggregate | 2.74 | 0.30% | 7.5 | NIL | NIL |
Compressive Strength/MPa | Flexural Strength /MPa | Setting Time/min | Specific Surface Area m2/kg | |||
---|---|---|---|---|---|---|
3 d | 28 d | 3 d | 28 d | Initial Setting Time | Final Setting Time | |
27.8 | 46.8 | 5.6 | 8.5 | 122 | 232 | 345 |
Beams | ρf (%) | ρsf (%) | Steel Fiber Shapes | fcu,k (MPa) | Actual Physical Properties of Concrete | |||
---|---|---|---|---|---|---|---|---|
fcu (MPa) | ft (MPa) | fc′ (MPa) | Ec (GPa) | |||||
B0.56C60V1.0S3 | 0.56 | 1.0 | 3D | 60 | 60.16 | 5.59 | 48.13 | 41.30 |
B0.77C60V1.0S3 | 0.77 | 1.0 | 3D | 60 | 74.99 | 5.70 | 52.45 | 42.70 |
B1.15C60V1.0S3 | 1.15 | 1.0 | 3D | 60 | 81.47 | 6.60 | 65.18 | 42.40 |
B1.65C60V1.0S3 | 1.65 | 1.0 | 3D | 60 | 76.47 | 5.84 | 61.18 | 42.40 |
B1.15C60 | 1.15 | 0 | — | 60 | 74.54 | 3.56 | 59.63 | 41.62 |
B1.15C60V0.5S3 | 1.15 | 0.5 | 3D | 60 | 69.00 | 4.88 | 51.75 | 41.00 |
B1.15C60V1.5S3 | 1.15 | 1.5 | 3D | 60 | 81.47 | 5.17 | 65.18 | 42.23 |
B1.15C60V1.0S4 | 1.15 | 1.0 | 4D | 60 | 83.89 | 5.83 | 62.92 | 42.38 |
B1.15C60V1.0S5 | 1.15 | 1.0 | 5D | 60 | 79.14 | 5.51 | 63.31 | 43.02 |
B1.15C30V1.0S3 | 1.15 | 1.0 | 3D | 30 | 44.00 | 3.36 | 34.00 | 35.00 |
Beams | Failure Modes | Mcr (kN·m) | Ms (kN·m) | Mu (kN·m) | Δmax (mm) | ω100 kN (mm) | Number of Cracks |
---|---|---|---|---|---|---|---|
B0.56C60V1.0S3 | BFRP bars rupture | 13.50 | 21.07 | 51.85 | 32.23 | 0.72 | 7 |
B0.77C60V1.0S3 | BFRP bars rupture | 14.10 | 23.40 | 73.28 | 35.23 | 0.70 | 8 |
B1.15C60V1.0S3 | Concrete crushing | 14.25 | 25.74 | 101.34 | 44.32 | 0.37 | 10 |
B1.65C60V1.0S3 | Concrete crushing | 15.00 | 28.23 | 101.43 | 46.83 | 0.35 | 10 |
B1.15C60 | Concrete crushing | 9.30 | 18.14 | 93.48 | 44.31 | 0.75 | 7 |
B1.15C60V0.5S3 | Concrete crushing | 13.50 | 21.27 | 94.92 | 46.03 | 0.52 | 9 |
B1.15C60V1.5S3 | Concrete crushing | 16.50 | 27.93 | 106.77 | 44.42 | 0.33 | 11 |
B1.15C60V1.0S4 | Concrete crushing | 15.00 | 25.50 | 103.53 | 46.04 | 0.35 | 10 |
B1.15C60V1.0S5 | Concrete crushing | 15.00 | 26.82 | 104.37 | 45.50 | 0.34 | 11 |
B1.15C30V1.0S3 | Concrete crushing | 9.75 | 22.90 | 80.50 | 46.45 | 0.50 | 10 |
Beams | Load (kN) | Δ1 (mm) | Δ1′ (mm) | Δ1/Δ1′ | Load (kN) | Δ2 (mm) | Δ2′ (mm) | Δ2/Δ2′ | Load (kN) | Δ3 (mm) | Δ3′ (mm) | Δ3/Δ3′ |
---|---|---|---|---|---|---|---|---|---|---|---|---|
B0.56C60V1.0S3 | 74.43 | 5.57 | 6.50 | 1.17 | 106.19 | 12.20 | 13.56 | 1.11 | 133.17 | 18.85 | 20.72 | 1.10 |
B0.77C60V1.0S3 | 78.53 | 3.59 | 4.20 | 1.17 | 119.00 | 9.54 | 10.51 | 1.10 | 160.93 | 15.74 | 17.39 | 1.10 |
B1.15C60V1.0S3 | 85.80 | 4.63 | 5.15 | 1.11 | 140.40 | 10.82 | 11.75 | 1.09 | 191.50 | 17.27 | 18.50 | 1.07 |
B1.65C60V1.0S3 | 130.90 | 5.77 | 6.60 | 1.14 | 169.40 | 8.76 | 9.50 | 1.08 | 229.00 | 14.87 | 16.19 | 1.09 |
B1.15C60 | 60.00 | 5.33 | 5.86 | 1.10 | 105.32 | 11.79 | 12.62 | 1.07 | 150.39 | 18.27 | 19.11 | 1.05 |
B1.15C60V0.5S3 | 71.00 | 5.02 | 5.60 | 1.12 | 124.90 | 11.55 | 12.28 | 1.06 | 175.10 | 17.97 | 18.95 | 1.05 |
B1.15C60V1.5S3 | 93.10 | 4.66 | 5.15 | 1.11 | 152.50 | 11.00 | 11.86 | 1.08 | 206.20 | 17.51 | 18.89 | 1.08 |
B1.15C60V1.0S4 | 85.00 | 4.88 | 5.30 | 1.09 | 147.40 | 11.19 | 11.86 | 1.06 | 201.70 | 17.52 | 18.70 | 1.07 |
B1.15C60V1.0S5 | 89.40 | 4.75 | 5.20 | 1.09 | 155.40 | 10.77 | 11.45 | 1.06 | 212.90 | 16.85 | 17.90 | 1.06 |
B1.15C30V1.0S3 | 76.33 | 5.79 | 6.32 | 1.09 | 130.28 | 12.18 | 13.27 | 1.09 | 175.49 | 18.62 | 20.10 | 1.08 |
Average value | 1.12 | 1.08 | 1.08 |
Beams | F1 (kN) | Δ1 (mm) | Δc (mm) | Δc /Δ1 | ΔBenm. (mm) | ΔBenm. /Δ1 | ΔBisch. (mm) | ΔBisch. /Δ1 | ΔAlsa (mm) | ΔAlsa /Δ1 | ΔISIS (mm) | ΔISIS /Δ1 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
B0.56C60V1.0S3 | 74.43 | 5.57 | 6.6 | 1.20 | 9.14 | 1.64 | 7.84 | 1.41 | 9.92 | 1.78 | 9.73 | 1.75 |
B0.77C60V1.0S3 | 78.53 | 3.59 | 5.84 | 1.63 | 8.02 | 2.23 | 6.22 | 1.73 | 7.96 | 2.22 | 7.79 | 2.17 |
B1.15C60V1.0S3 | 85.80 | 4.63 | 5.02 | 1.08 | 7.10 | 1.53 | 5.11 | 1.10 | 6.12 | 1.32 | 6.10 | 1.32 |
B1.65C60V1.0S3 | 130.90 | 5.77 | 7.58 | 1.31 | 9.63 | 1.67 | 8.36 | 1.45 | 9.16 | 1.59 | 8.99 | 1.56 |
B1.15C60 | 60.00 | 5.33 | 4.37 | 0.91 | 5.03 | 0.94 | 3.82 | 0.72 | 4.40 | 0.83 | 4.42 | 0.83 |
B1.15C60V0.5S3 | 71.00 | 5.02 | 4.34 | 0.86 | 5.72 | 1.14 | 3.74 | 0.74 | 4.95 | 0.99 | 4.81 | 0.96 |
B1.15C60V1.5S3 | 93.10 | 4.66 | 4.91 | 1.05 | 7.67 | 1.65 | 5.25 | 1.13 | 6.55 | 1.41 | 6.47 | 1.39 |
B1.15C60V1.0S4 | 85.00 | 4.88 | 4.89 | 1.00 | 7.05 | 1.44 | 4.83 | 0.99 | 6.00 | 1.23 | 5.94 | 1.22 |
B1.15C60V1.0S5 | 89.40 | 4.75 | 5.2 | 1.09 | 7.38 | 1.55 | 5.27 | 1.11 | 6.35 | 1.34 | 6.33 | 1.33 |
B1.15C30V1.0S3 | 76.33 | 5.79 | 5.22 | 0.84 | 6.82 | 1.18 | 5.40 | 0.93 | 6.39 | 1.10 | 6.33 | 1.09 |
Average value | 1.09 | 1.50 | 1.13 | 1.38 | 1.36 | |||||||
Coefficient of variation | 0.22 | 0.34 | 0.30 | 0.38 | 0.37 |
Beams | F1 (kN) | Δ1′ (mm) | Δc1′ (mm) | Δc1′ /Δ1′ | F2 (kN) | Δ2′ (mm) | Δc2′ (mm) | Δc2′ /Δ2′ | F3 (kN) | Δ3′ (mm) | Δc3′ (mm) | Δc3′ /Δ3′ |
---|---|---|---|---|---|---|---|---|---|---|---|---|
B0.56C60V1.0S3 | 74.43 | 6.50 | 7.33 | 1.13 | 106.19 | 13.56 | 12.43 | 0.92 | 133.17 | 20.72 | 17.35 | 0.84 |
B0.77C60V1.0S3 | 78.53 | 4.20 | 6.48 | 1.54 | 119.00 | 10.51 | 11.68 | 1.11 | 160.93 | 17.39 | 17.66 | 1.02 |
B1.15C60V1.0S3 | 85.80 | 5.15 | 5.57 | 1.08 | 140.40 | 11.75 | 10.73 | 0.91 | 191.50 | 18.50 | 16.20 | 0.88 |
B1.65C60V1.0S3 | 130.90 | 6.60 | 8.41 | 1.27 | 169.40 | 9.50 | 11.98 | 1.26 | 229.00 | 16.19 | 17.81 | 1.10 |
B1.15C60 | 60.00 | 5.86 | 4.85 | 0.83 | 105.32 | 12.62 | 11.06 | 0.88 | 150.39 | 19.11 | 17.42 | 0.91 |
B1.15C60V0.5S3 | 71.00 | 5.60 | 4.82 | 0.86 | 124.90 | 12.28 | 10.43 | 0.85 | 175.10 | 18.95 | 16.27 | 0.86 |
B1.15C60V1.5S3 | 93.10 | 5.15 | 5.45 | 1.06 | 152.50 | 11.86 | 10.65 | 0.90 | 206.20 | 18.89 | 15.98 | 0.85 |
B1.15C60V1.0S4 | 85.00 | 5.30 | 5.43 | 1.02 | 147.40 | 11.86 | 11.29 | 0.95 | 201.70 | 18.70 | 17.11 | 0.91 |
B1.15C60V1.0S5 | 89.40 | 5.20 | 5.77 | 1.11 | 155.40 | 11.45 | 11.91 | 1.04 | 212.90 | 17.90 | 18.02 | 1.01 |
B1.15C30V1.0S3 | 76.33 | 6.32 | 5.79 | 0.92 | 130.28 | 13.27 | 10.46 | 0.79 | 175.49 | 20.10 | 15.40 | 0.77 |
Average value | 0.99 | |||||||||||
Coefficient of variation | 0.16 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhu, H.; Li, Z.; Chen, Q.; Cheng, S.; Li, C.; Zhou, X. A New Analytical Model for Deflection of Concrete Beams Reinforced by BFRP Bars and Steel Fibres under Cyclic Loading. Polymers 2022, 14, 1797. https://doi.org/10.3390/polym14091797
Zhu H, Li Z, Chen Q, Cheng S, Li C, Zhou X. A New Analytical Model for Deflection of Concrete Beams Reinforced by BFRP Bars and Steel Fibres under Cyclic Loading. Polymers. 2022; 14(9):1797. https://doi.org/10.3390/polym14091797
Chicago/Turabian StyleZhu, Haitang, Zongze Li, Qun Chen, Shengzhao Cheng, Chuanchuan Li, and Xiangming Zhou. 2022. "A New Analytical Model for Deflection of Concrete Beams Reinforced by BFRP Bars and Steel Fibres under Cyclic Loading" Polymers 14, no. 9: 1797. https://doi.org/10.3390/polym14091797