Ductility Estimation for Flexural Concrete Beams Longitudinally Reinforced with Hybrid FRP–Steel Bars
Abstract
:1. Introduction
2. Experimental Study
3. Analytical Study
4. Results and Discussion
4.1. Crack Patterns and Failure Modes of the Tested Beams
4.2. Effect of Longitudinal Hybrid Reinforcement Ratio (Af/As)
4.3. Effect of Reinforcement Position
4.4. Strain Distribution in Cross-Sections with Hybrid Reinforcement
4.5. Neutral Axis Growth in Cross-Sections with Hybrid Reinforcement
4.6. Ductility of Cross-Sections with Hybrid Reinforcement
4.7. Effect of FRP Type
4.8. Neutral Axis Angle (α) and Displacement Index (δN)
5. Conclusions
- (1).
- The reinforcement ratio (Af/As) strongly influenced the capacity and cross-sectional ductility of hybrid reinforced concrete. The higher the hybrid reinforcement ratio, the greater the capacity, but at the cost of ductility, which decreased with increases in the hybrid reinforcement ratio.
- (2).
- The position of the reinforcement slightly affected the capacity and ductility of the beam. Differences in slope in the post-elastic area were seen in beams with lower hybrid reinforcement ratios. However, beams with higher hybrid reinforcement ratios did not show a significant difference in the slope of the load–deflection curve in the post-elastic region.
- (3).
- Cross-sections with Type I reinforcement positions showed higher flexural stiffness values than with Type II positions. A smaller hybrid reinforcement ratio resulted in a higher flexural stiffness value. Moreover, cross-sections with hybrid reinforcement using CFRP exhibited higher flexural stiffness values than those using GFRP.
- (4).
- The type of material used for FRP reinforcement (GFRP or CFRP) significantly affected the profile of the neutral axis curve, capacity, and ductility of hybrid reinforced cross-sections.
- (5).
- There were three regions on the neutral axis curve for cross-sections with hybrid reinforcement, i.e., the region before cracking, the region after cracking, and the region after yielding. The inclination of the neutral axis angle (α) after reinforcement yield depended on the type of FRP and the hybrid reinforcement ratio used.
- (6).
- The ductility of hybrid reinforced beams increased as the neutral axis angle increased. There were significant correlations between the neutral axis angle, neutral axis deformation index value, ductility, and deformation factor. The deformation factor increased with increasing neutral axis angles and deformation index values.
- (7).
- This result suggests that the neutral axis angle (α) and the deformation index value (δN) proposed in this paper can be used to evaluate the ductility of cross-sections with hybrid reinforcement.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Beam Notation | Width | Overall Depth | Clear Span Length | fc’ | ffu | fy | df | ds | Ef |
---|---|---|---|---|---|---|---|---|---|
(mm) | (mm) | (mm) | (MPa) | (MPa) | (MPa) | (mm) | (mm) | (GPa) | |
Data from this study [Experimental] | |||||||||
BFS-2 | 125 | 250 | 2000 | 20 | - | 375 | - | 13 | - |
BFS-4 | 125 | 250 | 2000 | 20 | - | 375 | - | 13 | - |
BFG-1 | 125 | 250 | 2000 | 20 | 788 | - | 13 | - | 43.9 |
BFG-2 | 125 | 250 | 2000 | 20 | 788 | - | 13 | - | 43.9 |
BFC-1 | 125 | 250 | 2000 | 20 | 2070 | - | 13 | - | 124 |
BFC-2 | 125 | 250 | 2000 | 20 | 2070 | - | 13 | - | 124 |
BHG-1 | 125 | 250 | 2000 | 20 | 788 | 375 | 13 | 13 | 43.9 |
BHG-2 | 125 | 250 | 2000 | 20 | 788 | 375 | 13 | 13 | 43.9 |
BHG-3 | 125 | 250 | 2000 | 20 | 788 | 375 | 13 | 13 | 43.9 |
BHG-4 | 125 | 250 | 2000 | 20 | 788 | 375 | 13 | 13 | 43.9 |
BHC-1 | 125 | 250 | 2000 | 20 | 2070 | 375 | 13 | 13 | 124 |
BHC-2 | 125 | 250 | 2000 | 20 | 2070 | 375 | 13 | 13 | 124 |
BHC-3 | 125 | 250 | 2000 | 20 | 2070 | 375 | 13 | 13 | 124 |
BHC-4 | 125 | 250 | 2000 | 20 | 2070 | 375 | 13 | 13 | 124 |
Data from this study [Parametric] | |||||||||
BHG-5 | 125 | 250 | 2000 | 20 | 788 | 375 | 16 | 13 | 43.9 |
BHG-6 | 125 | 250 | 2000 | 20 | 788 | 375 | 16 | 13 | 43.9 |
BHG-7 | 125 | 250 | 2000 | 20 | 788 | 375 | 19 | 13 | 43.9 |
BHG-8 | 125 | 250 | 2000 | 20 | 788 | 375 | 19 | 13 | 43.9 |
BHG-9 | 125 | 250 | 2000 | 20 | 788 | 375 | 16 | 10 | 43.9 |
BHG-10 | 125 | 250 | 2000 | 20 | 788 | 375 | 16 | 10 | 43.9 |
BHC-5 | 125 | 250 | 2000 | 20 | 2070 | 375 | 16 | 13 | 124 |
BHC-6 | 125 | 250 | 2000 | 20 | 2070 | 375 | 16 | 13 | 124 |
BHC-7 | 125 | 250 | 2000 | 20 | 2070 | 375 | 19 | 13 | 124 |
BHC-8 | 125 | 250 | 2000 | 20 | 2070 | 375 | 19 | 13 | 124 |
BHC-9 | 125 | 250 | 2000 | 20 | 2070 | 375 | 16 | 10 | 124 |
BHC-10 | 125 | 250 | 2000 | 20 | 2070 | 375 | 16 | 10 | 124 |
Aiello et al. [1] | |||||||||
A1 | 150 | 200 | 2700 | 45.7 | 1674 | 465 | 7.5 | 8 | 49 |
A2 | 150 | 200 | 2700 | 45.7 | 1366 | 465 | 10 | 8 | 50.1 |
A3 | 150 | 200 | 2700 | 45.7 | 1366 | 465 | 10 | 12 | 50.1 |
C1 | 150 | 200 | 2700 | 45.7 | 1674 | 465 | 7.5 | 8 | 49 |
Qu et al. [3] | |||||||||
B3 | 180 | 250 | 1800 | 33.10 | 782 | 363 | 12.7 | 12 | 45 |
B4 | 180 | 250 | 1800 | 33.10 | 755 | 336 | 15.9 | 16 | 41 |
B5 | 180 | 250 | 1800 | 34.40 | 778 | 336 | 9.5 | 16 | 37.7 |
B6 | 180 | 250 | 1800 | 34.40 | 782 | 336 | 12.7 | 16 | 45 |
B7 | 180 | 250 | 1800 | 40.65 | 778 | 363 | 9.5 | 12 | 37.7 |
B8 | 180 | 250 | 1800 | 40.65 | 755 | 336 | 15.9 | 16 | 41 |
Lau & Pam [4] | |||||||||
G0.3-MD1.0-A90 | 280 | 380 | 4200 | 41.3 | 588 | 336 | 19 | 25 | 39.5 |
G1.0-T0.7-A90 | 280 | 380 | 4200 | 39.8 | 582 | 597 | 25 | 20 | 38.0 |
G0.6-T1.0-A90 | 280 | 380 | 4200 | 44.6 | 588 | 550 | 19 | 25 | 39.5 |
Yinghao & Yong [5] | |||||||||
S2 | 150 | 250 | 1800 | 80.1 | 1301 | 374.5 | 12 | 24 | 75.98 |
S3 | 150 | 250 | 1800 | 80.1 | 1301 | 374.5 | 12 | 24 | 75.98 |
S4 | 150 | 250 | 1800 | 80.1 | 1301 | 374.5 | 12 | 24 | 75.98 |
Refai et al. [8] | |||||||||
2G12-1S10 | 230 | 300 | 3700 | 40 | 1000 | 520 | 12 | 10 | 50 |
2G12-2S10 | 230 | 300 | 3700 | 40 | 1000 | 520 | 12 | 10 | 50 |
2G12-2S12 | 230 | 300 | 3700 | 40 | 1000 | 520 | 12 | 12 | 50 |
2G16-2S10 | 230 | 300 | 3700 | 40 | 1000 | 520 | 16 | 10 | 50 |
2G16-2S12 | 230 | 300 | 3700 | 40 | 1000 | 520 | 16 | 12 | 50 |
2G16-2S16 | 230 | 300 | 3700 | 40 | 1000 | 520 | 16 | 16 | 50 |
Beam Notation | Af/As | First Crack Load | Stiffness | Type of Reinforcement | Reinforcement Ratio | Failure Mode |
---|---|---|---|---|---|---|
(kN) | (kN/mm) | |||||
BFS-2 | - | 3.6 | 3.91 | Steel | Under Reinforced | SY, CC |
BFS-4 | - | 5.3 | 3.71 | Steel | Under Reinforced | SY, CC |
BFG-1 | - | 4.6 | 1.33 | GFRP | Over Reinforced | CC |
BFG-2 | - | 6.2 | 1.27 | GFRP | Over Reinforced | CC |
BFC-1 | - | 3.7 | 2.24 | CFRP | Over Reinforced | CC |
BFC-2 | - | 3.9 | 2.21 | CFRP | Over Reinforced | CC |
BHG-1 | 0.5 | 5.5 | 3.16 | Steel and GFRP | Over Reinforced | SY, CC |
BHG-2 | 2.0 | 3.5 | 2.23 | Steel and GFRP | Over Reinforced | SY, CC |
BHG-3 | 0.5 | 5.1 | 2.79 | Steel and GFRP | Over Reinforced | SY, CC |
BHG-4 | 2.0 | 3.6 | 1.89 | Steel and GFRP | Over Reinforced | SY, CC |
BHC-1 | 0.5 | 5.3 | 3.71 | Steel and CFRP | Over Reinforced | SY, CC |
BHC-2 | 2.0 | 3.7 | 2.45 | Steel and CFRP | Over Reinforced | SY, CC |
BHC-3 | 0.5 | 3.2 | 3.17 | Steel and CFRP | Over Reinforced | SY, CC |
BHC-4 | 2.0 | 6.3 | 2.39 | Steel and CFRP | Over Reinforced | SY, CC |
Beam Notation | Af/As | δ | α | δN | My | μy | Mu | μu | DF | Type of FRP | Type of Cross-Section |
---|---|---|---|---|---|---|---|---|---|---|---|
(kNm) | (kNm) | ||||||||||
Data from this study [Experimental] | |||||||||||
BFS-2 | − | 4.9 | 77.7 | 1.7 | 28.2 | 1.4 | 29.1 | 7.2 | 5.4 | - | Type I |
BFS-4 | − | 6.3 | 58.8 | 1.6 | 25.1 | 1.4 | 27.4 | 6.0 | 4.8 | - | Type II |
BHG-1 | 0.5 | 6.6 | 19.6 | 1.4 | 21.2 | 1.3 | 29.9 | 5.8 | 6.4 | GFRP | Type I |
BHG-2 | 2.0 | 6.3 | 3.6 | 1.1 | 14.2 | 1.2 | 30.4 | 5.7 | 9.9 | GFRP | Type I |
BHG-3 | 0.5 | 6.1 | 25.7 | 1.4 | 20.6 | 1.3 | 27.2 | 6.1 | 6.0 | GFRP | Type II |
BHG-4 | 2.0 | 5.6 | 2.8 | 1.1 | 13.6 | 1.5 | 28.9 | 5.7 | 8.2 | GFRP | Type II |
BHC-1 | 0.5 | 5.4 | 8.5 | 1.2 | 24.4 | 1.4 | 38.1 | 4.3 | 4.9 | CFRP | Type I |
BHC-2 | 2.0 | 3.7 | −2.4 | 0.9 | 21.2 | 1.3 | 41.4 | 3.9 | 5.7 | CFRP | Type I |
BHC-3 | 0.5 | 4.5 | 12.2 | 1.3 | 22.7 | 1.4 | 33.4 | 4.6 | 4.9 | CFRP | Type II |
BHC-4 | 2.0 | 4.0 | −3.6 | 0.9 | 23.1 | 1.7 | 39.9 | 3.9 | 3.9 | CFRP | Type II |
Data from this study [Parametric] | |||||||||||
BHG-5 | 3.0 | 3.9 | 1.5 | 1.0 | 15.9 | 1.2 | 34.6 | 4.9 | 8.7 | GFRP | Type I |
BHG-6 | 3.0 | 3.2 | 0.5 | 1.0 | 15.7 | 1.5 | 33.1 | 4.9 | 6.9 | GFRP | Type II |
BHG-7 | 4.3 | 3.3 | −0.8 | 1.0 | 18.4 | 1.3 | 38.3 | 4.3 | 7.0 | GFRP | Type I |
BHG-8 | 4.3 | 2.5 | −1.2 | 1.0 | 19.2 | 1.6 | 36.8 | 4.3 | 5.2 | GFRP | Type II |
BHG-9 | 1.3 | 5.1 | 7.0 | 1.2 | 14.7 | 1.2 | 28.7 | 6.1 | 9.6 | GFRP | Type I |
BHG-10 | 1.3 | 5.2 | 9.4 | 1.2 | 13.9 | 1.3 | 24.6 | 6.5 | 9.0 | GFRP | Type II |
BHC-5 | 3.0 | 2.3 | −4.8 | 0.9 | 26.8 | 1.4 | 45.9 | 3.3 | 4.0 | CFRP | Type I |
BHC-6 | 3.0 | 1.8 | −6.6 | 0.9 | 15.7 | 1.5 | 33.1 | 4.9 | 6.9 | CFRP | Type II |
BHC-7 | 4.3 | 2.0 | −7.1 | 0.8 | 33.6 | 1.6 | 49.6 | 2.9 | 2.7 | CFRP | Type I |
BHC-8 | 4.3 | 1.3 | −7.8 | 0.8 | 38.8 | 2.1 | 48.1 | 2.9 | 1.7 | CFRP | Type II |
BHC-9 | 1.3 | 3.0 | 0.7 | 1.0 | 19.7 | 1.3 | 38.9 | 4.2 | 6.5 | CFRP | Type I |
BHC-10 | 1.3 | 3.4 | 2.6 | 1.1 | 17.3 | 1.3 | 32.6 | 4.6 | 6.7 | CFRP | Type II |
Aiello et al. [1] | |||||||||||
A1 | 0.9 | 7.7 | 3.6 | 1.1 | 8.8 | 1.9 | 20.2 | 11.9 | 14.4 | AFRP | Type II |
A2 | 1.6 | 6.4 | 3.1 | 1.1 | 10.4 | 1.9 | 25.8 | 10.0 | 12.7 | AFRP | Type II |
A3 | 1.0 | 4.8 | 8.7 | 1.1 | 20.0 | 2.2 | 34.1 | 7.6 | 5.8 | AFRP | Type II |
C1 | 0.9 | 7.7 | 11.2 | 1.1 | 9.7 | 1.8 | 21.2 | 11.9 | 14.5 | AFRP | Type I |
Qu et al. [3] | |||||||||||
B3 | 1.1 | 4.0 | 6.9 | 1.2 | 20.7 | 1.2 | 46.0 | 7.5 | 14.0 | GFRP | Type I |
B4 | 2.0 | 2.9 | 4.9 | 1.1 | 19.5 | 1.1 | 49.9 | 6.7 | 16.0 | GFRP | Type I |
B5 | 0.4 | 4.8 | 21.5 | 1.4 | 28.4 | 1.1 | 43.4 | 8.4 | 11.4 | GFRP | Type I |
B6 | 0.6 | 4.5 | 14.7 | 1.3 | 30.4 | 1.2 | 51.9 | 6.6 | 9.5 | GFRP | Type I |
B7 | 1.3 | 8.5 | 7.3 | 1.2 | 10.7 | 1.1 | 30.8 | 10.5 | 27.0 | GFRP | Type I |
B8 | 0.3 | 3.1 | 38.3 | 1.4 | 77.6 | 1.6 | 87.3 | 3.7 | 2.7 | GFRP | Type II |
Lau & Pam [4] | |||||||||||
G0.3-MD1.0-A90 | 0.3 | 1.9 | 21.9 | 1.4 | 114.9 | 0.8 | 166.3 | 5.0 | 9.4 | GFRP | Type I |
G1.0-T0.7-A90 | 1.6 | 3.9 | 6.3 | 1.1 | 160.7 | 1.2 | 237.3 | 3.6 | 4.4 | GFRP | Type I |
G0.6-T1.0-A90 | 0.6 | 4.2 | 17.1 | 1.3 | 195.4 | 1.1 | 250.1 | 3.8 | 4.3 | GFRP | Type I |
Yinghao & Yong [5] | |||||||||||
S2 | 0.3 | 2.6 | 19.9 | 1.4 | 66.7 | 1.6 | 93.1 | 5.5 | 4.7 | GFRP | Type II |
S3 | 0.3 | 3.8 | 29.9 | 1.6 | 72.8 | 1.4 | 95.2 | 5.8 | 5.5 | GFRP | Type II |
S4 | 0.3 | 1.7 | 24.6 | 1.6 | 75.0 | 1.3 | 103.2 | 5.5 | 5.7 | GFRP | Type I |
Refai et al. [8] | |||||||||||
2G12-1S10 | 2.9 | 5.3 | 0.7 | 1.1 | 15.2 | 1.4 | 47.3 | 8.2 | 18.5 | GFRP | Type I |
2G12-2S10 | 1.4 | 3.0 | 3.2 | 1.1 | 25.9 | 1.3 | 58.4 | 7.1 | 12.3 | GFRP | Type I |
2G12-2S12 | 1.0 | 4.4 | 5.5 | 1.1 | 31.1 | 1.5 | 55.7 | 6.8 | 8.2 | GFRP | Type I |
2G16-2S10 | 2.6 | 3.8 | 1.3 | 1.0 | 31.0 | 1.4 | 71.4 | 5.8 | 9.8 | GFRP | Type I |
2G16-2S12 | 1.8 | 2.4 | 2.6 | 1.1 | 37.4 | 1.4 | 70.9 | 5.5 | 7.3 | GFRP | Type I |
2G16-2S16 | 1.0 | 4.0 | 7.1 | 1.1 | 56.5 | 1.6 | 81.4 | 4.7 | 4.4 | GFRP | Type I |
Parameter | Recommended Value |
---|---|
α | >0° |
δN | >1 |
δ | >4 |
DF | >6 |
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Thamrin, R.; Zaidir, Z.; Iwanda, D. Ductility Estimation for Flexural Concrete Beams Longitudinally Reinforced with Hybrid FRP–Steel Bars. Polymers 2022, 14, 1017. https://doi.org/10.3390/polym14051017
Thamrin R, Zaidir Z, Iwanda D. Ductility Estimation for Flexural Concrete Beams Longitudinally Reinforced with Hybrid FRP–Steel Bars. Polymers. 2022; 14(5):1017. https://doi.org/10.3390/polym14051017
Chicago/Turabian StyleThamrin, Rendy, Zaidir Zaidir, and Devitasari Iwanda. 2022. "Ductility Estimation for Flexural Concrete Beams Longitudinally Reinforced with Hybrid FRP–Steel Bars" Polymers 14, no. 5: 1017. https://doi.org/10.3390/polym14051017
APA StyleThamrin, R., Zaidir, Z., & Iwanda, D. (2022). Ductility Estimation for Flexural Concrete Beams Longitudinally Reinforced with Hybrid FRP–Steel Bars. Polymers, 14(5), 1017. https://doi.org/10.3390/polym14051017