Study on Prestressed Concrete Beams Strengthened with External Unbonded CFRP Tendons
Abstract
:1. Introduction
2. Experimental Work
3. Numerical Model
3.1. FE Model
3.2. Element Types and Mesh
3.3. Constraints, Boundary and Loading Conditions
3.4. Material Characteristics
3.4.1. Steel
3.4.2. Concrete
3.4.3. CFRP
4. Validation of the Numerical Model
4.1. Primary Results
4.2. Failure Mode
4.3. Load-Deflection Curves
4.4. Load-Strain Curves
5. Parametric Study
5.1. Effect of CFRP Tendon Prestress
5.2. Effect of CFRP Tendon Diameter
5.3. Effect of Deviator Layout and CFRP Tendon Profile
5.4. Effect of End Anchorage Height
5.5. Effect of the Strand Prestress
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Components | Elastic Modulus (GPa) | Compressive Strength (MPa) | Tensile Strength (MPa) | Yield Strength (MPa) | Ultimate Strength (MPa) |
---|---|---|---|---|---|
Concrete | 36.8 | 72 | 3.7 | - | - |
Steel rebar | 196 | - | - | 724 | 752 |
Prestressing strand | 201 | - | - | - | 1860 |
CFRP tendon | 170 | - | - | - | 2300 |
Specimens | CFRP Tendons | Note | ||||
---|---|---|---|---|---|---|
Number | Df (mm) | Af (mm2) | fci (MPa) | Tf0 (kN) | ||
PCB-U-0 | - | - | - | - | - | Reference beam |
PCB-S-1 | 2 | 7 | 77.0 | 345 | 26.6 | Reinforced beams |
PCB-S-2 | 2 | 7 | 77.0 | 1150 | 88.5 | |
PCB-S-3 | 2 | 10 | 157.1 | 690 | 108.4 |
Models | Element Size (mm) | Element Number | Cracking Load (kN) | Ultimate Load (kN) | Analysis Time (s) | ||||
---|---|---|---|---|---|---|---|---|---|
EX | FE | Error (%) | EX | FE | Error (%) | ||||
PCB-C-1(10) | 10 | 194,992 | 50 | 49 | −2 | 130 | 134 | 3.1 | 258,882 |
PCB-C-1(15) | 15 | 99,083 | 49 | −2 | 134 | 3.1 | 105,751 | ||
PCB-C-1(20) | 20 | 70,299 | 50 | 0 | 135 | 3.8 | 34,344 | ||
PCB-C-1(25) | 25 | 58,870 | 50 | 0 | 135 | 3.8 | 20,276 | ||
PCB-C-1(30) | 30 | 51,870 | 51 | 2 | 137 | 5.4 | 16,545 | ||
PCB-C-1(35) | 35 | 47,450 | 52 | 4 | 139 | 6.9 | 13,307 | ||
PCB-C-1(40) | 40 | 43,910 | 54 | 8 | 140 | 7.7 | 11,903 |
Models | Elastic stiffness (kN/mm) | Cracking load (kN) | Ultimate load (kN) | Ultimate deflection (mm) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
EX | FE | Error (%) | EX | FE | Error (%) | EX | FE | Error (%) | EX | FE | Error (%) | |
PCB-U-0 | 5.82 | 5.99 | −2.8 | 40 | 40 | 0 | 100 | 100 | 0 | 54.44 | 60.17 | −9.5 |
PCB-S-1 | 6.25 | 6.28 | −0.5 | 50 | 50 | 0 | 135 | 130 | 3.8 | 63.34 | 67.17 | −5.7 |
PCB-S-2 | 6.21 | 6.4 | −3 | 70 | 70 | 0 | 145 | 140 | 3.6 | 63.2 | 68.98 | −8.4 |
PCB-S-3 | 6.31 | 6.83 | −7.6 | 75 | 80 | −6.3 | 160 | 155 | 3.2 | 66.38 | 68.92 | −3.7 |
Models | CFRP Tendon | Deviator Layout | Anchorage Position | Prestressing Strand | Numerical Results | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Diameter (mm) | Prestress (mm) | Number | Middle CFRP Length | Height (mm) | Angle of CFRP (°) | Prestress (MPa) | Initial Deflection (mm) | Initial Stiffness (kN/mm) | Post-Cracking Stiffness (kN/mm) | Cracking Load (kN) | Ultimate Load (kN) | |
PCB-U-0 | - | - | - | - | - | - | - | 0 | 5.8 | 1.12 | 40 | 100 |
D7-P300 | 7 | 300 | 4 | 1400 | 116 | 5.11 | 580 | −0.58 | 6.24 | 1.61 | 48 | 129 |
D7-P400 | 400 | −0.82 | 6.24 | 1.62 | 50 | 131 | ||||||
D7-P500 | 500 | −1.05 | 6.24 | 1.64 | 52 | 133 | ||||||
D7-P600 | 600 | −1.28 | 6.23 | 1.65 | 54 | 135 | ||||||
D7-P700 | 700 | −1.51 | 6.23 | 1.66 | 56 | 136 | ||||||
D7-P800 | 800 | −1.74 | 6.23 | 1.67 | 58 | 138 | ||||||
D7-P900 | 900 | −1.97 | 6.22 | 1.7 | 60 | 139 | ||||||
D7-P1000 | 1000 | −2.2 | 6.2 | 1.74 | 62 | 141 | ||||||
D5-P500 | 5 | 500 | 4 | 1400 | 116 | 5.11 | 580 | −0.53 | 6.17 | 1.49 | 45 | 124 |
D6-P500 | 6 | −0.76 | 6.22 | 1.56 | 48 | 128 | ||||||
D7-P500 | 7 | −1.05 | 6.24 | 1.64 | 52 | 133 | ||||||
D8-P500 | 8 | −1.34 | 6.27 | 1.7 | 56 | 136 | ||||||
D9-P500 | 9 | −1.68 | 6.31 | 1.81 | 59 | 143 | ||||||
D10-P500 | 10 | −2.02 | 6.35 | 1.93 | 61 | 151 | ||||||
Z4-L1400 | 7 | 500 | 4 | 1400 | 116 | 5.11 | 580 | −1.05 | 6.24 | 1.64 | 52 | 133 |
Z2-L1400 | 2 | 1400 | −0.99 | 6.22 | 1.62 | 52 | 132 | |||||
Z2-L1000 | 2 | 1000 | −0.94 | 6.22 | 1.62 | 51 | 132 | |||||
Z2-L800 | 2 | 800 | −0.92 | 6.21 | 1.59 | 51 | 131 | |||||
Z2-L500 | 2 | 500 | −0.87 | 6.21 | 1.57 | 50 | 130 | |||||
Z2-L400 | 2 | 400 | −0.86 | 6.2 | 1.56 | 50 | 129 | |||||
Z1-L0 | 1 | 0 | −0.8 | 6.17 | 1.53 | 50 | 128 | |||||
H110 | 7 | 500 | 0 | 2800 | 110 | 0 | 580 | −0.06 | 6.01 | 1.29 | 45 | 115 |
H90 | 90 | −0.28 | 6.05 | 1.31 | 47 | 117 | ||||||
H70 | 70 | −0.5 | 6.09 | 1.34 | 49 | 119 | ||||||
H50 | 50 | −0.72 | 6.12 | 1.38 | 51 | 121 | ||||||
H30 | 30 | −0.93 | 6.15 | 1.43 | 52 | 124 | ||||||
SP100 | 7 | 1000 | 4 | 1400 | 116 | 5.11 | 100 | −1.8 | 6.10 | 1.47 | 30 | 116 |
SP300 | 300 | −1.79 | 6.13 | 1.56 | 42 | 127 | ||||||
SP500 | 500 | −1.76 | 6.23 | 1.67 | 56 | 137 | ||||||
SP700 | 700 | −1.78 | 6.24 | 1.72 | 70 | 148 | ||||||
SP900 | 900 | −1.8 | 6.06 | 1.78 | 82 | 157 |
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Chen, L.; Qiang, X.; Jiang, X.; Dong, H.; Chen, W. Study on Prestressed Concrete Beams Strengthened with External Unbonded CFRP Tendons. Materials 2024, 17, 4622. https://doi.org/10.3390/ma17184622
Chen L, Qiang X, Jiang X, Dong H, Chen W. Study on Prestressed Concrete Beams Strengthened with External Unbonded CFRP Tendons. Materials. 2024; 17(18):4622. https://doi.org/10.3390/ma17184622
Chicago/Turabian StyleChen, Longlong, Xuhong Qiang, Xu Jiang, Hao Dong, and Wulong Chen. 2024. "Study on Prestressed Concrete Beams Strengthened with External Unbonded CFRP Tendons" Materials 17, no. 18: 4622. https://doi.org/10.3390/ma17184622