Shear Bearing Capacity Prediction of Steel-Fiber-Reinforced High-Strength Concrete Corbels on Modified Compression Field Theory
Abstract
:1. Introduction
2. Establishment of the Proposed Model
- The shear stress and normal stress experienced by concrete micro-elements are uniformly distributed when subjected to loads.
- The stress and strain of concrete refer to the average stress and strain in the cracking zone.
- The principal stress and principal strain directions of concrete are consistent.
- There is no bond slip between steel bars and concrete, assuming ideal bond conditions.
- Shear stress in steel bars is not considered: only the axial stress in the steel bars is taken into account.
2.1. Equilibrium Conditions
2.2. Constitutive Relations
2.2.1. Stress–Strain Relationship of Concrete in Tension
2.2.2. Stress–Strain Relationship of Concrete in Compression
2.2.3. Stress–Strain Relationship of Reinforcement
2.3. Compatibility Conditions
2.4. Stress Equilibrium of Steel Fibers at the Crack
2.5. Calculation Process
- Input corbels’ geometry and material parameters.
- Assume ε1, and the increment of ε1 is 0.0001.
- Assume θ.
- Calculate vci and w using Equations (25) and (26).
- Assume fsx0.
- Calculate f1 using Equation (11), and satisfy Equation (28).
- Calculate v using Equation (30).
- Calculate f2 using Equation (3), and f2 is limited by f2,max.
- Use Equation (14) to determine whether it is equal to the assumed fsx0. If it is, continue to the next step; otherwise, return to (6) to assume the stirrup stress again.
- Calculate axial load N using Equation (8), and whether the axial force is equal to 0. If it is true, the analysis of the corresponding principal tension strain state is completed. If not, return to (4) to assume the crack inclination again until it is equal.
- Calculate fsxcr using Equation (29), if fsxcr is less than fsxy, the calculation ends. Otherwise, return to (2) to re-assume the main tensile strain of concrete.
3. Model Verification
3.1. Experimental Work
3.2. Comparison with Test Results
3.2.1. Fattuhi Model [32]
3.2.2. Campione Model [33]
3.2.3. Russo Model [34]
3.2.4. Model Validity
4. Conclusions
- Based on the modified compression field theory, the contribution of steel fibers to the tensile strength of concrete at crack locations is considered. The constitutive relationship of cracked steel-fiber-reinforced concrete and the local stress equilibrium equation are modified. A calculation model for the shear bearing capacity of steel-fiber-reinforced high-strength concrete corbels is proposed.
- Compared with other scholars’ models, the predicted value of shear capacity calculated by the proposed model is closer to the experimental value. It can be effectively utilized for predicting and analyzing the shear bearing capacity of steel-fiber-reinforced high-strength concrete corbels, and has a clear mechanical model.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Specimens | Main Reinforcement | Ratio of Reinforcement | Stirrup | Stirrup Reinforcement Ratio | Shear Span Ratio | Effective Depth | Steel Fiber Dosage |
---|---|---|---|---|---|---|---|
MC01 | 4C12 | 0.55% | A10@100 | 0.785% | 0.2 | 400 | 1.5% |
MC02 | 4C12 | 0.55% | A10@100 | 0.785% | 0.3 | 400 | 1.5% |
MC03 | 4C12 | 0.55% | A10@100 | 0.785% | 0.4 | 400 | 1.5% |
MC04 | 4C12 | 0.55% | A10@100 | 0.785% | 0.3 | 400 | 1.5% |
MC05 | 4C12 | 0.55% | A10@100 | 0.785% | 0.3 | 400 | 1.5% |
MC06 | 4C12 | 0.75% | A10@150 | 0.390% | 0.3 | 400 | 1.5% |
MC07 | 4C12 | 0.98% | A10@200 | 0.520% | 0.3 | 400 | 1.5% |
MC08 | 4C12 | 0.55% | A10@100 | 0.785% | 0.3 | 400 | 0 |
MC09 | 4C12 | 0.55% | A10@100 | 0.785% | 0.3 | 400 | 0.75% |
Reinforcement Type | Diameter (mm) | Cross-Sectional Area (mm2) | Yield Strength (MPa) | Elastic Modulus (GPa) | Ultimate Strength (MPa) |
---|---|---|---|---|---|
HPB300 | 10 | 78.5 | 333.7 | 195.95 | 535.8 |
HRB400 | 12 | 113.1 | 425.2 | 172.6 | 541.4 |
HRB400 | 14 | 153.9 | 467.8 | 185.0 | 582.3 |
HRB400 | 16 | 201.1 | 427.3 | 192.5 | 587.7 |
Specimens | /kN | /kN | Vu/kN | Failure Patterns |
---|---|---|---|---|
MC01 | 270 | 400 | 879 | Diagonal shear patterns |
MC02 | 220 | 290 | 822 | Diagonal compression pattern |
MC03 | 166.5 | 255 | 695 | Diagonal compression pattern |
MC04 | 220 | 355 | 874 | Diagonal compression pattern |
MC05 | 193 | 386.5 | 981.5 | Diagonal compression pattern |
MC06 | 192 | 234.5 | 670.5 | Diagonal compression pattern |
MC07 | 164 | 240 | 751 | Diagonal compression pattern |
MC08 | 150 | 331 | 775 | Diagonal compression pattern |
MC09 | 180 | 381 | 767 | Diagonal compression pattern |
References | Specimens | b/mm | h0/mm | ρf | Vtest | Vtest/VF | Vtest/VC | Vtest/VR | Vtest/Vn |
---|---|---|---|---|---|---|---|---|---|
This study | MC01 | 200 | 400 | 1.50% | 879 | 0.859 | 1.768 | 1.120 | 1.113 |
MC02 | 200 | 400 | 1.50% | 822 | 1.116 | 1.420 | 1.208 | 1.041 | |
MC03 | 200 | 400 | 1.50% | 695 | 1.192 | 1.156 | 1.139 | 1.159 | |
MC04 | 200 | 400 | 1.50% | 874 | 0.978 | 1.534 | 1.201 | 1.107 | |
MC05 | 200 | 400 | 1.50% | 981.5 | 0.929 | 1.750 | 1.270 | 1.114 | |
MC06 | 200 | 400 | 1.50% | 670.5 | 0.911 | 1.159 | 1.227 | 1.102 | |
MC07 | 200 | 400 | 1.50% | 751 | 1.020 | 1.298 | 1.272 | 1.116 | |
MC08 | 200 | 400 | 0% | 775 | 1.018 | 1.342 | 1.148 | 1.144 | |
MC09 | 200 | 400 | 0.75% | 767 | 1.071 | 1.321 | 1.130 | 1.173 | |
Faleh et al. [35] | CF3-0.5 | 200 | 250 | 0.50% | 1125 | 1.25 | 1.480 | 1.397 | 1.162 |
CF3-1.0 | 200 | 250 | 1.00% | 1220 | 0.960 | 1.435 | 1.356 | 1.104 | |
CF3-1.5 | 200 | 250 | 1.5% | 1230 | 0.911 | 1.281 | 1.337 | 1.027 | |
Fattuhi et al. [36] | 1 | 150 | 125 | 1.70% | 153 | 0.917 | 1.436 | 1.453 | 1.132 |
2 | 150 | 125 | 1.70% | 160 | 0.990 | 1.449 | 1.470 | 1.104 | |
3 | 150 | 129 | 1.70% | 91.2 | 0.947 | 1.580 | 1.130 | 1.079 | |
4 | 150 | 127 | 1.70% | 93 | 0.952 | 1.647 | 1.208 | 1.029 | |
5 | 150 | 124 | 1.70% | 103 | 1.008 | 1.121 | 1.325 | 1.213 | |
6 | 150 | 125 | 1.70% | 95.7 | 0.940 | 1.075 | 1.276 | 1.003 | |
9 | 150 | 125 | 1.70% | 152.9 | 0.954 | 1.558 | 1.680 | 1.097 | |
10 | 150 | 124 | 1.70% | 102.9 | 1.024 | 1.166 | 1.418 | 1.068 | |
12 | 150 | 127 | 0.70% | 92 | 0.777 | 1.974 | 1.258 | 1.145 | |
13 | 150 | 125 | 1.70% | 111.7 | 0.920 | 1.674 | 1.424 | 1.143 | |
16 | 150 | 125 | 1.70% | 114.3 | 0.948 | 1.622 | 1.344 | 1.103 | |
18 | 150 | 125 | 1.00% | 119 | 0.820 | 1.921 | 1.422 | 1.052 | |
Yang et al. [37] | CW1 | 200 | 400 | 0% | 1271 | 0.964 | 1.615 | 1.252 | 1.115 |
CW2 | 200 | 400 | 0.50% | 1367 | 1.005 | 1.499 | 1.390 | 1.073 | |
CW3 | 200 | 400 | 0.75% | 1440 | 1.043 | 1.145 | 1.327 | 1.110 | |
Fattuhi et al. [38] | 20 | 153 | 124 | 1.75% | 126 | 0.851 | 1.342 | 1.313 | 1.056 |
21 | 156 | 122 | 1.50% | 118 | 0.821 | 1.455 | 1.460 | 1.041 | |
23 | 153 | 123 | 2.00% | 126.5 | 0.869 | 1.267 | 1.324 | 1.038 | |
27 | 153.5 | 124 | 2.50% | 171.5 | 0.850 | 1.681 | 1.358 | 1.204 | |
32 | 154 | 120 | 2.00% | 132.5 | 0.835 | 1.131 | 1.221 | 1.044 | |
39 | 153.5 | 124 | 2.25% | 144.5 | 0.843 | 1.231 | 1.420 | 1.219 | |
49 | 154.4 | 122 | 2.50% | 164.5 | 0.830 | 1.721 | 1.466 | 1.073 | |
Mean | 1.453 | 0.942 | 1.311 | 1.103 | |||||
Variance | 0.061 | 0.009 | 0.017 | 0.003 |
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Li, H.-M.; Zheng, J.-Y.; Li, S.-S. Shear Bearing Capacity Prediction of Steel-Fiber-Reinforced High-Strength Concrete Corbels on Modified Compression Field Theory. Buildings 2024, 14, 388. https://doi.org/10.3390/buildings14020388
Li H-M, Zheng J-Y, Li S-S. Shear Bearing Capacity Prediction of Steel-Fiber-Reinforced High-Strength Concrete Corbels on Modified Compression Field Theory. Buildings. 2024; 14(2):388. https://doi.org/10.3390/buildings14020388
Chicago/Turabian StyleLi, Hong-Mei, Jin-Yan Zheng, and Shu-Shan Li. 2024. "Shear Bearing Capacity Prediction of Steel-Fiber-Reinforced High-Strength Concrete Corbels on Modified Compression Field Theory" Buildings 14, no. 2: 388. https://doi.org/10.3390/buildings14020388