Performance Prediction of GFRP-Reinforced Concrete Deep Beams Containing a Web Opening in the Shear Span
Abstract
:1. Introduction
2. Model Development
2.1. Geometry of the Beam Models
2.2. Constitutive Laws of Materials
2.3. Types of Element and Boundary Conditions
3. Model Verification
3.1. Load-Deflection Response
3.2. Crack Pattern and Failure Mode
3.3. GFRP Stresses
4. Parametric Study
4.1. Deep Beam Models with Different Opening Sizes
4.1.1. Load-Deflection Response
4.1.2. Crack Pattern and Failure Mechanism
4.1.3. GFRP Stresses
4.2. Deep Beam Models with Different Opening Locations
4.2.1. Load-Deflection Response
4.2.2. Crack Pattern and Failure Mechanism
4.2.3. GFRP Stresses
5. Simplified Analytical Formulas
5.1. Deep Beam Models with Different Opening Locations
5.2. Deep Beams with a Web Opening Shifted from the Midpoint of the Shear Span
6. Conclusions
- For the beam models with yo/h values of 0.33 and 0.50, the strength increased with an increase in the distance measured from the face of the support within the shear span. The strength of the beam models with a yo/h of 0.33 tended to be higher than that of their counterparts with a yo/h of 0.50, and this behavior was more evident with an increase in the distance from the face of the support plate. The beam models with a yo/h of 0.75 exhibited an opposite trend, where the strength decreased with an increase in the distance measured from the face of the support within the shear span because such a movement resulted in an opening closer the load plate.
- For the beam models having a web opening closer to the support plate (xo/Xc = 0.25), strength reductions of 43 and 49% were recorded at yo/h values of 0.33 and 0.50, respectively. When the opening was pushed upward away from the natural load path (xo/Xc = 0.25 and yo/h = 0.75), a lower strength reduction of 34% was recorded.
- For the beam models having a web opening with an xo/Xc of 0.50, strength reductions of 24, 42, and 52% were recorded at yo/h values of 0.33, 0.50, and 0.75, respectively.
- The beam model with xo/Xc = 0.75 and yo/h = 0.33 exhibited a negligible strength reduction of 7% because the web opening was in the tension side and did not interrupt the natural load path. In contrast, the beam model with a web opening closer to the load plate (xo/Xc = 0.75 and yo/h = 0.75) exhibited a significant strength reduction of 56% because the web opening was in the compression zone close to the load plate and fully interrupted the natural load path.
- For the beam models with a web opening in the middle of the shear span, the strength decreased with an increase in either the opening width or height. The rate of the strength reduction caused by increasing the opening height was, however, more significant than that produced by increasing the opening width. At the same wo/a of 0.16, strength reductions of 31–49% were recorded for the deep beam models having an opening in the midpoint of the shear span with ho/h values of 0.17–0.33. More pronounced respective strength reductions of 39–61% were recorded for the deep beam models with the greater wo/a of 0.32.
- The existing empirical equation for concrete deep beams reinforced with conventional steel bars with a web opening provided unconservative and/or inconsistent predictions for the ultimate load of the beam models reinforced with GFRP bars.
- Refined empirical equations were introduced for shear strength prediction of GFRP-reinforced concrete deep beams with a web opening of different sizes and locations within the shear span. The refined analytical formulas tended to provide conservative/reasonable predictions for the shear capacity of the GFRP-reinforced concrete deep beams considered in the present study.
- The simulation models developed and verified in the present study can be used as a numerical platform in future research to study the effect of using different types of reinforcing bars (e.g., carbon, glass, steel with different yield strengths) on the behavior of concrete deep beams with and without a web opening in the shear span. Future research should further investigate the effect of the anchorage length and bond condition of GFRP reinforcing bars on the response of the GFRP-reinforced deep beams.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description | Value * | Unit |
---|---|---|---|
f’c | Compressive strength | 37.00 (45.00) | MPa |
Ec | Elastic modulus | 33,254.00 (35,496.00) | MPa |
μ | Poisson’s ratio | 0.2 | N/A |
ft | Tensile strength | 2.83 (3.33) | MPa |
Gf | Specific fracture energy | 70.75 (83.25) | N/m |
εcp | Plastic concrete strain at compressive strength | 0.0011 (0.0012) | N/A |
wd | Critical compressive displacement | 0.50 | mm |
Models | Ultimate Load (kN) | Deflection Capacity (mm) | ||||
---|---|---|---|---|---|---|
Experimental 1 | Numerical | Error (%) 2 | Experimental 1 | Numerical | Error (%) 2 | |
DB-S | 2904 | 2601 | −10% | 17.3 | 17.8 | +3% |
DB-O1 | 1328 | 1489 | +12% | 12.7 | 10.8 | +15% |
DB-O2 | 1619 | 1619 | 0% | 11.3 | 11.2 | −0.9% |
DB-O3 | 2067 | 1978 | −4% | 16.2 | 11.6 | −28% |
Model Designation | Opening Size (mm) | |
---|---|---|
wo * | ho ** | |
DB-W0.16-H0.17 | 200 | 200 |
DB-W0.16-H0.25 | 304 | |
DB-W0.16-H0.33 | 400 | |
DB-W0.27-H0.17 | 340 | 200 |
DB-W0.27-H0.25 | 304 | |
DB-W0.27-H0.33 | 400 | |
DB-W0.32-H0.17 | 400 | 200 |
DB-W0.32-H0.25 | 304 | |
DB-W0.32-H0.33 | 400 |
Model Designation | Opening Size (mm) | Ultimate Load (kN) | Deflection at Ultimate (mm) | |
---|---|---|---|---|
wo | ho | |||
DB-S | - | - | 2601 | 17.8 |
DB-W0.16-H0.17 | 200 | 200 | 1789 | 10.3 |
DB-W0.16-H0.25 | 304 | 1637 | 10.3 | |
DB-W0.16-H0.33 | 400 | 1327 | 9.5 | |
DB-W0.27-H0.17 | 340 | 200 | 1678 | 10.8 |
DB-W0.27-H0.25 | 304 | 1504 | 11.2 | |
DB-W0.27-H0.33 | 400 | 1239 | 11.9 | |
DB-W0.32-H0.17 | 400 | 200 | 1585 | 11.7 |
DB-W0.32-H0.25 | 304 | 1374 | 11.7 | |
DB-W0.32-H0.33 | 400 | 1019 | 13.0 |
Model Designation | Opening Location (mm) | |
---|---|---|
xo * | yo ** | |
DB-X0.25-Y0.33 | 262.5 | 400 |
DB-X0.25-Y0.50 | 590 | |
DB-X0.25-Y0.75 | 900 | |
DB-X0.50-Y0.33 | 525 | 400 |
DB-X0.50-Y0.50 | 590 | |
DB-X0.50-Y0.75 | 900 | |
DB-X0.75-Y0.33 | 787.5 | 400 |
DB-X0.75-Y0.50 | 590 | |
DB-X0.75-Y0.75 | 900 |
Model Designation | Opening Location (mm) | Ultimate Load (kN) | Deflection at Ultimate (mm) | |
---|---|---|---|---|
xo * | yo ** | |||
DB-S | - | - | 2601 | 17.8 |
DB-X0.25-Y0.33 | 262.5 | 400 | 1478 | 11.6 |
DB-X0.25-Y0.50 | 590 | 1337 | 9.2 | |
DB-X0.25-Y0.75 | 900 | 1714 | 9.6 | |
DB-X0.50-Y0.33 | 525 | 400 | 1971 | 11.5 |
DB-X0.50-Y0.50 | 590 | 1504 | 11.2 | |
DB-X0.50-Y0.75 | 900 | 1259 | 6.9 | |
DB-X0.75-Y0.33 | 787.5 | 400 | 2429 | 18.4 |
DB-X0.75-Y0.50 | 590 | 1881 | 11.4 | |
DB-X0.75-Y0.75 | 900 | 1139 | 9.7 |
Model | Ultimate Load (kN) | ||||
---|---|---|---|---|---|
Numerical | Kong’s Formula [38] Equation (1) | Refined Formula Equation (2) | |||
Prediction | Error (%) 1 | Prediction | Error (%) 1 | ||
DB-W0.16-H0.17 | 1789 | 1942 | +9 | 1378 | −23 |
DB-W0.16-H0.25 | 1637 | 1863 | +14 | 1373 | −16 |
DB-W0.16-H0.33 | 1327 | 1385 | +4 | 966 | −27 |
DB-W0.27-H0.17 | 1678 | 1928 | +15 | 1438 | −14 |
DB-W0.27-H0.25 | 1504 | 1709 | +14 | 1291 | −14 |
DB-W0.27-H0.33 | 1239 | 1242 | +1 | 892 | −28 |
DB-W0.32-H0.17 | 1585 | 1871 | +18 | 1405 | −11 |
DB-W0.32-H0.25 | 1374 | 1653 | +20 | 1258 | −8 |
DB-W0.32-H0.33 | 1019 | 1038 | +2 | 709 | −30 |
Model | Ultimate Load (kN) | ||||
---|---|---|---|---|---|
Numerical | Kong’s Formula [38] Equation (1) | Refined Formula Equation (3) | |||
Prediction | Error (%) 1 | Prediction | Error (%) 1 | ||
DB-X0.25-Y0.33 | 1478 | 1216 | −18 | 1436 | −3 |
DB-X0.25-Y0.50 | 1337 | 2264 | +69 | 1188 | −11 |
DB-X0.25-Y0.75 | 1714 | 3513 | +105 | 1848 | 8 |
DB-X0.50-Y0.33 | 1971 | 916 | −54 | 1825 | −7 |
DB-X0.50-Y0.50 | 1504 | 1709 | +14 | 1683 | 12 |
DB-X0.50-Y0.75 | 1259 | 2863 | +127 | 1349 | 7 |
DB-X0.75-Y0.33 | 2429 | 1042 | −57 | 2055 | −15 |
DB-X0.75-Y0.50 | 1884 | 1461 | −22 | 1877 | 0 |
DB-X0.75-Y0.75 | 1139 | 2399 | +111 | 910 | −20 |
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Sheikh-Sobeh, A.; Kachouh, N.; El-Maaddawy, T. Performance Prediction of GFRP-Reinforced Concrete Deep Beams Containing a Web Opening in the Shear Span. Fibers 2024, 12, 66. https://doi.org/10.3390/fib12080066
Sheikh-Sobeh A, Kachouh N, El-Maaddawy T. Performance Prediction of GFRP-Reinforced Concrete Deep Beams Containing a Web Opening in the Shear Span. Fibers. 2024; 12(8):66. https://doi.org/10.3390/fib12080066
Chicago/Turabian StyleSheikh-Sobeh, Amena, Nancy Kachouh, and Tamer El-Maaddawy. 2024. "Performance Prediction of GFRP-Reinforced Concrete Deep Beams Containing a Web Opening in the Shear Span" Fibers 12, no. 8: 66. https://doi.org/10.3390/fib12080066