# Shear Behavior of T-Shaped Concrete Beams Reinforced with FRP

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure

#### 2.1. Specimen Making and Reinforcement

#### 2.2. Test Setup and Process

#### 2.3. Materials, Properties and Specimens

## 3. Experimental Test Results

#### 3.1. Failure Modes

#### 3.2. Bearing Capacity Analysis

_{cr}is the pure bending section cracking load, ΔP

_{cr}is the pure bending section breaking load increase rate; P

_{cr1}is the bending-shear section breaking load, and ΔP

_{cr1}is the cracking load increasing the speed of the bending-shear section breaking load increasing rate; P

_{u}is the ultimate load, and ΔP

_{u}is the maximum load increasing rate. The meaning of the growth rate is the test value after strengthening, divided by the test value of the corresponding standard specimen.

#### 3.3. Discussion of Test Parameters

#### 3.3.1. Effect of Compressive Strength

#### 3.3.2. Effect of Longitudinal Reinforcement Ratio

#### 3.3.3. Effect of GFRP Surface Characteristics

#### 3.3.4. Effect of FRP Types

#### 3.3.5. Effect of Reinforcement Method

#### 3.3.6. Effect of GFRP Diameter

#### 3.3.7. Effect of GFRP Spacing

#### 3.3.8. Effect of Shear Span Ratio

#### 3.4. The Load-Deflection Relationships

#### 3.5. Carrying Capacity Formula Correction

#### 3.5.1. Calculation Formula of Shear Capacity

_{cv}is the shear capacity of inclined concrete 0.7 for general flexural members and for concentrated loads (including multiple loads, where focused loads are applied to the bearing section or the edge of the joint). An independent beam with a value of more than 75% of the total shear force, taking α

_{cv}as $\frac{1.75}{\lambda +1}$, $\lambda $ is the shear span ratio of the calculated section, which can be λ = a/h

_{0}. When λ is less than 1.5, take 1.5. When λ is greater than 3, take 3, a to take the full load point to the support section or node. The distance of the edge:

#### 3.5.2. Determination of the Utilization Factor of FRP

^{2}= 0.96, and the fitting is good. The utilization factor of the FRP is 0.2.

#### 3.5.3. Comparison of Experimental Values and Theoretical Values

## 4. Conclusions

- (1)
- The failure modes of the reinforced specimens are complex, including flexural failure and shear failure. Independent of failure mode, the stiffness degradation of the reinforced specimens is delayed and the displacement is reduced. The cracking load of the reinforced specimens in the pure flexural section did not increase, but the cracking load in the flexural section increased significantly, and the number and width of oblique cracks decreased significantly. Indeed, some cracks even stop developing when they encounter the FRP. The shear failure of the specimen strengthened by embedded optical circular GFRP bars is more likely than that by embedded thread GFRP bars. The bearing capacity of the reinforced specimen without the U-hoop is higher than that of the reinforced specimen with the U-hoop. However, since only one such specimen is designed, the dispersion of the results is large, and further verification is needed.
- (2)
- The concrete strength grade, longitudinal reinforcement ratio, surface characteristics, and the type and diameter of FRP bars have no effect on the mid-span displacement of the reinforced specimens. Conversely, the reinforcement method, FRP bar spacing, and shear span ratio of the specimens have a significant effect on the mid-span displacement of the reinforced specimens. The ultimate bearing capacity, stirrup strain and FRP bar strain of the strengthened specimens decrease with the increase in concrete strength grade and longitudinal reinforcement ratio. The increase rate of ultimate bearing capacity increases with the increase in concrete strength grade and decreases with the increase in longitudinal reinforcement ratio. The surface characteristics of FRP bars have a significant effect on the ultimate bearing capacity, ultimate bearing capacity increase rate, stirrup strain and FRP bar strain.
- (3)
- The shear failure mechanism of reinforced concrete beams strengthened with FRP embedded on the surface is similar to that of ordinary reinforced concrete beams, and the mechanism of FRP is similar to that of stirrups. Therefore, truss theory can be used for overall analysis. The test data show that using the method similar to that used for stirrups to calculate the shear capacity of FRP is also in line with the actual outcomes. According to the statistical results of the strain of FRP in the test and the results of data fitting, the utilization coefficient of FRP is determined to be 0.2.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Rebar and concrete strain gauge layout. (

**a**) Rebar strain guage layout. (

**b**) Concrete strain gauge layout.

**Figure 2.**Strain gauge arrangement of FRPs. (

**a**) FRP spacing 100 mm; (

**b**) FRP spacing 150 mm; (

**c**) FRP spacing 200 mm.

**Figure 6.**Influence of different parameters on bearing capacity of specimens. (

**a**) concrete strength grade, (

**b**) the longitudinal reinforcement ratio, (

**c**) CFRP surface characteristics, (

**d**) FRP type, (

**e**) the reinforcement method, (

**f**) the GFRP diameter and (

**g**) the GFRP spacing.

**Figure 7.**Load versus displacement curves. (

**a**) Different concrete strength grade thread GFRP reinforcement test pieces; (

**b**) different concrete strength grade light round GFRP reinforcement test pieces; (

**c**) different longitudinal reinforcement ratio GFRP reinforcement test pieces; (

**d**) different longitudinal reinforcement ratio light round CFRP reinforcement test pieces; (

**e**) different surface features GFRP S20C20; (

**f**) different surface features GFRP S18C30; (

**g**) different surface features GFRP S18C20; (

**h**) different types of FRP reinforcement test pieces; (

**i**) different reinforcement methods GFRP reinforcement test pieces; (

**j**) GFRP reinforcement test pieces with different diameter threads; (

**k**) GFRP reinforcement test pieces with different spacing; (

**l**) different shear span ratio GFRP reinforcement test pieces.

Diameter d/mm | Power Level | Yield Strength fyk/MPa | Ultimate Tensile Strength fstk/MPa | Elongation δ/% |
---|---|---|---|---|

8 | HPB235 | 307.5 | 537.5 | 30.5 |

12 | HRB335 | 365 | 550 | 28.5 |

18 | HRB335 | 375 | 625 | 29 |

20 | HRB335 | 355 | 520 | 28.5 |

Concrete Strength Grade | Cube Compressive Strength/MPa | Axial Compressive Strength/MPa | Modulus of Elasticity/GPa |
---|---|---|---|

C20 | 21.4 | 14.3 | 26 |

C30 | 31.5 | 21.1 | 31 |

Adhesive | Splitting Tensile Strength/MPa | Bending Strength/MPa | Compressive Strength/MPa |
---|---|---|---|

JGN-type planting glue | 12.5 | 65.5 | 90.5 |

FRP | Ultimate Tensile Strengthaverage/MPa | Modulus of Elasticity/GPa | Ultimate Tensile Strain/10-6 |
---|---|---|---|

GFRP | 1005 | 52 | 19,327 |

CFRP | 2060 | 145 | 14,200 |

Test Piece Number | Concrete Grade | Reinforcement Ratio | FRP Type | FRP Surface Characteristics | FRP Diameter | FRP Spacing | Shear Span Ratio | Reinforcement Method |
---|---|---|---|---|---|---|---|---|

BZS20C20 | C20 | 0.021 | — | — | — | — | 2.39 | — |

BZS18C30 | C30 | 0.017 | — | — | — | — | 2.39 | — |

BZS18C20 | C20 | 0.017 | — | — | — | — | 2.39 | — |

L-G8D150S20C20U | C20 | 0.021 | GFRP | Thread | 8 | 150 | 2.39 | Add U-hoop |

L-G8D150S18C30U | C30 | 0.017 | GFRP | Thread | 8 | 150 | 2.39 | Add U-hoop |

L-G8D150S18C20U | C20 | 0.017 | GFRP | Thread | 8 | 150 | 2.39 | Add U-hoop |

G-G8D150S20C20U | C20 | 0.021 | GFRP | Light circle | 8 | 150 | 2.39 | Add U-hoop |

G-G8D150S18C30U | C30 | 0.017 | GFRP | Light circle | 8 | 150 | 2.39 | Add U-hoop |

G-G8D150S18C20U | C20 | 0.017 | GFRP | Light circle | 8 | 150 | 2.39 | Add U-hoop |

L-C8D150S18C20U | C20 | 0.017 | CFRP | Thread | 8 | 150 | 2.39 | Add U-hoop |

L-G8D150S18C20 | C20 | 0.017 | GFRP | Thread | 8 | 150 | 2.39 | No U-hoop |

L-G6D150S18C20U | C20 | 0.017 | GFRP | Thread | 6 | 150 | 2.39 | Add U-hoop |

L-G10D150S18C20U | C20 | 0.017 | GFRP | Thread | 10 | 150 | 2.39 | Add U-hoop |

L-G8D100S18C20U | C20 | 0.017 | GFRP | Thread | 8 | 100 | 2.39 | Add U-hoop |

L-G8D200S18C20U | C20 | 0.017 | GFRP | Thread | 8 | 200 | 2.39 | Add U-hoop |

L-G8D150S18C20U | C20 | 0.017 | GFRP | Thread | 8 | 150 | 2.79 | Add U-hoop |

L-G8D150S18C20U | C20 | 0.017 | GFRP | Thread | 8 | 150 | 1.99 | Add U-hoop |

Sample Number | Specimen Number | Failure Mode | Maximum Mid-Span Displacement (mm) | Diagonal Crack Width (mm) |
---|---|---|---|---|

1 | BZS20C20 | Flexural failure | 29.87 | 4.40 |

2 | BZS18C30 | Flexural failure | 29.90 | 1.20 |

3 | BZS18C20 | Flexural failure | 28.37 | 1.48 |

4 | L-G8D150S20C20U | Flexural failure | 20.35 | 0.60 |

5 | L-G8D150S18C30U | Flexural failure | 23.23 | 0.48 |

6 | L-G8D150S18C20U | Flexural failure | 21.90 | 0.50 |

7 | G-G8D150S20C20U | Shear failure | 26.05 | – |

8 | G-G8D150S18C30U | Shear failure | 29.07 | – |

9 | G-G8D150S18C20U | Flexural failure | 23.71 | 0.90 |

10 | L-C8D150S18C20U | Flexural failure | 23.61 | 1.90 |

11 | L-G8D150S18C20 | Shear failure | 36.04 | 1.00 |

12 | L-G6D150S18C20U | Flexural failure | 22.38 | 0.40 |

13 | L-G10D150S18C20U | Flexural failure | 30.34 | 0.30 |

14 | L-G8D100S18C20U | Flexural failure | 29.66 | 9.40 |

15 | L-G8D200S18C20U | Shear failure | 26.64 | 0.35 |

16 | L-G8D150S18C20U (λ = 2.79) | Flexural failure | 26.60 | 0.50 |

17 | L-G8D150S18C20U (λ = 1.99) | Flexural failure | 32.29 | 0.90 |

Test Piece Number | P_{cr}/kN | ΔP_{cr} | P_{cr1}/kN | ΔP_{cr1} | P_{u}/kN | ΔP_{u} | Stiffness/kN·mm^{−1} |
---|---|---|---|---|---|---|---|

BZS20C20 | 17 | — | 17.7 | — | 104.8 | — | 3.51 |

BZS18C30 | 12.4 | — | 13.6 | — | 95.4 | — | 3.19 |

BZS18C20 | 16.7 | — | 16.7 | — | 106.6 | — | 3.76 |

L-G8D150S20C20U | 9.3 | −0.45 | 32.9 | 0.86 | 108.6 | 0.022 | 5.34 |

L-G8D150S18C30U | 12.3 | −0.008 | 38 | 1.79 | 109.8 | 0.151 | 4.73 |

L-G8D150S18C20U | 10.2 | −0.38 | 36 | 1.16 | 112.4 | 0.054 | 5.13 |

G-G8D150S20C20U | 13.2 | −0.22 | 54 | 2.05 | 111.5 | 0.064 | 4.28 |

G-G8D150S18C30U | 13.8 | 0.11 | 50 | 2.67 | 108.8 | 0.141 | 3.74 |

G-G8D150S18C20U | 8.7 | −0.47 | 50 | 1.99 | 114.4 | 0.073 | 4.82 |

L-C8D150S18C20U | 12 | −0.28 | 70 | 3.19 | 114.5 | 0.09 | 4.85 |

L-G8D150S18C20 | 9.3 | −0.44 | 61 | 2.65 | 119.8 | 0.12 | 3.32 |

L-G6D150S18C20U | 15.6 | −0.06 | 36 | 1.16 | 110.6 | 0.037 | 4.94 |

L-G10D150S18C20U | 13.5 | −0.19 | 27.2 | 0.63 | 109.5 | 0.027 | 3.61 |

L-G8D100S18C20U | 7.8 | −0.53 | 26 | 0.56 | 109.8 | 0.03 | 3.7 |

L-G8D200S18C20U | 16.1 | −0.03 | 32 | 0.92 | 107.5 | 0.0084 | 4.04 |

L-G8D150S18C20U (λ = 1.99) | 12.9 | — | 49.5 | — | 144.7 | — | 3.73 |

L-G8D150S18C20U (λ = 2.79) | 13 | — | 40 | — | 99.2 | — | 4.48 |

Test Piece Number | FRP Maximum Strain/με | Maximum Strain to Ultimate Strain Ratio |
---|---|---|

L-G8D150S18C30U | 7188 | 0.37 |

G-G8D150S20C20U | 909 | 0.05 |

G-G8D150S18C30U | 5597 | 0.29 |

L-G8D150S18C20 | 5483 | 0.28 |

L-G8D100S18C20U | 3562 | 0.18 |

Test Piece Number | Main Crack Angle | ${\mathit{V}}_{\mathit{f}\_\mathit{t}\mathit{e}\mathit{s}\mathit{t}}/\mathbf{kN}$ | ${\mathit{V}}_{\mathit{f}\_\mathit{e}\mathit{x}\mathit{p}\mathit{e}\mathit{c}\mathit{t}}/\mathbf{kN}$ |
---|---|---|---|

L-G8D150S18C30U | 47° | 7.2 | 7.15 |

G-G8D150S20C20U | 55° | 3.9 | 5.27 |

G-G8D150S18C30U | 49° | 6.7 | 6.66 |

L-G8D150S18C20 | 50° | 6.6 | 6.43 |

L-G8D100S18C20U | 63° | 4.1 | 5.5 |

Test Piece Number | ${\mathit{V}}_{\mathit{f}\_\mathit{t}\mathit{e}\mathit{s}\mathit{t}}/\mathbf{kN}$ | ${\mathit{V}}_{\mathit{f}\_\mathit{e}\mathit{x}\mathit{p}\mathit{e}\mathit{c}\mathit{t}}/\mathbf{kN}$ | ${\mathit{V}}_{\mathit{f}\_\mathit{t}\mathit{e}\mathit{s}\mathit{t}}/$${\mathit{V}}_{\mathit{f}\_\mathit{e}\mathit{x}\mathit{p}\mathit{e}\mathit{c}\mathit{t}}$ |
---|---|---|---|

L-G8D150S18C30U | 109.8 | 111.9 | 0.98 |

G-G8D150S20C20U | 112.6 | 97.94 | 1.15 |

G-G8D150S18C30U | 108.8 | 110.92 | 0.98 |

L-G8D150S18C20 | 119.8 | 100.26 | 1.19 |

L-G8D100S18C20U | 113.8 | 98.4 | 1.16 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Li, N.; Wang, Q.; Li, Z.; Qin, X.
Shear Behavior of T-Shaped Concrete Beams Reinforced with FRP. *Buildings* **2022**, *12*, 2062.
https://doi.org/10.3390/buildings12122062

**AMA Style**

Zhang Y, Li N, Wang Q, Li Z, Qin X.
Shear Behavior of T-Shaped Concrete Beams Reinforced with FRP. *Buildings*. 2022; 12(12):2062.
https://doi.org/10.3390/buildings12122062

**Chicago/Turabian Style**

Zhang, Yannian, Ning Li, Qingjie Wang, Zhijun Li, and Xiaoyan Qin.
2022. "Shear Behavior of T-Shaped Concrete Beams Reinforced with FRP" *Buildings* 12, no. 12: 2062.
https://doi.org/10.3390/buildings12122062