# Experimental and Finite Element Study on the Shear Performance of Existing Super-Span Concrete T-Beams Retrofitted with Glass Fiber-Reinforced Plastic

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Research

#### 2.1. Detail of Specimen

#### 2.2. Experimental Setup

#### 2.3. Experimental Process

#### 2.4. Analysis of Experimental Results

#### 2.4.1. Load–Displacement Curve

#### 2.4.2. Distribution of Shear Strain

## 3. Finite Element Analysis (FEA)

#### 3.1. Establishing an FEA Model

_{c}is the elastic modulus of concrete related to the ultimate strength of concrete f

_{c}’, which can be calculated according to Equation (1). ε is the strain of concrete. d

_{c}, called the compressive damage coefficient of concrete, is determined by Equations (2) and (3). In Equation (3), α

_{c}is the descending coefficient, f

_{c,r}and ε

_{c,r}are the compressive strength and corresponding strain of the peak point on the constitutive curve of the concrete, respectively. The ultimate compressive strain of concrete can be obtained from the table in GB50010. For the specific interpretation of the parameters in Equations (1)–(7), refer to GB50010. The classic damage model of Birtel [27] was adopted to define damage in concrete by the degradation of stiffness, which is suitable for RC beams with shear failure. The other parameters and settings are in accordance with the previous literature [27,28].

#### 3.2. Model Verification

#### 3.2.1. Ultimate State of the Specimen

#### 3.2.2. Load–Displacement Curve

#### 3.3. Analysis of Inner Steel Bars

#### 3.4. Influence Analysis of Loading Mode

#### 3.4.1. The Influence on the Ultimate State

#### 3.4.2. The Influence on Shear Bearing Capacity

#### 3.4.3. The Influence of Strain Distribution on the Web

#### 3.4.4. The Influence on the Strain of the Inner Steel Bar

## 4. Conclusions

- (1)
- Under shear loading, the failure process of the super-span T-beam strengthened by GFRP began with small cracks at the bottom of the mid-span web rather than at the bottom of the loading point.
- (2)
- The GFRP strips were effective in restraining the extension and connection of cracks in the initial stage. With an increase in load, multitudinous cracks gradually form an umbrella network. The diagonal cracks perpendicular to the GFRP strips appear earlier than the cracks parallel to or in the same direction as these strips.
- (3)
- For super-span concrete T-beams, the strain distribution in the web is complex. The shear strain of the two sides of the web is nearly symmetrically distributed. The strain of the web is distributed larger from the upper to the button.
- (4)
- Finite element analysis was especially significant for assessing an existing old concrete T-beam since the absence of information about its inner steel bars. The numerical analysis shows that the yielding of diagonally bent longitudinal steel bars, below the loading point, occurs earlier than that in other bars and maintained a larger strain at all times.
- (5)
- Since the regular double-point loading mode is invalid, finite element analysis is also significant for large-span beams subjected to shear load. Compared to the regular loading mode, the specimen tested using a single-point loading pattern has a slightly larger bearing capacity, and larger strain on the diagonal line of the web. In the former pattern, the largest strain on the inner steel bars appears in the bent section of the longitudinal bar and appears at the junction of the bent section in the latter pattern.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Experimental setup. (

**a**) The test device. (

**b**) The position of measuring points. (

**c**) The strain rosettes composed of 0°, 45°, and 90° gauges.

**Figure 5.**Crack propagation of the specimen. (

**a**) Initial cracks on the surface of webs; (

**b**) The cracks in 150 kN; (

**c**) The cracks in 300 kN; (

**d**) The cracks in 450 kN; (

**e**) The cracks in 600 kN; (

**f**) The cracks in 700 kN; (

**g**) The cracks in 1000 kN; (

**h**) The cracks in 1450 kN; (

**i**) The cracks in 1550 kN; (

**j**) The cracks in 1650 kN.

**Figure 6.**Cracks on the web. (

**a**) The cracks perpendicular to the fiber direction; (

**b**) The cracks parallel to the fiber direction.

**Figure 8.**Ultimate state of the specimen. (

**a**) Map-cracking under the loading point; (

**b**) Cutting off bent reinforcement at the flex point; (

**c**) Clipping point of the reinforcement.

**Figure 11.**Strain distribution of the web on two sides. (

**a**) Section 1-A; (

**b**) Section 1-B; (

**c**) section of specimen.

f_{cb}/MPa | f_{cp}/MPa | f_{y}/MPa | f_{u}/MPa | E_{s}/GPa | f_{GFRP}/MPa | E_{GFRP}/GPa | |
---|---|---|---|---|---|---|---|

Nominal value | 23 | 40 | 360 | 580 | 200 | 800 | 80 |

Measured value | 31.2 | 45.9 | 320.7 | 521.2 | 215.2 | _ | _ |

_{cb}—Compressive strength of concrete of T-beam. f

_{cp}—Compressive strength of concrete of pavement. f

_{y}—Yield strength of shear reinforcement. f

_{u}—Ultimate strength of shear reinforcement. f

_{GFRP}—Ultimate strength of GFRP. E

_{s}—Elasticity modulus of the main reinforcement. E

_{GFRP}—Elasticity modulus of GFRP.

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**MDPI and ACS Style**

Hou, D.; Hu, T.; Zhang, G.
Experimental and Finite Element Study on the Shear Performance of Existing Super-Span Concrete T-Beams Retrofitted with Glass Fiber-Reinforced Plastic. *Sustainability* **2023**, *15*, 2768.
https://doi.org/10.3390/su15032768

**AMA Style**

Hou D, Hu T, Zhang G.
Experimental and Finite Element Study on the Shear Performance of Existing Super-Span Concrete T-Beams Retrofitted with Glass Fiber-Reinforced Plastic. *Sustainability*. 2023; 15(3):2768.
https://doi.org/10.3390/su15032768

**Chicago/Turabian Style**

Hou, Dongxu, Tieming Hu, and Guanhua Zhang.
2023. "Experimental and Finite Element Study on the Shear Performance of Existing Super-Span Concrete T-Beams Retrofitted with Glass Fiber-Reinforced Plastic" *Sustainability* 15, no. 3: 2768.
https://doi.org/10.3390/su15032768