# Influence of Patching on the Shear Failure of Reinforced Concrete Beam without Stirrup

^{*}

## Abstract

**:**

## 1. Introduction

_{c}) of a reinforced concrete beam consists of the shear provided by the uncracked portion of concrete (V

_{cz}), the vertical component of the aggregate interlock force at the surface of the diagonal crack (V

_{iy}), and the dowel action of the longitudinal reinforcement (V

_{d}) [34,35,36,37]. The presence of the repair material can alter the development of the diagonal crack, redistribute a portion of the shear strength components, and eventually affect the ultimate shear strength of the reinforced concrete beam.

## 2. Materials and Methods

#### 2.1. Materials

^{3}of concrete was as follows: 388 kg of cement, 771 kg of sand, 941 kg of coarse aggregate, and 225 kg of water. The actual strength of the concrete was determined by the testing of cylinder specimens of 150 × 300 mm. The compressive strength obtained at 28 days was 23.80 MPa and 25.29 MPa for batch 1 and 2, respectively. Meanwhile, the repair material used for patching the reinforced concrete beam was a UPR mortar. It was made from the following constituents per m

^{3}: 950 kg of sand, 808 kg of cement, 143 kg of fly ash, 475 kg of UPR, and 24 kg of hardener. The compressive strength of the UPR mortar was determined following the ASTM C 579-01 [45]. The average compressive strength obtained at 1 day was 73.67 MPa.

#### 2.2. Beam Specimens

#### 2.3. Testing Beam Specimens

#### 2.4. Numerical Modelling

## 3. Results and Discussion

#### 3.1. Load-Deflection Behaviour

#### 3.2. Shear Cracking Failure

#### 3.3. Stress Distribution in Concrete Beam

_{xx}) due to flexural moment can be identified above and below the neutral axis, respectively. Similarly, negative and positive shear stresses (τ

_{xx}) due to the shear force can be observed at the left and right shear span, respectively. At this early stage of loading, no crack is found. Therefore, the normal stresses are distributed proportionately in the compression and tension zones. In the same way, a fairly equal distribution of shear stresses can be seen in the left and right shear span.

_{xx}) and shear (τ

_{xz}) stress at the inclined compression zone, leading to the development of diagonal cracks that cause beams failure.

#### 3.4. Reinforcement Strain

_{xx}) is presented in Figure 10. At the early stages of loading, the tensile strain along the longitudinal reinforcement follows the bending moment, where the maximum value occurs at the mid-span (strain#6). After flexural cracks occur at a load of 30 kN, the tensile strain of the longitudinal reinforcement at the mid-span (strain #6) start to deviate from the original straight line. Further increase of load up to about 50 kN will cause the strains at around the mid-span (strain #3–6) start to increase sharply. At a loading stage corresponding to the first diagonal cracks (i.e., 100 kN for BN and 130 kN for BR), an increase of tensile reinforcement strain can be observed in a wider zone (strain #1–6). This wider zone of tensile reinforcement strain is related to widespread cracking zone at this load level (see Figure 8 and Figure 9). It can be noted that the presence of UPR mortar tends to conserve the development of strains in the tensile reinforcement to the left of UPR mortar. Even the reinforcement strain #1 of BR is hardly increased. On the other hand, reinforcement strains to the right of UPR mortar (strain #4–6) exhibit higher values; it is interesting to note that strains #4–6 develop similar magnitude. This behaviour indicates that more stresses are distributed to the right of the UPR mortar. At the final stage of loading, high tensile strain extends almost along the whole of the longitudinal reinforcement, with the exception of strain #1 in BR. Examining Figure 8, Figure 9 and Figure 10 and especially the evolution of stress and strain distribution from the first diagonal cracks formation to the final stage of loading, one can see that there is a transition of the shear resistance mechanism from beam action into arch action.

#### 3.5. Shear Strength

## 4. Conclusions

- It causes the first diagonal crack appearing at a higher load compared to that of normal beam.
- The high tensile strength of UPR is beneficial to hamper the propagation of the diagonal cracks.
- It alters the stress distribution in such a way to cause the stresses in the span between support and UPR mortar decrease. On the other hand, the stresses in the span between UPR mortar and loading point increase.
- UPR mortar can increase the shear strength of the reinforced concrete beam about 15–20% at a variety of reinforcement ratios.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 11.**Influence of UPR mortar on shear strength of RC beam at various reinforcement ratios (numerical simulation).

Beam ID | Type of Beam | Tensile Reinforcement | Compressive Reinforcement | Stirrup at Half Shear Span | Concrete Compressive Strength ^{1} | UPR Mortar Compressive Strength ^{1} |
---|---|---|---|---|---|---|

BN-19 | Normal | 2D19 | 2D8 | D6-150 | 23.80 MPa | - |

BR-19 | Repair | 2D19 | 2D8 | D6-150 | 23.80 MPa | 73.67 MPa |

BN-22 | Normal | 2D22 | 2D8 | D6-150 | 25.29 MPa | - |

BR-22 | Repair | 2D22 | 2D8 | D6-150 | 25.29 MPa | 73.67 MPa |

^{1}Average value.

Material | Average Compressive Strength (Cylinder) (MPa) | Characteristic Compressive Strength (Cylinder) (MPa) | Characteristic Compressive Strength (Cube) (MPa) | Tensile Strength (MPa) | Yield Stress (MPa) | Elastic Modulus (MPa) | Material Model |
---|---|---|---|---|---|---|---|

Concrete (BN-19 & BR-19) | 23.80 | 15.80 | 18.59 | 1.66 | 24,350 | 3D nonlinear cementitious material 2 | |

Concrete (BN-22 & BR-22) | 25.29 | 17.29 | 20.34 | 1.78 | 25,640 | 3D nonlinear cementitious material 2 | |

UPR-mortar | 73.6 | 21.5 | 12,500 | 3D nonlinear cementitious material 2 | |||

Reinforcement D22 | 452 | 200,000 | Reinforcement-bilinear | ||||

Reinforcement D19 | 475 | 200,000 | Reinforcement-bilinear | ||||

Reinforcement D8 | 462 | 200,000 | Reinforcement-bilinear | ||||

Reinforcement D6 | 395 | 200,000 | Reinforcement-bilinear | ||||

Steel plate | 200,000 | 3D elastic isotropic | |||||

Horizontal support | 10,000 | Linear spring | |||||

Vertical support | Relative displacement −1, Stress 500,000 MPa Relative displacement +1, Stress 330–350 MPa | Nonlinear spring |

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**MDPI and ACS Style**

Kristiawan, S.A.; Saifullah, H.A.; Supriyadi, A.
Influence of Patching on the Shear Failure of Reinforced Concrete Beam without Stirrup. *Infrastructures* **2021**, *6*, 97.
https://doi.org/10.3390/infrastructures6070097

**AMA Style**

Kristiawan SA, Saifullah HA, Supriyadi A.
Influence of Patching on the Shear Failure of Reinforced Concrete Beam without Stirrup. *Infrastructures*. 2021; 6(7):97.
https://doi.org/10.3390/infrastructures6070097

**Chicago/Turabian Style**

Kristiawan, Stefanus Adi, Halwan Alfisa Saifullah, and Agus Supriyadi.
2021. "Influence of Patching on the Shear Failure of Reinforced Concrete Beam without Stirrup" *Infrastructures* 6, no. 7: 97.
https://doi.org/10.3390/infrastructures6070097