# Experimental Study on Shear Performance of Post-Tensioning Prestressed Concrete Beams with Locally Corroded Steel Strands

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Test Profile

## 3. Shear Performance Analysis

#### 3.1. Crack Propagation

#### 3.2. Failure Mode

#### 3.3. Deflection Analysis

#### 3.4. Ultimate Load

## 4. Calculation of Ultimate Shear Bearing Capacity

#### 4.1. Simplified Computational Analysis of Shear Bearing Capacity

_{u}is the shear bearing capacity of component and V

_{cs}represents the shear bearing capacity provided by stirrups and concrete. V

_{p}denotes the shear bearing capacity provided by the prestress, which is 0, since the structure will reach the ultimate bearing capacity when cracking, and it is stipulated in the code that the contribution made by the prestress component to shear resistance should not be considered. A

_{sb}and A

_{pb}represent the cross-sectional areas of bent-up bars and prestressed steel bars, respectively. α

_{s}and α

_{p}are the included angle of the longitudinal axis of the component with bent-up bars and bent-up prestressed steel bars on the oblique section, respectively. λ is the shear span ratio of each test beam; f

_{t}stands for the design axial tensile strength of concrete, which can be calculated as per f

_{t}= 0.26 f

_{cu}

^{2/3}. f

_{cu}is the cubic compressive strength of concrete, f

_{yv}is the design tensile strength of stirrups, A

_{sv}is the cross-sectional area of stirrups, s represents the spacing of stirrups, b and h

_{0}denote the rectangular cross-sectional with and without effective height, respectively.

_{0}, $\theta $ stands for the included angle between principal diagonal crack and beam axis, ${\alpha}_{s}$ is the included angle between stirrups and beam axis, ${\alpha}_{p}$ represents the included angle between steel strands on the principal diagonal rupture plane and beam axis. It could be seen from the test results that stirrups already yielded upon a failure, so the actual yield value is taken during the stirrup calculation, and the standard value (1860 MPa) is selected for steel strands.

#### 4.2. Numerical Simulation Analysis of Shear Performance

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Yang, Y.M.; Peng, J.X.; Liu, X.H.; Cai, C.S.; Zhang, J.R. Probability analysis of web cracking of corroded prestressed concrete box-girder bridges considering aleatory and epistemic uncertainties. Eng. Struct.
**2020**, 228, 111486. [Google Scholar] [CrossRef] - Shen, X.W.; Wang, R.H. Mechanics Effect Analysis of Pre-tensioned and Post-tensioned Pre-stressed Concrete Simply-supported Box Beams on High-speed Railway. China Railw. Sci.
**2004**, 25, 100–104. [Google Scholar] - Yang, Y.M.; Tang, H.; Wang, X.Z. Failure probability analysis of corroded RC structures considering the effect of spatial variability. Mag. Concrete Res.
**2022**. ahead of print. [Google Scholar] [CrossRef] - Yang, Y.M.; Peng, J.X.; Cai, C.S.; Zhang, J.R. Improved interval evidence theory–based fuzzy AHP approach for comprehensive condition assessment of long-span PSC continuous box-girder bridges. J. Bridge Eng.
**2019**, 24, 04019113. [Google Scholar] [CrossRef] - Peng, J.X.; Yang, Y.M.; Bian, H.B.; Zhang, J.R.; Wang, L. Optimisation of maintenance strategy of deteriorating bridges considering sustainability criteria. Struct. Infrastruct. Eng.
**2022**, 18, 395–411. [Google Scholar] [CrossRef] - Ma, Y.F.; Xu, F.Y.; Wang, L.; Zhang, J.R.; Zhang, X.H. Influence of corrosion-induced cracking on structural behavior of reinforced concrete arch ribs. Eng. Struct.
**2016**, 117, 184–194. [Google Scholar] [CrossRef] - Yang, Y.M.; Peng, J.X.; Cai, C.S.; Zhou, Y.D.; Wang, L.; Zhang, J.R. Time-dependent reliability assessment of aging structures considering stochastic resistance degradation process. Reliab. Eng. Syst. Safe
**2022**, 217, 108105. [Google Scholar] [CrossRef] - Juarez, C.A.; Guevara, B.; Fajardo, G.; Castro-Borges, P. Ultimate and nominal shear strength in reinforced concrete beams deteriorated by corrosion. Eng. Struct.
**2011**, 33, 3189–3196. [Google Scholar] [CrossRef] - Zhang, X.H.; Wang, L.; Zhang, J.R. Experimental RC beams research of shear performance of corroded arranged with diagonal reinforcement. Bridge Constr.
**2017**, 47, 77–82. [Google Scholar] - Ye, Z.; Zhang, W.P.; Gu, X.L. Modeling of Shear Behavior of Reinforced Concrete Beams with Corroded Stirrups Strengthened with FRP Sheets. J. Compos. Constr.
**2018**, 22, 04018035. [Google Scholar] [CrossRef] - Zhang, X.H.; Zhang, Y.; Liu, B.; Liu, B.W.; Wu, W.P.; Yang, C.Q. Corrosion-induced spalling of concrete cover and its effects on shear strength of RC beams. Eng. Fail. Anal.
**2021**, 127, 105538. [Google Scholar] [CrossRef] - Huang, L.; Ye, H.L.; Jin, X.Y.; Jin, N.G.; Xu, Z.N. Corrosion-induced shear performance degradation of reinforced concrete beams. Constr. Build. Mater.
**2020**, 248, 118668. [Google Scholar] [CrossRef] - Lu, Z.H.; Li, H.; Li, W.; Zhao, Y.G.; Tang, Z.; Sun, Z. Shear behavior degradation and failure pattern of reinforced concrete beam with chloride-induced stirrup corrosion. Adv. Struct. Eng.
**2019**, 22, 2998–3010. [Google Scholar] [CrossRef] - Soltani, M.; Abu-Abaileh, A.; Scott-Rowe, B. Statistical Approach to Modeling Reduced Shear Capacity of Corrosion-Damaged Reinforced Concrete Beams. Pract. Period. Struct. Des. Constr.
**2021**, 26, 04020073. [Google Scholar] [CrossRef] - Spinella, N.; Colajanni, P.; Recupero, A.; Tondolo, F. Ultimate Shear of RC Beams with Corroded Stirrups and Strengthened with FRP. Buildings
**2019**, 9, 34. [Google Scholar] [CrossRef] - El-Sayed, A.K. Shear capacity assessment of reinforced concrete beams with corroded stirrups. Constr. Build. Mater.
**2017**, 134, 176–184. [Google Scholar] [CrossRef] - Da, B.; Yu, H.F.; Ma, H.Y.; Yu, B.; Wu, Z.Y.; Guo, J.B. Study on shear behavior of reinforced coral aggregate concrete beam. Adv. Struct. Eng.
**2020**, 23, 2388–2398. [Google Scholar] [CrossRef] - Zhang, X.H. Strain Compatibility between Corroded Prestressing Strand and Concrete & Calculation Theory of Beam Capacity; Changsha University of Science & Technology: Changsha, China, 2016; pp. 22–23. [Google Scholar]
- GB 50010-2020; Code for Design of Concrete Structures. China Architecture and Building Press: Beijing, China, 2019.
- Guo, Z.H. Reinforced Concrete Theory, 3rd ed.; Tsinghua University Press: Beijing, China, 2012; pp. 246–259. [Google Scholar]
- Yang, R.H.; Dai, L.Z.; Wang, L.; Zhang, J.R. Calculation of flexural capacity of PC beams considering strength utilization of corroded prestressing tendon. J. Cent. South Univ. (Sci. Technol.)
**2018**, 49, 2593–2602. [Google Scholar] - Fang, Z.H.; Zhou, H.J.; Lai, S.Y. Choose of ABAQUS concrete stress-strain curve. Build. Struct.
**2013**, 43, 559–561. [Google Scholar] - Alfarah, B.; López-Almansa, F.; Oller, S. New methodology for calculating damage variables evolution in plastic damage model for RC structures. Eng. Struct.
**2017**, 132, 70–86. [Google Scholar] [CrossRef] [Green Version]

**Figure 2.**Loading diagram and measuring point layout. (

**a**) Loading and measuring point layout (unit: mm), (

**b**) Loading photo.

**Figure 3.**Crack distribution under the ultimate loading state. (

**a**) B1 beam; (

**b**) B2 beam; (

**c**) B3 beam; (

**d**) B4 beam.

**Figure 7.**Comparison of midspan load–deflection curves between test results and calculation results.

**Figure 8.**Tensile damage and cracking of concrete in test beams. (

**a**) B1 beam; (

**b**) B2 beam; (

**c**) B3 beam; (

**d**) B4 beam.

**Figure 9.**Compressive damage and cracking of concrete in test beams. (

**a**) B1 beam; (

**b**) B2 beam; (

**c**) B3 beam; (

**d**) B4 beam.

Type | Diameter/mm | Elastic Modulus/GPa GPAGGPa | Yield Strength/MPa | Ultimate Strength/MPa |
---|---|---|---|---|

Steel strand | 15.2 | 195 | 1412.4 | 1876.3 |

Ribbed steel bar (HRB400) | 6 | 200 | 412.5 | 561.2 |

Ribbed steel bar (HRB400) | 10 | 200 | 403.9 | 551.6 |

Ribbed steel bar (HRB400) | 25 | 200 | 424.1 | 574.8 |

Beam No. | B1 | B2 | B3 | B4 |
---|---|---|---|---|

Corrosion time (d) | 0 | 3 | 6 | 10 |

Area corrosion rate η (%) | 0 | 7.9 | 19.4 | 31.7 |

No. | η/% | P_{cr1}/kN | P_{cr2}/kN | P_{u}/kN | $\mathit{\theta}$$/\xb0$ | w/mm |
---|---|---|---|---|---|---|

B1 | 0 | 71 | 90 | 298 | 30 | 11.2 |

B2 | 7.9 | 63 | 81 | 281 | 36 | 11.7 |

B3 | 19.4 | 54 | 73 | 271 | 41 | 12.3 |

B4 | 31.7 | 42 | 56 | 252 | 35 | 12.9 |

_{cr1}stands for the load corresponding to the first bending crack, P

_{cr2}represents the load corresponding to the first diagonal crack, P

_{u}is the ultimate load, θ is the dip angle in the horizontal direction of the principal diagonal crack, and w is the midspan deflection under the ultimate load.

Test Beam No. | B1 | B2 | B3 | B4 |
---|---|---|---|---|

Corrosion rate/η % | 0 | 7.9 | 19.4 | 31.7 |

Ultimate load (KN) | 298 | 281 | 271 | 252 |

Relative ultimate shear strength ω | 1 | 0.9430 | 0.9094 | 0.8456 |

No. | η (%) | θ | sin α_{p} | k | r_{c} | ${\mathit{T}}_{\mathit{p}\mathit{c}}^{\prime}/\mathbf{KN}$ | ${\mathit{V}}_{\mathit{p}}^{\prime}/\mathbf{KN}$ | Vc/KN | V_{s}/KN | V_{u}/kN | V_{u1}/kN | V_{u1}/V_{u} | V_{ue}/kN | V_{ue}/V_{u} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

B1 | 0 | 30 | 0.271 | 0.051 | 0.9872 | 255.2 | 74.5 | 149.1 | 75.0 | 298 | 293.5 | 0.985 | 286.5 | 0.961 |

B2 | 7.9 | 36 | 0.221 | 0.056 | 0.9866 | 233.1 | 68.1 | 148.6 | 75.0 | 281 | 275.1 | 0.979 | 281.1 | 1.000 |

B3 | 19.4 | 41 | 0.210 | 0.063 | 0.9860 | 201.6 | 58.9 | 147.9 | 75.0 | 271 | 265.5 | 0.978 | 268.0 | 0.989 |

B4 | 31.7 | 35 | 0.223 | 0.071 | 0.9859 | 168.8 | 49.3 | 147.1 | 75.0 | 252 | 259.7 | 1.031 | 260.3 | 0.995 |

_{u}is the test ultimate load; V

_{u1}is ultimate load obtained through simplified calculation; V

_{ue}is the ultimate load obtained through numerical analysis and calculation.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yang, R.; Yang, Y.; Liu, P.; Wang, X.
Experimental Study on Shear Performance of Post-Tensioning Prestressed Concrete Beams with Locally Corroded Steel Strands. *Coatings* **2022**, *12*, 1356.
https://doi.org/10.3390/coatings12091356

**AMA Style**

Yang R, Yang Y, Liu P, Wang X.
Experimental Study on Shear Performance of Post-Tensioning Prestressed Concrete Beams with Locally Corroded Steel Strands. *Coatings*. 2022; 12(9):1356.
https://doi.org/10.3390/coatings12091356

**Chicago/Turabian Style**

Yang, Rihua, Yiming Yang, Peng Liu, and Xinzhong Wang.
2022. "Experimental Study on Shear Performance of Post-Tensioning Prestressed Concrete Beams with Locally Corroded Steel Strands" *Coatings* 12, no. 9: 1356.
https://doi.org/10.3390/coatings12091356