# Study on Failure Performance of the Thin-Walled Steel-Reinforced Concrete Pier under Low Cyclic Loading

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure

#### 2.1. Design of Specimens

#### 2.2. The Mechanical Performance of the Used Materials

#### 2.3. The Monitored Indicators and Layout of Sensors

#### 2.3.1. Cracks Monitoring

#### 2.3.2. Strain Measurement

#### 2.3.3. Displacement Measurement

#### 2.4. Test Setup

## 3. Analysis and Discussion of Experimental Results

#### 3.1. The Measured Load and Failure Mode

#### 3.2. Load–Displacement Curves

#### 3.3. Load–Strain Curves

#### 3.4. Ductility Results

## 4. Nonlinear Finite Element Analysis

#### 4.1. Finite Element Model of the Test Specimen

#### 4.1.1. Material Parameter and Element Type

#### 4.1.2. Geometric Model, Contact and Boundary Conditions

#### 4.1.3. Meshing

#### 4.2. The Comparative Study of Experimental and Analytical Results

#### 4.2.1. The Ultimate Load

#### 4.2.2. The Load–Displacement Curve

#### 4.2.3. The Failure Mode and Crack Development

#### 4.2.4. Extended Numerical Analysis on the Designed Parameters of a Thin-Walled Steel-Reinforced Concrete Pier

- (1)
- The Concrete Strength

- (2)
- The DWR

- (3)
- The ACR

## 5. Discussion on the Effects of ACR and DWR on the Failure Performance

#### 5.1. The Effects of ACR

#### 5.2. The Effects of DWR

## 6. Horizontal Ultimate Bearing Capacity Equation for Thin-Walled Steel-Reinforced Concrete Pier

## 7. Conclusions and Outlooks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The Dimension and Steel Arrangement of the Test Specimens. (

**a**) The dimensions of the test specimens. (

**b**) Reinforcement arrangement. (

**c**) H-shape steel arrangement.

**Figure 2.**The Manufacturing Process of the Test Specimens. (

**a**) Reinforcement skeleton. (

**b**) H-shape steel. (

**c**) Pouring of concrete.

**Figure 6.**The Distribution of Cracks and the Failure Modes. (

**a**) SRCZ-1 and its zoomed figure. (

**b**) SRCZ-2 and its zoomed figure. (

**c**) SRCZ-3 and its zoomed figure.

**Figure 12.**The Abaqus Finite Element Model. (

**a**) Overall Model. (

**b**) H-shape Steel. (

**c**) Reinforcement Skeleton. (

**d**) Contact Condition.

**Figure 13.**The Meshing of the Finite Element Model. (

**a**) Concrete. (

**b**) H-shape Steel. (

**c**) Reinforcement Skeleton.

**Figure 14.**The Comparative Results of Experimental and Analytical Load–Displacement Curves. (

**a**) SRCZ-1. (

**b**) SRCZ-2. (

**c**) SRCZ-3.

**Figure 16.**The Simulated Results of Different Concrete Strength. (

**a**) Load–Displacement Curves. (

**b**) The Ultimate Load.

**Figure 17.**The Simulated Results of Different DWR. (

**a**) Load–Displacement Curves. (

**b**) The Ultimate Load.

**Figure 18.**The Simulated Results of Different ACR. (

**a**) Load–Displacement Curves. (

**b**) The Ultimate Load.

Specimen No. | Length/mm | ACR/% | Steel Ratio/% | DWR |
---|---|---|---|---|

SRCZ-1 | 2000 | 7 | 3.2 | 8 |

SRCZ-2 | 1500 | 7 | 3.2 | 6 |

SRCZ-3 | 1500 | 14 | 3.2 | 6 |

Strength/MPa | Yielding Strength ${\mathit{f}}_{\mathit{y}}$ | Ultimate Strength ${\mathit{f}}_{\mathit{u}}$ | Yielding Strain ${\mathit{\epsilon}}_{\mathit{y}}$ | Elastic Modulus $\mathit{E}$ | |
---|---|---|---|---|---|

Item | |||||

Steel | Flange | 303.6 | 442.5 | 1430 × 10^{−6} | 2.35 × 10^{5} |

Web | 296.2 | 427.8 | 1380 × 10^{−6} | 2.23 × 10^{5} | |

Longitudinal reinforcement | 417.4 | 593.7 | 1530 × 10^{−6} | 2.01 × 10^{5} | |

Hooped reinforcement | 409.2 | 586.6 | 1360 × 10^{−6} | 2.03 × 10^{5} | |

Concrete | Specimen No. | SRCZ-1 | SRCZ-2 | SRCZ-3 | |

Compressive Strength/MPa | 33.27 | 33.66 | 33.42 |

Specimen No. | DWR | ACR/% | Load/kN | Displacement/mm | Failure Mode | ||||
---|---|---|---|---|---|---|---|---|---|

${\mathit{P}}_{\mathit{c}\mathit{r}}$ | ${\mathit{P}}_{\mathit{y}}$ | ${\mathit{P}}_{\mathit{u}}$ | ${\mathit{f}}_{\mathit{c}\mathit{r}}$ | ${\mathit{\delta}}_{\mathit{y}}$ | ${\mathit{f}}_{\mathit{u}}$ | ||||

SRCZ-1 | 8 | 7 | 80 | 321.93 | 421.03 | 2.51 | 21.08 | 71.36 | bending-failure |

SRCZ-2 | 6 | 7 | 100 | 431.06 | 491.85 | 2.02 | 17.06 | 57.82 | bending-failure |

SRCZ-3 | 6 | 14 | 180 | 466.91 | 530.02 | 4.61 | 13.74 | 53.63 | bending-failure |

Specimen No. | ACR/% | DDC | DWR | YDDR | UDDR |
---|---|---|---|---|---|

SRCZ-1 | 7 | 3.39 | 8 | 0.0105 | 0.0357 |

SRCZ-2 | 7 | 3.97 | 6 | 0.0114 | 0.0452 |

SRCZ-3 | 14 | 3.90 | 6 | 0.0092 | 0.0357 |

Average value | 0.01 | 0.039 |

Specimen No. | DWR | ACR/% | Ultimate Load ${\mathit{P}}_{\mathit{u}}/\mathbf{kN}$ | Analytical/Experimental | Ultimate Displacement ${\mathit{f}}_{\mathit{u}}/\mathbf{mm}$ | Analytical/Experimental | ||
---|---|---|---|---|---|---|---|---|

Analytical | Experimental | Analytical | Experimental | |||||

SRCZ-1 | 8 | 7 | 474.30 | 421.03 | 1.13 | 79.80 | 71.36 | 1.12 |

SRCZ-2 | 6 | 7 | 561.85 | 491.85 | 1.14 | 69.40 | 57.82 | 1.20 |

SRCZ-3 | 6 | 14 | 601.02 | 530.02 | 1.14 | 61.81 | 53.63 | 1.15 |

**Table 6.**The Calculated Results Based on Ref. [28].

Specimen No. | Shear-to-Span Ratio | ACR | ${\mathit{V}}_{\mathit{E}}/\mathbf{kN}$ | ${\mathit{V}}_{\mathit{A}}/\mathbf{kN}$ | $\frac{{\mathit{V}}_{\mathit{E}}}{{\mathit{V}}_{\mathit{A}}}$ |
---|---|---|---|---|---|

Ref. [28]-1 | 2 | 0.3 | 117 | 101.9 | 1.15 |

Ref. [28]-2 | 2 | 0.5 | 124 | 109.5 | 1.13 |

Ref. [28]-3 | 2 | 0.4 | 116 | 105.8 | 1.10 |

Average | 1.13 | ||||

Mean Square Error | 0.021 |

Specimen No. | DWR | ACR | ${\mathit{V}}_{\mathit{E}}$/kN | ${\mathit{V}}_{\mathit{A}}$/kN | ${\mathit{V}}_{\mathit{F}\mathit{E}\mathit{M}}$ /kN | $\frac{{\mathit{V}}_{\mathit{E}}}{{\mathit{V}}_{\mathit{A}}}$ | $\frac{{\mathit{V}}_{\mathit{F}\mathit{E}\mathit{M}}}{{\mathit{V}}_{\mathit{A}}}$ |
---|---|---|---|---|---|---|---|

SRCZ-1 | 8 | 7 | 421.03 | 443.31 | 474.30 | 0.95 | 1.07 |

SRCZ-2 | 6 | 7 | 491.85 | 468.69 | 561.85 | 1.05 | 1.20 |

SRCZ-3 | 6 | 14 | 530.02 | 480.69 | 601.02 | 1.10 | 1.25 |

Average Mean Square Error | 1.03 | 1.17 | |||||

0.062 | 0.076 |

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**MDPI and ACS Style**

Chen, H.; Xu, B.; Liu, Q.; Gu, J.
Study on Failure Performance of the Thin-Walled Steel-Reinforced Concrete Pier under Low Cyclic Loading. *Buildings* **2022**, *12*, 1412.
https://doi.org/10.3390/buildings12091412

**AMA Style**

Chen H, Xu B, Liu Q, Gu J.
Study on Failure Performance of the Thin-Walled Steel-Reinforced Concrete Pier under Low Cyclic Loading. *Buildings*. 2022; 12(9):1412.
https://doi.org/10.3390/buildings12091412

**Chicago/Turabian Style**

Chen, Huihui, Bing Xu, Qin Liu, and Jianfeng Gu.
2022. "Study on Failure Performance of the Thin-Walled Steel-Reinforced Concrete Pier under Low Cyclic Loading" *Buildings* 12, no. 9: 1412.
https://doi.org/10.3390/buildings12091412