# Seismic Performance of Concrete Column Connection with Square-Upper-Circular-Lower Steel Tube for Antique Buildings

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Finite Element Model Establishment and Verification

#### 2.1. Verification of USCFST-LCRC Column Connections for Antique Buildings

#### 2.1.1. Model Establishment

#### 2.1.2. Comparison between Finite Element Results and Test Results

#### 2.2. Validation of USSCR-LCRC Column Connections for Antique Buildings

#### 2.2.1. Model Establishment

#### 2.2.2. Comparison between Finite Element Results and Test Results

## 3. Seismic Performance of the USCFST-LCCFST Column Connection

#### 3.1. Finite Element Modeling

#### 3.1.1. Model Size

#### 3.1.2. Constitutive Relationship

#### CFST Column Concrete

#### Steel Principal Structure Relationship

#### 3.1.3. Modeling

#### 3.2. Comparative Analysis of the Seismic Performance of Column Connection

#### 3.2.1. Hysteresis Curve and Skeleton Curve Analysis

#### 3.2.2. Load-Bearing Capacity and Ductility Analysis

#### 3.2.3. Stiffness Degradation Curve Analysis

#### 3.2.4. Analysis of Energy Consumption Capacity

## 4. Variable Parameter Analysis of USCFST-LCCFST Column Connection

#### 4.1. Variable Parameter Design

#### 4.2. Effect of Yield Strength of Steel Tubes

#### 4.2.1. Analysis of Failure Morphology

#### 4.2.2. Hysteresis Curve and Skeleton Curve Analysis

#### 4.2.3. Load-Bearing Performance and Ductility Analysis

#### 4.2.4. Energy Consumption Capacity Analysis

#### 4.2.5. Stiffness Degradation Analysis

#### 4.3. Effect of Upper and Lower Column Linear Stiffness Ratio

#### 4.3.1. Analysis of Failure Pattern

#### 4.3.2. Hysteresis Curve and Skeleton Curve Analysis

#### 4.3.3. Load-Bearing Performance and Ductility Analysis

#### 4.3.4. Energy Consumption Capacity Analysis

#### 4.3.5. Stiffness Degradation Analysis

## 5. Conclusions

- (1)
- Compared to the conventional USCFST-LCRC and USSRC-LCRC column connection components, the USCFST-LCCFST column connection component proposed in this paper has fuller hysteresis curves and better peak loads, which can improve the ductility of the column connection component and result in a higher equivalent viscous damping coefficient in the damage phase. The stiffness degradation is good, indicating that the column connection component form for the USCFST-LCCFST has a good seismic performance.
- (2)
- The yield strength of the steel tube is recommended to be between 355 and 420 MPa because yield strength in this range can significantly improve the load-bearing capacity of the USCFST-LCCFST column connection component while reducing the ductility and slowing the rate of stiffness degradation.
- (3)
- The upper and lower column linear stiffness ratio of the connection should be strictly limited, and the recommended value is no less than 0.063. This is because when the upper and lower column linear stiffness ratio is small, the bearing capacity and ductility of the USCFST-LCCFST column connection components are significantly reduced, and column deformation would be too large, which would result in reduced seismic performance.
- (4)
- Since the connection forms for USCFST-LCCFST show excellent performances, it is recommended to adopt this connection form when designing column in the antique building.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Simulation and test results comparison of Specimen LJ-1: (

**a**) finite element stress cloud; (

**b**) test damage pattern; (

**c**) damage stress cloud.

**Figure 9.**Comparison of simulation and experimental results of USSRC-LCRC1: (

**a**) Finite element stress cloud diagram; (

**b**) Test damage pattern.

**Figure 13.**Meshing diagram of each component: (

**a**) circular steel tube meshing; (

**b**) square steel tube meshing; (

**c**) concrete meshing; (

**d**) overall model and meshing.

**Figure 16.**Comparison of stiffness degradation curves of the three types of column connection components.

**Figure 18.**The stress cloud of the steel tube of TY specimen at failure: (

**a**) TY-1; (

**b**) TY-2; (

**c**) TY-3; (

**d**) TY-4.

**Figure 19.**Hysteresis curve and skeleton curve of TY specimen: (

**a**) hysteresis curve; (

**b**) skeleton curve.

**Figure 21.**The stress cloud of steel tube for specimen LS at failure: (

**a**) LS-1; (

**b**) LS-2; (

**c**) LS-3; (

**d**) LS-4.

**Figure 22.**Hysteresis curve and skeleton curve of specimen LS: (

**a**) hysteresis curve; (

**b**) skeleton curve.

Specimen | Steel Tube Cross-Sectional Size (mm) |
---|---|

LJ-1 | 180 × 180 × 8 |

Phase | Yield Point | Peak Point | Failure Point | |||
---|---|---|---|---|---|---|

${\mathit{P}}_{\mathbf{y}}/\mathbf{k}\mathbf{N}$ | ${\mathit{\Delta}}_{\mathbf{y}}/\mathbf{mm}$ | ${\mathit{P}}_{\mathbf{max}}/\mathbf{k}\mathbf{N}$ | ${\mathit{\Delta}}_{\mathbf{max}}/\mathbf{mm}$ | ${\mathit{P}}_{\mathbf{u}}/\mathbf{k}\mathbf{N}$ | ${\mathit{\Delta}}_{\mathbf{u}}/\mathbf{mm}$ | |

Test | 55.25 | 33.54 | 71.86 | 83.82 | 61.08 | 147.84 |

Simulation | 58.64 | 35.78 | 76.38 | 84.00 | 64.923 | 135.89 |

Error (%) | 6.14 | 6.68 | 6.29 | 0.21 | 6.29 | 8.08 |

_{y}is calculated using the universal yield moment method; P

_{u}= 0.85 × P

_{m}.

Specimen | Metal Type | Ratio of Axial Compression | Longitudinal Reinforcement in the Upper | Longitudinal Support at the Lower | Stirrup Configuration |
---|---|---|---|---|---|

USSRC-LCRC1 | Q235b (100 × 68 × 4.5) | 0.3 | 420 | 620 | ϕ8@100 |

Phase | Yield Point | Peak Point | Failure Point | |||
---|---|---|---|---|---|---|

${\mathit{P}}_{\mathbf{y}}/\mathbf{k}\mathbf{N}$ | ${\mathit{\Delta}}_{\mathbf{y}}/\mathbf{mm}$ | ${\mathit{P}}_{\mathbf{max}}/\mathbf{k}\mathbf{N}$ | ${\mathit{\Delta}}_{\mathbf{max}}/\mathbf{mm}$ | ${\mathit{P}}_{\mathbf{u}}/\mathbf{k}\mathbf{N}$ | ${\mathit{\Delta}}_{\mathbf{u}}/\mathbf{mm}$ | |

Test | 24.97 | 23.30 | 32.94 | 55.49 | 28.00 | 87.39 |

Simulation | 24.18 | 25.14 | 31.28 | 57.90 | 26.59 | 96.05 |

Error (%) | 3.17 | 7.90 | 5.04 | 4.34 | 5.05 | 9.91 |

Specimen | Steel Tube Size (mm) | Axial Compression Ratio | Length to Slenderness Ratio | Steel Tube | Concrete Strength |
---|---|---|---|---|---|

C-1 | 180 × 180 × 8 | 0.25 | 61.35 | Q355 | C30 |

Density t/mm ^{3} | Young’s Modulus | Poisson’s Ratio | Dilation Angle | Eccentricity | fb0/fc0 | K | Viscosity Parameter |
---|---|---|---|---|---|---|---|

2.4 × 10^{−9} | 33,683.3 | 0.2 | 38 | 0.1 | 1.16 | 0.66667 | 0.01 |

Yield Stress | Plastic Strain | Damage Parameters | Inelastic Strain |
---|---|---|---|

15.88461008 | 0 | 0 | 0 |

22.97324533 | 0.000703841 | 0.447155833 | 0.000703841 |

26.50630226 | 0.001296779 | 0.563619489 | 0.001296779 |

28.42775095 | 0.001938553 | 0.64289235 | 0.001938553 |

29.52847376 | 0.002605198 | 0.69962601 | 0.002605198 |

30.17329051 | 0.003285658 | 0.74192038 | 0.003285658 |

30.5480548 | 0.003974301 | 0.779448462 | 0.003974301 |

30.75498954 | 0.004668031 | 0.800280601 | 0.004668031 |

30.85379147 | 0.005365037 | 0.821127858 | 0.005365037 |

30.88102445 | 0.006064211 | 0.838299099 | 0.006064211 |

29.27111322 | 0.007512997 | 0.871400333 | 0.007512997 |

25.98163115 | 0.009012678 | 0.901553528 | 0.009012678 |

22.520346 | 0.010517565 | 0.924978211 | 0.010517565 |

19.46283054 | 0.012010217 | 0.942166576 | 0.012010217 |

16.92110929 | 0.013487239 | 0.954633177 | 0.013487239 |

Yield Stress | Cracking Strain | Damage Parameters | Cracking Strain |
---|---|---|---|

3.067031 | 0 | 0 | 0 |

0.9 | 0.1 |

Density t/mm ^{3} | Young’s Modulus | Poisson’s Ratio | Yield Stress | Plastic Strain |
---|---|---|---|---|

7.85 × 10^{−9} | 2.72 × 10^{5} | 0.3 | 323.8 | 0 |

388.56 | 0.0235 |

Member | ${\mathit{\Delta}}_{\mathbf{y}}/\mathbf{mm}$ | ${\mathit{\Delta}}_{\mathbf{u}}/\mathbf{mm}$ | ${\mathit{P}}_{\mathbf{y}}/\mathbf{k}\mathbf{N}$ | ${\mathit{P}}_{\mathbf{max}}/\mathbf{k}\mathbf{N}$ | ${\mathit{P}}_{\mathbf{u}}/\mathbf{k}\mathbf{N}$ | $\mathit{\mu}$ |
---|---|---|---|---|---|---|

USCFST-LCCFST | 44.4 | 211.0 | 83.7 | 91.7 | 77.9 | 4.75 |

USCFST-LCRC | 33.5 | 147.8 | 55.2 | 71.9 | 61.1 | 4.41 |

USSRC-LCRC | 23.3 | 87.4 | 25.0 | 32.9 | 28.0 | 3.75 |

**Table 11.**Comparison of equivalent viscous damping coefficients of the three types of column connection components.

Member | Equivalent Viscous Damping Coefficients | ||
---|---|---|---|

Yield Phase | Peak Phase | Failure Phase | |

USCFST-LCCFST | 0.092 | 0.300 | 0.550 |

USCFST-LCRC | 0.093 | 0.183 | 0.281 |

USSRC-LCRC | 0.115 | 0.161 | 0.289 |

**Table 12.**Specific settings of the variable parameters of the USCFST-LCCFSE column connection components.

Specimen No. | ${\mathbf{f}}_{\mathbf{y}}/\mathbf{M}\mathbf{P}\mathbf{a}$ | ${\mathbf{f}}_{\mathbf{c}}/\mathbf{M}\mathbf{P}\mathbf{a}$ | ${\mathbf{i}}_{\mathbf{u}\mathbf{p}}/{\mathbf{i}}_{\mathbf{d}\mathbf{o}\mathbf{w}\mathbf{n}}$ | $\mathbf{n}$ | $\mathbf{b}/\mathbf{m}\mathbf{m}$ | $\mathbf{L}/\mathbf{m}\mathbf{m}$ |
---|---|---|---|---|---|---|

TY-1 | 235 | 30 | 0.063 | 0.3 | 8 | 1080 |

TY-2 | 355 | |||||

TY-3 | 390 | |||||

TY-4 | 420 | |||||

LS-1 | 355 | 30 | 0.012 | 0.3 | 8 | 1080 |

LS-2 | 0.027 | |||||

LS-3 | 0.063 | |||||

LS-4 | 0.159 |

Specimen | ${\mathit{\Delta}}_{\mathbf{y}}/\mathbf{mm}$ | ${\mathit{\Delta}}_{\mathbf{max}}/\mathbf{mm}$ | ${\mathit{\Delta}}_{\mathbf{u}}/\mathbf{mm}$ | ${\mathit{P}}_{\mathbf{y}}/\mathbf{k}\mathbf{N}$ | ${\mathit{P}}_{\mathbf{max}}/\mathbf{k}\mathbf{N}$ | ${\mathit{P}}_{\mathbf{u}}/\mathbf{k}\mathbf{N}$ | $\mathit{\mu}$ |
---|---|---|---|---|---|---|---|

TY-1 | 37.38 | 48.00 | 177.73 | 58.67 | 70.57 | 59.98 | 4.75 |

TY-2 | 44.38 | 87.99 | 211.00 | 84.71 | 91.70 | 77.95 | 4.75 |

TY-3 | 50.49 | 87.99 | 219.42 | 101.24 | 110.40 | 93.84 | 4.35 |

TY-4 | 53.32 | 87.99 | 224.44 | 105.29 | 118.26 | 100.52 | 4.21 |

Specimen No. | Equivalent Viscous Damping Coefficient | ||
---|---|---|---|

Yield Stage | Peak Stage | Failure Stage | |

TY-1 | 0.259 | 0.415 | 0.554 |

TY-2 | 0.092 | 0.300 | 0.550 |

TY-3 | 0.116 | 0.230 | 0.492 |

TY-4 | 0.105 | 0.200 | 0.469 |

Specimen | ${\mathit{\Delta}}_{\mathbf{y}}/\mathbf{mm}$ | ${\mathit{\Delta}}_{\mathbf{max}}/\mathbf{mm}$ | ${\mathit{\Delta}}_{\mathbf{u}}/\mathbf{mm}$ | ${\mathit{P}}_{\mathbf{y}}/\mathbf{k}\mathbf{N}$ | ${\mathit{P}}_{\mathbf{max}}/\mathbf{k}\mathbf{N}$ | ${\mathit{P}}_{\mathbf{u}}/\mathbf{k}\mathbf{N}$ | $\mathit{\mu}$ |
---|---|---|---|---|---|---|---|

LS-1 | 47.35 | 87.99 | 107.30 | 22.91 | 23.21 | 19.73 | 2.27 |

LS-2 | 45.99 | 87.99 | 119.07 | 47.29 | 49.16 | 41.78 | 2.59 |

LS-3 | 44.38 | 87.99 | 211.00 | 84.71 | 91.70 | 77.95 | 4.75 |

LS-4 | 42.83 | 88.00 | 247.15 | 115.98 | 128.86 | 109.53 | 5.77 |

Specimen | Equivalent Viscous Damping Coefficients | ||
---|---|---|---|

Yield Stage | Peak Stage | Failure Stage | |

LS-1 | 0.081 | 0.106 | 0.372 |

LS-2 | 0.142 | 0.144 | 0.355 |

LS-3 | 0.092 | 0.300 | 0.550 |

LS-4 | 0.180 | 0.253 | 0.508 |

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## Share and Cite

**MDPI and ACS Style**

Sun, X.; Guo, Q.; Xuan, Y.; Wu, B.; Gao, J.
Seismic Performance of Concrete Column Connection with Square-Upper-Circular-Lower Steel Tube for Antique Buildings. *Buildings* **2023**, *13*, 916.
https://doi.org/10.3390/buildings13040916

**AMA Style**

Sun X, Guo Q, Xuan Y, Wu B, Gao J.
Seismic Performance of Concrete Column Connection with Square-Upper-Circular-Lower Steel Tube for Antique Buildings. *Buildings*. 2023; 13(4):916.
https://doi.org/10.3390/buildings13040916

**Chicago/Turabian Style**

Sun, Xianghong, Qingwei Guo, Yunpeng Xuan, Bingxue Wu, and Jiabin Gao.
2023. "Seismic Performance of Concrete Column Connection with Square-Upper-Circular-Lower Steel Tube for Antique Buildings" *Buildings* 13, no. 4: 916.
https://doi.org/10.3390/buildings13040916