# Dynamic Response Analysis of RC Frame against Progressive Collapse Based on Orthogonal Test

^{*}

## Abstract

**:**

## 1. Introduction

_{imax}and the minimum value k

_{imin}in each factor’s average degree of influence in state i.

## 2. Finite Element Analysis Model

#### 2.1. Selection of Analytical Models

- The first-floor height was 4.9 m.
- The remaining floor height was 3.3 m.
- The span was 6 m.
- The reinforced concrete beams and columns dimensions were 300 mm×, 500 mm and 500 mm × 500 mm.
- C30 was selected for concrete.
- The constant load of the frame floor was 5.0 KN/m
^{2}. - The live floor load was 2.0 KN/m
^{2}.

#### 2.2. Fiber Beam Model

#### 2.3. Material Constitutive Selection

#### 2.4. Rayleigh Damping

#### 2.5. Example Verification

## 3. Application of Orthogonal Test Method

#### 3.1. Finite Element Analysis Steps

#### 3.1.1. Single-Factor Initial Condition Analysis

#### 3.1.2. Effect of Initial Condition Displacement

#### 3.1.3. Discussion of the Results

#### 3.2. Orthogonal Test Method

#### 3.2.1. Trial Arrangement

#### 3.2.2. Range Analysis

## 4. Conclusions

- (1)
- When the column failure time is close to 0.1 T, the failure time has little influence on the dynamic response of the structure.
- (2)
- By comparing the dynamic response of the structure under different initial displacement and velocity conditions, it is found that the progressive collapse analysis, without considering the initial condition, underestimates the influence of the initial condition on the structural deformation. The initial upward velocity and initial upward displacement will amplify the dynamic response of the structure. This will cause more severe damage to the structure, which is unfavorable to the progressive collapse resistance of the structure. The initial downward displacement and initial downward velocity are beneficial to the progressive collapse resistance of the structure, and the initial downward displacement will weaken the dynamic response of the structure.
- (3)
- In all three column failure cases, the most unfavorable combinations of structural dynamic response were 0.05 T failure time, 20 mm initial displacement, and 60 mm/s initial velocity. The failure time and initial velocity have little influence on the dynamic response of the structure, and the initial displacement has a more significant influence on the structure. At present, there are few studies considering the initial condition of the residual structure and the initial condition of the residual structure that affects the resistance of the structure to progressive collapse. Considering the initial condition of the remaining structure can more accurately analyze the progressive collapse resistance of the structure.

## 5. Further Research

- The dynamic responses of other structures and columns of different floors after failure should be studied, considering the initial condition of the remaining structure.
- The influence of the presence of floor slabs on the dynamic response of the structure under the initial condition of the remaining structure should be considered.
- The progressive collapse resistance of long-span space structures can be studied by an orthogonal test.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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User Parameter | |
---|---|

Mechanical constant | |

1 | 2.75 × 10^{7} |

2 | 0.0022 |

3 | 2.475 × 10^{7} |

4 | 0.00778 |

User Parameter | |
---|---|

Mechanical constant | |

1 | 2.06 × 10^{11} |

2 | 4.16 × 10^{8} |

3 | 0.005 |

Factor | Failure Time | Initial Velocity | Initial Displacement |
---|---|---|---|

K1 | 478.3 | 479.2 | 623.8 |

K2 | 476 | 471.2 | 521 |

K3 | 477.4 | 455 | 432 |

K4 | 464.1 | 477.9 | 399.1 |

K5 | 462.6 | 475.1 | 382.5 |

k1 | 95.66 | 95.84 | 124.76 |

k2 | 95.2 | 94.24 | 104.2 |

k3 | 95.48 | 91 | 86.4 |

k4 | 92.82 | 95.58 | 79.82 |

k5 | 92.52 | 95.02 | 76.5 |

R | 3.14 | 4.84 | 48.26 |

Factor | Failure Time | Initial Velocity | Initial Displacement |
---|---|---|---|

K1 | 425.9 | 426.8 | 547 |

K2 | 420.3 | 417.5 | 452.6 |

K3 | 417.4 | 398.2 | 376.1 |

K4 | 413 | 423 | 354.3 |

K5 | 407.8 | 418.9 | 354.4 |

k1 | 85.18 | 85.36 | 109.4 |

k2 | 84.06 | 83.5 | 90.52 |

k3 | 93.48 | 79.64 | 75.22 |

k4 | 82.6 | 84.6 | 70.86 |

k5 | 81.56 | 83.78 | 70.88 |

R | 3.62 | 5.72 | 38.54 |

Factor | Failure Time | Initial Velocity | Initial Displacement |
---|---|---|---|

K1 | 618.9 | 615.5 | 787.8 |

K2 | 617.1 | 614.2 | 681.1 |

K3 | 618.2 | 587 | 561.3 |

K4 | 604 | 615.6 | 530.5 |

K5 | 587.4 | 613.3 | 484.9 |

k1 | 123.78 | 123.1 | 157.56 |

k2 | 123.42 | 122.84 | 136.22 |

k3 | 123.64 | 117.4 | 112.26 |

k4 | 120.8 | 123.12 | 106.1 |

k5 | 117.48 | 122.66 | 96.98 |

R | 6.3 | 5.75 | 60.85 |

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**MDPI and ACS Style**

Ke, C.; Li, X.; Jiang, J. Dynamic Response Analysis of RC Frame against Progressive Collapse Based on Orthogonal Test. *Appl. Sci.* **2023**, *13*, 4317.
https://doi.org/10.3390/app13074317

**AMA Style**

Ke C, Li X, Jiang J. Dynamic Response Analysis of RC Frame against Progressive Collapse Based on Orthogonal Test. *Applied Sciences*. 2023; 13(7):4317.
https://doi.org/10.3390/app13074317

**Chicago/Turabian Style**

Ke, Changren, Xianwei Li, and Junling Jiang. 2023. "Dynamic Response Analysis of RC Frame against Progressive Collapse Based on Orthogonal Test" *Applied Sciences* 13, no. 7: 4317.
https://doi.org/10.3390/app13074317