# Comparison of Different Procedures for Progressive Collapse Analysis of RC Flat Slab Structures under Corner Column Loss Scenario

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of Reference Experiments

#### 2.1.1. Corner Support Loss Scenario for Reinforced Concrete Flat Slab

#### 2.1.2. Corner Column Loss Scenario for Two-Story Reinforced Concrete Flat Slab Frame

#### 2.2. Methodology for Simulation of Progressive Collapse

#### 2.2.1. Governing Equations

_{i}and ω

_{n}are the lower and upper limits of the damped frequency range; ζ

_{i}and ζ

_{n}are the damping ratios at the lower and upper damped frequencies, respectively.

_{i}and ζ

_{n}at the lower and upper damped frequencies were the same and were equal to 4% for concrete and 2% for steel, respectively.

#### 2.2.2. Finite Element Mesh

#### 2.2.3. Material Models

^{−1}and p = 5 are the strain rate parameters [68].

#### 2.3. Numerical Procedures for Progressive Collapse Analysis

## 3. Results

#### 3.1. Corner Support Loss Scenario for Reinforced Concrete Flat Slab

#### 3.2. Corner Column Loss Scenario for a Two-Story Reinforced Concrete Frame

_{max}, the vertical displacements at all points increased linearly (see Figure 8a). At this load, flexural damage occurred on the top faces of the floor slabs (Figure 9a).

_{max}, the slabs on the first and second floors above the failed column were completely damaged, which was not confirmed by the test data (see Figure 9b). The comparison of calculated vertical displacements with the experiment in Figure 8b shows that the nonlinear static analysis could not reliably describe the response of the RC frame under the corner column loss scenario.

## 4. Discussion

_{LIF}is the smallest m factor determined for each structural element directly connected or located above the removal column. For m

_{LIF}= 6, we obtained LIF = 8.

_{pra}is the plastic rotation angle and θ

_{y}is the yield rotation. Given that θ

_{pra}= 0.05 and θ

_{y}= 0.032, we obtained DIF = 1.26. Compared to the uniform multiplier of 2.0 proposed by the Russian standard [40], the calculated LIF and DIF following the DoD guideline [41] looked more reasonable. Using these values as multipliers to the masses loaded on the slabs above the removal column, we obtained the peak displacements equal to 61.8 mm and 54.7 mm from LSP and NSP, respectively (see Figure 13).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Cracking patterns on the top (

**a**) and bottom (

**b**) surfaces of the flat slab after corner support loss.

**Figure 3.**Time history of vertical displacements (

**a**) and geometry of the two-story reinforced concrete frame (

**b**).

**Figure 6.**Comparison of damage accumulated in the flat slab from nonlinear dynamic (

**a**) and nonlinear static (

**b**) analyses with the crack patterns from the experiment.

**Figure 8.**Vertical displacements obtained from nonlinear static analysis (

**a**) and its comparison with test data (

**b**).

**Figure 9.**Damage of the two-story RC frame from nonlinear static analysis at different load levels: (

**a**)—0.6·P

_{max}; (

**b**)—1.0·P

_{max}.

**Figure 10.**The state of equilibrium before corner column removal: (

**a**)—damage; (

**b**)—vertical displacements, mm.

**Figure 11.**The state of maximum displacements after corner column removal: (

**a**)—damage; (

**b**)—vertical displacements, mm.

**Figure 12.**Comparison of vertical displacements obtained from numerical simulations with test data for different points: (

**a**)—P2_11V; (

**b**)—P23_1/3V; (

**c**)—P23_2/3V; (

**d**)—P3_11V.

**Figure 13.**The maximum displacements obtained following DoD guideline from linear static procedure (

**a**) and nonlinear static procedure (

**b**), mm.

Method | Maximum Vertical Displacement | Residual Vertical Displacement | ||
---|---|---|---|---|

Value (mm) | Mismatch (%) | Value (mm) | Mismatch (%) | |

Test data | 47.4 | N/A | 46.0 | N/A |

Linear Static | 12.8 | 73.0 | 12.8 | 72.2 |

Linear Dynamic | 11.1 | 76.6 | 5.9 | 87.2 |

Nonlinear Static | 51.3 | 8.2 | 51.3 | 11.5 |

Nonlinear Dynamic | 45.9 | 3.2 | 46.7 | 1.5 |

Method | Maximum Vertical Displacement | Residual Vertical Displacement | ||
---|---|---|---|---|

Value (mm) | Mismatch (%) | Value (mm) | Mismatch (%) | |

Linear Static | 24.5 | 49.1 | 24.5 | 42.8 |

Linear Dynamic | 21.4 | 55.5 | 12.3 | 71.3 |

Nonlinear Static | 264.5 | 449.9 | 264.5 | 518.0 |

Nonlinear Dynamic | 48.4 | 0.6 | 44.1 | 3.0 |

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**MDPI and ACS Style**

Dmitriev, A.N.; Lalin, V.V.
Comparison of Different Procedures for Progressive Collapse Analysis of RC Flat Slab Structures under Corner Column Loss Scenario. *Buildings* **2021**, *11*, 405.
https://doi.org/10.3390/buildings11090405

**AMA Style**

Dmitriev AN, Lalin VV.
Comparison of Different Procedures for Progressive Collapse Analysis of RC Flat Slab Structures under Corner Column Loss Scenario. *Buildings*. 2021; 11(9):405.
https://doi.org/10.3390/buildings11090405

**Chicago/Turabian Style**

Dmitriev, Andrey Nikolaevich, and Vladimir Vladimirovich Lalin.
2021. "Comparison of Different Procedures for Progressive Collapse Analysis of RC Flat Slab Structures under Corner Column Loss Scenario" *Buildings* 11, no. 9: 405.
https://doi.org/10.3390/buildings11090405