## Progressive Collapse Under Abnormal LoadA progressive collapse is initiated as a result of local structural damage and develops into a failure that is disproportionate to the initiating local damage. Structural collapse can be initiated by many hazards such as earthquakes, fires, or terrorist attacks. On 9/11, the World Trade Center (WTC) towers failed because the terrorist attack led to progressive collapse. Earthquake is a low probability/high consequence event. Therefore, it is very important to analyze how a progressive collapse caused by a seismic hazard event can unfold. |

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### Contents

Contents Page | 1 |

List of Figures | 3 |

List of Tables | 5 |

Hazard Event | 9 |

Estimation of Failure Probability of a Column Due to Earthquake | 19 |

Progressive Collapse of a Structure under Local Damage | 50 |

Chapter 4 | 51 |

Determining an Optimal Design Based on Risk Assessment | 67 |

Chapter 5 | 76 |

Conclusions and Recommendations | 86 |

### Common terms and phrases

alternative path method annual probability base shear method beam 17 beam 25 Beams after Failure Chapter coefficient of variation Column 9 Fails compression force Table Cross-Section Area Increment Dead load Live determined different locations DPD FPHPH DPD due to earthquake earthquake load effective seismic weight equivalent base shear f Number kN Fails Column Failure of Beam failure of column Fang force and negative FPHPH DPD FP fragility curves gamma distribution HPH DPD FPHPH Hurricane Katrina illustrated in Figure kN kN-m kN/m2 limit state function Load Effects load Live Load localized damage man-made hazards MDL(kN-m Member Axial Force Monte Carlo Simulation Number kN kN-m optimal path method APM PLL(kN probability density function Probability of Column probability of condition probability of progressive progressive collapse due random variable risk assessment Ronan Point seismic hazard seismic load seismic response coefficient shown in Table Sichuan total expected cost uncertainty yield stress York City