Risk Prediction of Collapse for Buildings under Fire Using Key Element Index

Abstract

The official report on the total collapse investigation of the New York World Trade Center 7 (WTC-7) regarding the 9.11 incident, released by the National Institute of Standards and Technology (NIST) in 2005, had suggested that the total collapse was triggered by a severe damage of an important column of the building called the key element. Upon these circumstances, we investigated the relationship between the integrated values of a key element index, which indicates the contribution of a structural column to the vertical capacity of the structure, in various cases of fire range and the sum of the height of remains after collapse. The purpose of this study is to predict collapse risks of buildings under fire using the key element index. We applied an ASI (Adaptively Shifted Integration)-Gauss code, utilizing linear Timoshenko beam elements, to a ten-story steel framed structure model with various fire patterns. Fracture contact, contact release and re-contact algorithms were implemented in the code. Reduction curves of elastic modulus and yield stress of steel related to temperature shown by NIST were adopted to represent the structural effects of fire. Thermal expansion of materials was also considered. The numerical results of the fire-induced collapse analyses showed that the risk of total collapse tend to increase when a large range of fire occurred in the lower layer. In addition, the risk increased much higher in those cases when fire occurred at the peripheral area of the building, compared to those cases at the inner area. There was a specific threshold of the integrated value of key element index when the buildings started to collapse, and the threshold became smaller as the layer on fire rose up to higher level.