Collapse scale estimation of a steel-framed building under large-scale fire spread using key element index (2023)

A large-scale fire spread in buildings often causes severe damage, which can lead to catastrophic disasters. In fact, following the 9/11 terrorist attacks in 2001, Tower 7 of the New York World Trade Center (WTC-7) continued to burn for nearly 7h and eventually ended in a total collapse. The official report on the collapse investigation of WTC-7 by the National Institute of Standards and Technology (NIST) [1] suggested that this total collapse was induced from the severe damage of a critical column called the “key element.” In 2017, a fire broke out in the Plasco Building in Tehran, a 16-story steel-frame structure with a height of about 61m above the ground level, and continued to burn for almost 3.5h. The beam to column connections reached their critical temperatures first and failed to resist the local failure loads, and exposure of unshielded structural components to the fire had led to the progressive collapse of the tower section, causing 16 firefighters and 5 civilians to lose their lives in the rubble [2]. On the other hand, a large-scale fire does not necessarily lead to an instant, large-scale collapse. For instance, in 2005, the Windsor Tower in Madrid [3], which was a 32-story tower framed in steel-reinforced concrete, also suffered a large-scale fire but did not end up in an instant total collapse, despite its main structure being continuously heated by the fire for approximately 26h and steel members being almost scraped off. Concrete pillars of the core structure were the main load-bearing component of the building, which prevented the total collapse. To prevent large-scale collapse of buildings on fire, it is necessary to clarify the structural integrity of buildings under various fire locations, scales, and durations of fire spread. In this respect, Lange et al. [4] proposed a simple design assessment methodology that could estimate the upper-bound collapse mechanisms for tall buildings subjected to a range of multiple-floor fires. Rackauskaite et al. [5] modeled a two-dimensional (2D) 10-story, 5-bay, steel frame using LS-DYNA to investigate the response of a substantially different structural system subjected to travelling fires on multiple floors by varying the number of fire floors, including horizontal and vertical fire spreads. Moreover, Gernay and Gamba [6] adopted a nonlinear finite element method (FEM) to analyze the mechanisms of load redistribution in a structural system comprising a column subjected to a localized fire, with an emphasis on the effects of the cooling phase. Suwondo et al. [7] presented three-dimensional (3D) progressive collapse analyses of composite steel frames subjected to travelling fires resulting from fire compartment damage. They concluded that the spatial nature of the travelling fire and the inter-zone time delay have a significant impact on the survival of the building. Jiang et al. [8] investigated the effects of fire curves and fire spreading speeds on the collapse behavior and suggested that the duration of the heating phase has a significant effect on whether a building collapses or not, and the building is likely to collapse during the cooling phase due to the delayed increment of temperatures in the heated members.

Progressive collapse and related fields of structural engineering are relatively immature, and many of their aspects are not well understood [9], [10], [11], [12]. Sun et al. [13] developed a robust static-dynamic procedure to model the dynamic and static behaviors of steel buildings during both local and global progressive collapses of structures under fire conditions and performed some preliminary studies on the collapse mechanism of steel frames due to column failure under fire conditions. Malomo and DeJong [14] established a simplified discrete element macro-model to simulate various collapse scenarios of the unreinforced masonry façade of the Bank Buildings in Belfast (UK), which was severely damaged by a fire in 2018.

However, these studies did not aim to quantify the collapse scales of buildings in terms of the scale of fire range. Oi et al. [15] conducted several fire-induced collapse analyses of buildings by considering the strength weakening of structural members owing to highly elevated temperatures under various fire conditions with different fire locations in the horizontal and vertical directions to quantitatively clarify the collapse scales of buildings. The relationships between the collapse scales and the integrated values of a key element index (hereafter referred to as KI) [16], a parameter that indicates the contribution of columns to the overall strength of a building, were thoroughly investigated. The results confirmed that a large-scale collapse started when the integrated value of KI exceeded a certain threshold, which may enable the quantitative prediction of the collapse scales of buildings. On the other hand, the strength of the columns in the fire range was simultaneously lowered, and the spread of fire was not considered in [15]. However, in reality, it is most likely that the fire will gradually spread from the initial location, and this phenomenon may induce asymmetry in the strength distribution of buildings. Therefore, the collapse scales of buildings under such conditions warrants investigation.

The purpose of this study was to quantitatively estimate the collapse scales of buildings under large-scale fire spread using KI. Fire-induced collapse analyses were performed using a finite element code based on the adaptively shifted integration (ASI)-Gauss technique [17], [18], which is an upgraded version of the ASI technique [19], [20]. A ten-story steel-framed building model was constructed, and the relationships between the integrated values of KI and the sum of the height of the remains after the collapse in various fire ranges with different spreading patterns were examined. The thermal expansion of materials, as well as the reduction curves of the elastic modulus and yield strength of steel induced by elevated temperature [1], were adopted to consider the heat effect of fire.

The remainder of this paper is organized as follows. In Section 2, an outline of the numerical framework is described. In Section 3, the integrated value of KI used in this study is explained. In Section 4, fire-induced collapse analyses of a steel-framed building are presented, and the relationships between its collapse scales and integrated values of KI are discussed. In Section 5, conclusions drawn from the results are presented. Additionally, the time integration scheme based on the updated Lagrangian formulation used in the numerical framework is explained in Appendix A and the definition of KI is explained in Appendix B.