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.

Section snippets

Numerical framework

In this study, the ASI-Gauss code [18] based on FEM was employed to simulate the collapse behavior of buildings when a large-scale fire spreads. High computational efficiency can be achieved using this code for problems with strong nonlinear behavior, such as member fracture and contact. Owing to its numerous advantages and flexibility, this code has been utilized in various fields, such as impact loading [21], progressive collapse [22], seismic collapse [23], and demolition [16].

The main idea

Integrated value of key element index

In this study, the integrated value of KI is defined by accumulating all KI values of the columns in the spreading area of fire, and is expressed as follows:i=1Rj=1liKIi,mi,j=KI1,m1,1+KI1,m1,2++KI1,m1,l1+KI2,m(2,1)++KIR,m(R,lR)

Here, R,li,and mi,j denote the total number of floors, total number of columns in the spreading area of fire on the i-th floor, and column number of j-th column, respectively. For instance, suppose the strengths of the columns (No. a, b, and c) on the i-th floor of a

Numerical model

In this study, the collapse behavior of a ten-story, three-bay steel-framed building under various fire conditions was investigated. Fig. 1 illustrates the constructed numerical model. The floor height and span length in the lateral directions are 4.0m and 7.0m, respectively. As the ASI-Gauss code [18] was applied, linear Timoshenko beam elements were used to model the structural members: two elements for the columns and four for the beams per member. Square steel sections (SM490) were used


This study aimed to estimate the collapse scales of a ten-story, three-bay steel-framed building using KI values under various fire conditions, considering large-scale fire spread. The outbreak locations of fire were set to the middle and corner of the floors, with various fire ranges from the 1st to 10th floors. The collapse scales were determined by performing fire-induced collapse analyses using the ASI–Gauss code and by observing the sum of the heights of the remains. Accordingly, the

CRediT authorship contribution statement

Daigoro Isobe: Conceptualization, Methodology, Software, Writing – original draft, Writing – review & editing, Supervision, Project administration. Kana Itakura: Investigation, Resources, Data curation, Visualization.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

© 2023 Elsevier Ltd. All rights reserved.

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