Risk Estimation for Progressive Collapse of Buildings
Using Key Element Index
Kota Azuma1 and Daigoro Isobe2
1Graduate School, University of Tsukuba

Ibaraki 305-8573, Japans1620860@s.tsukuba.ac.jp
2

Division of Engineering Mechanics and Energy, University of Tsukuba
Ibaraki 305-8573, Japan
isobe@kz.tsukuba.ac.jp

In the case of an emergency such as an intense fire or the collision of an object with a building,there is a risk of progressive collapse [1]. This was the phenomenon that occurred at theWorld Trade Center (WTC) towers during the 9.11 terrorist attacks. The official statements
released by the Federal Emergency Management Agency (FEMA) in 2002 [2] and theNational Institute of Standards and Technology (NIST) in 2005 [3] and 2008 [4] concluded
that the details of the failure process after the decisive initial trigger that set the upper part inmotion were very complicated and their clarification would require large computer
simulations. Among the various papers published after the incident, the one published byBazant et al. [5] has become a milestone for numerous other works concerning the progressive
collapse of buildings. By defining an overload ratio, the ratio of the elastic strength of thelower structure to the total weight of the upper, falling structure, they explained that the force
applied to the lower structure by the upper overwhelmingly exceeded the design vertical load,and consequently, it would be practically impossible to design a high-rise tower to avoid a
progressive collapse such as that which occurred in the case of the twin towers. On the other
hand, they also admitted that numerous computer simulations should be carried out to clarify
the collapse process, because their estimations were performed without considering the tiltingof the upper structure, member fracture, and other details.
In this study, the collapse behaviors of steel-framed buildings were simulated to investigate
the relation between a key element index [6-7] and the damage due to progressive collapse.
The key element index is a parameter which indicates the contribution of a structural column
to the vertical capacity of the structure. The collapse behaviors of steel framed buildings weresimulated using the ASI (Adaptively Shifted Integration) -Gauss code [8], which canexplicitly express member fracture and element contact in the collapse process. The
progressive collapse phenomena were initiated by removing specific columns from themodels. The total potential energy values of structural members after the collapse were used
to estimate the damage of the buildings.
For the progressive collapse analysis, a ten-story, three-span steel framed building model wasconstructed. The columns were subdivided with two linear Timoshenko beam elements per
member, and the beams and floors were subdivided with four elements. Several models
designed based upon different axial force ratios were prepared to determine the effects ofvarious structural strengths on the collapse scale of a building. The locations of removed
columns were restricted to a single floor, and some patterns of removed columns wereinvestigated. An example of the collapse sequence is shown in Figure 1.
By evaluating the numerical results using the key element index, it is found that the larger theintegrated values of key element index, which are calculated by summing up all the keyelement index values for the removed columns, the risk of progressive collapse tends toincrease; however, some peculiar tendencies are observed in the cases of removed columns
with extremely symmetrical or asymmetrical locations. The threshold of the integrated valueof key element index to cause a large-scale progressive collapse tends to depend on thestrengths of models, and it cannot be generally decided. This is due to the fact that the key
element index is a parameter which does not relate to the strength of the building itself.
Therefore, the key element index may only be used to predict and compare the risks ofprogressive collapse in the same building, but this may be done even when various locations
for the removed columns are assumed.

1.9 s

3.0 s

4.0 s

10.0 sFig. 1 Progressive collapse sequence of a ten-story, three-span steel framed building

References[1] B.R. Ellingwood et al.: Best practices for reducing the potential for progressive collapse inbuildings, National Institute of Standards and Technology (NIST), 2006.
[2] FEMA/ ASCE: World Trade Center Building Performance Study: Data Collection,
Preliminary Observations, and Recommendations, 2002.
[3] NIST NCSTAR 1: Building and Fire Safety Investigation of the World Trade Center
Disaster: Final Report on the Collapse of the World Trade Center Towers, National Instituteof Standards and Technology (NIST), 2005.
[4] NIST NCSTAR 1A: Final Report on the Collapse of World Trade Center Building 7,
National Institute of Standards and Technology (NIST), 2008.
[5] Z.P. Bazant and Y. Zhou: Why Did the World Trade Center Collapse? –Simple Analysis,
Journal of Engineering Mechanics, pp. 2-6, 2002.
[6] D. Isobe: An Analysis Code and a Planning Tool Based on a Key Element Index forControlled Explosive Demolition, International Journal of High-Rise Buildings, Vol. 3, No. 4,pp. 243-254, 2014.
[7] K. Oi and D. Isobe: Collapse Risk Prediction of Buildings on Fire Using Key ElementIndex, Journal of Structural and Construction Engineering (Transactions of AIJ), Vol. 82, No.
738, 2017, to be published, in Japanese.
[8] K.M. Lynn and D. Isobe: Finite Element Code for Impact Collapse Problems of Framed
Structures, International Journal for Numerical Methods in Engineering, Vol. 69, No. 12, pp.
2538-2563, 2007.