Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions

Progressive collapse is a failure mode of great concern for tall buildings, and is also typical of building demolitions. The most infamous paradigm is the collapse of the World Trade Center towers. After reviewing the mechanics of their collapse, the motion during the crushing of one floor (or group of floors) and its energetics are analyzed, and a dynamic one-dimensional continuum model of progressive collapse is developed. Rather than using classical homogenization, it is found more effective to characterize the continuum by an energetically equivalent snap-through. The collapse, in which two phases—crush-down followed by crush-up—must be distinguished, is described in each phase by a nonlinear second-order differential equation for the propagation of the crushing front of a compacted block of accreting mass. Expressions for consistent energy potentials are formulated and an exact analytical solution of a special case is given. It is shown that progressive collapse will be triggered if the total (internal) energy loss during the crushing of one story (equal to the energy dissipated by the complete crushing and compaction of one story, minus the loss of gravity potential during the crushing of that story) exceeds the kinetic energy impacted to that story. Regardless of the load capacity of the columns, there is no way to deny the inevitability of progressive collapse driven by gravity alone if this criterion is satisfied (for the World Trade Center it is satisfied with an order-of-magnitude margin). The parameters are the compaction ratio of a crushed story, the fracture of mass ejected outside the tower perimeter, and the energy dissipation per unit height. The last is the most important, yet the hardest to predict theoretically. It is argued that, using inverse analysis, one could identify these parameters from a precise record of the motion of floors of a collapsing building. Due to a shroud of dust and smoke, the videos of the World Trade Center are only of limited use. It is proposed to obtain such records by monitoring (with millisecond accuracy) the precise time history of displacements in different modes of building demolitions. The monitoring could be accomplished by real-time telemetry from sacrificial accelerometers, or by high-speed optical camera. The resulting information on energy absorption capability would be valuable for the rating of various structural systems and for inferring their collapse mode under extreme fire, internal explosion, external blast, impact or other kinds of terrorist attack, as well as earthquake and foundation movements.     

Progressive Analysis Procedure for Progressive Collapse

Following the collapse of the World Trade Center towers in September 2001, there has been heightened interest among building owners and government entities in evaluating the progressive collapse potential of existing buildings and in designing new buildings to resist this type of collapse. The General Services Administration and Department of Defense have issued general guidelines for evaluating a building’s progressive collapse potential. However, little detailed information is available to enable engineers to confidently perform a systematic progressive collapse analysis satisfying these guidelines. In this paper, we present four successively more sophisticated analysis procedures for evaluating the progressive collapse hazard: linear-elastic static; nonlinear static; linear-elastic dynamic; and nonlinear dynamic. We discuss the advantages and disadvantages of each method. We conclude that the most effective analysis procedure for progressive collapse evaluation incorporates the advantageous parts of all four procedures by systematically applying increasingly comprehensive analysis procedures to confirm that the possibility of progressive collapse is high.     

What Did and Did Not Cause Collapse of World Trade Center Twin Towers in New York?

Previous analysis of progressive collapse showed that gravity alone suffices to explain the overall collapse of the World Trade Center Towers. However, it remains to be determined whether the recent allegations of controlled demolition have any scientific merit. The present analysis proves that they do not. The video record available for the first few seconds of collapse is shown to agree with the motion history calculated from the differential equation of progressive collapse but, despite uncertain values of some parameters, it is totally out of range of the free fall hypothesis, on which these allegations rest. It is shown that the observed size range (0.01–0.1?mm) of the dust particles of pulverized concrete is consistent with the theory of comminution caused by impact, and that less than 10% of the total gravitational energy, converted to kinetic energy, sufficed to produce this dust (whereas, more than 150?t of TNT per tower would have to be installed, into many small holes drilled into concrete, to produce the same pulverization). The air ejected from the building by gravitational collapse must have attained, near the ground, the speed of almost 500 miles per hour (or 223?m/s, or 803?km/h) on average, and fluctuations must have reached the speed of sound. This explains the loud booms and wide spreading of pulverized concrete and other fragments, and shows that the lower margin of the dust cloud could not have coincided with the crushing front. The resisting upward forces due to pulverization and to ejection of air, dust, and solid fragments, neglected in previous studies, are indeed found to be negligible during the first few seconds of collapse but not insignificant near the end of crush-down. The calculated crush-down duration is found to match a logical interpretation of seismic record, while the free fall duration grossly disagrees with this record.     

Partial Demolition and Extension of Kuwait Medical College Building

This paper presents a simplified approximate analysis of the overall collapse of the towers of World Trade Center in New York on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed.     

Dominant Factor in the Collapse of WTC-1

The behavior of the World Trade Center Tower 1 on September 11, 2001 is studied in light of experimental data on the effect of elevated temperature on mechanical properties of structural steel. It is concluded that the damage inflicted by aircraft impact on the insulation of the core framing was the dominant factor in the collapse of the structure.     

Preventing Disproportionate Collapse

“Disproportionate collapse” is structural collapse disproportionate to the cause; it is often, though not always, progressive, where “progressive collapse” is the collapse of all or a large part of a structure precipitated by damage or failure of a relatively small part of it. There have been many attempts to develop design guidelines and criteria that would reduce or eliminate the susceptibility of buildings to this form of failure. In recent years, the particular focus has been on the prevention of progressive collapse due to deliberate attack. The present study suggests, however, that these guidelines and criteria may be of limited value. Arguably the most important deficiency in the state of the art of design to prevent disproportionate or progressive collapse is uncertainty about the design event: We have the technology now to design for almost anything, but most recent building failures due to explosions and terrorist attacks have involved insults to the building not anticipated in design guidelines and criteria.     

Addendum to “Why Did the World Trade Center Collapse?—Simple Analysis”

The addendum presents the responses to several questions on a preliminary version (which arrived too late for publication as part of the paper). The questions deal with the aircraft impact at a higher floor of the World Trade Center towers on September 11, 2001 damage to the upper part of the collapsing tower, weakness of connections, plastic cushioning of vertical impact, estimation of the equivalent mass, and the collapse of the adjacent lower building.     

Behavior and Design of Commercial Multistory Buildings Subjected to Blast

The behavior of nonmilitary buildings subjected to blast is considered. Case studies from World War II are described, as well as more recent events from the detonation of large vehicle borne devices in the Middle East, North America, and Europe. Conventional methods for nonseismic design are shown to lead to frames with overstrong beams connected together by relatively weak connections. This may explain much of the evidence from bomb damaged buildings in which building connections have been observed to fracture in a brittle manner when subjected to blast. The risk of progressive collapse may be minimized by strengthening beam to column connections located at close proximity to potential vehicle borne devices and a capacity design method for such strengthening is advocated.     

Progressive Collapse of the World Trade Center: Simple Analysis

The collapse behavior of the World Trade Center towers is considered formally as a propagating instability phenomenon. The application of associated concepts enables the residual capacities of both towers after the onset of collapse to be formally estimated. This information is combined into a simplified variable-mass collapse model of the overall dynamical behavior. The resulting, nonlinear governing equation of motion can be solved in closed form, to yield compact information about the overall collapse conditions.