User:Peterhoneyman/sandbox/Zdeněk Bažant











Addendum to "Why Did the World Trade Center Collapse?—Simple Analysis" J. Engrg. Mech., Volume 128, Issue 3, pp. 369-370 (March 2002)

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.

doi:10.1061/(ASCE)0733-9399(2002)128:3(369) Submitted: November 28, 2001; accepted: December 7, 2001 Coden	 JENMDT doi	 10.1061/(ASCE)0733-9399(2002)128:3(369)

Bažant, Z.P. (2001a). ”Why did the World Trade Center collapse?” SIAM News (Society for Industrial and Applied Mathematics, M.I.T., Cambridge), 34 (8), October (submitted Sept. 14). Bažant, Z.P. (2001b). “Anatomy of Twin Towers Collapse.” Science and Technology (part of Hospodarske Noviny, Prague) No. 186, Sept. 25, p.1.

Within days of the attacks on the World Trade Center, Zdeněk Bažant prepared an analysis of the collapse of the towers, which he submitted to the Journal of Engineering Mechanices on September 13 and to SIAM News on September 14. He also made his initial analysis available on the web on September 14.

. He submitted a manuscript to SIAM News  to an engineering journal and made it available on the web.

7. Timothy Wilkinson, “World Trade Centre–New York—Some Engineering Aspects” (October 25, 2001), Univ. Sydney, Department of Civil Engineering; www.civil.usyd.edu.au/wtc.htm.

8. G. Charles Clifton, “Collapse of the World Trade Centers,” CAD Headlines, tenlinks.com (October 8, 2001); www.tenlinks.com/NEWS/special/wtc/clifton/p1.htm.

Thomas W. Eagar, the Thomas Lord Professor of Materials Engineering and Engineering Systems, and Christopher Musso, graduate research student, are at the Massachusetts Institute of Technology.



Background for the civil engineering design is given, and failure possibilities are provided. Various structural components, including the foundation slurry walls, the design of the column support system, and the performance of the floors are briefly described. The 110-story Twin Towers were constructed 30 years ago and utilized the latest engineering principles; they were stable, and workers as well as visitors often commented that the upper floors were comfortable and any sway was not noticeable during storms.

Closure to "World Trade Center Collapse—Civil Engineering Considerations" by Bernard Monahan Pract. Periodical on Struct. Des. and Constr., Volume 9, Issue 2, p. 121 (May 2004) Bernard Monahan doi:10.1061/(ASCE)1084-0680(2004)9:2(121.2)

Discussion of "World Trade Center Collapse—Civil Engineering Considerations" by Bernard Monahan Pract. Periodical on Struct. Des. and Constr., Volume 9, Issue 2, p. 121 (May 2004) K. Sivakumar doi:10.1061/(ASCE)1084-0680(2004)9:2(121)



This paper uses a finite-element model to investigate the stability of the Twin-Towers of the World Trade Center, New York for a number of different fire scenarios. This investigation does not take into account the structural damage caused by the terrorist attack. However, the fire scenarios included are based upon the likely fires that could have occurred as a result of the attack. A number of different explanations of how and why the Towers collapsed have appeared since the event. None of these however have adequately focused on the most important issue, namely ‘what structural mechanisms led to the state which triggered the collapse’. Also, quite predictably, there are significant and fundamental differences in the explanations of the WTC collapses on offer so far. A complete consensus on any detailed explanation of the definitive causes and mechanisms of the collapse of these structures is well nigh impossible given the enormous uncertainties in key data (nature of the fires, damage to fire protection, heat transfer to structural members and nature and extent of structural damage for instance). There is, however, a consensus of sorts that the fires that burned in the structures after the attack had a big part to play in this collapse. The question is how big? Taking this to the extreme, this paper poses the hypothetical question, ‘‘had there been no structural damage would the structure have survived fires of a similar magnitude’’? A robust but simple computational and theoretical analysis has been carried out to answer this question. Robust because no gross assumptions have been made and varying important parameters over a wide range shows consistent behaviour supporting the overall conclusions. Simple because all results presented can be checked by any structural engineer either theoretically or using widely available structural analysis software tools. The results are illuminating and show that the structural system adopted for the Twin-Towers may have been unusually vulnerable to a major fire. The analysis results show a simple but unmistakable collapse mechanism that owes as much (or more) to the geometric thermal expansion effects as it does to the material effects of loss of strength and stiffness. The collapse mechanism discovered is a simple stability failure directly related to the effect of heating (fire). Additionally, the mechanism is not dependent upon failure of structural connections.



An analysis is presented that calculates the temperature of the steel truss rods in the World Trade Center towers subject to a fire based on the building ventilation factor. The CIB correlation is used for the fire. Conduction analyses are made taking into account variable properties for the steel and the insulation. A structural failure model is described based on compression buckling of the truss rods due to a reduction in the Young’s modulus. The computed times for the estimated failure or incipient collapse of the floors in both towers has been computed as 105±20 min for WTC 1 (north) and 51±9 min for WTC 2 (south), compared to the collapse times from the aircraft impact of 104 and 56 min, respectively. The insulation thickness and the difference of 19.1 mm (¾") and 38.1 mm (1½") between the two towers appear to have been the root cause of the collapses.



This technical note presents the results from a nonlinear finite element analysis of a very simple two dimensional model of the World Trade Center Twin-Towers structural frame subjected to fire. The analysis was carried out for a large range of fire scenarios and was reported in detail in a recently published paper. The paper further investigates the results of this analysis to obtain the details of the collapse mechanism found. An interesting series of events leading progressively to overall collapse are discovered and described in detail. The main reason for the failure is found to be the low membrane capacity in compression of the composite steel truss and concrete deck slab floor system.



At the September 11, 2001, terrorist attacks on the New York World Trade Center (WTC) Towers, extensive structural damage, including localized collapse, occurred at several floor levels directly impacted by the aircraft. Despite this massive localized damage, each structure remained standing for approximately 1 h or 1 h 30 min. Although the damage to the beams and columns in the perimeter tube of each tower were clarified in the published ASCE/FEMA report, the damage to the floor system and inner core columns were not estimated. The purpose of this study is to determine why the towers remained standing after impact through several analytical studies, including impact analyses using a simplified model to estimate the overall damage, a rigorous finite element model to estimate the local damage, and stress analyses after some structural members are lost. The results of the stress analyses show why both buildings did not collapse immediately after impact, and WTC2 collapsed sooner than WTC1.



The World Trade Center collapse has brought attention to progressive collapse of tall buildings and the study of possible countermeasures. From the viewpoint of energy transfer, this analysis explains why the collapse could not stop by itself once began. By introducing a design parameter called collapse stability index that controls design against progressive collapse, it is found that conven- tional design of a tall building usually leads to an inherently unstable structure in the event of a progressive collapse. In a subsequent feasibility study in this paper, a heavy-duty metal-based honeycomb energy absorbing structure is proposed. Using a finite element analysis, it is demonstrated that the structure is capable of absorbing potential energy released in a tall building collapse. The added energy absorbing devices will only occupy a small percentage of the total floor space. By properly designing and installing such devices, a progressive collapse, should it happen in a tall building, may be arrested within a few floors, and hence, the building is inherently stable to the progressive collapse. The theory is also elaborated with the example of the World Trade Center collapse.



This paper presents some findings of the FEMA and SEI/ASCE sponsored studies of structural performance of New York’s World Trade Center (WTC) following the attacks of September 11, 2001, and the Murrah Building following the April 19, 1995, Oklahoma City bombing. The WTC collapses were caused not by aircraft impact alone but by the combination of impact and the resulting fire that weakened structural members and connections. On the other hand, the Murrah Building collapsed as a direct result of the blast. Although these studies call for further research in a number of areas, this report summarizes some of the lessons learned.



With the development of mechanics and computer technology, computer simulation has become an important tool in the structure analysis and design. Especially when the structures are under disaster load such as blast, penetration, impact of collapse or typhoon, it is difficult to analyze with test method, while the advantages of computer simulation method such as safe, efficient and cheap, are shown obviously in these problems. Various simulation systems are classified and discussed in this paper generally. And four practical examples are presented to demonstrate the function of simulation system. The first one is the analysis for the safety of blast-resist-doors under blast load. The second one is the study on new earth-penetration-weapons. The third one is the simulation on the collapse of World Trade Center (WTC) in New York. And the forth one is the real-time display system for bridge under typhoon. These examples are used to illuminate the advantage of computer simulation technology on disaster load conditions and emphasis some problems in the simulation.



A numerical simulation of the aircraft impact into the exterior columns of the World Trade Center (WTC) was done using LS-DYNA. For simplification, the fuselage was modeled as a thin-walled cylinder, the wings were modeled as box beams with a fuel pocket, and the engines were represented as rigid cylinders. The exterior columns of the WTC were represented as box beams. Actual masses, material properties and dimensions of the Boeing 767 aircraft and the exterior columns of the WTC were used in this analysis. It was found that about 46% of the initial kinetic energy of the aircraft was used to damage columns. The minimum impact velocity of the aircraft to just penetrate the exterior columns would be 130 m / s. It was also found that a Boeing 767 traveling at top speed would not penetrate exterior columns of the WTC if the columns were thicker than 20 mm.

add this citation to the bazant page Bazant, Z. P. (1966) Creep of Concrete in Structural Analysis (State Publishers of Technical Literature, Prague) (in Czech).