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Some Misunderstandings Related to WTC Collapse Analysis
Abstract and Figures
This article elaborates on variables associated with the collapse of the North Tower of the World Trade Center. The previously published quantifications of inertia, column capacity, and the assumptions related to the beginning of downward motion, are examined and corrected. The reasons for false conclusions reached in several previous analyses are presented.
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... Some authors [6] have challenged in 2013, using a detailed analysis, a series of papers by Bažant et al. who pretended to explain rationally the dominant narrative 1 regarding the World Trade Center skyscrapers collapses, which attributes them to fires weakening their structure. More recently (2016), others [7] using only simple mechanics have successfully shown this narrative to be incompatible with physics laws. ...
... It is very difficult to estimate the cooling contribution of this water, since it would require the knowledge of both the volumes and the temperature differences; an article submitted to the 23rd American Chemical Society National Meeting (Orlando, FL, April 7-11, 2002) stated [14] that for the first 10 days after the attacks, roughly 30 million gallons (≈ 114.10 3 m 3 ) water percolated through the debris, based on the pumping records. From this volume roughly 1 million gallon fell on the site (the so-called "bathtub" area) because of rain, 3 million gallons were hosed in the fire-fighting efforts 6 3.2 Estimating energy released from Ground Zero: the Fermi approach and consequently 26 million gallons, i.e. the main part, came from leaks in the "bathtub", which was proven to be seriously damaged. ...
... Furthermore, we must keep in mind that in most cases, when expressing chemical energy per unit mass this mass does not include all the reactants, since energy comes from an exothermic redox reaction and that the oxidizing agent is oxygen contained in the atmosphere, which is considered as free and unlimited. For instance, the combustion of 6 The well-known "ton oil equivalent" or toe equals 42 GJ, hence the energy per unit mass of oil is 4.2 × 10 7 J.kg −1 . 7 It is of common use to express energy released by an explosion in "TNT equivalent"; a ton of TNT equals by convention 4.184 GJ, hence the energy per unit mass of TNT is 4.184 × 10 6 J.kg −1 . ...
Are first and second laws of thermodynamics still valid? If so, then we should reconsider some very well-known events... and maybe the way we perform science.
Available online here:
https://hal.archives-ouvertes.fr/hal-02004696v3
... Taking these considerations seriously, a value of W = 1000 MJ up to W = 1300 MJ or maybe even more might be considered as realistic if the collapse mechanism is is based on the three-hinge buckling scenario. Note that in [SSJ13] a value of even 2700 MJ is proposed. ...
... Clearly, this is an overestimation of that height. It has already been pointed out in [SSJ13] that the mass of the falling block has been overestimated in [BaZh02,BaVe07,BLGB08]. The wrong height assumption is probably the origin of this error, because the values match the mass distribution functions given in [BaVe07, Fig. 6]. ...
A model of a gravity-driven collapse of a tall building has been proposed by Ba\v{z}ant et al. We apply this model to the collapse of the North Tower of the World Trade Center to determine the energy dissipation per storey during the collapse. Our findings are (at most) 250\,MJ during the first 4.6 sec. In the time interval between 4.6 and 7.7 sec after collapse initiation we find an additional energy dissipation per storey of 2500\,MJ. Because the steel columns increase in strength towards the ground this value corresponds to a value of 2000\,MJ for the storeys in the aircraft impact zone. After 7.7 sec the value reduces again. These results have two possible interpretations: (1) If due to the building design (column strength, shape etc.) the energy dissipation per storey cannot reach the high values which we observed, then the collapse cannot be described by the gravity-driven collapse model. (2) If the collapse is described correctly by the gravity-driven collapse model, then then we fond direct evidence that the collapse mechanism did not follow the same pattern during the whole of the collapse. The possible amount of energy dissipation was reduced by an order of magnitude during two long time time intervals. In both cases there is no a priori reason to justify the sometimes expressed belief that the collapse was inevitable even after the falling top section had gained a significant amount of momentum. In fact, if the amount of energy dissipation had stayed only little longer on the high level, then a gravity-driven collapse would have arrested. Note that (1) implies that if in principle the gravity-driven collapse model describes gravity-driven collapses of tall buildings, then the collapse was not gravity-driven.
... Tải trọng nổ lên công trình được minh họa trong Hình 1 [1]. Khi một vụ nổ ở gần hoặc tiếp xúc với kết cấu bê tông, trên bề mặt đối diện với vụ nổ, bê tông chịu nén và có thể phá hoại theo nhiều dạng khác nhau tùy vào đương lượng nổ, hoặc sinh ra hố lõm [2], hoặc dẫn đến mất hoàn toàn khả năng chịu lực của kết cấu dẫn đến công trình bị sụp đổ [3,4]. Các mảnh vụn bê tông sinh ra sau khi nổ sẽ có tốc độ cao có thể gây ra thương vong và thiệt hại về người và tài sản. ...
Bài báo này trình bày kết quả nghiên cứu thực nghiệm khả năng chịu tác động tải trọng nổ của bê tông chất lượng siêu cao (Ultra-High Performance Concrete - UHPC). Bê tông UHPC sử dụng trong nghiên cứu được chế tạo sử dụng các vật liệu sẵn có ở Việt Nam. Các tấm bê tông UHPC và bê tông thường có cùng kích thước (chiều dài 1000 mm, chiều rộng 800 mm và chiều dày 120 mm) đã được chế tạo và thí nghiệm nổ để so sánh. Tải trọng nổ sử dụng là thuốc nổ nhũ tương. Sự hư hại và phá hủy ở mặt trên, mặt dưới của các mẫu thí nghiệm và thành phần hạt của các mãnh vỡ bắn ra dưới tác động của tải trọng nổ được phân tích và so sánh giữa bê tông UHPC và bê tông thường. Từ khóa: bê tông chất lượng siêu cao; bê tông thường; tải trọng nổ; thực nghiệm.
... It has already been pointed out in [SSJ13] that M = 58 · 10 6 kg is too big and a value of M = 33 · 10 6 kg has been used based on [NIST1-6D, [Schn17a] a mass density of 0.6 · 10 6 kg /m is used for the top 30 storeys. This value is based on a total mass of 288,000 t of the tower, which is the value that has been estimated in [Uric07]. ...
The Simple Collapse Model of Ba\v{z}ant and Zhou is evaluated for a progressive floor collapse of a tall building. A sequence of energy estimates indexed by the collapsing floors is derived. Each of the estimates gives a sufficient condition to arrest the collapse at a given floor. The first estimate of this sequence has been stated by Ba\v{z}ant and Zhou and has been repeatedly cited later on. However, this estimate is not optimal in the sense that the following estimates give a weaker condition to arrest the collapse.
... For high rise buildings in modern city, failure of one or several key load-carrying members may trigger the disproportionate progressive collapse with catastrophic casualties and property loss [6,7]. The failure mechanism behind the progressive collapse phenomena has been under an ongoing discussion [8,9]. ...
Unlike ductile behaviour under static loads, a reinforced concrete structure can respond in a brittle manner with highly localised damage like concrete spalling, cratering and reinforcement rupturing under close-in or contact explosions. High speed fragmentation resulting from concrete spall may cause severe casualties and injuries. It is therefore important to have a better understanding of the concrete spall phenomena and fragments distribution. In the present study, contact explosion tests were carried out on concrete slabs to observe the concrete crater and spall damage. Seven slabs including two control specimens made of normal strength concrete (NRC) and five ultra-high performance concrete (UHPC) slabs are tested. The superior blast resistance capacity of UHPC slabs is verified through comparison against NRC slabs. The influence of longitudinal reinforcement spacing and slab depth on the spall resistance of UHPC slabs is investigated. Predictions through available empirical methods are made and compared with the test observations. The accuracy of these empirical methods is discussed. All fragments resulting from the contact blast tests are collected and analysed through sieve analysis. It is found that Weibull distribution can be used to model the fragments size distribution of NRC slabs while Log-normal distribution better models the fragments size distribution of UHPC slabs.
Executive Summary What follows is an attempt to define a research agenda for the ongoing study of 9/11 and related events. The aim of this agenda is to deepen our understanding of 9/11 and its consequences and to develop a broader understanding of the ways in which power is exercised in the contemporary world. This paper has been developed from the research agenda recently published by the International Center for 9/11 Justice and is intended as a living document that will be regularly updated in light of feedback and as significant research developments emerge. Understanding the 9/11 event • The official investigations upon which the official 9/11 narrative rests-the 9/11 Commission Report and the National Institute of Standards and Technology reports on the destruction of WTC 1, 2 and 7-are all demonstrably flawed. • The most likely explanation for the complete destruction of WTC 1, 2 and 7 is that of demolition planned prior to 9/11. • Multiple inconsistencies afflict the official narrative regarding the alleged hijackers, including with respect to their alleged movements and religiosity. Continued research into the history, behavior and activities of the alleged hijackers is warranted. • Multiple anomalies with respect to phone calls reportedly made by people onboard flights AA11, AA77, UA175 and UA93 indicate that they were not authentic. • It is highly unlikely the hijacked aircraft could have been flown by the alleged individuals in the manner claimed by US authorities. Further investigation is necessary into the supposed training and competencies of the alleged hijackers, the complexity of the flight maneuvers and their feasibility for the alleged hijackers, and the possible role of remote guidance technology. Journal of 9/11 Studies August 2024 2 • Developing a plausible and evidence-based account of what actually transpired with respect to the four airliners is a research priority. • Multiple inconsistences regarding key military and political officials, compelling evidence of insider trading prior to 9/11, multiple training exercises, and the 2001 anthrax attacks, all provide substantial circumstantial evidence that 9/11 was planned and executed by persons connected to the US government. • Continued research into 9/11-related financial crimes, military training exercises, and politically exploited acts of bioterrorism, or threats thereof, is necessary. • Further research is necessary regarding the possible involvement of other state and non-state actors including the roles of Saudi, UAE, Kuwaiti, British, and Israeli officials, corporations, and persons. • The most plausible proximal explanation for 9/11 is that a belligerent and expansionist neoconservative political block instigated and then exploited the event in order to initiate a series of major wars in the international system. Wider geopolitical and domestic consequences of 9/11 and deep events • The 'structural deep event' (SDE) and 'state crimes against democracy' (SCAD) concepts provide a basis for conceptually grounded and rigorous academic analysis of both the 9/11 event and its wider consequences. • Existing academic research on the 'global war on terror' that ensued 9/11, and the multiple conflicts fought under that banner, is severely limited because of its failure to properly understand what happened on 9/11 and its propensity to engage in insufficiently critical 'problem solving' or 'administrative' research. • Ensuing 'regime change' wars in countries and regions including, but not limited to, Afghanistan, Iraq, North Africa and Syria, as well as geopolitical developments with respect to Russia and Ukraine and now Israel-Palestine, require critical examination through the SDE and SCAD lenses and, alongside this, identification of strategic deceptions and propaganda. • At the domestic level, the 9/11 event led to a sharp reduction in civil liberties across liberal democracies and further concentration of political power. Sustained critical research is necessary into the rise of surveillance society, suppression of public dissent (and freedom of expression), co-optation of corporate media, corruption of legal structures, and the use of 'lower-level' false flags across democracies. Journal of 9/11 Studies August 2024 3 • Systematic and conceptually grounded comparative research into other SDEs and SCADs, such as the JFK assassination and the COVID-19 event, is now essential in order to accurately describe, understand and explain the extent to which democratic politics has been overturned by political and economic elites pursuing a politics of fear. • Attention needs to be given to developing structures and mechanisms that can avert SDEs and SCADS whilst strengthening the ability of citizens and social movements to counter concentrated elite power.
Ba\v{z}ant et al. have proposed a model for a gravity-driven collapse of a tall building that collapses after column failure in a single storey. Therein the collapsing building is described by three distinct sections. The top section which consists of the part above the first failing storey, the middle section which is pushed from above by the top section and consists of compacted building material, and the part of the building below which is still undamaged. The middle part is gaining height during the collapse, the lower section is loosing height. The resulting equation of motion is called Crush-Down equation. In a first approach Ba\v{z}ant and Verdure used a constant velocity profile for the middle section, namely the top section and the middle section are assumed to have the same velocity. In a second approach by Ba\v{z}ant, Le, Greening and Benson this assumption is dropped and the model is slightly modified. However, their modifications are based on unphysical assumptions and lead to an erroneous version of the Crush-Down equation. We give a detailed account of how to implement a non-trivial velocity profile for the middle section and thereby derive a more accurate version of the Crush-Down equation, but as it turns out, the difference between the solutions of the modified and unmodified Crush-Down equation is very small under realistic assumptions.
The circumstances leading to the collapse of the WTC Towers were described in numerous publications before but quantification of possible mechanisms published so far remains very limited. The basic observation is that columns of a 110-story building were weakened, over a relatively short segment of an upper part of the structure, to a degree where they were unable to support the building above them. As the upper part began to descend, successive buckling of columns caused flattening of the stories below. The process was presumably driven by the action of gravity until a complete destruction of the building. This article concentrates on progressive collapse of the core of the building. Several mechanisms are considered and quantified, to assess whether they offered a plausible explanation. One of the criteria used was whether the potential energy available was sufficient to cause the demolition in the assumed manner. The calculated duration of the event versus the available observation is regarded as the main criterion to qualify the postulated collapse mode. The details presented here are in reference to the North Tower. Some relationships presented here are also useful for a progressive collapse analysis of reinforced concrete structures.
A crucial element of structural and continuum mechanics, stability theory has limitless applications in civil, mechanical, aerospace, naval and nuclear engineering. This text of unparalleled scope presents a comprehensive exposition of the principles and applications of stability analysis. It has been proven as a text for introductory courses and various advanced courses for graduate students. It is also prized as an exhaustive reference for engineers and researchers. The authors' focus on understanding of the basic principles rather than excessive detailed solutions, and their treatment of each subject proceed from simple examples to general concepts and rigorous formulations. All the results are derived using as simple mathematics as possible. Numerous examples are given and 700 exercise problems help in attaining a firm grasp of this central aspect of solid mechanics. The book is an unabridged republication of the 1991 edition by Oxford University Press and the 2003 edition by Dover, updated with 18 pages of end notes. © 2010 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
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.
Until recently, the progression and time of collapse of structures has not been a prima ry objective of the structural engineering profession. However, such events are likely to be of ma jor interest in high rise building situations where a fire-initiated failure takes place, or where a controlled demolition is to be im plemented. The paper attempts to shed light on this problem and to develop velocity profiles during a collapse event, also potentially important, especially in built-up areas. Because of the complex nature of both the structural system and th e process of collapse, analysis methods need to be simplistic, which are yet realistic and are easily unde rstood by designers and code writers of the nature and cause of a building collapse. The objective of this paper is to shed light on this problem by e mploying the most basic equations of Newton's laws of motion. A formulation of the problem of a building frame of N stor ies, subjected only to gravity loading is postulated that involves an analysis employing a generic one-dime nsional discrete model of progressive collapse. The supporting elements within its nth story are suddenly degraded by whatever cause, with the velocity and time steps calculated. Several design scenarios are presented for the columns with prescribed ener gy dissipation properties ascertained at any level, thus allowing the motion to be determined in acc ordance with the known equations of energy and momentum. An example 10-story structure is proposed to illustrate the me thod, in which the column designs, utilizing square hollow sections and W-shapes, are governed by a combination of dead, l ive and wind loads. For the 6 designs postulated involving tubular columns alone, and with sequential removal of columns in each of t he 10 stories, it was found that progressive collapse was arrested in 90% for such hypothetical scenari os. For the other 10%, global collapse times exceeded that of free-fall by 57 to 228%.
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.