Mathematical Basis of ROOSD Propagation
The OOS Propagation model presented in sections 2.1 and 2.2 is a descriptive model of WTC1 and 2 collapse progression process. The reader does not need to read technical literature to understand the observations upon which the model is based.
Mathematical models of collapse front progression rates have been published in technical journals. The collapse progression mappings presented can also be used to review the concepts within these published papers for accuracy and application to the actual collapses of WTC1 and 2.
This section will probably be too difficult for those without much experience in calculus to understand. If so, it is not necessary to understand this subsection to grasp the OOS propagation model described earlier or other sections of the book.
But if one wishes to understand and skeptically analyze the technical literature or the actual written history of discussions on WTC1 and 2 collapse progression mechanics, it is necessary to be able to read and understand the technical literature that exists. My apologies in advance if the reader finds this section too difficult to read.
Mathematical Basis of ROOSD Propagation in WTC1 and 2
Mathematical approach to the study of ROOSD propagation as a simple 5 step process:
Step 1: GAIN AN OVERALL CONCEPTUAL AND VISUAL UNDERSTANDING OF WHAT ONE IS LOOKING AT
Step 2: RESEARCH AVAILABLE LITERATURE ON THE SUBJECT OF FLOORS IMPACTING FLOORS
Step 3: MEASURE THE COLLAPSE PROPAGATION RATE AS ACCURATELY AND COMPLETELY AS POSSIBLE
Step 4: EXAMINE A VARIETY OF PHYSICSBASED MATHEMATICAL APPROACHES TO THE COLLAPSE OF WTC1 AND 2 AND OF STACKED SYSTEMS IN GENERAL
Step 5: COMPARE MODELS IN STEP 4 TO INFORMATION IN STEPS 1  3 to see which models could match propagation behavior or teach something about it.
Each step in detail:
Step 1: GAIN AN OVERALL CONCEPTUAL AND VISUAL UNDERSTANDING OF WHAT ONE IS LOOKING AT
I'd recommend using parts 2.1 and 2.2 in my book.
There are two distinct ways to view the physics of a ROOSDtype process, as a
progressor or as an
initiator.
Obviously, this structure is composed of 3 main components:
The perimeter
The core
Flooring
The initiation of collapse, in general, can be classified as
1) Perimeter failure initiated
2) Core failure initiated
3) Floor slab failure initiated
The ROOSD process is vital to understanding the collapse progressions of WTC1 and 2, but it is also vital to understanding the initiation sequence. Progressive floor collapse initiated by failed floor slabs has always been one of the 3 basic logical possibilities for the initial failures of WTC1 and 2.
Some defining characteristics of the unique ROOSD progressions in WTC1 and 2:
The OOS progressions were confined by guide rails: Perimeter caging, combined with the outermost core columns, provide a perfectly vertical and very strong confinement of the OOS crush front.
The strength of the guide rails created a concentrated energy funnel: The crushing energy was concentrated on and funnelled toward the 208x208 ft floor space below. The unique perimeter architecture assured that crushing energy was funnelled inward to maximize the destructive power of the crush front.
The unique architecture of WTC1 and 2 created a physical condition I will call a
ROOSD basket. A ROOSD basket is essentially a containment vessel consisting of the flooring not yet destroyed and the 4 perimeter walls that act like caging. It is the dynamic and unique shape and nature of the '
ROOSD basket' containment vessel which steered and trapped the progressing crush fronts that explains so much of what is witnessed in the visual record.
Steady state progression rates were characterized by a near constant 8 floors per second crush rate with a steady state acceleration of zero.
The qualities of strong confinement, terminal velocity, and zero steady state acceleration means that
these OOS steady state progressions are highly regulated, very controllable, and very predictable processes.
Step one done correctly will lead to a recognition of a ROOSD process. If it is not done correctly every subsequent step will general and vague (see Seffen and BV, BL, BLGB for examples) or skipped completely. A researcher will then go to step 2. It is possible to see how well the actual WTC collapse propagation mechanism was recognized within the academic and engineering community simply by doing step 2.
Step 2: RESEARCH AVAILABLE LITERATURE ON THE SUBJECT OF FLOORS IMPACTING FLOORS
General Conditions of ROOSD mechanics will take the form:
for rubblized driving mass > M(1) moving at a downward velocity > V(1) , the runaway process is assured. (threshold limits to initiate ROOSD)
If driving mass M is large enough and the downward velocity V is large enough the conditions will probably escalate. (conditions in which ROOSD is sustained)
What is the minimum threshold to set off a ROOSD progression in the most vulnerable OOS floor spaces in the buildings?
One would think the NIST would have looked into this question. A review of available literature on this subject brings up this paper, published in 2007:
"Progressive Collapse of Multistory Buildings Due to Failed Floor Impact"
by A.G. Vlassis, B.A. Izzuddin, A.Y. Elghazouli and D.A. Nethercot, available at
this link.
ABSTRACT
This paper proposes a new designoriented methodology for progressive collapse assessment of floor systems within multi storey buildings subject to impact from an above failed floor. The conceptual basis of the proposed framework is that the ability of the lower floor for arresting the falling floor depends on the amount of kinetic energy transmitted from the up per floor during impact. Three principal independent stages are employed in the proposed framework, including : (a) determination of the nonlinear static response of the impacted floor system, (b) dynamic assessment using a simplified energy balance approach, and (c) ductility assessment at the maximum level of dynamic deformation attained upon impact. In order to calibrate the proposed method, the part of the kinetic energy of the impacting floor that is transferred to the impacted floor is first theoretically determined for the two extreme impact possibilities, namely fully rigid and fully plastic impact. Moreover, a series of numerical studies is carried out to further refine the accuracy of this new approach with respect to different impact scenarios, whilst the effects of detailed joint modelling and redundancy are also investigated. The application of the proposed methodology is demonstrated by means of a case study, which considers the impact response of a floor plate with in a typical multistorey steelframed composite building. Several possibilities regarding the location of the impacted floor plate, the nature of the impact event and the intensity of the gravity loads carried by the falling floor are examined. The application study illustrates the extremely onerous conditions imposed on the impacted floor resulting in an increased vulnerability to progressive collapse for structures of this type. Importantly, the likelihood of shear failure modes in addition to inadequate ductility supply under combined bending/axial actions is identified, thus establishing mthe need for further research work on the dynamic shear capacity of various connection types subject to extreme events.
The best mathematical approach to the study of ROOSD as
initiator I have found within all available literature is contained within this paper.
From the paper a deforming slab responding to impact:
From the introduction:
"It is concluded that such structures are susceptible to progressive collapse initiated by impact of a failed floor, mainly
due to insufficient ductility supply under combined bending and axial deformation modes. Moreover, the development of shear failure modes is identified, thus further increasing the observed vulnerability of the studied floor system. Since these shear modes of failure are expected to be even more pronounced when the actual dynamic rather than the static response of the impacted floor is considered, the need for further research work focussing on the shear capacity of a variety of connection types subject to extreme events is established. Finally, practical design recommendations that can improve the impact response of floor systems exposed to impact from the floor above are made."
page 24: "Hence, it can be easily concluded that in the event of failure and subsequent impact of a single floor plate onto the floor plate below, the lower impacted system, modeled using a grillagetype approximation, is highly unlikely to possess sufficient dynamic load carrying capacity to resist the imposed dynamic loads and prevent progressive collapse."
page 26: "Thus, although assessment is based on a simplified grillagetype approximation rather than a detailed slab model, the explicitness of the results leads to the conclusion that a floor system within a steelframed composite building with a typical structural configuration has limited chances to arrest impact of an upper floor. This is particularly true when the falling floor completely disintegrates and falls as debris without retaining any residual strength or spanning capability."
page 27: "To conclude, although there is room for further improvements with respect to its accuracy and applicability, the proposed assessment methodology provides an effective platform to rationally tackle the scenario of floor impact, which is one of the most prevalent progressive collapse initiation mechanisms."
Also consider the Ph.D thesis by the same author: Vlassis, A.G. (2007). Progressive Collapse Assessment of Tall Buildings, PhD Thesis, Department of Civil and Environmental Engineering, Imperial College London.
Step 3: MEASURE THE COLLAPSE PROPAGATION RATE AS ACCURATELY AND COMPLETELY AS POSSIBLE: A collapse front down the west face of WTC1 remained visible and measurable down to the lower floors. The movement shows a relatively constant velocity after quickly leveling off after collapse initiation. The velocity is approximately 25m/s, or about 8 floors per second being destroyed. To the author's knowledge this is the first time that the propagation rate of a progressive floor collapse was measured.
Mathematical approach to ROOSD as
progressor
Fundamental conditions:
for rubblized driving mass > M(1) moving at a downward velocity > V(1) , the runaway process is assured. The threshold conditions require a minimum M(1) traveling downward at velocity V(1).
The process requires progressive and runaway breakability of successive floortocolumn connections.
Examination of available literature: None
Measurements and observations of a first known documented case: WTC1 and 2 (roofline and collapse front)
A collapse front down the west face of WTC1 remained visible and measurable down to the lower floors. The movement shows a relatively constant velocity after quickly leveling off after collapse initiation. The velocity is approximately 25m/s, or about 8 floors per second being destroyed.
Initial data for linear ejecta traversal from West face of WTC 1 (Femr2, 2009):
http://femr2.ucoz.com/photo/linear_2/60217
http://femr2.ucoz.com/photo/602173 (1280x720px/74.6Kb)
Source video in H264 format (1280x720x25fps):
http://femr2.ucoz.com/ffdemhd_264.avi
Crop of West Face Ejecta:
http://www.youtube.com/watch?v=BMeTGfCZWMI
http://www.youtube.com/watch?v=2F5Tw2ITMF8
Position
^{4}:
http://femr2.ucoz.com/photo/602193 (1234x731px/67.0Kb)
Velocity:
http://femr2.ucoz.com/photo/602203 (1224x730px/87.3Kb)
What are the characteristic features of the progressor (steady state) portions of the curves? (Measured along the OOSsw crush front)
 Tendency toward terminal velocity
 A steady state acceleration of zero
What are the characteristic features of the initiator (initial movement to steady state) portions of the curves? (Measured along 2 points: roofline and crush front)
 Crush front seems to start on floor 95
 Quick take off velocity
 Short transitory phase (reaches steady state velocity and acceleration rapidly)
Step 4: EXAMINE THE VARIETY OF PHYSICSBASED MATHEMATICAL APPROACHES TO THE COLLAPSES OF WTC1 AND 2, AND OF 1DIMENSIONAL STACKED SYSTEMS COLLAPSING
1DIMENSIONAL STACKED SYSTEM MECHANICS
Here are a few different ways to set up the basic physics to the collapse propagation of a stacked system of masses in 1 dimension:
Models of Inelastic Accretion (OneWhiteEye, 2010)
Study of a Simple 1 Dimensional Stacked System (OneWhiteEye, 200910)
Explores the variety of interactions possible behind the type of 1 dimensional mechanics used by Bazant in BV by running simulations of this type of interaction using a slab and spring model in a physics game engine. Studies the effects of varying mass along the 1dimensional structure. or varying connection strength between adjacent masses up the structure, varying stretch, or varying cap mass. The study also examines the measurability of jolts along the roofline and the concept of terminal or steady state acceleration and simulations involving high velocity initial impact of the 1dimensional structure.
The simulations were found to produce a range of results, including:
mixed crush up and down
mostly crush down
exclusive crush down using only topmost floors
delayed crush down
Among the conclusions drawn from the results are:
 A discrete model, even highly idealized, is a dynamic problem with more than one degree of freedom if upper is not rigid
 The simplest representation, which conforms to typical discrete inelastic models, has TWO aggregate, generalized coordinates
 A 1D solid slab and spring model with many members, and which fails, has a propensity for crushup whether or not crush down occurs
Even in the highly idealized 1 dimensional mass interactions used to derive BV eqs 12 and 17, a variety of solutions for crush front motion other than 'crush down, then crush up' are possible.
WTC Asynchronous Impact CrushDown Model (Femr2, 2009)
Approaching the complex physics of a rubbledriven collapse:
The philosophy and attributes of a rubbledriven collapse
PHYSICSBASED MATHEMATICAL APPROACHES TO THE COLLAPSES OF WTC1 AND 2
A table of peerreviewed literature on the WTC collapse progressions has been prepared by Eastman and Cole and is available at
this link.
The table includes:
4 Bazant papers BZ(2002), BV(2007), BL(2008) and BLGB(2008), linked and reviewed
here
latest Bazant paper called: Why the Observed Motion History of World Trade Center Towers Is Smooth (2011),
linked here.
Frank Greening, Energy Transfer in the WTC Collapse (2006), linked and reviewed
here
Keith Seffen, Progressive Collapse of the World Trade Centre: a Simple Analysis (2008), linked and reviewed
here
Gordon Ross: Momentum Transfer Analysis of the Collapse of the Upper Storeys of WTC 1 linked
here
Cherepanov, Mechanics of the WTC collapse (2006), available through
this link
Thomas W. Eagar and Christopher Musso, Why Did the World Trade Center Collapse? Science, Engineering, and Speculation, JEM feature: Special Report (2002),
linked here
Usmani, Chung, Torero, HOW DID THE WTC TOWERS COLLAPSE: A NEW THEORY, Linked and reviewed
here.
The last entry in the table dates 2012. It is a paper called:
Equation of Motion Governing the Dynamics of Vertically Collapsing Buildings
by Celso P. Pesce, M.ASCE, Leonardo Casetta, and Flávia M. dos Santos. The paper is
linked here.
Some advice on how to read technical papers like these. First, locate what the author is doing in the paper and locate the key equations in the paper. Next, understand how the key equations are derived and how they are applied by the author.
Progressive collapse of the World Trade Centre: a Simple Analysis
K. A. Seffen
Page 1 to 15
Key derivations within the paper:
equation 12  Equation of motion for the collapse front
equation 16  speed of the crush front
equation 17  collapse time
Page 16 to 19: Dynamical predictions
Key dynamical predictions made by Seffen:
A steady state acceleration of g/2.
This is true of the WTC 1 and 2 buildings according to Seffen, but it is also true of many other systems. According to Seffen (p 1718),
What is Seffen is doing in the paper?
Abstract:
The collapse behavior of the World Trade Centre (WTC) towers is considered formally as a propagating instability phenomenon. The application of associated concepts enables the residual capacities of both towers after collapse to be formally estimated. This information is combined into a simplified variablemass collapse model of the overall dynamic behavior. The resulting, nonlinear governing equation of motion can be solved in closed form, to yield compact information about the overall collapse conditions.
He is deriving equations of motion of the crush front of the WTC towers.
What is the key equation in the paper?
Equation 12, which is the equation of motion of the crush front.
What does Seffen believe his eq 12 represents?
He writes his answer directly under the equation on p 13:
DERIVATION OF EQ 12
How did he model the WTC collapse in order to derive equation 12?
He modelled the WTC collapse as "a variablemass system where the mass, initially at rest, is entrained by a nonimpulsive action." He models it as a specific class of problems, all of which have steadystate accelerations that converge on g/2.
It appears that "entrained by impulsive action" would have been a better class of problems to work within. This becomes more clear when his model is compared to the BV model, the Greening model, and the stacked system mechanics of OneWhiteEye linked earlier.
APPLICATION OF EQ 12
Does Seffen make physical predictions about the propagation of the actual WTC collapse front from his paper by using eq 12?
Yes.
Pg 16, 17:
Is it possible to factcheck the dynamic predictions of Seffen using information within the OOS propagation model?
Absolutely.
What does his equation of motion predict about the acceleration of the crush front?
A steady state acceleration of g/2.
Can that prediction be tested?
Yes. Follow the 5 steps described in the mathematical approach to ROOSD propagation. The actual collapse front propagation rate is measured in step 3. Simply compare displacement, velocity and accelerations to the Seffen prediction.
Why didn't Seffen compare his prediction to actual measurements of the collapse front speed?
Because this information was not available when he wrote the paper. Researchers at that time including Bazant only had access to the first few seconds of WTC1 roofline or antenna drop measurement and the seismic records. Bazant states this clearly in BV.
Bazant seemed to have no concrete concept of a WTC collapse mode at all. Neither did Seffen. They both predicted the collapse front propagation from limited data and a limited conception of collapse mode.
Collapse fronts were later identified and the propagation of a collapse front was measured.
Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions
Zdenek P. Bažant, F.ASCE and Mathieu Verdure
I strongly recommend approaching analysis of the BV, BL, and BLGB papers through the following 6 perspectives:
1) Direct comparision between Bazant and Seffen methods and their key equations of motion (Seffen eq 12 compared to Bazant eqs 12 and 17).
2) A basic study of 1dimensional stacked system collision interactions with a variety of parameters altered
linked here. This gives one a simple, practical sense of 1dimensional multiple body interactions, like the type described in BV eqs 12 and 17, and the possible varieties of mechanical movements that can result from them.
3) Direct comparison of claims within BV to the actual collapse propagation rates which were recorded after the 20072008 Bazant papers were written.
4) Statements by Bazant in BL (the closure to BV) and BLGB demonstrating how he understood the relationship between BV eqs 12, 17 and the actual collapses of WTC1, 2.
5) Quotes by David Benson demonstrating how he understood the relationship between BV eqs 12, 17 and the actual collapses of WTC1, 2
linked here
6) Comparison of statements about WTC1 and 2 made within BV, BL, and BLGB directly with the visual record of events through the lens of the most accurate mappings of the WTC1, 2 collapse behavior (available in parts 2.1, 2.2, 2.3, and 2.4 of my book).
With the tools now available each of these separate lenses can help shed light on the accuracy and meaning of BV eqs 12 and 17. The first 3 perspectives are examined next. The last 3 perspectives will be examined in part 3.6: Bazant Misrepresentation of Collapse Progressions
What is Bazant doing in the paper?
Abstract:
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 onedimensional 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 snapthrough. The collapse, in which two phases—crushdown followed by crushup—must be distinguished, is described in each phase by a nonlinear secondorder 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 orderofmagnitude 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 realtime telemetry from sacrificial accelerometers, or by highspeed 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.
He is deriving a onedimensional continuum model for crushing front propagation of a collapsing building that meets 4 simplifying assumptions.
Key derivations within the paper:
Differential equations of progressive collapse or demolition
Equation 12
Equation 17
Equivalent versions of equations 12 and 17 are equations 20 and 21
What does Bazant believe his eq 12 represents?
Bazant states in BV:
Eqs. (12) and (17) show that Fc(z) can be evaluated from precise monitoring of motion history z(t) and y(t), provided that m(z) and lamda(z) are known. A millisecond accuracy for
z(t) or y(t) would be required. Such information can, in theory, be extracted from a highspeed camera record of the collapse. Approximate information could be extracted from a regular video of collapse, but only for the first few seconds of collapse because later all of the moving part of the WTC towers became shrouded in a cloud of dust and smoke (the visible
lower edge of the cloud of dust and debris expelled from the tower was surely not the collapse front but was moving ahead of it, by some unknown distance)."
From the BV quote above, does Bazant consider the identification of the crush front or the measurement of the displacement of the WTC crush front to be possible?
No. According to him the shroud of dust and smoke blocked moving parts of the WTC towers, like the collapse front, from view.
BV eq 12 is a second order differential equation in one variable, z. A differential equation like this is merely a relationship between the displacement, velocity, and acceleration of an object or a point on an object. From these relations one tries to find the displacement z(t).
The variable z(t) represents the displacement of what point?
In Seffen's eq 12 the variable maps the collapse front of WTC1.
In BV eq 12 there are 2 dynamic points along the collapsing building that can be measured: the crush front and the roofline. z(t) maps the crush front relative to the roofline,
DERIVATION OF EQ 12
How did he model the WTC collapse in order to derive equation 12?
The variables, parameters and assumptions used to derive BV eq 12 are all described in a single section titled, "OneDimensional Continuum Model for Crushing Front Propagation", reproduced below:
APPLICATION OF EQ 12
Does Bazant make physical predictions about the propagation of the actual WTC collapse front from his paper by using eq 12?
Yes. The BV paper is reexamined in discussions by Gourley and Szuladzinski and a closure by Bazant and Le, which is clearly an intended pointbypoint rebuttal of the Gourley and Szuladzinski discussions. Bazant makes a couple of physical predictions in BV within the quote below, but he makes quite a few more predictions about the actual WTC collapses in the closure paper.
His implications and conclusions for these equations are clearly listed on page 318:
Implications and Conclusions
1. If the total internal energy loss during the crushing of one story representing 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, collapse will continue to the next story. This is the criterion of progressive collapse trigger Eq. 5. If it is satisfied, there is no way to deny the inevitability of progressive collapse driven by gravity alone regardless of by how much the combined strength of columns of one floor may exceed the weight of the part of the tower above that floor . What matters is energy, not the strength, nor stiffness.
2. Onedimensional continuum idealization of progressive collapse is amenable to a simple analytical solution which brings to light the salient properties of the collapse process.
The key idea is not to use classical homogenization, leading to a softening stressstrain relation necessitating nonlocal fi
nite element analysis, but to formulate a continuum energetically equivalent to the snapthrough of columns.
3. Distinction must be made between crushdown and crushup phases, for which the crushing front of a moving block with accreting mass propagates into the stationary stories below, or into the moving stories above, respectively. This leads to a secondorder nonlinear differential equation for propagation of the crushing front, which is different for the crushdown phase and the subsequent crushup phase.
4. The mode and duration of collapse of WTC towers are consistent with the present model, but not much could be learned because, after the first few seconds, the motion became obstructed from view by a shroud of dust and smoke.
`
5. The present idealized model allows simple inverse analysis which can yield the crushing energy per story and other properties of the structure from a precisely recorded history
of motion during collapse. From the crushing energy, one can infer the collapse mode, e.g., singlestory or multistory buckling of columns.
6. It is proposed to monitor the precise time history of displacements in building demolitions—for example, by radio telemetry from sacrificial accelerometers, or highspeed optical
camera—and to engineer different modes of collapse to be monitored. This should provide invaluable information on the energy absorption capability of various structural systems, needed for assessing the effects of explosions, impacts,
earthquake, and terrorist acts.
Is it possible to factcheck the dynamic predictions of Bazant using information within the OOS propagation model?
Absolutely.
Limits in Bazant's understanding of WTC collapse mode and collapse features:
Why didn't Bazant compare his prediction to actual measurements of the collapse front speed?
The following quotes explain why he didn't.
BV from the abstract:
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 realtime telemetry from sacrificial accelerometers, or by highspeed 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.
From BV conclusions:
4. The mode and duration of collapse of WTC towers are consistent with the present model, but not much could be learned because, after the first few seconds, the motion became obstructed from view by a shroud of dust and smoke.
5. The present idealized model allows simple inverse analysis which can yield the crushing energy per story and other properties of the structure from a precisely recorded history
of motion during collapse. From the crushing energy, one can infer the collapse mode, e.g., singlestory or multistory buck ling of columns.
6. It is proposed to monitor the precise time history of displacements in building demolitions—for example, by radio telemetry from sacrificial accelerometers, or highspeed optical
camera—and to engineer different modes of collapse to be monitored. This should provide invaluable information on the energy absorption capability of various structural systems, needed for assessing the effects of explosions, impacts,
earthquake, and terrorist acts.
These were the limitations in WTC observation and measurement Bazant faced in 2007.
At that time it was commonly accepted that it wasn't possible to map motion of the crush fronts. It was believed that it was only possible to measure WTC1 roofline motion for only the first few seconds of the collapse and combine that information with seismic records which may indicate the moment of completion of the collapse.
In 2009 and 2010 Femr2, among others, was able to provide the very types of measurements that Bazant refers to as "invaluable information" in 2007.
Due to the 'shroud of dust and smoke', Bazant considered it impossible to either measure the collapse front or identify the collapse mode of WTC1 and 2 from the information he had available at the time.
After these papers were written these limitations were removed and much more accurate mappings became available for the first time since the collapses.
PARALLELS BETWEEN SEFFEN AND BV
There area a great number of parallels between the two papers with respect to meaning, application, and limitations. Parallels can be drawn on each topic listed below.
Meaning and application
 Purpose of paper
 Name of model
 Key equations, choice of variable and parameters
 Representation of key equations
 Derivation of key equations
 Application of key equations to predict collapse features
Limitations and mistakes
 Inability to verify predictions
 Limited understanding of WTC collapse features
 Inability to identify a specific WTC collapse mode
 Misrepresentation of the actual crushing process along the collapse front contact interface
Each parallel point is quickly reviewed below.
PURPOSE
What is Seffen doing in the paper?
Abstract:
The collapse behavior of the World Trade Centre (WTC) towers is considered formally as a propagating instability phenomenon. The application of associated concepts enables the residual capacities of both towers after collapse to be formally estimated. This information is combined into a simplified variablemass collapse model of the overall dynamic behavior. The resulting, nonlinear governing equation of motion can be solved in closed form, to yield compact information about the overall collapse conditions.
He is deriving equations of motion of the crush front of the WTC towers.
What is Bazant doing in BV?
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 onedimensional continuum model of progressive collapse is developed.
He is deriving equations of motion of the crush front and roofline of the WTC towers and to be tested on other collapsing towers.
NAME OF MODEL
Seffen: a simplified variablemass collapse model of the overall dynamic behavior
Bazant: a dynamic onedimensional continuum model of progressive collapse
KEY EQUATIONS
What is the key equation in the Seffen paper?
Equation 12, which is the equation of motion of the crush front.
What is the key equation in the Bazant paper?
Equations 12 and 17, which are the equations of motion of the crush front.
REPRESENTATION OF KEY EQUATIONS
What does Seffen believe his eq 12 represents?
The motion of the crush front
What does Bazant believe his eq 12 and eq 17 represents?
The motion of the crush front
DERIVATION OF EQ 12
How did Seffen model the WTC collapse in order to derive equation 12?
He modelled the WTC collapse as "a variablemass system where the mass, initially at rest, is entrained by a nonimpulsive action." He models it as a specific class of problems, all of which have steadystate accelerations that converge on g/2.
How did Bazant model progressive collapse in order to derive equation 12?
The same as Seffen, but the mass is entrained by impulsive action.
APPLICATION OF EQ 12 TO WTC1, 2
Does Seffen make physical predictions about the propagation of the actual WTC collapse front from his paper by using eq 12?
Yes.
APPLICATION of BV EQ 12 and 17 to WTC 1, 2
Does Bazant make any physical predictions about the WTC1, 2 collapses by applying BV eqs 12 or 17 to the WTC towers?
Yes. The BV paper is reexamined in discussions by Gourley and Szuladzinski and a closure by Bazant and Le, which is clearly an intended pointbypoint rebuttal of the Gourley and Szuladzinski discussions.
VERIFICATION OF PREDICTION
Why didn't Bazant compare his prediction to actual measurements of the collapse front speed?
He didn't consider it possible. He considered only roofline measurements to be possible and only during the first few seconds of collapse.
The mode and duration of collapse of WTC towers are consistent with the present model, but not much could be learned because, after the first few seconds, the motion became obstructed from view by a shroud of dust and smoke.
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.
Why didn't Seffen compare his prediction to actual measurements of the collapse front speed?
I don't know. Perhaps, like Bazant, he didn't know that it was possible.
LIMITATIONS AND MISTAKES
Both Seffen and Bazant are limited in their knowledge of the visual record in similar ways:
 Inability to verify predictions
 Limited understanding of WTC collapse features
 Inability to identify a specific WTC collapse mode
 Misrepresentation of the actual crushing process along the collapse front contact interface
The Bazant papers are examined in greater detail in part 3.6: Bazant Misrepresentation of Collapse Progressions
Each of the other listed papers which deal with the WTC collapse progressions can be studied in the same way. They can be examined individually or compared to any other using an identical set of questions.
PARALLELS BETWEEN ANY OF THE LISTED PAPERS
Meaning and application
 Purpose of paper
 Name of model
 Key equations, choice of variable and parameters
 Representation of key equations
 Derivation of key equations
 Application of key equations to predict collapse features
Limitations and mistakes
 Inability to verify predictions
 Limited understanding of WTC collapse features
 Inability to identify a specific WTC collapse mode
 Misrepresentation of the actual crushing process along the collapse front contact interface
What is ______ is doing in the paper?
What is the key equation in the paper?
What does ______ believe his key equation represents?
Key dynamical predictions made by _____:
DERIVATION OF KEY EQUATIONS
How did he model the WTC collapse in order to derive equation 12?
APPLICATION OF KEY EQUATIONS
Does ________ make physical predictions about the propagation of the actual WTC collapse front from his paper by using their key equation?
Is it possible to factcheck the dynamic predictions of _______ using information within the OOS propagation model?
What does his equation of motion predict about the acceleration of the crush front?
Can that prediction be tested?
Why didn't ______ compare his prediction to actual measurements of the collapse front speed?
Greening examined here
Cherepenov examined here
Ross examined here
Pesce examined here
Step 5: COMPARE MODELS IN STEP 4 TO INFORMATION IN STEPS 1  3 to see which models match the actual WTC1, 2 propagation behavior or teach something about it.
There are at least 3 ways by which the collapse models in step 4 can be examined:
1) For technical accuracy
2) For perception: As an indication of how each author understood the WTC1 and 2 collapse modes at the time they wrote their respective papers
3) As a study of propagating memes within a memeplex: as memes and memetics
We now know that at any time since 1970 accidental or intentional local detachment of only 2 floor slabs in only one portion of either of the buildings could have led to catastrophic failure of an entire building. This could have happened even without the loss of a single column.
This unique architecture had an equally unique weakness. This unique weakness led to an equally unique collapse geometry and mode. Has this fact been recognized within available professional and academic literature on the subject? We can easily verify whether it has or hadn't simply by reviewing the literature published since the collapses.
TECHNICAL AND PERCEPTUAL EXAMINATION
None of the listed authors of any model presented in step 4 seems to have a specific, concrete concept of collapse mode of WTC1 or 2 described in section 2.1 of this book. There is no evidence in the linked papers that the authors understood OOS propagation or the visual evidence to support the ROOSD collapse mode.
STUDIED AS EXAMPLES OF PROPAGATING MEMES IN A SCIENTIFIC ENVIRONMENT
This is a very interesting and revealing way to study technical literature on the WTC collapses. It reveals an underlying environment in which such limits of perception are normalized. These views become the 'norm', the dominant meme. It reveals common patterns that can be interpreted to imply consensus among authors and how that 'consensus' is obtained.
This is the approach taken by this author when studying the entirety of the written record of the WTC collapses in part 6 of this book,
6: WTC Collapse Records Studied as Meme Replication.
On to part
2.4: WTC1 Accurate Collapse History.
Created on 09/23/2014 03:22 PM by admin
Updated on 08/16/2015 07:46 AM by admin

