This section was written to provide a simpler step-by-step method for spotting incorrect statements made in papers published in the Journal of Engineering Mechanics by Zdenek Bazant and coauthors. Due to their technical nature the papers will be too difficult to read for many people who are interested in the written record of the WTC collapses. Therefore I provide direct quotes from the papers followed by simple questions which can be answered by most anyone just by looking at the quotes and spotting the answer.

It is my hope that this approach can allow anyone who wishes to see just how absurd some of the things Bazant wrote and the Journal of Engineering Mechanics uncritically published about the World Trade Center collapses without the veneer of scientific sounding jargon.


For the reader's reference the Bazant papers on the WTC towers written from 2007 to the present are listed and linked:



Part 1: Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions

Zdenek P. Bazant and Mathieu Verdure (BV), published in 2007, the paper linked here


Part 2: Closure to 'Mechanics of Progressive Collapse: Learning from World Trade
Center and Building Demolitions'� by Zdenek P. Bažant and Mathieu Verdure

Zdenek P. Bazant and Jia-Liang Le (BL), published in 2007,

March 2007, Vol. 133, No. 3, pp. 308�"319.
DOI: 10.1061/(ASCE)0733-9399(2007)133:3(308)
The paper is linked here





The third paper: What Did and Did not Cause Collapse of WTC Twin Towers in New York

Zdenek P. Bazant, Jia-Liang Le, Frank R. Greening and David B. Benson (BGLB) is linked here


The most recent Bazant paper on the WTC collapses is called: Why the Observed Motion History of World Trade Center Towers Is Smooth (2011), linked here.






>>>>>>>>>>>





I will first focus on the paper 'Closure to 'Mechanics of Progressive Collapse' by Bazant and Le. Jia-Liang Le was a graduate student at Northwestern University when this paper was written, so the comments within this paper are basically those of Bazant, a professor at Northwestern University at that time.


I will formulate 44 separate and highly specific questions on this paper. The specific questions are carefully formulated to help any impartial and honest reader to see mistakes made within the paper.








I'll begin by reviewing the outline of this paper. The paper is written as an answer to 2 critical responses to the collapse mechanics as written in the original paper by Bazant and Verdure. The critical inquiries to which Bazant and graduate student Le are responding were presented by people commonly known as 'truthers'. The inquiries are presented by James Gourley and Gregory Szuladzinski. All quotes are directly from the paper.




Gregory Szuladzinski begins:

The paper presents a very interesting concept of an accidental demolition, whereby heavy damage sustained by an intermediate
story of a building leads to the upper part of the structure crushing the lower one in a sequence of story collapse steps. The focus of
the paper is on the treatment of equations of motion and very few numbers are quoted; that is, numbers that relate to the physical properties of the structure discussed, namely the World Trade Center (WTC) towers. The following comments are intended to fill that gap as well as to ascertain the likelihood of the applicability of this concept.

This discussion describes flaws in the modeling and analysis of the World Trade Center collapses by Ba�ant and Verdure in their paper entitled "Mechanics of Progressive Collapse: Learning
from World Trade Center and Building Demolitions." First, the paper's two-phased approach to the collapse analysis will be considered. The writers will demonstrate that a two-phase collapse analysis is not representative of reality, because it disregards well-accepted laws of physics and therefore is not instructive. Second, the original paper's summary of the findings of the NIST report will be analyzed.

This discussion describes flaws in the modeling and analysis of the World Trade Center collapses by Ba�ant and Verdure in their paper entitled "Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions."

Discussion by James R. Gourley

The interdisciplinary interests of Gourley, a chemical engineer with a doctorate in jurisprudence, are appreciated. Although none
of the discusser's criticisms is scientifically correct, his discussion provides a welcome opportunity to dispel doubts recently voiced
by some in the community outside structural mechanics and engineering. It also provides an opportunity to rebut a previous similar discussion widely circulated on the Internet, co-authored by S. E. Jones, Associate Professor of Physics at Brigham Young University and a cold fusion specialist. For the sake of clarity, this closure is organized into the points listed subsequently and rebutted one by one.

1. Newton's Third Law

2. Are the Internal Forces in Upper and Lower Parts of
Tower Equal?

3. Localization of Energy Dissipation into Crushing Front

4. Can Crush-Up Proceed Simultaneously with Crush Down?

5. Why Can Crush-Up Not Begin Later?

6. Variation or Mass and Column Size along Tower Height

7. Were the Columns in the Stories above Aircraft Impact
Hot Enough to Fail?

8. Steel Temperature and NIST Report

Discussion by G. Szuladzinski

The interest of Szuladzinski, a specialist in homeland security, is appreciated. After close scrutiny, however, his calculations are found to be incorrect, for reasons explained in the following.

1. Load-Displacement Curve of Columns and Energy Absorption Capacity

2. Does Excess of over Gravity Load Imply Arrest of Collapse?

3. Is the Equation of Motion for Calculating the Duration of Fall Correct?

4. Could Stress Waves Ahead of Crushing Front Destroy the Tower?

"Discussion by James R. Gourley
3. Localization of Energy Dissipation into Crushing Front:
In the discusser's opinion: the hypothesis that "the energy is dissipated at the crushing front implies that the blocks in Fig. 2 may be treated as rigid, i.e., the deformations of the blocks away from the crushing front may be neglected." This is a fundamental misunderstanding. Of course, blocks C and A are not rigid and elastic waves do propagate into them."



But the wave velocity, given by v = ?Et / ? where Et = tangential e modulus of steel in the loaded columns and ? = mass density, tends to zero as soon as the plastic or racturing response is triggered, because in that case, Et ? 0. Therefore, as explained in courses on stress waves, no wave attaining the material strength can penetrate beyond the crushing (or plastic) front. Only harmless elastic waves can. Propagation of the crushing front is not a wave-propagation phenomenon. Destruction of many stories at the rate corresponding to the elastic wave speed, which would appear as simultaneous, is impossible. This is why the collapse is called progressive. Blocks C and A can, of course, deform. Yet, contrary to the discusser's claim, they may be treated in calculations as rigid because their elastic deformations are about 1,000 times smaller than the deformations at the crushing front."

"4. Can Crush-Up Proceed Simultaneously with Crush Down?It can, but only briefly at the beginning of collapse, as mentioned in the paper."

"Statements such as "the columns supporting the lower floors . . . were thicker, sturdier, and more massive,"
although true, do not support the conclusion that "the upper floors (i.e., the floors comprising Part C) would be more likely than the lower floors to deform and yield during collapse"� (deform they could, of course, but only a little, i.e., elastically)."

"More-detailed calculations than those included in their paper were made by Bažant and Verdure to address this question. On the basis of a simple estimate of energy corresponding to the area between the load-deflection curve of columns and the gravity force for crush down or crush up, it was concluded at the onset that the latter area is much larger, making crush-up impossible."

We have now carried out accurate calculations, which rigorously justify this conclusion and may be summarized as follows.

Consider that there are two crushing fronts, one propagating upward into the falling block, and the other down-ward. Denote v1 , v2 = current velocities of the downward and upward crushing fronts (positive if downward); x(t) , z(t)= coordinates of the mass points at these fronts before the collapse began (Lagrangian oordinates); and q(t) = current coordinate of the tower top. All the coordinates are measured from the initial tower top downward. After the collapse of the first critical story, the falling upper Part C with the compacted Part B impacts the stationary lower Part A. During that impact, the total momentum and the total energy must both be conserved. These conditions yield two algebraic equations

During impact, ? = 0.2 for the North Tower and 0.205 for the South Tower. For the North or South Tower: m0 = 54.18· 106 or 112.80· 106 kg, m1 = 2.60· 106 or 2.68· 106 kg, m2 = 3.87· 106 or 3.98· 106 kg, and ms = .627· 106 kg for both. For a fall through the height of the critical story, by solving Eq. (2) of Bazant et al. 2007, one obtains the crush-front velocity v0 = 8.5 m / s for the North Tower and 8.97 m / s for the South Tower. The solution of Eqs. (1) and (2) yields the following velocities after impact: v1 = 6.43 or 6.80 m / s, v2 = 4.70 or 4.94 m / s, and vcu = 2.23 or 2.25 m / s for the North or South Tower. These data represent the initial values for the differential equations of motion of the upper Part C and of the compacted layer B. If Lagrangian coordinates x(t) and z(t) of the crush-down and crush-up fronts are used, these equations can easily be shown to have the following forms:

"These two simultaneous differential equations have been converted to four first-order differential equations and solved
numerically by the Runge-Kutta method. The solution has been found to be almost identical to the solution presented in the paper, which was obtained under the simplifying assumption that the crush-up does not start until after the crush down is finished."

"The reason for the difference being negligible is that the condition of simultaneous crush-up, x ? 0, is violated
very early, at a moment at which the height of the first overlying story is reduced by about 1%."

"This finding further means that the replacement of the load-deflection curve in Fig. 3 of the paper by the energetically equivalent Maxwell line that corresponds to a uniform resisting force F? cannot be sufficiently accurate to study the beginning of two-way crush.)"

Therefore, a solution more accurate than that in the paper has been obtained on the basis of Eqs. (3) and (4). In that solution, the variation of the crushing force F? within the story was taken into account, as shown by the actual calculated resistance force labeled F(u) in Fig. 3 of the paper, by the force labeled F(z) on top of Fig. 4 of the paper, and by the resistance curves for the crushing of subsequent stories shown in Fig. 5 of the paper. The precise curve F(u) was calculated from Eq. 8 of Bazant and Zhou (2002). Very small time steps, necessary to resolve the changes of velocity and acceleration during the collapse of one story, have been used in this calculation. Fig. 1 shows the calculated evolution of displacement and velocity during the collapse of the first overlying story in two-way crush. The result is that the crush-up stops (i.e., (x) )_ drops to zero? when the first overlying story is squashed by the distance of only about 1.0% of its original height for the North Tower, and only by about 0.7% for the South Tower (these values are about 11 or 8 times greater than the elastic limit of column deformation)."

"Why is the distance smaller for the South Tower even though the falling upper part is much more massive? That is because the initial crush-up velocity is similar for both towers, whereas the columns are much stronger (in proportion to the weight carried)."

"The load-displacement diagram of the overlying story is qualitatively similar to the curve with unloading rebound sketched in Fig. (4c) of the paper and accurately plotted without rebound in Fig. 3 of the paper. The results of accurate computations are shown by the displacement and velocity evolutions in Fig. 1."

"So it must be concluded that the simplifying hypothesis of one-way crushing (i.e., of absence of simultaneous crush-up),
made in the original paper, was perfectly justified and caused only an imperceptible difference in the results."

"The crush-up simultaneous with the crush down is found to have advanced into the overlying story by only 37 mm for the North Tower
and 26 mm for the South Tower."

"This means that the initial crush-up phase terminates when the axial displacement of columns is only about 10 times larger than their maximum elastic deformation. Hence, simplifying the analysis by neglecting the initial two-way crushing phase was correct and accurate."

"5. Why Can Crush-Up Not Begin Later? The discusser further states that "it is difficult to imagine, again from a basic physical standpoint, how the possibility of the occurrence of crush-up would diminish as the collapse progressed."�

"Yet the discusser could have imagined it easily, even without calculations, if he considered the free-body equilibrium diagram
of compacted layer B, as in Fig. 2(f) of the paper."

"After including the inertia force, it immediately follows from this diagram that the normal force in the supposed crush up front acting upward onto Part C is

"The discussers' statement that "the yield and deformation strength of . . . Part C would be very similar to the yield and
deformation strength of . . . the lower structure"� shows a misunderstanding of the mechanics of failure. Aside from the fact that "deformation strength"� is a meaningless term (deformation depends on the load but has nothing to do with strength), this statement is irrelevant to what the discussers try to assert. It is the normal force in the upper Part C that is much smaller, not necessarily the strength (or load capacity) of Part C per se."

"Force F? acting on Part C upward can easily be calculated from the dynamic equilibrium of Part C (see Fig. 2g), and it is found that F? never exceeds the column crushing force of the overlying story. This confirms again that the crush-up cannot restart until the compacted layer hits the ground."

"6. Variation or Mass and Column Size along Tower Height:

This variation was accurately taken into account by Bazant et al. (2007). Those who do not attempt to calculate might be surprised that the effects of this variation on the history of motion and on the collapse duration are rather small. Intuitively, the main reason is that, as good design requires, the cross-section areas of columns increase (in multistory steps, of course) roughly in proportion to the mass of the overlying
structure. For this reason, the effect of column size approximately compensates for the effect of the columns’ mass."

Closing Comments Although everyone is certainly entitled to express his or her opinion on any issue of concern, interested critics should realize that,
to help discern the truth about an engineering problem such as the WTC collapse, it is necessary to become acquainted with the relevant material from an appropriate textbook on structural mechanics. Otherwise critics run the risk of misleading and wrongly influencing the public with incorrect information."

...a two-phase collapse analysis is not representative of reality, because it disregards well-accepted laws of physics and therefore is not instructive.

"On another matter, we ordinarily start with the simplest hypothesis and stik with it until some evidence shows the hypothesis must be modified. In the case of the top portion, the simplest is that it stayed on top most of the way down; say with the roof at around floor 25. Until someone develops some actual evidence to the contrary, I'll stick with that rather than unending speculation and new simulations of the resulting hypothesis."

"Assuming homogeneity, Bazaant & Le show thaqt zone C is almost industrucible. That's mechincs for you. The sturcture obviiously was not homogeneous and you have, in other threads, shown some distruction along the west and north walls. In of itself that mass loss is not important, but it does mean the floor trusses in those areas have been weakened. So an average of about 4--6 stories above floor 98 do not come close to satisfying the homogeneity condition. Fine. consider then that zone C is from floor, say, 102 up. To keep the equation simple, assume crush-down begins from there. As I mentiioned in this thread yesterday, this works well enough to match the additional observations by OneWhiteEye.
"

"Zone C simply disappears into the obscuring dusts. Not sufficient reason to assume it is being crushed first. If sufficiently close to homogeneous, then from Bazant & Le it is not being crushed at all."

"OneWhiteEye --- I've been thorugh all this before. Homogenization is fine when the tilt is taken into account; crushing proceeded on 3+ floors simultaneaously which is surely better represented by homogenization that by stepwise floor-by-floor model. However, both give essentially ythe same results; shagster actually went to the effort of running his own version of Greening's ideas using minifloors to demonstrate this; although, after some study, this is analytically obvious.

"Major_Tom --- B&V have four simplifying assumptions which lead to the crush-down ODE. These assumptions are reasonable for WTC 1 but not, by video timing, for WTC 2 after a few seconds. In the case of WTC 2 it is clear from the ABC video of the collpase proceeding down to the Mariott rooftop level that the collapse was proceeding much too slowly; the inference is that the top section broke apart and fell off rather early on.

But as BLGB indicates, this could not have happened to WTC 1 or the timing would be off."

"Major_Tom ---
Do you doubt Newton's Laws?
Do you doubt http://en.wikipedia.org/wiki/D'Alembert's_principle?
Do you doubt the applicability of the four simplifying assumptions in B&V?
If not, the conclusion of little early crush-up of zone C follows.
Further, the timing studies in BLGB show that most of zone C mass must have stayed on top most of the way down."

"No sign of zone C falling aprat as long as it can be seen. Unlike the case of WTC 2."

"OneWhiteEye --- I'm not the one with any doubts about the matter: there can be no significant early crush-up."

"Read Bazant & Le to understand why zone C can be consired to be essentially rigid during crush-down.
I offered to start a thread about how to build a table-top demonstrator that will allow one to see that,
indeed, zone C remains intact during crush-down. I didn't bother when I realized that nobody here would bother to actually build it, test it, and in the process dicover that the application of Newton's laws and
d'Alembert's principle in Bazant & Verdure agrees with reality."

"See Bazant & Le for a further exposition of why early crush-up is very small. It is, I admit, a difficult
point. But it is similar to a house riding down a landslide for which many examples have occurred in southern California."

"Albert Einstein once said something to the effect that a model should be as simple as possible, but no simplier. The B&V crush-down equation meets that criterion as long as one only considers measurements taken on the antenna mast. With your careful observations of perimeter wall sections breaking off at and above floor 98 and OneWhiteeEye's observation earlier on this thread to the effect that this led to a inhomogeneity in the structure, I then, as reported earlier on this thread, in effect moved zone C up to start at floor 102. That fits the antenna tower measurements and also (approximately) the additional observation that OneWhiteEye posted earlier on this thread, regarding the SW corner of WTC 1."

"So, the simplest possible model for WTC 1 collapse works very well even though I now conclude that some 4+ floors of early crush-up occurred due to the inhomogeneity introduced by missing perimeter wall sections. But not more early crushup than that. Once those were crushed, the homogeneity is re-introduced so that Bazant & Le then applies."

"OneWhiteEye --- B&L show little inital crush-up, not none at all. Since it is so small, the argument is that the crush-down only in B&V is a valid approximation."

"More complex equations simply are not required. Parsimony suggests the B&V crush-down equation with vertical avalanche resisting force together with starting the crushing front around floor 102, being good enough for the data in hand, is indeed good enough."

"The west and north walls peeled away sufficiently rapidly that deebris tended to move west and north near the spire. Similarly, but to a lesser extent, to south and east. There actually wasn't a gaping hole, just less density and in particular no structural steel to break connections."

"As for the core punching through the roof, I conjecture this occurred when the upper mechanical floors and up to the roof encountered the greater resistance offered around floors 75--79, about 30 stories (about 110 meters) down. No air escaping through such a puncture will be separately observable in any of the photos, IMO."

"Better to call the section cushed, rather than compressed, as it is inelastic. It did contain, for the most part, the core columns; only a few were bypassed."