Bazant's crush-down/crush-up model

[pgimeno]

BV abstract pg 308: "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. [...]"

You leave out the fundamental part (in blue):

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. [...]
​

Bolding mine. What he is saying here, when the relevant part of the quote is restored, is that in order to find the parameters needed for his model, he's trying to use videos. No hint of applying his model to the real building here, quite the contrary: he's trying to use the real building to find parameters for his model.

He is obviously suggesting that the 1-D stick model presented in this paper can be applied to real buildings. He is clearly arguing that the crush up and crush down equations (eqs 12 and 17) and the concept of crush down, then crush up can be applied to real 3-D buildings.

You are somewhat sloppy in the use of the words "obviously" and "clearly".

BV introduction pg 308, column 2: “A simplified one-dimensional analytical
solution of the collapse front propagation will be presented. It
will be shown how this solution can be used to determine the
energy absorption capability of individual stories if the motion
history is precisely recorded. Because of the shroud of dust and
smoke, these histories can be identified from the videos of the
collapsing WTC towers only for the first few seconds of collapse,
and so little can be learned in this regard from that collapse.
However, monitoring of tall building demolitions, which represent
one kind of progressive collapse, could provide such
histories. Development of a simple theory amenable to inverse
analysis of these histories is the key. It would permit extracting
valuable information on the energy absorption capability of various
types of structural systems in various collapse modes, and is,
therefore, the main objective of this paper.”

There is no doubt that he beleives these equations and the concept of crush down, then crush up represent the behavior of real buildings.

On the contrary, there is no doubt that he knows he's using a simplification. See the highlighted text. And there's no mention of crush direction whatsoever.

He suggests the equations can be used to extract valuable information for real buildings. He states that application to real buildings is the main objective of the paper.

And what prevents him from doing exactly that? He knows the limitations of his model and he can compensate for those limitations wherever they are relevant. The information provided by his model can be useful in many real world cases. Parameters like the "energy absorption capability of various types of structural systems in various collapse modes" mentioned in the text are not that affected by the use of a simplified model and can be validly extracted.

The rest of your citations fall under the same two mistakes: either he suggests using the real world to find parameters for his model, or he uses his model to draw valid conclusions from it, with full knowledge of its limitations.

Since you seem to have neglected to read an introduction on models and their limitations, let me give you a small example for the sake of comparison.

The real world is very often far too complex as to be modeled with perfect accuracy. Take the example of the Earth. You can use a sphere as a model of the Earth, if you know its limitations.

For example, such a model allows a pretty accurate estimation of the sunrise and sunset times. It can be expressed with formulas and it can be used to obtain data, like mapping coordinates relative to satellites or to other planets or to other points on the surface, up to a certain precision.

However, that model has limitations. It can't be used to determine the inclination of the surface with respect to the radius at any given point, because the model itself fixes it at zero despite the fact that the real Earth is more accurately described as a spheroid. It can't be used to obtain a very accurate estimation of the radius for each point of the surface either, because besides its spheroid shape, there are mountains and valleys and depressions. That's asking too much from the model, and pretending to do so is incurring in a fallacy.

You have not shown a single instance in which Bazant is making such a mistake as asking too much from his model. You mention the crush direction all the time, but he is not describing that as a reality in any of your citations, despite your hammering. Translated to the Earth example, it's as if you claim all the time that Bazant is using a model that lacks any inclination of the surface with respect to the radius and therefore is wrong, while he is actually drawing valid conclusions about the sunrise and sunset times. So what? The inclination problems (crush direction) don't invalidate his findings about sunrise time, etc. (energy absorption capability, etc.)

Finally, this thread was about crush direction, not Bazant's (non) application of it to the real world.

 

[Major_Tom]

2 examples from Bazant and Le of Dr Bazant applying results from the 1-D stick model presented in BV to WTC1 and 2 literally:
Link to the paper:

(BL=BVReply)Closure to “Mechanics of Progressive Collapse: Learning from World Trade
Center and Building Demolitions” by Zdenek P. Bažant and Mathieu Verdure

Zdenek P. Bažant and Jia-Liang Le

http://www.civil.northwestern.edu/pe... Replies.pdf


BL, Pg 917, column 2:
"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."

Please see the linked paper for the equations. The 1-D stick model equations of motion are calculated using 2 generalized coordinates instead of 1 as in BV. Now "upper block " roofline and the crush front are treated as independent variables and resulting equations of motion are rederived. Bazant uses the new results to further justify that the concept of crush down, then crush up is real and applicable to WTC1 and 2 as he explains next:

"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."

He freely applies predictions of the 1-D stick model like crush down, then crush up to the predicted behavior of WTC1 and 2. Observe what he concludes:

"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."

Does he honestly believe that the crush front can only advance millimeters into the upper portions of both towers due to column strength in the upper portion? What does he mean when he claims a 37mm advancement of the crush front for WTC1 upward?

He clearly applies the concept of crush down, then crush up and the BV crush up and crush down equations of motion to WTC1 and 2 literally.


The next example, a tribute to gullibility, BL, pg 919 column 1:

"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. 2f 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
Fc = Fc − delta(F),
deltaF = mcg − mcv˙ B = mcg − v˙ B
where Fc=normal force at the crush-down front; mc=mass of
the compacted zone B; vB= [(1−gamma(z))z˙+z˙ /2] =average velocity of zone B; and v˙ B=its acceleration. The acceleration
v˙ B rapidly decreases because of mass accretion of zone B and
becomes much smaller than g, converging to g/3 near the
end of crush down Bažant et al. 2007. This is one reason
that Fc is much larger than Fc . After the collapse of a few
stories, mass mc becomes enormous. This is a further reason
that the normal force Fc in the supposed crush-up front becomes
much smaller than Fc in the crush-down front. When
the compacted zone B hits the ground, vB suddenly drops to
zero, the force difference delta(F) suddenly disappears, and then
the crush-up phase can begin.
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 Fc acting on Part C upward can easily
be calculated from the dynamic equilibrium of Part C see
Fig. 2g, and it is found that Fc 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."

This may be the best single example of how gullible people can be when confronted by a scientific sounding idea from an authority figure. In plain english he is saying that crush down, then crush up must occur in real buildings because the upper columns are sufficiently strong to not buckle upwards while riding down on a magical cushion of debris. He said the same thing in the previous point 4.

Many of Bazant's readers still believe that some imaginary "upper block" in WTC1 rode a layer of rubble down to the earth, itself relatively undamaged. According to Bazant's most recent publications he still believes it himself.

He has obviously been applying his 1-D model in which the concept of crush down, then crush up is considered real and up, down movement occurs through successive column buckling to WTC1 quite literally. Many of his readers in the 9/11 debate have also without realizing that the argument rests on the strength of the "upper block" columns, as Bazant claims twice in this paper.

Notice the irony in his closing remarks, BL pg 921 column 1:

"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."

You mean incorrect information about how crush down, then crush up from a 1-D stick model in which damage is propagated upwards and downwards through column buckling can be applied to real buildings, especially WTC1 and 2? That kind of incorrect information? This forum provides proof that many people still believe the concept of crush down, then crush up can be applied to real buildings without understanding on what the argument originally rests.

 

[Major_Tom]

More examples of Bazant applying the 1-D stick model equations derived in BV and the concept of crush down, then crush up to WTC1 and 2, this time in Bazant, Le, Greening and Benson

Link to the paper: (BLGB)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

http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/476 WTC collapse.pdf


From BLGB, pg 894,5: “Generalization of Differential Equation
of Progressive Collapse

The gravity-driven progressive collapse of a tower consists of two
phases—the crush-down, followed by crush-up (Fig. 2 bottom)—
each of which is governed by a different differential equation
(Bažant and Verdure 2007, 312–313). During the crush-down
phase, the falling upper part of the tower (C in Fig. 2 bottom),
having a compacted layer of debris at its bottom (zone B), crushes
the lower part (zone A) with negligible damage to itself. During
the crush-up, the moving upper part C of the tower is crushed at
the bottom by the compacted debris B resting on the ground.
The fact that the crush-up of entire stories cannot occur simultaneously
with the crush-down is demonstrated by the condition
of the dynamic equilibrium of compacted layer B, along with an
estimate of the inertia force of this layer due to vertical deceleration
or acceleration; [see Eq. (10) and Fig. 2(f) of Bažant and
Verdure (2007)]. This previous demonstration, however, was only
approximate since it did not take into account the variation of
crushing forces Fc and Fc ‘ during the collapse of a story. An accurate
analysis of simultaneous (deterministic) crush-up and
crush-down is reported in Bažant and Le (2008) and is reviewed
in the Appendix, where the differential equations and the initial
conditions for a two-way crush are formulated. It is found that,
immediately after the first critical story collapses, crush fronts
will propagate both downward and upward. However, the
crush-up front will advance into the overlying story by only about
1% of its original height h and then stop. Consequently, the effect
of the initial two-way crush is imperceptible and the original hypothesis
that the crush-down and crush-up cannot occur simultaneously
is almost exact.”

He once again clearly states that he believes the concept of crush down, then crush up from the 1-D stick model based on successive upward and downward column buckling is applicable to WTC1 and 2. By doing so he makes the most absurd claims about how crush up is arrested by the strength of the upper columns, like:


BLGB, pg 945 column 1: “The aforementioned distance of initial crush-up would be
larger if the column cross sections changed discontinuously right
below or right above the first collapsed story. However, this does
not appear to be the case. A sudden change of column cross section
encountered after the crush-down front has advanced by
more than a few stories would not produce a crush-up because the
compacted layer B has already become quite massive and acquired
a significant kinetic energy.”

Just in case the reader cannot see that Bazant is clearly applying the 1-D model with the concept of crush down, then crush up to WTC1 and 2 literally, he draws you little pictures with captions describing what he believes to be the stages of the actual collapses to remove all doubt:

Fig. 2. (Top)Scenario of collapse; (bottom) crush-down and crush-up phases of collapse; (A) intact stationary (lower) part; (B) dense layer of crushed debris; and (C) intact moving (upper) part

Bazant is projecting qualities of the 1-D stick model and the concept of crush down, then crush up to WTC1 and 2. He believes that the concept of crush down, then crush up can be literally applied to WTC1 and 2 and shows you a drawing of the towers doing just that in two distinct phases. Isn’t is clear that he really believes crush down happened before crush up for WTC1?

Bazant proceeds to derive an improved version of the original crush up and crush down equations of motion (BV eqs 12 and 17) which are expressed as BLGB eqs 1 and 2 on pg 895 column 1. He obviously applies these equations to WTC1 and 2, claiming they match the actual roofline drop data extracted from video by (no kidding) holding a ruler up to a computer screen. He maps the data point and compares it to the crush down equations of the 1-D stick model in figure 7 below:

He is obviously using the results of the 1-D stick model crush down equation based on the concept of crush down, then crush up to map the WTC1 roofline to confirm his belief that these 1-D concepts are justifiably applicable to WTC1 and to try to convince the reader likewise.


From BGLB, Appendix. Can Crush-Up Proceed Simultaneously
with Crush-Down?, pg 906 columns 1:

"Fig. 9 shows the calculated evolution of velocity in the twoway
crush. As seen, the crush-up stops (i.e. (x˙) drops to zero)
when the first overlying story is squashed by only 1% of its original
height for the North Tower, and only 0.7% for the South
Tower (these values are, respectively, about 11 or eight times
greater than the elastic limit of column deformation). The difference
between the South and North Towers is very small, in spite
of the fact that the upper falling part of the South Tower was
much more massive. This is mainly because the columns at the
critical story of the South Tower are much stronger, roughly in
proportion to the overlying mass. Since the initial crush-up phase
terminates at a very small axial deformation, it must be concluded
that the simplifying hypothesis of one-way crushing is perfectly
justified and causes only an imperceptible difference in results
(Bažant and Le 2008).
If random fluctuation of column strength is taken into account,
the crush-up resisting force Fc ‘ in the first overlying story may be
lower or higher than indicated by the foregoing deterministic
analysis. If it is lower, the crush-up will penetrate deeper. But
even for the maximum imaginable standard deviation of the average
column strength in a story, the crush-up will be arrested
before it penetrates the full story height."

He is obviously projecting the qualities of the 1-D stick model to WTC1 and 2 to make absurd claims about WTC1 and 2 like crush up will be arrested before penetrating a single story.

Gullibility check: Do you honestly believe that crush up will be arrested before it reaches 1 story height? What is the claim based on? Answer: In the 1-D stick model upward force is insufficient to buckle columns upwards.
In reality, do you expect the "upper blocks" to be protected against crush-up due to it's column strength? Of course not, but that is what Bazant is claiming. Figure 9:

Isn’t it painfully obvious that Bazant is applying the 1-D stick model to actual WTC1 and 2 behavior, absurdly believing in the applicability of the concept of crush down, then crush up and the resulting equations of motion to the WTC towers?

 

[pgimeno]

2 examples from Bazant and Le of Dr Bazant applying results from the 1-D stick model presented in BV to WTC1 and 2 literally:
Link to the paper:

(BL=BVReply)Closure to “Mechanics of Progressive Collapse: Learning from World Trade
Center and Building Demolitions” by Zdenek P. Bažant and Mathieu Verdure

Zdenek P. Bažant and Jia-Liang Le

http://www.civil.northwestern.edu/pe... Replies.pdf

Unsurprisingly, your link doesn't work. Dude, you really need to learn how to use the quote function and corresponding button. And I don't mean only in this forum.

BL, Pg 917, column 2:
"4. Can Crush-Up Proceed Simultaneously with Crush
Down? It can, but only briefly at the beginning of collapse,
as mentioned in the paper. [...]

Let's add context to that quotation. It's a response to a criticism raised by chemical engineer James R. Gourley. Here's an excerpt of Gourley's words:

The physical reality for each tower, which any instructive collapse analysis must take into account, can be summarized as follows: for a particular tower, the upper part (Part C), lower section (Part A), and the crushing section (Part B) were all very similar to one another from a materials, engineering, and construction standpoint. Therefore, the only reasonable qualitative assumption to make when analyzing the ability of each section of the building to deform when the upper part (Part C) impacts the lower structure is that the plastic deformation and yield strengths, (as well as any other energy absorptive properties, such as elastic strain values) of the components of the lower structure (Part B and Part A) are roughly equivalent to the deformation and yield strengths of the components of the upper Part C. This qualitative assumption is required regardless of the quantitative assumptions that are made regarding the magnitude of such deformation and yield strengths or the mode of deformation used in the collapse analysis. Furthermore, this unavoidable qualitative assumption leads to the conclusion that when Part C impacts the lower structure Part B or Part A , the damage or deformation caused by the impact must be shared roughly equally between Part C and the lower structure. The justification for this conclusion lies in the application of Newton's Third Law.
​

From this, it should be clear that Gourley is criticizing the principle behind Bazant's crush direction model, and that is what the closure addresses. It is still a theoretical point of view, no matter how you try to push the contrary. Again, Bazant is not claiming anywhere that the crush-up did not happen in reality in either WTC.

I agree with you, however, in the irony in Bazant's closing comments. Your very attempts to discredit him are the very proof of how true they are.

Plus, this thread is still for discussion about crush direction physics, not about Bazant's (non) application of it to the real world.

 

[Major_Tom]

Pgimeno, my posts are about crush direction and the 1-D concept that crush down runs to completion before crush up can begin.

It is based on an illusion created by taking a 1-D toy model too seriously just because an authority figure told you it can be applied to the towers.

If you fact-check the argument you will see it depends on an absurd statement that the upper columns receive insufficient upward force to buckle upwards.

A neat math trick in 1-D but totally meaningless with real 3-D buildings.

 

[pgimeno]

As for your latter message, AGAIN, do read something about models, their utility and their limits!

The comparison of the roof drop speed with his model is something that might or might not be subject to the limits of the model. That may well be the very reason why such comparison is done (my guess is that it is), and it is found to match well within the uncertainty limits of the measurements. The rational conclusion is that the fact of using that simplified model does not affect its applicability to initial fall speed. It's a reassurance of the quality of the model, and that is STILL independent of the differences in actual crush-up behavior of the top, which your quote STILL does not show that Bazant is taking as happening in reality in the WTC.

Notice how, in the part that you've left out, the paper goes to a certain length to correct for the tilt that his model does not account for, in order to extract the data you have posted. The lack of tilt is a well-known limitation which is compensated for before making any calculations.

Now, please, you can go on if you wish with your self-debunking in the OOS thread which was mostly dedicated to your smearing of Bazant and NIST, but stop derailing this one.

 

[pgimeno]

It is based on an illusion created by taking a 1-D toy model too seriously just because an authority figure told you it can be applied to the towers.

It is NOT a toy model. It is a valid simplified model. It has limitations and these are known. Really, read on models and their limits and stop your derailing.

If you fact-check the argument you will see it depends on an absurd statement that the upper columns receive insufficient upward force to buckle upwards.

The model depends on it. The conclusions they draw from it don't. The comparison with reality is a validation of the applicability of the model to the real world. The simplifying assumptions do not change certain properties of the model, which can then be used to draw conclusions and make predictions. You fail to understand that again and again, and base your attack solely on such misunderstanding.

 

[ozeco41]

Pgimeno, my posts are about crush direction and the 1-D concept that crush down runs to completion before crush up can begin.

It is based on an illusion created by taking a 1-D toy model too seriously just because an authority figure told you it can be applied to the towers.

If you fact-check the argument you will see it depends on an absurd statement that the upper columns receive insufficient upward force to buckle upwards.

A neat math trick in 1-D but totally meaningless with real 3-D buildings.

The confusion/overlap between "What actually happened with WTC1 and WTC2" AND Bazants Model with its actual limitations certainly causes confusion in threads like this.

Setting aside whether Bazant's model is correct within whatever limits he places on it and thinking of what actually happened with the WTC Twin Towers:

This statement "...crush down runs to completion before crush up can begin..." is/was not true for WTC1 and WTC2.

This statement "...taking a 1-D toy model too seriously just because an authority figure [presented it]..." is obviously true in a lot of debunker claims because they take the model too far in application to WTC collapses and into territory where it does not apply. Certainly going outside the limitations which (I think) are clearly identifiable whether or not Bazant has clearly identified same OR whether he stays within the limits he claims.

This statement "...the upper columns receive insufficient upward force to buckle upwards..." is true but only because there was probably near zero force on those columns in the way that the WTC towers collapsed WHETHER OR NOT the claim may be true in a more general case. The lack of force upwards on those columns is not a consequence of momentum or energy transfer limits as commonly explained. It is simply because few if any upper columns had lower columns aligned with them and transferring any significant load.

 

[pgimeno]

I have what I think is a related question to the topic.

In an axial impact, the affected floor's columns will fail if enough energy is applied.

My question is, why only in that floor and not in any other? Is there something that prevents propagation of the impact received by the column to the columns below, so that the weakest one fails?

There must be, as proved by e.g. vérinage, but I fail to see it. Understanding the reason might clarify an aspect related to Bazant's collapse direction.

 

[cmcaulif]

I have what I think is a related question to the topic.

In an axial impact, the affected floor's columns will fail if enough energy is applied.

My question is, why only in that floor and not in any other? Is there something that prevents propagation of the impact received by the column to the columns below, so that the weakest one fails?

There must be, as proved by e.g. vérinage, but I fail to see it. Understanding the reason might clarify an aspect related to Bazant's collapse direction.

The assumption is not only do the floors away from the collapse front not fail, but they also do not dissipate energy. The assumption is reasonable if the only plastic straining occurring in the collapse front, and not outside of it. Bazant makes this assumption on the basis that columns will buckle and form plastic hinges which will fracture, preventing a wave of plastic deformation from being transmitted to floors neighboring the collapse front.

Essentially Bazant treats the collapse as a stability problem rather than a wave propagation problem.

 

[grmcdorman]

As I understand it (IANAE - I Am Not An Engineer) the elements that would transfer the force fail first.

Pretty obvious if you think about it, actually: if the elements could propagate a force sufficient to break the next element down, then - provided they are similar - they are propagating a force above their own failure threshold.

 

[pgimeno]

Crush direction figured out?

So, roughly it's just that the transmission speed of the wave is not fast enough, and the material yields before transmitting most of it. I think it must be related to the speed of sound in steel, which is about 6,000 m/s, and that is not fast enough... wow. Kind of shocking.

Anyway, I think that the answers to this question have produced results. I've found a key part that makes me understand how a crush-down only can be justified. It comes from an explanation I was given in another forum:

It is the yielding of the material itself. It cannot transmit more force than the peak of the load displacement curve.

(source). I also think it matches this sentence from Ryan Mackey, but I didn't fully understand its implications before:

The peak stress in the upper block is the failure stress of the floor at the collision interface. It simply cannot transmit any higher stress than that.

Ok, I think I am now in the position to elaborate a theoretical scenario that justifies crush-down only based on the assumptions.

The starting point of my assumed scenario is two sections of a building, a top section which is hanging and a bottom section fixed to the ground. No columns in between; the first impact is assumed to be floor slab against floor slab. The top is assumed to be able to produce a progressive collapse, so I don't care much about height, weight, etc.

The top is dropped until it impacts the bottom. What will happen on the first impact?

Wait, there's a little detail, in strict application of the above principle. A column cannot transmit more force than its yield force. But that principle must apply in both directions for each of the sections. That is, the action force that makes the column yield, is accompanied by a reaction force that is exerted against the other column.

There can be negligible differences, e.g. the weight of a column (it must be able to support itself) plus the weight it supports are forces that will only be acting on the bottom part, thus in a perfect setup the stress on the bottom will be slightly greater than that on the top. But let's not be that picky. I'll assume that both floors are crushed at the same time.

So, right after impact we have a top with one less floor and a bottom with one less floor, and between them there's a layer of rubble consisting of two floors, which is initially equidistant to both.

But gravity pushes only in one direction. The rubble layer is attracted by gravity and starts to accelerate downwards. The top plus the rubble will push down on the bottom. Assuming that the rubble arrives first (due to gravity, otherwise they would arrive at the same time), the bottom will be able to arrest the impact of two floors, but then comes the top.

What happens now is the key. The bottom columns are supporting their own weight and the corresponding floor, plus a two floor rubble layer. That's three times the weight that we neglected to consider before. We can no longer neglect the stress that those three floors exert on the bottom. Now the top impacts. The stress on the bottom columns is that of the top columns, plus that of the rubble. They can't transmit back more reaction force than their yield strength, and the rubble layer keeps pushing down due to gravity and thus subtracting from that force, so the force on the top will now be clearly less (and no longer negligibly so) than the yield stress that broke the bottom columns. The top will resist.

If it's still considered negligible, repeat a second time. That means two top floors crushed. The amount of rubble is now 4 floors, plus the floor the bottom columns are already holding, makes 5 floors inducing stress on the bottom structure. Now there's little excuse to say it's negligible.

Also, the rubble layer will soon gain enough mass as to be able to crush the bottom by itself without the need for the top.

Now I may have screwed up somewhere. If so, I'd like to know where.

Plus, I'd like to know if this explanation holds any relationship with the way Bazant explained it. For what I remember, Bazant always started at a point where there was already a rubble layer in between.

 

[cmcaulif]

So, roughly it's just that the transmission speed of the wave is not fast enough, and the material yields before transmitting most of it. I think it must be related to the speed of sound in steel, which is about 6,000 m/s, and that is not fast enough... wow. Kind of shocking.
.

There will be elastic waves that travel out of the collapse front. Bazant is ignoring these waves because they don't dissipate nearly as much energy as waves resulting in plastic straining. An elastic-plastic wave has an elastic 'precursor' wave which travels at the speed of sound, ahead of the plastic wave (which is slower).

Second, yielding doesn't prevent the plastic wave from traveling out of the collapse front, but rather buckling does.

Here is an interesting paper on the interaction of buckling and plastic wave propagation in axial impact. The columns modeled are stockier than the WTC columns, but the results are illustrative none the less.

Some important conclusions are that at lower strain rates the response is buckling dominated, while at very high strain rates (corresponding to blast loading) the response is dominated by the compressive plastic wave, resulting in higher energy dissipation than in the prior case.

The paper also shows the importance of strain hardening as well as strain rate hardening in the energy dissipated, which Bazant does not account for.

 

[ozeco41]

...Here is an interesting paper on the interaction of buckling and plastic wave propagation in axial impact. The columns modeled are stockier than the WTC columns, but the results are illustrative none the less....

"illustrative"???

Illustrative of what?

The results may be "illustrative" of some theoretical situation BUT they have little if anything to do with the actual collapse mechanisms of the WTC Twin Towers in their global collapse stages. So the reference to the columns being "stockier" than WTC risks inferring that there is some valid analogy. There isn't.

So can we keep it explicitly clear that this is a theoretical exercise and has no relevance to WTC on 9/11?

 

[pgimeno]

Some important conclusions are that at lower strain rates the response is buckling dominated, while at very high strain rates (corresponding to blast loading) the response is dominated by the compressive plastic wave, resulting in higher energy dissipation than in the prior case.

Is it correct to assume that such high strain rates could be safely dismissed by Bazant in his limiting case to arrive to the conclusions?

 

[cmcaulif]

"illustrative"???

Illustrative of what?

The results may be "illustrative" of some theoretical situation BUT they have little if anything to do with the actual collapse mechanisms of the WTC Twin Towers in their global collapse stages. So the reference to the columns being "stockier" than WTC risks inferring that there is some valid analogy. There isn't.

So can we keep it explicitly clear that this is a theoretical exercise and has no relevance to WTC on 9/11?

We are discussing Bazant's model, which is a theoretical exercise. In this model, as you mention, the actual failure mechanism of the WTC towers is not considered. On the other hand, Bazant was trying to create a scenario which could represent an upper bound of the towers' resistance. Whether or not he is correct in that depends on the validity of his assumptions. In particular, the assumption that there is no energy dissipated outside of the collapse front. In other words, dissipation is localized to the front.

Again, this is reasonable if there is plastic straining in the collapse front only. Plastic straining could occur outside of the collapse front if a plastic wave were allowed to propagate through the impacted column to the column below. Bazant claims this is not possible because the impacted column will buckle plastically and form hinges which fracture, preventing the transmission of the plastic wave. The paper shows that, depending on the column slenderness and the strain rate, buckling can be delayed significantly, resulting in a response dominated by the propagation of the axial plastic wave, i.e. a scenario in which the rationale for the localization assumption is not valid. On the other hand, in loading regimes closer to the tower collapses early on, the response is dominated by buckling, which is the scenario Bazant's assumption relies on. Since the columns studied were less slender that those in the towers, I would expect also, that these, under the axial impact proposed by Bazant, would buckle similarly. For this reason I think the localization assumption is valid.

 

[Major_Tom]

Complete crush down before any significant crush up makes perfect sense in a 1-D stick model based on a buckle down and/or buckle up propagation mechanism.

I think that Bazant correctly shows that there is unsufficient upward force acting through debris buffer zone "B" to buckle the upper columns upward. It is not hard to see how the upward force in this case can hardly exceed a threshhold value necessary to make the first upward buckle.

So for the record I don't have much problem with his 1-D stick model.


My complaint is when people apply concepts like crush down, then crush up and the magical debris buffer zone "B" to 3-D blocks, real buildings and especially the WTC towers.

I think we all agree on that and the only argument left is what can we consider "crossing the line" between 1-D sticks and 3-D blocks, real buildings and the WTC towers in particular. (To be addressed on the "applicability' thread?)

Seems reasonable?

 

[Major_Tom]

Ozeco post #41: "So the reference to the columns being "stockier" than WTC risks inferring that there is some valid analogy."

He walks that fine line many times in the papers BL and BLGB. I think he crosses the line, especially in BL (=BVReply).

In BV, Bazant is deriving the crush up, crush down equations of motion (BV eqs 12 and 17) in a general sense, only briefly mentioning the WTC towers.

In BL, out of the blue he seems to be freely applying the concept of crush down, then crush up to the WTC towers, with no clear indication he is correctly recognizing that the crush down and crush up equations only apply to a 1-D stick model and not to the towers.

But maybe it is best to explain the particulars in the "applicability' thread.

 

[beachnut]

Ozeco post #41: "So the reference to the columns being "stockier" than WTC risks inferring that there is some valid analogy."

He walks that fine line many times in the papers BL and BLGB. I think he crosses the line, especially in BL (=BVReply).

In BV, Bazant is deriving the crush up, crush down equations of motion (BV eqs 12 and 17) in a general sense, only briefly mentioning the WTC towers.

In BL, out of the blue he seems to be freely applying the concept of crush down, then crush up to the WTC towers, with no clear indication he is correctly recognizing that the crush down and crush up equations only apply to a 1-D stick model and not to the towers.

But maybe it is best to explain the particulars in the "applicability' thread.

This is nonsense. Put this in a letter and send it to the Journal where Bazant published his work. They need to see some delusions and nonsense. Why do you insist on exposing your lack of engineering skills?
Get an engineer to help you.

Your post is nonsense. You keep proving you don't understand models; I know your don't understand models, you have made your point many times, move on!

 

[ozeco41]

Ozeco post #41: "So the reference to the columns being "stockier" than WTC risks inferring that there is some valid analogy."

He walks that fine line many times in the papers BL and BLGB. I think he crosses the line, especially in BL (=BVReply).

In BV, Bazant is deriving the crush up, crush down equations of motion (BV eqs 12 and 17) in a general sense, only briefly mentioning the WTC towers.

In BL, out of the blue he seems to be freely applying the concept of crush down, then crush up to the WTC towers, with no clear indication he is correctly recognizing that the crush down and crush up equations only apply to a 1-D stick model and not to the towers.

But maybe it is best to explain the particulars in the "applicability' thread.

I have partly explained my position in the other thread. Basically I detest digging through academic style papers with masses of complex and impressive looking mathematics when the foundation assumption on which the maths rest are wrong. Nor do I have the academic's interest in writing a rebuttal paper and publishing same via peer reviewed processes.

Contrary to the often wrongly implied situation here the validity of Bazant or any other persons published academic work does not rest on the fact that it is published peer reviewed. It rests on the more fundamental issue of is it right or is it wrong. And, if I happen to identify errors in peer reviewed work, the validity of my opposing claims does not depend on peer review publication. It rests primarily on whether I am right or wrong. Peer review and publication is only one measure and not the only one.

That said I have no interest in pursuing how close to the line of inapplicability Bazant goes. His overall model is IMO globally valid in that it shows that there was energy to spare for the global collapses of WTC1 and WTC2. Sadly that "proof" is trivially irrelevant and I see no reason to use it as support for a proof of "no demolition".

Why?

Because the towers collapsed in a global collapse which progressed all the way down AND there was no demolition. So the real world example says "enough energy" and doing sums, no matter how impressive, adds nothing to our knowledge.

Now go below that "global truism" and look at how people have tried to apply Bazant in detail and sooner or later you come to the claim that there was not enough upward force to buckle top block columns.

Wow! Let's look at that claim. True or false? Trivial or significant? Taking the easy case of the top block outer columns. They did not fall axially on the lower part of those columns. Because the initial collapse had the top block falling. So the top block columns were falling past the lower block columns at that point in time. What mechanism other than pure chance to put those broken column halves back in apposition to their lower sections? (And how could "pure chance" achieve that?)

From there those top block columns were either falling inside or outside their lower parts. And only "falling inside" has any possibility of exerting a force on those columns. And in that situation, whether exerted through intervening rubble OR direct floor contact the main force applied to the columns is derived from the strength of the next impacted lower floor. And no single floor could resist with a force of column buckling magnitude.

And I got that far without resort to obfuscating complex maths. Does the applicability or otherwise of Bazant's "crush up/crush down" change that claim?

And, yes, I can argue the position more rigorously.