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Old 22nd August 2010, 02:35 PM   #1
pgimeno
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Bazant's crush-down/crush-up model

I'm trying to understand Bazant's crush-down/crush-up model, which I know is widely accepted. I am not questioning it, I merely want to understand it, and hopefully the explanation will be useful for someone else too.

In order to explain where my doubts arise, I propose the following thought experiment.

Consider a "WTC top" composed of the top 12 WTC1 floors, just floating freely in space. No gravity there.

Consider also a "WTC bottom" made of the bottom 98 floors of WTC1, attached to a rigid, indestructible platform which has some rockets mounted. These rockets are assumed to be able to put a thrust to the "WTC bottom + platform" mount and are regulated so that once started, in the platform an accelerometer always measures 9.81 m/sē. The "WTC bottom" is aligned with the "WTC top" just like the real building was, and is separated from it just the distance of two floors, which IIRC was Bazant's assumption.

Here's a simple diagram of the setup:



At a given point of time, the rockets are started. From within a camera in the platform, the crushing should look just like the collapse predicted by Bazant (this thought experiment is assumed to be set up exactly like in Bazant's model, including the column-to-column collisions).

What I'm doing with this setup is merely to change the reference frame with respect to Bazant's description, defining the "WTC top" as having zero velocity. If it has a theoretical pitfall which causes it not to be equivalent to Bazant's model, I'd like to know.

But if it is, can someone please explain why the "WTC top" is not significantly crushed by the impact and successive force exerted on it until it reaches the platform, just as the "WTC bottom" is? That's the part that I'm not getting, and I believe it's the part that most people have trouble with.

Obviously, in this experiment the "WTC top" will accelerate at the first impact, reaching about 1/3 of g as it crushes the "WTC bottom", since the top's downward acceleration was about 2/3 of g.

The only explanation I can find for the top not being crushed is that the crush front will "lag" with respect to the accelerating platform's reference frame, thus its global acceleration will be less than g, possibly allowing for the "WTC top" to resist the force, because it's less force given that the acceleration of the crush front is reduced due to that "lag". Is that the cause? If so, why doesn't the same happen to the "WTC bottom"?
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Old 22nd August 2010, 02:47 PM   #2
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Interesting way to frame the problem. There is a slight difference between your schematic and the real problem, however -- it's only equivalent if you assume the rockets are firing for a long time, and there's no remaining dynamic response in the intact tower, before you yank away the supports between the lower and upper portions leaving the upper portion to be at constant velocity while the rest continues to accelerate. But it's a minor detail.

There is a second important detail: Your rockets will have to throttle down as the collapse continues. They're providing a constant acceleration only on the intact portion of the lower block, i.e. a lower force as the mass of that block decreases with time. You have it drawn correctly, specifying a constant acceleration rather than a constant force, but it's a bit counter-intuitive for rocket engines.

Ideally you will get the same kind of "crush down / crush up" behavior. What happens is that at impact, the accelerating lower block hits the nonaccelerating (and thus slower) upper block, damage occurs to both. But the remainder of the upper block has been accelerated, being pushed by the mass below, at a rate lower than 1 g. And -- this is the key point -- the rubble interface layer between is at the same velocity as the upper block, and is not accelerating at 1 g.

As the lower structure continues to accelerate through the rubble layer and upper block, it suffers increasingly more damage at the top of the lower block. It has the same force pushing up, but it hits an increasingly larger mass and thus is opposed by more and more inertia.

The upper block, on the other hand, never feels any worse acceleration than it did at initial contact. At least, that is, until it hits the rocket platform itself, which we have declared to be ideal and indestructible, at which point the upper block begins to be destroyed in the "crush down" phase.

So, one more time: As the collapse progresses, the rocket-accelerated lower block is being driven at constant acceleration into a growing, larger and larger mass. Correspondingly, the resisting force goes up, and the lower block continues to suffer damage. The upper block, however, becomes a smaller and smaller fraction of the total impacted mass, and the force upon it actually decreases -- it suffers its worst damage at first contact, and afterwards will tend to survive.

Have you read Dr. Bazant's papers? In particular, have you read where he clarified this issue to Frank Gourley?

Last edited by R.Mackey; 22nd August 2010 at 02:57 PM. Reason: Added need for throttle-down and summary
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Old 22nd August 2010, 03:19 PM   #3
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Even with the ideal and simplified Bazantian abstracted model, this portion stands out at this point...

Originally Posted by R.Mackey
[WTC Top] suffers its worst damage at first contact, and afterwards will tend to survive
To me this clearly implies simultaneous crush-up and crush-down at all times, even if you accept one side crushing more than t'other.

Of course these simplified abstractions don't directly apply to real world behaviour and are, as is made clear, a limiting case. Real world behaviour of, say, WTC 1 was clearly quite different.

ETA...
Originally Posted by R.Mackey
at which point the upper block begins to be destroyed in the "crush down" phase.
Did you mean "Crush up" ?

Last edited by femr2; 22nd August 2010 at 03:22 PM.
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Old 22nd August 2010, 03:31 PM   #4
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Originally Posted by pgimeno View Post
Consider a "WTC top" composed of the top 12 WTC1 floors, just floating freely in space. No gravity there...

What I'm doing with this setup is merely to change the reference frame with respect to Bazant's description, defining the "WTC top" as having zero velocity. If it has a theoretical pitfall which causes it not to be equivalent to Bazant's model, I'd like to know.
Well, if it's floating in space then it will ride with the acceleration upward of the lower rocket block indefinitely. If it's hitting against some immutable resistance or force then yes, it will be crushed between the lower rocket block and the force. So your intuition about it is correct, and you are not to be blamed for having "trouble" with it or "not getting" it.
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Old 22nd August 2010, 04:23 PM   #5
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Thanks for your answer. "Putting the E in the JREF", as I've seen some say

Originally Posted by R.Mackey View Post
Interesting way to frame the problem. There is a slight difference between your schematic and the real problem, however -- it's only equivalent if you assume the rockets are firing for a long time, and there's no remaining dynamic response in the intact tower, before you yank away the supports between the lower and upper portions leaving the upper portion to be at constant velocity while the rest continues to accelerate. But it's a minor detail.

There is a second important detail: Your rockets will have to throttle down as the collapse continues. They're providing a constant acceleration only on the intact portion of the lower block, i.e. a lower force as the mass of that block decreases with time. You have it drawn correctly, specifying a constant acceleration rather than a constant force, but it's a bit counter-intuitive for rocket engines.
Sorry for any real-world inaccuracies. The experiment was designed for the intuition to make it easier to shift the reference frame. The pretended effect was that the situation was the same exact one, just as an aid in understanding. Seems I got it "right enough".

Originally Posted by R.Mackey View Post
Ideally you will get the same kind of "crush down / crush up" behavior. What happens is that at impact, the accelerating lower block hits the nonaccelerating (and thus slower) upper block, damage occurs to both. But the remainder of the upper block has been accelerated, being pushed by the mass below, at a rate lower than 1 g. And -- this is the key point -- the rubble interface layer between is at the same velocity as the upper block, and is not accelerating at 1 g.
Indeed; however the rubble part is accelerated as well and pushes the upper block, which in itself also opposes an inertia which results in a force in the interface between itself and the rubble layer. If (emphasis on the if) the force is enough to crush it, then as it is crushed there will be less mass of it that opposes the movement and its crush-up will eventually be arrested, because of lack of mass, until the platform comes (unless the platform comes before that happens). That's how I see it.

So the problem is, in my view: is there something that ensures that the force between the rubble and the top will always be less than needed for crushing it?

Or is the no-crush-up just a specific case studied for the situation with the towers (and maybe applicable to some other buildings), but not valid in general? I'm starting to think that this is the explanation.

Originally Posted by R.Mackey View Post
As the lower structure continues to accelerate through the rubble layer and upper block, it suffers increasingly more damage at the top of the lower block. It has the same force pushing up, but it hits an increasingly larger mass and thus is opposed by more and more inertia.
This part is perfectly clear. That's the obvious reason for the crushing to be produced at all.

Originally Posted by R.Mackey View Post
Have you read Dr. Bazant's papers? In particular, have you read where he clarified this issue to Frank Gourley?
Seems that that will be my next reading

I have only read the first article (BZ) and have been waiting for an excuse to read the rest. Major Tom almost got me to read more of them, pity he didn't focus on one of them.
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Old 22nd August 2010, 04:28 PM   #6
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Originally Posted by femr2 View Post
To me this clearly implies simultaneous crush-up and crush-down at all times, even if you accept one side crushing more than t'other.
Pending R.Mackey's reply and a reading of the explanation to Gourley on my side, will you at least concede my point that even if it is crushed, it would be eventually arrested as the top loses mass?
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Old 22nd August 2010, 04:44 PM   #7
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Originally Posted by pgimeno View Post
Sorry for any real-world inaccuracies. The experiment was designed for the intuition to make it easier to shift the reference frame. The pretended effect was that the situation was the same exact one, just as an aid in understanding. Seems I got it "right enough".
Like I said, it's an interesting approach, and one that might help shed light on the issue. I just wanted to be thorough because it's a little bit more complex than it appears.

Originally Posted by pgimeno View Post
Indeed; however the rubble part is accelerated as well and pushes the upper block, which in itself also opposes an inertia which results in a force in the interface between itself and the rubble layer.
Ah, but no.

Think about your model. The rocket engines are accelerating the "ground." That means the only parts that accelerate with the rocket engine are those for which there is a stable load path going back to the ground. Everything else is not accelerating, and being hit by this structure.

The rubble does not have a stable load path to ground. They are free objects. They are not reliably carried by the lower structure's columns, but are instead impacting all over the place -- columns, floors, eccentrically, and so on. Thus, the rubble counts as part of the detached mass, which includes the upper block.

Originally Posted by pgimeno View Post
So the problem is, in my view: is there something that ensures that the force between the rubble and the top will always be less than needed for crushing it?
Yes, there is. Think of it like this -- F = m a, right? The forces on the upper block, once there is a significant rubble layer, are inertial forces. If you measure the aggregate deceleration of the upper block, you know the stress in that block.

As the upper block + rubble layer increases, m increases. F, on the other hand, is decreasing in your reframe of the problem -- the rockets have to throttle down. As a result, a decreases. That means the stress in the surviving upper block decreases as the collapse continues.

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. So we expect to see some damage to the upper block at the initial contact, followed by very little damage to the upper block afterward, until it again hits the "immovable" rocket platform at which point it will fail floor-by-floor in the crush up phase.

Originally Posted by pgimeno View Post
Or is the no-crush-up just a specific case studied for the situation with the towers (and maybe applicable to some other buildings), but not valid in general? I'm starting to think that this is the explanation.
It is valid in general. But there are some special cases. In the case of verinage, for instance, we also see a "crush down -- crush up" sequence, although the degree of near symmetric crushing at impact tends to be higher. This has more to do with the real details of the problem, where Bazant's hypothesis is an ideal case. Reality has to account for the actual failure modes of materials and connections.

In the real WTC situation, we don't have a true "crush down / crush up" anyway. What actually happens is the core and perimeter structure of the lower block funnels falling material onto the floors. The truss floors preferentially fail downward, whereas the beam-framed floors in the core preferentially fail upward. I wrote a cartoon describing this in the supporting presentation for my debate with Tony Szamboti, which you can read here: http://www.911myths.com/index.php/Ryanmackey (pages 20-25 of the presentation, downloadable as PPT or PDF).

Originally Posted by pgimeno View Post
I have only read the first article (BZ) and have been waiting for an excuse to read the rest. Major Tom almost got me to read more of them, pity he didn't focus on one of them.
Well, consider this an excuse. No reason not to read it for your own education.

What the Truthers do wrong is neglect the rubble layer. If the rubble layer didn't exist, somehow swept away as soon as it was produced, then the impact of upper and lower block would result in relatively symmetric damage. However, after the upper block has shrunk by only four or six floors, the rubble layer outmasses the surviving upper block, and you absolutely cannot neglect its behavior. Your reformulation of the problem is useful because it clarifies that the rubble layer must be treated as a free object, and thus is more accurately lumped with the upper block than the lower block. Once you get this point straight, the correct result should be intuitive.
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Old 22nd August 2010, 04:52 PM   #8
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Originally Posted by pgimeno View Post
will you at least concede my point that even if it is crushed, it would be eventually arrested as the top loses mass?
I don't understand what you are asking. If what is crushed ? What would be arrested ?

If you are suggesting that in a purely mathematical sense, not directly applicable to the real world, that the relative amount of crush-up as opposed to crush-down would be equal to zero, then, as Ryan has said it could tend towards zero.

But of course, that's just maths. Bazant never intended on modelling the real-world behaviour.

Even the terms crush-down and crush-up can only be loosely associated with the towers destruction when describing the real world behaviour.
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Old 22nd August 2010, 05:00 PM   #9
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Originally Posted by R.Mackey View Post
What the Truthers do wrong is neglect the rubble layer.
How thick is this rubble layer? Where do we see evidence of it? I might believe in it if I could see it. Anywhere.

Quote:
If the rubble layer didn't exist, somehow swept away as soon as it was produced, then the impact of upper and lower block would result in relatively symmetric damage. However, after the upper block has shrunk by only four or six floors, the rubble layer outmasses the surviving upper block, and you absolutely cannot neglect its behavior.
You mean this behaviour? :

Quote:
The rubble ... are free objects. They are not reliably carried by the lower structure's columns, but are instead impacting all over the place -- columns, floors, eccentrically, and so on. Thus, the rubble counts as part of the detached mass, which includes the upper block.
The rubble's eccentricity means it must therefore be coupled with the upper block? Why? And why in both cases?
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Old 22nd August 2010, 05:03 PM   #10
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Let me make a slight correction to the "throttling down" comment --

The rocket thrust would throttle down, but the actual thrust profile would have to match the timing of the overall collapse. My observation above that the thrust should be equal to 1 g times the mass of the surviving lower block is not quite right; there is an additional thrust component opposing the "downward" force exerted by the impacted pieces, which will be some fraction of their mass and difficult to predict.

The idea is simply to move with the reference frame of the interface, whatever thrust profile that may be. That interface will not accelerate at 1 g, but rather will have a varying acceleration over time. This is what I mean by "throttling down."
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Old 22nd August 2010, 05:11 PM   #11
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Originally Posted by pgimeno View Post
But if it is, can someone please explain why the "WTC top" is not significantly crushed by the impact and successive force exerted on it until it reaches the platform, just as the "WTC bottom" is? That's the part that I'm not getting, and I believe it's the part that most people have trouble with.

As a lay person with no engineering background or knowledge of the mechanics of the tower collapses:

I think the top will be crushed. It will be completely ruined. You won't be able to hold meetings there or, really, get any work done. However, that doesn't look like it matters. The mass of the top won't change whether it is crushed or not. It will weigh the same. So the damage that it's going to do to your thought experiment rocket will stay the same (adding to it the mass of each new crushed section) so long as the rocket's acceleration into the top is 32 ft/sec2 or whatever gravity is these days.


ETA: Having now read Mackey's response, I realize that I have absolutely no idea what I am talking about and should, in all probability, just be ignored.
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Last edited by Loss Leader; 22nd August 2010 at 05:18 PM.
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Old 22nd August 2010, 06:10 PM   #12
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Originally Posted by femr2 View Post
I don't understand what you are asking. If what is crushed ? What would be arrested ?
Sorry, let me rephrase:

Will you at least concede my point that even if the top is crushed-up as the collapse progresses, its crushing would be eventually arrested(*) as the top loses mass (because it's converted in rubble), since the total force would be decreasing and thus the columns will eventually be able to support the force?

(*) "Stopped" might be a better word? Sorry, English is not my first language.

(note that this question was previous to Mackey's clarification, which I am still in the process to digest)
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Old 22nd August 2010, 06:24 PM   #13
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Originally Posted by pgimeno View Post
Sorry, let me rephrase:

Will you at least concede my point that even if the top is crushed-up as the collapse progresses, its crushing would be eventually arrested(*) as the top loses mass (because it's converted in rubble), since the total force would be decreasing and thus the columns will eventually be able to support the force?

See, this one I think I know. It wouldn't be arrested because the top is not losing mass. So long as you're still accelerating a static body into it, you're going to get the full force. Force=MA is not Force=M(that's still all in one piece)A. The M never changes. In fact, as Mackey has said, the M grows as lower floors are crushed because they stop being part of the static mass and become part of the thing it's hitting.
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Old 22nd August 2010, 06:30 PM   #14
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Originally Posted by Loss Leader View Post
See, this one I think I know. It wouldn't be arrested because the top is not losing mass. So long as you're still accelerating a static body into it, you're going to get the full force. Force=MA is not Force=M(that's still all in one piece)A. The M never changes. In fact, as Mackey has said, the M grows as lower floors are crushed because they stop being part of the static mass and become part of the thing it's hitting.
Yup.

Think about it this way, if it helps: What about the very top floor? When does it fail?

The force on the top floor is only equal to its own mass times its deceleration. That deceleration will be some fraction of 1 g, thus it never collapses -- its load is actually less than it was when it was free-standing and static -- until it suddenly hits an immovable object, and has to dissipate all of its built-up momentum in a hurry.

As a result it's easy to see that the very top of the upper block will outlast the entire lower block, no matter what, in the ideal case. The situation for the floor just below the very top is similar, except it's also loaded with the inertial force of the floor above. And so on. In short, the load on the upper block stays bounded, regardless of how much the debris layer in between grows. The same cannot be said for the lower block.

Last edited by R.Mackey; 22nd August 2010 at 06:32 PM. Reason: Added quote
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Old 22nd August 2010, 06:31 PM   #15
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Originally Posted by Loss Leader View Post
It wouldn't be arrested because the top is not losing mass.
pgimeno is not referring to *collapse arrest*, but rather to *crush-up arrest*.
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Old 22nd August 2010, 06:33 PM   #16
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Quote:
as the top loses mass (because it's converted in rubble)
The mass is still there, just in a different form. 1 pound weighs 1 pound regardless of the form it's in.

The old adage "The straw that broke the Camels back" comes to mind. That one straw weighing a single gram was "The final straw".

Truthers seem to forget this basic principal when discussing the falling rubble. It's not the individual pieces that count, it's all of the individual pieces almost simultaneously piling onto the lower floors one or two floors at a time in one chaotic event that counts. Even if those pieces could be carefully placed, one after the other over a week or more per floor the end result would be the same. The floor will fail and it will take out all of the floors below it in sequence.
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Old 22nd August 2010, 06:51 PM   #17
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Originally Posted by R.Mackey View Post
Yup.

I'm so proud. I printed out your post and showed it to my wife.


Originally Posted by femr2 View Post
pgimeno is not referring to *collapse arrest*, but rather to *crush-up arrest*.

Maybe. But, then, why does his question include this phrase:
Originally Posted by pgimeno View Post
and thus the columns will eventually be able to support the force?
That sounds like he means that the crush-down should eventually be arrested when the top floor of the top section is finally destroyed.
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Old 22nd August 2010, 06:59 PM   #18
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Originally Posted by Sam.I.Am View Post
The mass is still there, just in a different form. 1 pound weighs 1 pound regardless of the form it's in.
Under the "rubble is able to crush the top" assumption, the mass of the top is converted into rubble as the crushing progresses, thus the top loses mass which now forms part of the rubble layer. As the top has less and less mass, it has less inertia too, which is what causes the force between the rubble and the top in this assumption. Eventually, the force will be less than the structure can resist and the crush-up will be arrested. That's what I meant. You are right and my assertion that the top loses mass was correct. I neglected to specify that that mass is converted to rubble, which apparently has caused confusion.

---

Originally Posted by femr2 View Post
However it's important to ensure there is clear understanding that the Bazant model does not, and is not intended to, reflect the real world WTC behaviour.
I don't lose track of it at any moment. But it proved that the gravity collapse was unstoppable once started, something that many people still contend.

---

Sorry, I badly need some sleep, almost 4am here, not in a good condition for this kind of brain frying

Hopefully I will get it tomorrow with a fresher mind.
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Old 22nd August 2010, 07:06 PM   #19
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Quote:
I neglected to specify that that mass is converted to rubble, which apparently has caused confusion.
Ok, that makes much more sense. After rereading what you wrote I admit that I misunderstood what you were getting at.
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Old 22nd August 2010, 10:02 PM   #20
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Can the Bazant concept of crush down, then crush up be applied to WTC1?

In this thread people tend to agree that it cannot.

But Bazant applies it to WTC1 in BLGB. From 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/pe...20collapse.pdf






"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 (Ba?zant and Verdure 2007, pp. 312-313). During the crush-down, the falling upper part of tower (C in Fig. 2 bottom), having a compacted layer of debris at its bottom (zone B), is crushing the lower part (zone A) with negligible damage to itself. During the crush-up, the moving upper part C of tower is being crushed at 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 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 Bazant and Verdure (2007). This previous demonstration, however, was only approximate since it did not take into account the variation of crushing forces Fc and F0c during the collapse of a story. An accurate analysis of simultaneous (deterministic) crush-up and crush-down is reported in Ba?zant and Le (2008) and is reviewed in the Appendix, where the differetial 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 downwards and upwards. However, the crush-up front will advance into the overlying story only by about 1% of its original height h and then stop. Consequently, the effect of the initial two-way crush is imperceptible and the hypothesis that the crush-down and crush-up cannot occur simultaneously is almost exact."


Does Bazant seem to believe that the concept of crush down, then crush up can be applied to WTC1? From the above quote, clearly he does.

We see him applying crush down, then crush up to WTC1 in a paper entitled "What Did and Did not Cause Collapse of WTC Twin Towers in New York" yet the posters here tend to agree that we cannot apply this concept to WTC1.

Well, you should let Dr Bazant know.
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Old 22nd August 2010, 11:46 PM   #21
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In the paper BL there is no doubt that Bazant believes that the concept of crush down, then crush up applies to WTC1 and WTC2.

Bazant & Le
Closure to "Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions"
http://www.civil.northwestern.edu/pe...%20Replies.pdf

In the section titled "Reply to R Gourley", points #4 and 5 clearly show that Dr Bazant believes the concept of crush down, then crush up can be applied quite literally to the cases of WTC1 and 2.

Point 4 entitled "Why cannot crush up proceed simultaneously with crush down?"

Point 5 entiled "Why cannot crush up begin later?"


There is no doubt that Dr Bazant is applying his idea of crush down, then crush up literally to the case of WTC1 and 2. It is also clear from the quote from BLGB in my last post.

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Old 22nd August 2010, 11:58 PM   #22
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SO who is correct, the posters who believe that crush down, then crush up cannot be literally applied to WTC1 or 2 , or Dr Bazant?


Ironically, you are right and your expert is wrong in this case.
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Old 23rd August 2010, 01:19 AM   #23
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Originally Posted by Major_Tom View Post
SO who is correct, the posters who believe that crush down, then crush up cannot be literally applied to WTC1 or 2 , or Dr Bazant?
...

Would I go out on a limb if I answered "both, to some extent"?

The Bazant model is, of course, a model: It assumes some ideal condictions, like a homogeneous, horizontal crush front. It neglects some mass loss due to lateral ejections. It ignores tilt. It ignores the fact that the core is stronger than the rest of the structure and actually managed to penetrate the rubble front. Etc.

As a result, one would expect the crush-up-crush-down scenario, only dirtier due to many deviations of the real world from model.
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Old 23rd August 2010, 02:03 AM   #24
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Mod WarningRemain on topic and avoid making personal attacks.
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Old 23rd August 2010, 02:29 AM   #25
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By the way: Interesting approach to changing the point of view, and excellent arguments from R.Mackey! Thanks all!
I did read (well, skim) the Bazant papers, including the annotations, but didn't really get it until now why the top part should experience less stress and destruction.
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Old 23rd August 2010, 02:31 AM   #26
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I think Bazant went badly astray when he referred to "crush-up." This does not invalidate his assertion that there was potential energy enough acvailable to cause total collapse. All I see occuring is crush-down. The top block is constantly crushing its own lower regions ab initio. As I understand such things, it does, however, remain a "geometric solid." It is just not a homogenous solid. Whether discombobulated rubble and steel elements, or a nicely-constructed box, it still has mass and volumn. That mass and volumn continue to increase as collapse continues.

And it still hammers the structure below it.

My problem with the rocket anology is that the rocket must be constantly accelerating, as was the top block in each of the towers.
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Old 23rd August 2010, 02:41 AM   #27
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Originally Posted by leftysergeant View Post
I think Bazant went badly astray when he referred to "crush-up." This does not invalidate his assertion that there was potential energy enough acvailable to cause total collapse. All I see occuring is crush-down. The top block is constantly crushing its own lower regions ab initio. As I understand such things, it does, however, remain a "geometric solid." It is just not a homogenous solid. Whether discombobulated rubble and steel elements, or a nicely-constructed box, it still has mass and volumn. That mass and volumn continue to increase as collapse continues.

And it still hammers the structure below it.
I guess the point of the theory, besides being purely interesting (because counter-intuitive) on its own merits, is that it shows that not much kinetic energy was "wasted" on structural deformatin in the top block, and thus more was available to crush the lower portion. Even though that is not necessary in order to explain why total collapse occurred at all (there was enough energy around to make that inevitable), but it might add a little velocity to the event.


Originally Posted by leftysergeant View Post
My problem with the rocket anology is that the rocket must be constantly accelerating, as was the top block in each of the towers.
Uhm, that's what rockets do as long as they fire...

Last edited by Oystein; 23rd August 2010 at 02:43 AM. Reason: ETA "in order to explain", plus spelling
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Old 23rd August 2010, 02:54 AM   #28
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Originally Posted by Oystein View Post
I did read (well, skim) the Bazant papers, including the annotations, but didn't really get it until now why the top part should experience less stress and destruction.
At some point in the collapse the core pierced the upper section and it was "crushed up". Bazant's just shown mathematically it doesn't matter. It's amusing how this frustrates the hell out of the truthers.
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Old 23rd August 2010, 03:39 AM   #29
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Originally Posted by Oystein View Post
I did read (well, skim) the Bazant papers, including the annotations, but didn't really get it until now why the top part should experience less stress and destruction.
The top part had only to resist the downward acceleration of its own mass (which mass was decreasing as it disintegrated) while the bottom had to resist the mass of the top part, plus the increasing amount of its own mass that was being accelerated downward.
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Old 23rd August 2010, 06:16 AM   #30
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Originally Posted by 3bodyproblem View Post
At some point in the collapse the core pierced the upper section and it was "crushed up". Bazant's just shown mathematically it doesn't matter. It's amusing how this frustrates the hell out of the truthers.
Bazants model assumes crush-up does not occur until after full-cycle crush-down. It is clear that no such behaviour actually ocurred.

Even the terms crush-up and crush-down can only be loosely applied to the towers...
Originally Posted by R.Mackey
In the real WTC situation, we don't have a true "crush down / crush up" anyway. What actually happens is the core and perimeter structure of the lower block funnels falling material onto the floors. The truss floors preferentially fail downward, whereas the beam-framed floors in the core preferentially fail upward.
In the scenario above, shortly after initiation there is no real semblance of upper block remaining. There are several zoned debris avalanches causing essentially internal pancaking, with a tangled mess of core lagging behind and sections of perimeter either being ejected or peeling even further behind. In addition, whilst floor destruction progressed to ground, core destruction arrested.

Could you expand on what you mean by *it doesn't matter* ?
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Old 23rd August 2010, 06:18 AM   #31
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Originally Posted by Oystein View Post
it shows that not much kinetic energy was "wasted" on structural deformatin in the top block, and thus more was available to crush the lower portion. Even though that is not necessary in order to explain why total collapse occurred at all (there was enough energy around to make that inevitable), but it might add a little velocity to the event.
It sounds like you are applying the Bazant model behaviour to the real-world events.

As we have agreed the Bazant model behaviour does not and was not intended to match real world behaviour.

Could you clarify your intent ?
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Old 23rd August 2010, 06:24 AM   #32
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Originally Posted by femr2 View Post
It sounds like you are applying the Bazant model behaviour to the real-world events.

As we have agreed the Bazant model behaviour does not and was not intended to match real world behaviour.

Could you clarify your intent ?
I did not participate in any such agreement. See my post 23.
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Old 23rd August 2010, 06:40 AM   #33
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Originally Posted by femr2 View Post
Bazants model assumes crush-up does not occur until after full-cycle crush-down. It is clear that no such behaviour actually ocurred.
Actually that's not technically correct. With the mathematical proof it's no longer an "assumption" per se, but a validated simplification.

It's clear that it adequately describes the actual behaviour.
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Old 23rd August 2010, 06:41 AM   #34
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Originally Posted by Oystein View Post
I did not participate in any such agreement. See my post 23.
Okay, then...

Quote:
it shows that not much kinetic energy was "wasted" on structural deformatin in the top block
Do you agree that in the real world there was no real semblance of *top block* shortly after initiation ?

Quote:
and thus more was available to crush the lower portion.
Do you agree that core destruction and floor *pancaking* propogation was separated by considerable distance ?

Quote:
there was enough energy around
Agreed, and imo the primary valid result of the model. Other behavioural properties of the model simply don't match the real world events.

Quote:
but it might add a little velocity to the event.
Floor destruction propogation (ROOSD) attained a fairly constant velocity after about 4s. Core destruction arrested.

Are you sure you're not inadvertently applying model behaviour to the real world inappropriately ?
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Old 23rd August 2010, 06:49 AM   #35
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Originally Posted by 3bodyproblem View Post
Actually that's not technically correct. With the mathematical proof it's no longer an "assumption" per se, but a validated simplification.
No. Floor destruction propogation did not involve an *upper block* at all, and was basically driven entirely by a *rubble layer*. Core destruction arrested. Perimeter essentially peeled.

Quote:
It's clear that it adequately describes the actual behaviour.
As the limiting case, it shows there was enough energy available and given it's simplfying assumptions that propogation to ground would ensue in those conditions, but it does not describe the actual behaviour at all.
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Old 23rd August 2010, 07:46 AM   #36
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Originally Posted by femr2 View Post
No. Floor destruction propogation did not involve an *upper block* at all, and was basically driven entirely by a *rubble layer*. Core destruction arrested. Perimeter essentially peeled.


As the limiting case, it shows there was enough energy available and given it's simplfying assumptions that propogation to ground would ensue in those conditions, but it does not describe the actual behaviour at all.
I'm not sure how you figure breaking it up makes any difference? Bazant has already shown it doesn't matter. You have a variety of ways to get from A to B. Either way you end up at B.
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Old 23rd August 2010, 08:09 AM   #37
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Originally Posted by 3bodyproblem View Post
I'm not sure how you figure breaking it up makes any difference?
I'm highlighting to you that stating *it adequately describes the actual behaviour* is not correct. The real world behaviour and the behaviour of the Bazant model are very different, obviously.

Quote:
Bazant has already shown it doesn't matter.
What doesn't matter ? Please cite where Bazant uses a model without the *top block*, and also includes early *crush up*. You can infer from the energetics results that there was enough energy available, sure. *Showing it doesn't matter* in this context is your inference, not something Bazant has shown. The energetics inferences are totally different to stating that the model behaviour matches real world behaviour. That's just not true.

Quote:
You have a variety of ways to get from A to B.
Sure, and my point is that it is erronious to apply crush down/up behaviour of Bazants model to the real world events literally. Again, as I'm sure you'll listen to Ryans' words more than mine...
Originally Posted by R.Mackey
In the real WTC situation, we don't have a true "crush down / crush up" anyway. What actually happens is the core and perimeter structure of the lower block funnels falling material onto the floors. The truss floors preferentially fail downward, whereas the beam-framed floors in the core preferentially fail upward.
This description does not match the Bazant model behaviour well at all. The vast majority of floor destruction does not involve a top block at all, and simply a *rubble layer*.

Quote:
Either way you end up at B.
Bazant does not mention tipping cores. IF the large core remnant of WTC 1 that remained after core destruction arrest had not dropped, would you still describe the outcome as *B* ? That core portion was not destroyed by *crush-down*, and so is not accounted for by the model.
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Old 23rd August 2010, 08:45 AM   #38
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Originally Posted by femr2 View Post
I'm highlighting to you that stating *it adequately describes the actual behaviour* is not correct.
Sure, and my point is that it is erronious to apply crush down/up behaviour of Bazants model to the real world events literally.
It's pretty clear it's not meant to describe the events literally, but it's adequate.

It seems to me you're just playing a game of semantics?
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Old 23rd August 2010, 09:55 AM   #39
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Originally Posted by 3bodyproblem View Post
It's pretty clear it's not meant to describe the events literally
Of course. That is why I asked you to clarify *It's clear that it adequately describes the actual behaviour.*, and pointed out the actual behaviour was very different.

Quote:
but it's adequate.
For it's intended purpose, limiting case energy availablility, it's okay. Not a whole lot different in that sense to other simplified models kicking around. Applying it to actual behaviour is, again, wrong.

Minimal axial column impacts.
Minimal column buckling.
No true crush-down or crush-up in the Bazantian sense.
No *upper block* shortly after initiation.
Separate and different floor, core and perimeter modes of destruction.
Arrest of core destruction for a significant proportion of the core.
etc.

Quote:
It seems to me you're just playing a game of semantics?
Not at all. I'm simply making sure that the model is not used incorrectly. As there is enough energy in the limiting case for complete destruction, does that mean the model can be used to state there is enough energy for alternate modes of destruction...sure, but does it mean that the behaviour matches alternate modes of destruction (such as the actual real world event) ? No.

Perhaps you could highlight a number of real world behaviours that do match the behaviour of the Bazant model ?
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Old 23rd August 2010, 09:56 AM   #40
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Originally Posted by R.Mackey View Post
Think about your model. The rocket engines are accelerating the "ground." That means the only parts that accelerate with the rocket engine are those for which there is a stable load path going back to the ground. Everything else is not accelerating, and being hit by this structure.
But that (the bolded part) is not accurate because the top is accelerating as is the rubble, otherwise in the gravity version the top and the rubble would have fallen in freefall, or what am I missing?

In the freefall case it's obvious that the top wouldn't be crushed until reaching the ground.

Originally Posted by R.Mackey View Post
The rubble does not have a stable load path to ground. They are free objects. They are not reliably carried by the lower structure's columns, but are instead impacting all over the place -- columns, floors, eccentrically, and so on. Thus, the rubble counts as part of the detached mass, which includes the upper block.
My problem keeps being that both the rubble and the top are also pushed by the bottom, experimenting an acceleration (if the top fell at 2/3 g in the gravity version, the acceleration of the top and rubble in the rocket version would be 1/3 g).

Originally Posted by R.Mackey View Post
Yes, there is. Think of it like this -- F = m a, right? The forces on the upper block, once there is a significant rubble layer, are inertial forces. If you measure the aggregate deceleration of the upper block, you know the stress in that block.

As the upper block + rubble layer increases, m increases. F, on the other hand, is decreasing in your reframe of the problem -- the rockets have to throttle down. As a result, a decreases. That means the stress in the surviving upper block decreases as the collapse continues.
Hum... That makes sense. But that doesn't prevent the possibility of a few more floors destroyed, does it?

In my view, ignoring the ejection of mass from the system and the non-homogeneous nature of the rubble layer, the total thrust of the rockets will be a simple function of the intact bottom mass which must accelerate at g, and the rest of the mass which must accelerate at 1/3 g. That's my way of understanding that the thrust must decrease in order to maintain the acceleration: as the mass of the bottom decreases and the mass of the rest increases, the required force will be less because the increasing mass requires less acceleration. That result is surprising and counterintuitive for me, but that's life

Originally Posted by R.Mackey View Post
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. So we expect to see some damage to the upper block at the initial contact, followed by very little damage to the upper block afterward, until it again hits the "immovable" rocket platform at which point it will fail floor-by-floor in the crush up phase.
I see why there's less damage but I don't see why there's very little damage to the upper block afterward.

I still would understand it if it were the parameters from the WTC and maybe other buildings that make the crush-up not to happen but not in general, but you said that's not the case. Wonder what I'm missing.

I've read the explanation to Gourley from Bazant. I didn't understand most of it, but I see that he uses conservation of momentum and energy and that he introduces factors such as mass shedding ratio and mass compaction ratio, which makes me wonder if the rubble layer acts like a cushion as it is compacted, that dampens the dynamic load on the top, making it able to support itself when it's an "almost static" load with the additional advantage of reduced acceleration.

It also seems relevant to me that he employs real world data to feed the equations instead of solving them in general, which would settle the universality of the phenomenon.

Originally Posted by R.Mackey View Post
In the real WTC situation, we don't have a true "crush down / crush up" anyway. What actually happens is the core and perimeter structure of the lower block funnels falling material onto the floors. The truss floors preferentially fail downward, whereas the beam-framed floors in the core preferentially fail upward. I wrote a cartoon describing this in the supporting presentation for my debate with Tony Szamboti, which you can read here: http://www.911myths.com/index.php/Ryanmackey (pages 20-25 of the presentation, downloadable as PPT or PDF).
Thank you very much. Not fully understood but let's leave that for another occasion
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