OOS Collapse Propagation Model

[ozeco41]

Don't mean to answer for Oystein, but B&V make quite clear their purpose: a generalized model applicable to demolitions and other progressive collapses.

Correct - they are explicit. I don't think that point is contentious - it was apparent that it was Bazant's long term goal.

BUT if you are reading BV look at how they sought to validate it:

Expressions for consistent energy potentials are formulated and an exact analytical solution of a special case is given.

..what was the "special case". and was it a valid enough approximation.

Taking the engineering up a level of sophistication - I don't think he can achieve his goal if he relies on 1D homogenisation/approximations. He may get close enough if he puts in a variable energetics factor to deal with column spacing - say 3-4-5 broad classes - maybe "ROOSD wide open <> Middle range spacing and/or multiple tubes <> traditional grid spacing. I've suggested that one several times but it has been ignored - out of range of comfort zones and interest for forum discussion.

BUT given the esoteric shapes emerging in tower buildings over the last ~20 or so years that is still chasing a diminishing market of application. [/EndStrategicGuessworkMode]

Last time I checked, this was the 9/11 conspiracy theories subsection. Back when the 9/11 truth movement existed, people cared very much about limit cases - they played a key role in the argument against the plausibility of CD. That might not serve a purpose germane to your goals, but they certainly serve a purpose in the conversation known as "9/11 conspiracy theories."

Take care - there be lots of history and tigers down that path.

 

[ozeco41]

Ozzie,
It seems like some fellas can't seem to see that Mr B et al's work re the twin towers though "scientifically sound" explains nothing that anyone needs to know. It's a diversion and a derail from what ACTUALLY happened. You see it, I do, Tom and perhaps others do. But the "usuals" can't let go with their limit case "excuse" as its relevancy.

You have give NIST some back door credit.. they use the term something like... global collapse was inevitable or ensued.... which goes to the issue of settled engineering... you over load slabs in a high rise and they fail, fall crush, fracture and a high rise with slabs on the loose is not going to stand. This likely will destroy bracing and make columns unstable... They should have identified and explained... but used "global" which did not help.

Sure Sander. The issues in contention are both much simpler and a damn sight more complicated. And whichever way I approach it - simple outline or address all complications - many of the counter claims choose the other one. I'm trying to keep to the rational reasoned argument approach - but that needs both parties to agree to discussion methodology and that agreement is hard to get explicitly.

CC's ideas are not terribly different in type that Greening's latest... lots of assumptions... little to no data. Not sure of how the fuel air blasts are destroying the building... because it appears to be a progress downward moving gravity driven... wave of destruction.

Yes I comprehend the broadly linked school of thought among some former compatriots.

 

[Myriad]

Frankly it's pretty self evident that a floor collapse would not arrest. No need for a "limit case". Whatever the design load of the floor system.. 60 psf, 70 psf, 100psf It's settled engineering that that a super imposed load on a floor which exceeds its yield strength will FAIL... and this is precisely why the code has PSF limits for various uses.

It's trivial... pile up X number of floors on a typical floor and you have a "runaway" progressive and quite rapid collapse of the entire floor system BELOW. Any freshman who took statics knows this.

How many 9/11 conspiracy theorists circa 2009 were freshmen who took statics?

I posit, based on experience in discussing 9/11 events with a great variety of people of all educational levels and numerous walks of life, that it is not at all self-evident that a floor collapse would not arrest. If you had surveyed people prior to 9/11 asking them what they thought would happen if the columns on a WTC tower a floor a dozen floors below the top were to become damaged or weakened to the point where they could no longer statically support the structure above, well fewer than one in a thousand would have answered that nearly the entire structure would collapse all the way to the ground.

BZ's acceptance for publication strongly suggests that the editors felt that it was not self-evident to all of their far more technically specialized readership either. Do self-evident findings normally get published? Perhaps those editors were wrong about that. If you think so, go argue with them. I'm sure they'd be willing to discuss it in detail. Oh, wait, no, they'll probably ignore you, thus depriving us all of hilarious debate.

In any case, there were 9/11 conspiracy theorists here arguing that the collapse should have arrested. There really were. They were really here, sometimes in significant numbers, making that argument. And oddly enough, they didn't regard "it's self-evident that you're wrong" or "it's settled engineering" as an adequate or even useful response (though that often was the response offered by many, for which debunkers were also criticized). Nor would it have been. Some of us offered sounder responses, including referring to BZ which was and remains (as Dave Rogers just explained yet again) a correct and valid counter-argument to claims that the collapse should have arrested or that the energy to cause the collapse was insufficient without false flag sabotage.

Of course they were wrong. In many cases they were hopelessly irrational. Does that mean we should not have addressed their arguments? Have you ever looked around this web site, all the different sub forums? Have you noticed what kinds of discussions actually go on here?

"WHAT made the towers collapse?" is not and was not the issue HERE in the 9/11 CONSPIRACY THEORIES subforum. The issue HERE with regard to the Towers (and wtc7) is, was the collapse of the buildings caused in whole or in part by false flag sabotage?

Please keep telling people who were here through all the arguments with actual conspiracy theorists about actual conspiracy theories that they were discussing "the wrong issue" all along. Please keep claiming that people curious about Truther claims, who needed and benefitted from careful explanations to dispel their mistaken notions about what should have happened, really knew otherwise all along because it was so obvious. That is hilarious.

 

[Crazy Chainsaw]

Ozzie,
It seems like some fellas can't seem to see that Mr B et al's work re the twin towers though "scientifically sound" explains nothing that anyone needs to know. It's a diversion and a derail from what ACTUALLY happened. You see it, I do, Tom and perhaps others do. But the "usuals" can't let go with their limit case "excuse" as its relevancy.

You have give NIST some back door credit.. they use the term something like... global collapse was inevitable or ensued.... which goes to the issue of settled engineering... you over load slabs in a high rise and they fail, fall crush, fracture and a high rise with slabs on the loose is not going to stand. This likely will destroy bracing and make columns unstable... They should have identified and explained... but used "global" which did not help.

CC's ideas are not terribly different in type that Greening's latest... lots of assumptions... little to no data. Not sure of how the fuel air blasts are destroying the building... because it appears to be a progress downward moving gravity driven... wave of destruction.

How would fuel air blasts destroy the building, simply making the case for added mass shedding, that allows the faster mechanism ROOSD, to be slower than a model of ROOSD should be, in other words fluid dynamics from natural explosions and sound waves have the potential to slow the buildings collapses, not speed them up.

 

[JSanderO]

...... That is hilarious.

YES I did not come to this debate early on. And I didn't really understand that this forum was where "truthers" came to get a lesson in basic engineering which I referred to as "trivial".

NO NEED TO REFUTE THEIR DISBELIEF

Mr B et al did not really help because despite the accuracy of his math... it flies way way over the head of truthers don't care because of THEIR disbelief and science denial and hang on to CD, false flag driven by their "politics" nothing to do with understanding the engineering or physics.

As Ozzie writes ALL THE time... the burden of proof ... so to speak... is on those who make these CD, false flag claims. LET them MAKE THEIR CASE with rational thinking and science/engineering.

When they try (feebly) it's pretty lame and laughable.

++++

Admittedly my interest is more technical in understand the mechanisms of the initiation... which are hardly discussed except in the very broadest terms... mech damage and fire.... Well duh... that doesn't shed light on what happened.

I've even started a thread about single column failures leading to total building collapse and it really produced nothing IMSHO.

I've even questioned the conventional wisdom to explain the fact that the NIST 7wtc sim does not look anything like the actual collapse. That's my assertion and I see no good "rebuttal".

And there are more bits.

 

[Myriad]

How would fuel air blasts destroy the building, simply making the case for added mass shedding, that allows the faster mechanism ROOSD, to be slower than a model of ROOSD should be, in other words fluid dynamics from natural explosions and sound waves have the potential to slow the buildings collapses, not speed them up.

This is an interesting idea. One approach for testing it is with energetics. You should be able to compare the energy needed to keep the collapse at a near-constant velocity (assuming the excess energy other energetics calculations yield is in fact generated and needs to be absorbed or counteracted in some way) with the energy that your hypothesized chemical reactions would generate. If they're within an order of magnitude (maybe two because there's a lot of uncertainty in both figures) then you can dig deeper.

I suspect there's a different explanation, which is that an increasing amount of energy is absorbed in comminution of the floor slabs as the collapse accelerates, until it reaches a velocity equilibrium. Large portions of the upper floors at lower velocities "snap" off their supports, but at higher velocities, more crushing occurs and they "crunch" off their supports instead, absorbing more kinetic energy.

It would be interesting to see whether the physical model design I described in 2009 would exhibit continuous acceleration, or slowing acceleration. That model is based on dynamic loads from floors impacting on floors overloading and breaking the connections between floors and columns; the columns, left unsupported, then collapse on their own. (Hey, 2009 was a year before "ROOSD," how is that possible? I must be a time traveler.) The model wouldn't have mass shedding or any of the chemical reactions you're hypothesizing, but it would have comminution.

 

[JSanderO]

(Hey, 2009 was a year before "ROOSD," how is that possible? I must be a time traveler.) The model wouldn't have mass shedding or any of the chemical reactions you're hypothesizing, but it would have comminution.

Wrong on the date I believe...

When I wandered over to 911FF in early 2010.. ROOSD was already presented and I assume some time in '09. My own version came at the end of 2009 and early 2010... and I believe Ozzie was onto it during the same time frame.

Why does it matter?

I was looking for explanations and came up with my own and emailed it to Gage and Gordon Ross calling it a vertical avalanche and mentioning Euler buckling... in Feb 2010 or maybe March...

 

[JSanderO]

How would fuel air blasts destroy the building, simply making the case for added mass shedding, that allows the faster mechanism ROOSD, to be slower than a model of ROOSD should be, in other words fluid dynamics from natural explosions and sound waves have the potential to slow the buildings collapses, not speed them up.

I don't think mass shedding has a thing to do with this.

I think there was some mass pushed or pulled out with the air over pressure as the slab came down onto the next undamaged one...

My guess is that the amount of force once the collapse got going was more than enough to bust through the slab in an instant with negligible slowing in fracturing the intact floor. And it was not measurable in any case... How would you propose to measure it? All you can do is time and compute the velocity of the ejections moving down a small section of the tower which was captured on video.

 

[Crazy Chainsaw]

This is an interesting idea. One approach for testing it is with energetics. You should be able to compare the energy needed to keep the collapse at a near-constant velocity (assuming the excess energy other energetics calculations yield is in fact generated and needs to be absorbed or counteracted in some way) with the energy that your hypothesized chemical reactions would generate. If they're within an order of magnitude (maybe two because there's a lot of uncertainty in both figures) then you can dig deeper.

I suspect there's a different explanation, which is that an increasing amount of energy is absorbed in comminution of the floor slabs as the collapse accelerates, until it reaches a velocity equilibrium. Large portions of the upper floors at lower velocities "snap" off their supports, but at higher velocities, more crushing occurs and they "crunch" off their supports instead, absorbing more kinetic energy.

It would be interesting to see whether the physical model design I described in 2009 would exhibit continuous acceleration, or slowing acceleration. That model is based on dynamic loads from floors impacting on floors overloading and breaking the connections between floors and columns; the columns, left unsupported, then collapse on their own. (Hey, 2009 was a year before "ROOSD," how is that possible? I must be a time traveler.) The model wouldn't have mass shedding or any of the chemical reactions you're hypothesizing, but it would have comminution.

Yes that's why I am comparing ROOSD to Banzant based on structural energy, potential energy from gravity and air resistance.

Anything left over has to be going into mass shedding, via hot heated air expelling dust at high rates of speed.

 

[WilliamSeger]

Ozzie,
It seems like some fellas can't seem to see that Mr B et al's work re the twin towers though "scientifically sound" explains nothing that anyone needs to know.

Isn't there any chance you might change your mind about that if you actually read the papers? A couple of times, I've invited you to read one particular section:

Bazant & Zhou 2002[/b]]
The likely scenario of failure is approximately as follows.

*snip*

The vertical impact of the mass of the upper part onto the lower part stage 4 applies enormous vertical dynamic load on the underlying structure, far exceeding its load capacity, even though it is not heated. This causes failure of an underlying multifloor segment of the tower stage 4, in which the failure of the connections of the floor-carrying trusses to the columns is either accompanied or quickly followed by buckling of the core columns and overall buckling of the framed tube, with the buckles probably spanning the height of many floors stage 5, at right, and the upper part possibly getting wedged inside an emptied lower part of the framed tube stage 5, at left.

*snip*

The basic question to answer is: Can the fall of the upper part be arrested by energy dissipation during plastic buckling, which follows the initial elastic deformation? Many plastic failure mechanisms could be considered, for example: (1) the columns of the underlying floor buckle locally (Fig. 1, stage 2); (2) the floor-supporting trusses are sheared off at the connections to the framed tube and to the core columns and fall down within the tube, depriving the core columns and the framed tube of lateral support, and thus promoting buckling of the core columns and of the framed tube under vertical compression (Fig. 1, stage 4, and Fig. 2(c));or (3) the upper part is partly wedged within the emptied framed tube of the lower part, pushing the walls of the framed tube apart (Fig. 1, stage 5). Although each of these mechanisms can be shown to lead to total collapse, a combination of the last two seems more realistic (the reason: multistory pieces of the framed tube, with nearly straight boundaries apparently corresponding to plastic hinge lines causing buckles on the framed tube wall, were photographed falling down, "Massive 2001"; American 2001).

The above is a reasonably lucid narrative which includes what M_T wants to call ROOSD, minus M_T's irrelevant details and false generalizations. Neither you nor M_T has commented on that quote, but after reading it, how can you say that "Mr B et al's work... explains nothing that anyone needs to know," yet consider ROOSD to be important insight? Do you think the irrelevant details and false generalizations are the insight? If so, then I am correct that ROOSD is misleading.

It's a diversion and a derail from what ACTUALLY happened. You see it, I do, Tom and perhaps others do. But the "usuals" can't let go with their limit case "excuse" as its relevancy.

What I can't let go of is the constant attempts to conflate "why" with "how" and the "limit case" used in the energy argument with the theoretical propagation model. It doesn't seem to me that it's the "debunker" side that's responsible for most of that conflation, since I haven't yet seen either you or M_T even acknowledge that they are two completely different things.

 

[Crazy Chainsaw]

This is an interesting idea. One approach for testing it is with energetics. You should be able to compare the energy needed to keep the collapse at a near-constant velocity (assuming the excess energy other energetics calculations yield is in fact generated and needs to be absorbed or counteracted in some way) with the energy that your hypothesized chemical reactions would generate. If they're within an order of magnitude (maybe two because there's a lot of uncertainty in both figures) then you can dig deeper.

I suspect there's a different explanation, which is that an increasing amount of energy is absorbed in comminution of the floor slabs as the collapse accelerates, until it reaches a velocity equilibrium. Large portions of the upper floors at lower velocities "snap" off their supports, but at higher velocities, more crushing occurs and they "crunch" off their supports instead, absorbing more kinetic energy.

It would be interesting to see whether the physical model design I described in 2009 would exhibit continuous acceleration, or slowing acceleration. That model is based on dynamic loads from floors impacting on floors overloading and breaking the connections between floors and columns; the columns, left unsupported, then collapse on their own. (Hey, 2009 was a year before "ROOSD," how is that possible? I must be a time traveler.) The model wouldn't have mass shedding or any of the chemical reactions you're hypothesizing, but it would have comminution.

2008 got you beat, but the model was too fast, 1/4th faster than column crushing, unless another force was applied to reduce the mass.

You may be right though energy may be absorbed in another way but it does not seem likely.

 

[Oystein]

Oystein you were the last person I would expect to descend to this depth of dishonest debunker denialism.

Can you say exactly what it is that I deny, along with an example of what I deny? That would help.

I think you may have muddied the waters sufficiently to ensure that discussion with Myriad cannot progress. So I face two possibilities of ways forward with you rather than with Myriad.

Actually, since I replied to you addressing Myriad, I am more interested in how your debate with Myriad pans out.

"The later papers by Bazant et al are wrong where they apply 1D simplification models to the WTC real event".

I stand by that assertion and am prepared to support it in reasoned argument.

This may or may not be true - I don't know as I never fully read the later papers by Bazant (which is, by the way, the best reason why you ought not invoke "our" alleged position on Bazant - I simply have none beyond the "limit case" concept of BZ), and I don't care. What I do care about is the arguments made on this thread and subforum.

The objections to that assertion come in two forms (a) outright denial OR (b) claims that 1D can be a sufficiently valid approximation. I am prepared to consider (b) "sufficiently valid approximation" if it is ever supported by reasoned argument. I know of no such argument.

You are forgetting c): Claims that Bazant's 1D approximation to real world in the later papers is not interesting as no one here applies those models to explain or described the real world events in those terms.

Now there is a missing link in Myriad's assertions and your understanding of them as expressed by these quotes:
and the earlier version
Those assertions are true. Most importantly you confirm that Myriad rested on BV (specifically BV at this stage) I agree that also. It is HALF of my key point.

Thanks. That's good then than ALL of my key points in that post are true.

The other HALF is that BV itself applies the 1D approximations to WTC real event. I didn't create the conflation - it is in BV.

Maybe, but Myriad is crystal clear that this is NOT what he is talking about. He talks about the model as such, and the math, and explicitly avoids applying it to the real case. So maybe you didn't create the conflation, but you are the one who keeps dragging it back in right after someone (in this case: Myriad) explicitly rejected the conflation.

A point of argument for which I was preparing the ground in my response to Myriad before your "pre-emptive strike". Myriad by "calling up" BV also calls up the 1D applied to real event conflation. Not me - I simply identify it.

Now that is NOT "fully reasoned argument" merely an outline of the claim I would make.

I agree this is not a "fully reasoned argument". I would add that it also fails to respect and address the argument you were replying to.

If we are to progress discussion on a reasoned basis I would prefer to do it in two stages - Stage 1 discuss and reach agreement on the limits of validity of B&Z and any issues arising from that THEN Stage 2 address the later papers BV, BLe etc.

I want to point out at this point that I am personally not interested in discussing the models in Bazant's later papers, let alone their applicability to the real collapses. I am more interested in setting the record straight on the meta-debate of who used BV etc for what and how.

I have outlined the basis of my position several times recently. The most relevant was directed at Major_Tom in this post

If I simply extract the facts from that post theyare:

Please note that I am trying to start from a clean sheet. I am not commenting either way on past history.

Are you prepared to enter reasoned discussion in the two stages I propose?

If so do you agree that each of the facts is true fact? 1a, 1b, 1c, 2, 3, 4 and 6?
(AKA a valid premise for debate if you prefer to not call them "facts")

I was about to say: 6 ("...should...") is not a "fact"
"Arguments should not be confused over the two mechanisms and any relationship they may have." -> I don't see anyone confusing the mechanisms - I don't think anyone here claims that column crushing was a major factor in the actual collapse.

If not can you state your objections or ask for further clarification point by point?

If we can progress to agreement on those facts plus any you think I have missed at that foundation level we can then go to Stage2. Which should address the problems with BV - possibly BLe.

Finally let me take a "rain check" on the other issues you raise.

Again, I am not myself interested in discussing BV or BL - in fact, I haven't read them.

Again, I object to your constant implication that resident posters such as Myriad are applying the models in BV, BL to "explain" the actual collapses, or are claiming that Bazant's own application of those models to the collapses was a good idea. I do not recall having read any post here by anyone to that effect, and most assuredly the two posts where Myriad just quoted himself from 4.5 years ago do not use or imply that conflation - quite the contrary. He made it clear that he wants to debate the model in its own mathematical merits.

I don't see any "Bazantophile" in the sense that you seem to imply - taking the gospel according to Bazant hook, line and sinker. My impression from reading along is that people just don't care.

 

[WilliamSeger]

You are forgetting c): Claims that Bazant's 1D approximation to real world in the later papers is not interesting as no one here applies those models to explain or described the real world events in those terms.

It might become interesting if someone could answer the "so what" question, but apparently that ain't gonna happen.

I don't see any "Bazantophile" in the sense that you seem to imply - taking the gospel according to Bazant hook, line and sinker. My impression from reading along is that people just don't care.

In the sense that he seems to imply, "Bazantist" or "Bazantite" might be more appropriate than "Bazantophile" (and a better match with the "NISTian" strawman ).

 

[ozeco41]

Can you say exactly what it is that I deny, along with an example of what I deny? That would help.

You assert that I am wrong - that I have a beam in my eye - when you should know me better. You base that assertion on multiple examples of what you regard as errors - mostly framed in process meta level - yet you admit you do not understand and are not interested in the relevant technical details. Contrast that position with the position I adopt towards your expertise on chemistry of thermXte OR my position towards Sunstealer on the same issues OR towards beachnut on aviation matters. I take all three of you as almost certainly correct and accept your explanations as default unless I see a better argument. I don't think I have ever seen a valid rebuttal of any one of your claims - all three of you that is.

But you assert that I am wrong in my own speciality arena? With no reasoned comprehensive argument despite my multiple descriptions of the fuller context. And on your own admission repeated multiple times in this latest post that you don't understand and are not interested in the technical topic.

On the example I am about to address that position is begging for ridicule. At two levels:
Base level: "I don't understand it but you are wrong:
Meta process level: "you have asserted that there are two halves to the argument. I disagree with one so I will ignore it."

The other HALF is that BV itself applies the 1D approximations to WTC real event. I didn't create the conflation - it is in BV.

Maybe, but Myriad is crystal clear that this is NOT what he is talking about. He talks about the model as such, and the math, and explicitly avoids applying it to the real case. So maybe you didn't create the conflation, but you are the one who keeps dragging it back in right after someone (in this case: Myriad) explicitly rejected the conflation.

That is confused logic. Whether he is trying to be clear or not Myriad is not crystal clear - his recalled 2011 position is a classic example of the prevailing wisdom held on this forum till at least 2010 and the remnants of it still carry on.

However three points for us to discuss here and now are (a) "is he or is he not calling up BV?" ; (b) "does BV apply 1D approximations to the real event?" and (c)
"By doing so does he endorse the application of 1D approximations to the real event?"

You and I agree (a) - he is.
On (b) I assert that BV does aptly 1D to real - you say you don't know and are not interested; AND
We dispute (c) - I say he cannot call up BV whilst ignoring parts of it which are inconvenient.

In the broader picture I am also identifying that the confusion over that issue is one of several similar confusions which are still continuing.

But lets deal with the specific issue:
You are asserting - supporting Myriad - that he can call up parts of the BV material WITHOUT calling up those parts of BV - the basis on which BV rests. I disagree - at least until you or Myriad prove YOUR claim. Which is a meta-process claim splitting the BV paper.

And I've even covered my arse on that meta-process position - you can take one of two positions:

A) Assert and prove that BV does not attempt to apply 1D approximations to the WTC real event. I say it is explicitly clear that is does; OR
B) Assert and prove that 1D approximations including crush down/crush up are valid for application to WTC Twin towers. I'm prepared to accept that the ID approximations may be valid and sufficiently accurate for WTC collapse explanation if someone posts/publishes persuasive argument that they are valid. No one has.

So that is only one of many points in your post. It is the keystone issue at this stage of debate. You have several options - rebut my assertions, agree with them, walk away or simply ignore them.

I would prefer -as always - reasoned discussion addressing my arguments OR a fully reasoned counter-claim.

If we can amicably progress this aspect then we may be able to follow through other concerns.

 

[Oystein]

...
But you assert that I am wrong in my own speciality arena? ...

No, not at all.
I am at a loss trying to comprehend how you could misread me so egregiously.

Your own speciality arena is explaining the actual collapse mechanism of the WTC collapses on a systems level, with engineering thinking.
You are great at that.


Myriad did not make a post that touches upon this speciality arena.
Neither did I.

Try again.

 

[Crazy Chainsaw]

I don't think mass shedding has a thing to do with this.

I think there was some mass pushed or pulled out with the air over pressure as the slab came down onto the next undamaged one...

My guess is that the amount of force once the collapse got going was more than enough to bust through the slab in an instant with negligible slowing in fracturing the intact floor. And it was not measurable in any case... How would you propose to measure it? All you can do is time and compute the velocity of the ejections moving down a small section of the tower which was captured on video.

You just described the Banzantian reason for a homogeneous mass.

Not that interested that much in what is going down, also looking at what is going up and the fluid dynamics.

 

[Crazy Chainsaw]

To all, my Ideas and theories are my own based, on my own experiments, not on any work by anyone
Else, I am fully capable of doing my own experiments and blowing my own self Up.
Ideas solely the property of Crazy.

 

[pgimeno]

...
But you assert that I am wrong in my own speciality arena? ...

No, not at all.
I am at a loss trying to comprehend how you could misread me so egregiously.

Gross misrepresentation of my words or position has been one of my fights with Ozeco for a very long time. I take that as part of his SOP.

 

[Bravin Neff]

BUT if you are reading BV look at how they sought to validate it:

Expressions for consistent energy potentials are formulated and an exact analytical solution of a special case is given.

..what was the "special case". and was it a valid enough approximation.

I think that's backwards. B&V don't validate their argument with the WTC example, they are arguing for the nature of the parameters of their model (the compaction ratio, or lambda, the mass ejected outside, and the crushing energy per unit height, or Wf), and to show the different effects by varying these parameters. They show that the model is most sensitive to Wf and least sensitive to compaction ratio (lambda).

You seem to be arguing that B&V is an argument to validate some prediction about WTC when, as I read it, its just an argument about the mean energy dissipation per story, and (to use their language) therefore "the energy absorption capacity of various structures." This is meant to generalize across many stuctures. Yes, they use the WTC timings as an input (figure 6), but this is meant to corroborate the parameters they estimated in B&Z - namely, the 2.4 GNm value for Wf and what the other values would be at various collapse timings.

Let me summarize in one sentence: B&V is not a model of WTC per se, it is a model about progressive collapse based on three parameters, of which WTC is but one of an infinite number of potential examples.

ETA: When I say "you seem to be arguing that B&V is an argument to validate some prediction about WTC," I mean some prediction about the way it collapsed, or the speed it collapsed, or something like that. I don't see how its any of those things.

 

[Crazy Chainsaw]

I think that's backwards. B&V don't validate their argument with the WTC example, they are arguing for the nature of the parameters of their model (the compaction ratio, or lambda, the mass ejected outside, and the crushing energy per unit height, or Wf), and to show the different effects by varying these parameters. They show that the model is most sensitive to Wf and least sensitive to compaction ratio (lambda).

You seem to be arguing that B&V is an argument to validate some prediction about WTC when, as I read it, its just an argument about the mean energy dissipation per story, and (to use their language) therefore "the energy absorption capacity of various structures." This is meant to generalize across many stuctures. Yes, they use the WTC timings as an input (figure 6), but this is meant to corroborate the parameters they estimated in B&Z - namely, the 2.4 GNm value for Wf.

Let me summarize in one sentence: B&V is not a model of WTC per se, it is a model about progressive collapse based on three parameters, of which WTC is but one of an infinite number of potential examples.

Exactly why I was comparing it to ROOSD.