WTC: Rate of Fall (rate of crush)
- Thread starter George B
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OneWhiteEye
Senior Member
The result is entirely dependent on the model and the numbers used. Bazant has calculated one thing, Tony would calculate another - same basic model. One leads to continued collapse, the other arrest.
The assignment of average residual capacity is the lynchpin of a model like this. There is a theoretical value which could be obtained if a given story were placed in some gigantic hydraulic press and crushed in a perfectly axial, ideal manner, but that has little or no practical value. That's what Tony's calculations amount to. Literally, it's calculating the performance of the whole building as as if each of the constituent parts were in a lab test apparatus being individually crushed between plates.
It's silly to get out a magnifying glass and tally up all the best estimates for as-built performance when even relatively small misalignments render it all moot. For something this complex, and at this stage of engineering advance, there is still (IMO) no option besides observe and learn. If both of the towers are disallowed from consideration because they might be CDs, there's nothing empirical on which to base an expectation for these structures. The verinage examples involve entirely different architecture affording massive redundancy in load paths and some inevitable recrushing of vertical supports, not comparable at all. In fact, these structures are ones which could be intuitively categorized as having load-displacement characteristics where the peak doesn't exceed the average by much, if at all.
OneWhiteEye
Senior Member
If understand your diagram correctly, and I think I do, yes.
There are formulas for all manners of things in this regard, but are they meaningful? Anything beyond a simply-shaped, isotropic solid with a limited number of applied forces or simple static frames is starting to get into the domain of numerical (FEA) analysis. Hand calculations are useless for complicated structures undergoing large scale dynamic multi-modal deformation in far from equilibrium (and largely unknown) conditions. And FEA itself has not typically been done to the scale and level of detail this would require, definitely fringe of reliability or beyond.
Because of the uncertainty in initial conditions and complete invisibility of so many chaotic variables, the only sensible analytic approach having a relationship to the real collapse would have to be stochastic in nature. It would speak of likelihood of some outcome, not produce singular results to the nearest 0.1 m/s. And it would be driven in large part by empirical results.
The citations being discussed right now? That's an entire subdiscipline of people with advanced degrees trying to characterize the performance of small single tubes with a high degree of uniformity, crushing under tightly controlled conditions.
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qed
Senior Member
My point is that if it is clearly (or obviously, or by the simplest approximation formula) weaker, then Tony's model of two or more story arrest is false.
OneWhiteEye
Senior Member
This response was a misinterpretation of your question. The diagram made your question clear to me, qed. So ignore this.
So what would your analysis be in terms of speed at impact as opposed to the resultant 19mph that Bazant supposed?
OneWhiteEye
Senior Member
I assume you mean an analysis of predictive nature as opposed to a video analysis to determine what it was. I don't have such an analysis. Bazant assumed freefall, clearly that didn't happen. It's very easy to assume a resistive force and calculate what motion would result from that, but to start from initial conditions and engineering estimates and try to predict what it should be --- no, no idea I'm afraid. More than zero resistance, but I wouldn't even hazard a guess beyond that.
OneWhiteEye
Senior Member
If, on the other hand, you do mean how fast was it actually going at impact...
There are several sets of measurements which are quite accurate, but please keep in mind that these represent the motion of a single point or small region... the motion is not strictly vertical nor linear... the notion of "impact" time/location is at best fuzzy and at worst academic... it depends on tilt and full compaction height IF columns or spandrels actually collided to any great degree... simultaneity of impact is out of the question. I'm not one of those people that believe measuring vertical deflection in the image plane of one point on the roofline fully characterizes the motion of the upper block, I'm not even someone who believes there was anything resembling an upper block after a short period of time.
Edit: nor do I consider the notion of an upper block anything more than a sometimes useful simplification. Fiction.
There are several sets of measurements which are quite accurate, but please keep in mind that these represent the motion of a single point or small region... the motion is not strictly vertical nor linear... the notion of "impact" time/location is at best fuzzy and at worst academic... it depends on tilt and full compaction height IF columns or spandrels actually collided to any great degree... simultaneity of impact is out of the question. I'm not one of those people that believe measuring vertical deflection in the image plane of one point on the roofline fully characterizes the motion of the upper block, I'm not even someone who believes there was anything resembling an upper block after a short period of time.
Edit: nor do I consider the notion of an upper block anything more than a sometimes useful simplification. Fiction.
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I agree, Bazant got it hopelessly wrong and exaggerated velocity to support his preferred conclusion.
So it should be easy therefor to see how accurate Bazant actually was, by calculating the momentum transfer that would occur if indeed we simplify, as he did, and think about 2 blocks. In such an analysis the collapse would be arrested in one or 2 floors.
Why not?
Neither am I, the upper block is not actually observed to be causing damage to the building below at the start of the collapse. For what reason do you not believe that the upper block remained intact at the point at which it would be impacting that part of the building below?
qed
Senior Member
@OneWhiteEye
Given that multi-story arrest is out of the way, we have only "single" story arrest to refute. The italicised "single" pertains to the following questions.
When the critical floor breaks:
[pre]
|_____________|
|_____________|
|_____________|
|_____________| _
| _ _ _ _ _ _ | _ ↕ 3.7m
|_____________|
[/pre]
An auxiliary question: what is the technical name for the 36' (11m) long sections that are spliced together every three floors?
Given that multi-story arrest is out of the way, we have only "single" story arrest to refute. The italicised "single" pertains to the following questions.
When the critical floor breaks:
[pre]
|_____________|
|_____________|
|_____________|
|_____________| _
| _ _ _ _ _ _ | _ ↕ 3.7m
|_____________|
[/pre]
- Is the buckling column 3.7m long or 7.4m long?
- Which value does Tony take when "justifying" the column to be stout?
- When the falling upper part encounter the next story, has it fallen 3.7m or 7.4m?
- Am I correct that I read that Tony assumes 3.7m?
An auxiliary question: what is the technical name for the 36' (11m) long sections that are spliced together every three floors?
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qed
Senior Member
@Tony Szamboti
Your only route out from the flaw in your argument for two story arrest, is to provide us with a realistic value (with justification) for the energy capacity of the second "column", which you falsely assumed undamaged, after the floor broke when the upper section impacted.
The state of the system would be a column extending freely 3.7m above its last supporting floor.
[pre]
Eₖ₀
? ⇓
⇑ |_________| } 3.7m
[/pre]
Your only route out from the flaw in your argument for two story arrest, is to provide us with a realistic value (with justification) for the energy capacity of the second "column", which you falsely assumed undamaged, after the floor broke when the upper section impacted.
The state of the system would be a column extending freely 3.7m above its last supporting floor.
[pre]
Eₖ₀
? ⇓
⇑ |_________| } 3.7m
[/pre]
- What is the energy capacity ? of the column assuming no other damage?
- What is the buckling load in this state?
OneWhiteEye
Senior Member
He did choose a drop of 1 story to initiate, but then he went back and re-figured (using his numbers) to see what the threshold would be to precipitate collapse and found a drop height value of 0.5m. That amounts to an impact speed considerably less than actual.
Again, it's all in whose numbers are used and in what way. The easiest way to render Bazant wrong or irrelevant is to note the actual collapses didn't conform to the model he uses. Problem is (if you're trying to show arrest), that same argument also applies to Tony Szamboti, who uses the same model. Bazant's shtick has been that his model represents a bounding case which requires the maximum energy to crush and would therefore tend towards survival as much as is possible.
We've just seen how freefall through an entire story is excessive, and I do not dispute Tony's engineering estimate which holds the as-built capacity should be considerably greater than Bazant calculated, as well the driving mass considerably less. So Bazant does NOT describe the most optimistic case for survival, just an optimistic one. If the real collapses did not conform to these optimistic conditions, then not only is the model incapable of producing realistic expectations, we also know the expectation has to be less optimistic.
What Bazant did was try to show that it collapses even in the best case scenario. What Tony has done is show that it might not collapse in the best case scenario, after corrections to the estimates. That's not entirely useless in itself, after all, it could replace Bazant's analysis as the most conservative. What it does not do is show the structure should have survived, which is Tony's intent.
I'm a true believer in the adage "once the top starts moving, there's no stopping the collapse." That belief is not based on calculation, but not on faith, either. The problem is resolved through observing that no viable load paths emerged during the early stages of collapse which were capable of supporting the static load, let alone dissipate the momentum of a moving load. This, of course, is the point Tony is arguing with me - his position being there HAD to be be full (or near) capacity load paths available and so the structure would arrest. The disagreement comes down to this: Must there be full capacity, or must there not be?
The motion of the upper section, even assuming the upper section to be a rigid integral unit, is not simply vertical displacement. If it were, then measuring the motion of a single point would be representative of the block as a whole. When there's displacement and rotation in multiple axes, and unknown amounts of disintegration of the unit, it becomes less so. Fortunately, the motion was predominantly vertical right after release, and it could take a while before the upper section is dissociated significantly. The closer the measurement is to the release time, the better.
I should clarify: it may have been mostly intact after the descent of one story (first impact), but likely not for long.
OneWhiteEye
Senior Member
We have to make sure your model comports with Tony's or it will be rejected out of hand as irrelevant to the argument. I believe it does, but let me describe and verify.
The entire blue section moves downward as a unit, the green remains stationary. The black part with the dashed line and height indicator is the initial failed story. The vertical lines representing the columns of the failed story shorten (buckle) until the blue slab is in proximity of the dashed slab, then "impact" occurs. At this moment, the black columns are fully compacted and none of the blue or green are buckled at all. All floor slabs are essentially intact.
1) The buckling is 3.7m at maximum in this scenario. It actually could be taken as shorter because the spandrels fix the ends at less than a story height.
2) It seems he considers 3.7m to be stout, but I have seen him use the reduced length. He might actually have something in the latter case - theoretically, but not practically.
3) 3.7m assuming the full story height, definitely not 7.4m. In addition to an effective reduction in length based on where the ends are fixed, there is also the fact that the columns will not squash to zero height. It's customary to consider full compaction to be 10-20% of original height, but this is usually done with an original height of 3.7m; the spandrels are rolled in with the buckled column (and only exist on the perimeter).
4) Yes, for impact distance. That's not very consistent of him, because he's noted both conditions of effective length shortening and finite compaction height. So one could argue even Tony has not yet concocted the most optimistic scenario theoretically possible. If the first impact takes place sooner (less drop), the lost PE is correspondingly less.
If there were angels, and if they danced on pins, and if enough of them decided to do so on one pin at the same time, determining maximum capacity of the pin might have some value.
For the perimeter assemblies, trees. For the core, just columns.
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qed
Senior Member
@OneWhiteEye
When the critical floor sags and buckling begins, why is it only the upper black | (3.7m) that buckles, rather than both the upper black | and the lower green | as a 7.4m buckling unit?
When the critical floor sags and buckling begins, why is it only the upper black | (3.7m) that buckles, rather than both the upper black | and the lower green | as a 7.4m buckling unit?
qed
Senior Member
In the diagram
[pre]
|_____________|
|_____________|
|_____________|
|_____________| _
| _ _ _ _ _ _ | _ ↕ 3.7m
|_____________|
[/pre]
I am only drawing from the left outer column to the start of the central columns. That is, column, floor, column. The left third.
A full floor would be
[pre]
|_____________|_|_|_|_|_|_|_____________|
[/pre]
[pre]
|_____________|
|_____________|
|_____________|
|_____________| _
| _ _ _ _ _ _ | _ ↕ 3.7m
|_____________|
[/pre]
I am only drawing from the left outer column to the start of the central columns. That is, column, floor, column. The left third.
A full floor would be
[pre]
|_____________|_|_|_|_|_|_|_____________|
[/pre]
OneWhiteEye
Senior Member
I've argued with Tony long enough to know that his response will be, "No, it isn't out of the way. My calculations/paper show that arrest is inevitable after at most two stories' of descent."
THIS is the problem in the debate. I've probably done more than my share of muddying the waters because it just happened to be at a time when my "angle" has been to retain as many of Tony's assumptions as possible, no matter how unrealistic, and yet still show the position to be wrong. It emphasizes the point if you already know all of the other legitimate objections, otherwise it may just obscure the point. It might give the impression that stick figure illustrations which are just 2D representations of a simple 1D model can meaningfully represent the kinematics of a complex, differentiated 3D collapse.
Don't worry, qed and Jazzy, your stick figures follow in a long tradition of doing so - performed by countless people, some with PhDs after their name, some not (like me). It is possible to adapt and refine a 1D model to incorporate all manners of phenomena which exist outside of 1D (see Bazant, Le, Greening and Benson) and obtain a more accurate approximation, but there's only so much polish you can put on a turd.
The best way to understand the kinematics is observe the collapse. Once you get an idea of WHAT happened, regardless of WHY it happened, you'll quickly give up on trying to discriminate through quantification. The generic ideas of things like collapse time and crush front velocity lose all meaning.
Unfortunately, if you leave open the possibility that it's not natural in either or both of initiation or progression, then you can't use the observed kinematics to say this is what a natural collapse of the towers looks like. I see variants of that more than you think - the prime example being anyone invoking Bazant et al to say the theory matches observables so therefore it's a natural collapse. That is most certainly a bad leap. The narrative is so different from the actual that drawing correspondence is an ivory tower exercise. Mind you, it's an exercise anyone trying to argue (with e.g. Tony) should go through, but it's not the answer to the dynamics. It's a tool.
All I'm saying is, the argument is outside the realm of decision based on kinematics alone. One must venture outside the numbers into the qualitative domain to develop confidence. The funny thing is, one person looks at the images and sees a natural collapse - very obviously - and another looks and sees an obvious CD. Now, it's all up to interpretation! Naturally, if it were possible achieve a proof in the domain of physics, it would be a holy grail for those who (already) believe in CD. The person who finds the Holy Grail....
That's what you're seeing here.
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OneWhiteEye
Senior Member
I didn't see these while I was writing the above.
If it's outside the scope of a literal 1D storywise approximation, Tony will not admit it into the discussion. It was like pulling teeth to get him to admit to any eccentricity at initiation! He will probably say something to the effect of "the sag only affected the limited areas of inward bowing on the south side and correcting for this wouldn't change the result significantly, especially since we already account for a loss of capacity in the failure zone."
Yes, I'm at the point of putting words in his mouth.
Quick answer: it's not part of Tony's scenario. It should be. There are so many angles, I hadn't even called that one out yet. Good job.
If it's outside the scope of a literal 1D storywise approximation, Tony will not admit it into the discussion. It was like pulling teeth to get him to admit to any eccentricity at initiation! He will probably say something to the effect of "the sag only affected the limited areas of inward bowing on the south side and correcting for this wouldn't change the result significantly, especially since we already account for a loss of capacity in the failure zone."
Yes, I'm at the point of putting words in his mouth.
OneWhiteEye
Senior Member
qed
Senior Member
@OneWhiteEye
- Notice that Tony is no longer really participating in this thread.
- If Tony can publish that, then surely a sound counter-argument is also publishable. Even if it must be in the same "journal", it would still embarrass him and weaken his effect.
OneWhiteEye
Senior Member
1) hahahaha.... uh huh. He'll be back, though, I predict. He's got a life and work takes him out of the house 12 hours on weekdays.
Also, he hasn't gotten enough mileage yet out of simply ignoring and denying points made, though I trust you've seen that in play already. Hasn't even pulled the anonymity card yet; it's possible that objection was covered in advance, but I doubt it. Very likely to announce departure, because it gives the opportunity to spin. "None of the arguments are valid, I've refuted them all, bye."
Lest anyone think I'm personalizing my argument, please allow me disabuse you of that uninformed opinion. The argument is indeed personalized. Tony made it so. His tactics over the last few years have consistently been as I described upthread. These are not legitimate debate tactics, which go from pretending an opponent doesn't exist to declare-victory-then-cut-and-run. Sweeping one-line denials of painstakingly assembled walls of text with references does not an argument make. If I can't call this out as arguing against the argument, rather than against person, then I'm arbitrarily hamstrung for no legitimate reason and this lets the offender repeat the cycle.
If I didn't call it out in advance, you'd all figure it out after he's gone and history repeats itself. If I call it out and if it influences him to be less likely to resort to such tactics, my prediction will be wrong but there will be a more interesting argument.
2) Yeah, but what a pain in the ass for questionable results. No one of repute except his current co-author (who's reputation is known to some degree) takes this seriously. Most people with relevant skills are not looking at this debate, whether their rationale is good or not. If they do look into it with sufficient depth to judge the merit, the vast majority will not side with Tony.
The lack of interest in this "smoking gun" amongst the engineering community at large says a lot. My supposition that most would find against Tony's conclusion is not a given, but I'd bet large sums on it. It's absurdly unrealistic. It's hard not to find a hole in every other paragraph. Peer-reviewed, my ass. In that respect, it falls on its own merit.
The only thing a comparably placed paper would achieve is to have something to wave at those waving Tony's paper. They don't understand Tony's paper and they won't understand yours. They won't read either one in much detail or at all. People argue for/against Bazant/Szamboti all the time without reading and understanding either side. You'll end up arguing the specifics in a simplified fashion, as we're doing here.
OneWhiteEye
Senior Member
qed
Senior Member
@OneWhiteEye
Do you see any scientific objection with considering a 7.4m buckling unit rather than a 3.7m?
While I understand your concerns with tracking the flag, I am looking at Chandler's velocity-time diagram on page 8 (and the h-t diagram on the previous page) and it fits this picture.
The acceleration decreases at about 2.1-2.25 sec (7-8m) which is when it impacts the second floor. The first floor impact does not decrease the acceleration because it was already broken and the column buckling above and below it. Impacting the second floor, however, does decrease the acceleration slightly.
If 3.7m is stout, 7.4m is not.
Please think about this.
Do you see any scientific objection with considering a 7.4m buckling unit rather than a 3.7m?
While I understand your concerns with tracking the flag, I am looking at Chandler's velocity-time diagram on page 8 (and the h-t diagram on the previous page) and it fits this picture.
The acceleration decreases at about 2.1-2.25 sec (7-8m) which is when it impacts the second floor. The first floor impact does not decrease the acceleration because it was already broken and the column buckling above and below it. Impacting the second floor, however, does decrease the acceleration slightly.
If 3.7m is stout, 7.4m is not.
Please think about this.
OneWhiteEye
Senior Member
Unfortunately, while work only (usually) takes me out of the house once or twice a week, I still have a pretty full plate today, so I'll be back later.
OneWhiteEye
Senior Member
Just a quick point. Aren't the 'trees' the bits at the bottom of the tower which transition from 19 main to 57 outer columns(per face)?? They go from one to three columns. Trees is not a term for the outer columns really apart from these transitions. I have a drawing for them somewhere if you want I could look it out. The term for the outer columns is just that. The "outer columns".
qed
Senior Member
Thanks Gerry.
- Is there a technical term for the 11m single units that get spliced together to make one outer column?
- Is the buckling dynamics similar for one such 22m single unit compared to two spliced 11m units acting as one column?
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qed
Senior Member
Are you saying
- I cannot consider the initial buckling column as 7.4m (above and below the sagging floor),
- or that I can and that it makes a big difference?
It seems to me that it really is a 7.4m buckling system and that this does make a big difference. The 7.4m unit is far less stout, will offer less resistance, and will buckle like a classical 3-hinge.
I would just call these box steel sections. As for the buckling, the slenderness ratio, and the 3-hinge thing, I personally don't think that it is as straightforward as it may seem. The paper that Tony was involved with goes into some great detail as to the application of the different methods used in these calculations. For example, Euler theory is often cited but as the paper shows, it is not applicable to columns of this kind of thickness. The structural make up of the transition itself is also relevant. At the upper stories the box columns would transition to heavy rolled wide flange sections ('H' shaped), so again, there isn't a one size fits all example for transitions.
edit - I just noticed you were asking about outer, sorry. I would just call these perimeter sections. They would be made up on a jig in the shop, and obviously the outside dimensions would remain constant, but the wall thickness would decrease with height. There is a pamphlet from 1964. "Contemporary Steel Design," Vol. 1, No. 4." that may help you on terms, and is an interesting read even if it doesn't. http://www.engr.psu.edu/ae/WTC/AISI/wtcaisi1.pdf is the link to the first page. You just change the number in the link to see the rest from 1 up to 5.
edit - I just noticed you were asking about outer, sorry. I would just call these perimeter sections. They would be made up on a jig in the shop, and obviously the outside dimensions would remain constant, but the wall thickness would decrease with height. There is a pamphlet from 1964. "Contemporary Steel Design," Vol. 1, No. 4." that may help you on terms, and is an interesting read even if it doesn't. http://www.engr.psu.edu/ae/WTC/AISI/wtcaisi1.pdf is the link to the first page. You just change the number in the link to see the rest from 1 up to 5.
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I guess on paper, the 22m is more slender, but like i said, there's a lot more to it. There's a good shot of them here which shows that the connections were staggered. The holes are where the rigger would reach in and bolt them up
http://911research.wtc7.net/mirrors/guardian2/wtc/fig-2-8.jpg
qed
Senior Member
- I would like to go with splicing is similar or slightly stronger than non-spliced units.
It seems correct and eases the modelling.
But, if you (or anyone) ever comes to learn that spliced units are significantly stronger, please call me on it.
OneWhiteEye
Senior Member
I guess FEMA didn't get the memo.
Not saying you're wrong, just saying that the term 'tree' is commonly used for the perimeter assemblies in general.
OneWhiteEye
Senior Member
OneWhiteEye
Senior Member
Yes, I admitted there might be a case for another axial compression mode (if it mattered at all). However, he has disavowed the other failure modes and claims he's working with three-hinge, so there you go. He didn't seem to know what I was referring to when I brought it up.
Tony Szamboti
Active Member
Buckling failure for columns with a slenderness ratio below 100 is called inelastic buckling and it requires compressive sresses very near yield strength to occur. We explained this in the paper. This is different from Euler buckling, which can occur in situations where the compressive stresses are in the elastic range but only when the slenderness ratio is high.
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OneWhiteEye
Senior Member
Excuse me but the notion of three hinge buckling in this context has never been considered as any thing but plastic. Look in Bazant. Everywhere the word "hinge" appears, the word "plastic" appears before it. This has never been about elastic buckling. With respect to concertina, diamond, mixed and Euler axial failure modes, Euler buckling is used to refer to all macrobuckling.
The columns would in reality go through three phases of distortion when buckling. As for Euler, that is only really applicable to the most slender of steel elements. Have you actually read the paper that Tony refers to? I did and I think it brings up many salient points.
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