AE911 New Collapse Hypothesis

econ41

Senior Member
I'm all for an "Econ & Orling" 9/11 thread. ;)
Any time. Actually, Jeffrey and I have "discussed" the same issues many times on several forums. We mostly agree but have one big difference in our approach to reasoned argument. One simple example: I can legitimately argue the proof of the sequenced cascading failure of columns driven by load redistribution. My argument based on "the first column to fail was followed by the second column >> third>> fourth...etc WITHOUT ever being able to define which specific column was "first"..... We can never know the specific sequence of column failures. I say we don't need to. Stated more generically you can often progress a generic argument validly without needing specific details. Many engineers and applied science professionals are not comfortable with that process.
 

arsyn

New Member
I'm pretty sure any student with first-year knowledge can do that. After all, I've done it above. :p
You don't need to be able to re-do all of the analysis to understand the nature of the fallacy: to understand that the mathematical model in the paper doesn't match what actually happened.

It's not a rookie mistake, it's an "ivory tower" mistake: he's devised his own theoretical model and uses it without having ascertained that it works in practice.

1. He's a mathematician.
2. Being a mathematician does not make him an expert in physics.
3. He makes rookie mistakes in physics.
4. This means he's a rookie.
Finite Element Analysis is so powerful because we know where it works, and what its limitations are - something that can't be said for Schneider's method. Schneider is a 42-year-old research mathematician and not an engineer, and that's the reason.
I don't know why you mention finite element methods. Whether he used finite element, finite difference or whatever method is irrelevant. He entered the fields of physics and structual engineering assuming he knew the fields without knowing the fields. He made sweeping conclusions in the empirical domain not based on real empirical evidence. Thus he's guilty of speaking of stuff he didn't know shit about. Or, alternatively, he's just being incompetent.
 

Thomas B

Active Member
In any case, the model is one-dimensional, it assumes a progressive collapse of one floor at a time. With the one-dimensional approach, he attempts to calculate the energy dissipation of the collapse, and argues that the extra inserted "resistance" force should be sufficient to arrest the collapse.
Doesn't Schneider at least pose an interesting question that we can actually answer?

The model is "one-dimensional" in the sense that it only worries about the rate of fall. (Technically, that's two-dimensional since it includes time.) It focuses our attention on the fall of two points along the height of the building over time: (A) the roofline, (B) the crushing front (initially the impact floors). We would all agree that the limit for both points would be free fall. Schneider suggests that there will be some "algebraic relation" between the fall of the roofline and the crushing front. This may be debated, but it doesn't matter for my point.

Whatever Schneider is arguing, it should be possible to draw two curves for each of four scenarios. (1) Free fall of both the roofline and the crushing front. (2) Roofline and crushing front according to Schneider's "observations". (3) Roofline and crushing front as would be expected under demolition. And, finally, (4) Roofline and crushing front as it actually happened.

The last scenario will not be based on observations but on the predictions of the ROOSD model. Surely, these eight curves can actually be plotted and compared?
 
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Oystein

Senior Member
... Schneider suggests that there will be some "algebraic relation" between the fall of the roofline and the crushing front. This may be debated, but it doesn't matter for my point.

Whatever Schneider is arguing, it should be possible to draw two curves for each of four scenarios. (1) Free fall of both the roofline and the crushing front. (2) Roofline and crushing front according to Schneider's "observations". (3) Roofline and crushing front as would be expected under demolition. And, finally, (4) Roofline and crushing front as it actually happened.

The last scenario will not be based on observations but on the predictions of the ROOSD model. Surely, these eight curves can actually be plotted and compared?
This gave me an idea:

Schneider's assertion that there will be some "algebraic relation" between the fall of the roofline and the crushing front - he is coming from an assumption that the top block is pretty much stable, except for the accretion at its bottom of one crushed floor after the next. But that is, I think, not actually what the ROOSD model would predict: In the ROOSD model, floor systems detach pretty easily from core and perimeter, and this would happen not only for "bottom block" floors getting impacted from above, but also (albeit at a lower rate) for the lowest of the floors of the falling "top block". These would tend to shear upon impact with the debris layer, while the perimeter might continue at a higher downward velocity.

Because of this, the roofline, early on, would be moving downwards faster than the crushing front - Schneider probably believes it's the other way round.

Schneider is surprised that, in his data, the collapse appears to have slowed a lot just as he switches from measuring roofline to measuring crushing front - but the error could well be that the motion of the roofline is NOT a good proxy for the motion of the crushing front.
In other words: His data can be interpreted disproving "Crush Down before Crush UP" rather than proving that structural resistance increases, then decreases.

----

Having said that: Yes, in principle it should be "possible" to plot your eight curves and compare them. In practice: Not so much.
(1) Freefall is of course trivial. Except it is not exactly clear what "freefall" means for the crushing front, as the debris layer keeps growing. Not a fundamental problem though.
(2) According to Schneider's observations: Ditto - he has plotted this already.
(3) "Under demolition" - well, which demolition? No one has actually proposed a plausible demolition plan.
(4) The ROOSD model is, afaik, worked out only as a qualitative mental model, with some real world observations identified as part of that mechanism. I have calculated for my own elucidation a "momentum transfer model of floor slabs only", that ignores all vertical elements (floors are suspended in mid air until hit by crushing front, whereupon it gets released). I can plot that, and would be reasonably satisfied it models the crushing front. How does the steel cage above interact with the building below? Far more complicated, and I am not sure anyone has come close to quantifying the forces involved, or the balances of energy and momentum, if that is computationally easier. Part of the problem is that some of the perimeter would fall outside the footprint, some inside, and some would cut through perimeter below, edge on edge, with significant resistance that greatly influences the stability of both parts, has the potential to introduce significant angular momentum, and this could only be modeled, I think, with a full, detailed FEA.
 

Thomas B

Active Member
How does the steel cage above interact with the building below?
Yes, that's the question that the one-dimensional model might help us discuss with truthers in simple terms.

In the model, the building below is represented as resistance to the descent of the crushing front, i.e., the bottom edge of the "cage". So we now have a falling cage with a top edge and a bottom edge that are falling at different rates. If the top is falling (i.e., accelerating) faster than the bottom, as you suggest, then the cage is getting shorter, i.e., it is being crushed as it falls.

It gets crushed. It gathers speed. It loses mass and, as Schneider reminds us, runs into gradually stronger columns.

We can plot the position of the top and bottom of the cage from 0 to, say, 16 seconds after the crushing front starts moving.

This would eventually give us a way to describe, second-by-second, the ROOSD of a (very theoretical) 1000-foot building with 100 slabs (10' ceilings) and a single tapered column, which is severed at, say, the 80th floor and its load is shifted onto the floor slab below. (This is just a simplification of Mick's model.)

We just have to describe the state of the structure that corresponds to the locations on the y-axis of the bottom (crushing front) and top (roofline) of the cage at each second along the x-axis.

The ROOSD model is, afaik, worked out only as a qualitative mental model, with some real world observations identified as part of that mechanism.
Yes, the next step would be to translate this into closer qualitative approximations of the actual WTC ROOSD at each second.
 
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econ41

Senior Member
Yes, that's the question that the one-dimensional model might help us discuss with truthers in simple terms.
I simply do not understand how anything can be gained by attempting to mislead truthers further with a false model.
In the model, the building below is represented as resistance to the descent of the crushing front, i.e., the bottom edge of the "cage". So we now have a falling cage with a top edge and a bottom edge that are falling at different rates. If the top is falling (i.e., accelerating) faster than the bottom, as you suggest, then the cage is getting shorter, i.e., it is being crushed as it falls.
Which is utter nonsense. Why not simply explain what really happened
 

Thomas B

Active Member
I simply do not understand how anything can be gained by attempting to mislead truthers further with a false model.
The one-dimensional model is not false, except in the sense that all models are simplifications. It is simply true that the crushing front advanced and the roofline fell (both along the same vertical dimension). Some truthers like Schneider's model, so it's a good place to find common ground. ROOSD, I assume, arrives at different rates of fall & advance than Schneider (ROOSD implies different curves on his coordinate system). Starting with those differences and then explainining how the actual structure produced them makes good sense to me.
 

Mendel

Senior Member.
Because of this, the roofline, early on, would be moving downwards faster than the crushing front - Schneider probably believes it's the other way round.
I confirm that in Schneider's paper, equation (1) makes the crushing front faster than the roofline by a constant factor based on the crush-down.
It gets crushed. It gathers speed. It loses mass and, as Schneider reminds us, runs into gradually stronger columns.
Yes. Schneider's theory departs from reality at that point, because the floor collapse happened differently from the column collapse. (We've both talked at length about the floors and NIST FAQ 18, so I know you're aware of this.)
 

Mendel

Senior Member.
Schneider is surprised that, in his data, the collapse appears to have slowed a lot just as he switches from measuring roofline to measuring crushing front - but the error could well be that the motion of the roofline is NOT a good proxy for the motion of the crushing front.
Could you please elaborate on the first part of that quote?
 

Jeffrey Orling

Senior Member
Once the top blocks dropped... there was no alignment of the columns from the upper block with the lower section of the towers.
The ROOSD mass was contents from the interior which may have included some core columns and bracing... but it was principally the slabs and super imposed loads on them. Its descent reached a "terminal velocity" of about +/- 100'/ second which was measure from timing the bursts of material through the facade ahead of the "ROOSD crush front".

Columns of the lower section offered no resistance to the ROOSD mass.

Facade columns peeled away and were pushed outward by the contained ROOSD mass.

The math is academic basic physics.... and engineering. Each floor offered insignificant resistance to the ROOSD mass... but it slow the descent below "free fall". ROOSD descent was mostly through "air" as the towers are 95% air. There was over pressure which compressed air between the ROOSD mass and the floor it was about to descend on This blew out glazing and forced the destroyed floor contents out the openings.z

The core columns that lasted after the ROOSD hit ground were too slender to stand without the bracing that ROOSD destroyed. There was a "ROOSD" inside the core as well.
 

Thomas B

Active Member
I would expect a bright graduate student in physics or applied mathematics to see through the fluff and dissicate Schneider's paper
I'm pretty sure any student with first-year knowledge can do that. After all, I've done it above.
Let me offer a word of caution.... Temper your optimism as to what other people "see" or don't "see" when it is bleeding obvious to you.
I'd like to see this line of thinking continue. As I "see" it, the following should be be possible:
  1. Draw a curve of the fall of the roofline.
  2. Draw a curve of the progression of the crushing front.
Drawing these curves and explaining them is really what this is all about. It puzzles some people that the roofline and crushing front could progress in one way and, to some, it's an obvious sign that there must have been some additional source of destructive energy. To others, there's nothing strange about it. The curves would just as obviously come out some other way.

Or maybe the curves are not controversial, just the mechanism that produced them. Instead of "desiccating" Schneider, I'd like to see the disagreement explicated in these terms and, ideally, settled.

I don't really see why this shouldn't be possible. The collapses are understood well enough by science.
 

Mendel

Senior Member.
Drawing these curves and explaining them is really what this is all about. [..] I don't really see why this shouldn't be possible.
Please go ahead and cite the data from Schneider's paper (and maybe other sources), and draw the curves.
 

Thomas B

Active Member
Please go ahead and cite the data from Schneider's paper (and maybe other sources), and draw the curves.
I'm working on it, actually. It's not easy.

One thing I've had to acknowledge is this point made by Arsyn:
it assumes a homogeneous "crush down"-front that completely destroys previously undamaged storeys one by one. After seeing posts #119 and #120 in another thread [3], it occured to me that the basic assumptions Schneider - and also Bažant et al. (see references 2,3,4 in ref. [1]) - have made with the crushing front are false,
This is a tough one. But the lower sections of the towers were of course ultimately completely destroyed, so the destruction must have "passed through" them at some (perhaps average) rate (I'm not sure, maybe the average of the lowest destroyed point and the highest intact point.)

And I've been assuming that the hat truss hits the ground in more or less one piece. So its fall is a relatively homogeneous process.
 

Thomas B

Active Member

Because it is at the very top of the mass that is destroying the rest of the building. It's hard to imagine what would tear it apart* before it hits the ground.

If I'm wrong about this, it's something I'd love to read more about. Just imagining the state of the hat truss at 2, 4, 6, 8, 10, ... seconds into ROOSD would clarify a great deal about the "top block" for me.

*[Edit: To clarify, my assumption is that the hat truss is a well-defined structural element that cohers as a unit and would need to be broken apart by the forces that were also busy breaking up the towers below. As I imagine it, it would bind the top three floors together quite rigidly; after all, that's what it was designed in part to do and it was strong enough to transfer loads to the perimeters when the cores were failing. Those forces apparently didn't tear the truss system apart. And it's generally agreed that the lower sections didn't provide a lot of resistance to the falling mass, so, again, I don't see where the forces needed to break up the hat truss would come from.]
 
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Jeffrey Orling

Senior Member
I believe there is evidence that the "crush front" of the ROOSD mass was not footprint "shaped" but some regions of the office space floors led and some lagged behind...
Additionally, the hat truss region contained massive tanks and mech equipment and likely partially broke apart in the early stages of the "initiation" as the ROOSD mass(es) were aggregating. Hat truss was supported by the core and if and when the core failed... hat truss would likely follow and lose some support. It was not a structure supported on the perimeter as much as one distributing some loads (antenna + mech equipment) to many of the columns in core and 16 columns of the facade.
 
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Mendel

Senior Member.
It's hard to imagine what would tear it apart* before it hits the ground.
You still haven't played any civil engineering/bridge buildung games, have you?
And you have not learned from our previous conversation that a strong structure is only strong in the environment it was designed for.

Tilt and irregular fall introduce forces into the truss it was not designed to withstand, so it's not predictable whether it withstood them or not.

Wikipedia:
Argument from incredulity, also known as argument from personal incredulity, appeal to common sense, or the divine fallacy,[1] is a fallacy in informal logic. It asserts that a proposition must be false because it contradicts one's personal expectations or beliefs, or is difficult to imagine.
Content from External Source
 

Thomas B

Active Member
Tilt and irregular fall introduce forces into the truss it was not designed to withstand, so it's not predictable whether it withstood them or not.
I presume you're suggesting something like the forces that broke the Titanic in half when the stern rose above the water. If something like that happened to the hat truss after the collapse started, it could be known quite precisely.

The load paths in the hat truss (and the upper three stories as a whole) are exceedingly well understood. After all, it was designed to redistribute loads. The effect of the application of irregular loads could be predicted with great accuracy. If you could tear it appart by removing supports in the structure below, an engineer could tell you exactly which supports would need to be removed.

If merely tilting and joltling it would do the trick, this too could be described.
 

Thomas B

Active Member
You still haven't played any civil engineering/bridge buildung games, have you?
...forces into the truss it was not designed to withstand, so it's not predictable whether it withstood them or not.
Do you see the contradiction here? The games you keep suggesting that I get my engineering education from are based on the predictability of the effects of forces on structures.

The games work by letting you design something, and then test it by applying gravity loads (irregularly, as it happens, when something has to drive across the bridge.) If you did not design it to withstand the forces that the problem the game poses implies then your bridge will (predictably!) fail.

Likewise, there doesn't have to be any mystery about what happened to the hat truss because its design is well understood.
 

Mendel

Senior Member.
Do you see the contradiction here? The games you keep suggesting that I get my engineering education from are based on the predictability of the effects of forces on structures.
You still haven't played it?
If you did not design it to withstand the forces that the problem the game poses implies then your bridge will (predictably!) fail.
I always design the bridge to withstand the forces, but it usually fails in a way I did not predict.

As the WTC tower breaks apart, there are unknown parts of the building still attached to the truss, subjected to unknown forces not designed for, some of which could be sideways (imagine two opposite columns being pushed apart, which would be levers to bend the truss), and your assumption that the hat truss can withstand these forces as easily as the different forces it was designed to withstand when in place at the top of an intact building is simply not warranted.
 

econ41

Senior Member
@Thomas B - the sidetrack into a discussion of the hat-truss is derailing the topic for no discernable purpose. But, given that you and @Jeffrey Orling both see the hat truss as of some so far undefined significance here are some brief responses to your comments:
If something like that happened to the hat truss after the collapse started, it could be known quite precisely.
No it wouldn't. @Mendel's point of principle is valid. We don't know precisely for the real event. We have no need to know for a false analogy to "sinking the Titanic".
The load paths in the hat truss (and the upper three stories as a whole) are exceedingly well understood. After all, it was designed to redistribute loads.
In the as designed for scenario. It was NOT designed with fire-induced collapse as the scenario for analysis. And the fire collapse scenario cannot be defined sufficiently to allow such post hoc analysis. (It may be plausible with a full-scale investigation of the scale of the NIST work. BUT given that you have no defined reason for such analysis... We don't need to go there.)
The effect of the application of irregular loads could be predicted with great accuracy.
Not so either for the actual collapse scenario or for any other scenario your ambiguous claim is open to.
If you could tear it appart by removing supports in the structure below, an engineer could tell you exactly which supports would need to be removed.
Once again you propose alternate goalposts. We cannot know which supports were actually removed in the real event. And what is the point of speculating about other scenarios which are not the "real event"?
If merely tilting and joltling it would do the trick, this too could be described.
Strawman unless you explain why you are discussing the hat truss otherwise it is "off topic".
 

Thomas B

Active Member
I always design the bridge to withstand the forces, but it usually fails in a way I did not predict.
My point is that the computer can predict the failure.
your assumption that the hat truss can withstand these forces as easily as the different forces it was designed to withstand when in place at the top of an intact building is simply not warranted.
If we imagine the truss like a bridge in the game, it's clear that the computer can calculate the stresses that would cause it break at particular points.

But I'm a bit unclear what we're arguing about now. Are you saying you think the hat truss would probably have come apart or just that there is no way to know? My original assumption was that the hat truss would survive mostly in tact until it hit the ground. I thought you were saying you believe otherwise, and I was just asking you to say a little more about when/how you think it did come apart. How many pieces? And how far apart (in time) did they hit the ground?

I sounds like you're now saying that you have no idea what happened to the hat truss because it is in principle impossible to know. I don't think that's correct.

The key issue (to get back to Schneider) is whether there is a mathematical relationship between the fall of the hat truss and the progress of the crushing front. They are obvioulsy causally related. My assumption is that the physics of that relationship can expressed as a function. (As the games you're talking must certainly do it.)
 

Mendel

Senior Member.
My point is that the computer can predict the failure.
It doesn't. It simulates a failure. The bridge doesn't exist in the real world, so it's not actually a prediction. The computer can do the simulation because it has complete information on the state of the simulated bridge. There's also an element of randomness involved, e.g. in one game, outcomes could differ depending on how long you let the bridge "settle" before dispatching the vehicles.

It sounds like you're now saying that you have no idea what happened to the hat truss because it is in principle impossible to know.
Yes! There's no video of it because it disappeared in a huge dust cloud, and there's not a lot of forensic evidence because search and rescue were priorities. We don't know enough about the exact collapse sequence to accurately model the forces acting on the hat truss.

I'm also saying that it might be possible in principle; because I don't know the forensic evidence, I can't do it; and it certainly isn't possible for you, Thomas, either, based on what you have demonstrated that you know.

You have been called out on an unsupported assumption ("hard to imagine"), and you have provided insufficient support for it; you are now debating whether the assumption is supportable or not, a matter you could settle easily by properly supporting it; but you don't.

Concede that you don't know when the hat truss broke apart (or give evidence), and I'm happy.
 
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Thomas B

Active Member
It doesn't. It simulates a failure. The bridge doesn't exist in the real world, so it's not actually a prediction.
As far as I've been able to tell, these simulations do have a certain amount of realism (which, I assume, is why you suggest them as learning tools). The point is just that, given the initial state of the structure (which is known in the case of the hat truss) we can compute the effects (on that structure) of loading it in various ways.

We don't know enough about the exact collapse sequence to accurately model the forces acting on the hat truss.
But we know the range of possible forces (the available gravity loads) and we know, in broad outlines, how the buildings were affected. We know that the hat truss, in whole or in pieces, hit the ground in less than 20 seconds, not several minutes, for example. (And we certainly know that it didn't stop altogether at some point.) So it is possible to imagine some different scenarios. It's possible to sketch what the structure might have look liked at 2,4,6,8,10, ... etc., seconds.

Btw, I agree with you that the fact that the core columns remained standing a little longer than the rest suggests that the hat truss must have suffered some damage by that point. It's possible that it had completely disintregrated by the time it reached the top of "the spire". I just don't get how.
 

Thomas B

Active Member
Concede that you don't know when the hat truss broke apart (or give evidence), and I'm happy.
I'm happy to concede this point. That's why I stated it as an assumption. I'm not sure that calling an openly stated assumption an assumption amounts to "calling it out".

And I'm not really sure why this remains so adversarial. We're all trying to make the error in Schneider's analysis clear, right?
 

Jeffrey Orling

Senior Member
As I understood it... the hat truss was designed to redistribute a concentrated 360 ton load of the antenna which was atop 3 of the smallest cross sectioned columns. The HT had 8 trusses in each axis and so it was really a 3D space frame not a 2D truss. Each if the 8 trusses had an out rigger to the facade. Some loads were transferred to the facade... but it also function to maintain the geometry of the top of the top block... a sort of "end plate" to the tube structure. Large mech equipment loads were also on the floors of the hat "truss". The core columns supported the hat truss. If there were interruptions of continuity of the core columns there would be loads redistribution via the hat truss... and the columns and their loads above the interruption would then hang from the truss rather than support it. I suppose someone could model what would happen to the hat truss as columns were interrupted and or failed as a result of heat.
It seems reasonable to imagine that at some point remaining intact core columns were at yield strength and further heating or column failure would led to all core columns failing and the hat truss as well as the core side of the outside the core floors losing support.. That would be the "moment of release" when to top block moved downward and likely translated because of asymmetrical support. This was much more pronounced in 2WTC. But it hard to imagine a symmetrical loss of capacity in either tower given the way a fire would behave and the asymmetrical plane damage.

I suspect the hat truss largely maintained integrity until it came down upon the lower block more intact structure. At that point it began to break apart and "joined" the runaway collapsing mass... both inside and outside the core. Floor plates in the top section were also stiffening the upper block's tube shape. They "held" until the impact with the lower block's upper slabs.
 

Thomas B

Active Member
but [the hat truss] also function to maintain the geometry of the top of the top block... a sort of "end plate" to the tube structure.
Yes. This was my understanding as well.
I suspect the hat truss largely maintained integrity until it came down upon the lower block more intact structure.
I don't understand this part. Wouldn't the hat truss always be separated from the lower block by some of the mass of the upper block? As I understand ROOSD, the crushing front was really a chaotic (almost fluid) mass of falling rubble with intact structure above and below being gradually destroyed and added to rubble (and some being ejected).

If I'm understanding @Mendel's objection, it is possible (even likely?) that the destruction that was going on several floors below the hat truss caused irregular stresses on the top floors, i.e., the floors bound together by the hat truss, ultimately tearing it appart. But that still implies an intact structure between the crushing front (rubble) and top floors to transfer those stresses.

But what you seem to be saying, Jeffrey, is that at some point there was no mediating layer of rubble between the hat truss an the "lower block", and only at that point were the stresses sufficient to break the hat truss apart. This could be the point I'm thinking of here, I guess:
I agree with [Mendel] that the fact that the core columns remained standing a little longer than the rest suggests that the hat truss must have suffered some damage by that point. It's possible that it had completely disintregrated by the time it reached the top of "the spire". I just don't get how.
I think your idea, Jeffrey, is a little more plausible: at some point the hat truss encounters the lower portion of the undestroyed core directly and is skewered by it. Since
the columns and their loads above the interruption would then hang from the truss rather than support it
we can imagine the inertia of the perimeter columns (with some floors still attached, "hanging") continuing unsupported downwars and the sudden slowing of the core as it impacts the lower core finally doing the hat truss in. But this could happen even with quite a lot of intact structure (to transfer forces) between the hat truss and lower section. So long as the perimeter is being destroyed faster than the core, this irregularity (with the perimeter "hanging" off the truss and the core resisting its fall will be present.

I don't know if this makes sense in light of all the observations. But I think it's possible. Thanks.
 

Thomas B

Active Member
Please go ahead and cite the data from Schneider's paper (and maybe other sources), and draw the curves.
I think I've found a way to represent my take on this visually. I'd love to hear what you all think. I have incorporated Mendel's suggestion that the hat truss translated and disintegrated on the way down. And I've represented the lagging collapse of the core as as well.

(TL;DR: What I'd like to hear from people here is whether ROOSD actually implies somewhat different curves than the ones of I've drawn here. The more accurately I represent ROOSD, the better. I think I'm starting to understand it.)

IMG_0534.JPG
This isn't a strictly mathetmatical model, but it captures some interesting things. One way to read it is simply as two continuous curves of height over time (meters on the y axis, seconds on the x). I plotted it simply as a function of 2/3 g, a bit slower than free fall, but continuously accelerating. The blue line starts at 400 meters (bottom edge of the hat truss) and the red line at 340 meters (lowest impact floor). Notice that the red line "widens", which we can take as the top and the bottom of the crushing front (the mass of rubble proposed by ROOSD).

But a more interesting reading takes each second as a "snapshot" of the state of the tower spaced one second apart. The tilt of the hat trust increases, and the crushing front has a lowest and highest point. Notice I've drawn the core in as well. It gets shorter and shorter (but remains intact) between the crushing front and the hat truss. At 8 seconds we reach the tip of the "spire" seen in the photos. Here I imagine (on Mendel's suggestion) that the hat trust must have broken into pieces and then continued to fall around the core, some pieces held back a little by the remaining core and some pieces falling faster or slower on top of the rubble.

After the crushing front (rubble mass) reaches the ground and the hat truss soon follows (the velocities are of course quite high at this point) the base of the core apparently gave out and the spire fell. I've indicated that in rough form as well.

All of this is of course approximate. And the next step would be to look at time-indexed photographs to adjust each snapshot to make it more realistic.

But the point I was trying to make is that this must be something like what happened. The descent of the hat truss and crushing front must be continuous functions and the front necessarily "leads" the hat all the way down.

This can be compared to Schneider's curves. He notes a change of acceleration around the 5 second mark that, to him, would have arrested the collapse at 300 meters after about 4 more seconds if not for some additional destructive energy. I assume we agree that that's just empirically wrong, the result of poor data.

Again (per TL;DR above), what I'd like to hear from people here is whether ROOSD actually implies somewhat different curves than the ones I've drawn here. The more accurately I represent ROOSD, the better. I think I'm starting to understand it.
 

Mendel

Senior Member.
I think I've found a way to represent my take on this visually.
Other than the height of the building and the height of the spire, what data from the actual collapse is represented in that drawing?

(My position is not that the hat truss disintegrated on the way down, my position is that we don't know whether it did.)
 

Thomas B

Active Member
Other than the height of the building and the height of the spire, what data from the actual collapse is represented in that drawing?
There were a few more things I looked up.

I used the NIST FAQ to locate the intersection of the red and blue lines with the x axis between 10 and 12 seconds.

This confirmed something I think @econ41 said about the average resistance being roughly 1/3 g.

NIST also has the spire standing for about 10 seconds which seems to work nicely with it beginning to fall roughly at the time the hat hits the ground. But shifting the onset of spire collapse a few seconds to the right wouldn't change much as far as I can tell.

The initial distance between the hat truss and the crushing front is also factual.

Like I say,
All of this is of course approximate. And the next step would be to look at time-indexed photographs to adjust each snapshot to make it more realistic.

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(My position is not that the hat truss disintegrated on the way down, my position is that we don't know whether it did.)
Yes, I wanted to see what that possibility could look like. The alternative, I guess, is that it tilted so far that it was essentially perpindicular to the ground when it reached the top of the spire and finally landed on its side. This would affect the curves, just the distribution of those blue bits.

Your suggestion made me realize that something must have happened that left the core standing without stopping the hat truss from falling.
 

Thomas B

Active Member
It broke apart like all the rest of the beams and bracing... and fell down WITHIN the ROOSD mass.
Interesting. But were elements able to fall faster within the ROOSD mass than the crushing front itself progressed to the ground? That is, can we imagine pieces of the hat truss moving to the bottom (or even middle) of the ROOSD mass before the crushing front (the bottom edge of the mass) gets to the ground? And can we imagine the hat truss outpacing (and outmaneuvering) pieces of the floor trusses of the, e.g., 101st floor?
 
What's the best theory of how it got there?
Legit question: why the focus on the hat truss? Why would we expect it to ride the collapse downward without breaking apart, when very clearly no other major assembly did? Consider the antenna. I don't recall seeing it lying in (or atop) the rubble pile in aerial shots. At least one of the very topmost floors of each tower was an equipment floor, with a reinforced floor pan. Those were completely shattered, weren't they? The building cores were of solid I-beam construction - and they were completely ripped apart above the 50th floor or thereabouts.
 
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