WTC: Rate of Fall (rate of crush)

[Tony Szamboti]

And that lateral force was produced on both occasions. Visibly, for all to see. The "tilt" not being small at all.

OneWhiteEye has just taken the words right out of my mouth: "Insisting that columns MUST remain aligned due some imaginary pseudophysics when it's apparent from direct observation that they were NOT... I mean, come on. Bam! Your entire argument swept away in one sentence."

You seem to live in a different world with what you observe.

 

[Tony Szamboti]

Eh? People are just supposed to take your word for it after the 180-degree-column-bend-with-"no"-fracture debacle, where you can't even acknowledge you were wrong?

It's possible that a great deal of the discussion we've had here cannot be evaluated by readers, but that particular case is glaringly obvious to everyone. It's regrettable that so many aspects are not resolved so easily. Personally, I feel that ALL of your mistakes are that obvious. Insisting that columns MUST remain aligned due some imaginary pseudophysics when it's apparent from direct observation that they were NOT... I mean, come on. Bam! Your entire argument swept away in one sentence.

That box column did not fracture immediately and it only fractured on the tensile side at that. You have to know that. The only argument you can seem to make at all, when it comes to the energy dissipation being large, is that there would be some fracturing. But you can't quantify it and probably won't even try as it would be shown to occur late in the game.

The reality is that there would have been tremendous energy dissipation by the columns in a natural collapse and at the very least an enormous jolt, if not an arrest, after a one or two story collapse.

Bazant was shown to be fibbing in his January 2011 paper. The Plastic Moment (Mp) value of 0.32 MNm, that he gave for the columns, was far below the reality of at least 0.64 MNm. You know this too and yet don't comment on it. He also fibbed about the floor mass to diminish the inertial resistance. He did both of these in addition to using an upper section mass nearly twice what it was in reality and using free fall through the first story in a vanishing story concept to embellish the kinetic energy.

It is obvious that Bazant was stretching things far beyond reality in an attempt to bolster the official lie on how those buildings came down. Bazant is a disgrace and so is anyone who supports his work on the WTC.

 

[OneWhiteEye]

You seem to live in a different world with what you observe.

Attached is another WTC structural member with 180 degree bending. No fractures are observed. We can't see the entire tensile side, but even if there were some small amount of fracture it would not affect the energy dissipation during buckling to any large degree.

 

[OneWhiteEye]

That box column did not fracture immediately and it only fractured on the tensile side at that. You have to know that. The only argument you can seem to make at all, when it comes to the energy dissipation being large, is that there would be some fracturing. But you can't quantify it and probably won't even try as it would be shown to occur late in the game.

The reality is that there would have been tremendous energy dissipation by the columns in a natural collapse and at the very least an enormous jolt, if not an arrest, after a one or two story collapse.

Bazant was shown to be fibbing in his January 2011 paper. The Plastic Moment (Mp) was far above his value of 0.32 MNm which he simply stated without giving a wall thickness for his 14 inch square box columns. You know this too and yet don't comment on it.

Are there laughing dog gifs on this forum? I generally disapprove of them - strongly - but I found myself searching for one just now.

 

[qed]

Bazant was shown to be fibbing in his January 2011 paper. The Plastic Moment (Mp) value he gave for the columns of 0.32 MNm was far below the reality of at least 0.64 MNm. You know this too and yet don't comment on it.

We are focussing on your paper that "proves" arrest in one or two stories.

And please answer my questions above.

 

[OneWhiteEye]

We are focussing on your paper that "proves" arrest in one or two stories.

And please answer my questions above.

Does he have you on ignore? 'Cause he sure is doing that.

 

[OneWhiteEye]

I have limited time to respond to this nonsense, not just because I've got 15 minutes to spare before leaving to do something interesting... life itself is too short. I'm only going to say these things one more time.

That box column did not fracture immediately...

BS. There is actually more than 180 degrees end rotation but, if you reverse that rotation back to where the wall is beginning to peel - the point in time of fracture - I'd estimate the total rotation to be only about 50-60 degrees max. And that's over what looks like about a story's length or more. Very small radius of curvature at the point of fracture. Nowhere near the 70-170 degree bends in a small fraction of a story height which your partner's FEA displays. The corresponding local strain in this REAL column which DID fracture is shown empirically to be far less than his FEA would predict. Exactly what I've been saying all along - excessive ductility.

... and it only fractured on the tensile side at that.

Hahaha... three of four walls in a box column are fractured. Yes, it was only the tensile side. That should inform you somewhat on the real world behavior of crack formation and propagation. I cannot believe I'm talking to a mechanical engineer. Do you have a licensing agency?

You have to know that.

Hahahaha...

The only argument you can seem to make at all, when it comes to the energy dissipation being large, is that there would be some fracturing.

False. I have many arguments and most have been tabled in front of you before. That you choose to ignore them until you flee is not a deficiency on my part. Fracture of columns is WAY down on the list. There was less evidence of fracture in the debris than simple deformation! How the hell could that be my only argument? It's a minor part of a large tree of arguments that get down to all the minute details you get wrong. You are about as wrong as you can be.

Here's the first objection again: Insisting that columns MUST remain aligned due some imaginary pseudophysics when it's apparent from direct observation that they were NOT.

But you can't quantify it and probably won't even try as it would be shown to occur late in the game.

The column you introduced into evidence proves otherwise.

The reality is that there would have been tremendous energy dissipation by the columns in a natural collapse and at the very least an enormous jolt, if not an arrest, after a one or two story collapse.

Blah, blah, blah. I'll say one thing for you, you sure can stay on message in the face of adversity. It's a common CT trait, though. Bye.

 

[qed]

@Tony Szamboti

In you paper, how long is the initial buckling column?

 

[Tony Szamboti]

I have limited time to respond to this nonsense, not just because I've got 15 minutes to spare before leaving to do something interesting... life itself is too short. I'm only going to say these things one more time.


BS. There is actually more than 180 degrees end rotation but, if you reverse that rotation back to where the wall is beginning to peel - the point in time of fracture - I'd estimate the total rotation to be only about 50-60 degrees max. And that's over what looks like about a story's length or more. Very small radius of curvature at the point of fracture. Nowhere near the 70-170 degree bends in a small fraction of a story height which your partner's FEA displays. The corresponding local strain in this REAL column which DID fracture is shown empirically to be far less than his FEA would predict. Exactly what I've been saying all along - excessive ductility.


Hahaha... three of four walls in a box column are fractured. Yes, it was only the tensile side. That should inform you somewhat on the real world behavior of crack formation and propagation. I cannot believe I'm talking to a mechanical engineer. Do you have a licensing agency?


Hahahaha...


False. I have many arguments and most have been tabled in front of you before. That you choose to ignore them until you flee is not a deficiency on my part. Fracture of columns is WAY down on the list. There was less evidence of fracture in the debris than simple deformation! How the hell could that be my only argument? It's a minor part of a large tree of arguments that get down to all the minute details you get wrong. You are about as wrong as you can be.

Here's the first objection again: Insisting that columns MUST remain aligned due some imaginary pseudophysics when it's apparent from direct observation that they were NOT.


The column you introduced into evidence proves otherwise.


Blah, blah, blah. I'll say one thing for you, you sure can stay on message in the face of adversity. It's a common CT trait, though. Bye.

What happened to your concertina argument? Why is there no fracture after 180 degree bends in the attached example of it on a box section?

And what happened to the large H column in the attached? There is no fracture there.

The reality is that structural steel is quite ductile and fracture is not guaranteed during buckling as it depends on bend radius and the amount of stretch relative to the length of the bend. There is no chance for fracture at the 50 to 70 degrees of rotation that you want to claim. If it happens at all it would be much later than that.

What is guaranteed is that the columns would have absorbed a lot more energy than what Zdenek Bazant claims and that there should have been an enormous deceleration in the fall of the North Tower in a natural collapse after a one or two story fall.

The refutation of his January 2011 paper proves that Zdenek Bazant is fibbing in his papers on the WTC, and by association so are those who are capable of understanding the issue but still support his work.

 

[qed]

@Tony Szamboti

We both know that you are refusing to answer my questions for fear of incriminating yourself.

While this is legitimate behaviour in court or in politics, it is scientifically immoral.

So I will ask again.

@Tony Szamboti

In you paper, how long is the initial buckling column?

 

[Mick West]

I have seperated out the Kuttler discussion to its own thread:
https://www.metabunk.org/threads/kuttlers-paper-estimates-for-time-to-collapse-of-wtc1.2794/

 

[Ron J]

The bottom line here is that a natural one or two story fall of the 12 story upper section of the North tower would have arrested due to the column energy absorption being greater than the kinetic energy available.

Bazant deceptively embellishes kinetic energy and underestimates column energy absorption in a surreal fashion, to even make his hypothesis plausible. It isn't just a small engineering disagreement.

Theory vs reality. Maybe if two floors were removed and the top 12 floors suspended in mid air, then dropped in perfect alignment to the the columns 2 floors down, the columns might literally be able to withstand the impact absorbtion in a perfect world, but when the upper floors of WTC1 fell down upon the rest of the building, a perfect world was not the condition of the building at the moment of collapse.

I am not an engineer, but i cannot see how a one or two story fall would have been arrested, in the context of the fire which was damaging the Tower.

 

[MikeC]

1 story collapsing is often all that is required to demolish a building as demonstrated by verinage - see any of those here.

 

[Ron J]

What happened to your concertina argument? Why is there no fracture after 180 degree bends in the attached example of it on a box section?

And what happened to the large H column in the attached? There is no fracture there.

The reality is that structural steel is quite ductile and fracture is not guaranteed during buckling as it depends on bend radius and the amount of stretch relative to the length of the bend. There is no chance for fracture at the 50 to 70 degrees of rotation that you want to claim. If it happens at all it would be much later than that.

What is guaranteed is that the columns would have absorbed a lot more energy than what Zdenek Bazant claims and that there should have been an enormous deceleration in the fall of the North Tower in a natural collapse after a one or two story fall.

The refutation of his January 2011 paper proves that Zdenek Bazant is fibbing in his papers on the WTC, and by association so are those who are capable of understanding the issue but still support his work.

How do you get a one or two story arrested fall? I fail to see how that happens. Once the failing elements started a global collapse, it just kept on going. The fact is that we couldn't see what was happening to the Tower, except from the outside. At least one person in WTC1 said in a phone conversation, that floors were collapsing. What was the caller specifically describing? We don't know.
How did those collapsing floors relate to the manner in which the columns behaved at the moment of global collapse, we don't know. We only saw what was occurring to the outside of the building and from a great distance, by way of TV cameras.

 

[OneWhiteEye]

What happened to your concertina argument? Why is there no fracture after 180 degree bends in the attached example of it on a box section?

[and etc]

At the moment, I have no time to give you the education in mechanical engineering that your alma mater should've given you if they were going to confer a degree. I will later. This is really basic stuff. A clue can be found in your own words:

...it depends on bend radius...

You'll notice I used the term "radius of curvature" and specifically said "...total rotation to be only about 50-60 degrees max. And that's over what looks like about a story's length or more..." and "70-170 degree bends in a small fraction of a story height...", all of which refer to a rotation angle within a specified length of column. I'm quite clear on this. Aw, you didn't notice, that's why you thought you were schooling me with your remark.

Rotation angle in itself does not determine strain in a member. Any fool knows it's possible to bend a steel rod into a closed loop without fracture, so long as it's not too tight a radius of curvature relative to the thickness. The ratio of arc length of the neutral axis radius to the arc length of the outer radius in tension is a good first approximation to the maximum strain differential in a piece being bent. There will be a minimum radius of curvature associated with the material and section width which specifies the elongation limit above which fracture can be expected.

For steel having ductile elongation limit of 20%, that works out to -

Solid prismatic section
r: radius to neutral axis
w: width of section

arc lengths:
s = rθ
s' = (r + w/2)θ

ratio of arc lengths:
s'/s = (r + w/2)/r = 1.2
=>
r/r + w/2r = 1 + 0.2
=>
w/2r = 0.2
=>
r = 2.5w

Then, for the elongation limit, the following relations hold true:
inside diameter - 4w
neutral axis - 5w
outside diameter - 6w

The outside diameter will describe the minimum allowable hinge thickness in rotations of 180 degrees or more. You could save me the unpaid remedial tutorial and recognize for yourself why this allows concertina folding with ~180 degree folds and no fracture. The studies you and your partner cite used 16 gage thickness (roughly 0.06") for their ASTM A36 thin wall tests. The outside diameter of those folds can therefore be 0.06(6) = 0.36 inches. That is, with this simple model of strain in bending, 180 degree folds could be as small as 0.36 inches without fracture for thin wall members. A column with a 16" section width, however, would require a minimum of 16(6) = 96 inches outer diameter to accomplish a 180 degree bend.

This simple model uses a solid section, which of course is not accurate for a box or H configuration. But later you'll see just how bloody good an approximation it is when it's applied. Unless you wisely post your concession first.

 

[OneWhiteEye]

I was unnecessarily prickish in the last post. The points could be made without the jabs. It is difficult to ignore past history, and even more difficult to pretend that the current situation resembles a reasonable technical discussion.

Anyone who wants to believe that a 144" tall column of width 14-16" can turn two 90 degree bends and one 180 without fracture... I don't think I can fix that. I can try.

Even Szuladzinki's FEA shows fracture top and bottom, and an inability to keep the top segment plumb despite restraining forces, thus the sum of angles is not zero and it's more like two 70's and a 180. My point, very simply, was always that the fracture depicted was insufficient and did not reflect reality. If his sim has any credibility at all, it shows that fracture is indeed mandatory, even when you let the elements stretch to 5x their ductile limit and survive. No argument has been made as to why the 20% ductile limit does not apply to his FEA. If it did, the column would've broke long before the final deformation depicted. Therefore it necessarily exaggerates residual capacity, probably greatly.

I'd like to proceed with the foundation set down above. I can expound on it if desired, but I'm going to work with the expression r = 2.5w relating minimum radius of curvature to a solid steel section of width w. The simple first approximation is to use differential arc lengths based on radius of curvature. Obviously hollow sections and I or H configurations can deform in such a way as to change the inner and outer radii, and more esoteric factors like transverse shear and so on are ignored. This is planar analysis and ignores the other horizontal dimension of the member. Deformations are assumed elastic without work hardening, even though this is patently unrealistic anywhere near the ductile limit. This is the absolute simplest model possible for bending deformation.



The figure labeled A represents a solid prismatic steel column with height:width ratio of 9:1 with fixed endpoints. If it were 144 inches high, it would be 16 inches wide. Figure B shows the same column deformed into a circular arc (constant radius of curvature) of just a little over 200 degrees end rotation. Note that column bowing is NOT a circular shape, and bending would not assume such a shape unless the ends were constrained as shown. But, being bent into this circular shape by constraint, the relations I derived above hold true (more or less).

The color shading represents the distribution of tensile and compressive strain in the member, with blue being compression, red tension, and green nominal (no distortion). The neutral axis, where the strain crosses from tension to compression, is shown as a dotted line. The radius of this axis from the center of the arc is set according to the relation for maximum elongation at the edge without fracture, 2.5 times the column width. This axis divides the cross section into regions of tension and compression, and the circumference at the outer edge is 1.2 times longer (the ductile limit) than the circumference at the neutral axis, which is at nominal length. For a 144" nominal length, the outside edge is stretched to 172.8 inches, and is on the verge of tensile fracture.

This circular arc is the tightest bend that can be done in this model without fracture. The end rotation is over 200 degrees, no problem. If the column were taller, it could go all the way around, 360. BUT, if the radius of curvature is decreased (circle gets smaller) while keeping the same width, the outer edge length will exceed 1.2 times nominal and fracture. Likewise, if the radius were kept constant but the width increased, same thing - fracture. The column cannot be bent tighter and a wider column can't be bent this tight.

The geometry of this arrangement is independent of absolute size, it only depends on the proportion of width to radius of curvature. Therefore, this representation applies to a column or sheet of any size, theoretically. This leads to figure C, which is simply completing the circle. The purpose of this is to provide a template against which to judge the tightest bend possible. It's only necessary to scale the circle so that the width of the circular band matches the width of the column in question. In images which have roughly orthogonal perspective, the circle can overlay the column bend and show where the minimum radius of curvature is exceeded by a bend.

This model predicts fracture for members bending tighter than the curvature of the circle, and survival for those less tight. We'll see.

 

[OneWhiteEye]

First exhibit - the core column featured in the last series of images. I was fortunate enough to find an orthogonal view, not typically the case and unfortunately not so for the few to follow.



On the left is the photo itself and it obscures the serious fracture much the way Tony's first posted photo did. He claimed there was no fracture or some but insignificant. As we saw from the other angle, the fracture eliminated three of four column walls entirely, but let's pretend we don't know that. The bad fracture is hidden here, too; what will the 'magic circle' have to say about whether or not there's a hidden fracture?

On the right, the circle has been scaled so that the thickness of the band matches the thickness of the column. It has been placed at the end of the bend with edges aligned as best as possible. Result: It should be fractured, slam dunk, no doubt. And, it is, as we know.

In fact, in comparing left and right you can see there is an edge dimple where some side fracture has occurred and a wrinkle has developed. If you look closely, it's apparent the radius of curvature of the column slightly exceeds the circle's exactly where that dimple is. The model predicts the onset of fracture under this condition, and sure enough it's there.

 

[OneWhiteEye]

Going back to this picture...



That one surviving column wall is bent at a pretty tight angle, but it is a much thinner section. It's not fractured. What does the circle say?

 

[OneWhiteEye]

Circle says...



No fracture! Right again.

This is not as nice because there is perspective distortion in the image and the circle is in the image plane. Still, it's close enough to get a rough idea. I've added tangents and a vertical line to assist with the perspective.

 

[Tony Szamboti]

Buckling starts as a sine wave. The bend radius does not get tight until very late in the game.

 

[OneWhiteEye]

How about the diamond folding pattern in Szuladzinksi's SHS FEA?



I've set one circle adjacent to the column so it's easier to tell that I've matched the column wall thickness satisfactorily. Several others are placed into folds and conform well, including in a tight one. The folds at the ends are tighter, however, and would be predicted to fracture. Bear in mind, this is a gross approximation and these are clearly borderline cases. I have accused Szuladzinski of excessive element ductility, and this could be another case. Is my circle right and he is wrong?

Not sure, I wouldn't want to call it, but I think the circle is wrong. There is such a thing as work hardening, as well as other mitigating factors, which might see a thin wall exceed the tightness specified by the simple model. In any case, the difference in the radii is not large and so this doesn't represent a gross violation of prediction, whereas the large column was a gross deviation.

So far, the circle is doing pretty well. It definitely shows that I have no firm expectation of fracture in concertina/diamond folding, from a sound theoretical basis and not in conflict with my other expectations concerning a three hinge buckle.

 

[OneWhiteEye]

Buckling starts as a sine wave. The bend radius does not get tight until very late in the game.

Agreed. I did say "Note that column bowing is NOT a circular shape, and bending would not assume such a shape unless the ends were constrained as shown." However, all that matters is the instantaneous radius of curvature at a given tangent point. It can be a noodly shape, but every point has an associated radius. Since we are concerned with the smallest radius allowable, the circle depicts only this radius.

 

[OneWhiteEye]

Although, the bit about "late in the game" is very much subject to interpretation. In three hinge buckling, severe angles come early in the game, compared to pinned ends.

 

[OneWhiteEye]

In any case, the difference in the radii is not large and so this doesn't represent a gross violation of prediction, whereas the large column was a gross deviation.

Eh, a couple of them are as far off as the big column. It is at this point that I might lean in the direction of favoring the circle, even given mitigating factors and seeing that my circle is actually a tad too thick. I don't want to be too pigheaded in clinging to an admittedly too-simple model. On the other hand, the researcher who did the FEA already allows elements to distort 5x the ductile limit in another sim, that's not easy to disregard. Based on the circle's wisdom, I'm going to do a literature search to see if fracture is predominantly observed at the ends of columns undergoing concertina folding.

 

[qed]

@Tony Szamboti

 

[OneWhiteEye]

I did find a lot of stuff on bend radius when looking, as one might expect. It turns out my "first principles" analysis is not the go-to method, also as one might expect. However, I did find similar treatments packaged as very rough estimates, and the very deep treatments (which were geared towards margin of safety in bending) were pretty darn close to what I'd have if I doubled my critical value to provide a factor of safety; in one case, it was exactly that. So I feel the analysis is valid as a rough first approximation in common variants of this problem, which is probably why it fit the few actual instances of extreme bending without fracture so well.

Edit: it's worth noting that there is disagreement on means of predicting most fracture scenarios, and quite a wide range of expectations depending on circumstance. It is apparent that making a hard and fast eyeball claim on a marginal case is not feasible for the vast majority of scenarios. Things which tend to extremes are another matter.

The only pertinent difference between what I did and what you'll find in the literature, aside from ridiculous simplicity, is the industry convention of expressing things in terms of the inner radius as opposed to the neutral axis radius. Many other differences are there, including the observed fact that the neutral radius is typically closer to the inside diameter and can be at midpoint at the most, not beyond. These differences are not germane to my point and, practically speaking, my magic circle is close to what others conclude for certain classes of bending problems with much more complicated analysis.

In reviewing the field, I learned many things. There are circumstances which can result in tighter folding than what my circle says. It depends on many factors, very complicated stuff. Generally speaking, though, for solid and hollow A36 steel sections, the recommended bend radii I found described larger circles than mine. This means radii between theirs and mine are considered unsafe in practice.

The tight diamond folding of a thin wall square tube shown in Szuladzinski's FEA can be tighter than predicted by the circle. In fact, his FEA looked pretty much like standard fare for that class of axial failure mode. That is not to say I know that it's valid for calculating energy dissipation in this failure mode for that column configuration. I believe it is, because similar folding configurations and load displacement graphs can be found everywhere you look.

On the other hand, NOWHERE did I find anything which corroborated his FEA results for three hinge buckling (but remember, this one was not cited in the discussed paper). In fact, everything seemed to strongly suggest just the opposite. I even found a company that brags about their special process being able to bend pieces to that degree without fracture or excessive strain! Solid or hollow section.

It seems exceedingly likely at this point that my off-the-cuff assessment of the excessive ductility of this model is correct. Even though it was not cited in the paper, Tony is currently using it as justification for the input parameters used in the paper. I'd ask that he either admit the paper uses the other FEA's results, which makes the discussion of three-hinge buckling moot, or else justify the results seen in the FEA experiment. The proper way to do the latter is to show he's not the only person in the world getting this result. His work is NOT peer-reviewed, it carries no more weight for being published on his own website than me talking here.

 

[OneWhiteEye]

What happened to your concertina argument? Why is there no fracture after 180 degree bends in the attached example of it on a box section?

I believe the concertina argument is quite intact. Do you agree or not?

And what happened to the large H column in the attached? There is no fracture there.

Your attached picture (once again) does not really show the whole picture. The particular image you chose is a cropped image. Here's the full image. For me, seeing the entire bend changes the impression given, I don't know about you. Even with the perspective, it's beginning to look like that bend is not so sharp after all. Here's another angle where the bend radius can be more accurately judged. It's tight, but frankly it doesn't appear to tighter than the template circle I prepared. If so, not by much.

I'm willing to allow that there's going to be a certain amount of variation but that only adds to the unpredictability of this whole affair. You're keep making hard and fast claims that it must be this, it can't be that. I'm not trying to do that except in the case of your partner's 3-hinge FEA where I believe the excess ductility is far too unrealistic. It's not a marginal case like the H-column, which is clearly very similar to the proportions of the circle I made. That circle has done a far better job of calling fracture/no fracture than you have.

The reality is that structural steel is quite ductile and fracture is not guaranteed during buckling as it depends on bend radius and the amount of stretch relative to the length of the bend.

What bend radius depends on for a given material and geometry (box, H, tube, etc) is the width of the section. That's it. All the formulas you'll find express allowable bend radius in terms of the piece width. As you observed, total rotation angle has little to do with it, except in the sense that bend radius is related to total rotation. Therefore, it's perfectly permissible for an enormous column to bend more than 180 degrees so long as the radius at every point in the bend is greater than the critical minimum. It looks the H column you attached is very near its limit, but not grossly beyond. Similarly, the thin wall concertina/diamond folding in your other attachment is like your partner's other FEA, which IS backed by widespread empirical observation as well as simulation. Still, these >180 turns within very small segments on average tend to have proportions similar to my circle.

There is no inconsistency in my argument at all. I've produced a crude template from the most basic principles that could make the correct call on several examples given, including one you got wrong. That template says the 3-hinge FEA is far too ductile.

There is no chance for fracture at the 50 to 70 degrees of rotation that you want to claim.

This is an example of the sort of absolute certainty in your claims that I'm talking about. It's not very credible coming from someone who missed by a mile on their own example. Let's go back to that one, which is a gem because it's real world and not FEA or analytical treatment. Fortunately, there's an orthogonal view which allows measurement of the angle to the fracture point:



That's 60 degrees. Even allowing for 20 degrees of snapback, which is bound to occur, that's a total rotation of 80 degrees which resulted in fracture. Based on what I've been reading, 20 degrees is very generous. Here we have a real world column from the WTC which DID fracture at 80 degrees over a length of what appears to be at least a half story. Given the uncertainty for predicting crack scenarios precisely, which you'll find all over in the literature, it seems that fracture at 70 degrees is more than possible, it's plausible, maybe even likely. Survival certainly cannot be guaranteed above 80 degrees because the real world experiment proving it is right there.

Your partner's FEA shows a column of slightly less section width undergoing two 70s and a 180 in a story's length. Real world experiment with WTC box columns indicates this is not possible.

Now, take a closer look at where the lesser fracture occurs, where the weld seam failed and the wall towards the camera is buckling out. This bend is the only reason it got to 60 (70, 80) degrees in the first place. It is a sharper radius which violated my circle criteria and it is sure enough fractured, just a lesser fracture. The integrity and strength of that column is greatly diminished by this alone, particularly with respect to resisting bending. Resistance to applied torque at the bend locations is THE way a three hinge column provides axial resistance. This happens at well under 70 degrees.

If it happens at all it would be much later than that.

Apparently not.

What is guaranteed is that the columns would have absorbed a lot more energy than what Zdenek Bazant claims and that there should have been an enormous deceleration in the fall of the North Tower in a natural collapse after a one or two story fall.

Based on how wrong you've been, and I'm not talking about what you've admitted to since you're way behind on that count, there is no reason for anyone to take such a statement seriously.

 

[OneWhiteEye]

I didn't count the additional rotation on the other side of the fracture. That's harder to do with the images available. It may be necessary to address this objection in advance. As has been established, it's not the total rotation angle that counts, but the bend radius. It is somewhat misleading to even discuss total rotation angles but, since I did, this will relate it to radius.

A quick guess puts the rotation on the other side to be at least 45 degrees. There is some pinching at the end which would tend to exaggerate angle, but call it 60. If so, a total maximum bend of 120 degrees is indicated, more with some snapback involved. However, closer observation provides better clarity. Three interdependent points:

1) The sidewall weld fracture allows a tighter bend radius than would otherwise be possible; thus total rotation includes another significant but lesser fracture.

2) The area in between major and minor fracture is relatively straight. Note how the tangent line I added is nearly collinear with the column edge for quite a distance. The radius of curvature, as already established, is not constant over the bend. This looks like two plastic corners emerging in the bend, even if not simultaneously.

3) Adding the segment on the other side of the fracture doubles the length of the arc so of course total angle is doubled. A constant equivalent bend radius or pair of equal angles will do that.

There are two fractures here. BOTH of them occur within roughly 60 degrees final rotation from their respective column ends, and both occur over similar lengths measured from where the deformation begins. More importantly, both separately violate a crude critical bend radius I established above. As such, there are really two independent confirmations of fracture at "60 degrees" for this particular column type in one example. The major fracture would certainly relieve the stress on the minor, if they were developing simultaneously. (Edit: and the bend radius would be tighter near the major fracture in any case, which it is)

For these types of columns, it appears the crude prediction of fracture radius given above is a reasonable starting point. The circle was not constructed to match the column, it was approximated according to material property, and it happens to work with that column hinge and others.

 

[OneWhiteEye]

This is no small contention with what Tony Szamboti has said here.

Summary so far:

- He has repeatedly insisted the energy dissipation from column resistance calculated for the Some Misunderstandings paper is based on three hinge buckling
- He says the basis for the dissipation value used derives from a technical note written by his co-author
- The paper does not cite this technical note (64) at all
- The paper cites another technical note (56) which doesn't involve three-hinge buckling
- The paper borrows entire sentences from TN56; it is clearly based on TN56 (diamond folding)

=> He does not know the foundations of his own paper OR the paper is muddled and fails to cite a source for three-hinge values.

- Both technical notes are reports on private FEA experiments and are not reviewed
- There are two other independent citations for diamond axial failure mode, which in turn cite many other sources
- None of these sources analyze three-hinge buckling

=> There is at most one technical source for the three-hinge energy dissipation values used, if any, and it is one author citing himself for uncorroborated work.

- The un-cited, un-reviewed technical note on three-hinge is in significant disagreement with other work by recognized and widely cited experts
- It differs in arriving at a much higher energy dissipation value
- On close examination, it is observed that element elongation is at least twofold on some surviving elements
- This stretch is 5x the acknowledged ductile limit of A36 steel
- This anomaly tends to exaggerate energy dissipation significantly

=> It is unlikely the FEA of TN64 is valid for the purpose Tony and his co-author use it, if in fact it is used at all. It may well be accurate for early stage deformation but the high dissipation values depend on integrating force over the full travel.

- Off the cuff remarks by Tony concerning the likelihood of fracture in bending have been startlingly inaccurate
- When checking actual WTC columns which are severely bent, his claims of survivability are unequivocally proven wrong by observation
- The scenario of three-hinge buckling of real columns without MAJOR fracture has been shown extremely unlikely

=> There is no independent supporting evidence offered for the energy values obtained from TN64, either from other research or physical experiment.

- The Some Misunderstandings paper is critically dependent on this dissipation value
- Cutting this value in half will halve the energy dissipated and greatly affect the mechanics
- Cutting this value in half starts to bring it in line with other research for FULL CAPACITY
- The paper starts with overinflated full residual capacity through several meters of descent but deducts a modest capacity for damage and fire
- Even after this deduction, the energy exceeds a valid bounding case

=> In the best case, this paper necessarily overestimates structural dissipation by a substantial margin in the bounding case scenario of perfect axial alignment.

- The bounding case scenario does not apply to the real collapses; the bounding case requires:
-- no significant column fracture
-- no significant eccentric loading
-- no appreciable oblique loading
-- no appreciable angular momentum of the upper section
-- undistorted and plumb column ends
-- full cross section of load bearing surface area
-- lateral support points be maintained
-- welds and fasteners do not fail first
- Most of these requirements are directly refuted in photos, video and forensic survey
- All of them are theoretically impossible
- All of them act to decrease residual capacity
- Total reduction can be expected to be an order of magnitude or more

=> The bounding case greatly overestimates average residual capacity and cannot be representative of the actual collapses.

- The Some Misunderstandings paper is an overinflated bounding case

=> It is inapplicable to the towers


Of all the points, it is only the last which actually matters.

 

[Tony Szamboti]

You can' say what you are saying about other research for full capacity if you are including Zdenek Bazant's column energy dissipation values. We proved in the JEM Discussion attached here that he was underestimating it by at least 2 to 1. In that case, Richard Johns and I determined the energy dissipation using a plastic moment equation like Bazant used.

The trick Bazant used to get lower than actual dissipaton values was to give a much lower Mp value than what the columns actually had. He was caught.

You have not commented on the fraudulent values Bazant used in that January 2011 JEM paper. Why not?

 

[OneWhiteEye]

You can' say what you are saying about other research for full capacity if you are including Zdenek Bazant's column energy dissipation values.

That's a rather specific nit on an extensive list of bullets covering a much broader spectrum of objections, but okay.

Yes, I do include Bazant. Why shouldn't I? In the past, I've never disputed the numbers you've plugged in, but neither have I endorsed them. Based on the cumulative effect of a string of absurd claims, I see no reason why I should give the estimates any further benefit of the doubt. If they are correct, they'd be among the few things you have done correctly. Bazant is world-renowned, and you are? I'm sorry to have to put it that way, but you ARE in conflict with experts, even if you happen to be right.

My statement "Cutting this value in half starts to bring it in line with other research for FULL CAPACITY" is true and does not even pass judgement. Others can pass judgement based in part on your performance here.

We proved in the JEM Discussion attached here that he was underestimating it by at least 2 to 1. In that case, Richard Johns and I determined the energy dissipation using a plastic moment equation like Bazant used.

This is the submission which was rejected for publication, correct? You're going to have a hard time making the case a rejected comment proves anything. But let's have a look:

The calculation of Mp for the core columns is laborious, since the columns are a variety of sizes and steel types. They are wide-flange columns, with flange dimensions ranging from 16.695” x 3.033” down to 8” x 0.528”, and either 36, 42, 45, or 50 ksi. (See the publicly available NIST SAP2000 model data, reproduced by MacQueen and Szamboti (2009), pp. 22-3.) The Mp values range from 2.01 MNm down to 0.09 MNm, with the average being 0.75 MNm. Again, this is far above the authors’ estimate of 0.32 MNm.

I don't see any calculations there, just claims and a vague reference to "publicly available NIST SAP2000 model data, reproduced by MacQueen and Szamboti". When I search for "MacQueen Szamboti SAP2000 plastic moment", all I get is TMJ and this discussion paper and I didn't see the calcs in TMJ. Apparently a reviewer had the same problem:

For the calculation of Mp, I looked at the referenced MacQueen and Szamboti (2009), which
listed column Fy and dimensions for core columns, but did not list any plastic moment
values. Given the Mp equation above, the values listed for Mp are suspect.

and your rebuttal:

All the necessary data to do so are provided in the supplied MacQueen and Szamboti reference.

I didn't find it just now so maybe you can point me to it. I'm not saying it's not there, it probably is, I didn't look very hard.

The trick Bazant used to get lower than actual dissipaton values was to give a much lower Mp value than what the columns actually had. He was caught.

I read through some of the back and forth between you and the reviewer comments. There are a couple of places where it looks like you're right. There are things I can't evaluate without further knowledge. I don't know at this point if it amounts to what you say it does, I'll wait on further reference. It looks like "he said, she said" where one side is a highly published expert in the field and the other is you. Given your statements about fracture and so on here, your bare assertions should be subjected to at least minimal scrutiny.

You have not commented on the fraudulent values Bazant used in that January 2011 JEM paper. Why not?

Because there's a huge list of things up there that doesn't depend on it. I'll strike the one item you're nitpicking if a rigorous evaluation can be done which shows you're right. No one should have to take your word.

Edit: and I'll strike "overinflated" from in front of full capacity and remove the line about "exceeds valid bounding case."

 

[OneWhiteEye]

I do think they should've published this submission all the same.

 

[OneWhiteEye]

Okay, I read one sentence further and found it.

 

[OneWhiteEye]

Revised list:

- He has repeatedly insisted the energy dissipation from column resistance calculated for the Some Misunderstandings paper is based on three hinge buckling
- He says the basis for the dissipation value used derives from a technical note written by his co-author
- The paper does not cite this technical note (64) at all
- The paper cites another technical note (56) which doesn't involve three-hinge buckling
- The paper borrows entire sentences from TN56; it is clearly based on TN56 (diamond folding)

=> He does not know the foundations of his own paper OR the paper is muddled and fails to cite a source for three-hinge values.

- Both technical notes are reports on private FEA experiments and are not reviewed
- There are two other independent citations for diamond axial failure mode, which in turn cite many other sources
- None of these sources analyze three-hinge buckling

=> There is at most one technical source for the three-hinge energy dissipation values used, if any, and it is one author citing himself for uncorroborated work.

- The un-cited, un-reviewed technical note on three-hinge is in significant disagreement with other work by recognized and widely cited experts
- It differs in arriving at a much higher energy dissipation value
- On close examination, it is observed that element elongation is at least twofold on some surviving elements
- This stretch is 5x the acknowledged ductile limit of A36 steel
- This anomaly tends to exaggerate energy dissipation significantly

=> It is unlikely the FEA of TN64 is valid for the purpose Tony and his co-author use it, if in fact it is used at all. It may well be accurate for early stage deformation but the high dissipation values depend on integrating force over the full travel.

- Off the cuff remarks by Tony concerning the likelihood of fracture in bending have been startlingly inaccurate
- When checking actual WTC columns which are severely bent, his claims of survivability are unequivocally proven wrong by observation
- The scenario of three-hinge buckling of real columns without MAJOR fracture has been shown extremely unlikely
- The Some Misunderstandings paper is critically dependent on this dissipation value

=> There is no independent supporting evidence offered for the energy values obtained from TN64, either from other research or physical experiment.

- The bounding case scenario does not apply to the real collapses; the bounding case requires:
-- no significant column fracture
-- no significant eccentric loading
-- no appreciable oblique loading
-- no appreciable angular momentum of the upper section
-- undistorted and plumb column ends
-- full cross section of load bearing surface area
-- lateral support points be maintained
-- welds and fasteners do not fail first
- Most of these requirements are directly refuted in photos, video and forensic survey
- All of them are theoretically impossible
- All of them act to decrease residual capacity
- Total reduction can be expected to be an order of magnitude or more

=> The bounding case greatly overestimates average residual capacity and cannot be representative of the actual collapses.

- The Some Misunderstandings paper is a bounding case

=> It is inapplicable to the towers


Of all the points, it is only the last which actually matters.

 

[OneWhiteEye]

Remarks:

I removed the entire section:

- Cutting this value in half will halve the energy dissipated and greatly affect the mechanics
- Cutting this value in half starts to bring it in line with other research for FULL CAPACITY
- The paper starts with overinflated full residual capacity through several meters of descent but deducts a modest capacity for damage and fire
- Even after this deduction, the energy exceeds a valid bounding case

=> In the best case, this paper necessarily overestimates structural dissipation by a substantial margin in the bounding case scenario of perfect axial alignment.

and moved the line:

- The Some Misunderstandings paper is critically dependent on this dissipation value

to the section above.


After reading through the reviewers' criticisms in detail, I found most quite weak and some questionable. Without looking at the original paper by Bazant & Le which this addresses, I can only see some things through a foggy lens. It is therefore not possible to precisely evaluate the merits of some of the disputes, but the one of concern here - plastic moment values for core and perimeter - seems to be more coherently presented by Tony and more consistent both internally and with other references. As well the upper section mass value.

I knew there was a reason I'd instinctively refrained from questioning the numbers Tony uses to plug in to Bazant's formula up until now. Mainly because I didn't want to go through the drudge of verification, which only now was done to marginal depth. Enough to see, though, that he does have his ducks in line on a couple of aspects, and I no longer care to invoke or defend Bazant in these aspects.

I have said for some time that I felt this submission should be published, so nothing's changed on that front.

The case in Tony's attachment above is compelling enough to remove the parts indicated, even though the bulleted points apply to an entirely different paper.

 

[OneWhiteEye]

I am and am not a fan of Bazant. He's done some great stuff, no doubt, and I've learned a lot in studying his work. I have also found "things" - notably how he got exclusive crush-down to occur with a two degree of freedom initiation. That took a couple of years of meandering, but eventually I realized the answer was staring at me all along and it was... questionable. Technically valid. Inarguably stilted, to the point where the term "dry-labbing" involuntarily comes to mind. It's a god-awfully narrow window, but it's consistent and justifiable if you stick to his rules.

I will, at this time, be happy to throw Bazant under the bus.

He lost me a long time ago when he started treating his "limiting case scenario" like a true and accurate kinematic narrative of the collapses. It's not. What Mick described in the Kuttler thread for applicable model objectives would satisfy the role of a narrative. It is, however, a wicked problem if not entirely intractable. So... analytical models which are coincidentally narratives should not be expected any time soon. Bazant and Seffen are basically the be-all and end-all of analytical treatments, and they aren't all that. How could they be? They're 1D models.

All of this bickering with Bazant and his crew has been interesting, in an academic sense. It has nothing to do with the mechanics of the actual collapses, which are best understood qualitatively. Hence the last line of my bulleted list. This is not a new position.

Yes, Bazant is a titan in the field, and yes, he's also tricky-dicky at times. Also surprisingly dense about choosing to act as if his model was a description of the collapses. There is no out for him in saying "hey, it's only a bounding case!" He dug himself in real deep and it does indeed look like Tony has him on the run in an argument about angels and pins. Too bad for him.

I still have that out. It's no skin off my butt to say the limiting case is arrest after a couple of stories. The limiting case is not the discriminator between natural and intelligently assisted collapse. How could it be? It's a 1D model. Things were not so ideal.

 

[qed]

@Tony Szamboti. Hi.

• How long is the initial buckled column in your paper.
• Is the data for your partner's FEA "experiments" publicly available (or is it a secret)? Your entire argument now rests of #64. Can the model data be made available for public review?

 

[Tony Szamboti]

I am and am not a fan of Bazant. He's done some great stuff, no doubt, and I've learned a lot in studying his work. I have also found "things" - notably how he got exclusive crush-down to occur with a two degree of freedom initiation. That took a couple of years of meandering, but eventually I realized the answer was staring at me all along and it was... questionable. Technically valid. Inarguably stilted, to the point where the term "dry-labbing" involuntarily comes to mind. It's a god-awfully narrow window, but it's consistent and justifiable if you stick to his rules.

I will, at this time, be happy to throw Bazant under the bus.

He lost me a long time ago when he started treating his "limiting case scenario" like a true and accurate kinematic narrative of the collapses. It's not. What Mick described in the Kuttler thread for applicable model objectives would satisfy the role of a narrative. It is, however, a wicked problem if not entirely intractable. So... analytical models which are coincidentally narratives should not be expected any time soon. Bazant and Seffen are basically the be-all and end-all of analytical treatments, and they aren't all that. How could they be? They're 1D models.

All of this bickering with Bazant and his crew has been interesting, in an academic sense. It has nothing to do with the mechanics of the actual collapses, which are best understood qualitatively. Hence the last line of my bulleted list. This is not a new position.

Yes, Bazant is a titan in the field, and yes, he's also tricky-dicky at times. Also surprisingly dense about choosing to act as if his model was a description of the collapses. There is no out for him in saying "hey, it's only a bounding case!" He dug himself in real deep and it does indeed look like Tony has him on the run in an argument about angels and pins. Too bad for him.

I still have that out. It's no skin off my butt to say the limiting case is arrest after a couple of stories. The limiting case is not the discriminator between natural and intelligently assisted collapse. How could it be? It's a 1D model. Things were not so ideal.

The above is as lucid and impartial an appraisal as I have seen you do thus far.

I am now curious to hear your take on the NIST WTC 7 report's omissions of critical structural features in its collapse initiation analysis. There is a thread on it here. The drawings showed that stiffeners were omitted from the end of the critical girder (A2001) that would have kept the flange from failing when the web was past the seat. Lateral support beams were also omitted from the northmost beam in an alternative scenario that stated that the beam would buckle due to restrained expansion. With those support beams included the beam's slenderness ratio is reduced by about 16 times and it does not buckle. The drawings also showed the seat to be 12 inches long, not the 11 inches originally claimed in the NIST WTC 7 report. Interestingly, the maximum expansion of the east side beams at 600 degrees C was 5.5 inches. This creates serious problems for the Erratum issued in June 2012, where the 12 inch long seat width was admitted to, but it was simply stated that the lateral walk-off distance was 6.25 inches. This can't just be hand waved, as it needs to be shown where the additional 3/4 of an inch comes from. In addition, with the partial height stiffeners included in the analysis the girder could be pushed far beyond 6.25 inches and still not fall off its seat.

I am not sure if you are aware but Zdenek Bazant was involved in a number of things concerning the NIST report and so was Kaspar Willam, who is the present chief editor of the Journal of Engineering Mechanics. You might be surprised to hear that when refusing to publish the Discussion paper by Richard Johns and I, taking Bazant's January 2011 paper to task, he said it was "out of scope". This was also after sitting on it for 27 months with no formal reply from Bazant. I am not saying these things because I want to. There are problems here.

 

[Hitstirrer]

I am and am not a fan of Bazant. .... Inarguably stilted, to the point where the term "dry-labbing" involuntarily comes to mind.........I will, at this time, be happy to throw Bazant under the bus..........Yes, Bazant is a titan in the field, and yes, he's also tricky-dicky at times........ He dug himself in real deep and it does indeed look like Tony has him on the run in an argument about angels and pins. Too bad for him.

Thank you for having the integrity to write that.

 

[Jazzy]

The above is as lucid and impartial an appraisal as I have seen you do thus far.

I hope it rubs off enough on you enough to acknowledge qed - some day.

I am now curious to hear your take on the NIST WTC 7 report's omissions of critical structural features

I bet you are. Actually so am I, but for different reasons.