WTC: Rate of Fall (rate of crush)

It doesn't matter what you believe. You clearly have no analyses contradicting what is said in the paper concerning the energy absorption values we give for the twin tower columns.

You just seem to be looking for ways to try and discredit or somehow place into doubt legitimate analyses showing the energy absorption of columns like those in the twin towers would be quite high during three hinged buckling.

In reality, you have no argument and this is a waste of my time.
 
It doesn't matter what you believe.
No, it doesn't, I'm pretty clear on that. Are you clear that the same is true for you?

You clearly have no analyses contradicting what is said in the paper concerning the energy absorption values we give for the twin tower columns.
The analysis you claim to be using (Technical Note 64, NOT cited) is exceedingly weak, to be generous. Look at the distortion of the elements in the folds. Excessive ductility; no fracture, he just manually "eliminate(d) elements showing excessive distortion". When you Skype him next, tell him he missed a few (hundred). It's a private, non-peer-reviewed FEA with absolutely zero empirical backing. And wholly inapplicable to the connection dominated failure mode in the towers.

You just seem to be looking for ways to try and discredit or somehow place into doubt legitimate analyses showing the three hinged energy absorption of columns like those in the twin towers would have high average resistance during three hinged buckling.
I'm not looking for ways to discredit it, they jump out and bitch-slap me upside the head.

What I am impressed with on your part is that it seems you are right there ready to respond whenever I post.
I get an email when posts occur. I'm working at my computer late on a Friday night. I don't believe you've convinced anyone here of anything, so don't think I'm desperate to counter your schmack.

In reality, this argument is a waste of my time. Good bye.
Run. It wouldn't be the first time. Probably won't be the last.
 
No, it doesn't, I'm pretty clear on that. Are you clear that the same is true for you?


The analysis you claim to be using (Technical Note 64, NOT cited) is exceedingly weak, to be generous. Look at the distortion of the elements in the folds. Excessive ductility; no fracture, he just manually "eliminate(d) elements showing excessive distortion". When you Skype him next, tell him he missed a few (hundred). It's a private, non-peer-reviewed FEA with absolutely zero empirical backing. And wholly inapplicable to the connection dominated failure mode in the towers.


I'm not looking for ways to discredit it, they jump out and bitch-slap me upside the head.


I get an email when posts occur. I'm working at my computer late on a Friday night. I don't believe you've convinced anyone here of anything, so don't think I'm desperate to counter your schmack.


Run. It wouldn't be the first time. Probably won't be the last.
You have no basis to say the analysis shown in TN64 by Gregory Szuladzinski, concerning the column energy absorption values, is weak, but you try anyway.

Sorry Charlie, but it isn't running away to refuse to continue a debate when your opponent cannot provide anything to contradict the information you provided, since the reality is that there is no debate. You have shown nothing here but incorrect insinuations along with bombastic commentary.
 
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You have no basis to say the analysis shown in TN64 by Gregory Szuladzinski, concerning the column energy absorption values, is weak, but you try anyway.
I just told you why: 1) there is no fracture incorporated in his elements which distort well past 20% elongation, and 2) the depicted failure mode is inapplicable to the tower.

A useless FEA is just that. Cite it all you want, it's a very simplistic hack backed by nothing and proving nothing. If he'd crushed a real column, I'd pay attention to it. Too lazy to use non-linear elements with fracture? Not impressed.

Why do you never explain why there is no three-hinge buckling evident in the debris pile? Everywhere you look, however, there are weld/bolt/bracket failures. Can't seem to find any columns blown apart. Can you?

It isn't running away to refuse to continue a debate when your opponent is just making bombastic comments which do not contradict the information provided.
My comments are very straightforward and hardly subject to interpretation. The paper you co-authored derives its average residual capacity from three cited works which do not employ three-hinge buckling. You didn't even know that. Shameful.
 
From TN64:

ai41.tinypic.com_2qntz55.png

Gee, there's an awful lot of eccentricity even though he's trying to force the ends to stay fixed. Apparently even the Hand of God (spatial constraints applied by decree in LS-DYNA) can't keep that end plumb. You think there's a decent amount of horizontal reaction force coming from that column? Hahaha!

Moving along:

ai41.tinypic.com_2hib8js.png

Hahaha, and the welds survive!!! Ah, that's right, there are no welds, only imposed environmental constraints. You should Skype him and ask him what the maximum tensile strain was. Then you can come back here and apologize to me.


PS Tell me again where TN64 is referenced in your paper... hahahaha!!!!
 
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For those who might not know,

ASTM A36 is a very ductile steel and requires about 20% elongation before fracture. On a 12 foot tall column that would be about 2.4 feet or 29 inches of stretch. I can say with confidence there is not 29 inches of stretch anywhere on the buckled 12 foot long column sections in the analyses done for TN64 and shown here. These analyses were done using LS-Dyna software, which is non-linear, and would have shown fractures if they existed.

The welds are between the flanges and the web. The buckling takes place in the weak axis parallel to the flanges so the welds would have been in tension and compression like the flanges. However, they are at a short distance from the centroid and thus are under far less strain than the edges of the flanges. They are also made with E70 weld metal which is quite ductile also and actually has an elongation of 22% and the strain would have been nowhere near its ductility limit. See http://www.rbcompany.com/wp-content...L-PROPERTIES-OF-E60-E70-SERIES-ELECTRODES.pdf

There is only one person making comments involved in the discussion here, which could be considered those of a hack, and it isn't anyone who gives their real name. This person has now been shown to be wrong on both the column failure mechanism, used for calculating energy absorption in the paper, and why there is a lack of fracture. It is telling that those who advocate natural collapse either don't know what they are talking about or are being disingenuous. It is essentially because they are trying to defend the indefensible.

Buckling is needed in a natural collapse analysis for at least the first several stories and the energy absorbed would have been much greater than the kinetic energy available to continue the collapse with the result being arrest after a one or two story fall. The reason this did not happen is that the collapses were not due to natural causes.
 
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@Tony Szamboti
@Tony Szamboti

I would like to understand your theory of arrest within one floor.

From attempting to read your paper, I understand that the initial conditions at t₀ (moment of beginning of collapse) are as follows.
Code:
┃
┠───────      c+1     ─
⎞                     ⥌  3.7m
⎬┄┄┄┄┄┄┄┄ →  c        ─
⎠
┠───────      c-1
┃

Critical floor c was sagging and induced the straddling column to buckle. At t₀ the buckled column was no longer strong enough to support the weight of the floors above. At this point the system becomes dynamic and the floors c+1 and above begin to subside.

(1) Am I correct in these initial conditions?
(2) What (and how) do you calculate the slenderness ratio of the column to be?


From reading your paper, I understand that the system must stabilize at time t₁ before floor c+1 reaches floor c (unless pre-weakened).

(3) Can you sketch us a picture of what the column and floor would look like at t₁ (or textually if that is too much).
 
For those who might not know,

ASTM A36 is a very ductile steel and requires about 20% elongation before fracture. On a 12 foot tall column that would be about 2.4 feet or 29 inches of stretch. I can say with confidence there is not 29 inches of stretch anywhere on the buckled 12 foot long column sections in the analyses done for TN64 and shown here. These analyses were done using LS-Dyna software, which is non-linear, and would have shown fractures if they existed.

The welds are between the flanges and the web. The buckling takes place in the weak axis parallel to the flanges so the welds would have been in tension and compression like the flanges. However, they are at a short distance from the centroid and thus are under far less strain than the edges of the flanges. They are also made with E70 weld metal which is quite ductile also and actually has an elongation of 22% and the strain would have been nowhere near its ductility limit. See http://www.rbcompany.com/wp-content...L-PROPERTIES-OF-E60-E70-SERIES-ELECTRODES.pdf

There is only one person making comments involved in the discussion here, which could be considered those of a hack, and it isn't anyone who gives their real name. This person has now been shown to be wrong on both the column failure mechanism, used for calculating energy absorption in the paper, and why there is a lack of fracture. It is telling that those who advocate natural collapse either don't know what they are talking about or are being disingenuous. It is essentially because they are trying to defend the indefensible.

Buckling is needed in a natural collapse analysis for at least the first several stories and the energy absorbed would have been much greater than the kinetic energy available to continue the collapse with the result being arrest after a one or two story fall. The reason this did not happen is that the collapses were not due to natural causes.


The collapse occurred where out of control fire had been raging. In WTC1, the top 15 floors fell down upon the remaining 95, once a catastrophic failure occurred. In and of itself the fire was a natural occurance, started by an unnatural act, flying a jetliner into the building. I fail to see any reason that the collapse should have been only a floor or two, if it was a natural collapse due to fire. At least one caller from within WTC1 had said that floors were collapsing. How many floors or segments of floors had collapsed, or maybe more correctly sagged, during the time WTC1 remained standing?

In WTC2, along the east wall, debris began to collapse down from above the floor where columns were bowed in. In a fraction of a second, debris was collapsing onto floors immediately below where the columns were bowed in, and like a domino effect, it continued all the way down to the lobby. I see nothing unnatural occurring in that avalanch, from the moment it began.

The floor where the columns were bowed in due to the fire, was at that point unstable. Debris falling upon it from above, as that floor failed, would have dropped onto a weak floor, collapsing it down onto the next, which can be seen in the video, was not able to inhibit the debris from causing that floor to fail, as well.
 
For those who might not know,

ASTM A36 is a very ductile steel and requires about 20% elongation before fracture.
That's why I said 20%. So you agree with me. Good, because I first heard that figure from you and then I looked it up to verify it.

On a 12 foot tall column that would be about 2.4 feet or 29 inches of stretch. I can say with confidence there is not 29 inches of stretch anywhere on the buckled 12 foot long column sections in the analyses done for TN64 and shown here.
WTF are you talking about? Do you really not understand the simplest of words? Let me talk in pictographs, then:

ai39.tinypic.com_2vvuw74.png

ai41.tinypic.com_9ve8sl.png

I'm talking about elements!!! Either you didn't understand something really simple, which makes your credibility nil, or you're desperate to evade valid criticism and hope to deliberately sham the readers here.

YOU SAID 20% elongation. Look at those elements. I know you haven't read your co-author's work before now, but look at those elements. I was being conservative at eyeballing them above 50%. Those elements should've fractured long before this point.

These analyses were done using LS-Dyna software, which is non-linear...
True, it supports non-linear elements. Doesn't mean any given model is non-linear.

...and would have shown fractures if they existed.
Generally false. Only if it's modeled correctly! No fracture unless you model it that way. Fracture in LS-DYNA, at its simplest, is implemented by removing elements experiencing strain above a specified threshold. The mesh granularity at expected fracture zones should be orders of magnitude finer than the bulk material mesh and, even then, it's hardly an ideal tool for accurately probing crack initiation and propagation. I suppose it would be acceptable for this purpose for deformation up to first fracture.

You'll note there is fracture depicted in the simulation. As Szuladzinski said:

One should also note a certain degradation of the results because of numerical reasons. At about the mid-path on the abscissa in Fig.6 the plot becomes jagged. This is due to erosion (loss) of elements caused by the user settings during the run. It was necessary to eliminate elements showing excessive distortion, but such an elimination has somewhat decreased the axial capacity of the column.

The results are indeed degraded once fracture occurs, and fracture does indeed reduce axial capacity. He seems disappointed that some elements were removed by "user settings" as if the results would be more accurate if those elements were retained. Why didn't the user settings remove the elements in severe tensile elongation? Rhetorical. The simulation isn't worth a bucket of spit.
 

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The welds are between the flanges and the web. The buckling takes place in the weak axis parallel to the flanges so the welds would have been in tension and compression like the flanges. However, they are at a short distance from the centroid and thus are under far less strain than the edges of the flanges. They are also made with E70 weld metal which is quite ductile also and actually has an elongation of 22% and the strain would have been nowhere near its ductility limit. See http://www.rbcompany.com/wp-content...L-PROPERTIES-OF-E60-E70-SERIES-ELECTRODES.pdf
That's all fine and well but I'm looking right at elements which are elongated well past 50% (some appear to have doubled in length!), and now so is everyone else. Clearly, your co-author's model does not accurately capture the characteristics of steel in tensile strain according to your own oft-repeated criteria. It's even doubtful the welds at their location are at less than 22% elongation given the level of gross element distortion shown.

But, hey, let's pretend that steel and E70 weld metal can survive > 22% elongation like your colleague's simulation shows. Notice the deviation of the column end plane on top from horizontal. If you're going to insist that the ends remain connected, then the columns above are severely distorted as well. Do you agree or not? The columns below would also be distorted, if the bottom end weren't perfectly fixed by way of "user settings." Do you agree or not? The situation depicted is extreme eccentricity in end loading. How could it be anything else? You do agree, don't you?
 
Let me re-iterate "for those who might not know":

ASTM A36 is a very ductile steel and requires about 20% elongation before fracture.

It not only requires that much elongation to fracture, it WILL fracture above that elongation. I just did a quick measurement to compare element length between two elements, BOTH in tension. The element on the outside edge has length 70% greater than the inner element.

How many ways to I have to state the obvious before you'll understand it? You're dodging, and it's pathetic. It's too late for you to backpedal (or should I say 'backpeddle'?) on your criterion of 20%, and there's no doubt your colleague's simulation exceeds this criterion by a country mile. Therefore, it's a profoundly unphysical model which would tend to greatly exaggerate the axial capacity.
 
Let me re-iterate "for those who might not know":



It not only requires that much elongation to fracture, it WILL fracture above that elongation. I just did a quick measurement to compare element length between two elements, BOTH in tension. The element on the outside edge has length 70% greater than the inner element.

How many ways to I have to state the obvious before you'll understand it? You're dodging, and it's pathetic. It's too late for you to backpedal (or should I say 'backpeddle'?) on your criterion of 20%, and there's no doubt your colleague's simulation exceeds this criterion by a country mile. Therefore, it's a profoundly unphysical model which would tend to greatly exaggerate the axial capacity.

You aren't even doing the simple math right. It is not the relative difference between the inner and outer elements that counts. It is the absolute elongation from nominal that matters. In other words, if the column was nominally 144 inches long there would need to be a stretch to 173 inches to generate cracks. The column is a long way from being stretched to 173 inches on its outer edge.

You probably didn't realize the E70 weld metal had an elongation of 22% either before I told you and I doubt you realized the fact that the welds were much closer to the centroid made a difference.

The fracturing argument you are trying to make is not legitimate for 144 inch tall structural steel columns with E70 weld metal used in their fabrication. It is also silly that you presume a little cracking would make a big difference. That in itself shows the futility and desperation of your argument. Of course, this is similar to what Zdenek Bazant did in his extreme exaggeration of kinetic energy and underestimation of column energy absorption.

Your big attitude is incredible for your low knowledge level here and if it weren't for the need to correct your erroneous comments, so others were not taken in by them, I wouldn't even bother.
 
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You aren't even doing the simple math right. It is not the relative difference between the inner and outer elements that counts.
That's not how I figured it. In my next post, I'll show you how I did it.

It is the absolute elongation from nominal that matters.
It is the absolute elongation of an element from nominal that matters. You didn't know that?

In other words, if the column was nominally 144 inches long there would need to be a stretch to 173 inches to generate cracks. The column is a long way from being stretched to 173 inches on its outer edge.
Did you see the 'NO!!!' pictogram above?

You probably didn't realize the E70 weld metal had an elongation of 22% either before I told you...
That is true. Just like I didn't know ASTM A36 had a ductile elongation limit of 20%. I checked you on that and you were right, and also admitted such above. Big deal, I've never contested that even once. This time I took your word on E70 weld metal properties. After all, you've proven time and again at being very good at looking up numbers in tables.

What are you are NOT very good at is engineering mechanics, or the underlying physics.

...and I doubt you realized the fact that the welds were much closer to the centroid made a difference.
No, I did not realize the relative placement was as you say, but it doesn't matter because I've shown above that the deformation in TN64 is severe enough to exceed the elongation with respect the steel itself. In all likelihood, if your colleague had modeled the welds, they would've far exceeded the 22% criterion simply based on the gross deformation observed. You can argue circumstances will cause the weld to survive, but you can't argue that BOTH the steel and weld survive, can you? Not based on his model, you can't, and I'll show that next.

The fracturing argument you are trying to make is not legitimate for 144 inch tall structural steel columns with E70 weld metal used in their fabrication.
False. It's totally valid. What matters is the local deformation. You're trying to say that the force required to break a rod in tension is equal to force supplied in bending moment to cause edge fracture! It isn't, and I hope you know better than that, but at this point it's beginning to look otherwise. As I said in the very beginning, your colleague's model shows excessive ductility for steel, by your own criterion. The issue is not the length of the column, it's the elongation of the elements themselves.

It is also silly that you presume a little cracking would make a big difference. That in itself shows the futility and desperation of your argument. Of course, this is similar to what Zdenek Bazant did in his extreme exaggeration of kinetic energy and underestimation of column energy absorption.
Bazant is internationally renowned, has hundreds of publications in highly respected peer-reviewed journals in multiple specialties going back decades, and textbook credits as well. Szuladzinski, by contrast, has two published textbooks and a modest list of non-reviewed proprietary articles on his company website. Most of them describe results of crude FEAs which seem to be interpreted as being representative of real materials under extreme conditions, but which seem to lack even an appreciation for the special considerations usually given to such topics. Oh, yes, and there's the B&L discussion (shot down) and your current paper.

Your big attitude is incredible for your low knowledge level here and if it weren't for the need to correct your erroneous comments, so others were not taken in by them, I wouldn't even bother.
Please, keep bothering. I'm beginning to think you're the only one present who doesn't understand the fundamentals involved here.
 
Consider the following zoomed view of the bottom column end on which I've added annotation:

ai40.tinypic.com_2i7bfvd.png

I've indicated regions which are in tension versus compression, also the area of removed elements. The region overlaid with the translucent magenta rectangle represents the band of elements running along the length of the column which include the transition from compressive to tensile strain. This band therefore includes elements which are at or near equilbrium length. A net axial force dictates that this equilibrium line is not exactly centered in the column face, but it's not far off.

I've placed lines over element edge lengths at three different locations within the same row of elements. The yellowish rectangle indicates that increased thickness in the weld area was at least minimally addressed in the bottom row of elements by increased thickness, thus these do not distort nearly as much as the row I've measured, which is purely column wall. Because the total subtended angle of this area is small, perspective variation should be safely ignored and the projected line length will be very close in ratios to the actual edge lengths. Here are the x,y components and resulting lengths of the lines :

Green
(4.730, 21.044) => 21.57
Orange
(5.496, 29.209) => 29.72
Red
(8.657, 40.077) => 41.68

Comparing the pairs of these for elongation:
Green-Orange 38%
Orange-Red 40%
Green-Red 93%

Very conservatively, the green line might well be in tension, but even if it represents nominal length, the outer element is nearly twice as long.

You say steel is not this ductile, and you're right. So what does that say about the realism of this simulation? When an element stretches 5x beyond its ductile limit, it will provide unrealistic levels of tensile stress if the stress-strain relation is linear or even if it's plastic and equal to the peak. Those elements should have been long discarded in fracture. The compressive elements which were discarded due to "excessive distortion" were on the compression side. My guess is he only eliminated these elements because they were so severely distorted that there was interpenetration of the faces (i.e. singularity).

Who's the hack?
 
I'd also like to remind you that we're discussing the particulars of TN64, which is a vague report on someone's individual FEA effort, and is not referenced in your paper.

The one that IS, TN56, is not three hinge buckling.

Why, lookie here - here's text from TN56 copied verbatim in your paper:

The resulting estimates are conservative, as they do not take one important factor into account. When the vertical deflection exceeds some 2/3 of the length, the walls of a column are folding and leaning on one another and possibly on the floor. As the process continues and deflection progresses, it leads to quite large resisting forces being developed. The simulation presented here refrained from going into that range deflections and taking advantage of this effect, based on the reasoning that there is a limit to what the columns in a story below can support, even under dynamic conditions.

TN56 is for SHS columns and the failure mode is this:


Still think you know what your own paper says? Be sure not to run...
 
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I'd also like to remind you that we're discussing the particulars of TN64, which is a vague report on someone's individual FEA effort, and is not referenced in your paper.

The one that IS, TN56, is not three hinge buckling.

Why, lookie here - here's text from TN56 copied verbatim in your paper:



TN56 is for SHS columns and the failure mode is this:


Still think you know what your own paper says? Be sure not to run...
The statement in the paper is about three hinged buckling as evidenced by the point made about contact with the floor. Your lookie here comment is conflating the concertina compression failure which can't "hit the floor".

If you think you are so right about whether Gregory's LS-Dyna analysis should have shown fracturing you should write to the LS-Dyna people and tell them you discovered a flaw in their non-linear analysis software.

Just so others can see, they should take a look at the attached photo of buckled beams from the twin towers. There is no fracturing of the beam due to its ductility. OneWhiteEye seems to be OneBlightedEye.
 

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The statement in the paper is about three hinged buckling as evidenced by the point made about contact with the floor. Your lookie here comment is conflating the concertina compression failure which can't "hit the floor".
This is absurd. I said the quote came directly from TN56. The word "floor" is not even mentioned in TN64, which is not referenced by your paper.

How can you possibly be so wrong every time when I spoonfeed you the answers?

If you think you are so right about whether Gregory's LS-Dyna analysis should have shown fracturing you should write to the LS-Dyna people and tell them you discovered a flaw in their non-linear analysis software.
You're trying to shift the blame from an inept user to the software vendor. I have a better idea. You explain how elements of steel can be stretched to twice their length without fracture.

Just so others can see, they should take a look at the attached photo of buckled beams from the twin towers. There is no fracturing of the beam due to its ductility. OneWhiteEye seems to be OneBlightedEye.
Oh my god!!! Look at those shallow hinge angles. Of course they haven't fractured yet. You still haven't yet dug up one photo of three hinge buckle failure. I have seen one concertina column end. Good luck.
 
I am saying the points made here by OneWhiteEye about when the 20% elongation and fracture occur are not legitimate.

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.

WTC structural steel bending.jpg

I think OneWhiteEye needs to show us his/her calculations for the energy dissipation during buckling of a floor of columns at about the 97th floor of the North Tower, since he/she is claiming that the energy calculations in the paper by Gregory Szuladzinski, Richard Johns, and I are not accurate.

Somehow I doubt we will see any calculations and will not hold my breath.
 
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@Tony Szamboti

Please can you also answer my questions. This is a forum.

@Tony Szamboti

I would like to understand your theory of arrest within one floor.

From attempting to read your paper, I understand that the initial conditions at t₀ (moment of beginning of collapse) are as follows.
Code:
┃
┠───────      c+1     ─
⎞                     ⥌  3.7m
⎬┄┄┄┄┄┄┄┄ →  c        ─
⎠
┠───────      c-1
┃

Critical floor c was sagging and induced the straddling column to buckle. At t₀ the buckled column was no longer strong enough to support the weight of the floors above. At this point the system becomes dynamic and the floors c+1 and above begin to subside.

(1) Am I correct in these initial conditions?
(2) What (and how) do you calculate the slenderness ratio of the column to be?


From reading your paper, I understand that the system must stabilize at time t₁ before floor c+1 reaches floor c (unless pre-weakened).

(3) Can you sketch us a picture of what the column and floor would look like at t₁ (or textually if that is too much).
 
I am saying the points made here by OneWhiteEye about when the 20% elongation and fracture occur are not legitimate.
Do you think you could bother to say why? On the previous page you said:

ASTM A36 is a very ductile steel and requires about 20% elongation before fracture.

But when I unequivocally show 100% elongation of elements in your partner's FEA, that property of steel is magically waived and somehow my points are not legitimate. Surely you can explain that.

Attached is another WTC structural member with 180 degree bending. No fractures are observed.
You aren't looking very closely. Maybe it will be more obvious from the other side:

ai44.tinypic.com_2889vlh.jpg

You can't get anything right, can you?

I'm perfectly aware of that specific column, I can even dredge up much better examples than that, and in pictures big enough to see! I did so for psikeyhacker who, like you, seemed unable to come up with more than two examples on his own. But, as I pointed out to him, for every one mangled column you can find, I'll find a hundred that are barely deformed.

I think OneWhiteEye needs to show us his/her calculations for the energy dissipation during buckling of a floor of columns at about the 97th floor of the North Tower, since he/she is claiming that the energy calculations in the paper by Gregory Szuladzinski, Richard Johns, and I are not accurate.
You are so clueless. Your value of η doesn't come from a calculation at all! It comes from an FEA. Not analytic derivation, not laboratory experiment - an FEA, done by one guy and cited by no one except himself. The SHS FEA, not the three hinge FEA.

Somehow I doubt we will see any calculations and will not hold my breath.
1) I don't have to do my own calculations to show the flaws in your work.
2) You've got a fair bit of nerve challenging me about calculations, given our first encounter when I corrected you on your initial dismal foray into basic mechanics.
3) Long before you figured out the right formula to use for three-hinge buckling, I latched on to it courtesy of Bazant. Here it is:

ai43.tinypic.com_wwdqn7.png

4) There's nothing hard about that formula; arithmetic and square root. Read on from that point to see how I implemented a linear approximation of it in a physics simulation.
5) The energy dissipation calculated in three-hinge buckling is a purely academic exercise; it did not happen (you still haven't found one example of it).
6) But I can do it again, if you insist.

When one uses the load displacement relation of Bazant and Cedolin, it's immediately apparent that being scaled to mg as it is, one only need determine the Maxwell line for equivalent force as a fraction of peak capacity or imposed load. There's no need to evaluate that function every time a number is needed. For Bazant's estimates, it's about 15% of peak and about 38% of mg. So, 0.38mgh. There, that wasn't hard.
 
Bazant is lying and dramatically underestimating the energy dissipation, as we proved in our refutation of his January 2011 paper using his own equations. In this paper, Bazant gives a fraudulent value for the Plastic Moment (Mp) of the columns.

You have had a copy of this refutation for about a year, so there is no excuse for you. If you are agreeing with Bazant, as it appears you are here, you are lying also. I am again attaching the refutation of his paper for others.

Bazant also dramatically embellishes the kinetic energy available. See the graph at the end of the attachment for what should have happened if the actual kinetic energy available and energy dissipation are considered, using the real input values with Bazant's equations.
 

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Bazant is lying and dramatically underestimating the energy dissipation, as we proved in our refutation of his January 2011 paper using his own equations.
...where you used the very same formula I show above. The only parametric differences allowable are the length of the plastic phase and the overall scaling of magnitude. For the latter, Bazant used an overall FOS of 2.5 whereas you basically doubled that. You can say Bazant is lying, but from the sidelines, it looks like a disagreement on engineering estimates. In your discussion submission, you were indeed using a three-hinge buckling model and the Bazant/Cedolin formula. The analytical form does not differ, only the numbers you choose to plug in to the formula.

For the record, I have NEVER quibbled with your engineering estimates, and this isn't the first time I've said that in your presence.

You have had a copy of this refutation for about a year, so there is no excuse for you, and if you are agreeing with Bazant as it appears here, you are lying also.
I said "for Bazant's estimate, 0.38mg." For your "refutation", double it. I don't care which it is. Three hinge buckling is essentially irrelevant to the collapse mechanics of the towers.
 
For your "refutation", double it.
Your plastic phase is probably longer so more than double it. I don't keep track of nitpicky details like that. I already know more about your latest work than you do, so I don't feel too bad letting an iota slip here and there.
 
I also don't feel bad when you stoop to simply ignoring the fact that the 180 bend column which you claim was not fractured was severely fractured. Doesn't it bother you that you're wrong so much? It bothers me that you don't admit it.
 
You're very frickin' quick to cry fraud. Were you being fraudulent when you posted that photo which hid the gross fracture of the column? Hm?
 
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.
 
@Tony Szamboti

Please.

@Tony Szamboti

I would like to understand your theory of arrest within one floor.

From attempting to read your paper, I understand that the initial conditions at t₀ (moment of beginning of collapse) are as follows.
Code:
┃
┠───────      c+1     ─
⎞                     ⥌  3.7m
⎬┄┄┄┄┄┄┄┄ →  c        ─
⎠
┠───────      c-1
┃

Critical floor c was sagging and induced the straddling column to buckle. At t₀ the buckled column was no longer strong enough to support the weight of the floors above. At this point the system becomes dynamic and the floors c+1 and above begin to subside.

(1) Am I correct in these initial conditions?
(2) What (and how) do you calculate the slenderness ratio of the column to be?


From reading your paper, I understand that the system must stabilize at time t₁ before floor c+1 reaches floor c (unless pre-weakened).

(3) Can you sketch us a picture of what the column and floor would look like at t₁ (or textually if that is too much).
 
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.
That would be the least "natural" of all, wouldn't it?

The fall where the tower-top collapses straight down?

The one where (obviously) every column on a single floor gives up the ghost simultaneously?

The impossible case where alignment is maintained?

Where every part of that floor has been evenly heated (there being no prevailing wind)?

Where there has been no preceding mechanical damage to the structure?

It isn't just a small engineering disagreement.
It isn't even about engineering. Yet.

There's a commonsense hurdle you have yet to cross.

.
 
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Jazzy, to misalign the columns you need a very large lateral force to move the 73 million lb. 12 story upper section horizontally. The small tilt does not provide it.
 
I am saying the points made here by OneWhiteEye about when the 20% elongation and fracture occur are not legitimate.

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.
Some better photos:


a911research.wtc7.net_wtc_evidence_photos_docs_hanger17_core4.jpg
ad38zt8ehae1tnt.cloudfront.net_Bent_WTC_Core_Columns__3949.jpg_0ee8167facf0f413bdde6e251c4649e7.jpg
afiles.abovetopsecret.com_files_img_kg4f427b64.jpg
 
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I seem to remember being told some years ago that Bazant's initial calculation assumed that the upper block dropped at the rate of freefall for 13 feet ( height of one floor said to be the damaged impact zone) to strike the intact lower building at a velocity consistant with that calculation. ( 19mph rings a bell ).

Then he used that impact velocity and mass of the ( intact ) upper block as part of the data to calculate the next phase, and so on.

Is that correct? Or was I misinformed ?

If that is correct - can someone please explain to me how all resistance across the entire building instantaneously disappeared, to allow that 13 foot drop at freefall, in order to reach the velocity claimed ?
 
OWE. But as I said before, it was turning into an academic dispute where I was being asked to believe both Kuttler and yourself without the tech knowledge to check either of your assertions. I suspect that reading the thread for the last few weeks won't help either.

It seems not only are you rejecting counterarguments out of hand but are petulantly demanding someone whip up the same three course meal for you right here. So you can send it back???
 
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.
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.
 
Jazzy, to misalign the columns you need a very large lateral force to move the 73 million lb. 12 story upper section horizontally. The small tilt does not provide it.
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."
 
It is hilarious reading OWE & Jazzy's responses without having to bother trying to comprehend the original!!:D;)
 
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