WTC: Rate of Fall (rate of crush)

[Tony Szamboti]

I think you destroy the "missing jolt" argument with one very succinct observation:
http://the911forum.freeforums.org/n...boti-and-graeme-macqueen-t119-315.html#p21945

The impacts could not be simultaneous if 1 degree tilt is assumed.

(and of course the tilt increases quite significantly after a few floors)

Mick, the tilt does not affect the fulcrum, which would be the north face. What do you postulate happened there to obviate a deceleration?

You are also going along with a presumption that a 1 degree tilt spreads out the deceleration so that it wouldn't be observed. The deceleration in a fall of one or two stories in a natural collapse of the North Tower would have been enormous, as I showed here, and a 1 degree tilt would not eliminate it so it was unobservable. The recovery time would be much greater than the slight pause between impacts a 1 degree tilt would provide.

[...]

 

[Mick West]

Mick, the tilt does not affect the fulcrum, which would be the north face. What do you postulate happened there to obviate a deceleration?

You are also going along with a presumption that a 1 degree tilt spreads out the deceleration so that it wouldn't be observed. The deceleration in a fall of one or two stories in a natural collapse of the North Tower would have been enormous, as I showed here, and a 1 degree tilt would not eliminate it so it was unobservable. The recovery time would be much greater than the slight pause between impacts a 1 degree tilt would provide.

[...]

A fulcrum is different from a center of rotation. I very much doubt it simply hinged around a point on the north face. What actually would happen is a very complex non-rigid body problem. But it would seem for very large and heavy objects, rotation would tend to be around the center of mass, not a fulcrum. This was certainly observed with the WTC2 rotation.

1 degree of tilt is about 3.5 vertical feet. 5 degrees is 18 feet. so clearly quite quickly the "impact" would be spread out through time, and there would be no need for "jolts".

And has been shown, the likelihood of the columns remaining aligned seems quite unlikely - even impossible.

 

[Tony Szamboti]

A fulcrum is different from a center of rotation. I very much doubt it simply hinged around a point on the north face. What actually would happen is a very complex non-rigid body problem. But it would seem for very large and heavy objects, rotation would tend to be around the center of mass, not a fulcrum. This was certainly observed with the WTC2 rotation.

1 degree of tilt is about 3.5 vertical feet. 5 degrees is 18 feet. so clearly quite quickly the "impact" would be spread out through time, and there would be no need for "jolts".

And has been shown, the likelihood of the columns remaining aligned seems quite unlikely - even impossible.

It doesn't sound like you are going by the observations and measurements. The north face was a fulcrum for a very short time. The upper section actually came down very evenly, as all four corners started moving down in no more than 0.7 seconds of each other. So 1 degree is a maximum.

Your use of the term impossible is not supported at all. It sounds like you are just saying what you want to believe.

 

[Mick West]

It doesn't sound like you are going by the observations and measurements. The north face was a fulcrum for a very short time. The upper section actually came down very evenly, as all four corners started moving down in no more than 0.7 seconds of each other. So 1 degree is a maximum.

Your use of the term impossible is not supported at all. It sounds like you are just saying what you want to believe.

I'm saying what I think. If I'm wrong, then I'm sure it can be clearly explained why in a way that leaves no doubt. (Or at the very least, clarifies the nature and the parameters of the uncertainty).

 

[OneWhiteEye]

Mick, the tilt does not affect the fulcrum, which would be the north face.

You don't understand the point, or at least give that impression. No one said tilt affected the fulcrum (whatever that means in this context), and it's not obvious what the fulcrum has to do with conditions at first impact beyond the geometric considerations inherent to your model.

Perhaps you mean that the columns of the north face were intact up to initiation, as opposed to the south side where deformation was already present. If so, I won't contest that at this stage, except to point out the BIG, GAPING HOLE which you treat in your model as fully intact columns.

What do you postulate happened there to obviate a deceleration?

In actuality? Aside from the aforementioned gaping hole? The upper north wall went outside the lower, at least a lot of it did. Insignificant column-to-column impact would greatly reduce the expectation of deceleration above that point. But your statements bring a very important question to mind: is your model 1D or not? 'Cause I know it isn't 3D, and I see exactly zero assumptions or calculations in 2D. You're asking about the deceleration specifically associated with the north face and not referring to a unit rigid body descending vertically in 1D... yet, that's what your mechanics are for.

Are you switching contexts freely without bothering to mention it? The single biggest problem with your work is that you use a 1D model which is suitable only for academic first approximation and then insist on direct comparison with the actual collapses. You have a ONE DEGREE OF FREEDOM model to represent the heterogeneous 3D collapse of a differentiated structure! It's one smaller rigid line segment crushing another larger compressible line segment. It's a great model, I've used it for so much over the years, but it doesn't reflect the kinematics of the actual collapses.

It is possible to introduce correction factors into a 1D model to account for actions which fall outside the realm of 1D, like tilt. Indeed, that has been done, but not by you. It's possible to adjust measurements made at a specific location (antenna, roofline, etc) for the actual kinematics to allow meaningful comparison of actuals to 1D model. That, too, has been done, but not by you. These things are precisely the nature of the complaint about your work you're trying to address right now.

How do you choose to address it? By dipping into 3D kinematics and asking about deceleration at a specific point on the structure!

Well, I answered your question. There was insignificant column-to-column contact below the point you chose to measure. But that has NOTHING to with the criticisms of your work.

You are also going along with a presumption that a 1 degree tilt spreads out the deceleration...

Ah, now to the meat. Do you agree a 1 degree tilt results in a corresponding homogenization of structural resistive force, yes or no?

...so that it wouldn't be observed.

Yes. Even with your numbers. Did you read my link? If not, you don't even know what you're arguing against. Shooting blind.

There's more than one reason no deceleration is expected in your analysis. Homogenization is one, and it's clearly more important than you think. Read the posts starting at the link. Take note there's an error I called out in a recent post here, I haven't fixed it. Doesn't affect the conclusions. No jolt expected but, if there was, you'd not see it with your measurement techniques.

We've been over all of this before.

 

[OneWhiteEye]

The first significant refinement to the naive 1D model is to account for tilt, even in the most rudimentary fashion.

Which is: acknowledge that the associated differential vertical displacement homogenizes the structural resistive force and account for it by averaging over the extended distance.

Now, if you want to make a case that the distribution of columns is not uniform north to south, that would be one thing. Correct, but largely irrelevant. Averaging is much better than assuming a single, coherent impact, because that's nothing but pure fantasy. Of no value, empirical or academic.

Bazant homogenizes to story granularity using the Maxwell construction, which is easily justified when seeking an approximate solution. It's really the only sensible approach for an analytic treatment. That obviously won't work for you, since that degree of homogenization produces no jolts, by definition. Still, with your numbers, a much slower initial descent is expected using this method. (Or arrest, depending on which set of your figures are used.)

Why on earth aren't you taking this angle instead of talking about transient deceleration?

Incredibly, it's the same argument from a general mechanics standpoint, but automatically dispenses with an entire area of legitimate criticism of your work. It doesn't fix things, not by a long shot, but I have to be frank in saying it would reduce the number of issues which make a critical observer incredulous. In other words, you'd drop a lot of baggage in one fell swoop, at zero cost.

You're welcome.

If you were the least bit conservative in your approach, you'd use an average force figure over the staggered distance, as I've done. You wouldn't want to look like you were stacking everything (possible or otherwise) in favor of unrealistic expectations which support your predetermined conclusions, as you've done.

If you could show a deceleration is expected even with this averaged approximation, you'd be dramatically closer to having a case. Dramatically closer in this instance, however, doesn't mean close. Instead, you claim it's so without even checking. I did the work for you, using your numbers. It doesn't pan out in your favor.

(minor edit to improve clarity)

 

[OneWhiteEye]

That's very much the purpose. Collections of bunk are like weeds. If you chop them down then they will return, even if you get some great tools to do the chopping, even if you get lots of people to help. What's needed is the discovery and cultivation of the antibunk - the collection of factual observations and reasoning that will annihilate the bunk on contact. Plant the antibunk near the bunk, or at least keep it handy.

Diagrams are an important part of antibunk. They take longer to grow, but they work a lot better than walls of text - wall are always full of holes.

The reason we don't have much high quality antibunk is the work required and the lack of motivation. It's fun to swing the machete of reason. It's fun (for a while) to play whack-a-mole. It's rewarding to free some lost soul tangled in the weeds. It's less fun, and more work, to carefully cultivate appropriate antibunk that will render those temporary measures unnecessary.

I've given a bit of thought to your sentiments on the issue; I appreciate the metalevel discussion of this concern for both academic and practical considerations. It's much easier to take apart and respond to an engineering argument than find something intelligent and non-trivial to say on this subject, despite the number of thoughts it provokes. Pardon me for just dropping random, scattered thoughts.

It's not a total drudge. I love to argue. I think the dreariness comes from lack of progress, repetitive cycles, etc. As you say, preparing an intensive canned response lacks the immediate satisfaction of motivated response. It's been too much bother in conditions lacking immediacy and urgency, and no time for it when putting out fires.

Someone has already compiled links to repeated instances where either Tony is shown wrong, presents an insufficient case, or simply evades an argument. Check it out, it's huge, it's damning. It only concerns interactions in one thread. It's possible to create much larger compilations spanning multiple forums over years, but this alone should be sufficient for any truly interested party to arrive at a conclusion.

Problem is:

1) Most people don't follow links
2) Most people don't read arguments at all
3) Those who do read arguments prefer arguments directed at them

By "most people" I mean the typical target audience who profess an interest in and would greatly benefit from reading all of that context. Those capable of making an argument don't need to but are probably more likely to click on a link and read all (quality) arguments available to be best prepared.

#1: They say or imply they follow links but, no, not really. Not unless or until it's necessary to respond in a way that requires knowledge of the linked content, and then it's easier to just blow it off. Witness that in the current situation.

#2: Short attention span, limited skills, greater commitment to belief than understanding.

#3: What genuine interest exists is more elevated if someone receives a direct, personalized explanation rather than a link to another argument somewhere else, particularly if they have to do any sifting. Understandable. But doesn't excuse not clicking the link at all to assess how much wading needs to be done.

The chances of having someone click on a link which is presented as both the best and most concise explanation of an issue is greater than any other target, but how great it is I don't know. After that, depends on the implementation and the viewer. Wall of words is not the best approach for most people. If there were a way to incorporate all the remedial physics and engineering necessary to grasp certain arguments into a powerpoint instead of a lot of words, that's probably how the subjects would be taught. No doubt, there are many superb online visualization and learning aids for all sorts of technical subjects, and something could be done in this fashion.

Except...

- the work involved to rigorously refute a claim or render the status as indeterminate usually far exceeds the work of making the claim, even without a fancy dog and pony show
- remedial instruction factors in heavily for claims that appeal to intuitive (but incorrect) notions of physics/engineering; invariably "too boring" and "too technical"
- the audience, by and large, are disinterested ingrates feigning consideration of your arguments to cover for their pre-existing beliefs


Probably the biggest thing for me is this: I want to convince the original source of the argument that they're wrong. I don't care so much about onlookers, although I haven't had much problem in that regard except for the stubborn ideological types who don't follow links and don't read text. I'm not crafting my arguments for the short attention span audience or ideologues and certainly not to "win hearts and minds" of the general public. I want the person who's telling me I'm wrong to see their error.

Alternately, they could show me the error of my ways. Good luck with that.


<the post above has been close-captioned with selective bolding for the attention span impaired>

 

[OneWhiteEye]

Arrgh, ****! It figures as soon as I start beating my chest over this...

Alternately, they could show me the error of my ways.

Third alternative: I find the error.

Not going to lose any sleep over this, but the ADD version is: using Tony's numbers, a deceleration IS expected even with a 1.1m vertical offset south to north. The first bolded statement in this post is wrong and the calculation in this post is wrong and therefore the bolded statements in it are false. The error is failing to include the 3rd segment of my linear approximation to his load displacement response, which I estimate to be 219MN.

If one assumes the 219MN leg applies above and below the crush front, then the expected acceleration is about 23% of g directed upwards; that is, deceleration. The homogenized resistive force over 1.86m of travel is 400MN, where the mass used is 33.18Mkg for an imposed static load of 325.4MN. Ergo, it decelerates over about half a story.

I'm not going to softpedal it, it's a huge error on my part. From a mechanician's point of view, kind of embarrassing especially since I've been making such a point of it. I made a mistake, was delighted with the result, and my hubris took me down.

 

[OneWhiteEye]

I'm not at the apology stage, oh no, no, no. While I consider my mistake quite boneheaded and shameful, it should be understood that it changes little of the overall argument. It also doesn't rise to the level of the mistake I caught in the Missing Jolt which Tony later passed off as nothing. So keep it in perspective and balance.

What I attempted to show was that, using ALL of Tony's figures and model assumptions without question, 1 degree of tilt alone is sufficient to eliminate the expectation of deceleration. It's not like there aren't a large number of far more substantial objections right behind it:

Severe perimeter column misalignment (observed)
Perimeter panel detachment (observed)
Substantial and increasing eccentricity (observed)
Core column misalignment (inferred from upper section motion)
Fracture in both columns and connections (observed and expected)
Concurrent interior collapse removing lateral bracing (inferred)
Suboptimal or no load bearing contact surfaces (observed and inferred)

All act to diminish resistive force.

It really doesn't take much in the way of misalignment relative to the size of the structure as a whole to render this 1D model's capacity estimate moot. In the Sauret video, which is the clearest and most useful for fine motion detection, one pixel of lateral displacement is enough to throw Tony's load displacement curve out the window.

Having said that, and having revisited the unpublished Szamboti/Johns discussion paper, I do feel it should have been published and deserved a reply from Bazant. They did play the game according to his rules and he needs to either indicate where the errors are in the engineering estimate, or admit his was not the most optimistic bounding case scenario. Of course, there's a huge difference between winning the trophy for most optimistic 1D model and proving demolition of the towers.

 

[qed]

Does anyone have a link to some version of the @Tony Szamboti paper?

 

[Mick West]

Does anyone have a link to some version of the @Tony Szamboti paper?

There's a few:
https://www.google.com/search?q=Szamboti+wtc+filetype:pdf

 

[OneWhiteEye]

The one I refer to is a discussion paper submitted to JEM. You may have to talk to Tony for a copy.

 

[qed]

The north face was a fulcrum for a very short time. The upper section actually came down very evenly, as all four corners started moving down in no more than 0.7 seconds of each other.

Short time!

That's almost a second of massive chaotic differential.

And please can you refer me to the source of this figure.

 

[MichaelStox]

OneWhiteEye has been very polite imo even though I don't agree with him

 

[qed]

@Tony Szamboti

I am on my second scan of your paper, but I am no structural engineer, so please can you explain some of the details to a layperson like me.

On page 121 you conclude:

Both quantities are identical, therefore the arrest takes place over the critical story.

• What exactly does the conclusion "the arrest takes place over the critical story" mean?

 

[qed]

There's a few:
https://www.google.com/search?q=Szamboti wtc filetypedf

Thanks for the "link", but there are so many @Tony Szamboti "papers" out there.

The one I am reading is http://rethink911.org/wp-content/uploads/2013/07/Szuladzinski.Johns_.Szamboti.pdf (I think).

 

[OneWhiteEye]

@Tony Szamboti

I am on my second scan of your paper, but I am no structural engineer, so please can you explain some of the details to a layperson like me.

On page 121 you conclude:

Both quantities are identical, therefore the arrest takes place over the critical story.

• What exactly does the conclusion "the arrest takes place over the critical story" mean?

He set the average residual capacity equal to the imposed load and (remarkable coincidence) the energy required to crush the story exactly matches the potential energy lost in descent through that story. The critical story is the initial failed story. What he's saying, with some not so fancy math, is that the building cannot collapse from a quasi-static decay of capacity.

 

[OneWhiteEye]

"remarkable coincidence" is to be interpreted as sarcasm, by the way.

 

[qed]

He set the average residual capacity equal to the imposed load and (remarkable coincidence) the energy required to crush the story exactly matches the potential energy lost in descent through that story. The critical story is the initial failed story. What he's saying, with some not so fancy math, is that the building cannot collapse from a quasi-static decay of capacity.

The maths certainly ain't that fancy!

The National Institute of Standards and Technology (NIST) determined that the North Tower
failure initiation occurred at the 98th story [9], putting the upper section size at 12 stories. The
actual mass of this 12 story section can be found in the NIST report (NCSTAR 1-6D, p. 176,
Table 4–7), which states the actual total load on the columns between floors 98 and 99 to be
73,143 kips, i.e. 325.4 × 106 N or 33.18 × 106 kg. This is corroborated by the independent
analysis shown in [8].

NIST determines W (W is weight not mass. This is corroborated by the independent analysis shown in [8]).

The motion began when the strength of the columns on the critical floor fell just below
the weight those columns were supporting, therefore P = W = 325.4 × 106 N. This was an
average strength in the assembly of columns involved. Many of those columns must have
been damaged, bent out of shape and distorted in various ways. Those that were intensely
heated would increase their deviation from straightness. Probably only a minority of columns
retained the straight-line axis. It was not much of buckling in the traditional sense that
followed. It is an open question as to what the characteristics of such columns could be.
However, there is a clue in Fig.1, which indicates near-constant acceleration, typical of near-
constant resistance. As shown in [3] as well as below, the above Pav is itself only a small
fraction of the undamaged buckling strength, so it seems reasonable to use it, in the first
approximation, as a typical, average resistance along the downward path. (For this reason Pav
was used here rather than Pcr.)

Trivially P = W. (P is strength of column)

The energy absorbed by columns over the first story travel is
then
∏ = Ph = 325.4 × 106 N × 3.7 m = 1,204 × 106 N-m.
The potential energy for a one-story drop is:
U = Wh = 325.4 × 106 N × 3.7 m = 1,204 × 106 N-m.

Hence P times h = W times h (although scientists like @Tony Szamboti write Ph = Wh)

Both quantities are identical, therefore the arrest takes place over the critical story.

Since LHS=RHS, the arrest takes place over the critical story.

• Notice that the argument is independent of both h and W.
• Notice further that the term P is bound.

@Tony Szamboti Can't say I can fault your maths.

 

[OneWhiteEye]

Hahaha! Yeah, you've got it.

 

[OneWhiteEye]

Nothing like saying "Aha, x=x!" is there?

One of the primary arguments in the paper you're reading is that the load displacement response* for the columns in the tower is not of the hinge buckling sort assumed by Bazant and others for slender columns, but rather that associated with a short, squat column. The difference in the response is that the former drops dramatically in resistance over a relatively small crushing distance and the latter may not. The latter may actually increase in resistance the further it's crushed.


Bazant's load displacement diagram:

The vertical axis is force and the horizontal is position. Notice in the early phase of crushing, the resistance is high - much more than the imposed load indicated by the dashed line labeled mg. Over most of the crushing displacement, though, the force is much less than mg for this example's factor of safety.

Contrast this with the crushing of a paperboard tube:

Here the resistance after initial crush drops little or not at all. The failure mode here is not buckling, it's like the axial crush mode of this aluminum tube simulation:

The authors are making a case that the response of the tower columns should be more like this. Thus, in the portion you quoted, the effective capacity drops to the point where it's equal to the load and just sits there, or at worst eases downward a little and settles to a stop.


* this term simply refers the value of resistive force provided by a column at each position as it is being deformed/crushed, if you didn't already know.

 

[OneWhiteEye]

Did you see much of this in the debris pile?

So it's fairly safe to say this didn't happen. The argument is now down to demonstrating why it should've happened but didn't. I do believe that would be a very tough (edit: impossible, actually) nut to crack, and it still doesn't connect at all with some discrepancy which can only be resolved by introduction of artificial assistance. Even the hinge buckling scenario didn't happen on any appreciable scale.

 

[qed]

* this term simply refers the value of resistive force provided by a column at each position as it is being deformed/crushed, if you didn't already know.

I didn't. Providing such definitions regularly in a thread helps readers.

 

[OneWhiteEye]

I didn't. Providing such definitions regularly in a thread helps readers.

Okay, cool. I'm sorry it's something I don't do much of. I mostly forget what it was like when I was wading into all of this anew.

 

[Tony Szamboti]

Did you see much of this in the debris pile?

So it's fairly safe to say this didn't happen. The argument is now down to demonstrating why it should've happened but didn't. I do believe that would be a very tough (edit: impossible, actually) nut to crack, and it still doesn't connect at all with some discrepancy which can only be resolved by introduction of artificial assistance. Even the hinge buckling scenario didn't happen on any appreciable scale.

The above is not what the energy calculations we have done were based on. The energy absorption calculations were based on three hinge buckling at the beginning of the collapse.

It is hard to understand why you would even put images on like you have, unless of course you don't understand or are trying to deceive.

 

[OneWhiteEye]

The above is not what the energy calculations we have done were based on. The energy absorption calculations were based on three hinge buckling at the beginning of the collapse.

It is hard to understand why you would even put images on like you have, unless of course you don't understand or are trying to deceive.

I'm fully aware that the energy calculations done in prior work up the most recent JEM submission are based on three hinge buckling, as well it is mentioned in the paper linked above (http://rethink911.org/wp-content/uploads/2013/07/Szuladzinski.Johns_.Szamboti.pdf):

Because the columns in the WTC towers were stout by any criterion, one can expect that, in the large deformation range, the columns would exhibit a minimum resistance being a significant fraction of Pcr. Consequently, Szuladzn′ ski [3] employed the same approach, as that of Bazant described above, except that he placed a higher estimate on the resisting capability of columns. With this, he concluded that arrest of the downward motion would take place quite promptly, just outside the zone affected by the aircraft impact.

But this refers to the B&L Discussion reply from years ago, nothing new. Next, there's this:

A further insight into the level of resistance by stout columns was offered by
Szuladzin′ ski [5], who conducted a FEA simulation of a large deflection squashing of a
rectangular, hollow section column (RHS).

I'm not forking over $30 to find out one way or another, so I'll just take your word for it that this analysis also uses three hinge buckling. But then this:

Another study, conducted by Korol [4a], involved closed- and open-section beams. Using semi-experimental formulas by Wierzbicki and Abramowicz [4b] it showed the resistance levels in the η = 0.4 range or somewhat below. It is anticipated that thinner open-section beams may have η < 0.4, and probably closer to η = 0.3. A detailed calculation of the nominal column strength of the assembly and the expected resistance is provided in Appendix A.

And THIS is what I based my comment on. The citation (Korol [4a]) is Korol, R.M., "Collapse Time Analysis of Multi-Story Structural Steel Buildings". The Open Civil Engineering Journal, 2011, 5, pp.25–35., which is the paper you tossed at me earlier this year over at DebatePolitics. Your last statement above suggests that your "detailed" calculation for nominal column strength in Appendix A is based on this work. Let's go to your Appendix A:

A minimum column energy absorption capacity, over a fall through one floor height, can be calculated with η = 0.3 as...

There's the value for eta mentioned earlier from the paragraph citing Korol, 0.3. Here it is used without any derivation leading to the value, which indicates the analysis from Korol is indeed the basis. Let's go have a look at Korol, which is here.

In the paper by Bazant and Zhou [1], the authors identify various ways in which steel columns can fail and then progress to a total crushed state. They considered a 3-hinged buckling mode, arguing that such an assumption maximizes the plastic energy dissipation. They considered such as an assumption regardless of shape, location, or value of the effective non-dimensional slenderness ratio, of the columns. That assumption may seem reasonable, and it likely is, for wide flange columns that are poorly supported at upper and lower floor levels while buckling about their minor axes. However, when square tubular members are employed, essentially fixed at each floor level, the effective slenderness ratio is significantly reduced to computational values roughly equivalent to those in axial crush tests undertaken by DiPaolo, et al., [10] and DiPaolo and Tom [15].

The authors indicate Bazant uses three-hinge buckling, but they argue that effective slenderness ratio is comparable to the crush tests of DiPaolo. Okay, so let's go have a look at the two papers by DiPaolo, which are here and here. Here are some screencaps to make it easy:

Am I getting my point across now? Does this look three-hinge buckling to you? Or does it look like what I posted?

Continuing back with Korol, we read:

As such an analysis based on tubular crushing may be appropriate when the tubular dimensions and effective lengths warrant it. Research done by Wierzbicki and Abramowicz [8] and later by Abramowicz and Jones [17] on both quasi-static and dynamic crushing of tubular members, is deemed to have relevance in estimating the energy dissipation of such columns during a story collapse event. From their analytical and experimental study, a formula was developed by Wierzbicki and Abramowicz [8] for the average crushing resistance, Pm, during which progressive stages of plate element folding, compressing, and sequential propagation occurred, until the member became totally squashed.

Seems like these authors are going with the axial crush mode depicted above, but let's check the latest citation of Wierzbicki and Abramowicz. From the abstract:

Assuming a rigid-plastic material and using the condition of kinematic continuity on the boundaries between rigid and deformable zones, a basic folding mechanism is constructed. This mechanism closely reproduces all the main features of folds and wrinkles actually observed on typical crumpled sheet metal structures.

Not going to pay the $25 here, either, but a Google image search for Wierzbicki Abramowicz "On the crushing mechanics of thin-walled structures" nets citations in related studies and, whaddya know, they look like what I posted.



Your response acted like I was insane to post such an image. You know what I think? I think you didn't even read the references you cited, on which your work is based.

 

[OneWhiteEye]

I have seen ONE column from the debris pile deformed in manner depicted by the cited works of DiPaolo, Abramowicz and Wierzbicki, as I recall.

 

[Tony Szamboti]

I'm fully aware that the energy calculations done in prior work up the most recent JEM submission are based on three hinge buckling, as well it is mentioned in the paper linked above (http://rethink911.org/wp-content/uploads/2013/07/Szuladzinski.Johns_.Szamboti.pdf):



But this refers to the B&L Discussion reply from years ago, nothing new. Next, there's this:



I'm not forking over $30 to find out one way or another, so I'll just take your word for it that this analysis also uses three hinge buckling. But then this:



And THIS is what I based my comment on. The citation (Korol [4a]) is Korol, R.M., "Collapse Time Analysis of Multi-Story Structural Steel Buildings". The Open Civil Engineering Journal, 2011, 5, pp.25–35., which is the paper you tossed at me earlier this year over at DebatePolitics. Your last statement above suggests that your "detailed" calculation for nominal column strength in Appendix A is based on this work. Let's go to your Appendix A:



There's the value for eta mentioned earlier from the paragraph citing Korol, 0.3. Here it is used without any derivation leading to the value, which indicates the analysis from Korol is indeed the basis. Let's go have a look at Korol, which is here.



The authors indicate Bazant uses three-hinge buckling, but they argue that effective slenderness ratio is comparable to the crush tests of DiPaolo. Okay, so let's go have a look at the two papers by DiPaolo, which are here and here. Here are some screencaps to make it easy:

Am I getting my point across now? Does this look three-hinge buckling to you? Or does it look like what I posted?

Continuing back with Korol, we read:



Seems like these authors are going with the axial crush mode depicted above, but let's check the latest citation of Wierzbicki and Abramowicz. From the abstract:



Not going to pay the $25 here, either, but a Google image search for Wierzbicki Abramowicz "On the crushing mechanics of thin-walled structures" nets citations in related studies and, whaddya know, they look like what I posted.



Your response acted like I was insane to post such an image. You know what I think? I think you didn't even read the references you cited, on which your work is based.

I read the references and you aren't only accusing me of somehow inflating the energy absorption of the columns in the towers, but also the 1st author of the paper, Gregory Szuladzinski, who is also the author of the below linked book

http://books.google.com/books?id=CTJMUt_7KnYC&pg=PP1&lpg=PP1&dq=Formulas for Mechanical and Structural Shock and Impact&source=bl&ots=0dsdXixg37&sig=vh1LY0hJccJMT9j3u4WUSDFg2U0&hl=en&sa=X&ei=F4iIUoHFNMvc4AOOzIHoDg&ved=0CEgQ6AEwAw#v=onepage&q=Formulas for Mechanical and Structural Shock and Impact&f=false

Three hinged buckling of stout low slenderness ratio steel columns, like those in the Twin Towers, have an average resistance during the buckling process of Pav which is at least 0.3Pcr. You are trying to compare different sections which are crushed, but have no idea as to what the three hinged buckling value should be, and just seem to think that because it does not look exactly the same to you that the energy absorption would be vastly different. So, as with many of the contentions I have seen you make, it is without a basis and what you are doing is not valid. You certainly are taking the proverbial leap without looking, and some might consider that insane. I'll just say in your case here it is unethical, unless you can claim the other condition as a reason for it.

The point of the "Some Misunderstandings Related to WTC Collapse Analysis" paper was to show that Bazant underestimated the energy absorption in a three hinged buckle of the twin tower columns by at least three times and overestimated the kinetic energy of the upper section of the North Tower by about four times. I am sure you can't show different.

 

[qed]

@Tony Szamboti

• What buckling model are you sticking too?

Your paper is very unclear!

As a layperson, the following quote from your paper,

It was not much of buckling in the traditional sense that
followed. It is an open question as to what the characteristics of such columns could be.
However, there is a clue in Fig.1, which indicates near-constant acceleration, typical of near-
constant resistance.

compared with,

Bazant's load displacement diagram:

The vertical axis is force and the horizontal is position.

Notice in the early phase of crushing, the resistance is high - much more than the imposed load indicated by the dashed line labeled mg. Over most of the crushing displacement, though, the force is much less than mg for this example's factor of safety.

Contrast this with the crushing of a paperboard tube:

Here the resistance after initial crush drops little or not at all.

commits you to some model with rapidly decreasing load displacement response (the resistive force provided by a column at each position as it is being deformed/crushed)?

 

[qed]

@Tony Szamboti

Please can you explain, to the layperson, how, once the column starts buckling from the weight of the upper level, and the mass begins falling and increasing momentum, this fall is arrested.

I think this contradicts the mean value theorem.

 

[OneWhiteEye]

I read the references...

If that's so, why did you act so incredulous that I would post an image of concertina folding when it's the basis of the results in the fourth citation you give? Seems to me a more plausible response might have gone something like this:

"OneWhiteEye, I realize that the axial failure mode you depict is of the type discussed by two of our citations, and the only two independent citations which are sources for an axial failure mode dissipating more energy than Bazant claims, so it's understandable that you'd think we used this axial mode in our calculations, but we did not. We relied instead on the citations to my co-author's prior work finding a much higher dissipation energy with three-hinge buckling.

I also realize that, in one of our recent discussions, I posted a link to the Korol paper to show you that there are higher order failure modes which can dissipate even more energy than three-hinge, so it's reasonable for you to conclude these were employed in this paper, especially since we cite Korol last. Especially since we mention Korol in the same breath as the appendix where we go on to use the eta values obtained from Korol, DiPaolo, Wierzbicki, Abramowicz and Jones, which have nothing to do with three-hinge buckling. But we didn't."

Do you understand how a reasonable person with more than passing familiarity with your work and its history might come to the conclusion that you've shifted gears in choice of failure mode? For you to instead respond as if making that connection is either lack of understanding or deception on my part suggests...

It's lack of understanding or deception on your part. Despite your recent trend towards prevarication in other forums, my money is on the former. You didn't know the body of work you cited concerned axial failure modes other than Euler buckling. Exclusively. To the point where, when you search Wierzbicki and Abramowicz, that's ALL you see. Their work and the related study citing them is concerned with investigation of structures which dissipate the MAXIMUM energy in crushing relative to their strength and weight.

Crumple zones! Crush tubes! These studies serve the concerns of occupant safety in vehicles and protection of equipment from the environment, etc. In all the papers I surveyed last night in the citation chain outward from Korol, I did not see three-hinge buckling mentioned once, and only the general concept of Euler buckling mentioned as an outlier zone of no interest and an annoying test failure trial when it happened. Which, it turns out, is very likely to occur unless the test setup is intelligently crafted to avoid it, and sometimes happens anyway. Invariably the resistance drops drastically when this occurs. Not once did I see mention of these columns (usually called tubes, not columns) in use as a load-bearing structural member, certainly not as used in building construction.

Does that failure mode seem like it has anything to do with the failure mode of the towers? I can see why you'd want to distance yourself from it in this thread. So why did you cite it in your paper?

 

[Tony Szamboti]

@Tony Szamboti

Please can you explain, to the layperson, how, once the column starts buckling from the weight of the upper level, and the mass begins falling and increasing momentum, this fall is arrested.

I think this contradicts the mean value theorem.

The columns have more energy absorption capacity than the kinetic energy which can be developed over a one or even a two story fall.

 

[qed]

The columns have more energy absorption capacity than the kinetic energy which can be developed over a one or even a two story fall.

I think one story arrest is impossible, but @OneWhiteEye is better placed than I to challenge you on that front.

Let us laypeople continue with two story arrest.

Continuing from my previous summary.

One
can also choose to be more conservative and degrade the average resistance by another 25%.
Thus, the energy absorbed over the first story travel will be
∏ = 0.75 Pav h = 0.75 × 325.4 × 106 N × 3.7 m = 903 × 106 N-m.
This time U > ∏, therefore stopping is not complete over this story and further motion
must be considered.
Noting that the gross kinetic energy available to overcome the resistance
of the next story below is
Ek0 = 1,204 – 903 = 301 MN-m

• Suppose, on the other hand, that the column could not stop the fall.
• Then the top part hits the next floor with extra kinetic energy.

Before further motion continues, there is an energy loss incurred due to the accretion of
the slab. When this is treated as a fully plastic collision, that loss, according to [5] is

∆Ek = [edit: "complicated" mathematical expression that won't mark up nicely]

where Mb = 33 × 106 kg is the mass of the descending part of the building and Ms = 2.74 ×
106 kg is the mass of the accreted slab and its tributaries. After substituting, one finds ∆Ek =
23 MN-m. Consequently, at the outset of travelling down by a further story, the following status
develops. The moving part now has M = (33 + 2.74) × 106 kg = 35.74 × 106 kg and its potential
energy relative to the next floor is U = Mgh = 1,297.3 × 106 N-m. The energy available to
overcome the column resistance is now
Ek0 – ∆Ek + U = (301– 23.0 + 1,297.3) × 106 = 1,575.3 × 106 N-m.

• The top part smashes through the floor and exerts even more force on the "next" column than it did on the first. ("next" because column units straddled three floors)

The energy absorption capacity of undamaged columns is estimated, in Appendix A, as
2,720 MN-m. The NIST report predicts up to 20% of the core columns to be severed or
severely damaged in the North Tower and it is known from observation that approximately
15% of the perimeter columns were severed or severely damaged. To be conservative, the
remaining capacity of the story below the critical one can also be assumed degraded. Even
if only three-fourths of the undamaged capacity is preserved, we are left with 2,040 MN-m.
This is more than the total energy available, 1,575.3 MN-m, which indicates the arrest of
motion during travel along this story.

• Surely this is a mistake?

• Given that the columns buckled originally because of the breaking of the column supporting floor (due to fire), breaking the next floor will similarly damage the "next" column?

In which case you should conclude that the next floor did not arrest the fall, and on recursively with increasing energy?

 

[OneWhiteEye]

qed, I believe the answer to that is they degrade the estimated capacity of the first (defect) story twice in two separate steps and the second story only once.

 

[qed]

qed, I believe the answer to that is they degrade the estimated capacity of the first (defect) story twice in two separate steps and the second story only once.

Is this degradation accounted for in Tony's analysis yielding the value 2,720 MN-m?

 

[OneWhiteEye]

Is this degradation accounted for in Tony's analysis yielding the value 2,720 MN-m?

No, but he lops 25% off that before calculating the balance, using 2040MN-m.

 

[qed]

Has anyone done the analysis of the buckling load of the column after the next floor support is gone?

I can now see why it is twice first and then one next.

[pre]
|------------|
| |
|------------|
|------------|

vs

| |
|------------|
[/pre]

 

[OneWhiteEye]

Has anyone done the analysis of the buckling load of the column after the next floor support is gone?

Tony has purported to, but just extend his scenario further to imagine how it goes. He's going to use the full capacity as-designed, if that's enough of a hint. He once sent me a graph which showed arrest after five(?) stories. Now's he lobbying for arrest at first impacted story. I guess he'd say going further is moot, now.

 

[qed]

I appreciate the full-capacity error, but is this calculation number known?

 

[qed]

@Tony Szamboti

Do you claim arrest within one floor?