psikeyhackr wrote:I suppose another way would be to use a cup and put something in it, water, sugar, sand. whatever.

I didn't see your post until I'd already gone with the beans. The one I was looking for didn't get as far as the beans, though.

I have seen digital postal scales that are pretty cheap. I don't know how accurate it was.

Excellent idea. Probably essential.

Here's what I've got. It took a while to find the sweet spot because there's a lot of variability. It was more or less an accident. I put the second plate on, and was checking it to make sure the load was pretty well centered and, as I watched, it slowly crept down to about half height and stopped. Took pictures of that one and a couple of the earlier fast and complete crushings.

One of these things is not like the others...


(top view and side view)

Note wrinkling is much less for the one on the right and it's a little taller. They all spring back up after removing the load, but the relative heights indicate the difference in the creep failure.

One instance is really not good enough, especially with the high variability, but it shows the idea. It did seem very much like they were snapping at first, and maybe some would, but this one didn't. This one displays a more or less flat load displacement response, going up a bit in resistance as it crushes. Supports like this will barely hold a static load but dissipate a lot of energy when that same load impacts it. This situation appears to be as I suspected.

However, there are three things which need to be said.

First, you've come closer to getting a collapsing model than those other experiments. I don't mean a little, I mean a lot - orders of magnitude closer. It's just a better model all around, god you're not hoisting cinder blocks and all that shit. This is designed! I take back all the "piece of shit" remarks, that was mostly about frustration anyway. I do not believe I could have come this close, this easily, at this height. I mean, all I have to think of is something to replace the paper loops with, but.... well, that's the problem. Most materials are much worse than what you selected. This is a very small model.

Second, you got bidirectional crushing. This is a major issue that SOOO many people have with Bazant and the magic rigid top. Even I had a problem with that right away. You don't need to take my word for it but I spent a fair bit of time going over the math he presented to show why only crush down happens even without a rigid top and, technically, it was right. BUT, only for an extremely narrow range of conditions in a 1D arrangement, almost everything else in the world (including your model and the real towers) does not act that way.

This is part of the surreal nature; everyone knows you smack a VW into a VW, they get equal damage. So why any different for a skyscraper? Even with a vertical bias from gravity, that would seem to only bias the destruction downwards. That's what happens in your model and all of mine, too. Unless I make the top artificially rigid. Your model behaved more like the real building than Bazant's in this regard.

Third, it's a 1D model. Let's suppose someone does come up with a collapsing model in 1D. Does it really mean the towers must have collapsed in that fashion? No, it certainly doesn't. The blade cuts both ways. Even if I made a collapsing model tomorrow, it won't prove it applies to the towers. This is one of the other reasons it's hard to get motivated. It would show it possible, but only for structures very much like it. All the same, I'll keep thinking if there's any way to modify your setup to get it to collapse, because you are right when you say no one's made it happen. That's about the strongest motivation, so that it's been done at least once.

What we may not agree on is how deep and wide the probability trough is on the 9/11 event.

Very well stated. I think that sums it up.

You see I don't think there is there is any fine line between the chance of destruction of the towers versus not happening at all.

For the towers? No, I don't think the line is fine. I would not be willing to gamble more than a few dollars on how many towers out of a hundred would collapse like that, given the same initial conditions. For these 1D models, the line is much finer.

If it could happen then it should be easy to make a physical model. If it could not happen then it should be nearly impossible to make any kind of self supporting model completely collapse.

I'm going to try.

I think that highlighted statements demonstrates what he prefers to believe. He does not like the conclusion my model tends to lead to.

I do agree with him but I also think the reverse is true. I don't think any of the models - physical, analytical, computational, will give definitive results. But that's just me, I'm very cautious. The kinds of problems I've had to deal with over the years have been humbling; as in, the source of the problem is almost never what you think it is (that's why it ends up on my desk). It does affect your thinking after a while because it's way too easy to be wrong and very fucking hard to be right. Sooo, it pays to be careful. Though maybe I take it too far.

Even you used the word "tends", which I think shows you're aware that it's confidence - not certainty - that comes from modeling. This is why I try to stick to little pieces and parts of the puzzle, they're less glamorous but more manageable.

Kat, your move to experimentation is commendable (an I commend Psykey for that as well). You may well learn something useful from reproducing Pyikey's washer tower. However, you are very likely to get the same results that he did, for the same reasons he got them.

Kat Dorman wrote:Second, you got bidirectional crushing. This is a major issue that SOOO many people have with Bazant and the magic rigid top. Even I had a problem with that right away. You don't need to take my word for it but I spent a fair bit of time going over the math he presented to show why only crush down happens even without a rigid top and, technically, it was right. BUT, only for an extremely narrow range of conditions in a 1D arrangement, almost everything else in the world (including your model and the real towers) does not act that way.

This is part of the surreal nature; everyone knows you smack a VW into a VW, they get equal damage. So why any different for a skyscraper? Even with a vertical bias from gravity, that would seem to only bias the destruction downwards. That's what happens in your model and all of mine, too. Unless I make the top artificially rigid. Your model behaved more like the real building than Bazant's in this regard.

Third, it's a 1D model. Let's suppose someone does come up with a collapsing model in 1D. Does it really mean the towers must have collapsed in that fashion? No, it certainly doesn't. The blade cuts both ways. Even if I made a collapsing model tomorrow, it won't prove it applies to the towers. This is one of the other reasons it's hard to get motivated. It would show it possible, but only for structures very much like it. All the same, I'll keep thinking if there's any way to modify your setup to get it to collapse, because you are right when you say no one's made it happen. That's about the strongest motivation, so that it's been done at least once.

This is very true. If the top core was crushing down through the core structure below it, and nothing else was going on, the top section must be destroyed before the larger lower section.

I see a critical difference between "crushing" and "peeling". I think the falling debris effectively formed a wedge than unpeeled the structure by breaking thr floor joints and pushing both in and out. This produced an avalanche of increasing mass and kinetic energy as the towers collapsed. This eventually became to energetic and abrasive that it smashed the lower parts of core apart. With the base of the core smashed what remained of the core could no longer support itself and also fell.

There is video evidence that the core did not crush-down all the way in the initial collapse. Just as in the VW analogy.

Kat Dorman wrote:I don't think any of the models - physical, analytical, computational, will give definitive results. But that's just me, I'm very cautious. The kinds of problems I've had to deal with over the years have been humbling; as in, the source of the problem is almost never what you think it is (that's why it ends up on my desk). It does affect your thinking after a while because it's way too easy to be wrong and very fucking hard to be right. Sooo, it pays to be careful. Though maybe I take it too far.

Agreed.

I would like to see a collapse model that at least gets the basics of the observed collapse right. Solid indestructible floors and crushable vertical supports are not going to collapse in an avalanche. They can't. I think you must have an avalanche mechanism to get an avalanche. You must have relatively heavy friable floor masses and relatively weak column joints. You must have the removal of lateral support from columns. You must have column section that can fall in pieces to damage lower parts of the structure.

While it is probably impossible to build a physical model that could ever give a definitive answer on the details of the tower collapses, I am sure a model can be made that demonstrates that the top 15% of a self-supporting structure can produce a progressive and total collapse after initiation. I suggest that any new modelling activity focusses on that and doesn't expend valuable time on a model that we know arrests.

psikeyhackr wrote:I suppose another way would be to use a cup and put something in it, water, sugar, sand. whatever.

Whatever floor mass you use, it should fall into the structure in heavy lumps when the floor support fails. I think this is an essential feature of the observed progressive collapse and a major deficiency in your model. See my more detailed post, above, on this to Kat. Indestructible washers, cups or plates will not do he job. Fine powerd will not do the job. Think "avalanche of wrecking balls".

I suggest a revision to my woodblock tower. Scaling results in low mass per unit length, and what we need in a good collapse is lots of falling mass. We should make the column sections and floor loads as heavy as possible with relatively weak joints. slender Steel rods are better than wooden blocks. Paper is entirely the wrong material. Falling paper will break nothing, and the model doesn't even allow it to fall!

GrahamH wrote:...While it is probably impossible to build a physical model that could ever give a definitive answer on the details of the tower collapses, I am sure a model can be made that demonstrates that the top 15% of a self-supporting structure can produce a progressive and total collapse after initiation. I suggest that any new modelling activity focusses on that and doesn't expend valuable time on a model that we know arrests.

I continue to advise caution that we don't get lost by blurring the "loops model" and the "Real tower collapse".

Given that those two models are the extremes of a range of possibilities separating two different mechanisms.

The loops model demonstrates collapse where the primary vertical supports are the elements taking part in the collapse and the relationship of the falling weight to the strength of those vertical supports is what is modelled.

At nearly the other extreme - that of the real towers - AND only the open office space component - the interaction is between falling weight and what is essentially a trigger mechanism. That trigger of stripped off floors releases the outer perimeter columns so they can fall having played no first order part in the collapse. Column axial loads are a second or even lower order factor.

It is easy to envisage a range of options between those two extremes - say a conventional grid of columns structure. (In fact, if daring to mention this one doesn't throw anyone, the core of the real towers was of that type.)

Those three require totally different modelling if the modelling is to mean anything.

So, whilst your comments refer to the real towers and you say "...it is probably impossible to build a physical model that could ever give a definitive answer on the details of the tower collapses," I would agree that "a physical model" is probably impossible. However my emphasis on "a" is possibly not what you had in mind. I think it would be impractical to build a single model given that the real towers progressive collapse was three main and nearly concurrent mechanisms. I see little point and lots of difficulty in modelling the Open Office Space pancaking - even if using the lumps of rubble to create an avalanche effect. Modelling the "peel off" would be trivial but shows nothing of value. Leaving the core where modelling would be a challenge even though more conventional modelling. Then how to add the three together into one model???

Leaving those comments I am intrigued by this statement "If the top core was crushing down through the core structure below it, and nothing else was going on, the top section must be destroyed before the larger lower section." I would have expected either dead heat or biased to lower part falling apart first. What am I missing that makes you so confident with the "must"?

econ41 wrote:

GrahamH wrote:...While it is probably impossible to build a physical model that could ever give a definitive answer on the details of the tower collapses, I am sure a model can be made that demonstrates that the top 15% of a self-supporting structure can produce a progressive and total collapse after initiation. I suggest that any new modelling activity focusses on that and doesn't expend valuable time on a model that we know arrests.

I continue to advise caution that we don't get lost by blurring the "loops model" and the "Real tower collapse".

Given that those two models are the extremes of a range of possibilities separating two different mechanisms.

The loops model demonstrates collapse where the primary vertical supports are the elements taking part in the collapse and the relationship of the falling weight to the strength of those vertical supports is what is modelled.

At nearly the other extreme - that of the real towers - AND only the open office space component - the interaction is between falling weight and what is essentially a trigger mechanism. That trigger of stripped off floors releases the outer perimeter columns so they can fall having played no first order part in the collapse. Column axial loads are a second or even lower order factor.

It is easy to envisage a range of options between those two extremes - say a conventional grid of columns structure. (In fact, if daring to mention this one doesn't throw anyone, the core of the real towers was of that type.)

Those three require totally different modelling if the modelling is to mean anything.

So, whilst your comments refer to the real towers and you say "...it is probably impossible to build a physical model that could ever give a definitive answer on the details of the tower collapses," I would agree that "a physical model" is probably impossible. However my emphasis on "a" is possibly not what you had in mind. I think it would be impractical to build a single model given that the real towers progressive collapse was three main and nearly concurrent mechanisms. I see little point and lots of difficulty in modelling the Open Office Space pancaking - even if using the lumps of rubble to create an avalanche effect. Modelling the "peel off" would be trivial but shows nothing of value. Leaving the core where modelling would be a challenge even though more conventional modelling. Then how to add the three together into one model???

Psykey made a model, and on the basis of his results claimed that no self-supporting structure could undergo total gravitational collapse from a drop of the top 15%. It is that claim that I am addressing with suggestions for a better model.

A scale model isn't going to tell us much about the real tower collapses, but it can answer this "physical principle" claim. Remember that his model does not distinguish a core structure, we are only talking about self-supporting structure.

econ41 wrote:Leaving those comments I am intrigued by this statement "If the top core was crushing down through the core structure below it, and nothing else was going on, the top section must be destroyed before the larger lower section." I would have expected either dead heat or biased to lower part falling apart first. What am I missing that makes you so confident with the "must"?

Dead heat might be about right. Given that then the 15% of height in the top must be destroyed for the destruction of 15% of the lower section. That would leave 70% of the core standing (which might have been the case. Has anyone produced a good estimate of the hight of the core remnant before it fell?)

There are plenty of complications, of course. The hat truss was probably quite a bit heaver and stronger than the core structure below it because of all the cross-bracing, but it seems improbable that it could have been so must stronger that it could destroy 85% of the structure for its 15%.

I was perhaps unwise to say "must", but it seems reasonable. How do you think the smaller section could destroy almost all of the larger section?

All of a sudden, this is getting very interesting. Thanks much for the comments, GrahamH.

GrahamH wrote:However, you are very likely to get the same results that he did, for the same reasons he got them.

Yes, I absolutely agree. To within the error from the quality control variability, which at >30 stories would tend to converge on a mean pretty close to his. Never did find that paper cutter...

I agree so much that even my rigid-top program was able to closely approximate his model, based only on his static and drop tests. This data is essential for defining the support properties, it's not cheating or tweaking. Basically it means, if I had the calibration data before the actual collapse, I would've been able to predict the number of stories destroyed. (and can make predictions now about different drop heights, numbers of stories dropped and so on)

I see a critical difference between "crushing" and "peeling". I think the falling debris effectively formed a wedge than unpeeled the structure by breaking thr floor joints and pushing both in and out. This produced an avalanche of increasing mass and kinetic energy as the towers collapsed. This eventually became to energetic and abrasive that it smashed the lower parts of core apart. With the base of the core smashed what remained of the core could no longer support itself and also fell.

I believe that is a very good description of the events. All I can add, for the North Tower, is that the core itself is partially responsible for its own demise. By that I don't mean just self-weight buckling, although that initiated the process. A taller portion of core, missing beam connections in the upper portion, buckles with a hinge towards the lower to mid height of most of the remaining core. As the section falls, there is horizontal reaction force in the hinge and a lateral impulse is imparted to the larger core section which visibly displaces it and sets up oscillations. After a short period, it drops. I assume this to be part of the cause (see here) with the remainder being debris dispersal at ground impact. That IS like the ice in the video.

Solid indestructible floors and crushable vertical supports are not going to collapse in an avalanche. They can't. I think you must have an avalanche mechanism to get an avalanche. You must have relatively heavy friable floor masses and relatively weak column joints. You must have the removal of lateral support from columns. You must have column section that can fall in pieces to damage lower parts of the structure.

YES! Very labor-intensive.

I am sure a model can be made that demonstrates that the top 15% of a self-supporting structure can produce a progressive and total collapse after initiation.

Me, too. Glass is the only thing I can think of, not cheap and not fun to clean up. I've thought of all kinds of weird shit like sand with cyanoacrylate binder cast in molds, glass filaments in various geometries, all too exotic (but almost guaranteed to work). There will always be something better to do than mess around with that! The problem is, the towers were delicate at their scale. If you were scaled accordingly and merely brushed against them, you'd fuck them up. Like a house of cards. (opinion and speculation alert)

I suggest that any new modelling activity focusses on that and doesn't expend valuable time on a model that we know arrests.

Seconded.

The natural evolution is to go brittle. Cast thin walled sugar tubes (oh shit, stop it, there will be no mold making...).

Seriously, though, as noted many times an interior avalanches faces uniform, periodic structure - the floor membranes. Indeed, this is where my real interest has been for some time. See here for try and fail of the standard inelastic accretion model (pancaking with mass transport in/out of crush zone) and here for what will be my first stab at a fluidized model, nothing done yet. It is from the generic side, as econ41 would put it, but I am a physics junkie. The difference between the treatments I have in mind and all the 1D rubbish so far is they would be motivated by what is really sloshing around in there.

Statistical physics has had great successes in describing large systems with only a few variables. The idea is, just as a Tinkertoy lattice structure might have exactly the same load-displacement response as cases of beer if you put them in a hydraulic press, granulation and granular flow in this case may be able to be described well by a phase transition and subsequent laminar compressible flow, analogous to melting. It's radical, and developing such an idea is a bit ambitious for me, so there it sits for the time being. I intend to draw on a lot of existing work: fiber bundle models, motion of non-Newtonian fluids, fracture mechanics, cascading failures, etc. Also the fine work of Frank Greening on the notion of concrete comminution (brief example here), though concrete itself is a little too... ahh... concrete and specific, material-wise. Generic.

The Benson avalanche model is, as I mentioned, the gold standard for functional form in the global sense. This concerns more the local propagation, but similarly will attempt to handle details in aggregation to reduce the number of parameters required to obtain a fit description.

Physical models are not my thing because it's not my talent, they cost time AND money, and there's a huge body of literature on physical experiments available to draw on when you want to calibrate to reality. If ever.

GrahamH wrote:...cups or plates will not do he job. Fine powerd will not do the job.

Just to clarify, those were not collapse model components but rather the means to load test the loops. I wanted to characterize the loops' dynamic failure properties in the most expedient way possible, to show the load displacement curve was somewhere near flat, as I've been claiming for (how long now, psikeyhackr?)... long time. It was just finally time to walk the walk with the real paper. I'm VERY confident the original explanation for arrest has always been correct.

Think "avalanche of wrecking balls".

Now, that's the approach.

I should add that, in the theoretical treatment I envisage, the core and the perimeter only minimally (but crucially) participate. Once the crush zone has locally passed a level, the core and perimeter above may as well not exist.

econ41 wrote:Leaving those comments I am intrigued by this statement "If the top core was crushing down through the core structure below it, and nothing else was going on, the top section must be destroyed before the larger lower section." I would have expected either dead heat or biased to lower part falling apart first. What am I missing that makes you so confident with the "must"?

Because there's less of it .

http://i41.tinypic.com/t7msya.gif

It's heavily biased downward, but even at the reduced rate, crush up still finishes before crush down.
(wink wink nod nod - see those generics do come in handy)

Kat Dorman wrote:Glass is the only thing I can think of, not cheap and not fun to clean up. I've thought of all kinds of weird shit like sand with cyanoacrylate binder cast in molds, glass filaments in various geometries, all too exotic (but almost guaranteed to work). There will always be something better to do than mess around with that! The problem is, the towers were delicate at their scale..

Based on evidence of the real collapses it doesn't seem essential to a generic collapse to bend or break columns. What we are after here is separation of column sections at joints and fracturing of floor mass into weighty lumps (which are pulverised as they cascade down and impact the lower structure.

As a first pass the static friction of column ends to cardboard floors are breakable joints and enough to answer Psykey's "physical principle". Moving on from there various strength glue could be applied to the column joints, from candle wax to spots of super glue.

Kat Dorman wrote:I should add that, in the theoretical treatment I envisage, the core and the perimeter only minimally (but crucially) participate. Once the crush zone has locally passed a level, the core and perimeter above may as well not exist.

Once the collapse front has passed a point then material formerly part of the core and perimeter is falling mass (more wrecking balls)

Kat Dorman wrote:

econ41 wrote:Leaving those comments I am intrigued by this statement "If the top core was crushing down through the core structure below it, and nothing else was going on, the top section must be destroyed before the larger lower section." I would have expected either dead heat or biased to lower part falling apart first. What am I missing that makes you so confident with the "must"?

Because there's less of it .

http://i41.tinypic.com/t7msya.gif

It's heavily biased downward, but even at the reduced rate, crush up still finishes before crush down.
(wink wink nod nod - see those generics do come in handy)

Only when the crushing is constrained (pancaking). A block of upper core crushing through a block of lower core will not pancake. The bits that break all go one way, whether they were on the top part or the bottom. They all join the avalanche. Block crushing similar block will destroy the smaller block first, but avalanche can keep growing and falling.

GrahamH wrote:Has anyone produced a good estimate of the hight of the core remnant before it fell?

Here and here.

There are plenty of complications, of course. The hat truss was probably quite a bit heaver and stronger than the core structure below it because of all the cross-bracing, but it seems improbable that it could have been so must stronger that it could destroy 85% of the structure for its 15%.

Rubble alone could do it, but a hat truss-perimeter (remnant) wedge would probably do it much faster. It would erode away at some point, probably, but after taking the fast plunge down one side of the floorspace and cleaving the perimeter off. Just one scenario.

Kat Dorman wrote:

GrahamH wrote:Has anyone produced a good estimate of the hight of the core remnant before it fell?

Here and here.

Thanks. Is there a number in there?

On one view the remnant seems significantly taller than WT7, so 50+ stories high? That is consistent with crush-up / crush-down.

Kat Dorman wrote:

There are plenty of complications, of course. The hat truss was probably quite a bit heaver and stronger than the core structure below it because of all the cross-bracing, but it seems improbable that it could have been so must stronger that it could destroy 85% of the structure for its 15%.

Rubble alone could do it, but a hat truss-perimeter (remnant) wedge would probably do it much faster. It would erode away at some point, probably, but after taking the fast plunge down one side of the floorspace and cleaving the perimeter off. Just one scenario.

I was considering the hat truss being the wedge that might un-zip and cleave off a significant part of the core. It wouldn't take much to cleave the perimeter. The rubble from a few floor slabs dropping onto an intact floor slab would probably be enough, given the factor of safety per floor.

GrahamH wrote:Only when the crushing is constrained (pancaking). A block of upper core crushing through a block of lower core will not pancake. The bits that break all go one way, whether they were on the top part or the bottom. They all join the avalanche. Block crushing similar block will destroy the smaller block first, but avalanche can keep growing and falling.

I do have the habit of tossing things out with zero explanation. First thing is the 'camera' in that simulation tracks with the roofline, so it pans downward at the same rate as the collapse. While it looks like there's crushing upwards, there isn't. The term crush up is also misleading: nothing goes up, everything goes down, it's just referring to whether the upper or lower sections are being destroyed (and by whatever process; pancaking, buckling). The only distinction mechanics-wise I think is the core interpenetrates so is not full accretion like pancaking. And by pancaking, I never mean floor wide, only local. Thus you can see spill over from one region to another is possible with debris originating in the open floor area, not just in the core (which can also just continue down the core's open area).

Perhaps I should have pulled this out instead?

http://the911forum.freeforums.org/progression-attributes-of-enik-s-core-simulation-t406-45.html#p12443

Surprisingly, or not so, the 1D accretion thing works pretty well on this, too. I pulled out the GIF above because this is one of those things where it pretty much tastes like chicken, and that breaks it down to its simplest appearance.

GrahamH wrote:Thanks. Is there a number in there?

Hard to find, I know. Tallest lingering spire on WTC1 was floor 77-78. There were taller ones that survived the passage of the upper block but succumbed shortly after, possibly as high as 90. The bulk was well below that, stepping down at around mid 60's then again mid 50's. WTC2, I'll have to look.

On one view the remnant seems significantly taller than WT7, so 50+ stories high? That is consistent with crush-up / crush-down.

Well, not precisely as Bazant states it which is with everything participating equally and at the same time across the footprint. However, locally core-core impacts would be expected to conform to it, yes. It's just that the framework ceases to become useful at that point. It's equivalent to having a ridiculous spread about the mean.

Kat Dorman wrote:

GrahamH wrote:Only when the crushing is constrained (pancaking). A block of upper core crushing through a block of lower core will not pancake. The bits that break all go one way, whether they were on the top part or the bottom. They all join the avalanche. Block crushing similar block will destroy the smaller block first, but avalanche can keep growing and falling.

I do have the habit of tossing things out with zero explanation. First thing is the 'camera' in that simulation tracks with the roofline, so it pans downward at the same rate as the collapse. While it looks like there's crushing upwards, there isn't. The term crush up is also misleading: nothing goes up, everything goes down, it's just referring to whether the upper or lower sections are being destroyed (and by whatever process; pancaking, buckling). The only distinction mechanics-wise I think is the core interpenetrates so is not full accretion like pancaking. And by pancaking, I never mean floor wide, only local. Thus you can see spill over from one region to another is possible with debris originating in the open floor area, not just in the core (which can also just continue down the core's open area).

Perhaps I should have pulled this out instead?

http://the911forum.freeforums.org/progression-attributes-of-enik-s-core-simulation-t406-45.html#p12443

Surprisingly, or not so, the 1D accretion thing works pretty well on this, too. I pulled out the GIF above because this is one of those things where it pretty much tastes like chicken, and that breaks it down to its simplest appearance.

I understood the gif. Of course nothing is going up, but in the gif, and in Psykey's washer model, nothing from above the "perimeter collapse front" has any effect below the collapse front. In contrast, floors that break up and gain significant velocity can be penetrating ahead of the visible collapse. This is especially true in the core where debris can fall down shafts and gaps between beams. It could also be true in open floor areas if debris can punch holes through the floors. Such debris could be running ahead of perimeter collapse, once things really get moving. Perhaps.

GrahamH wrote:What we are after here is separation of column sections at joints and fracturing of floor mass into weighty lumps (which are pulverised as they cascade down and impact the lower structure.

Yes, that's what the glass/sand is for, too: floor pans, fasteners, column welds (though I'm not opposed to fracturing columns, too)

As a first pass the static friction of column ends to cardboard floors are breakable joints and enough to answer Psykey's "physical principle". Moving on from there various strength glue could be applied to the column joints, from candle wax to spots of super glue.

Excellent.

Once the collapse front has passed a point then material formerly part of the core and perimeter is falling mass (more wrecking balls)

Yes for the core and upper section perimeter, but not too much lower perimeter participated because of the peeling. Mass lost, but strength lost, too.

GrahamH wrote:...Psykey made a model, and on the basis of his results claimed that no self-supporting structure could undergo total gravitational collapse from a drop of the top 15%. It is that claim that I am addressing with suggestions for a better model....

Understood. In that claim psikey is paralleling Gage and Heiwa and it is as wrong when psikey says it as it was when those other two said it. Details notwithstanding. And WTC1, WTC2 managed it on 9/11 - a fact demonstrable by logic paths independent of the current consideration of modelling so I am not arguing circularly. The fact that there are (at least) those two exceptions disproves the claim of "...no self-supporting structure could undergo total...etc" There are other "proofs".

GrahamH wrote:...A scale model isn't going to tell us much about the real tower collapses, but it can answer this "physical principle" claim. Remember that his model does not distinguish a core structure, we are only talking about self-supporting structure....

hence my attempted rigour in identifying the three component mechanisms of the real tower collapse.

GrahamH wrote:

econ41 wrote:Leaving those comments I am intrigued by this statement "If the top core was crushing down through the core structure below it, and nothing else was going on, the top section must be destroyed before the larger lower section." I would have expected either dead heat or biased to lower part falling apart first. What am I missing that makes you so confident with the "must"?

Dead heat might be about right. Given that then the 15% of height in the top must be destroyed for the destruction of 15% of the lower section. That would leave 70% of the core standing (which might have been the case. Has anyone produced a good estimate of the hight of the core remnant before it fell?)

There are plenty of complications, of course. The hat truss was probably quite a bit heaver and stronger than the core structure below it because of all the cross-bracing, but it seems improbable that it could have been so must stronger that it could destroy 85% of the structure for its 15%.

I was perhaps unwise to say "must", but it seems reasonable. How do you think the smaller section could destroy almost all of the larger section?

Three key points in that lot. I'll take them out of sequence. (And I am still referring to the real tower collapse)
1) "The hat truss...seems improbable that it could have been so must stronger that it could destroy 85% of the structure for its 15%." For simplicity of explanation I will stay with first order approximations. The ratio or comparison of 85% to 15% is a red herring. The global collapse occurred because the falling top block had sufficient weight/impact to overwhelm the floors immediately below it. It would have done the same if there had been another thousand feet of similarly constructed tower below. It was absolute weight/impact that caused the first floor of progressive collapse NOT the ratio of what was falling versus what was below it. Remember that is the Gage, Heiwa error. From there it was the accumulated falling mass versus the next floor down.

In the early stages the primary effect of the hat truss would be to transfer "surplus" OOS weight onto the core. Failing the "next floor down"# only required a portion of the available overwhelming weight falling in the OOS. That falling weight was only resisted by the dynamic forces needed to shear the joist to column connectors. So the surplus falling weight from the top block whilst it remained an integral structure was available for transfer via the hat truss to the core area. (all that written in pseudo static terminology for simplicity. We can translate into a more rigorous dynamic/elastic/plastic framing if we need.)

2) "...Given that then the 15% of height in the top must be destroyed for the destruction of 15% of the lower section. That would leave 70% of the core standing..." Begging the question of the dead heat such that 15% = 15%. We are still discussing the real towers. Claiming 15% destroyed 15% is probably losing touch with what happened - remember the OOS floor strip down was observably way ahead of outer perimeter fall over and arguable somewhat ahead of core strip down. So there is no measure of 15% of the lower tower.

Setting that aside if we focus only on the OOS pancaking (for want of a better term - maybe avalanche) when 15% had broken down 15% there was 30% falling to destroy the lower 70%.

However you seem to either be focussing on core or switching to core at this point. So dealing with core which is falling and therefore is causing beams to be stripped off the columns similar to the OOS we have accumulated (most of) 30%& and it has the weight/impact to continue downwards. And it continues downwards because the absolute level of weight falling with impact was sufficient to keep stripping off beams. Again it is not a matter of ratios.

3) " How do you think the smaller section could destroy almost all of the larger section?" Already addressed. It is not a "ratio" issue. The OOS collapse was a triggered release rather than a crushing. Key factor being shearing of the floor joist to column connections. Trivial strength compared with the massive falling weight applied dynamically. Hence effectively a trigger released at minimum force (put that in energy terms if you wish as per previous disclaimer) All that the "smaller section" had to do was shear off the next level of the OOS.# The outer perimeter fell at its own discretion ( ) The core fails by beams stripping from columns - initially with al the "surplus" OOS weight to assist transferred via hat truss (and allowing for it being dynamic - not pseudo statics as I have described it for simplicity.)


# Yes - it was not flat slab on flat slab pancaking BUT the manner in which some zones led, others followed and some break up occurred does not change the nett effect of the "top lot" falling on effectively the next floor down.

& Possibly some "leakage" of debris from core to OOS. Plus small bits to dust etc...

Kat Dorman wrote:Yes for the core and upper section perimeter, but not too much lower perimeter participated because of the peeling. Mass lost, but strength lost, too.

We see perimeter column sections ejected outward, but it is possible that a significant proportion of sections might have gone inward if the vertical load on them was dominant, rather than outward pressure from debris. Failing floors would tend to pull the bottom of a column section inward. Debris pressure might push the upper edge outward. It might be presuming too much to say that very few of the perimeter sections fell inside the perimeter. We don't have the data. Details were hidden in the dust and intact structure.