The 9/11 Forum

David B. Benson wrote:I don't think so. The fit to the data is simply too good. No detectable humps or bumps: smooth descent of antenna mast feature.

Crumple zones in cars make crashes much smoother. On a smaller and non-destructive scale, shock absorbers and springs smooth out the potholes.

3) The bigger the spire, the more is bypassed.

Too trivially light to be bothered with. Most of the mass of each tower was associated with the actual floors, not the structural steel.

Oh no, you've got my intention backwards. Most (all) of the strength of the structure is in the core and perimeters, yet very little of the overall mass as you say. Bypassing a substantial portion of the core and perimeter means a considerable amount of resistance is bypassed; a similar driving mass above has much less to overcome below. All this with very little sacrifice of driving mass as all the dead load is still there. This condition is already observed so doesn't need to be postulated. It actually needs to be accounted for.

Much less strength => less Zone C mass needed to maintain collapse rate.

You were saying a drop in resistive force of about 14% is required in order to let half of the top fall off half way through. The lower half is where the perimeters peeled off in great strips, and the surviving core portions become more substantial. This is precisely the region where a lot of the structural components were bypassed. There's greater capacity lower down, but a 14% reduction doesn't seem out of the question if 40-50% of the columns are still standing, however briefly.

Remember, too, if the block falls off it doesn't happen in a flash like flipping a switch.

Just thinking.

Avalanche in a chute could be intrinsically faster, closer to pure momentum transfer as described by Greening.

That's the best choice of resistive force to match the data; I now use it in preference to the BLGB formulation. Zone C is like you on the top edge of your flowing snow avalanche.

I like the whole concept. It seems close to reality, besides being the best fit. Maybe that's why it is the best fit.

Some things don't come through so well in still images. There's a particular close-up of the north wall of WTC2 as it fails, the one I used to create the column buckling GIF. Once the collapse is underway, the camera zooms out to capture the big picture and you can see stuff flowing past the still-standing portions of core and perimeter. This is not just dust and pulverized concrete, though there's plenty of that. It's everything that was there, that was solid, just a second ago. It's largely a fluid phenomena. Or borderline, certainly.

The word 'metastable' comes to mind and, if I may coin a term - externally organized criticality. Avalanche seems the closest analogy. Rapid phase transition from a stable but locally high energy minimum to a much lower energy state nearby in phase space.

With that in mind, there are some amazing avalanche videos on this page, almost worth getting a player on that box:

http://valtellina.myblog.it/tag/valanga

What I experienced (hiking, not skiing) was tiny and slooow by comparison. Only a little scary. These are massive, terrifying slides.

And a link to some avalanche research. Physical models using fluid.

http://actualites.epfl.ch/presseinfo-com?id=323

Heiwa wrote:In your simulations, where part C has same structure as part A, it seems that energy and forces applied at contact are not correctly simulated.

That's quite possible. In some cases, I'm fairly sure of it. That may not be why the results are contrary to your expectation.

The forces on A and C at contact interface are equal and should produce similar deformations and failures there.

Hmm. What about B? If you look closely at some of my earlier animations, that is indeed what happens - at first.

Suggest you test your model with different energy inputs (inital drop heights) as follows:

Consider it 'in work' - after we resolve a few details.

1. Chose drop height so that only deformation of elements (columns) in A and C take place.

I am limited (right now) to survive/fail using fixed joints. These are, I suspect, actually implemented as springs with an enormous spring constant, where a force and torque capable of breaking the joint can be specified. Until I move on to more sophisticated joints, structures will be quite rigid though not necessarily brittle.

Result should be a bounce. What was the drop height? It must be just a fraction of the floor/floor height.

The strength of the joints can be set to anything you want. They can be strong enough to have 200 stories bounce off 2, or so weak the bottom gives out immediately. Quite a lot of latitude. To try to narrow the scope a bit, and impose control, I've sometimes used the convention of finding the joint strength that just barely fails when a block of N stories is dropped from exactly one story height. What I'm trying to say is, unless you add more constraints to the model, the resulting drop height can be anything you want and still obtain the 'deformed' result. It matters how strong the connections, how massive the slabs, and how high the stories.

2. Chose drop height so that two sets of columns will fail. Result should be that one set of top columns in A and one set of bottom columns of C fail.

So far, that seems to be a pretty typical result, though not universal.

3. As 2 but so that four sets of columns will fail.

Scaling up, yes. So far it seems I've actually done most of this, in one sense or another. I need to report the results! Although, I have already reported the results in some cases. It's not always equal destruction, as you say it should be; usually isn't, although there are a number of 'islands' in the parameter space where exclusive crush-up or a near-perfect mix of both exist. The easiest and most naive structures seem to go like this:

- slight mixed crush up/down
- top rides all crush down until bottom of Zone B hits
- crush up of the remaining top

Depends on the parametric input. Things make sense, in most cases, when you take the settings into account. You really need to let the fact sink in that I already have reproduced your anticipated results and it is a special case, not a general case. Simply telling me that something is not correctly simulated because it doesn't produce the result you expect is not concrete enough to act on. Perhaps you can tell me what's right about the 50-50 zero-g collision instead, unless you think it's wrong, too.

It is recognized that above assumes that floors remain undamaged and are stacked on top of one another after columns fail. So when all columns in C has failed an equal number of columns in A has failed. Then remaining columns in A fail and the result is a nice stack of floors (or pan cakes) on ground.

Like I say, that is observed, under certain conditions.

Therefore:

4. Assume that columns do not buckle but that C columns slice A top floor and A columns slice C bottom floor at first impact and consequent further dropping by C. Each damaged floor is then supposed to hinge down around the column connections. Result will be a lot of floor parts rubbing against each other and you have to consider friction between these elements.

<gasp> A little beyond my capabilities at this point. I'm still working with slabs, though they can have static and dynamic friction values assigned. The reason I'm trying to keep it simple is because I don't want to push this environment to the limit of what it can reliably handle; plus, simplicity abstracts and isolates the variable factors, allows pure concepts to show through.

That is just for start. I look fwd to simulations 1 - 4.

I hope you're patient!

In my opinion WTC1 structure part A full scale cannot be crushed down by part C and this is the basic reason why you cannot model the contrary at any scale. Note that at first crush there is no part B. Reason that part C cannot crush part A is that part A crushes part C before part C can crush part A. Evidently crushed parts of C (or part B for that matter) cannot crush intact part A. Crushed parts C (and B) cannot apply sufficient energy to damage A.

Benson suggests that his differential equations apply at full scale but not in any other scale as he has big problems to do it! It is a funny excuse. Test at scale 1/2 or 1/4! At what scale is suddenly global collapse or rather crush down impossible? Try to answer that and you may find the answer why crush down at scale 1/1 is not possible.

Heiwa wrote:In my opinion WTC1 structure part A full scale cannot be crushed down by part C...

I do respect your opinion.

...and this is the basic reason why you cannot model the contrary at any scale.

But here's where I have to part ways with you. To repeat, I have modeled it, on many scales. Already. Successfully. Upthread. In posts you read.

You just don't accept the modeling as valid, and I respect that, too. Mind you, I'm hardly sold on aspects of it myself, however I do think the first few I posted are pretty close to genuine dynamical behavior. All I'm asking for is something a little more concrete than it's wrong because it conflicts with your opinion.

Note that at first crush there is no part B.

True. Later, sometimes quickly, there can be. Things change considerably when that happens. Not saying all structures will do this, but slabs do it readily.

You did say:

...it seems that energy and forces applied at contact are not correctly simulated.
...
The forces on A and C at contact interface are equal and should produce similar deformations and failures there.

Somewhat specific, and the last part is OK up to a point but you have to ask yourself what happens after that in an accelerated frame.

Right out of the box, it confirmed David B. Benson's opinion. And mine. I had to probe around to find the exceptions, which represent diverse categories of behavior - some much less realistic when I compare to everyday experience. I have less confidence in most of these scenarios having a real physical correspondence than the simple, small original forms that crushed down and collapsed completely. I can make 1000m towers of slabs 10m on a side, that weigh a kilogram each but have more bounce than a tennis ball... how real is that? The more sensible ones so far tend towards crush down, just not exclusively.

Obviously, you can't tell me details to play with if the environment is unknown to you. As time goes along, I should like to characterize and validate the simulation environment more fully. For example, joint failure is specified according to force (tension, compression) and torque (applied tangentially to the axis of the joint). Force is easy but static, so a relation between joint programmable parameters and energy consumed in failure under dynamic loads must be established by extensive trial. Because this is 3D, the torque is problematic. It has a tremendous influence; column-wise, it's the bending or lateral force. Non-axial hits are chaotic unless cleverly damped. Simple systems usually give repeatable results. Big, complex ones not so much.

Ah, but the problem: how to validate dynamics of a complex system? Two body collision, pendulum, tipping pencil... newton's cradle? What else can be done analytically?

Please set up the equations of motion for this, so as to double-check its accuracy: http://www.cinderella.de/files/HTMLDemos/5P05_Momentum.html

At least I have an analytical model (several) to work from for tower collapses to see how well the simulations conform. I welcome you to present an alternative sufficient to verify the accuracy of this, or any other, complex simulacra.

OneWhiteEye wrote:
Somewhat specific, and the last part is OK up to a point but you have to ask yourself what happens after that in an accelerated frame.

Exactly. Use part A base as reference as it does not accelerate. Then consider C. As it is an assembly of elastic elements, the elements accelerate differently. You can evidently lump C together as one element/mass but then we are back to solid mechanics - like your models seem to be. Evidently A behaves like C; as A also is an assembly of elastic elements, they all accelerate differently; the bottom ones not at all, the top ones due to deformations/displacements.

Then we have part B. To form part B you must break off part A top elements at both ends and then accelerate all these (B) elements to the velocity of C. As the B elements rub against each other you must consider friction. At full scale it seems you only need 0.05 kWh/ton to form B rubble elements, which is amazingly low. I wonder what that would be in scale 1/100. How these B rubble elements later can destroy further part A top elements is beyond me.

Pls remember that to shred a car (full scale) in a modern re-cycling plant you need abt 37 kWh/ton.

It is quite easy to verify how much energy is required to (a) first disconnect 1 ton of part A top elements at two ends and (b) then compress them to part B rubble density and then finally accelerate that 1 ton of rubble. If you get a figure close to 0.05 kWh for (a+b), then you might be up to something.

And you must remember that it is part C that is supposed to produce this rubble assisted by gravity only.

Actually the figure 0.05 kWh/ton is a measure of the strain energy of one ton of part A top elements. You should wonder, if that was sufficient to carry part C in the first place and if part C above could be held together at all!!!

Anyway, good luck with your model.

Most (all) of the strength of the structure is in the core and perimeters, yet very little of the overall mass as you say. Bypassing a substantial portion of the core and perimeter means a considerable amount of resistance is bypassed; a similar driving mass above has much less to overcome below. All this with very little sacrifice of driving mass as all the dead load is still there. This condition is already observed so doesn't need to be postulated. It actually needs to be accounted for.

Yup. That is the whole ticket. That is the part that you can completely ignore in 1-D

If we expand to basic 2-D we see that the resistive forces are quite different depending on if you are in the chute, core or right in the perimeter wall. I can even invent a very basic function to describe relative resistance which, with some tweaking, may be pretty close to reality.



The resistance that falling debris encounters is very different between the three regions. Debris naturally will gather in the chutes.

The perimeter caging forms a strong barrier between "inside" and "outside".


Notice how in 1-D all these differences are mixed together into some "alphabet soup". Everything changes in 2-D.

None of this violates the B&V ODE which uses homogeneity as one of the simplifying assumptions.

That assumption disappears in 2-D. Considering how differently you can expect resistance to be in the chute compared to through the core and the fact that the perimeter peels away must leave one wondering how anyone could have expected accurate fall time results from a 1-D "alphabet soup" model.

We need to redefine fall time in terms of how fast debris can plow through the chute and contacts earth creating a detectable wave within the earth.

Some things don't come through so well in still images. There's a particular close-up of the north wall of WTC2 as it fails, the one I used to create the column buckling GIF. Once the collapse is underway, the camera zooms out to capture the big picture and you can see stuff flowing past the still-standing portions of core and perimeter. This is not just dust and pulverized concrete, though there's plenty of that. It's everything that was there, that was solid, just a second ago. It's largely a fluid phenomena. Or borderline, certainly.

Yup. You can see the collapse front ejecting dust. You can see it is trapped within a perimeter caging. The caging is solid and contains this initial rubble very effectively. It's like fluid.

By a sound track, the west wall finished crashing into West Street at very close to 18 seconds, according to shagster. I calcuated that this should have taken about 3 seconds after the crushing front passed floor 10; that before I even knew about the seismograph determination. So there are two lines of evidence which give the timing. For this to occur, under the assumption that the resistive force determined from the first few seconds applies throughout, requires that most of the mass of the upper portion stay up there until story 98 is about at the floor 12--16 elevation. Maybe a bit higher.

If you view the initial collapse fronts as progressing in the chutes, your assumptions in terms of a 1-D formulation have very little meaning.

Initial assumptions of resistance provided by the core or perimeter to the speed of the collapse front must be wrong.

You can't possibly group core, perimeter and chute resistance together, cram them all into 1 dimension and think that this will yield results that can predict fall time.

Collapse time is a chute phenomenon.

WTC 1 – Part C crushing Part A

How to model it? Let's do it 1-D!

Let’s assume part A consists of 96 (floor) elements A96, A95 … A1 on top of each other connected by 95 spring elements AS96/95, AS95/94 … AS2/1. Floor element A1 is connected to Ground by spring element AS1/G.

Let’s assume part C consist of 14 floor elements C97, C98 … C110 on top of each other connected by 13 spring elements CS97/98, CS98/99 … CS109/110.

Let’s assume each floor element has mass m. Part C with mass 14 m is assumed resting on part A with mass 96 m via spring elements ACS96/97. The spring elements have no mass.

Let’s assume that each spring element carries the masses above it and deforms elastically, so that the stress in the spring is 0.3 of the spring breaking stress. Thus spring element AS1/G v=carries 110 m, top spring element CS109/110 only 1 m. All spring elements are thus compressed elastically to same stress.

Now we suddenly remove spring elements ACS96/97 and allow part C with mass 14 m to drop on and impact part A with mass 96 m with velocity v. Thus 14 floor elements C each with mass m accelerate down.

When part C free falls no load acts on spring element CS97/98, CS98/99 … CS109/110. So stress in these elements becomes zero. Part C expands as no load is acting on the springs.

Likewise, when part C free falls, part A’s spring elements AS96/95, AS95/94 … AS2/1 carry 14 m less load and stress is reduced, e.g. spring element AS96/95 has stress 1/14th of before. Part A is thus unloaded by 14 m and expands. Thus, all spring elements in parts C and A are immediately aware of the free fall and their stresses are reduced and they expand. But not for long.

At impact element A96 is thus contacted by element C97. Other A or C elements are not yet aware of the contact! But, a fraction second later, elements C98-C110 each with mass m know about the impact and compress the spring elements CS97/98, CS98/99 … CS109/110. Likewise, elements A96-A1, also with mass m, become aware of the impact and compress spring elements AS96/95, AS95/94 … AS2/1. Finally spring element AS1/G is compressed and sends a strong signal to the Ground.

What happens then? It depends on the energy input E at impact. If E is below a certain value, you would expect all spring elements to deform elastically and thus part C will bounce on part A.
If E is above a certain value, one spring element may break – the weakest! Which one? Is it, e.g. AS96/95 or CS97/98? Benson assumes it is AS96/95. But isn’t spring element CS97/98 a little weaker? Or doesn’t it matter?

Let’s assume one spring element breaks, be it AS96/95 or CS97/98 or someone else and that all other spring elements just deform elastically until then. That would result in the famous jolt, part C free fall slowing down, that MacQueen & Szamboti have not been able to observe.

Anyway, let’s assume one spring element fails and allows a second free fall of whatever part is now above the broken spring element. The same thing, as happened before, should now happen again. Upper part spring elements get zero stress, lower part spring elements are subject to reduced stress, masses are displaced (upwards) by elastic decompression until the second impact, when all spring elements are compressed again and one fails. If the process runs out of energy after first or second impact, it will evidently stop - collapse arrest. If not it will continue.

Global crush down of AS springs by part C will then take place, while part C (14 m) accelerates.

According Benson it is always the AS spring elements that fail 95 times at 95 impacts, and A floor elements with mass m that are accelerated , while the CS spring elements and all part C masses remain intact at increasing velocity due to gravity and little resistance by part A.

Benson evidently forgets that all spring elements are unloaded between impacts and must be reloaded/compressed again at subsequent impacts. The floor masses m above/below a broken spring element will displace upwards before each impact, etc.

OK, Benson suggests that the energy at first impact is sufficient to both compress all A and C spring elements and break one spring element, and that one broken spring element will provide extra energy (another drop by gravity) to repeat the performance 95 times.

Actually, Benson suggests that the energy at first impact was 8 times bigger than required to compress all spring elements in parts C and A and to break one spring element (below!) in part A and that it is the reason why subsequent compressions and breaking of a spring element (95 times in part A) can take place at increasing speed and shorter intervals (and forget any arrest).

However, if the energy E applied was 8 times bigger than required to compress all spring elements in parts C and A and to break only one spring element below at first impact, you really wonder how part C spring and floor elements could have resisted it? Benson suggests that part C will only be subject to negligible damages at first and subsequent impacts, so that part C can drive the crush down of part A.

If part C is destroyed or crushed up or stopped at first or second impact, there will evidently not be any crush down. This is what normally happens in gravity driven collapses. Smaller part C is simply stopped by bigger part A of identical structure. This might be difficult to simulate in 1-D as the mass above is still acting on a broken spring. Allow for mass above dropping off, then it becomes more clear very quickly. So better do simulation it in 2-D or 3-D.

However, the model will explain that global collapses of structures will take place as suggested by Bazant or simply confirm that the Benson theory is nonsense!

Major_Tom wrote:If we expand to basic 2-D we see that the resistive forces are quite different depending on if you are in the chute, core or right in the perimeter wall. I can even invent a very basic function to describe relative resistance which, with some tweaking, may be pretty close to reality.

Yes! Absolutely. Your picture is worth a thousand words. More.

Must discuss; back after some sleep.

elements of the core (mainly the outer core columns) started to fall down about 0,7 seconds before the start of the NT tillting ( tillting = first observable movement of the exterior...)


and then continued to the ground at freefall acceleration

any model should take this ionto consideration

Major_Tom & OneWhiteEye --- But that 2-D layout is not where the resistive force is coming from. The main resistive force is due to the comminution of concrete, floor pans, trusses,,office furnishings, ..., everything but the structural steel. In the core, mostly just the connections failed, little column buckling. That is what one sees at Ground Zero; almost no floor pans, only one pix of a recognizable section of truss, lots of well ground materials.

In my computer program, an attempt to use the force function of BLGB together with the avalanche forse ressults in setting the BLGB constant to zero, or nearly so, for best fit; essentially all the resistance during the period of measurements is due to comminution. Now that is a bit harder for the ordinary concrete in the core floors, but on the other hand there are no trusses to break up either, just (I suppose) a floor pan and then connections of beams to columns.

Nor does all this happen just at the crushing front, as BLGB supposes. It clearly extends throughout the entire zone B during the period of measurements. It is certainly possible that after the crushed zone B grows sufficiently thick that the resistance only develops over a constant thickness lower portion, the top of zone B being quiesient. Such a (highly believable) effect does not show up in the first 3.75+ seconds. If this idea is right, then more mass shedding (possibly some of zone C, the upper portion) is necessary to have the correct crush-down time of close to 15 seconds.

Greetings, this is my first post.

There is no math or coding or animation in these models but distribution of mass should affect the results.

http://www.youtube.com/watch?v=LXAerZUw4Wc

http://www.youtube.com/watch?v=z0kUICwO93Q

The vertical collapse demo has a problem because the washers are tilted on the toothpicks so the falling washers do not hit them flat. I presume that causes the stationary washers to undergo a kind of lever action so part of the washer is actually moving upward when it finally comes into complete contact with the falling mass. I should have used thin copper wire instead of toothpicks but I didn't think of it until the video was shot.

psik

psikeyhackr wrote:Greetings, this is my first post.

There is no math or coding or animation in these models but distribution of mass should affect the results.

http://www.youtube.com/watch?v=LXAerZUw4Wc

http://www.youtube.com/watch?v=z0kUICwO93Q

Welcome. Very interesting stuff.

The vertical collapse demo has a problem because the washers are tilted on the toothpicks so the falling washers do not hit them flat. I presume that causes the stationary washers to undergo a kind of lever action so part of the washer is actually moving upward when it finally comes into complete contact with the falling mass.

Friction may still be an issue in the arrangement, in this case between the washer inner diameter and the rod. The tilt indicates a loose fit around the rod which might lead to transient binding at the maximum tilt angle. I'd imagine the diameter of the dowel is a matter of expediency (best fit from the hardware store), but it might be a significant energy sink; maybe you've seen the phenomena of rings 'walking' down poles, instead of freely sliding, because of off-axis oscillations. It wouldn't be necessary for the effect to be visibly noticeable to dissipate a fair bit of system energy.

The edge of a washer could even momentarily bite into the surface of the rod. Not saying there will be visible divots in the surface as a result, it doesn't have to be that severe (though you might want to hold the rod up to a light and get the proper angle to examine reflection off the surface, and see if any are visible). In any case, the lever action and attendant mechanics is a possible energy sink, though who knows to what extent.

My suggestion for minimizing this influence on the experiment is to lubricate the rod. Even light oil would probably be too adhesive and admit significant drag. A dry lubricant like silicone spray applied after light sanding with 400 then 600 grit would probably make the surface greased lightning. If it is possible to use a slightly larger diameter dowel, that would be good because it would eliminate the lever action as well.

Not trying to make more work for you, just eliminate possible wildcards. Excellent effort!

PS do you have the results of your trials in tabular form?

David B. Benson wrote:Major_Tom & OneWhiteEye --- But that 2-D layout is not where the resistive force is coming from. The main resistive force is due to the comminution of concrete, floor pans, trusses,,office furnishings, ..., everything but the structural steel.

****, imagine that.

In the core, mostly just the connections failed, little column buckling. That is what one sees at Ground Zero; almost no floor pans, only one pix of a recognizable section of truss, lots of well ground materials.

Same with the perimeters, and here we are attempting to fit this reality against a published model of 100% column buckling! Little do MT and I know, that's not the model anymore!

Some confusion comes in when we freely intermingle Greening/BZ/BV/Seffen and the avalanche theory - details of which are not widely disseminated at this point. I know you've laid it out in some detail at physorg over a span of months. Regardless, I have a fairly dim picture of it, even of the particulars in making comparisons between alternate forms of resistive force. It would certainly be useful to me, and I suspect others, if you were to post a basic summary. Not to give away the goose if some of the stuff is proprietary, but just enough so I don't bumble through this trying to whack moles you've already clobbered. Y'know?

In my computer program, an attempt to use the force function of BLGB together with the avalanche forse ressults in setting the BLGB constant to zero, or nearly so, for best fit; essentially all the resistance during the period of measurements is due to comminution.

Zero? Seriously? I'll not concern myself anymore with the lack of buckling then!

I really thought the avalanche resistive force had this component rolled into it, even if not separable by term. A snow bank has structural strength!

Nor does all this happen just at the crushing front, as BLGB supposes. It clearly extends throughout the entire zone B during the period of measurements.

I was going to get to that next (simultaneous crush front over dozens of stories) but obviously you beat me to it. Your personal research is apparently far ahead of the common knowledge about the academic work. Most of us come at this from the point of view of hinge buckling, 8.4x the KE on first impact, energy dissipation only at the crushing front, rigid upper block, etc. Is there such a great lag in publication time, or am I not reading the existing publications with understanding? My concept of what is the current theory grows ever more vague, in proportion to the amount of time I study it. Suggests to me I find a new hobby.

psikeyhackr:

OneWhiteEye wrote:PS do you have the results of your trials in tabular form?

Hadn't seen your other post. Edit: never mind, now that I'm reading it; different data.

PS. I assume you've read ENERGY TRANSFER IN THE WTC COLLAPSE by F. R. Greening. ?

Major_Tom:

In my mind, I'd put together an engaging commentary on your most recent post. I believe I'll hold that until I know WTF I am doing here.