The 9/11 Forum

OneWhiteEye wrote:

Heiwa wrote:You cannot crush a structure A by a part C of itself (C = 1/10 A) by dropping part C on A using gravity. Part C either bounces on A or gets damaged in contact with A and is stopped by A that is also damaged a little.

In my domino system, an upper block destroyed a lower block 9x bigger, in a variety of circumstances. What about these simulations, in your opinion, fails to capture physical reality accurately? I showed a zero-g case where damage was equivalent. Does this one seem realistic to you? If so, and knowing the difference was absence of uniform force field, why do you suppose one result is realistic and the other not?

As I mentioned, there are results I haven't posted. Such as equal crush up/down and total arrest, even bounce, all under gravitational force. These correspond very well to what you're asserting. If you are correct, those sims are also correct. Why are these correct and not the ones that correspond to what Dr. Benson asserts? Is it merely random happenstance and all the sims are worthless, except twice a day - like a broken clock?

Just curious.

As both parts A and C have identical structure and A is bigger than C (mass of A bigger than mass of C), at contact (C dropped on A) to produce a crush, both parts suffer identical damages absorbing energy. These damages affect the structure and as C is smaller than A, C is destroyed first or just ends up stuck on A ... or bounces.

Heiwa wrote:As both parts A and C have identical structure and A is bigger than C (mass of A bigger than mass of C), at contact (C dropped on A) to produce a crush...

Yes...

...both parts suffer identical damages absorbing energy. These damages affect the structure and as C is smaller than A, C is destroyed first or just ends up stuck on A ... or bounces.

The axiom. Why do some of the simulations correspond to this assumption, notably those without gravity, but the vast majority over a broad spectrum of material and connection properties do not? What am I doing wrong?

I suppose all of this happens with 1.5 seconds of collapse initiation,although I would like some timings! Thereinafter the collapse is closer to "pure" crush down. In any case, B&L indicate the possiblity of some early crush-up and so even having two sections of exterior wall ripped out is only a quite modest portion of zone C.

There is no way to justify the use of the upper block mass in the 1-D BV Lagrangian without a rigid interconnecting structure.

In the 1-D model the entire mass of the upper block minus some shedding is treated as a point mass at the collapse front.

So how is the KE in the higher floors of the upper block transmitted to the collapse front? Through the intact upper structure.

You must justify the use of the upper block mass term in the BV Lagrangian in the absence of a unified upper block structure. Until this is explained there is no way the BV formulation is consistent with with an upper block falling to pieces very early in the fall.


In terms of general energy considerations it would have been much more interesting to compare how the lower open office space could be expected to resist a building "avalanche" in the "chute" (the weak, vulnerable space between the perimeter caging and the core).

Many people have tried to explain that the true energy imbalance leading to progressive failure are how perimeter sheets can fall inside the the lower perimeter caging and "shear" floor connections.

This makes sense to me in that floor connections along the perimeter most probably cannot compete against a perimeter sheet "hammer" acting against them.

But now we see the process happening in reverse: The lower perimeter sheet stripping the upper block perimeter of it's flooring.

A chute avalanche is still quite possible but upper perimeter is being stripped away and kicked outside the footprint.

There is most probably a fatal imbalance of energy within the chute but there is no way a person can justify upper block mass being used in the 1-D BV lagrangian as it is.


OWE may wonder how the BV 1- D has some match to the actual fall time. I think it is because a wide range of approaches probably yield similar solutions and fall times. It does not mean the BV assumptions are justified by the results.

I suspect that efforts to justify an intact upper block stem from a desire to cling to the 1-D formulation and the BV Lagrangian in it's present form.

I would guess that if you totally reformulated a 1_D Lagrangian based on building debris vs intact flooring within the chute (a 1_D "chute progression"), you'd get similar results.

Lagrangian Mechanics Made Simple
http://www.worldforge.org/project/newsletters/May2002/LMMS_index

The B&V crush-down equation is an ODE involving position, derivatives thereof, first and second, and force. There are no terms derived from energy. For such an approach, see Keith Seffen's paper on crush-down.

Major_Tom --- B&V have four simplifying assumptions which lead to the crush-down ODE. These assumptions are reasonable for WTC 1 but not, by video timing, for WTC 2 after a few seconds. In the case of WTC 2 it is clear from the ABC video of the collpase proceeding down to the Mariott rooftop level that the collapse was proceeding much too slowly; the inference is that the top section broke apart and fell off rather early on.

But as BLGB indicates, this could not have happened to WTC 1 or the timing would be off.

Now there is an abundance of excess power available in my crush-down computer program, monotonically increasing amounts of it. Some might go into mushing up the upper portion. I don't care so long as most of the top portion remains on top of the crushed zone B, most of the way down. None of this violates the B&V ODE which uses homogeneity as one of the simplifying assumptions.

The theory, based on the four assumptions, leads to the "little early crush-up" theorem. Indeed, for WTC 1, we observe little early crush-up.

David B. Benson wrote:Major_Tom --- B&V have four simplifying assumptions which lead to the crush-down ODE.

I'm glad you go on to explain further. I think you could re-read his post with either 'BV' or 'Lagrangian' omitted, the point would be the same and it would be the one he was trying to make. From your perspective, I can only imagine that the endless insistence on considering the fate of the upper block has grown tiresome. I hope, in this post, to give you some sense of why it keeps coming up.

These assumptions are reasonable for WTC 1 but not, by video timing, for WTC 2 after a few seconds. In the case of WTC 2 it is clear from the ABC video of the collpase proceeding down to the Mariott rooftop level that the collapse was proceeding much too slowly; the inference is that the top section broke apart and fell off rather early on.

I see a lot of the top section of WTC2 falling off. Very clearly, no question.

But as BLGB indicates, this could not have happened to WTC 1 or the timing would be off.

How much time are you talking about?

Here's the problem. I see the very top section of WTC1 falling off, too. Not as clearly, not as surely, but multiple angles show the antenna mast diving over like a second hand on a clock. That doesn't mean most of the mass is off the footprint, but it does mean it wasn't a smooth ride. If the block was anything close to intact, it fell off as WTC2 did. Otherwise, it was rubble, and that would permit much of the mass to remain inside the perimeter. Of one thing I'm fairly certain after examining the spire, whatever passed through that sieve did so in little pieces.

'Bageling' as you've put it in the past.

Simpler for me as a lay person to conclude:

- BZ was a statement of best case -> no survival to show how collapse is expected
- 1D, homogenous model is heavy enough for me, rejoice that it gives good agreement
- real, 3D heterogenous system far from equilibrium while undergoing catastrophic phase transition is, in theory, nothing like the above
- real system, in practice, not that far off in displacement-time but differing significantly in qualitative features

In some respects, ignorance is bliss because all these things can coexist peacefully. Natural curiousity arises, though. Isn't it interesting that rubble can produce the same collapse time? It doesn't surprise or bother me.

Now there is an abundance of excess power available in my crush-down computer program, monotonically increasing amounts of it. Some might go into mushing up the upper portion. I don't care so long as most of the top portion remains on top of the crushed zone B, most of the way down.

It obviously doesn't bother you, either.

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

The visual evidence does not support a rigid body past mid-tower, if that's OK with the theory that's OK by me, though d'Alembert's principle applies to rigid bodies. I'm not going to question its application by someone with this publication list. But I will raise my hand each and every time if the simplified model demands I ignore the evidence I see directly to resolve a discrepancy between the two.

The theory, based on the four assumptions, leads to the "little early crush-up" theorem. Indeed, for WTC 1, we observe little early crush-up.

But only because that's not available to be observed directly in that time period. The same can be said of crush down. After all the time looking, I can't say I've seen early crush down, either. The mix can only be inferred from theory and other visuals, with solid visuals trumping theory.

If the choice is rubble inside OR rigid body on top, it's rubble for me. Is this a matter of 'you call it rigid, I call it rubble'?

OneWhiteEye ---- At the right scale it is rigid; contained in perimeter walls, mostly, most of the way down. So I don't object to using d'Alembert's principle; but it is interesting that Keith Seffen, using an energy approach, while obtaining the same functional form, has one of the fixed parameters to be 1/2 in comparison the B&V's 1.

By use of the seismograph record, the collapse took about 15 seconds to complete, both crush-down and crush-up, if any. 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.

But by around that point we know that it fell apart because AFAIK very few of the exterior wall sections or individual column members were found "inside the footprint". Instead these are heaped just outside the footprint (and, of course, further away).

The theory, based on the four assumptions, leads to the "little early crush-up" theorem. Indeed, for WTC 1, we observe little early crush-up.

Who is we? I thought you don't watch videos. Wouldn't you want to leave that statement to be made by those that do? What info do you cite which proves this? May I look at it to see if the analysis of what we should see early on is correct?



Thanks for the lesson on the Lagrangian. Does the mathematical term used in either case involve mass? How is the mass applied to the lower "block" (1-D "stick")? Could you please explain the term in whichever equations you choose (BV or Seffren) which describes the accruing mass of the upper block?

Since it is only 1-D it should be very easy to show on the one dimensional line where the upper block mass is and how it is treated.

Even before you answer I will guess that it is treated mathematically equivalent to a point mass located directly above and in contact with what is below. The entire mass of the upper block, minus shedding, at any moment in time, is treated mathematically equivalent to a concentrated point mass.

That is the point.

Major_Tom --- I watch what you post and I've seen those stills before (with betterr resolution). I think you are doing very well at PI. I know quite a bit about the mass distribution in WTC 1 and the two sections you state come from the upper portion are only a small part. B&V's ODE is good enough for WTC 1.

That equation, I forgot to mention, describes the location, z, of the crushing front (and time derivatives thereof). In that equation m(z) is the mass at and above location z. I don't understand the point you seem to be attempting to make, sorry.

David B. Benson wrote:OneWhiteEye ---- At the right scale it is rigid; contained in perimeter walls, mostly, most of the way down. So I don't object to using d'Alembert's principle; but it is interesting that Keith Seffen, using an energy approach, while obtaining the same functional form, has one of the fixed parameters to be 1/2 in comparison the B&V's 1.

This is a fascinating difference you'd mentioned once at physorg. I must go back and compare the two more closely.

By use of the seismograph record, the collapse took about 15 seconds to complete, both crush-down and crush-up, if any. 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.

Assume the timing good then, unless forced to revisit it.

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.

Bolding mine. How much of a tweak on the resistive force is required if, say, half of the mass of the original block is gone by the 50th floor but little or nothing lost thereafter?

OneWhiteEye --- If the crushing front is at floor 50, zone B consists of 80% of stories 50--97 and 100% of stories 98--111 (for simplicity) for zone C. Assuming all mass the same, the driver is 38.4+14 = 52.4 mass units. Dropping 7 leaves but 45.4. So the resistive force has to decrease by to about 45.4/52.4 = 0.866 of prior value. Implausible.

However, if zone C continues to bleed mass as observed in the first few seconds, then the resistance force calculation is fine. Ha! I didn't realize that before just now.
Edited to add: But it isn't quite right. I'll have to think this through more carefully and post on it later.
Edited to add: Close enough, provided zone C doesn't disappear completely before near the end of crush-down.

Ok, some more PI work is needed for the two sections of zone C. Do those wounds continue to bleed? We know that happened for the sector 2 pieces from stories 92--97, for quite some time maybe?

Major_Tom wrote:OWE may wonder how the BV 1- D has some match to the actual fall time. I think it is because a wide range of approaches probably yield similar solutions and fall times. It does not mean the BV assumptions are justified by the results.

That puts it pretty well.

A chute avalanche is still quite possible but upper perimeter is being stripped away and kicked outside the footprint.

Yes.

David B. Benson wrote:OneWhiteEye --- If the crushing front is at floor 50, zone B consists of 80% of stories 50--97 and 100% of stories 98--111 (for simplicity) for zone C. Assuming all mass the same, the driver is 38.4+14 = 52.4 mass units. Dropping 7 leaves but 45.4. So the resistive force has to decrease by to about 45.4/52.4 = 0.866 of prior value. Implausible.

OK, thanks. A reduction of 13.4% doesn't seem like a lot to me - like the difference between sharp and dull knives.

We've discussed things before that could speed it up. Some items:

1) "...the resistive force determined from the first few seconds..." is based on early displacement? If so, and if energy were actually expended in early zone C destruction, wouldn't this then lead to an over estimate of resistive force if one also assumes only crush down? Maybe it doesn't come out of KE as you calculate excess power available early, but it might.

2) If 75% of the perimeter is only peeling away below a certain point, and the remainder is being shoved aside by overhanging block (see WTC2), it's not really participating as the 1D model dictates. Small mass loss but large capacity loss.

3) The bigger the spire, the more is bypassed. Same as #2.

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

However, if zone A continues to bleed mass as observed in the first few seconds, then the resistance force calculation is fine. Ha! I didn't realize that before just now.
Edited to add: But it isn't quite right. I'll have to think this through more carefully and post on it later.
Edited to add: Close enough, provided zone C doesn't disappear completely before near the end of crush-down.

I don't know about zone A loss in the last half, it looks fairly well contained. Things are happening inside well ahead of perimeter peeling on at least three sides. I'm making (wildass) guesses about mass loss based solely on the tip angle and possible top location, not on materials being ejected.

I encourage playing with the numbers to see what is possible and reasonable.

PS In a few days I want to have some more simulations set up. Just to stay on topic.

OneWhiteEye wrote:

Heiwa wrote:As both parts A and C have identical structure and A is bigger than C (mass of A bigger than mass of C), at contact (C dropped on A) to produce a crush...

Yes...

...both parts suffer identical damages absorbing energy. These damages affect the structure and as C is smaller than A, C is destroyed first or just ends up stuck on A ... or bounces.

The axiom. Why do some of the simulations correspond to this assumption, notably those without gravity, but the vast majority over a broad spectrum of material and connection properties do not? What am I doing wrong?

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

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

1. Chose drop height so that only deformation of elements (columns) in A and C take place. Result should be a bounce. What was the drop height? It must be just a fraction of the floor/floor height.

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. C (without bottom columns) will then continue to drop and I assume bounce on A (without top columns) as in 1. Here the time to damage the columns must be considered

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

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.

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.

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

OneWhiteEye wrote:1) "...the resistive force determined from the first few seconds..." is based on early displacement?

Yes, first 3.75+ seconds, long past crushing all of sector 2.

If so, and if energy were actually expended in early zone C destruction, wouldn't this then lead to an over estimate of resistive force if one also assumes only crush down?

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.

2) If 75% of the perimeter is only peeling away below a certain point, and the remainder is being shoved aside by overhanging block (see WTC2), it's not really participating as the 1D model dictates.

B&V used 20% mass loss from zone A. The rest becomes the crushing front. Not an issue. Anyway, the ODE is highly insenstive to this matter as it just changes the constant on the resistive force.

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.

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 don't know about zone A loss in the last half,

I meant zone C, the upper portion. I'm going to go back an edit in this correction.