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Old 17th April 2016, 01:11 PM   #1
tfk
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Another Crush down / Crush up thread

I'm starting this to discuss with Oz (or anyone else) the assertion that Bazant's asymmetric crush down is false. I am quite sure that it is true (straight out of the math), and the following is my attempt to put it into simple to understand language, without the math.

There are only 2 factors that need to be true in order for Bazant’s “asymmetric crush down” approximation to be true. Both are, IMO, irrefutable.

I’ll address “asymmetric crush down” in this post, and save "Crush up" for a later one.

The two factors:
  1. The principle determinant of the amount of damage occuring in any two “similarly constructed assemblies” that collide is the relative speed of impact, with the damage proportional to the speed squared (the work done in causing the damage is proportional to the kinetic energy of impact). 

  2. Once some structure has been ripped from its supports, it begins to fall immediately.

That’s it. If you’re going to “prove Bazant wrong”, then you’ve got to prove that both of these assertions are wrong.

Here’s how it ties together.
__

First, a word on “conservation of momentum”.

This principle has been badly abused in several “collapse analyses” that I’ve seen.
Momentum is NOT conserved during the collapse. A moment’s thought will prove that to be true: The upper block starts out at a small velocity, and (relatively) small mass. Over time, the mass grows & the velocity grows. The momentum does NOT stay constant.

Momentum only stays constant as long as there are no other forces inputting energy into the system. In any vertical collapse, gravity is constantly inputting potential energy (mg ∆h) into the system (where ∆h = the drop from instant to instant).

Several analyses have asserted that momentum is conserved over the duration of the impact. If the collision between floors were instantaneous, then this would be true, because there would be zero time for any drop.

But the collisions are NOT instantaneous.
The collisions are spread over significant distance & significant times. During these intervals, gravity is adding energy (& momentum) to the falling mass.

A combination of factors made the collision virtually continuous, not discrete events.
The two primary factors are tilt of the upper block & the build-up of a large irregular mass of debris (roughly “bullet shaped”) below the upper block. The bullet shape results from the debris near the external walls of the building being preferentially ejected compared to the debris towards the center of the building.

This needs to be understood:
The collision at each floor would require a decrease in velocity (aka, a deceleration) ONLY IF the collision between floors were instantaneous.

For a non-instantaneous vertical collision, the energy added to the system by gravity can produce velocities during the collision that are less than, equal to, or greater than the velocity prior to the collision. Therefore, while the acceleration during the collision will always be less than it was before the collision, the magnitude of the acceleration can be positive, zero or negative.

It is NOT necessary that the velocity decrease (i.e., that there be a deceleration) during a non-instantaneous vertical collision.

Momentum is NOT conserved (locally) during this typed of collision.

[For the physics purists, and the merely curious, momentum is ALWAYS conserved. Always. In this case, if you include the entire system - the building & the planet earth - you can resolve this apparent contradiction.)
__

Back to Crush Down
First, I’ll use the “one floor collapse” idealization.

The figure below show an IDEALIZED version of an upper block after it has crushed down 5 stories & is about to crush down the 6th floor.




To the right, I’ve shown the impact velocity between each floor (n) & the floor beneath it (n+1).
Then the impact energy (in arbitrary units) of each collision.
Then the relative velocity between the Upper Block & the 1st crushed floor during each of the lower collisions.
Finally the energy of the collision between the Upper Block & the first crushed floor during each of the lower collisions.


For the calculations, I’ve assumed a starting mass of 12 floors, and each collision adds (1-EF)m mass to the descending mass (where EF = ejected fraction of material = 0.2). Lamda is Bazant’s “stretch”, considered a compaction factor. The crushed floors end up being about 0.15h thick, where h = 12’, the height of one floor. I've used the 0.65G measured acceleration for calculating velocities & energies.

Note that the "Impact Energy" column is the kinetic energy of the Upper Block plus Debris Layer at the moment of each collision (in arbitrary units: (= (m*v^2)/1000.) This is NOT the energy dissipated in each impact. This is the energy that the lower block would have to absorb if it were to be able to halt the collapse.

The energy consumed / dissipated in each impact is far lower than the kinetic energy of the Upper Block plus Debris Layers. At a minimum, it need only be the energy required to break 1/2 of the existent connections between the trusses & the truss support brackets. That’s all. A tiny amount.

In reality, a lot more energy goes into crushing & fracturing components, hurling things around, generating sound & wind, etc. The calculation of all these energy sinks is very complex, subject to all kinds of arguments. This is why it was very smart of Bazant to do his limiting case, to avoid these arguments.

But the energy absorbed per floor is limited to only that amount of crushing that can be done up to the time the truss bracket connections give way. After that, the floors are falling, and very little crushing takes place. It is necessary to constrain the debris both above & below in order to get any effective crushing to occur.

As stated above, the 2 columns at the right are the relative velocity & impact energies between the Upper Block & the first floor compacted debris, during all of the subsequent collisions.

It is easy to see that the initial collision between the upper block & the first floor is a low-velocity, low energy collision, producing some damage to the Upper Block.

After that collision, the crushed mass of the first floor is moving downwards WITH the upper block.

This is a re-telling of the fact that the Upper Block does NOT impact the Lower Block. The lowest portion of the crushed debris layer impacts the uppermost floor of the Lower Block.

During subsequent collisions, the relative velocity between the upper block & the uppermost layer of the compacted debris is (approximately) zero. Approximately zero relative velocity means approximately zero damage inflicted between the two.

The impact velocity between the bottom of the debris layer and the about-to-be-crushed floor is high. It gets higher & higher as the upper block plus debris layer accelerates. This high relative velocity produces a massive amount of destruction between the bottom layer of debris and the top layer of the bottom block.
__

The second factor mentioned above is that, as soon as the supports for any subsystem (up to the entire floor) are ripped apart, those components begin to fall. Immediately. These components do NOT hang stationary in the air.

This is exactly the stupidity of Gage’s new fantasy of “the crushed & destroyed upper block” as shown here:

www.youtube.com/watch?v=FvuKUmK9eB0&t=2m07s

Gage draws some meaningless line at the crush floor, and then leaves the line stationary in the air. Even though Gage doesn't say it, that stationary line depicts floors getting crushed ... but still hanging motionless in the air.

He can only get away with this stupidity because he’s showing a video that hides the descent of the impact layer behind the cloud of debris. This allows him to claim, falsely, that the upper block is being destroyed by the collapse.

If he were to show a video from the NW corner, which gives a view thru the debris clouds, you’d see that the collapse front does NOT hang stationary in space, but begins to descend immediately, at some acceleration less than G.

So, Oz, this is my description of why Bazant’s “asymmetric crush down” is an accurate approximation to the actual events. It ain’t perfect. The upper block does not descend like an unblemished flower. These are violent collisions. But this model is 90 - 95% correct (for the first 10 stories or so).

Further, from the energy calculations, you can see that this only has to hold true for a couple of floors of descent in order to guarantee collapse to the ground.

This is my description of why the alternative theory (“equal crush up & crush down”) is completely wrong.

Please tell me what you disagree with.

Last edited by tfk; 17th April 2016 at 01:17 PM.
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Old 17th April 2016, 01:17 PM   #2
Dave Rogers
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Speaking a little out of turn here, but it's not the analysis but the basic assumption that the top block crushes the bottom block that I would take issue with. The actual collapse appears to have involve the floors collapsing due to impact of falling rubble, the support columns then losing lateral bracing and becoming too slender to support the upper structure, and the upper structure being somewhat retarded by their remaining structural strength. The result is that the collapse is asymmetrically biased in favour of destruction of the lower block, but not by the mechanism - and hence not described by the mathematical model - of Bazant et al.

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Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right?

Tony Szamboti: That is right
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Old 17th April 2016, 05:53 PM   #3
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As a proponent of the necessary deceleration during descent, I think I need to make a clarification.

My proposed scenario where deceleration is necessary is the collapse of the floors that occurred ahead of the huge dust cloud. In other words, it applies to the part of the collapse causing the ejections seen on the wall here:



I'll try to be very precise with what I'm asserting:

Let's call v1 the vertical speed of the falling piece of rigid material that first touches a floor assembly, right at the instant before it touches it. By "rigid material" I mean the steel from the columns, girders, beams, trusses and floor pans and the concrete of the floors.

Let's call v2 the vertical speed of the floor assembly's centre of mass once it is detached and falls with the rest of the debris.

Assuming that the collision between the piece and the floor assembly is overwhelmingly of a plastic nature, I assert that v2 < v1. In other words, the collision will result in a loss of vertical speed, a.k.a. deceleration.


Originally Posted by tfk View Post
The collision at each floor would require a decrease in velocity (aka, a deceleration) ONLY IF the collision between floors were instantaneous.
I would refine this as follows:

If the apparent weight of a descending object exceeds m·g at any instant, then it necessarily experiments net deceleration at that instant.

And for the apparent weight to not exceed m·g during a collision, the cushioning effect must be big, so the materials must be reeeeeeally soft and easy to compress.

Steel and concrete aren't, therefore v2 < v1.

Do you agree?
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Old 17th April 2016, 06:23 PM   #4
Norman Alexander
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You do know there is this thing called "air" between the floors? And it needs to get out of the way when one falls on another?
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Old 17th April 2016, 07:12 PM   #5
pgimeno
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Originally Posted by Norman Alexander View Post
You do know there is this thing called "air" between the floors? And it needs to get out of the way when one falls on another?
If you're talking to me, yes, I'm well aware of its existence, and that is completely irrelevant to my point, because air pressure is not what is assumed to make the floor connections fail (otherwise it would be be significant). So what's your point?
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Old 17th April 2016, 08:03 PM   #6
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Originally Posted by pgimeno View Post
As a proponent of the necessary deceleration during descent, I think I need to make a clarification.

My proposed scenario where deceleration is necessary is the collapse of the floors that occurred ahead of the huge dust cloud. In other words, it applies to the part of the collapse causing the ejections seen on the wall here:

http://femr2.ucoz.com/_ph/6/2/139901890.gif

I'll try to be very precise with what I'm asserting:

Let's call v1 the vertical speed of the falling piece of rigid material that first touches a floor assembly, right at the instant before it touches it. By "rigid material" I mean the steel from the columns, girders, beams, trusses and floor pans and the concrete of the floors.

Let's call v2 the vertical speed of the floor assembly's centre of mass once it is detached and falls with the rest of the debris.

Assuming that the collision between the piece and the floor assembly is overwhelmingly of a plastic nature, I assert that v2 < v1. In other words, the collision will result in a loss of vertical speed, a.k.a. deceleration.



I would refine this as follows:

If the apparent weight of a descending object exceeds m·g at any instant, then it necessarily experiments net deceleration at that instant.

And for the apparent weight to not exceed m·g during a collision, the cushioning effect must be big, so the materials must be reeeeeeally soft and easy to compress.

Steel and concrete aren't, therefore v2 < v1.

Do you agree?
However the Collisions are not plastic in nature, rapid formation of fulcrums from compression forces induce rapid sheer, pressure is exerted by collisions on the side of the columns by the falling mass. Collisions in the retained mass induce fractures in the columns themselves as collisions occurs not only between the building and the falling mass but also by column and floor segments within the mass.

The Columns do not have to impact end to end for crush down crush up, the mass and movements and forces will occur with column misalignments as well as long as the two masses interact, destruction of any structure will be governed by collisions of mass with mass. So it is not as simple as ROOSD, or Crush Down, Crush Up, there is also side crush and peal because energy is never solely Vector.

I know this most likely disagrees with My Friends Frank, and DBB. And with Oz, who I deeply respect but experiments real experiments have shown me that the columns received impacts from the sides significantly strong enough to shatter welds, on Columns.
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Old 18th April 2016, 02:37 AM   #7
pgimeno
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Originally Posted by Crazy Chainsaw View Post
However the Collisions are not plastic in nature, rapid formation of fulcrums from compression forces induce rapid sheer, pressure is exerted by collisions on the side of the columns by the falling mass. Collisions in the retained mass induce fractures in the columns themselves as collisions occurs not only between the building and the falling mass but also by column and floor segments within the mass.
Nothing in your message contradicts the fact that the collisions were overwhelmingly plastic (or to use another word, inelastic).

But it doesn't matter. Thinking more about it, it suffices that the collisions were not overwhelmingly elastic, to have v2 < v1.

Here's a rule-of-thumb mind experiment. Think about what'd happen if you were sitting on the falling piece of debris (imagine it's a complete floor and you're sitting on it). If you picture your butt hurting when it collides (that would indicate that the apparent weight >> m·g), then there's deceleration.
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Old 18th April 2016, 02:43 AM   #8
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Hi pg,

Sorry for the length...

Nope. Everything depends on the duration of the collision. This is the key difference between a vertical collision & a horizontal one.

In a horizontal collision, what you're saying is exactly correct, as long as there are no forces accelerating either block horizontally.

In a vertical collision, gravity is constantly adding energy to the system.

Let's run a thought experiment.
This is not precisely, numerically rigorous, but I think that it'll get the idea across. And the rigorous numbers will be very close.

Imagine a large mass falling at G.
It will plastically impact a smaller mass with an near-instantaneous collision, such that, after the collision, the velocity (by the usual v2 = v1*(m1/(m1+m2)) the speed of the assembled 2 masses is 10 ft/sec slower than prior to the collision.

[Note:
"plastic" & "instantaneous" are incompatible. But we can use "near instantaneous".

Also, we assume that the supports for the lower block absorb little energy when they fail.]

Great. Near instantaneous collision. Velocity the instant after the collision MUST be slower than the one mass's velocity the instant before the collision. There must be deceleration.

But now we modify the lower block. We put a bunch of air pockets into the stationary mass (keeping the total mass the same as before), such that the collision takes 1 full second from start to finish.

At G, gravity will add 32.2 ft/sec of velocity to the upper block for each second's worth of free fall. As before, once the collision is complete, the added mass of the lower block will have taken 10 ft/sec out of the speed of the combined block, but the energy added by gravity will have added 32.2 ft/sec over this same interval.

The net result is that, over the course of the collision, the velocity increases by 22.2 ft/sec.

Since the velocity increases over this time interval, the acceleration is positive, averaging 22.2 ft/sec2.

The acceleration has decreased (from 32.2 to 22.2 ft/sec2), but it hasn't gone negative.
__

Now let’s look at your take on it…

Originally Posted by pgimeno View Post
As a proponent of the necessary deceleration during descent, I think I need to make a clarification.

My proposed scenario where deceleration is necessary is the collapse of the floors that occurred ahead of the huge dust cloud. In other words, it applies to the part of the collapse causing the ejections seen on the wall here:

http://femr2.ucoz.com/_ph/6/2/139901890.gif

I'll try to be very precise with what I'm asserting:

Let's call v1 the vertical speed of the falling piece of rigid material that first touches a floor assembly, right at the instant before it touches it. By "rigid material" I mean the steel from the columns, girders, beams, trusses and floor pans and the concrete of the floors.

Let's call v2 the vertical speed of the floor assembly's centre of mass once it is detached and falls with the rest of the debris.
First, those ejections look like air pressure relief, not mechanical collisions.

Next, we’ve got a complication here. Because it took some time (∆t) for the floor to accelerate to v2, then v1 would have accelerated on its own by v1 + a ∆t.

Originally Posted by pgimeno View Post
Assuming that the collision between the piece and the floor assembly is overwhelmingly of a plastic nature, I assert that v2 < v1. In other words, the collision will result in a loss of vertical speed, a.k.a. deceleration.
The problem is that you are thinking of a system in which momentum is conserved over arbitrary intervals of time, such as something rolling on a table. For those cases, momentum is conserved over intervals in which there are collisions, and intervals in which there are no collisions.

A falling object is not the same. Momentum is not conserved during its fall. Momentum is constantly increasing. Without collision, for any distance, h, the object falls, then due to conversion of potential energy to kinetic, the velocity increases by (a h)^0.5, and the momentum by m (a h)^0.5, where a = the downward acceleration.

For any collision between a falling object & a stationary object which takes an interval of time (∆t), or some interval of distance (∆h), energy (speed) is added to the falling mass as it falls.

Originally Posted by pgimeno View Post
I would refine this as follows:

If the apparent weight of a descending object exceeds m·g at any instant, then it necessarily experiments net deceleration at that instant.
And right here is an error that Tony Sz always insists on making, which gives him the wrong answer.

IF the falling objects “apparent weight” = 0, then it’s descending at an acceleration of G.
IF the falling objects “apparent weight” = mg, then it’s descending at an acceleration of 0.
IF the falling objects “apparent weight” > mg, then it’s descending at an acceleration of less than zero, i.e., decelerating.

Yes.

But it is a complete fallacy that the upper block has to exert a force >mg in order to crush down the lower structure.

Allowing for Factor of Safety, the upper block WOULD have to exert a force of about 2 mg … IF the lower structure were “as built” & the forces were directed properly thru the appropriate load paths.

But due to the damage to the building, and to the loads being applied to components that were never meant to carry them (e.g., the concrete floors), the descending weight need apply forces that are much less than mg in order to get these weakened, non-load carrying structures to fail.

Therefore, since the “apparent weight” of the falling block can be less than mg, the acceleration seen in that block will be 0<a<G. In other words, the acceleration can (& in the case of the towers, will) be greater than zero, and the descending block can be constantly increasing in speed.

Originally Posted by pgimeno View Post
And for the apparent weight to not exceed m·g during a collision, the cushioning effect must be big, so the materials must be reeeeeeally soft and easy to compress.
It’s not a cushioning effect.
mg is the weight of the upper block.

The right way to look at it is NOT “∑F = mg - Fr = m a”, where Fr is the resisting force. This makes it appear the F is the dependent variable. It is not.
“a” is the dependent variable. It adjusts to Fr (since m is determined by the falling mass). So view it as a = (mg - Fr)/m.

Now you can see that the net acceleration of the CG of the falling body is completely determined by Fr.

IF Fr < mg, then a stays positive, and there is no deceleration.
IF Fr = mg during the collision, the a = 0 over this interval & the velocity stays constant.
IF Fr > mg, then the acceleration is negative & the velocity must decrease.

The key, again, is that, in its highly damaged state with loads applied to non-load carrying members, the resisting force Fr will be less than mg.

After the supports break away, then the inertial factors, including the derationof the collision (described in the first part of this post) come into play.

[quote=pgimeno;11234999]
Steel and concrete aren't, therefore v2 < v1.
[/QUOTE

You don’t ant to consider the bulk modulus of steel or concrete. This is the very, very low “compliance” you’d get out of solid hunks of those two materials.

You want to consider the compliance of the assembly, which will be orders of magnitude larger.

So, yes, compared to the weight of the upper block, the structure of any floor, when the loads are not applied thru the columns, IS very compliant. aka, “soft & easy to compress”.

Make sense?

Last edited by tfk; 18th April 2016 at 03:07 AM.
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Old 18th April 2016, 04:46 AM   #9
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Originally Posted by tfk View Post
I'm starting this to discuss with Oz (or anyone else) the assertion that Bazant's asymmetric crush down is false.
I don't see what there is to discuss with me on this issue.

My position unchanged for some years with two straight forward conclusions:

1) I agree that Bazant's "crush down - crush up" hypothesis is a good starting point for Bazant's goal of developing a generic model for progressive collapse. And I have posted numerous explanations of it together with expressions of my support.

2) I do not accept that it is a valid model for WTC 9/11 Twin Towers collapse progression stage. For simple reasons that any engineering or applied physics competent person should understand.

However on another thread tfk is challenging me with a range of discourteous or false claims and the only valid technical claim is a strawman.

A strawman false generalisation plus lie by innuendo to be more pedantic.

He is asserting that I disagree with Bazant's "crush down - crush up" - which conflates the two aspects of my true position. I agree with crush down <> crush up within its limits of valid application. I disagree that it is valid for WTC. (And for those specialists in "bet both ways" mental gymnastics - I have never seen a valid argument that cd<>cu can be an adequate approximation in the WTC Twins collapses which were by a totally different mechanism to that subsumed in Bazant's cd<>cu modelling.)

I agree with Bazant's cd<>cu for those cases where is is valid. I disagree that it is valid for WTC. And the proof is accessible to any person of High School level physics or better reasoning skills. I don't see any reason to complicate debates nor do I subscribe to notions that only engineers can understand matters of applied physics.

Originally Posted by tfk View Post
I am quite sure that it is true (straight out of the math), and the following is my attempt to put it into simple to understand language, without the math.
tfk's version of "simple to understand language" is different to mine.
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Old 18th April 2016, 07:06 AM   #10
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I believe the simple reason that Bazant's model shows cd/cu is because it assumes the same destruction mechanism -- plastic column buckling -- as the energy sink for both the top and the bottom blocks. You could make Bazant's model more realistic by approximating the energy absorbed by more realistic failure modes, but if you use that same function for the destruction of both the top and the bottom block, you would still get cd/cu. That's because the reaction force of the lower block is acting against the weight and inertia of both the top block and the debris layer, but only up to the point that the lower structure fails. At that point, the reaction force acting on just the top block must be less than what it took to fail the bottom block (the difference being that part of the reaction force acting on the debris layer), and therefore it's not enough to destroy the top block by the same mechanism.

If we don't see cd/cu in the WTC towers, then that must mean that the upper block was being destroyed in ways that required less energy than what was happening in the lower block.

Last edited by WilliamSeger; 18th April 2016 at 07:08 AM.
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Old 18th April 2016, 08:29 AM   #11
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Originally Posted by WilliamSeger View Post
I believe the simple reason that Bazant's model shows cd/cu is because it assumes the same destruction mechanism -- plastic column buckling -- as the energy sink for both the top and the bottom blocks. You could make Bazant's model more realistic by approximating the energy absorbed by more realistic failure modes, but if you use that same function for the destruction of both the top and the bottom block, you would still get cd/cu. That's because the reaction force of the lower block is acting against the weight and inertia of both the top block and the debris layer, but only up to the point that the lower structure fails. At that point, the reaction force acting on just the top block must be less than what it took to fail the bottom block (the difference being that part of the reaction force acting on the debris layer), and therefore it's not enough to destroy the top block by the same mechanism.
Probably true for an idealised model which is homogeneous across the floor plan AKA a "1D Approximation" as assumed by Bazant for the B&Z "Limit Case" and carried forward into his crush down<>crush up hypothesis. Could also be the idealised solution for a non-homogeneous model BUT only if it got started by Bazant's assumed initiation mechanism and that didn't happen for the WTC Twins. I would doubt that either could be guaranteed in practice because of the pragmatics of a real initiation process and the requirement for uniformity in the progression. Dunno that I could "prove" it sufficient to put money on it - I'd need to give it more thought.
Originally Posted by WilliamSeger View Post
If we don't see cd/cu in the WTC towers, then that must mean that the upper block was being destroyed in ways that required less energy than what was happening in the lower block.
Actually the real reason was simpler in the case of each of the actual Twin Towers collapses on 9/11. The transition from the initiation stage cascade failure to the "Three Mechanisms" of progression stage ensured concurrent dismember down <> dismember up. i.e. at the very start of progression - in the first few floors of falling. So the Top Block did not survive to be subject to crush up AFTER crush down. Avoiding the term "crush" because it was floor joist shearing dues to the impact of still intact perimeter column ends with the office space floors. Not the buckling failure of overloaded columns which is subsumed in the normal use of "crush" terminology.

Last edited by ozeco41; 18th April 2016 at 08:37 AM.
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Old 18th April 2016, 09:00 AM   #12
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Originally Posted by ozeco41 View Post
Probably true for an idealised model which is homogeneous across the floor plan AKA a "1D Approximation" as assumed by Bazant for the B&Z "Limit Case" and carried forward into his crush down<>crush up hypothesis. Could also be the idealised solution for a non-homogeneous model BUT only if it got started by Bazant's assumed initiation mechanism and that didn't happen for the WTC Twins. I would doubt that either could be guaranteed in practice because of the pragmatics of a real initiation process and the requirement for uniformity in the progression. Dunno that I could "prove" it sufficient to put money on it - I'd need to give it more thought.
Originally Posted by WilliamSeger
If we don't see cd/cu in the WTC towers, then that must mean that the upper block was being destroyed in ways that required less energy than what was happening in the lower block.
Actually the real reason was simpler in the case of each of the actual Twin Towers collapses on 9/11. The transition from the initiation stage cascade failure to the "Three Mechanisms" of progression stage ensured concurrent dismember down <> dismember up. i.e. at the very start of progression - in the first few floors of falling. So the Top Block did not survive to be subject to crush up AFTER crush down. Avoiding the term "crush" because it was floor joist shearing dues to the impact of still intact perimeter column ends with the office space floors. Not the buckling failure of overloaded columns which is subsumed in the normal use of "crush" terminology.
I think you're mainly agreeing with what I said but going into the details of why any 1D theoretical model would have limitations -- no doubt about that -- and why the real-world destruction processes were different in the upper and lower blocks. All I'm suggesting is that, if cd/cu didn't happen, then they must have been rather different processes, (ETA) and the upper block processes required less energy.

Last edited by WilliamSeger; 18th April 2016 at 09:09 AM.
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Old 18th April 2016, 09:19 AM   #13
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Originally Posted by WilliamSeger View Post
I think you're mainly agreeing with what I said but going into the details of why any 1D theoretical model would have limitations -- no doubt about that -- and why the real-world destruction processes were different in the upper and lower blocks. All I'm suggesting is that, if cd/cu didn't happen, then they must have been rather different processes, (ETA) and the upper block processes required less energy.
Yes - we are in full agreement as far as I can see up to that last point where there is a slight - unimportant - difference. And I was just adding a bit more explanation about why cd/cu did not - could not - happen for the WTC Twins. PLUS the generic issue which probably gets lost.

cd/cu presumes an initiation mechanism that starts the "Limit Case" column crushing mechanism from B&Z. Didn't happen for WTC. More to the point it could not happen.

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Old 18th April 2016, 09:55 AM   #14
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Originally Posted by ozeco41 View Post
...
cd/cu presumes an initiation mechanism that starts the "Limit Case" column crushing mechanism from B&Z. Didn't happen for WTC. More to the point it could not happen.
Can you make this a little more explicit?
I think your point, while true, is not very relevant. B&Z's assumption can be substituted by one that is true, and (nearly) equivalent, and still support their conclusions.
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Old 18th April 2016, 10:52 AM   #15
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Originally Posted by ozeco41 View Post
cd/cu presumes an initiation mechanism that starts the "Limit Case" column crushing mechanism from B&Z. Didn't happen for WTC. More to the point it could not happen.
Well, as I understand it -- anyone correct me if I'm wrong -- but Bazant presumes plastic column buckling throughout, but only to get an energy absorption function for his differential equations. What I'm saying is that, whatever energy absorption function you put into that kind of model, if you use it for both the top and bottom block, you'll get cd/cu. Are we disagreeing yet?
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Old 18th April 2016, 11:29 AM   #16
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Originally Posted by ozeco41 View Post
cd/cu presumes an initiation mechanism that starts the "Limit Case" ...
The only initiation mechanism he assumes is that the top block descended one floor, and that most of its gravitational potential energy was converted to kinetic energy because little could have been absorbed by the hot columns that failed on that floor. (He calculated that cold columns could have only absorbed about 12% by plastic buckling.) That's really all he cares about to construct his energy arguments. Taking that to mean columns disappearing and the top falling straight down is a red herring.

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Old 18th April 2016, 12:40 PM   #17
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Thanks for the reply.

Originally Posted by tfk View Post
Hi pg,

Sorry for the length...
I should say the same. I've replied to most of your post, so my reply is quite long in turn.


Originally Posted by tfk View Post
Nope.
I'll address this specific part later. I've separated this sentence from the rest of the paragraph because I agree with the rest and I wanted to note the points of agreement:
Originally Posted by tfk View Post
Everything depends on the duration of the collision. This is the key difference between a vertical collision & a horizontal one.

In a horizontal collision, what you're saying is exactly correct, as long as there are no forces accelerating either block horizontally.

In a vertical collision, gravity is constantly adding energy to the system.

Let's run a thought experiment.
This is not precisely, numerically rigorous, but I think that it'll get the idea across. And the rigorous numbers will be very close.

Imagine a large mass falling at G.
It will plastically impact a smaller mass with an near-instantaneous collision, such that, after the collision, the velocity (by the usual v2 = v1*(m1/(m1+m2)) the speed of the assembled 2 masses is 10 ft/sec slower than prior to the collision.

[Note:
"plastic" & "instantaneous" are incompatible. But we can use "near instantaneous".

Also, we assume that the supports for the lower block absorb little energy when they fail.]

Great. Near instantaneous collision. Velocity the instant after the collision MUST be slower than the one mass's velocity the instant before the collision. There must be deceleration.

But now we modify the lower block. We put a bunch of air pockets into the stationary mass (keeping the total mass the same as before), such that the collision takes 1 full second from start to finish.

At G, gravity will add 32.2 ft/sec of velocity to the upper block for each second's worth of free fall. As before, once the collision is complete, the added mass of the lower block will have taken 10 ft/sec out of the speed of the combined block, but the energy added by gravity will have added 32.2 ft/sec over this same interval.

The net result is that, over the course of the collision, the velocity increases by 22.2 ft/sec.

Since the velocity increases over this time interval, the acceleration is positive, averaging 22.2 ft/sec2.

The acceleration has decreased (from 32.2 to 22.2 ft/sec2), but it hasn't gone negative.
All agreed, assuming the instant deceleration in the horizontal case is not greater than g at any time. If it's greater at any instant, the deceleration will exist at that instant. Average acceleration does not tell us whether there is instant deceleration at any point, like average velocity does not tell us if a car deserved a speeding ticket.


Originally Posted by tfk View Post
__

Now let’s look at your take on it…



First, those ejections look like air pressure relief, not mechanical collisions.
Of course. They are exactly what I expect to happen if the floors are pancaking behind the perimeter columns. They are described by FEMA as the floors pancaking. Even Bazant assumed that it would happen, when he describes the limitations of his model in the 2001 paper, and later in the 2002 paper.


Originally Posted by tfk View Post
Next, we’ve got a complication here. Because it took some time (∆t) for the floor to accelerate to v2, then v1 would have accelerated on its own by v1 + a ∆t.
Agreed.


Originally Posted by tfk View Post
The problem is that you are thinking of a system in which momentum is conserved over arbitrary intervals of time, such as something rolling on a table. For those cases, momentum is conserved over intervals in which there are collisions, and intervals in which there are no collisions.

A falling object is not the same. Momentum is not conserved during its fall. Momentum is constantly increasing. Without collision, for any distance, h, the object falls, then due to conversion of potential energy to kinetic, the velocity increases by (a h)^0.5, and the momentum by m (a h)^0.5, where a = the downward acceleration.

For any collision between a falling object & a stationary object which takes an interval of time (∆t), or some interval of distance (∆h), energy (speed) is added to the falling mass as it falls.
No, that's not even close to what I'm thinking. I agree with what you say. What I'm actually thinking is that ∆t must be necessarily low. Low enough to overwhelm the effect of gravity.

Let's rewind back to your example. You used 1 second collision time from start to finish. For comparison, a WTC floor that starts from zero initial vertical speed would take about 0.86 seconds to fall in free fall to reach the next floor. Actual impact times up to the point of detachment must be much smaller, even before beginning to consider the fact that the initial speed isn't zero. I think that setting an upper limit of 0.1 seconds for the floor to be detached upon impact of the falling debris is being extremely generous; I'd tend to think it's at least an order of magnitude less. Gravity has no time during that short interval to accelerate substantially the objects involved. The momentum increase due to gravity during that time is too small; so small, in fact, that we can assume as a good approximation that momentum is conserved.

Look at the picture again:



The gif lasts about 2 seconds; during that time, the amount of floors crushed appears to be at least 10. That's at most 0.2 seconds per floor; the detachment of the floor alone happens in a much shorter time.


Originally Posted by tfk View Post
And right here is an error that Tony Sz always insists on making, which gives him the wrong answer.

IF the falling objects “apparent weight” = 0, then it’s descending at an acceleration of G.
IF the falling objects “apparent weight” = mg, then it’s descending at an acceleration of 0.
IF the falling objects “apparent weight” > mg, then it’s descending at an acceleration of less than zero, i.e., decelerating.

Yes.

But it is a complete fallacy that the upper block has to exert a force >mg in order to crush down the lower structure.
I agree. I'm not falling into that. I used apparent weight (no quotes needed) very carefully. I'm talking about inertia, momentum conservation and impact forces exclusively, not about the forces involved in connection failure. See this post for a simplified model I made, where connection failure does not cause deceleration but momentum conservation does. The description of the model is here.


Originally Posted by tfk View Post
Therefore, since the “apparent weight” of the falling block can be less than mg, the acceleration seen in that block if that happens will be 0<a<G. In other words, the acceleration can (& in the case of the towers, will) be greater than zero, and the descending block can be constantly increasing in speed.
I've added the underlined bit for clarity.

The part I've highlighted needs proof. In this post I'm outlining the reasons why I don't think it's right.


Originally Posted by tfk View Post
It’s not a cushioning effect.
I call "cushioning effect" the phenomenon of having |Fr| < mg (Fr being the resistance force as in your explanation). I use that expression because in order to obtain such a low force on impact, the impacting objects must be "soft like cushions".

Originally Posted by tfk View Post
mg is the weight of the upper block.

The right way to look at it is NOT “∑F = mg - Fr = m a”, where Fr is the resisting force. This makes it appear the F is the dependent variable. It is not.
“a” is the dependent variable. It adjusts to Fr (since m is determined by the falling mass). So view it as a = (mg - Fr)/m.

Now you can see that the net acceleration of the CG of the falling body is completely determined by Fr.

IF Fr < mg, then a stays positive, and there is no deceleration.
IF Fr = mg during the collision, the a = 0 over this interval & the velocity stays constant.
IF Fr > mg, then the acceleration is negative & the velocity must decrease.
All agreed. And I still affirm that Fr >> mg. Not just > but >>.


Originally Posted by tfk View Post
The key, again, is that, in its highly damaged state with loads applied to non-load carrying members, the resisting force Fr will be less than mg.

After the supports break away, then the inertial factors, including the derationof the collision (described in the first part of this post) come into play.
I disagree with this. In the first paragraph, you've shifted focus from the impact force due to inertia, to the force of the connections. I don't care about the strength of the connections for this discussion; a zero-force connection would have the same effect. If the floor was thrown upwards so that its velocity was zero when the top falling material reached it, the deceleration would still exist (defining v2 would be harder, though).

The sequence in your second paragraph is wrong. The inertial factors start to come into play at the very instant of the contact, as the first two molecules start to repel each other. It's debatable whether these factors take long enough to last until the connection is broken or not, but that doesn't matter in this case, because my definition of v2 was the vertical speed at the time the floor assembly becomes completely disconnected.


Originally Posted by tfk View Post
You don’t ant to consider the bulk modulus of steel or concrete. This is the very, very low “compliance” you’d get out of solid hunks of those two materials.

You want to consider the compliance of the assembly, which will be orders of magnitude larger.
That doesn't matter. An assembly falling onto another assembly would still make your butt hurt if you were sitting on the top one (that's an understatement; actually I think that such a deceleration might cause severe injuries).

Any volunteer to ride one?
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Old 18th April 2016, 12:42 PM   #18
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Originally Posted by ozeco41 View Post
I don't see what there is to discuss with me on this issue.

My position unchanged for some years with two straight forward conclusions:

1) I agree that Bazant's "crush down - crush up" hypothesis is a good starting point for Bazant's goal of developing a generic model for progressive collapse. And I have posted numerous explanations of it together with expressions of my support.

2) I do not accept that it is a valid model for WTC 9/11 Twin Towers collapse progression stage. For simple reasons that any engineering or applied physics competent person should understand.

However on another thread tfk is challenging me with a range of discourteous or false claims and the only valid technical claim is a strawman.

A strawman false generalisation plus lie by innuendo to be more pedantic.

He is asserting that I disagree with Bazant's "crush down - crush up" - which conflates the two aspects of my true position. I agree with crush down <> crush up within its limits of valid application. I disagree that it is valid for WTC. (And for those specialists in "bet both ways" mental gymnastics - I have never seen a valid argument that cd<>cu can be an adequate approximation in the WTC Twins collapses which were by a totally different mechanism to that subsumed in Bazant's cd<>cu modelling.)

I agree with Bazant's cd<>cu for those cases where is is valid. I disagree that it is valid for WTC. And the proof is accessible to any person of High School level physics or better reasoning skills. I don't see any reason to complicate debates nor do I subscribe to notions that only engineers can understand matters of applied physics.

tfk's version of "simple to understand language" is different to mine.
That's probably because it was not intended as a model but as a "worst case analysis".

https://en.wikipedia.org/wiki/Worst-...rcuit_analysis
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Old 18th April 2016, 01:31 PM   #19
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Originally Posted by Oystein View Post
Can you make this a little more explicit?
I'm concerned that I should need to and I have little interest in EITHER pursuing the "make it very complicated" path OR derailing from tfk's mission.

Originally Posted by Oystein View Post
I think your point, while true, is not very relevant.
Thank you and "wanna bet?"

Originally Posted by Oystein View Post
B&Z's assumption can be substituted by one that is true, and (nearly) equivalent, and still support their conclusions.
Take care with drifting objectives. "and still support their conclusions." their for cd/cu is B&V NOT B&Z. And what it needs to support is their mechanism.

I've said that I don't think - don't see how - such a mechanism can be initiated. That refers to the non WTC situation - the generic case...because the WTC real event(s) never reached that stage.

You say it can be "substituted by one that is true, and (nearly) equivalent.." Can tell me how? Leave out the reference to the B&Z version if you wish - but how do you do it? How do you get the axial column loadings neded to sustain the crushing AKA buckling of the columns?
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Old 18th April 2016, 01:49 PM   #20
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Originally Posted by WilliamSeger View Post
Well, as I understand it -- anyone correct me if I'm wrong -- but Bazant presumes plastic column buckling throughout, but only to get an energy absorption function for his differential equations. What I'm saying is that, whatever energy absorption function you put into that kind of model, if you use it for both the top and bottom block, you'll get cd/cu. Are we disagreeing yet?
Not yet but keep working at it.

You have actually missed the point(s) I was making - drifting back towards defence of B&Z which I have never had problems with.
Originally Posted by WilliamSeger View Post
The only initiation mechanism he assumes is that the top block descended one floor, and that most of its gravitational potential energy was converted to kinetic energy because little could have been absorbed by the hot columns that failed on that floor. (He calculated that cold columns could have only absorbed about 12% by plastic buckling.) That's really all he cares about to construct his energy arguments.
That is defence of B&Z. Not needed and not the topic I was addressing. I have no problem with the B&Z modelling concepts which should cause concern in this discussion.

Originally Posted by WilliamSeger View Post
Taking that to mean columns disappearing and the top falling straight down is a red herring.
My post refers to B&V and the concept of cd/cu which is the topic of this thread. The point I made - repeated to Oystein in the previous post - is "How does the 1D approximation for CD/CU get started?" I'm sure you would be more comfortable avoiding any suggestion that Bazant could be wrong. So take Bazant's initiation out if the picture - show me how it could be done.
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Old 18th April 2016, 01:59 PM   #21
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Originally Posted by tsig View Post
Originally Posted by ozeco41 View Post
2) I do not accept that it is a valid model for WTC 9/11 Twin Towers collapse progression stage.
That's probably because it was not intended as a model but as a "worst case analysis".
Take care - you are "switching horses in mid-stream".
I am discussing crush down/crush up ["cd/cu"] which is the topic of this thread. The worst case analysis was B&Z - and I've already stated several times in recent days - must be dozens of times over the years - that I understand B&Z.

cu/cd arose as a later development of the same modelling concepts put forward in B&Z.

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Old 18th April 2016, 02:11 PM   #22
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Ozeco

Let’s get rid of the noise, first.
Right now, you’re responding like Truthers do when asked simple questions.

Originally Posted by ozeco41 View Post
However on another thread tfk is challenging me with a range of discourteous or false claims and the only valid technical claim is a strawman.

A strawman false generalisation plus lie by innuendo to be more pedantic.
I asked you, politely, about your background.
I stated, politely, what I remembered that you’d said from previous discussions.
I asked you, politely, to correct me if I was wrong.
Your response: nothing.

You may interpret my question as “insulting”. I don’t. And it wasn’t intended that way. Engineers generally have thicker skins than that.

The mods have made it perfectly clear that you have every right to not answer.
Most debunkers feel no need to avoid this question.

If you can point at a single lie that I’ve ever told, to you or anyone else on this forum (or anywhere else), please do so.
If not, I’d ask you to rescind that your assertion that I “lied by innuendo”.
__

Now to the matter at hand.

Originally Posted by ozeco41 View Post
I don't see what there is to discuss with me on this issue.
We disagree about a key technical point.
You’ve been asserting to people here your opinion, in no uncertain terms (something I admire), as tho it were proven fact.

An opinion that I believe to be wrong.
So the admiration diminishes a bit.

This is exactly the situation that discussions were made for, don’t you think?

Originally Posted by ozeco41 View Post
My position unchanged for some years with two straight forward conclusions:
Consistency is good.
Consistently wrong is … not so good.
One of us has been consistently wrong.

A discussion might help figure out whom that might be.

Originally Posted by ozeco41 View Post
1) I agree that Bazant's "crush down - crush up" hypothesis is a good starting point for Bazant's goal of developing a generic model for progressive collapse. And I have posted numerous explanations of it together with expressions of my support.
“… a good starting point …”??
We’ll come back to that.

“… for Bazant's goal of developing a generic model for progressive collapse…”
That’s not at all “why” he proffered the assertion.

He did some math. CD/CU jumped right out of it.
It wasn’t a goal.
It was a consequence of the equations of motion for ANY collapse that started midway up some tall, uniform cross-section building.

I apologize that I have missed your expressions of support for CD/CU.
I do confess that I’m puzzled at your belief that constantly saying “he’s wrong” constitutes “expressions of support” for CD/CU.

Originally Posted by ozeco41 View Post
2) I do not accept that it is a valid model for WTC 9/11 Twin Towers collapse progression stage. …
Ahh, so you don’t support Bazant’s CD/CU theory applied to the collapse of the towers. Which is the singular place (in this event) that Bazant applied it.

And it is this waffling back & forth that is problematic.
“I agree & support the idea”, one minute.
“I disagree, it is wrong”, the next.
Truthers do this with nonsense like “explosives … thermite … explosives”.
I don’t expect if from you.

CD/CU fell right out of Bazant’s analysis of the collapse of the Towers.
If you think the it is “wrong in the case of the collapse of the towers”, then you disagree with the concept.

If you think that “It is not valid for WTC progressive stage collapse” (for which it was specifically presented), then I have no idea how you can say that you think that it is a “good starting point”.

If I consider something to be wrong, or inapplicable, then I consistently identify that as a “bad starting point”.

“I accept it where it is valid, I don’t accept it where it is not” is content-free, if you do not identify “exactly what you think distinguishes applicable regimes from inapplicable ones?”

Originally Posted by ozeco41 View Post
2) … For simple reasons that any engineering or applied physics competent person should understand.
And this is very Trutherish.

Reasons that anyone should understand.
Feel free to elucidate.

Originally Posted by ozeco41 View Post
He is asserting that I disagree with Bazant's "crush down - crush up" - which conflates the two aspects of my true position. I agree with crush down <> crush up within its limits of valid application. I disagree that it is valid for WTC.
So you agree with it.
But you disagree with it.

Bazant presented it as an effect in the collapse of the WTC Towers.
You say that you disagree with “CD/CU applied to the collapse of the Towers”.

Bazant applied “CD/CU to the collapse of the Towers”.

So it’s fair to say that you disagree with Bazant.

I don’t know of anyone who has ever discussed CD/CU in any other context than “the collapse of the towers”. Do you?

Originally Posted by ozeco41 View Post
(And for those specialists in "bet both ways" mental gymnastics - I have never seen a valid argument that cd<>cu can be an adequate approximation in the WTC Twins collapses which were by a totally different mechanism to that subsumed in Bazant's cd<>cu modelling.)
Your suggestion that CD/CU is dependent upon the failure mechanism does not bode well.

CD/CU came right out of the math describing the motion of the various components (upper block, crushed layers, lower block). It is wholly independent of the failure mechanism.

Originally Posted by ozeco41 View Post
I agree with Bazant's cd<>cu for those cases where is is valid. I disagree that it is valid for WTC.
You agree.
You disagree.

Originally Posted by ozeco41 View Post
And the proof is accessible to any person of High School level physics or better reasoning skills.
Challenge accepted.

Bazant’s CD/CU came directly out of the equations of motion.
Please show his math error.

Present your proof.
Mathematical or physical.
Or point me to where you’ve presented it, hopefully in clear detail, elsewhere.

Originally Posted by ozeco41 View Post
I don't … subscribe to notions that only engineers can understand matters of applied physics.
You were complaining about what you believed to be “innuendo” in one of my previous posts.

Perhaps you could clarify if you are implying that I have ever made that assertion.
Anywhere.
Ever.

Originally Posted by ozeco41 View Post
tfk's version of "simple to understand language" is different to mine.
We agree that we have a difference of opinion on “simple to understand language”.
See, we’re making progress.

If I agree with something, I say, “I agree.”
If I disagree, I say, constantly, “I disagree”.
I consider that to be simple, clear, & easy to understand.

I don’t say, “I agree. I disagree.”

That’s not “simple to understand.”
__

I presented a very simple statement of “what causes damage” in my OP.

You haven’t responded to any of that.
That sort of evasiveness is something that I'd expect out of a truther.
Not from you.
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Old 18th April 2016, 02:21 PM   #23
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Originally Posted by pgimeno View Post
No, that's not even close to what I'm thinking. I agree with what you say. What I'm actually thinking is that ∆t must be necessarily low. Low enough to overwhelm the effect of gravity.
Yes, yes, yes. I agree with you.

I wanted to get back. I don't have time right now.
My avaricious Uncle Samuel demands my attention.

The question of whether the acceleration decreases, goes to zero, or goes negative depends entirely on the numbers that enter the equations.

I just pulled "1 second & 1G" out of my ... hat ... because they were easy numbers & illustrative of the principle that the acceleration doesn't have to be negative.

We'll work some numbers over the next couple days, as time permits.

Cheers.
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Old 18th April 2016, 02:26 PM   #24
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Originally Posted by pgimeno View Post
That doesn't matter. An assembly falling onto another assembly would still make your butt hurt if you were sitting on the top one (that's an understatement; actually I think that such a deceleration might cause severe injuries).

Any volunteer to ride one?
I just saw this. Gotta answer, then gotta run.

Yes, I've already ridden a couple.

When I was a kid, I lived adjacent to a wild forest (in a part of Boston). Shows how long ago I was a kid.

On several occassions (I won't say how many, but it wasn't double digit. barely ...), we would go into the woods & "ride trees". One kid would climb to the top & the other would cut it down.

It was great fun, and a very gentle stop, thanks to the branches.

Yeah, I know it ain't exactly the same. But if I were to ride a telephone pole down, I know exactly which side of the pole I'd be scrambling to on the way down.

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Old 18th April 2016, 02:55 PM   #25
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Originally Posted by tfk View Post
We'll work some numbers over the next couple days, as time permits.

Cheers.
Thanks, I'm curious! I think I could put some numbers in, but not without making some assumptions that may or may not be based on reality.
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Old 18th April 2016, 03:06 PM   #26
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Originally Posted by ozeco41 View Post
I'm concerned that I should need to and I have little interest in EITHER pursuing the "make it very complicated" path OR derailing from tfk's mission.

Thank you and "wanna bet?"


Take care with drifting objectives. "and still support their conclusions." their for cd/cu is B&V NOT B&Z. And what it needs to support is their mechanism.

I've said that I don't think - don't see how - such a mechanism can be initiated. That refers to the non WTC situation - the generic case...because the WTC real event(s) never reached that stage.

You say it can be "substituted by one that is true, and (nearly) equivalent.." Can tell me how? Leave out the reference to the B&Z version if you wish - but how do you do it? How do you get the axial column loadings neded to sustain the crushing AKA buckling of the columns?
You had written:
"cd/cu presumes an initiation mechanism that starts the "Limit Case" column crushing mechanism from B&Z. Didn't happen for WTC. More to the point it could not happen."
And I had said that the initiation mechanism can be substituted.
By what?
By simply assuming that the top part has a downward momentum equivalent to that gained by dropping 1 story

What I meant is that the specific mechanism isn't relevant, just that some momentum / KE already exists.

You ask by what mechanism other than the free-drop mechanism of B&Z this much momentum / KE could practically be achieved, right? I admit I have no answer to this[1]. But I would submit that this problem is no different from the problem of explaining what happens during the crush-down phase of B&V - how would one practically picture axial column loadings maintained all the way to the ground?

You counted two problems - they are essentially the same: Axial alignment can't be maintained at the real WTC.



[1] Not sure I need an answer - me not having an answer doesn't imply there is none. I am sure one mechanism can be engineered, ten can be engineered, and all are equally irrelevant. What's relevant is that KE already exists.
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Old 18th April 2016, 03:22 PM   #27
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Originally Posted by tfk View Post
...
He did some math. CD/CU jumped right out of it.
It wasn’t a goal.
It was a consequence of the equations of motion for ANY collapse that started midway up some tall, uniform cross-section building.
...
Ahh, so you don’t support Bazant’s CD/CU theory applied to the collapse of the towers. Which is the singular place (in this event) that Bazant applied it.
I think oz's point is that the WTC towers were not examples of "some tall, uniform cross-section building", since they didn't have a "uniform cross-section". Therefore, the math model that "CD/CU jumped right out of" cannot be validly applied to the WTC.

Bazant's math done to his model is (probably; I didn't check) correct.
Bazant pretending the model describes the actual WTC buildings and their collapse mechanisms is incorrect.


Of course I could misunderstand him, or you, or both.
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Old 18th April 2016, 03:46 PM   #28
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Originally Posted by ozeco41 View Post
... So the Top Block did not survive to be subject to crush up AFTER crush down. Avoiding the term "crush" because it was floor joist shearing dues to the impact of still intact perimeter column ends with the office space floors. Not the buckling failure of overloaded columns which is subsumed in the normal use of "crush" terminology.
And here is where I take exception as I have for a while... the falling mass within the upper block was most likely not shearing of the slabs by descending misaligned columns.. but the slabs broke apart into falling chunks from several mechanisms such as the failure of the local belt girder.. pulled inward by failing perimeter core columns... buckling or pulled by heat distorted bracing... and or dynamic load impacts from falling material above.

Before the facade of the top begins to move down and slighting misaligned... the insides has already seen a lot of the slabs collapse and the tall tale is the pre descent movement of the antenna in tower 1. For it to have moved down... what has beneath it has come apart.
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Old 18th April 2016, 09:15 PM   #29
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Originally Posted by ozeco41 View Post
You have actually missed the point(s) I was making -
Apparently so, and guess I still am.

Quote:
drifting back towards defence of B&Z which I have never had problems with.

That is defence of B&Z. Not needed and not the topic I was addressing. I have no problem with the B&Z modelling concepts which should cause concern in this discussion.
I believe that what I stated is the starting point for both B&Z and B&V, and I have no idea what else you could mean by "initiation mechanism."

Quote:
My post refers to B&V and the concept of cd/cu which is the topic of this thread. The point I made - repeated to Oystein in the previous post - is "How does the 1D approximation for CD/CU get started?"
I really don't know what you mean; how does what get started? As far as I can see, "it" gets started by overwhelming kinetic energy. B&V takes that initiation assumption and plugs it into a model that uses plastic column buckling as an energy sink, but there's no reason another energy absorption function can't be plugged in. Cd/cu is not any sort of assumption in the model; it's a result.

Quote:
I'm sure you would be more comfortable avoiding any suggestion that Bazant could be wrong. So take Bazant's initiation out if the picture - show me how it could be done.
Wrong about what? Using plastic buckling as the energy sink? Yes, that's wrong if he was looking for "what really happened" but I don't believe that was ever his intent. He is a theoretical scientist constructing a theoretical model which attempts to reduce a complicated problem to a small set of equations that can be solved without a finite element analysis (which is what Bazant has suggested all along would be necessary to get a better idea of "what really happened"). In the paper, he talks about recording results from actual demolitions to get better estimates of energy absorption rates (i.e. solving for energy absorption rates when given known collapse rates) to make the model's predictions more accurate, and he suggests that such predictions might be useful for future demolitions. I'm willing to be shown that Bazant was wrong about any part of any paper; are you willing to consider that perhaps you are wrong about his intent?

Last edited by WilliamSeger; 18th April 2016 at 10:22 PM. Reason: clarify
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Old 19th April 2016, 07:31 AM   #30
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This and the 'ROOSD' thread are reminiscent of the theologians argument about "how many angels can dance on the head of a pin"
The presume that angels actually dance, and that the answer is actually significant in some way. It's really an analysis of a chaotic event that will require hundreds of billions of degrees-of-freedom (at least), and has no bearing on anything in reality
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Old 21st April 2016, 02:54 AM   #31
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Old 25th April 2016, 11:51 AM   #32
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I'll re-state the same thing I said in the OP.

Originally Posted by tfk
There are only 2 factors that need to be true in order for Bazant’s “asymmetric crush down” approximation to be true. Both are, IMO, irrefutable.

I’ll address “asymmetric crush down” in this post, and save "Crush up" for a later one.

The two factors:
  1. The principle determinant of the amount of damage occuring in any two “similarly constructed assemblies” that collide is the relative speed of impact, with the damage proportional to the speed squared (the work done in causing the damage is proportional to the kinetic energy of impact). 

  2. Once some structure has been ripped from its supports, it begins to fall immediately.

That’s it. If you’re going to “prove Bazant wrong”, then you’ve got to prove that both of these assertions are wrong.
I guess that I can re-iterate the obvious fact that, during collision after the first one, the top floor of the lower block is NOT colliding with the upper block. But is instead colliding with the bottom of the crushed debris layer. And this impact velocity gets greater & greater as the building collapses. So one would expect more & more damage to the impacting structures as the collapse progresses. For the debris layer, however, you cannot get any "more damaged" than "completely crushed". But the damage to the upper floor of the lower block gets more & more & more violent, due to the greater weight of the upper mass & its higher impact velocity.

In contrast, the "impact velocity" of the bottom floor of the upper block with the top of the debris layer remains zero, for all collisions after, say, the 2nd floor impact. (one floor of real impact, and a second of a bit of additional compaction of the debris). And therefore the damage to the bottom floor of the upper block quickly approaches zero for all collisions after the first one or two.

Does anyone disagree with the principles that I've laid out here?
If so, why?
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PS. pg, I'll get back to your ideas soon. I'm not ignoring you. Just a little busy.

Last edited by tfk; 25th April 2016 at 11:56 AM.
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Old 25th April 2016, 12:24 PM   #33
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The so called top "block" is not colliding with anything. By the time downward movement is observed a whole lot of the floors of the "top block" have already been "destroyed" broken apart and have dropped and are no longer being supported AT the level of the top block axial system.

The reason for the above is that the effect of heat was experience more on the BEAMS and less at the columns. The beams expanded.. distorted and failed knife splices, dropped sagged and the slabs inside and outside the core were losing local support and breaking up and dropping in bits and pieces...

The downward motion was made possible mostly because columns had there column to column connections forced out alignment and failed. When a muli part clumn fails the columns above are still pulled down and their loads are either supported by the hat truss... which would redistribute them... or they "break free" and drop unloading the hat truss but up loading what they come down on.

It's likely that the last moments before downward movement saw an interior avalanche of the floor material, disengaged columns leaving basically the skin which was a pretty rigid 4 sided membrane to drop... the few remaining core columns buckled over causing the lateral displacement of the dropping facade held largely square by what was left of the 3 D rigid hat truss matrix.

There was no up crushing of the top block... only destruction of the slans of the lower part as the disengaged material from above rained down.

Last edited by JSanderO; 25th April 2016 at 12:38 PM.
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Old 25th April 2016, 12:50 PM   #34
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Energy from mgh is absorbed at every collision by both the static and dynamic components of the building. If that energy exceeds the capability of the part (s) to remain intact, they break.
Okay?
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Old 25th April 2016, 01:21 PM   #35
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Originally Posted by rwguinn View Post
Energy from mgh is absorbed at every collision by both the static and dynamic components of the building. If that energy exceeds the capability of the part (s) to remain intact, they break.
Okay?
YES! but how to free those parts to collide... that is the question! Once the ball is rolling... it's a no brainer and Mr B's gross analysis has no relevance.
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Old 25th April 2016, 01:43 PM   #36
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Exactly. Getting them free is what the NIST Report describes so well and accurately.
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Old 25th April 2016, 02:45 PM   #37
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Originally Posted by rwguinn View Post
Exactly. Getting them free is what the NIST Report describes so well and accurately.
Maybe.... there are other scenarios... depends on where you believe the fire was doing its thing.
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Old 25th April 2016, 03:18 PM   #38
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Belief is one thing. Evidence is another, entirely.
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Old 25th April 2016, 05:21 PM   #39
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Originally Posted by rwguinn View Post
Belief is one thing. Evidence is another, entirely.
The evidence of where the fire was, how hot it was and how long it burned for is sketchy at best. It's based on visuals of flame, and smoke.. maybe some thermal imaging... which is clearly not a complete evidence set. So the fire evidence is really assumptions as far as hard data is concerned. There were no transducers and there was no real time survey of field data.

There is without doubt evidence of fire.
There is science related to the effect of fire on building materials and assemblies.
There is probably data on behavior of office fires etc.
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Old 2nd May 2016, 09:11 AM   #40
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Originally Posted by JSanderO View Post
The so called top "block" is not colliding with anything. By the time downward movement is observed a whole lot of the floors of the "top block" have already been "destroyed" broken apart and have dropped and are no longer being supported AT the level of the top block axial system.
I beg to differ. Since it was descending at around 0.65G, it was colliding with something that provide an upward force of 0.35W, where W = the weight of the entire upper block.

This is a huge force.

If it were colliding with "nothing", then it's downward acceleration would have been 1.0G.

Originally Posted by JSanderO View Post
The reason for the above is that the effect of heat was experience more on the BEAMS and less at the columns. The beams expanded.. distorted and failed knife splices, dropped sagged and the slabs inside and outside the core were losing local support and breaking up and dropping in bits and pieces...
Which knife splices in the towers?

In the rest of your post, it’s not clear (to me, at least) your sequence of events.
Would you care to list them in order?

But, more pertinent to this thread, would you care to comment on my comments in the OP?

Tom
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