I return to the scenario that the collapse began just above the sub station... again interior and not visible from the far off cameras which caught the collapse. We don't have visuals on the likely initiation location for the twins which was unobstructed by buildings... but again by the facade of the buildings themselves. Why blame NIST for the fact that WE can't see past the facade?
We can ask NIST why didn't they investigate core led collapse scenarios in all three buildings.
SnowCrash wrote:If I may, although I very much appreciate the discussion of 'blocks' and 'blockheads' to lay bare a rigid frame of mind, and a tendency to think in dogma, one can overshoot the target.
Good point. We're trying to counter the chronic undershoot, so the presentation tends to be somewhat unbalanced. Still, let's be sure we're talking about the same thing.
Blocks (even of irregular shape) are the basis of the finite element method and related approaches. Indeed 'finite element' says it all, the element is a block of finite size. Element size is a huge consideration. Apply your intuition to this mesh used for crack growth propagation:
The tip of the defect is in the middle of a fine mesh. Far away from the point of interest, the mesh is coarse. Now, imagine trying to do that same experiment (for that's what it is) with two elements - two blocks. The example is a little more extreme than the application to collapse, but the basic analogy holds. That's the objection. I uses blocks because they simplify things tremendously, but unfortunately it does so to the point that the mechanics no longer bears a resemblance to the system being modeled.
Since I'm an IT guy, you can chalk me up as a typical blockhead. The WTC collapses were an extremely large set of interacting collisions and sub-collisions resulting in the orderly chaos we all saw on TV, or, if you were unlucky enough to be there, with your own (spherical) eyes. Years ago, a brilliant teacher in 3D design already tried to tell me not to think of the WTC collapse in terms of Newtonian mechanics alone, but to consider quantum mechanics as well. Perhaps this should have been posted in one of Major Tom's excellent threads, but I'll post it here:
Oh yeah? Well, I see you...
and raise you...
As stated in the above Youtube video description: "Newtonian determinism is bullshit."
This is why the best analytical model will undoubtedly have a stochastic foundation. In order to accurately characterize the phenomena, we must give up the ability to precisely predict the outcome of any one instance. That's my feeling.
If you increase the granularity of a block-based Newtonian simulation you can approximate complex collisions well enough to yield a meaningful result. The rub is in the granularity chosen, and made possible by the technological means available. Like a 4x4x2 picture can't properly render a circle, a 4000x4000x2^24 picture can, and the higher the resolution and the color depth, the better the approximation of the abstract, non-block object.
I agree. I think if the blocks were finite elements 10cm on a side such that an assembly like Major_Tom posted above would look continuous at the scale of the image, the possibility is good that meaningful simulations can be done.
I agree with and appreciate the objections made about blocks and blockhead thinking. But I disagree with the a priori dismissal of block-based analysis as hopelessly inadequate.
It is possible to introduce terms to correct which, to some varying degree, reflect a real aspect of the system. Examples would be tilt, mass shedding, interpenetration, none of which are truly native to a simple homogenized block system.
If there was any way for us to incorporate quantum mechanics into any simulation, we should and we probably would.
I once had to calculate the wave function of a space shuttle in orbit, which was to illustrate the magnitude of quantum effects in an acknowledged macroscopic domain. Close enough to a continuum, and deterministic, to a staggering degree.
Major_Tom, it may amuse you to find out that Seffen's work might be in error as to the magnitude of terminal acceleration achieved, claimed to be g/2.
OWE, do you have follow-up work with the Seffen g/2 thing?
..............
When looking at WTC1 and 2, I think it helps to know some basic mechanics of some simple, stacked systems of masses, and the first 4 pages of this thread demonstrate this type of motion better than anywhere else.
A second set of threads on simple mechanics of stacked systems:
The basic mechanics of stacked systems is discussed in the following papers in relation to the WTC collapses:
Frank Greening, Energy Transfer in the WTC Collapse linked here All 4 Bazant papers BZ, BV, BL and BLGB Keith Seffen, Progressive Collapse of the World Trade Centre: a Simple Analysis linked here
another paper related to the mechanics of stacked masses by Gordon Ross: Momentum Transfer Analysis of the Collapse of the Upper Storeys of WTC 1 linked here
The basic mechanics of stacked systems in relation to the WTC collapses is discussed in the following papers :
Frank Greening, Energy Transfer in the WTC Collapse, linked here All 4 Bazant papers BZ, BV, BL and BLGB, linked and reviewed here Keith Seffen, Progressive Collapse of the World Trade Centre: a Simple Analysis, linked here
Gordon Ross: Momentum Transfer Analysis of the Collapse of the Upper Storeys of WTC 1 linked here
From the list in the last post, I think that the best way to learn about basic properties of a simple system of stacked masses is through the model described in the first 4 pages of this thread.
In this thread OWE states very clearly that he is examining motion of a simple stacked set of masses in 1 dimension and this does not represent anything like the behavior of an actual building.
As described in my "book", a proverbial average Joe or Joe Student doesn't have access to descriptions of simple systems of stacked masses given by OWE in this thread. Instead, they have access to the published papers of Greening, Bazant, Seffen and Ross linked earlier. And, just to add to the confusion, Joe also has access to the Chandler 3rd law paper.
For Joe Average and Joe Student, the mechanics of stacked masses in relation to the WTC collapses are treated by:
Greening Bazant Seffen Ross Chandler
Note once again how in this thread OWE is very careful to distinguish between the behavior of the stacked masses in his toy simulation and real behavior of a highly complex object like a building.
From those on the list available to Joe, only Greening is careful to differentiate between a 1-D system of stacked masses and real building behavior.
Major_Tom, it may amuse you to find out that Seffen's work might be in error as to the magnitude of terminal acceleration achieved, claimed to be g/2.
OWE, do you have follow-up work with the Seffen g/2 thing?
Nothing formal. In simply reading further and contemplating the situation, what was initially somewhat opaque became transparent... or translucent, at least. If there are impulsive inelastic losses involved in the mechanism of accretion, Seffen's model is not applicable. While it is true that Seffen's model is conservative (non-impulsive), and therefore the equations of motions developed are correct for the model, it's straightforward to demonstrate that any conceivable real failure mode is impulsive and largely inelastic by nature.
Early on, I felt that even the continuous case where the load displacement response follows the peak/snapthrough/compaction sequence constitutes an impulsive action - and clearly one which is inelastic. Now, I'm quite certain of it and it represents the closest thing to non-impulsive one can imagine as a failure mode. Since it's the Bazantine failure mode, and wasn't reality, it's not really a consideration but once again merely marks a boundary where even going to that extreme does not alter the result.
Seffen's model is even more divorced from reality. The self-consistency is there; since the model is extremely homogenized, the mechanics should reflect that fact and it does. But this is not the mechanics of building collapse. It's idealized for the spontaneous collapse of a physical object no more complex than a homogenous rod. Solid is the right idea, but it is hard to conceive of a spontaneous conservative density change without having voids in the object. A real building does have voids, but with voids contact dynamics becomes applicable, and collision in the real world - with those materials - is inelastic.
When looking at WTC1 and 2, I think it helps to know some basic mechanics of some simple, stacked systems of masses, and the first 4 pages of this thread demonstrate this type of motion better than anywhere else.
Thank you for saying that. You're one of the few people who has been around and saw through the tongue-in-cheek presentation, which I could not resist.
Major_Tom wrote:In this thread OWE states very clearly that he is examining motion of a simple stacked set of masses in 1 dimension and this does not represent anything like the behavior of an actual building.
I really thought it was important to explore a gross simplification while remaining clear on what it is and what applicability it has. On one hand, it applies to nothing at all in the exact sense, but has pretty broad applicability as a rule of thumb for certain systems. We develop and carry mental models of all kinds of everyday physics scenarios. Some of these are quite sophisticated and are used for processing mechanics in real time (e.g., hitting a curve ball or catching a fly ball in a high wind). Progessive collapse is not an area where most people have a sound intuition, myself included. Stacks are the easiest way to approach it.
I remember shagster at physorg posting a video clip of the Three Stooges collapsing a triple-decker bed from the top bunk. It was rigged but real. There it is, in all its glory. I just needed to add more stooges and take data.
Major_Tom wrote:OWE, if he is correct in saying that g/2 convergence is expected in a whole class of problems, that is worth double checking. He calls it a "variable-mass system where the mass, initially at rest, is entrained by a non-impulsive action. "
Hmmmm...
Thank you for highlighting it in this way. Common knowledge...
Major_Tom wrote:Quote from page 6 of this thread. Link goes to phys.org.
The last post in that thread is dated January, 2012.
Was there any follow-up between you and Dr B?
No. He seemed interested when those posts were made, that's as far as it went.
Did you write more on the Seffen g/2 thing anywhere else or does the linked thread cover the latest of your comments?
No, that and a couple of threads here is all of it.
Entrained by a non-impulsive action? A rubble-driven collapse is practically ALL impulsive. When he says non-impulsive, it's quite clear how it applies to the model he constructs, being a continuum mass distribution with an associated residual capacity. Whether or not one considers a conservative/non-conservative distinction, this aspect alone dictates the applicability of the model to an actual collapse, particularly the towers. As you point out, I don't consider the stacked slab models to be very tower-like, either, but if I have to choose between the two as a better representation, I have to go with the slab. Even column rehardening effectively amounts to a(n inelastic) collision, which is impulsive.
Do I still have the last word over on the physorg thread? Let me see... yes. As it should be. I have a problem with finishing things. That's something I didn't start but do intend to finish.
Is it just me, or an early sunday morning server problem? http://www.sharpprintinginc.com/ and all sublinks give me an error message "Unable to load database indicated by configuration file."
