The 9/11 Forum

This thread is for examination of the class of cascading failures I call toppling failures or more appropriately toppling reactions. 'Failure' is a misnomer for many systems included in this category, especially since some are designed to topple in entertaining ways. It's more general to refer to these as gravity-driven (self-sustaining or) cascading processes where there is no connection between members. Examples are:

- domino chains
- houses of cards
- jenga towers
- some parts of Rube Goldberg machines

As far away from building collapses as these systems may seem to be, the parallels are very strong. The general definition provided above need only have the qualifier of 'no connections' removed in order to be the broad definition of progressive collapse in a building. I feel there is much to learn in consideration of these systems. Dr. G mentioned dominoes in his Physical Models thread:

http://the911forum.freeforums.org/physical-models-of-the-twin-towers-and-collapse-mechanisms-t62-15.html#p781

to somewhat mixed reaction (mine was enthusiastic). Later in the thread, I touched on several classes of cascading reactions including toppling (http://the911forum.freeforums.org/post2221.html and the next post). Obviously, there is not only a physical analog to progressive collapse in such systems, progressive collapse goes to this category of system in the limit of small connection strengths.

One of the most profound aha experiences I had about the collapse of the towers was precipitated by a post newton made at physorg linking to a house of cards collapse on YouTube:

http://www.physforum.com/index.php?showtopic=12383&st=6105
and the video itself: http://www.youtube.com/watch?v=Yx_XMV6Etgo&NR=1

newton may have intended exactly the opposite effect, but I saw this as one of the best analogs for a tower collapse yet. This was a very strong house of cards! By deviation from as-built geometry, it can disintegrate to completion. This case had an arrest (wrt displacement of a crushing front) midstream, then a continuation. I acquired displacement data on it, which I'll post later.

Major_Tom recently brought up the issue of teminal velocity and how it could be reached so quickly in the interior failure of WTC1:

http://the911forum.freeforums.org/solid-mechanics-simulacra-of-the-toy-variety-t163-15.html#p8792

This is in the context of looking at progressive collapses simulated by solid mechanics. It got me thinking about how one obtains effective resistive forces with velocity dependence from the structure or geometry, apart from material surface friction. These systems seem like fertile ground for exploration.

tfk recently started a thread on JREF about a toppling failure:

A perfect demo of why the towers dropped straight down

I find the title quite ironic for someone who went out in a blaze of glory here complaining about the misleading and useless WTC 3D core model, made from plans and prints! Well, in this case, I don't necessarily agree with his point, but I do agree with the idea of using this sort of thing as an analog. Obviously, 'cause here I am. In fact, I posted the same video almost exactly a year ago:

http://the911forum.freeforums.org/the-pub-t82-75.html#p2221

so, once again, old news. Wonder if tfk would have disparaged posting this video if he'd seen it here first?

He is getting some flak because it's a poor analogy. Maybe it is for his purposes, since I find his thread title perhaps overly ambitious. (The Irony!!!*). But the principle is not wrong. I first went down the toppling route in July 2008:

http://www.physforum.com/index.php?showtopic=12383&view=findpost&p=358254

linking to this video of a jenga tower collapse:

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


*check out the defense given by Macgyver1968 for tfk use of a stack of pieces of wood as a 'perfect demo' of some aspect of a tower collapse.

This is not a demonstration of the collapse of the WTC. It is demonstration of ONE aspect of physics in the collapse of the WTC. It demonstrates why the towers didn't fall over like trees.

Hmm. A perfectly reasonable justification, reminds me so much of the WTC Core model thread. Why do I think the same person, if over here, would instead be claiming a pile of wood is a useless truther model because the tower was made of welded and bolted steel and concrete and was over 400m tall!

Displacement data from the house of cards video newton found:



'Roofline', various locations, pixels and frames.

Note the temporary arrest of progress partway through, followed by continuation to completion. Also see the nearly linear segments. The type of propagation occuring achieves terminal velocity quickly, almost instantaneously. There is no crushing or buckling and no connections to break. Geometry and minimal friction keep the structure standing after multiple aerial assaults, until one impact initiates the instability.

The data above does not cover the entire collapse, in case anyone is wondering why they don't see the arrest in the video.

Here is a smear of the entire collapse:



and a zoom and flip for the area graphed above:

OneWhiteEye wrote:Displacement data from the house of cards video newton found:



'Roofline', various locations, pixels and frames.

Note the temporary arrest of progress partway through, followed by continuation to completion. Also see the nearly linear segments. The type of propagation occuring achieves terminal velocity quickly, almost instantaneously. There is no crushing or buckling and no connections to break. Geometry and minimal friction keep the structure standing after multiple aerial assaults, until one impact initiates the instability.

I've seen this pattern before in simulations of cascading failure in networks. Here's the output of a simulation of load-sharing driven failure in a 500 node network after 43 iterations



In this instance there was an arrest after 73% of the nodes failed. The analogy is probably clear, but for the sake of clarity: One can think of the network as representing a series of inter connected components (such as steel columns) redistributing load after the initial failure of a single component.

Here's another similar run on a much smaller network:

Wow. Cool.

Can you do me a favor? When you get a chance, have a look at this thread

http://the911forum.freeforums.org/wtc-1-collapse-initiation-t172-15.html#p3410

and tell me if the simulations you perform are similar to the fiber bundle models described there. Seems to be.

OneWhiteEye wrote:Wow. Cool.

Can you do me a favor? When you get a chance, have a look at this thread

http://the911forum.freeforums.org/wtc-1-collapse-initiation-t172-15.html#p3410

and tell me if the simulations you perform are similar to the fiber bundle models described there. Seems to be.

Yep, they are formally equivalent. Cool thread.

These types of sim capture the latent period, and the tendency to arrest (or psuedo arrest), but the physical property of having a natural rate of collapse, or a terminal maximum is lost. As you point out, an iteration is not a fixed unit of time.

One thing I like about this approach is that (for exapmle) the 500 node model I posted above could be a model of a 500 column/beam segment of the core, or 500 interconnected components in a floor assembly, or 500 linked molecules in an ounce of structural concrete. The principle is basically scale free, and applies to any subsystem you care to look at.

The least interesting model of all is a linear chain of 110 nodes which, when it collapses, does so in a single iteration (if at all)

Thanks for the tip, that's a cool thread.

Its going to take forever to "catch up" with what you guys have done.

War Wheel wrote:Yep, they are formally equivalent.

Awesome, I thought so. A few simple principles can go a long way.

The least interesting model of all is a linear chain of 110 nodes which, when it collapses, does so in a single iteration (if at all)

Indeed. Only somewhat more interesting if the properties at each node vary. Quite a bit more interesting if the failure criteria are made to depend on a dynamic property.

OneWhiteEye wrote:Quite a bit more interesting if the failure criteria are made to depend on a dynamic property.

The loads in the network model are "dynamic" in the sense that the load on a given node can shift depending on how many of its neighbors have already failed. This does not happen over "time" but over iterations.

What exactly did you have in mind?

War Wheel wrote:This does not happen over "time" but over iterations.

I should have parenthetically prefixed "dynamic" with "(pseudo)", for I meant to include step dependency.

What exactly did you have in mind?

Nothing specific, but I'm sure I can think of some things!

I made this velocity graph (same data, two different smoothing procedures)



from an analysis of the audio track from this video:

http://www.youtube.com/watch?v=JwGDO2wknLE

There does appear to be some acceleration, and in a very interesting pattern.

War Wheel wrote:from an analysis of the audio track from this video:

Audio? Interesting. Do tell.

Sorry, I've been spotty in keeping up.