The 9/11 Forum

DBB:

This is why I like the idea of models of the Twin Towers made from something akin to real world dominoes because such models nicely illustrate "domino theories" of the collapse.

Consider one of those domino collapse extravaganzas we have seen on TV. If we say that the energy needed to "collapse" (that is push over) one domino is E1, the energy released when 100 dominoes fall over is 100E1.

Now in those domino collapse demonstrations it only takes a light touch, a mere "breath of wind", on one domino to collapse thousands of dominoes.

Is it possible that the failure of a few bolts or welds at one location in a WTC tower could have led to the failure of the whole building?

Dr. G wrote:Is it possible that the failure of a few bolts or welds at one location in a WTC tower could have lead to the failure of the whole building?

Not what was observed. After damage and fire, south wall began to pull-in. For about 20 minutes towards the west side. Then the east side of the south wall buckled and away it went.

That's large scale creep!

Is it possible that the failure of a few bolts or welds at one location in a WTC tower could have led to the failure of the whole building?

Scary thought. The comparison of dominos, which represent the extreme in a large avalanche effect created by the tiniest push, to a building's structure, which is designed to safely house human beings for many years normally without any ugly incidents of groups of tennants being crushed by falling beams and such, may be pushing it a bit.

Imagine if tall buildings are so sensitive. A small local failure and just the right push at just the right sensitive spot can topple the whole thing.


The domino analogy is interesting. You are referring to a local collapse initiation event which dominos into collapse initiation? And this leads to the beginning of what we call progression, which further dominos the building down?

So this domino idea can be applied to both the physics of collapse initiation and collapse progression (and the transition in between).



Isn't this actually the way people who believe the collapse a natural extension of some Al Qaida attack see collapse initiation? As a local failure which quickly propagates to collapse initiation?

But then again, Max MIHOP would see it the same way. Max MIHOP would see the same local failure quickly propagating, but certain connections were weakened with some additional assistance.

So both are a domino effect. How do you distinguish them?


In the case of MT MIHOP, in the case of WTC 1, the video clips of collapse initiation show certain queer events which are not consistent with the propagation of a local failure which leads to collapse initiation. I've been discussing them on the "perimeter failure line" thread.

That's large scale creep!

Reports and photos of this creep are very important. Was it on the south face, east side floor 93-7?

The photo record of this event is very important to us. Is this the said local failure which is said to cause the whole collapse? I've had a very hard time finding decent photos of this event. Anyone else experience that?


Since we all seem to be interested in collapse initiation, WTC 1, why don't we talk about it? Is this the best thread?

DBB & Major Tom:

One point I would like to stress about my "domino" theory of collapse initiation and propagation is that it is (i) Yet another simplified model, and (ii) Applicable to WTC 1 & 2 only as a consequence of the serious damage inflicted to these buildings by the aircraft impacts and fires.

Obviously two weakly spliced columns can stand vertically "for all eternity" if never subjected to impact damage, fire or lateral forces. The same is true for a house of cards or my domino tower. However, asymmetric damage changes everything; now these structures are metastable and very prone to collapse.

However, asymmetric damage changes everything; now these structures are metastable and very prone to collapse.

For WTC 2, the building fell eastward and both the core and perimeter columns that were damaged by the impact were on the east side of the building. Makes more sense.

For WTC 1, the plane hit square on the north side and the building fell slightly south initially. That is a bit strange.

Wtc 7, assymetrical damage? Pretty darn weird.

Major_Tom wrote:Was it on the south face, east side floor 93-7?

Yes.

I've had a very hard time finding decent photos of this event.

It is in the NIST report in several subvolumes, for example, NCSTAR1--6D.

Since we all seem to be interested in collapse initiation, WTC 1, why don't we talk about it? Is this the best thread?

Yes.

Dr. G:

I like the domino model as an exercise in understanding self-sustaining reactions. Dominoes must exceed a threshold energy to fall over but are otherwise tipping pencils. A very small input energy triggers a phase transition to a lower potential energy state (assuming inelasticity). Some observations:

If we say that the energy needed to "collapse" (that is push over) one domino is E1, the energy released when 100 dominoes fall over is 100E1.

A single domino will 'collapse' when it has been tipped such that the center of mass has moved laterally past the fulcrum edge below. If quasi-static, the energy expended E1 is the gain in potential energy from the modest height increase of the cm as the domino tips until cm is at top dead center over the edge. This is the 'activation energy' or potential barrier to be overcome to get out of the local minimum of potential energy. In a chain, the domino has a final resting position not quite flat, as it lies partly on the next domino which it toppled, but with the cm much lower than originally. If the system were elastic and frictionless, the domino would not come to rest, but that's another matter. The difference in PE between the initial and final states is what I take to be energy released and would be somewhat greater than N*E1 for N dominoes.

Introduce a collision with a second domino in a uniform chain. If the first domino does not transfer sufficient energy (E1) to the next, the reaction stops, otherwise it continues to completion. It's an interesting analog for progressive vertical collapse but with the curious difference of propagating horizontally, orthogonal to the driving force. The members cease to participate in the reaction past a certain point, where the members in contained vertical collapse continue to participate unless shed. The analogy, then, is strongest when you have high mass shedding fraction in vertical collapse, though of course the dynamics are different. (Edit: the shedding fraction needs to result in a constant upper mass after a short time).

A real chain of dominos will have many in the process of falling at the same time, each at an incremental angle between vertical and final rest. There isn't impulse alone but an initial impulse followed by a sustained application of force before and after the next domino reaches the point of no return. The only period of uncoupled action is the tip of the first domino until contact, after that they ride each other's back on the way down. Because energy well in excess of E1 is available to pass to a successive domino, proper geometry could allow a single chain to begin toppling two chains, as is sometimes seen. A pyramidal arrangement of toppling should also be possible. The total energy change is limited only by the size of the arrangement, and the rate of energy change (power) can grow geometrically.

Classic chain reaction.

Is it possible that the failure of a few bolts or welds at one location in a WTC tower could have led to the failure of the whole building?

Not what was observed, but it's fair to ask if it can happen. What is the minimum number of bolts required to fail in order to fail the whole structure? Make those pyro bolts, and the chemical energy liberated by firing them would be capable of taking the whole thing down. Not very much, I'd think, just what it would take to drop a couple of floors anywhere above the 5th story.*

*ETA: under the presumption that two floors free falling will take out all the others below, and that 5+ stories loss of horizontal bracing would render the perimeter unable to handle its imposed load at the bottom, and that the lateral pressure as debris hit bottom would be the perturbation to get the 'pencil' of the core tipping.

Major_Tom wrote:Since we all seem to be interested in collapse initiation, WTC 1, why don't we talk about it? Is this the best thread?

There are a couple of threads specifically for initiation, though it's appropriate in any discussion of collapse.

http://the911forum.freeforums.org/the-problem-of-collapse-initiation-t34.html

http://the911forum.freeforums.org/collapse-initiation-in-wtc1-t27.html

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This is a nice thread. I think we've had this discussion in circles at physorg and we didn't have a solution. I don't buy the domino theory.

Einsteen:

When you say: "I don't buy the domino theory."

That's fine with me; I'm certainly not trying to sell it!

It's just another option on offer in the "Collapse Theory Emporium" ....

einsteen wrote:This is a nice thread. I think we've had this discussion in circles at physorg and we didn't have a solution. I don't buy the domino theory.

It's not an accurate dynamic model of the towers, for sure, but it is a system with which most people have some familiarity and presents an example of self-sustaining mechanical reaction. Understanding such a system is helpful in the same way practicing arpeggios assists in playing a composition.

There aren't many examples of small energy input initiating a cascading mechanical reaction. Chemical and nuclear, yes, but mechanical? Avalanches, landslides, dominoes, and progressive collapse... am I missing any? There are contrived systems people make that are like domino chains: something rolls down a ramp and lands on a balance, which tips and strikes a match that burns through a string which releases a marble that rolls down a track, etc, etc.* I don't know what these things are called, but I take them as special cases of a more general system type which includes domino chains. Avalanches and landslides, as well, strike me as being special cases of a more general system. Toppling would seem to be in here somewhere. **

There are, then, very few general types of mechanical systems that display a cascading or self-sustaining effect, and I'm not sure they really are distinct categories. If you look at Seffen's paper, you'll see a graph depicting capacity over displacement - the initial spike of capacity until failure, where capacity drops off rapidly, then a third and final phase of rapid capacity increase tending towards infinite. Unbuckled column, buckling column, squashed column. Domino tipping, falling, coming to rest. How different are they?

Now, observing the parallels in terms of activation energy, sustaining energy, and arresting resistance, I have to wonder what else can be gleaned from study of such a system. Domino chains are relatively simple (yet quite an analytical nightmare if you look at it) so may yield some useful insights into the nature of propagation of instability. One thing that jumps out at me is the ability to 'snowball' without continual accrual of the mass of previously involved members. The peculiarities of a physical system dictate how energy can be distributed, how quickly transition from one form of energy to another can occur, and how much power (defined by energy loss per unit time) can be generated by the system at each instant.

I'm particularly absorbed by the last item, power. This is technically a result of a proper dynamic solution, not a dictum or causative factor. Nevertheless, the power-limiting nature of a domino chain seems to be one of the most elegant dynamical values to consider, perhaps most directly reflective of the geometry of the structure. While we often consider losses at the elementary level, it is a different matter to consider gains at the global level: the domino chain's instantaneous power is only limited by the amount of 'reactants' currently engaged, which can grow at least geometrically.

A pancaking floor collapse is a vertical domino chain, precisely. I think dominoes are a better model than avalanche for pancaking. Both are discrete systems fundamentally based on unit transactions, the floors being initially separated and finally layered. We see immediately from domino chains that such systems can have energy in excess of that required to sustain the reaction, even without mass accumulation beyond a certain constant amount.

This means that pancaking is a plausible scenario for a somewhat slower progressive collapse that has energy to expel debris, shatter concrete, shed the perimeters and laterally destroy most of the core. Initial energy deficit (if any is found in comparison with observation) in a pure lower block pancaking scenario can come from the upper block. If not much is needed, let the mass shedding be high and have the upper block fall off early - as it seems to have done anyway. Thus you have a collapse initiated by tilting and upper block descent but propagated in the later stages by internal debris flow, resulting in collapse front ahead of shed perimeters and standing spire, also in agreement with visual evidence.

Not saying it is the case, but surely an interesting thought.

* I saw a video of one of these things, constructed by university students in a warehouse, that perpetuated itself for about 20 minutes, as I recall. The camera followed the reaction as it progressed, only the active portions were lit. I wish I could remember the name of the university or what these Wile E. Coyote / Rube Goldberg machines are called, I'm sure it's on YouTube.

** I put toppling in the domino category. Toppling can be a single domino, tree, or antenna falling over. Or it can be like this jenga tower: http://www.youtube.com/watch?v=RdNeaSgqcFg
Wow, is all I can say.

As if the above were not long enough, a few more thoughts to add.

A common feature of all the above systems is gravity is most of the driving force, if not all. Self-sustaining, purely mechanical reactions from quasi-static initial conditions must necessarily derive the bulk of ongoing energy loss from loss of height. Strain (and even chemical, in the Wile E. Coyote machines) potential may contribute, and I do wish to examine that aspect in more detail, but first gravitational.

With near complete loss of resistance in the initiation zone and the ensuing near free fall, there is no question of overcoming the activation energy to collapse - the famous 8.4x - otherwise, it's a matter of degrees. At the actual 0.6g for WTC1, the KE at 'first impact' under this scenario would only be 0.36(8.4) = 3x the KE required - though with tilting and such that's kind of meaningless (OnEdit: I'd also say the calc is wrong, back to that caffeine thing, or lack thereof). Pretty decisive on the extreme case favoring survival, though, eh?

Take, instead, a hypothetical quasi-static descent through the first floor. In a discrete 1D model without compaction, that's the end of collapse. Impossible to even initiate in a homogenous 1D continuum, and the heterogenous case delivers anything desired by assumptions of distribution and is therefore trivial and uninteresting.

Energy per unit time available for structural compromise is one limiting factor in the energy transfer from potential to destruction, the other is the ability of the structure to absorb the immediately available energy in that manner, as opposed to favoring other energy distributions. Kinetic energy not quickly converted to buckling or fracture of load bearing members is not necessarily available later to do the same, possibly having been lost to the ever-present and proximal dissipative sinks all around.

Potential energy can be liberated at a slower rate than can be absorbed by the structure in internal degrees of freedom. Collapse can be arrested, based only on total instantaneous energy considerations; nevertheless, I think the set of circumstances that lead to an overall collapse include many categories of quasi-arrest. Like the house of cards video I analyzed... it's that domino thing again, and one must consider failure modes in which available power is sometimes leveraged like a domino pyramid to propagate collapse, at other points is available but dissipated before doing useful work in destruction.

It's unreasonable to rule out failure modes which propagate damage, or even instability, ahead of falling mass. I've argued against the idea that falling rooflines can show real accelerations greater than g, but the argument does not apply to the position of a collapse front over time.

There may be some disagreement on the definition of a specific location of instability propagation, but I can imagine propagation faster than g under most definitions. It happens a lot in the simulations I've done to date because the structures are quite rigid, more like glass than steel or plastic. Drop a rigid upper block onto a rigid lower block and the catastrophic destruction can propagate through the extent of both nearly instantaneously, sort of a Newton's cradle effect. The pieces still fall at g, or less if there are large numbers of particle collisions on the way down.

From a layman's perspective, I'm unable to yet correctly judge the peril in relying too much on certain assumptions.

Take plastic deformation. Of course, this is the failure mode of steel at the temperatures under consideration, so why question it? For one thing, there are welds with characteristics vastly different from the columns themselves. Given the actual three dimensional nature of the collapse, what do we expect to see and what is confirmed by observation? Columns in many cases were shoved aside, from glancing eccentric blows or sustained sliding contact with a horizontal force component. When this is factored in, in contrast to the 1D assumption of hinge buckling, I'd think failure can be propagated ahead of the falling mass.

A column undergoing hinge buckling is certainly limited in the force it can transmit vertically, though I'm still trying to get a full grasp on the nature of this situation, more on that later. The question is, to what extent can failure of floor connections and welds be propagated ahead of what might normally considered the collapse front, the leading edge of the debris zone? A sustained lateral force to a column, initially applied at the top and rapidly moving down the length will almost certainly cause weld and/or connection failure in advance of the actual mass front reaching the floor level. Yes, the energy is expended all the same but could result in some displacement in advance of a discrete contact or compaction-based failure event.

When I first heard of the fracture theory, without actually reading the paper or knowing the proposed mechanism, I thought the notion sounded reasonable. After reading the paper, I can understand some of the negative reactions; it wasn't what I'd envisioned at all. I do have to wonder if the baby has been thrown out with the bathwater, though. Anything that can induce damage ahead of the collapse front can potentially diminish the reserve capacity of the structure.

Strain release may be non-existent or insignificant in the other systems, but I'm not so sure it can be ignored in progressive collapse of a structure. There had been some discussions at physorg about sudden unloading at collapse initiation. I think this is a fertile area for futher examination. While some quick calculations, as I recall, apparently revealed the expected displacement at the top of the upper block would be small, I don't think effects upon the structure can therefore be immediately dismissed. One must also consider the effect of unloading on the upper block, the effect of horizontally differential unloading and, perhaps most important, the resulting stresses as the strain is rapidly redistributed about the heterogenous structure, which previously only experienced quasi-static load changes.

While the displacement is small, the effects could be catastrophic in some structures simply because of the sudden impulse provided to key members. Intuitively, I'd imagine the structural response to a step discontinuity in loading would be a sigmoid displacement curve; moreover, the unloading is not instantaneous, so there's no reason to expect significant jerk when considering the mass as a whole, but it's impossible a priori to rule out a distribution of spatial accelerations over time, i.e., a wave; reflection within the heterogeneous structure and additive interference may result in substantial peak forces beyond the local capacity in whatever direction they're applied. This has the potential to distribute damage to far-reaching areas in advance of any collapse front.