The 9/11 Forum

David B. Benson wrote:OneWhiteEye --- B&L show little inital crush-up, not none at all. Since it is so small, the argument is that the crush-down only in B&V is a valid approximation.

Yes, but what was it, 1% of a story height? 37mm, I guess I can see it without a microscope, but it's still not knee-high. No failure of the upper story from that - is there? That's what 4cm of crush means, if it were a story it would be > 3m. So, in a discrete story-by-story sense, it's an exclusive crush-down.

Maybe, if the upper block were separated from the lower by a clean laser slice in a perfect horizontal plane, then carefully lifted to a story height and dropped, the result would hold. Even then, I'm not so sure. I don't think real structures behave like that in any circumstance. I'd liken it to getting a pencil to stand on end - theoretically possible, never happens.

Edit: just to forestall any objection that I'm confusing simplified model with reality, let me emphasize that I'm not.

OneWhiteEye wrote:When, exactly, did varying strength enter the picture in your mind? After you proclaimed my earlier simulations invalid? Why is greater connection strength below now a neccessity to produce your expected results? Do you still claim the previous sims are invalid (yes/no will suffice)?

Evidently from day one I got interested in this matter. Stronger elements in a structure always destroy weaker elements in a collision contact, e.g. horizontal stringers in the side of ship is good collision protection like a bumper on a car. But normally you don't fit them for other reasons. I have studied plenty of (ship) structures under various dynamic, short-lived impact loads (both ship/ship collisions and ship/wave contacts) and what happens due to them. The energy applied is converted into pressure/force and displace the adjacent elements, so you have to start there. What happens to the energy? If failures occur (plenty energy consumed) and the interface changes, you have to see what happens then. In ship/wave collisions the ship structure may fail and the water will splash! In ship/ship collisions both structures fail. I just apply the same method to WTC 1.

Result is that there is too little energy available to initiate, e.g. total destruction. Read my paper! Energy applied can only elastically deform the total structure C+A and produce some local failures at contact. And one-way crush down of big A by little C is simply not possible, as A and C have identical structures apart from A columns getting stronger lower down; Strong elements/columns in A destroy the weak elements/floors in C and vice versa and, as I see it, collapse arrest follows at once.

But subject is one-way Crush-down models or sims. Evidently you must then consider that columns get much stronger and weaker away from the contact interface, &c. Your sims are simple solid mechanics sims - masses colliding in a gravity field - and the connections between these masses do not seem realistic.

Depending on energy input I expect the following of any model/sims:

1. Little energy input E1! Both sections A and C deform elastically and there will be a bounce.
2. A little higher energy input E2! Both sections A and C deform elastically and there are very local plastic deformations of elements in contact followed by a bounce.
3. Medium energy input E3! Both sections A and C deform elastically and strong elements destroy weak elements in both A and C. Interface changes. Arrest follows.
4. Medium energy input E4! As 3 but for some reason strong elements are affected, e.g. C columns fail! Then C may drop off, &c.
5. High energy input E5! All adjacent elements in contact (weak and strong) fail at one connection in both A and C. Interface changes. Elements get entangled into one another. Friction must be considered. C may drop off, &c.
6. Energy input E6 for Crush-down. It is not clear how that can be done!

From above it is clear that if 5 takes place, it also includes all effects of 1-4.

So any model/sims must be tested with various energy inputs E1-E6 to ensure that 1 and 3 actually takes place when 4-6 follow. You will also get a good feel how strong the model is to resist various energy inputs.

Some people will argue that in, e.g. the E6 case, the energy is applied so fast that events 1-3 do not really happen! So model is to be adjusted for, e.g. drop height 3.7 m and associated contact velocity due to gravity.

David B. Benson wrote:In theory, there is no difference between theory and practice.
In practice, there is.

So in theory it is possible that C crushes A, but in practice it is not possible. Or what are you saying? Any progress to report on your one-way Crush-down models. Has it crushed anything yet?

What always amazes me, when there is a technical problem, how many experts pop up with solutions. Take topic! Let's build a crush-down model! There are plenty of proposals and none crushes anything. Why is that?
For once, crush is not defined. Let's define it, e.g. one crush is to rip an element into two pieces.
What kind of element? Let's say a joint of some kind (between a floor and a column?).
How do we do that? We shear it off! OK! How? And how much energy is required for that.
Where does the energy come from? Gravity! OK, a guillotine is a nice French invention to cut things - crush - them in two parts using gravity.
But can a guillotine be used for multiple crushes, etc, etc.?
No, we start again. What shall crush what? Aha, an upper part C of some kind shall crush some lower part A of some kind. What part? A building! OK, a part C of building shall crush another part A of same building. C is 1/10 A. C is dropped on A by gravity and A is crushed say 97 times into 97 pieces.

So how much energy is required to crush A 97 times in 97 pieces?

That should be easy to calculate!

Start to calculate how much energy is required to crush just one piece of A. Say it is X Joule. If it is less than X J, there is no crush - just a bounce.

Now, where does the energy come from? Yes, part C is dropped on A! That produces energy to crush one piece of A. Good!

Next calculate how much energy is required to crush two pieces of A. Is it 2X J ? Or 1.5 X J, Or still only 1 X J? In the latter case the crush-down goes by itself.

And so on! It is quite easy!

How much energy is required to crush A into 97 pieces? 97X J or only 1X J? Or somewhere in between. Maybe Y J ?

A good engineer can calculate how much energy is required to crush A into 97 pieces!

Good. So now we know how much energy Y we must apply to crush A into 97 pieces.

Next problem! Can part C apply Y J by gravity. Of course - it is just a question of drop height h!

Now, a serious problem! Can part C apply Y J without destroying itself?

That's an engineering problem. Structural engineering problem!

OK, of course a good engineer can produce a part C that can apply Y J in a collision without damaging itself (or just negligibly). So part C becomes very strong (rigid!).

But ... now another problem. Part A shall be similar to part C! But if part A also becomes very strong (rigid), the amount of energy to crush A becomes enormous.

And that's the background of the Björkman Axiom of structures:

You cannot one-way crush an isotropic or composite 3-D structure part A by a part C of itself (C = 1/10 A) by dropping part C on part A using gravity. Part C either bounces on part A or gets damaged in contact with part A and is stopped by part A that is also damaged a little. It is quite basic and all due to gravity. Materials, size and particulars of the elements of the structure part A doesn't matter the least. Part C of part A cannot destroy part A.

Heiwa wrote:

OneWhiteEye wrote: Do you still claim the previous sims are invalid (yes/no will suffice)? I bold this as a subtle reminder

Stronger elements in a structure always destroy weaker elements in a collision contact...

Agreed. Of course. But it does not follow that the weaker elements cannot destroy the stronger elements. Ignoring for a moment the precise definition of destroy, this can and does happen. It is not the norm of everyday experience because the weaker part must impart sufficient energy to destroy the larger. I know you're aware of some examples - foam/shuttle comes to mind. The key is in understanding how and why it can happen, then see if that fits the situation being considered.

But subject is one-way Crush-down models or sims. Evidently you must then consider that columns get much stronger and weaker away from the contact interface, &c. Your sims are simple solid mechanics sims - masses colliding in a gravity field - and the connections between these masses do not seem realistic.

It IS masses colliding in a gravity field, for sure. Because of that, when properly configured, it represents a many-body solution applying the most elementary classical mechanics. Buyer beware! But it does show that a predominant crush-down can be obtained using an extremely simplified model which obeys physical laws, and it also shows a smaller structure can destroy a larger one. I made my disclaimers up front - it does not (necessarily) represent any real physical system. That doesn't mean it's useless.

So any model/sims must be tested with various energy inputs E1-E6 to ensure that 1 and 3 actually takes place when 4-6 follow. You will also get a good feel how strong the model is to resist various energy inputs.

I intend to explore a wide range of structures and parametric input. You've seen a few. Ignore the lessons they illustrate at your own peril, else you will not "get a good feel how strong the model is to resist various energy inputs."

Heiwa wrote:For once, crush is not defined. Let's define it, e.g. one crush is to rip an element into two pieces.

In the past, one of your objections was that discretely breaking a single connection between two elements did NOT constitute crushing. I'm glad you've gotten past that idea. That makes it possible to move forward to more complicated cases that represent the common definition of crushing, and then perhaps later we can discuss whether these sorts of crushing accurately represent the mechanics of building collapse. In the meantime, I do not distinguish between propagation of a crushing front and propagation of failure of any sort.

Start to calculate how much energy is required to crush just one piece of A. Say it is X Joule. If it is less than X J, there is no crush - just a bounce.

Possibly some plastic deformation, as well. Leading to eccentric and universally sub-optimal loading, which can lead to further failure. Really, now, must I supply a justification for the preceding statement?

Now, a serious problem! Can part C apply Y J without destroying itself?

A lot of discussion has taken place questioning the survival of the upper block of WTC1, which is a separate issue from "Can part C apply Y J when not intact?"

David B. Benson wrote:In theory, there is no difference between theory and practice.
In practice, there is.

That's nice! Now, there's an axiom.

Hey, while we're waxing philosophical, I have a question and some comments:

According to the Akaike Information Criterion, together with the preponderance of astronomical observables prior to 1900, which would be preferred, if either: general theory of relativity or Newtonian mechanics?

GR is very compact and elegant, but unnecessary except for high precision or extreme conditions. How can such competing models be evaluated for correctness without sufficient resolution AND incidence of occurrence in the observables?

To the extent that evaluation depends on clarity of observables, conclusions reached without such clarity are subject to revision upon collection of new observations. Processes to aid in model selection should never introduce unwarranted inertia into this most important element of forward progress. Preference in fitness criteria should never shunt the collection of observables which might later change the evaluation.

Nature does not universally prefer parsimony. Human scientists do. Hmm...

OneWhiteEye wrote: Stronger elements in a structure always destroy weaker elements in a collision contact ...

Agreed. Of course. But it does not follow that the weaker elements cannot destroy the stronger elements.

The weaker elements destroying the stronger elements ... in a collision contact???

You mean twenty ants crushing ten elephants?

Pls clarify. I do not follow!

In meantime I have done a full scale model - only 111 elements, 410.7 meters tall - very big - but upper 14 elements section C has still problems to crush down the 97 elements section A. http://heiwaco.tripod.com/mac5.htm .

I can scale it up 10/1 and the model becomes 4107 m tall - but how to crush it?

OneWhiteEye --- I dunno. Precession of Mercury was already inadequately explained by Newtonian gravity. Since Newtonian gravity is a special case of GR its not immediately clear to me how to apply AIC.

Heiwa wrote:The weaker elements destroying the stronger elements ... in a collision contact???

Yes.

You mean twenty ants crushing ten elephants?

No.

Pls clarify. I do not follow!

Intuitively, I know that twenty ants will not crush ten elephants. If the question were changed to:

You mean twenty ants destroying ten elephants?

I can't rely on my intuition to answer it. I believe that, at sufficient relative velocity (say 0.9999c) in a vaccum, twenty ants can possess sufficient kinetic energy to vaporize ten elephants; whether or not the KE would be dissipated in that fashion in any given collision, I cannot say. I suspect the first elephant in a line would fare the best.

In meantime I have done a full scale model - only 111 elements, 410.7 meters tall - very big - but upper 14 elements section C has still problems to crush down the 97 elements section A. http://heiwaco.tripod.com/mac5.htm .

I'll look it over.

David B. Benson wrote:OneWhiteEye --- I dunno. Precession of Mercury was already inadequately explained by Newtonian gravity.

Yes, I chose the time frame because, to my knowledge, perihelion precession of Mercury was the only astronomical observable available not adequately covered by classical mechanics. GR came around at a time when not much was wanting in celestial mechanics. It is only because of the precision of measurement inherent in astronomy that an otherwise miniscule discrepancy of 43 arc-seconds demanded an explanation.

http://www.mathpages.com/rr/s6-02/6-02.htm

More recently, efforts have been made to explain some or all of Mercury's precession by oblateness in the shape of the sun. In 1966 Dicke and Goldenberg reported that the sun's polar axis is shorter than its equatorial axes by about 50 parts per million. If true that would account for 3.4" per century, so the unexplained part would be only 39.6", significantly different from GR's prediction of 43". The Brans-Dicke theory of gravity can account for 39.6" precisely by adjusting a free parameter of the theory.

This effort was erroneous, but it is suggestive of how additional information could have invalidated GR, since GR has no latitude for this discrepancy.

Since Newtonian gravity is a special case of GR its not immediately clear to me how to apply AIC.

I'm fascinated by things like AIC and Schwarz criterion. Very, very interesting from a conceptual standpoint. However, the first thing that concerns me is the manner in which penalty for parameters are assigned. Notably, there's a difference between the two methods. This indicates a degree of subjectivity, or at least well-defined weighting based on vaguely defined meta-criteria, as opposed to derivation from first principles in accordance with axioms of foundation. The second thing that concerns me is applicability to real-world situations where the distributions may not conform precisely to the assumptions of the method.

The third issue is more of a question than a concern. How exactly does one count parameters in the general case?

H1: y = a0 + a1*x
H2: y = a0 + a1*x + a2*x^2

H1 is a special case of H2. For small x, or small dx, second-order resolution is required to discriminate. Thus, a set of observations below a certain resolution or spanning only a limited range may not allow one to distinguish between the two hypotheses. To automatically assign penalties - and their specific weight - for additional parameters without enfolding the notion of dataset dependence on discrimination seems... naive? Not in the stupid way, in the mathematical sense.

To rephrase, the situation between data and analysis is obviously reflexive, but to what degree do these sorts of metatheories account for that? There seems to be an implicit notion of "if all else is equal" but when is that ever the case in practice?

OneWhiteEye wrote:

psikeyhackr wrote:But it has just occurred to me what else could be used for falling masses.

HARD DISK DRIVES!

Good idea.

What to use as crushable supports that would still be strong enough for the static load though?

The cardboard tubes from toilet tissue rolls. Cut them down to one inch in height. Varying the number of one inch tubes between the drives would vary the stength at each level. It would be more realistic than the toothpicks in the dowel since the stack could be deliberately made weaker going up to support the reduced weight of fewer drives. So 22 drives would be less than 44 inches tall.

psik

psikeyhackr wrote:The cardboard tubes from toilet tissue rolls.

Nice! In some respects, it's beautiful. Start collecting now; even if your proclivity is towards voluminous 'output', it might take awhile. On the other hand, if you have more than two kids, the collection could grow quite quickly.

Cut them down to one inch in height.

Won't the height be dictated by the masses of the drives and unit energy to crush the tubes (which, in turn, is a not-intuitively-obvious function of the tube height)? That is, to get a non-trivial result, i.e. avoid immediate arrest.

I hope you don't see me as trying to dump water on your parade. Quite the opposite. I think it's an excellent exercise, I wish it success and am very interested in the outcome. I mean, the toothpicks were pretty cool, already.

OneWhiteEye --- BIC, aka Schwartz Information Criterion, is named that because Schwartz gave a Bayesian reason for adopting it. I haven't studied AIC enough to understand the reasoning, just enough to know that AIC does not penalize extra parameters anywhere nearly as strongly as BIC. (Thre is a whole industry of producing still more ICs, with reasons for each...)

These I can do:

Code: Select all

H1: y = a0 + a1*x
H2: y = a0 + a1*x + a2*x^2

H1 has two and H2 has three parameters. These are data D and residuals for best fitting parameters for each of H1 and H2. The residuals and plugged into the AIC (or BIC) forulae and the difference is used to determine model equivalence or inequivalence. If the delta-AIC is small, less than 5, the models are equivalent. If the delta-AIC is large, greater than 10, the models are not equivalent; use the model with the smallest AIC value. If in between then more data is required to settle the matter.