You know - there is always equilibrium at the contact point - and we have to look around to see what happens elsewhere.
No. There are equal forces. This is hardly the same as claiming there is
equilibrium.
Subject is What happened after collapse initiation? and we all seem to agree that further local failures took place. Bazant however suggests in two papers that these failures only take place in the lower structure, while the upper block remains intact during his 'crush down', but we know better than that.
Also the upper block gets damaged.
More or less, and as near as can be determined from analyses which require assumptions.
All these local failures, deformations, buckling, ripping apart, etc, absorb energy released that would slow down the destruction.
Correct. And this is where the roles of gravity and momentum becomes very important. Remember, as more of the lower section is destroyed, more mass is added to the falling section.
For the falling sectoin to stop, the building has to provide enough force to couter not only the initial moving mass, but the mass gained as is moves downwards.
If the building is incapable of providing a sufficient amount of retarding force, the falling section will accelerate, thus requiring even
more force to bring it to a stop.
Even more important is that failed parts come in contact with and rub against each other and that friction develops that absorbs big amounts of energy.
But is it enough? You seem to be asserting that it is. Please preovide calculations backing this argument up.
The structure is volume wise 95% air so the failed parts can displace in various directions and will contact each other.
Uhh... Sure.
This is why the floors and everything in between wound up compacted together.
Bazant assumes some sort of uniform density of the structure; there are no sub-parts that can fail and shift location, etc.
Bazant has apparently never heard of friction and NIST strangely does not mention it either in its report. NIST only mentions strain energy absorbing energy when parts fail.
Bazant made his assumptions, made his justifications for them, and backed them up with calculations. I'm not going to say his paper is perfect. Nothing with assumptions can be. Unfortunately, in engineering, assumptions are necessary or solutons will never be found. WHich is why engineers typically try to err on the side of caution when making calculations.
If I am recalling correctly (I could have different papers mixed up), Bazant made assumptions favouring the halting of the collapse.
I suggest that friction absorbs 10-100 times more energy than strain energy and that the destruction would be arrested after a few floors have been locally damaged.
Excellent! An assertion. I assume, since you are an engineer and well-experienced in such things that you have the calculations to back up this claim. Please provide them or I shall defer to the explanations of those who have provided such calculations.
The friction between parts in contact evidently develop reaction forces elsewhere in the structure.
Evidently these reaction forces cannot damage the structure.
Seeing as the towers were destroyed, I do not see how such conclusions are "evident". Please provide your justifications. Calculations would be nice.
Take your example - the brick on a table. You push the brick and when the pushing force exceeds the friction force between brick and table, the brick moves at constant speed due to a certain force, let's call it F.
To push the brick distance s metres requires energy F times s.
So far, so good.
Evidently force F cause an opposite reaction force of equal size in the table top, [...continued below...]
Not quite. The force
F, being applied to the brick, does not have an equal and opposite reaction on the surface of the table. If it did, the forces would be in balance and the brick would not move.
Rather, is is the force of friction (which I shall call
H) that has an equal and opposite reaction on the table.
The force of friction between the brick and the table is, of course, the perpendicular force to the contact plane (weight, in this case, which is mass x gravity) multiplied by the coefficient of friciotn between the surfaces.
H can at most be F, and if the brick is moving
must be less than F.
[...continuation...]which is transmitted (as shear) to the legs of the table, and through the legs down to the bottom of the legs and, due to friction between legs and floor, to the floor!
Ignoring the confusing of force applied to the brick and friction, this seems correct.
If the friction between table legs and floor is smaller than between the brick and the table top, pushing the brick will evidently cause the table to move, etc, etc.
Correct.
If the legs are really weak they may shear off before that due to the lateral force applied on the brick. The table collapses!
Correct.
Regardless - energy is wasted.
Energy is always being wasted. Sometimes I feel just bothering to post in the CT subforum is a waste of energy.
Your example is excellent. It shows what analysis you have to do, when applying a load on loose item on a table top. A very simple excersize!
My example was merely attemtping to illuminate what I thought was a misunderstanding between you and Mackey, the there would also have to be aforce of friction acting downwards against the lower structure in your scenario, equal to the one retarding the motion of the upper section.
Grizzly Bear has pointed out that I may have misunderstood the misunderstanding.
NIST failed to do a similar analysis with the upper block in contact with the lower structure and just assumed the lower structure would collapse. They failed to analyse what local failures developed after initiation and energies lost then. NIST further failed to analyse what happened to the locally failed parts and what displacements occured and what forces developed between these parts and energy wasted due to friction then, etc, etc. The method to do the analysis is known but NIST didn't use it. Sloppy work.
It seems some participant on this thread has intimate contacts with NIST. Let's hear from NIST!
NIST had one goal, and that goal was not to perform an in-depth analysis of the collapse.
NIST was only concerned with what happened up to collapse initiation, and then showed that once initiated, the building was of insufficient strength to arrest the collapse.
This has been pointed out to you before, so please stop harping on NIST for not doing something that wasn't part of their job.
There are other competant and knowledgeable individuals who have taken more detailed looks at collapse progression, and their findings have agreed with NIST at least insofar as saying that once started, the process was unstoppable.
Worried about that? Or you could not do it yourself? It is simple! Anybody can do my experiment.
Except, it would seem, the individual who designed it, uses it as a principle argument, and figures children should do it. And who has so far been unable to provde any calculations validating the model as an accurate scale representation of WTC 1 or 2.
After all, it only costs a few hundred dollars, and involves fire and dangerous substances. Perfect for children!
Do you perhaps mean adolescents (14ish-18ish), Hiewa? "Kids", in the Western world, is generally assumed to mean young children. Under the age of 14 or so.
Do you really think 9-year-olds should be attempting your experiment?