Re: Is there any way to cure a truther?
See lads, that's how you rise to a challenge
Thanks for the kind characterization.
It should be stated, though tipping my hand, that every now and again I put something out there that I know better... just to see who refutes it and how, if at all. You are the first to call me on this. It kinda helps weed out who knows their sh*t and who doesn't. I find it just as telling who didn't call me on it.
However, I'm not retracting the statement as a whole, just it's over the top generalization.
That's enough for me to say that boring discussion is not that helpful here, and may contain little new of interest for you.
I should also say that I reject Bazant, et al theory of progressive collapse mechanics almost entirely.
I think there's a little wheat in there amongst the chaff. More detail to follow.
The crush down crush up phases are utterly hysterical.
Yes. As a narrative, pure nonsense. As a highly contrived scenario within the narrow confines of his model, it's barely reasonable to present it even as a theoretical oddity, though technically correct.
I spent some time trying to figure out what was up with that, and it's not too easy to condense, but here goes: there is a
very narrow solution space within the framework of
his model which does indeed produce one-way crush down. However, the vast majority of (realistic) parametric input in a two degree of freedom solution gives mixed crush direction or even exclusive crush UP; Bazant chose conditions which supported his assertion of one way crush down and (IMO) abandoned rational and objective principles for grudge ****ing.
Bear in mind this is a very simple model, and when we are talking about Bazant, we are NOT talking about the towers. Having said that, read on, I think there's some useful mechanical insight to be gleaned from his treatment.
Plus, anecdotally, I've broken enough stuff to know that with sufficient mass or velocity, an object under gravity alone can break through a point of resistance, seemingly as though there is nothing there. However, when there are successive points of resistance, especially 90 of them, each built to withstand more mass than is available during the collapse due to debris outside the footprint of the buildings, complete global collapse is very unlikely. So the only real variable is how much did the effective mass increase with it's velocity? Am I wrong? Are there other forces being added other than gravity induced velocity?
Gravity is the only downwardly directed force. There's only one net upward force under the label
resistive force, which derives from multiple sources. The primary two are structural resistance and momentum exchange between the upper portion in motion and the stationary structure below. It is useful to consider each in isolation even though both are present because the forces are simply additive.
In order for an existing collapse to arrest, the kinetic energy dissipated per unit length of descent must exceed the potential energy change in the corresponding distance - at a minimum. An equivalent statement is that the average resistive force must be greater than the static load of the moving mass. Then the point of arrest is determined by the initial velocity and material properties (including spatial distribution) which dictate the actual resistive force over time. Most everyday structures dissipate far more energy in crushing than is lost in a descent through that same height, therefore have a propensity for arrest.
The question is, can steel columns display the opposite, contrary to intuition? Bazant says yes, and the reasoning is solid. Toothpaste would probably do a better job at slowing collapse, though incapable of supporting the static load and thus incapable of arresting collapse.
It's important here to distinguish between the model and the numbers which are plugged into the model. I hate to have to cover objections in advance, but I can see Tony taking exception to the 'correctness' of Bazant but, for the most part, he has quibbled about the
numbers which he plugs into essentially the same model. I'm not talking about numbers and have no interest in that - just general principles.
There are two competing continuum models, Bazant and Seffen, and they are not the same. However, the difference is quite esoteric and the results differ by showing convergence on g/3 and g/2, respectively. That's kinda big, in one way, but it's not a shakeout between arrest and not. I'm talking about the equations of motion for material accretion, which are essentially the inverse of the rocket equation for thrust. This is a sound approach regardless of the difference between the two particular models, and there are solutions which lead to progressive collapse.
Both account for structural resistance and momentum conservation (contrary to popular belief). It is in fact the difference in how the momentum conservation is treated which distiguishes their approaches. Bazant's model is non-conservative (inelastic) and Seffen's conservative, which explains the greater acceleration of Seffen's model. Obviously, they can't both be right, but the distinction is too fine for our discussion. There's nothing wrong with the mechanics.
Do these models indicate the towers are subject to progressive collapse? Yes, but that is first and foremost a question of applicability and I say the models are inapplicable, so the result is of little interest for that problem. Then, and only then, should any consideration of plugging in numbers arise. Again, my opinion is no, that's tilting at windmills. If the model is inapplicable, its utility is either unknown or known to be poor or useless. Plugging in 'better' numbers is folly. You can explore (approximately) the entire solution space in an afternoon with less than 100 lines of code.
