Originally posted by metamars
Calladine and English are meaningless in this instance, as they test they preformed was on steel plate, do to the geometry of the steel in the world trade center and its ability to form fulcrums in the structure and tear the weld joints Calladine and English do not apply.
Intuitively, a steel plate is so many steels rods (square-ish cross section), sitting right next to each other. I expect the relationship to be strictly linear (wrt the weight of the apparatus), or failing that, calling for truly minor corrections. Presumably, somebody could show this rigorously.
Even when dealing with (non-hollow) square rods, you are still not mimicking the actual structure of the WTC columns,
exactly. And geometry does matter, as the CE paper itself, makes clear.
When you write
Exactly my point they are not steel flat plate, I work with steel all the time I have to take this stuff into consideration. The shape of the material drastically effects the way it is effected by stress. Before you can use Calladine and English, to correct Bazant, you must first correct Calladine and English for the shape of the materials in question. I believe that Bazant wrote a paper or an editorial on it some time back with the calculations to correct mechanical stress analysis for different shapes. IN a journal of fracture mechanics , though I am not sure when it was published or what volume it is in. I will try to find it though.
you are actually re-iterating a suggestion I made elsewhere, viz., that the Calladine and English apparatus and their Type II structure be modified to be more relevant to the WTC.
However, your claim is that the CE results and the WTC structure are
so different that no useful corrections to BZ and Greening can occur strikes me as incredible. However, even that claim, were it to be true, would be well served with a mathematical demonstration.
NO it most certianly has not it is just that no one else has come up with a better model.
In light of CE, this statement (if true) strikes me as a crying shame. Happily, it's a situation that I believe is easily rectifiable.
I agree there are minor corrections to Bazant but not from Calladine and English, as they are not testing in any comparable way the structure or the integrity of hollow steel columns that work on in a different manor that flat plate steel.
See above.
Then you do not understand Cherepnov's fracture wave paper. Columns acquire their strength from leverage, the ability to resist Buckling flat plate is easy to bend but Columns are not. Columns actually absorb more impact energy than flat plate which will dissipate it though oscillations faster. That is why Calladine and English are meaningless you would first have to correct Calladine and English for hollow square Columns before it would have relevancy.
? I suppose, then, by leverage you mean second moment of inertia?
Since "columns absorb more impact energy than flat plate", perhaps somebody can figure out
how much?, and furthermore, what is the relationship wrt speed of impact? At the end of the day, I'd like to see a quantitative answer, anyway. Also, I believe (though I'm not sure) that Calladine and English was a seminal paper. It's almost natural to expect that somebody has extended their work using I-beams and square and box columns.
I'm skeptical that you know this to be the case for dynamic impacts. I suspect that you are assuming that energy figures determined under quasi-static compression has the same relationship in the dynamic case of impacts.
In any event, if a tall thin piece of metal absorbs X amount of energy in a given impact scenario,
and buckles but does not break, it has demonstrated the ability to absorb
all of the kinetic energy that impacted upon it.
If it were true that a tall thin piece of metal, of the same weight and height but with with a hollow box cross section was
capable of absorbing even more energy, I think that would be irrelevant, as the non-hollow case would constitute an upper bound of energy that was actually needed to absorb the blow. Remember, the bottom of the apparatus is fixed. There will be some losses of energy through the bottom, but I believe they're negligible.
Think of the CE apparatus as Las Vegas. What happens in Las Vegas, stays in Las Vegas!
BTW, one of the reasons I've called for expanded CE experiments, is because even in CE, the bottom of the apparatus is essentially fixed. This matches the (unstated) BZ assumption that the topmost floor is sitting atop a perfectly rigid base. (Until the collapse front descends to the next floor.)
In real life, though, the columns of any given floor are likely to be sitting atop identical, or very similar, other columns. There is no particularly good reason to presume that the bottoms of the columns of the impacted floor must "sit and wait", so to speak, while their respective columns sections are getting crushed.
In short, I expect the most reasonable elaborations of CE to the WTC scenario to favor survival, in an axial strike.
But, one thing at a time.