Dr. Greening,
I raised some concerns about your derivation
here. Perhaps you missed them or got distracted by the antics of Ace, our lovable resident jackanape, but I think you should take a look. Let me explain again using your latest:
My discussion of the WTC collapse initiation may be simple, but it’s based on the NIST Report. NIST’s key statement concerning the WTC collapse-initiating event, is:
The change in potential energy due to the downward movement of
building mass above the buckled columns exceeded the strain energy
that could be absorbed by the structure. Global collapse then ensued
As I said before, I think NIST is talking about the second and successive collapses here,
not the first floor. I'll make this clear below.
The mass specific elastic strain energy capacity of structural steel is 57 J/kg. If we take one floor as the minimum size of the impact damage zone for each Tower, and note that the mass of structural steel on one floor is 900,000 kg, the elastic strain energy capacity of one WTC floor is 51.3 MJ.
As before, the strain energy capacity of the initial collapse floor is lessened by both (a) heating of the steel and (b) damage from the aircraft impact. You're still overestimating the initial collapse energy threshold.
But we also need to evaluate the plastic strain energy dissipated by the buckling of columns in the damage zone of the towers. This may be estimated from the area under a load vs. vertical displacement curve for a representative WTC column.
... An estimate of the vertical displacement to failure of a column is needed to evaluate the plastic buckling. Inspection of NIST’s load displacement curves for a WTC tower show that a 0.3 m lowering within the elastic response of the core columns accounts for about 50 MJ – a conclusion that is consistent with my estimate of 51.3 MJ for the elastic strain energy for one floor. The vertical displacement due to plastic deformation of a single column is about 1 meter, from which I estimate the energy for the buckling of the core columns on one floor to be 284 MJ. And please note that this calculation is derived from data in the NIST Report
No.
You're assuming that all of the displacement that matters is vertical in nature. It's simply not true. Lateral strain, caused by heating and sagging, is also critically important.
Because you're only counting vertical displacement to estimate the strain energy accumulating in the collapse floor, you've underestimated it.
And like I mentioned before, this is why you get answers that don't agree for WTC 1 and WTC 2 -- when you plug in the estimated vertical displacement, you get failure energies that, assuming all floors are created equal, should match. But they don't, they're about a factor of six apart.
If we take into account that WTC 1 was damaged much more significantly than WTC 2 by the initial impact, and use the total strain energy rather than the vertical creep (which favors WTC 2 since it stood longer, which you interpret as meaning more vertical descent and thus more gravitational potential energy loss), you won't have this mismatch. But you also will probably find yourself agreeing with NIST.
See, what you've done here is to refute the "pancake model" of collapse initiation. In that model, the column strain is purely vertical, and crush-down of the upper block probably is the dominant factor. As you've argued, effectively, that theory doesn't hold up once we put numbers to it.
However, NIST already knows that, and they've already abandoned the "pancake model" -- at least for
the first floor. Once the collapse gets moving and builds up momentum, the "pancake" is probably not a bad guess, but it's not why the first floor failed. There's that confusion with first floor vs. second and following again.
The
NIST FAQ explains, and photographs clearly demonstrate, that
horizontal bowing of the perimeter columns was a key feature of the collapse. This horizontal bowing does not appear in your derivation.
NIST FAQ said:
Instead, the NIST investigation showed conclusively that the failure of the inwardly bowed perimeter columns initiated collapse and that the occurrence of this inward bowing required the sagging floors to remain connected to the columns and pull the columns inwards. Thus, the floors did not fail progressively to cause a pancaking phenomenon.
Therefore, I cannot accept your conclusions. I don't agree with your model of the situation, and I require a more accurate accounting of energy and strain. I'm still satisfied with the NIST conclusion.
Regarding NIST's conduct, however... I haven't tried to speak to them directly. It is a shame that you've been given the brush-off. I've seen this in my own agency (NASA, whom I am not speaking for in any capacity, all opinions mine alone) and it's frustrating to no end. Particularly when lives are literally at stake. Try giving the
Columbia Accident Investigation Report a read sometimes... lost opportunity abounds, as it does in virtually any large bureaucracy.
This is one of the reasons I participate in the discussions here. I remain indebted to you for your questions and insights, even if we disagree on some of the findings.
choose your "barking mad measurement"):
CFist confirmation bias at its finest.