Ron, ask and ye shall receive.
I'll make this summary general and unreferenced in the interest of time. Real Life is interceding.
First of all, "have I changed my mind about anything?" The answer is no, not yet at least; however I have thought quite a bit more about this subject than ever before, and there are some interesting wrinkles. I am, of course, referring to the true mass of the WTC Towers. I summarize the discussion so far as follows:
1. What is the true mass of a WTC tower, pre-collapse?
Most sources cite a mass between 400,000 and 500,000 tons, assumed to be "short tons," but on further inspection it is not clear how firm an estimate this is. I will assume this answer is at best soft to 20%. Thus far no detailed analysis of the tower mass has been found, with the most detailed being an unsigned, unverified, and incomplete analysis found linked to a scurrilous pile of anti-semitism -- but the calculations themselves appear at least useful for discussion.
Poster Gregory Urich has produced his calculation estimating a vastly lower mass of approximately 279,000 tons. Because this number conflicts with the established figures, the burden of proof lies upon him, and he has appeared here to defend his conclusions accordingly.
Poster Gregory Urich has produced his calculation estimating a vastly lower mass of approximately 279,000 tons. Because this number conflicts with the established figures, the burden of proof lies upon him, and he has appeared here to defend his conclusions accordingly.
2. Can we answer this question based on how much rubble was retrieved?
Probably, but there are still some loose ends. The figure of debris taken to Fresh Kills also has some softness, but is estimated at 1.6 million tons. However, this total also includes other structures as well, and thus far I have seen nothing more than a back-of-envelope estimate about any of them.
The more important question raised, however, is just what do we count in a WTC tower, anyway? In particular, do we consider the basement? The parking garage? Where do we draw the line? It should be clear that a substantial fraction of the total WTC mass was in the sublevels, so should we count that or not?
This question remains open, and the standard literature references do not specify either, making a direct comparison less definite. To avoid confusion, I would suggest we all re-declare our definition of exactly what mass we are referring to.
The more important question raised, however, is just what do we count in a WTC tower, anyway? In particular, do we consider the basement? The parking garage? Where do we draw the line? It should be clear that a substantial fraction of the total WTC mass was in the sublevels, so should we count that or not?
This question remains open, and the standard literature references do not specify either, making a direct comparison less definite. To avoid confusion, I would suggest we all re-declare our definition of exactly what mass we are referring to.
3. Does Gregory Urich correctly account for the vertical distribution of structural steel?
It is correct to say that the steel in the WTC Towers diminished with height; in particular the core columns started slimming in profile as low as Floor 7, and there was much more cross-bracing in the bottom floors than anywhere above. On the other hand, perimeter columns actually triple in total mass above Floor 7, due to the "column trees," and maintain that density for some height, using lower grades of steel rather than diminishing in cross-section, until very high in the structure when they too taper off.
It is not completely clear that Mr. Urich has adequately handled this feature, and several posters question his assumptions here. Personally, I find his assumptions reasonable, if simplified, and his conclusion plausible.
It is not completely clear that Mr. Urich has adequately handled this feature, and several posters question his assumptions here. Personally, I find his assumptions reasonable, if simplified, and his conclusion plausible.
4. Does Mr. Urich correctly handle superimposed dead loads?
In my opinion, this is a definite "no." The superimposed dead loads refer to all material that is permanent, part of the building rather than tenant-defined, but non-structural in nature. In NIST NCSTAR1-1, these loads are specified as approximately 55 psf outside the core and 75 psf inside the core on mechanical floors, and NIST NCSTAR1-2A lists loads outside the core for the other floors as 12.5 psf, loads inside the core as 29 to 49 psf depending on usage.
In Mr. Urich's original paper, he only applies SDL for areas outside the core, and applies a figure of 8 pounds per square foot.
In arguing his choices for the core, Mr. Urich points to the large amounts of empty space left by the elevators. While this is true, figures such as 1-4 in NIST NCSTAR1-2A show the empty space to be on the order of 10% of the core area.
In Mr. Urich's original paper, he only applies SDL for areas outside the core, and applies a figure of 8 pounds per square foot.
In arguing his choices for the core, Mr. Urich points to the large amounts of empty space left by the elevators. While this is true, figures such as 1-4 in NIST NCSTAR1-2A show the empty space to be on the order of 10% of the core area.
5. Does Mr. Urich correctly handle live loads?
This is open for some debate. We are agreed on how much load the Towers could handle; instead, it comes down to how much stuff we believe it did handle.
Roughly speaking, the design live load is about 100 psf, with some reduction figured due to live load reduction practices, and some additions in high-traffic areas. Mr. Urich and I agree that the actual strength of the structure was tested to be much higher than this, with an additional safety factor of ~ 2.5. The issue is just how close we think the design load was to the actual load experienced at time of impact.
Mr. Urich is positing that the actual load was about 25% of the design load, and he has assembled some simple calculations explaining his basis. I and several others feel his calculations are serious underestimates, and besides do not account for the variety of functions carried out in the Towers. Given the enormous real safety factor that would result if the design load was so heavily padded, the fact that surveys were regularly carried out to make sure the Towers weren't overloaded, and the Towers were occasionally modified in places to accomodate heavier loads, I believe the actual load was much higher, perhaps 75% or more of the design load.
This is difficult to prove either way without a far more detailed look at the Tower contents. Furthermore, this factor accounts for perhaps 170,000 tons, which is by itself enough to close much of the argument.
Roughly speaking, the design live load is about 100 psf, with some reduction figured due to live load reduction practices, and some additions in high-traffic areas. Mr. Urich and I agree that the actual strength of the structure was tested to be much higher than this, with an additional safety factor of ~ 2.5. The issue is just how close we think the design load was to the actual load experienced at time of impact.
Mr. Urich is positing that the actual load was about 25% of the design load, and he has assembled some simple calculations explaining his basis. I and several others feel his calculations are serious underestimates, and besides do not account for the variety of functions carried out in the Towers. Given the enormous real safety factor that would result if the design load was so heavily padded, the fact that surveys were regularly carried out to make sure the Towers weren't overloaded, and the Towers were occasionally modified in places to accomodate heavier loads, I believe the actual load was much higher, perhaps 75% or more of the design load.
This is difficult to prove either way without a far more detailed look at the Tower contents. Furthermore, this factor accounts for perhaps 170,000 tons, which is by itself enough to close much of the argument.
6. Is the mass of the Towers significant in estimating whether it could experience global collapse, as well as the timing of that collapse?
Mr. Urich has answered both in the affirmative without strong support. I oppose both. The work of Dr. Bazant demonstrates the energy surplus after first floor collapse to be so much higher than needed to trigger a progressive collapse that a mere factor of two will not change the result.
As far as the speed of collapse is concerned, Dr. Greening has shown that the speed of collapse is not a strong function of floor energy, and by inference, it is not a strong function of floor mass, either. This is intuitively seen because it is momentum that principally governs the collapse time, and if the Towers are lighter than thought, both impactors and impacted floors diminish in mass and therefore inertia, and we get the same situation as we had before, from a timing perspective.
As far as the speed of collapse is concerned, Dr. Greening has shown that the speed of collapse is not a strong function of floor energy, and by inference, it is not a strong function of floor mass, either. This is intuitively seen because it is momentum that principally governs the collapse time, and if the Towers are lighter than thought, both impactors and impacted floors diminish in mass and therefore inertia, and we get the same situation as we had before, from a timing perspective.
7. Were the Towers intended to survive a high-speed airliner impact?
No. This argument is a non-starter. NIST explored this in depth and could find no trace of a defensible calculation backing up the assertion that the Towers would survive the full phenomenology of such an impact. It is difficult to imagine how, in the mid-1960's, engineers could arrive at any firm conclusion without massive overdesign given the tools available at the time.
Even if there was such an assertion made, it does not change the facts on the ground. If anyone, including the designers, had made such a claim, their claim would be no stronger than the work they put into it. That work does not exist and has never surfaced.
The only claim that can be made is this: Whoever said the Towers would stand was wrong. Their assertions, even if real, are not evidence that the Towers should have survived; this is merely an appeal to authority.
Even if there was such an assertion made, it does not change the facts on the ground. If anyone, including the designers, had made such a claim, their claim would be no stronger than the work they put into it. That work does not exist and has never surfaced.
The only claim that can be made is this: Whoever said the Towers would stand was wrong. Their assertions, even if real, are not evidence that the Towers should have survived; this is merely an appeal to authority.
I hope that clarifies things.
I've stated it before, and I'll say it again: I don't know the true Tower mass. Getting a rigorous estimate is a hard problem. At this point I'd believe any figure between, oh, say 380,000 tons and 550,000 tons. But I still have problems with Mr. Urich's answer, and his methods.
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