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The second error made by Dr. Bazant is his failure to take account of the factor of safety
designed into the towers' construction. He makes no mention whatsoever of this crucial
design parameter. This failure leads to a major underestimation of the ability of the
columns to resist the downward acting forces.
The effect of this error by Dr. Bazant is an error in his ratio of energies. If this is adjusted
to take account of a factor of safety of 4 the ratio is reduced from his value of 8.4 to 2.1.
It must also be noted that the ratio mentioned by Dr. Bazant is relevant only to the first
collision after a freefall of one storey. He is specifically dealing with a situation where
the energy of the fall through two storeys is resisted by the columns of one storey. The
continuation of the collapse would not have these conditions but rather have the fall of
one storey resisted by the columns of one storey. Without the period of uncontested
freefall the ratio of energies would be reduced for the remaining duration of the collapse
from Dr. Bazant's figure of 8.4 to 1.05.
Since Dr. Bazant has stated that his figure of 8.4 corresponds with the observed collapse
times of the towers, we can easily reverse this logic to say that if 8.4 corresponds to
the collapse times which were present, then 2.1 certainly does not. Indeed examination of
a simple series of calculations such as Dr. Bazant mentions shows a theoretical, total
collapse time of about 11 seconds, but adjustment of the ratio to give due consideration to
the safety factor increases the theoretical collapse time to about three times this figure,
about 35 seconds. Thus even using his flawed analysis and assumptions, and making only
one change to take account of the safety factor, it can be simply shown that the collapse
times obtained by this analysis do not correspond to the collapse times which were
observed in reality.
Originally posted by bsbray11
PLB claimed earlier in the thread that Bazant's model was enough to prove that a collapse could not be arrested after the first undamaged floor failed. But immediately he refused to discuss the actual assumptions of that model.
reply to post by -PLB-
It is an overestimation. The reason this is done is because the actual events are unknown. So you start to figure out what would happen in the most optimitic case. If in the most optimitsic case the collapse would not arrest, it would also not arrest in a less optimitic case. This is sound logic, just like my example with the rope. Unless of course you can point out relevant assumtions that were ignored or wrong. But it is not wrong by default.
Originally posted by Darkwing01
The paper is loaded with unsubstantiated assumptions made simply on the basis of denying any possibility of CD.
Originally posted by -PLB-
Such as? You may start with listing a single one, and explain how the assumption was made on the basis of denying any possibility of CD.
Originally posted by -PLB-
Like I said I rather discuss the subject with someone who understands it.
The text you quoted is fundamentally wrong. They confuse forces with energy. The forces exceeded 31 times the design load capacity according to Bazant.
Even if Bazant did not include the 4 times safety margin, the load would still exceed the load capacity by a large margin.
Originally posted by -PLB-
As expected you don't understand why the quoted text is fundamentally wrong, yet you do realize that forces and energy is not the same.
On top of that it is based on absolutely nothing that Bazant left out a savety factor in his calculations. In fact, he says he made an approximation himself because detailed information was missing. This garbage isn't worth discussing.
Originally posted by bsbray11
I just explained to you that force and energy are related through the physics concept of work. Force applied across a distance is work, and the amount of work is dependent upon energy. Therefore energy is directly related to how much force can be applied across a distance. If you never learned physics 101 and this is all new and complicated to you then do some Google searches and figure it out yourself.
No kidding this garbage isn't even worth discussing. That's why you didn't want to discuss it in the first place. If it actually proved something you would be cramming it in our faces. Instead you want to hide it under the rug, when it's your own source. Yes, Bazant made lots of "approximations" in the face of missing data it seems. He also incorrectly applied all of the energy of the upper block onto the first floor directly below only. As Ross explained himself, if the upper block is transferring force through floors to the bottom of the block, then you can't pretend the same force wouldn't also be absorbed by the lower block, and try to force it all to act on the uppermost part of it only. Yet this is also exactly what Bazant did in order to lie about there being more than enough energy to complete a collapse.
Originally posted by -PLB-
Originally posted by bsbray11
I just explained to you that force and energy are related through the physics concept of work. Force applied across a distance is work, and the amount of work is dependent upon energy. Therefore energy is directly related to how much force can be applied across a distance. If you never learned physics 101 and this is all new and complicated to you then do some Google searches and figure it out yourself.
Yet the person you quote doesn't understand any of this, and applies the safety factor of the load (which is a force) directly to the energy consumed in bending the columns. Even you can figure out that this is totally wrong.
The forces would very likely either make a column in the upper part fail or a column in the lower part, but both failing at exactly the same time seems extremely unlikely.
Such as? You may start with listing a single one, and explain how the assumption was made on the basis of denying any possibility of CD.
Originally posted by Darkwing01
In the end though it doesn't matter which assumptions you make if your conclusions can be consistently empirically validated. Bazant's can't. Even if he made no unrealistic assumptions and only used all his equations correctly, if his model still failed to predict reality it would be the engineering equations that would be up for review, not reality.
As it is (fortunately) the engineering equations are perfectly safe.
It is better to be approximately right than precisely wrong.edit on 25-5-2011 by Darkwing01 because: ly
This paper presents a simplified approximate analysis of the overall collapse of the towers ofWorld Trade Center in New York
on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load
carrying capacity, the whole tower was doomed.
Originally posted by esdad71
Look It was drafted less than a week after the attack and, in his words, ...
A simplified and approximate analysis. If you read the paper from an outside point of view it is actually very informative.
I suspect many of you read the simplified version such as this one...
911research.wtc7.net...
But not the actual report.
www.civil.northwestern.edu...
Is not that bad.