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Originally posted by LeftBehind
With that paragraph taken out of context is does appear that way, however you notice that he isn't leaving it at that assumption. He clearly states that he goes into it in depth in section 4.2. In that section he actually calculates the value for E1.
...
So as you can see he is not just guessing or lying about the value for E1. In fact he is breaking down his position peice by peice to fully account for all of his figures something completely lacking in the Jones paper.
Where does this 80% of the mass figure come from? I would agree that 80% of the debris was ejected outward. However the steel, which was most of the mass, ended up in a huge pile at the base of the towers.
How does the collapse speed not slowing immediately indicate that?
As you can see from the graph Greening made from his figures the resistance is readily apparent.
...
Starting at the same speed and then slowing is exactly what we should expect from the resistance as the collapse proceeded.
It is very encouraging that the energies reported in Table 1 show an acceptable balance between the energy inputs to the towers and the energies dissipated by the destruction of the aircraft and the WTC floor supports. For our calculations to show this level of internal consistency argues well for their validity. And while we acknowledge that the energies in question could be determined with greater precision by more detailed calculations, we would suggest that the values in Table 1 are a useful first approximation.
Originally posted by Phoenix
Ok, even with the flying debris calculated (on the high side IMHO) then the seemingly accepted number for weight of WTC 1 or 2 is around 300,000,000 Kg divided by 110 = roughly 2,720,000 Kg per floor then subtract 80% to arrive at an added 544,000 Kg's additional momentum per floor for each floor overtaken in addition to the total weight of how ever many floors were above the original collapse point.
I am very skeptical that 80% ejecta is even close to the true figure and agree with Valhal that a little common sense is in order. Visually the videos can not be relied upon for this figure most of that is a dust cloud of very much lighter weight particles - is there any expert evidence to support 80% or is that just a non-expert opinion formed from watching the video.
Originally posted by bsbray11
And certainly you don't think that the cap remained intact?
I may get the figures to actually show that there couldn't have been a decrease in collapse velocity tomorrow if I can find something to indicate when the actual collapse reached the ground (maybe some seismic stuff?), but I have a research paper due tomorrow that I haven't started and it's getting late.
[edit on 29-1-2006 by bsbray11]
And then a follow-up, realizing that the lower floors were made stronger than the upper floors, don't you think there would, in fact, possibly be a slowing - that's not from any calculations but just from intuitive reasoning. If not a slowing, possibly a leveling out of sorts?
Originally posted by LeftBehind
And as Valhall has previously pointed out, the debris would only pile up so high before spilling down.
Why are you insisting that the collapse never slowed down?
You have said that you know it didn't fall at free fall, so obviously some resistance was encountered. Please don't make me post that free fall pic again.
Now, my question for you. Do you have better figures for what happened during the collapse?
Where has he made mistakes in his equations?
BTW, the heavier columns would still not be able to withstand the forces being applied to them.
Are you trying to say that you expected the towers to collapse a few floors and then stop?
Originally posted by Valhall
I think there is video evidence that indicates the "cap" (but I need to be sure we're using that term the same way) was intact. I'm using it as at least the "roof" of the building", and not assuming anymore than that. Please see my second video link in the post I had early on in this thread.
Two, is there some particular reason we can't use both my work with your work (i.e. my work shows 18 second collapse time), and that's with the "roof" hitting the ground (which would actually be the pile, right?)
Just because we don't see these things the same way, doesn't mean that either one of our work shouldn't be considered by the other, and I'd be curious to see what using my collapse time would do for you.
And then a follow-up, realizing that the lower floors were made stronger than the upper floors, don't you think there would, in fact, possibly be a slowing - that's not from any calculations but just from intuitive reasoning. If not a slowing, possibly a leveling out of sorts?
So for the sake of simplicity let's pretend for a minute that once a floor is impacted and fails and causes a negative Jerk to the floor(s) impacting it, that the next 10 feet are freefall. What I'm trying to verify with you is, don't you agree that as the impacted floors get lower (into the stronger constructed floors) the negative Jerk will increase?
With the actual mass of the building at live load it does not come to 1.5kwh.
This is what i got.
Ti= 1/2 (330, 000, 000/110) x (8.5)2 = 108, 375, 000 J that is 59, 693, 181.82 J less than the figure Greening got!!!
If we use the dead load this is what we get: 55, 501, 136.36 J!!!! That's less than the difference in energy of the live load vs Greenings magic number!!!
KE for the combined floors: Ta = 1/2 (330, 000, 000/110) x (8.5/2)2 = 27, 093, 750 Joules
Now let's calculate that energy for the floor collapse.
The KE before impact is show below
T1 (wtc) = 14 X 1, 083, 750, 000 = 1, 517, 250, 000 J
T2 (wtc) = 29 x 1, 083, 750, 000 = 3, 142, 875, 000 J
The KE lost as heat is calculated as follows
Q (WTC 1) = 1/(1 + N) x Ti (WTC 1) = 14/15 x 1, 083, 750, 000 J = 101, 150, 000 J
Q (WTC 2) = 1/(1 + N) x Ti (WTC 2) = 29/30 x 1, 083, 750, 000 J = 104, 762, 500 J
The precent of energy lost as heat for each tower:
Tower 1 = Q/T1 x 100 = 6.67 percent
Tower 2 = Q/T2 x 100 = 3.33 percent
One thing Greening forgot to mention was how much energy was also lost as sound and that is something that can't really be calculated unless decible readings were taken, then we can calculate the energy lost to sound as well.
OH before I forget to mention it....the weight of one floor is NOT 4, 360, 000kG!!! It is in fact 3, 000, 000Kg. and that is our live load!!!! the dead load is actually 1.56 million Kg per floor.
Moving on.....
If we now assume, as previously
discussed, that the yield strength of the core columns is about 6.7 times higher than the
yield strength of the exterior columns, we estimate that an additional 3.60 ? 108 J are
required to collapse the 47 core columns supporting each floor. Thus, based on T.
Wierzbicki et al. calculation, we estimate a total of 6.29 ? 108 J of impact energy was
required to collapse one WTC floor, a value that is remarkably close to Baants estimate
of 5.0 ? 108 J for the plastic energy dissipated by the collapse of one floor.
Greening says 62, 900, 000, 000 J is required to collapse one floor of the WTC Towers....
Now as you can see from my calculations.....it isn't even close to that!!!
The maximum kinetic energy of each WTC tower collapse occurred at the end of
the 1st stage of the two-stage collapse. At this point in time the falling material, consisting
of at least 80 floors weighing about 370, 900, 000 kg, was moving at about 50 m/s. We will therefore assume that each tower had a maximum kinetic energy of
x 370, 900, 000 x (50)2 J or 4.6 ? 1011 J.
Again because his mass is wrong....this throws everything off again...
80 floors equates to 72.2% of the building....so we multiply that by the mass of the building and we get the weight of the 80 floors.
The figure we get is 240, 000, 000Kg!!! Which is about 130, 900, 000 KG difference!!!!
so let's do the kinetic energy
1/2 x 240, 000, 000 x (50)2 = 30, 000, 000, 000 J.
Greening Got 46, 000, 000, 000 J so we have a difference 16, 000, 000, 000 J of energy here!!!
From photos of the debris pile produced by each WTC tower collapse it is evident
that steel columns and trusses, aluminum fasciae, glass windows, gypsum wallboards and
other construction materials were all fractured and pulverized to varying degrees during
the collapse events. Thus only a fraction, f, of the 4.6 ? 1011 J of kinetic energy, was
available to crush the WTC concrete. For the present calculation we will assume a value
for f of ~ 0.75, giving 3.5 ? 1011 J of available kinetic energy.
Lets consider the beginning of the 1st sage of the collapse of each tower. For
WTC 1 we will take as an example 14 floors, and for WTC 2, 29 floors impacting the
floor below with a maximum velocity of 8.6 m/s. It follows that the kinetic energy on
impact was ? 14 ? (510, 000, 000/110) ? (8.6)2 joules = 2.4 ? 109 J for WTC 1, and the
K.E. was ? 29 ? (510, 000, 000/110) ? (8.6)2 joules = 5.0 ? 109 J for WTC 2. If we
assume 50 % of this energy was available to crush concrete, we have 1.2 ? 109 J available
for WTC 1, and 2.5 ? 109 J available for WTC 2. This is sufficient to crush the concrete
on the impacted floor to 175 ?m particles.
Some have suggested that even if Greening used an incorrect value for mass that his calculations still hold true and that a smaller mass would still lead to a collapse. This is not true as demonstrated here:
Tower 1: X 14 ? (510, 000, 000/110) ? (8.6)2 joules = 2.4 ? 109 J for WTC 1, (Greening)
1/2 x 14 x (330, 000, 000/110) x (8.6)2 = 1, 517, 250, 000 J Almost 1.5 billion J Difference!!!!
Tower 2: x 29 x (510, 000, 000/110) x (8.6)2 joules = 5.0 x 109 J for WTC 2. (Greening)
As a scientist Greening should know that rounding off numbers skews your results...in fact the correct figure for that calculation is 4, 857, 170, 455 J
1/2 x 29 x (330, 000, 000/110) x (8.6)2 = 3, 142, 875, 000 J
a difference of 1, 714, 295, 455 J!!!!!
Now if 50% of the energy is required to crush the concrete this is what we'll get for both towers:
Tower 1: 1/2 x 1, 517, 250, 000 J = 758, 600, 000 J
Tower 2: 1/2 x 3, 142, 875, 000 J = 1, 571, 437, 500 J
Consider now the newly formed mass of (14 + 1) floors of WTC 1, and (29 + 1)
floors of WTC 2, impacting on the floor below. Because of momentum transfer, the
impact velocities are slightly lower than the 8.6 m/s impact speed for the first floors hit:
8.1 m/s for WTC 1, and 8.3 m/s for WTC 2. The maximum kinetic energy prior to impact
is x 15 x (510, 000, 000/110) x (8.1)2 joules = 2.3 x 109 J for WTC 1, and x 30 x (510, 000, 000/110) ? (8.3)2 joules = 4.8 ? 109 J for WTC 2.
This is essentially the same result as the previous impact calculation and the kinetic energy released is therefore also sufficient to crush the concrete on the impacted floor to 175 ?m particles.
This is where he goes wrong!!!! HE says it requires 190, 000, 000, 000 J to crush concrete to 100 micro metre particles!!! Guess what; we don't have that enery!!!!
Let's do it using his 15 and 30 floor results
for 15 floors I got: 1, 625, 625, 000 J
for 30 floors I got: 3, 251, 250, 000 J
Greening got: 2, 300, 000, 000 J for 15 floors and 4, 800, 000, 000 J for 30 Floors.
See the big mistake!!!!
Frank Greening:
"Finally, we will calculate the energy needed to crush all the concrete in a single
WTC tower (= 48, 000, 000 kg) to particles of a specified size. As we have noted before,
the energy required to crush all of the concrete in one tower to 60 ?m particles = 3.2 ?
1011 J which is only slightly less than the 4.6 ? 1011 J of energy available. However, the
energy required to crush concrete to 100 ?m particles is 1.9 ? 1011 J, which is well within
the crushing capacity of the available energy. Hence it is theoretically possible for the
WTC collapse events to have crushed more than 90 % of the floor concrete to particles
well within the observed particle size range.'
WRONG!!!! WRONG!!! WRONG!!!!
Originally posted by Phoenix
If bsbray or Valhall or someone else would agree on a few points I could figure up the initial velocity, force or impact on the next existing intact floor as a starting point for figuring out the rest of the puzzle. These numbers are key to later velocity that you guys are talking about in above posts.
Heres what I need;
number of intact floors of the "hammer"
agreement on average weight of each floor including vertical elements and "live" load.
agreement on number of floors compromised by aircraft impact.
distance traveled before "contact" with anvil. (verticle distance of compromised floors not initially providing much resistance)
do this for both wtc1 and wtc2
Originally posted by LeftBehind
As to the mountain of steel.
Yes. Here are a ton of pictures showing these huge piles of twisted steel in the footprint.
www.glasssteelandstone.com...
BTW, the heavier columns would still not be able to withstand the forces being applied to them. Are you trying to say that you expected the towers to collapse a few floors and then stop?
According to a uniform building code book I have the density of lightweight concrete is that which weighs less than 115 lbs per cubic foot.
Is that agreeable to you?
What square footage of total floor area and percentage of penetrations for elevator shafts etc. do you use?
I use an average thickness of 6" (could be as much as 8") for the concrete floor, do you agree?
I am talking to a structural engineer about relative strength of columns, my opinion from photos is they were not crushed, many bent, but rather the welds and attachment points were the weak spot. Also many can be assumed to have had lateral forces acting on them along with the vertical component especially the exterior columns, I'm not refering to the "bow" before collapse but rather the debris "push" (lateral) once in motion.
Live load (equipment, files, cubes, furniture, partitions etc.) 50psf which is a very very common rating in the industry.
The dead load of a floor was 1,818 tons. The floor area was rated 40-150 psf (1.9-7.18 kPa), depending on what the area was going to be used for. Higher load ratings generally were for areas that would support larger than normal loads such as mechanical equipment. Below are floor load estimates based on a review of WTC data contained in a 2005 NIST report.
Originally posted by Phoenix
bsbray
Most misunderstand the term "live" load
The lateral force simply explained comes into play much as dumping a load of dirt and rock into a container - there is "force" on the sides is there not?
I view it this way - the intact exoskeleton of structural beams form the "container wall (for very short time) catching the debris from areas above, granted some will spill out the top as can be seem in video showing heavier elements falling out of dust cloud
- this action is allowed specifically because there was indeed some resistance offered by the structure as surmised by the fall time you and Valhall seemed to agree on.
A fair proportion of that debris would have made lateral force outwards on the exoskeleton.
I believe that once the forces involved are stated in plain english then some headway might be made.