The 9/11 Forum

OneWhiteEye --- I use the B&V crush-down equation with a resistive force proportional to

Bs^2

where B is the instantaneous mass of the crushed zone B and s is the material speed (not the crushing front speed, v, which is faster). Wowzer! What a winner in fitting the collapse curve properly.
That is the vertical avalanche resistive force.

So far not in the literature.

The BLGB resistive forces can be summarized as

k0 + k1v^2,

with k0 due to column buckling, connections breaking, etc. and k1 to comminution at the crushing front alone together with air resistance at the crushing front alone. All I can say is that in doing parameter estimation of that with the vertical avalanche force that both k0 and k1 get driven to zero or very close to that. What that says is that neither was but the most minor contributor to the resistance over the first 3.75+ seconds.

Hasn't been published yet, but despite that, I do hope you'll stick around.

Great summary, thank you. Assimilation has begun.

Did you also try fits with a linear term in v? Seem to recall that.

David B. Benson wrote:Hasn't been published yet, but despite that, I do hope you'll stick around.

Yeah, can't help it, I'm addicted.

OneWhiteEye wrote:Did you also try fits with a linear term in v? Seem to recall that.

Yes and other crazy stuff for the stretch function with various different resistive forces.

The best fitting stretch function is proportional to

exp(-k4(B+C)v)

where (B+C) is the instantaneous mass of zones B and C. This starts with a stretch around 0.26 and slowly declines to about 0.2 at the end of crush-down. Dunno why this gives the best fit, but it does seem sorta realistic.

OneWhiteEye wrote:psikeyhackr:

OneWhiteEye wrote:PS do you have the results of your trials in tabular form?

Hadn't seen your other post. Edit: never mind, now that I'm reading it; different data.

PS. I assume you've read ENERGY TRANSFER IN THE WTC COLLAPSE by F. R. Greening. ?

I had a little problem with Frank on JREF last May. He goes by the handle Apollo20. I said he made a faulty assumption on page 3 about the distribution of mass and therefore everything was wrong after that. He has not responded since then.

Distrib o Mass

The only data in tabular form is what I wrote on a piece of paper while I was recording the data on broken toothpicks while shooting the videos. Let me tell you, removing broken toothpicks from holes and sticking in new toothpicks and putting washers on all of them is REALLY EXCITING.

I have thought about doing calcs on the energy required to break toothpicks and how rapidly they decelerated the mass but haven't gotten to that. I am just relieved to have finally gotten this finished.

psik

psikeyhackr wrote:

Well, at least you aren't Greening. That would be most embarrassing! I think I'd retire from message boards if I made that gaffe.

psikeyhackr wrote:I said he made a faulty assumption on page 3 about the distribution of mass and therefore everything was wrong after that.

You mean this part?

Greening wrote:...where mf is the mass of one WTC floor, assumed to be 1/110 the mass of an entire WTC tower, namely mf = (510,000,000 / 110) kg ≈ 4,636,000 kg

It is a first approximation, after all. But, as you've noted, it does make a difference if the mass varies in the vertical dimension.

Let me tell you, removing broken toothpick from holes and sticking in new toothpicks and putting washers on all of them is REALLY EXCITING.

Haha, no doubt it is. Glad somebody's doing it.

Note: this board mangles links without the URL tag enclosing them

Note: this board mangles links without the URL tag enclosing them

Thanks, it's fixed now.

It is a first approximation, after all. But, as you've noted, it does make a difference if the mass varies in the vertical dimension.

My pledge father was an architect and we could see the Sears Tower being constructed when I was in college. After 9/11 I spent two weeks trying to simulate in my head what would happen. I concluded the skyscraper could not collapse straight down but my analysis assumes the quantity of steel must get stronger and therefore heavier. His assumption about the constant distribution of mass made no sense to me.

The man that wrote this did not make that absurd assumption.

Lets suppose that the bottom floors contained roughly twice the amount of steel of the upper floors (since the lower floors had to carry more weight). So we estimate that the lower floors contained about 1,100 tons of steel and the upper floors about 550 tons = 550 x 907.2 ≈ 500,000 kgs.

http://911research.wtc7.net/mirrors/guardian2/wtc/how-hot.htm

According to Lon Waters' site on Core Columns some were 20 times as heavy at the bottom as the top.

psik

psikeyhackr wrote:Distrib o Mass

I wrote:You mean this part?

Greening wrote::
...where mf is the mass of one WTC floor, assumed to be 1/110 the mass of an entire WTC tower, namely mf = (510,000,000 / 110) kg ≈ 4,636,000 kg.

Damn, I'm good.

I had a little problem with Frank on JREF last May. He goes by the handle Apollo20. I said he made a faulty assumption on page 3 about the distribution of mass and therefore everything was wrong after that. He has not responded since then.

You might think that your disagreement with his "absurd assumptions", or even comments like "But how can he possibly make mistakes that dumb?" is what put him off, but my money is that it's because you referred to him as an engineer.

It's worth exploring the effect of varying mass and resistive force. Both Drs. Greening and Benson have done so in various ways. Good that you should pop in right now since the nature of the actual resistive force is being discussed, I'm trying to get my mind around it.

Psikeyhackr:

I suppose you dont know that since last July I'm banned for life at JREF ..... (Yes, really, FOR LIFE!)

I guess they didn't like me from day one on that *!#*#*! site!

I wrote my Energy Transfer paper back in 2005 when everybody used Bazant's mass for the Twin Towers.

And as for the number of floors in those towers, .... well pardon me for being so dumb!

I was really mainly interested in presenting a mathematical formalism to quantify the collapse times. You can plug any mass or energy loss values you like into the equations I presented in my paper and then we can argue about the results......

But yes, over the past few years, I have done lots of WTC collapse calculations with different masses and energy losses as pointed out by One White Eye. I can post some results if you are interested; but in the meantime, could I see some of your calculations?

Dr. G wrote:I was really mainly interested in presenting a mathematical formalism to quantify the collapse times. You can plug any mass or energy loss values you like into the equations I presented in my paper and then we can argue about the results......

But yes, over the past few years, I have done lots of WTC collapse calculations with different masses and energy losses as pointed out by One White Eye. I can post some results if you are interested; but in the meantime, could I see some of your calculations?

Hallo Dr. G. Say that you are going to crush structure A with structure C, i.e. you drop C on the top of A. As C have similar structure as A but less mass, mass C = 1/10 mass A, wouldn't you expect that something happens to C at contact with A? C may bounce! C may get locally damaged?

And take A! A is a big structure and if we assume that it is isotropic, it is highest stressed at its bottom far away from the top,assuming top and bottom have same cross area. It will deform, when C contacts it at the top, but it could very well fail at the bottom, where it is highly stressed!

We could adjust structure A so that it has uniform stress throughout (like a pyramid). And then we drop C on A. What happens? A is crushed? Why isn't C crushed?

Another example! Again we have structure A but now we drop a part B on it, mass B = 1/5 mass A! B has thus twice the mass as C above at first impact. But the only difference is that B is rubble = structure A in small pieces and 4X the density. So now we drop rubble B on structure A. Do you really expect B to crush A?

Dr. G wrote:Psikeyhackr:

I suppose you dont know that since last July I'm banned for life at JREF ..... (Yes, really, FOR LIFE!)

I guess they didn't like me from day one on that *!#*#*! site!

I didn't know. You have my sincerest respect and admiration for being banned. I have been banned permanently from the Chomsky site, though I don't know why. And had two one month bans from Dawkins and am waiting for the third to attain permanent status. LOL

I wrote my Energy Transfer paper back in 2005 when everybody used Bazant's mass for the Twin Towers.

And as for the number of floors in those towers, .... well pardon me for being so dumb!

I was really mainly interested in presenting a mathematical formalism to quantify the collapse times. You can plug any mass or energy loss values you like into the equations I presented in my paper and then we can argue about the results......

But yes, over the past few years, I have done lots of WTC collapse calculations with different masses and energy losses as pointed out by One White Eye. I can post some results if you are interested; but in the meantime, could I see some of your calculations?

My attitude it that MATHEMATICS IS NOT PHYSICS. It is useful to physics but that is all. It is excellent for gravitational calculations of the motions of planets since they don't touch each other and no friction or breakage is occuring but even that broke down with the precession of Mercury and didn't get fixed until Einstein came along.

I went to college for Electrical Engineering. I have never taken a structrural engineering course in my life. I have NO IDEA how to calculate how much energy is required to crush one level of a building even if the amount of steel is known. But I am ABSOLUTELY CERTAIN that changing the amount of steel is going to change the amount of energy required. So I regard doing calculations without that data as a useless intellectual exercise.

So it is shocking to me that for the last SEVEN YEARS so many people with degrees RELEVANT TO THE SUBJECT have not been DEMANDING THAT OFFICIAL SOURCES provide data on the distribution of steel and concrete in HUMAN READABLE FORM, not just SAP databases, about the WTC towers.

But then we have this 911 PSYCHOSIS of people who don't seem to know the most simple things about physics BELIEVING that a 150 ton airliner can destroy a 400,000 ton building in less than 2 hours.

For every level of the lower portion of the north tower destroyed a level of the top falling portion had to be destroyed. So even assuming gravity helped the falling portion, those 16 falling stories should not have been able to destroy 32 stationary levels. So I think saying that 49 levels could have been destroyed is more than generous. That would still leave 60 intact levels of the north tower. So why aren't ALL OF THE ENGINEERING SCHOOLS AND STRUCTURAL ENGINEERS accounting for this? I seem to notice a lot of silence.

This country has gone nuts. The NIST is telling us the buildings came down so fast because they were 70% air by volume.

http://www.pbs.org/wgbh/nova/wtc/cons-flash.html

That is 15 tons of air per level by the way. The buildings averaged 862 tons of steel per level.

So I created these demonstrations to show that the distribution of mass mattered for both horizontal and vertical forces.

http://www.youtube.com/watch?v=LXAerZUw4Wc

http://www.youtube.com/watch?v=z0kUICwO93Q

And I was looking forward to a fun fight with you on JREF but you had to go and get yourself banned. LOL

psik

PSIK:

Nice videos!

But I dont think the amount of information available on the Twin Tower's steel and concrete is quite as bad as you claim.

You ask how many tons of concrete were on each floor of the Twin Towers

You can calculate the mass of concrete on each WTC floor as follows:

Core floor area = 862 m2

Out-of-core (Office space) floor areas:

2 long one-way slabs = 1,225 m2
2 short one-way slabs = 486 m2
4 two-way slabs = 1,137 m2

Total out-of-core area = 2848 m2

The floors in the core areas were made of normal weight concrete, density 1760 kg/m3

The floors in the office areas were made of lightweight concrete, density 1500 kg/m3

Volume of 5-inch normal weight concrete per floor = 109.5 m3

Weight of normal weight concrete per floor = 193 tonnes

Volume of 4-inch thick lightweight concrete per floor = 289.4 m3

Weight of lightweight concrete per floor = 434 tonnes

Total weight of concrete on one WTC floor = 627 tonnes


As for the steel, you have a lot of good information on the loadings of the upper floors of WTC 1&2 in NIST NCSTAR 1-6D and NCSTAR 1-5G. For the lower floors you have extensive core column data on the site wtcmodel.wikidot.com. This data set gives column specs that include the weight per linear foot for every core column.

Finally you have the excellent work on the mass distributions in the Twin Towers carried out by our very own Gregory Urich.

All of this information should be more than enough for some diligent engineer to do some detailed calculations......

From a variety of simulations, not just mine, the fact that the tower mas per story declined slowly with height makes very little difference. One can hardly tell the difference between a uniform structure and the mass distribution worked out by Greg Ulrich or available from NIST's SAP stuff, now publically available.

Heiwa:

I will answer your question with this:

I think you are familiar with the "verinage" demolition of the Balzac (ABC) building in France since it was discussed on this website a few months ago. An upper block of floors of the building was made to drop on the lower part using hydraulic rams, (No explosives - sorry!)

According to your "axiom" this is impossible; so it looks like your axiom has been falsified!

Dr. G wrote:PSIK:

As for the steel, you have a lot of good information on the loadings of the upper floors of WTC 1&2 in NIST NCSTAR 1-6D and NCSTAR 1-5G. For the lower floors you have extensive core column data on the site wtcmodel.wikidot.com. This data set gives column specs that include the weight per linear foot for every core column.

I just did Google searches of that site with:

+lb +site:http://wtcmodel.wikidot.com
+lbs +site:http://wtcmodel.wikidot.com
+weight +site:http://wtcmodel.wikidot.com
+pounds +site:http://wtcmodel.wikidot.com
+tons +site:http://wtcmodel.wikidot.com
+kilogram +site:http://wtcmodel.wikidot.com
+kilograms +site:http://wtcmodel.wikidot.com

The only thing that turned up was:

+kg +site:http://wtcmodel.wikidot.com

http://wtcmodel.wikidot.com/lu-jiang-model

Are you talking about this:

http://wtcmodel.wikidot.com/steel-wide-flange-i-beams

I just find it so curious that EVERYBODY doesn't just want a simple table that lists the tons of concrete and steel on every level. It is always, go calculate this and that and the NIST hasn't provided it already in 10,000 pages with supposedly 3 years of work and $20,000,000. And of course they haven't told us the number and weights of the 12 types of perimeter wall panels. It didn't take SEVEN YEARS to design those buildings.

psik

Major_Tom & OneWhiteEye --- But that 2-D layout is not where the resistive force is coming from. The main resistive force is due to the comminution of concrete, floor pans, trusses,,office furnishings, ..., everything but the structural steel. In the core, mostly just the connections failed, little column buckling. That is what one sees at Ground Zero; almost no floor pans, only one pix of a recognizable section of truss, lots of well ground materials.

In my computer program, an attempt to use the force function of BLGB together with the avalanche forse ressults in setting the BLGB constant to zero, or nearly so, for best fit; essentially all the resistance during the period of measurements is due to comminution. Now that is a bit harder for the ordinary concrete in the core floors, but on the other hand there are no trusses to break up either, just (I suppose) a floor pan and then connections of beams to columns.

So if we view it in 2-D, how would you guess the different parts of the tower resisted being destroyed?

As I understand your post you would favor a type of relative resistance similar to the green plot below? (The red one would be more my guess).




You seem to be saying the core doesn't do much more than the open space flooring to resist being destroyed. What modifications should I make to the green plot to express your views?