Mathematics, and the case of the missing concrete.

[jschurchin]

First off let us assume (yeah, I know) a few facts. First, there was 450,000 cubic yards of concrete used in the construction of the towers. Second, there was 200,000 tons of steel used in the construction.
Each tower weighed in at 500,000 tons for a total weight of 1,000,000 tons. We know that there was 200,000 tons of steel, but how much does concrete weigh?

I did a google search asking that same question, answer: wet 3,900 lbs per cubic yard. Cured 3,500-3,700 lbs per cubic yard. So a little math 450,000*3,600=1,620,000,000lbs or 810,000 tons. A little more math 200,000(steel)+810,000(concrete)=1,010,000tons divided by 2 towers equals 505,000 tons. Pretty close huh?

It is safe to assume that all of the concrete was used in the construction of the towers.

Now, how much concrete was used on each floor? We know the dimension's of the building were 208'x208'. Since concrete is measured in cubic yards we need to convert this to yards. 208 divided by 3 equals 69.03 yards. Now how thick are the floors? I used an average 4 inches for the floor and to convert that to yards we divide 4 by 36 resulting in .111. Now to figure cubic yards 69*69*.111=528.471 cubic yards per floor. 110 floors per tower 220*528.471=116,263.620 cubic yards.

We are missing a whole lot of concrete. Where did it go? Christophera might have the answer.

[gbwarming]

1. It is not safe to assume all concrete was used in the towers

Putting aside for the moment where these numbers came from - There was a huge amount of underground work done in the WTC complex including the slurry wall and several basement levels.

[jschurchin]

4. I believe it is.......

I have done some preliminary calculations to determine if, in fact, that is where the missing concrete is (bathtub, underground parking level's and shopping mall). Needless to say I wouldn't have started this thread if I thought it was there. The figures don't back it up.
Don't believe me, use your brain and your computer. Do the search's and find the figures, they are out there. Do your own calculation's and prove me wrong. I am a man, when I am proven wrong I will promptly admit, I fucked up I was wrong. I am human, I make mistakes, thats how I learn.

[mirandapriestly]

2. hmmm, what else could account for the weight? nt

[Kevin Fenton]

3. Can I just ask

I have seen very different figures for these. Where did you get these numbers (450,000 cubic yards of concrete, 200,000 tons of steel and 500,000 tons) from?

Some of the floors (on the technical floors) were much thicker than 4 inches.

At one point in the NIST reports it says that the South Tower tower weighed 250,000 tons, not 500,000 tons: "The shudder as the more than 250,000 tons of steel, concrete and furnishings hit the ground was felt way beyond the site." (p. 32 of the main report - p. 82 of the .pdf)

The basement obviously used a lot of concrete. However, the weight of the above-ground portion of the towers is usually taken to be 500,000 tons and this number is used by scientists when calculating whether the towers should have collapsed or not. If we could show that all that concrete was used in the basement, then that would be really useful.

[jschurchin]

5. Hi Kevin. Here are some links

"I have seen very different figures for these. Where did you get these numbers (450,000 cubic yards of concrete, 200,000 tons of steel and 500,000 tons) from?"

Let me preface this by saying, I cannot find the link that I got the 450,000 from but these all show 425,000

http://www.public-action.com/911/jmcm/wtc1.html
http://www.infoplease.com/ipa/A0903568.html
http://www.foxnews.com/story/0,2933,34255,00.html

"Some of the floors (on the technical floors) were much thicker than 4 inches."

I agree, but I do not believe it makes up for the large amount of weight that is missing though.

"At one point in the NIST reports it says that the South Tower tower weighed 250,000 tons, not 500,000 tons: "The shudder as the more than 250,000 tons of steel, concrete and furnishings hit the ground was felt way beyond the site." (p. 32 of the main report - p. 82 of the .pdf)"

That is definitely a large difference, and it could nullify my calculations, I need to check and see what their source was.

"The basement obviously used a lot of concrete. However, the weight of the above-ground portion of the towers is usually taken to be 500,000 tons and this number is used by scientists when calculating whether the towers should have collapsed or not. If we could show that all that concrete was used in the basement, then that would be really useful."

I did some preliminary calculations to do just that, It is a possibility.

[Kevin Fenton]

6. Basement + wall

Bathtub wall dimensions:
"Before foundation excavation began, the 500 x 1,000-ft site was enclosed by a 3-ft-thick, 70-ft-high concrete cutoff wall built by the slurry trench wall method and keyed 3 ft into rock."
http://www.simplytaty.com/broadenpages/historyofwtc.htm

So the bathtubs dimensions in yards are 1,000 (length of wall) x 1 (thickness) x 23 (height). That accounts for a mere 23,000 cubic yards.

What about the floors in the basement?
The area of one floor should be 1,000 feet x 500 feet, or 333 yards x 167 yards, I'll take 4 inches as the floor thickness.
So 333 (l) x 167 (w) x 0.111 (t) gives us 6172.821.
6172.821 times 6 (number of floors) is 37,036.93. Maybe the floors in the basement were thicker, but not by that much.

That's a start, but it's not much. We have 116,236.620 (your figure for the floors) + 23,000 (bathtub) + 37,036.93 (basement floors) = 176,272. That gives us a deficit of a mere 249,000 cubic yards of the damn stuff. Where the hell did they put it? There are the anchors (but how big can one anchor be?) and possible vertical elements (structural and non-structural) in the basement. Maybe the 425,000 cubic yards includes the other buildings as well (excepting 7, which was built much later).

[jschurchin]

7. We are getting there huh!!!!

I gotta get ready for work, it is 6:07 a. I gotta be there @ 7. I will be back in touch later today, kind of a mystery huh! Were is it at?

[Kevin Fenton]

12. Other buildings

Some articles suggest that all the 425,000 (or 450,000) cubic yards of concrete were all in the towers. Some don't, for example:
"About 425,000 cubic yards of concrete were poured during construction, from 1966 to 1973, according to the lead architects at Minoru Yamasaki Associates in Rochester Hills, Mich."
http://www.washingtonpost.com/ac2/wp-dyn/A28067-2001Sep13?language=printer
The way I read this, the figure of 425,000 includes everything built between 1966 and 1973, i.e. the Twin Towers plus the bathtub and basement, and maybe some of the other buildings.

Anyway, these are my calculations for the amounts of concrete in the floors of WTC 3 and 5 - WTC 7 wasn't part of the original development, so there's no way we can count it in the 425,000.

WTC 3 (Marriot Hotel)
Link: http://www.house.gov/science/hot/wtc/wtc-report/WTC_ch3.pdf (FEMA/ASCE)
Was designed in the late seventies and opened in 1981.
It had 22 floors above ground and 6 below. It was generally 64 feet by 330.
So 330 x 64 x 0.33 (assuming the floors are 4 inches thick, that's 1/3 of a foot) x 28 floors (assuming the basement floors are as thick as the aboveground ones, actually they're probably thicker, but never mind for now) = 195148.8 cubic feet, about 7250 cubic yards.
That's not much, and I'm not even sure if it counts. If it does count, there may well be more (vertical) concrete in it.

My total in post six is 172,272, so now we have 180,000.

WTC 5
Link: http://911research.wtc7.net/mirrors/guardian2/wtc/WTC_ch4.htm
Floors: 4 inches, nine stories, floor area of 120,000. We divide 120,000 by three to get 40,000 cubic feet and we divide that by 27 to get about 1,500 cubic yards. Mulitplied by the number of floors (9), that's 13,500.
Note: I found another source that gave a smaller floor area, but that was Fox, so I ignored it.
No idea about the basement.
Running total: 193,500 cubic yards.

[Christophera]

9. Steel Reinforced Concrete Floors In SUB Parking Lots Up To 12 Inches

in less supported areas.

Here is the account of the building engineers in the basement. Supporting walls are ususally at least 8 inches depending on the spans they support.

Explosions In The Basement.

Mike told his co-worker to call upstairs to their Assistant Chief Engineer and find out if everything was all right. His co-worker made the call and reported back to Mike that he was told that the Assistant Chief did not know what happened but that the whole building seemed to shake and there was a loud explosion. They had been told to stay where they were and "sit tight" until the Assistant Chief got back to them.

...............

The two decided to ascend the stairs to the C level, to a small machine shop where Vito Deleo and David Williams were supposed to be working. When the two arrived at the C level, they found the machine shop gone.

"There was nothing there but rubble" Mike said. "We’re talking about a 50 ton hydraulic press - gone!" The two began yelling for their co-workers, but there was no answer. They saw a perfect line of smoke streaming through the air. "You could stand here," he said, "and two inches over you couldn't breathe. We couldn't see through the smoke so we started screaming." But there was still no answer.

........

The two made their way to the parking garage, but found that it, too, was gone. ‘There were no walls, there was rubble on the floor, and you can't see anything’ he said

[LARED]

10. If you don't mind me asking

where did you get the figure of 12" from?

[Kevin Fenton]

11. Come on LARED

Help us out here. Do you agree with the figure of about 800,000 tons of concrete in the OP? If so, where did they put it all?

[Make7]

13. That figure could be off by a significant percentage...

..depending on the weights of the different concretes used.

Some lightweight concretes can weigh less than 2500 lbs. per cubic yard. That's slightly different then than 3900 lbs. per cubic yard (average normalweight concrete) figure cited in the OP.

What were the percentages, of the total amount used for the WTC, for the various weights of concrete?

I think it would be best to do estimations based on the volume of concrete, if one is just trying to account for the concrete reportedly used.

- Make7

[Kevin Fenton]

20. Thank you for your input

The floors mostly were lightweight concrete, weren't they? It's only the mechanical floors that used another, heavier type. Haven't I seen you post a document specifying what type of concrete was used on what floors? If some of the floor concrete in the towers were lightweight, we could pack more concrete into it without increasing the weight, maybe getting rid of an extra 30,000 cubic yards. I haven't worked out the percentages of various weights yet, but I suppose I will have to sooner or later.

It probably is better to do estimations based on the volume of concrete.

Do you know anything about concrete in the basement?

[Make7]

25. Here is that document:

It would appear that the roof is concrete. That is also stated in the inspection reports - which can be found in the NIST summary. One example:

Roof

Roof framing, which consisted of rolled steel wide flange beams supporting a structural concrete slab, was found to be in good condition. Hairline cracks in the fireproofing and in the underside of the concrete slab were found at various locations.

http://wtc.nist.gov/pubs/NISTNCSTAR1-1C.pdf   (pdf page 96)

Also from that document:

The masonry walls in WTC 1 were also damaged by the explosion (Woodson 1993). The 6 in. thick walls on the south side of WTC 1 were breached over distances of approximately 50 ft to the east and 120 ft to the west of the blast origin. The 20 ft long masonry wall that formed part of the mechanical plenum that was located 10 ft inside of WTC 1 (near columns 321, 324, and 327) was completely destroyed. The masonry walls of the elevator shafts located approximately 60 ft inside of WTC 1 were also damaged. Other masonry walls inside of WTC 1 were damaged at distances of up to 90 ft from the blast origin. None of the damaged walls were load bearing, and none were supported at the top. The walls were built to 1 in. below the structure above; the joint was subsequently caulked. Many of the damaged walls deflected as though they were free at the top.

http://wtc.nist.gov/pubs/NISTNCSTAR1-1C.pdf   (pdf page 156)

It appears at the very least that the perimeter of the Towers and also the perimeter of the core had concrete walls below ground. In addition, the passage above indicates that concrete walls were also used to enclose the mechanical areas in the basement. The size and location of these mechanical areas is not given.

Along the south face of WTC 1, the damaged concrete spandrel beams were demolished and replaced.
Figures 4–10 and 4–11 show the details of the repair between Columns 318 and 330 at Levels B3 and B4,
respectively. Similar repairs were made to the concrete spandrel between Columns 333 and 345 at
Level B3.

http://wtc.nist.gov/pubs/NISTNCSTAR1-1C.pdf   (pdf page 156)

The cross-sectional drawings of these beams indicate that they are 3'3" by 1'6". However, I did not find what distances were spanned by these beams - so I don't know how long they were or even how many of these beams there actually were.

Damaged concrete encasement around existing steel beams was also repaired as required. Figure 4–13 shows a typical reconstruction detail for a beam located at Level B2. The extent of concrete encasement reconstruction at Levels B1 and B2 is shown in the drawings that were prepared by LERA (LERA 1993c).

http://wtc.nist.gov/pubs/NISTNCSTAR1-1C.pdf   (pdf page 165)

The drawing on the previous page of the document indicates 4 inches for the thickness of the encasement, but not at what level it started or stopped. (Although it seems likely that it started at the lowest level.) The numbering and shape of the columns indicate that this is for the perimeter columns - I did not find any information about whether or not this was done for the core columns.

Also found throughout the document are serveral references to concrete used for fireproofing of steel beams. This was apparently employed on the mechanical floors, areas near the roof, and typically on the beams within the core that ran parallel to its shorter side.

The information above is only for the Towers, not the rest of the site. There definitely are more questions than answers regarding the construction details - so getting a reasonable estimate of the concrete used is likely to be rather difficult. Although a guess based on what information is available may prove to be useful.

- Make7

[jschurchin]

29. Thank You So much.....

Make 7. That is very helpful. By trying to estimate the concrete used I was relying on an above ground parking structure where concrete spandrel's are common. I was not sure if a underground garage used the same type support system. Your post confirmed that they do. Thanks again.

[Kevin Fenton]

44. Many thanks again

First an aside: Looking at the document I see that it only goes down to sub level 5 (although there were supposed to be 6 basements) and that there is a "service level" between sub level 1 and floor 1. I suppose that the service level must be the concourse and that WTCers helpfully refered to the second underground floor as "sub level 1".

Another aside: looking for the floor thicknesses in the core area I came across this, discussing a perimeter section that had fallen:
"three sides of each column were protected from fire by 2 inches of sprayed concrete whilst the fourth, the inner face, was protected from fire by a 2 inch layer of vermiculite plaster"
This is by John Knapton, who I suspect of being the source of the famous BBC diagram showing the "concrete core", so perhaps we should take this with a pinch of salt.
He later says:
"The core comprises steel beams and columns with reinforced concrete infill panels."
http://www.john-knapton.com/wtc.htm
I shan't read it any further, for fear of what I might find.

I seem to remember that the floors on the mechanical floors were thicker than the others (7 inches?). I also remember something about the floors in the cores being thicker. You wouldn't happen to know this off-hand, would you?
I suppose it's one way of interpreting this:
"Also found throughout the document are serveral references to concrete used for fireproofing of steel beams. This was apparently employed on the mechanical floors, areas near the roof, and typically on the beams within the core that ran parallel to its shorter side."

OK, the roofs:
1..208...208...0,33...0,037...528,25344
2..208...208...0,33...0,037...528,25344
3..64....330...0,33...0,037...257,8752
4..84500.......0,33...0,037...1031,745
5..120000......0,33...0,037...1465,2
6..67000.......0,33...0,037...818,07
..............................4329
For 1-3 the first two numbers of length and width of the roof, for 4-6 the first number is the area per one floor. 0.33 means I'm assuming the roofs are 4 inches thick, so I'm dividing by 3 to get cubic feet and 0.037 is for conversion to cubic yards. I then looked at this diagram:

Hmm, 5 doesn't look almost twice as big as 6. Nevermind. The running total is now nearly 255,000 cubic yards.

This image of the bathtub:

indicates that both towers were inside the bathtub - i.e. their walls were not the outer bathtub walls, although I'm not quite sure why this was the case or what they did with the rest of the bathtub.
Anyway, 208 (length of wall) x 0.5 (thickness of wall in feet) x 70 (height of wall up to ground level) x 8 (number of walls in both towers) x 0.037 (conversion to cubic yards) = 2155.
If the core were 89x138 and its walls 6 inches thick that would give us 1175 cubic yards in the core wall.
Plus maybe some other concrete walls inside the tower basements.

I'm going to leave the spandrel beams for now.

Fireproofing of perimter beams:
1,5 (width of beam (14 inches) + width of coating in feet) x 0,3 (width of coating in feet) x 4 (sides of column) x 70 (height of basement) x 236 (number of perimter columns) x 2 (number of towers) x 0.037 (conversion to cubic feet) = 2200.

My running total is just over 260,000 cubic feet. Where the hell did they put the rest of it? There must be lots of concrete walls in the basement outside the towers, maybe it's there.

Aside: there's an article by one of the people who built the bathtub here:
http://www.nae.edu/nae/bridgecom.nsf/weblinks/CGOZ-58NLJ9?OpenDocument
Irritatingly, the pdf version, which contains the diagrams, doesn't work. He says that the dimensions are 980 x 520 feet, but that the slurry wall is 3,500 feet long. I can't see that.

[Make7]

45. Damn these posts are getting long. LOL!

I actually am almost on my way out the door, I'll respond in more detail later. (Hopefully tonight.) But I did want to make a few comments.

Posted by Kevin Fenton:

I seem to remember that the floors on the mechanical floors were thicker than the others (7 inches?). I also remember something about the floors in the cores being thicker. You wouldn't happen to know this off-hand, would you?

I don't know about the mechanical floors, but I seem to remember that the concrete was 5 inches thick within the core. Don't recall the source for that right now though.

Posted by Kevin Fenton:

OK, the roofs:
1..208...208...0,33...0,037...528,25344
2..208...208...0,33...0,037...528,25344
3..64....330...0,33...0,037...257,8752
4..84500.......0,33...0,037...1031,745
5..120000......0,33...0,037...1465,2
6..67000.......0,33...0,037...818,07
..............................4329

I'm not going to go over the numbers right now - I just wanted to give you a hint on displaying tables. You can use the html <pre> tags to preserve the spaces in your text and make all the characters the same width. For example this code:

[font color="#000099"][pre]
      area   thickness  cu. yds.   total
1. 208 x 208    0,33     0,037    528,25344
2. 208 x 208    0,33     0,037    528,25344
3.  64 x 330    0,33     0,037    257,8752
4.     84500    0,33     0,037   1031,745
5.    120000    0,33     0,037   1465,2
6.     67000    0,33     0,037    818,07
[/pre][/font]

Will result in this:

      area   thickness  cu. yds.   total
1. 208 x 208    0,33     0,037    528,25344
2. 208 x 208    0,33     0,037    528,25344
3.  64 x 330    0,33     0,037    257,8752
4.     84500    0,33     0,037   1031,745
5.    120000    0,33     0,037   1465,2
6.     67000    0,33     0,037    818,07

I did the same thing you did for my first few tables, but didn't really like the result. Just thought I'd share that in case you wanted to use it.

Posted by Kevin Fenton:

I'm going to leave the spandrel beams for now.

Me too! I don't even know where to start - almost no information except the cross-sectional area for those.

Posted by Kevin Fenton:

Fireproofing of perimter beams:
1,5 (width of beam (14 inches) + width of coating in feet) x 0,3 (width of coating in feet) x 4 (sides of column) x 70 (height of basement) x 236 (number of perimter columns) x 2 (number of towers) x 0.037 (conversion to cubic feet) = 2200.

The perimeter columns of the tower were combined in groups of three above ground in the "trees" and then went to the foundation in a reduced number of larger columns. I don't know the numbers and dimensions off the top of my head.

Posted by Kevin Fenton:

My running total is just over 260,000 cubic feet. Where the hell did they put the rest of it? There must be lots of concrete walls in the basement outside the towers, maybe it's there.

I think it's probably all in those spandrel beams. :)

Actually, I'm not sure about a lot of this yet, but I applaud your efforts to work on this estimate with such limited information available. I hope the results will help answer some questions.

More to come...

- Make7

[Kevin Fenton]

51. What do they need spandrel beams for?

First an aside about the sub-level: the reason I'm interested in this is that Rodriguez (remember the basement blast?) says that he was on the first sub-level when the blast happened. I've always wondered which floor this actually was. If it really was the second underground floor, then that narrows the number of elevators running from the impact floor to his level down to 1 - car 50A, which might come in handy later.

Thank you for the tip about tables, I will try to apply it next time.

If the basement walls weren't load bearing, then what would they need spandrel beams for? Wouldn't the only use of a spandrel beam be in a doorway in a concrete wall, so that the space between the top of the door and the ceiling could be concreted?

5 inch core floors.
139 (core length) x 89 (core width) x 0.083 (1 extra inch) x 0.037 (conversion to cubic yards) x 220 (number of above-ground floors in both towers) = 8,300 cubic yards.

The running total is now about 268500

[Christophera]

57. Architects Concrete Schedule Shows Type-MECH. Floor Very Thick

I thought the 48th floor had the major elevator motors and was very thick, but thiis schedule doesn't show it. The steel changed there too.

[Kevin Fenton]

58. Elevator motors

There were definitely no elevator motors at all on floor 48, because no elevators ended on floor 46 or 47 - the motors were above the elevator shafts. There were never more than 12 or so shafts that ended at the same floor.

[Christophera]

61. Elevator Motors And Pulleys-Weight Of Motors, Reels Too Much For Upper

floors.

Pulleys systems reached from the top down. No point in putting all that weight up there. There may have been some other critical component on the 78th floor. Seems I remember something about elevators and that floor.

[Christophera]

62. Three Sky Lobbies Divided Buildings Into Zones

http://www.elevator-world.com/magazine/archive01/9805-003.html-ssi
The twin 110-story New York World Trade Center (WTC) towers are a perfect example of stacked office building applications. Each 33-story portion is serviced by four zones each with six single-deck local lifts, with the local lifts of zone II and III separated by two sky lobbies. Building tenants or visitors desiring elevator transport to the floors of zone II or III must first travel on a sky-lobby shuttle elevator to the upper sky-lobby and then transfer to the appropriate local lift for final transport to their destination. A passenger departing an upper-zone floor must first travel via a local lift to the sky-lobby and then transfer to a sky-lobby shuttle elevator for final travel to the ground floor. The WTC sky-lobby shuttles are some of the largest passenger elevators ever constructed. They have a duty of 4,500 kilograms at 8.0 mps and are equipped with front and rear openings, to ease passenger flow. Each cab has a net platform area of 7.8 square meters and is designed to accommodate up to 50 persons, with 30- to 35-person nominal load. Each tower is equipped with 23 shuttle units, with 12 units capable of serving Zone II's 44th-level lower sky lobby and 11 units having service capability to Zone III's 78th-level upper sky lobby.

[Kevin Fenton]

64. Yes yes yes

"Each cab has a net platform area of 7.8 square meters"
That's exactly what I needed.

If you look at page 14/52 of the NIST report on the elevators, which you can find here:
http://wtc.nist.gov/NISTNCSTAR1-7.pdf
you will see a diagram of the elevators at the concourse level. There are two rows of 11 and 12 express elevators (marked with crosses) at the top and bottom of the core. There are also four banks of 6 express elevators in the middle. The fireball that hit the concourse (and other) levels in WTC 1 is supposed to have come down freight elevator shaft 50, but which one is this and how big is it?
The small elevator at the bottom of the "cross" is not on the diagram on page 11/49 (a typical floor) so we can exclude that. The hatch door blowout was supposed to be by the local elevators, so I think it's one of the two equally sized elevators in the middle.
Assuming the platform area of the express elevators is 2.25m x 3.45m (7.5 times 11.5 feet), then the area of freight elevator 50 should be about 8.5 x 8.5 feet, adding 3 inches on either side for the elevator walls and leeway we get an area of 9 x 9 = 81 square feet. The distance from the top to the bottom of the shaft (floor B6 to 108) should be about 1450 feet, so the total volume of the shaft is 117,450 cubic feet. Right? How much jet fuel do they need to fill it?

[jschurchin]

65. You are not going to..........

believe this Kevin. The shaft will hold 878,587.013 U.S. gallons or 3,325,813.646 liter's. How big is the fuel capacity of a 767 again? Oh yeah, I remember, 23,000 gallons or 90,000 liter's.

Source for the conversions: http://www.onlineconversion.com/volume.htm

[Christophera]

66. With Heated Fuel, 1,000 GAL.'s Enough For Fireball From Enclosed Space

And it will have lots of concussion too. All it takes is vapor and a spark to detonate.

The north tower had a hole punched through the concrete core by one engine. The fuel ran down, flaming, flaming debris, vapor pressure, boom. Fireball. The core was a chimney of fuel vapor and thick fuel smoke.



The awareness of how impossible it was to leave the north tower from above the impact area brought a memory of what I haven't read for a year at least. When I do, I get angry and need justice.




EYEWITNESS AT WTC

For me, there were many moving experiences... I will never forget the tens of thousands of bobbing heads stumbling across the East River bridges. Or, the dazzled tattered bleeding blackened crowd walking north from the scene up Broadway, Green, Mercer, 6th Avenue... - that was moving...But above and beyond everything, the one thing I will never forget to my dying day, is the view of the people on the roof and higher floors of the World Trade Center lined up in the windows and on railings. You cannot see their expressions, but it is amazing what a 40 power telescope reveals. They often huddled, probably talked about their chances, and sometimes went back into the building, or maybe, just laid on the floor. But then, some went to the edge, and jumped.

Some jumped in pairs, holding hands. I doubt if they were married or lovers. I think it was just two people, alone, desperate, black, white, oriental, who cares - the telescope didn't allow me to distinguish age and race. They would just pair up and jump. I have thought all day about this. If I were on the roof, and I saw flames on all sides of the building, I would almost certainly jump rather than fry. And if I saw another trembling human alongside of me, I would be much happier holding their hand, and jumping as a pair. Somehow to jump as half of a pair, even if the other half is an ad hoc recent acquaintance, seems to me an infinitely more human way to pass on to the next step, than to take the next step alone.

A follow-up letter (full text here): I did not mention it in the first letter, but it seems to me relevant to something. When a person jumped alone, s/he went to the edge, stopped, looked over, and jumped like you would go into a pool. Those that went in pairs simply came out of a smoky nowhere inside of the building and walked over the edge with no pause, hesitation, or last second spring.

Ray Dougherty, Professor of Linguistics, New York University
Eyewitness

[Kevin Fenton]

67. Fuel expands in a fireball

It expands a lot. The plane had 10,000 gallons when it hit the tower.

NIST says:
"Less than 15 percent of the jet fuel burned in the spray cloud inside the building. A roughly comparable amount was consumed in the fireballs outside the building. This, well over half of the jet fuel remained in the building, unburned in the initial fires... Some of the burning fuel shot up
and down the elevator shafts, blowing out doors and walls on other floors all the way down to the basement." (p. 24/74)

This is Thomas Eagar talking about the fireballs outside the towers.
"Thus, if the jet fuel was consumed mostly in the first few moments, three things must be present. First, there would have been a fireball of fuel 500 times as large as the liquid fuel multiplied by 5 times as much air as the oxygen required (because air is only 20 percent oxygen) or a fireball 2,500 times the volume of the liquid fuel that was consumed."
http://www.pbs.org/wgbh/nova/wtc/letters.html

So we need to divide 878,587.013 by 2,500. I get about 350 gallons in the shaft before the doors start to be blown out. That sounds unlikely, but not impossible.

[Christophera]

68. Good Work! Fully Possible, Even Likely

Is that WTC 1 or 2 eagar refers to?

[Christophera]

34. Yes, Volumes Best, Then Convert, BUT, Is 425k cu yd Figure Above Ground Or

a total for both towers and the basement, or just the towers?

I calculate 210,000 cubic yard above ground including the inner core walls every other floor. Twice that is very close to the 425k figure. Meaning that the statement may be actually "425,000 cubic yards in the towers". Then, .......... as it got handed down it changed to "425, 000 cubic yards in the WTC".

According to my site plans there were 5 floors of solid concrete at the center below the tower, outside its footprint which was acres.

[Christophera]

37. jschurchin, Check This Post. Fundamental Question Resolved, .... Perhaps

Below ground there my have been a million cubic yards of concrete in the center.

[Make7]

38. Could you explain your post in more detail?

What fundamental question do you believe has been resolved?

How did you arrive at your figure of 1,000,000 cubic yards of concrete below ground? Were you planning on just posting a number with no explanation at all?

More than a million cubic yards of dirt had to be removed to make way for the Trade Center's foundations. The excavated earth was placed in the Hudson River adjacent to the site, to create more than 23 acres of new land, land which was donated to the city of New York.

Source: Building the World Trade Center, produced by the Port Authority of New York and New Jersey in 1983

http://www.pbs.org/wgbh/amex/newyork/sfeature/sf_building_pop_01_tr_qry.html

And according to the dimensions that Kevin Fenton previously posted (see Post #6) the entire volume of the "bathtub" would be roughly 1,300,000 cubic yards. Do you feel that the majority of that space was filled with concrete?

- Make7

[Christophera]

41. I Stated Opposite. Possible 1mil CU. YD's In Center. 425k In Towers

I guessed at 1 million in the entire WTC including the towers.

The floors and walls of the below ground structures plus foundations over the acres in the center would constitute a significant volume.

My point was that the above ground concrete with a concrete core matches very closely the 425k CU. YD. figure. Actually the only real match that exists amongst all the possibilities.

[Make7]

42. I may have misinterpreted.

Posted by Christophera:

Fundamental Question Resolved, .... Perhaps

Below ground there my have been a million cubic yards of concrete in the center.

http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=125&topic_id=71293&mesg_id=71930

Posted by Christophera:

According to my site plans there were 5 floors of solid concrete at the center below the tower, outside its footprint which was acres.

http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=125&topic_id=71293&mesg_id=71861

To me, those statements made it sound like you thought there was a million cubic yards of concrete below ground.

It was always my impression that the 425,000 cubic yards figure was for the entire site. Are you basing your contention that the 425,000 cubic yards figure was only for the two towers on something?

- Make7

[jschurchin]

47. Make 7, from the site....

http://www.infoplease.com/ipa/A0903568.html

they state the information as follows:

Twin Towers Stats
—200,000 tons of steel

—425,000 cubic yards of concrete

—43,600 windows

—12,000 miles of electric cables

—198 miles of heating ducts

—23,000 fluorescent light bulbs

Each Tower
—110 floors

—208 ft by 208 ft at base

—1,368 ft high (north tower)

—1,362 ft high (south tower)

—Weighed 500,000 tons

—97 elevators for passengers, 6 for freight

It makes it sound as if these statistics are for the towers. This is only one site and really needs some corroboration, standing alone it could give the impression that this is just for the towers. I got the night off and am going to be doing some surfing to see what I can find.
If all goes well my head won't explode. LOL.

[Kevin Fenton]

49. Not one site

It's not just one site. All sites on the WTC I have seen all present the information that way, as if the 425,000 cubic yards was for just the two towers and they each weighed 500,000 tons. If you ask me (the only "official site" that disputes this is NIST), they are all wrong - the elevator numbers are wrong too, it's 99 passenger and 8 or 9 freight.

Steel is supposed to be the main structural element, using the above figures, it only accounted for 1/5 of the towers' weight, whereas concrete, of which there is relatively little according to absolutely everybody, accounts for 60-80 percent of the towers' weight, depending on what type of concrete and how heavy it was. This doesn't make any sense. Besides, there are dozens of references to concrete in the basement, concrete perimeter, core and room walls, concrete spandrel beams, concrete column fireproofing, etc. so there must be lots of it there.

[Christophera]

63. Right Breakdown, Weight To Volumes-Floor Weight Can Be CALC.ed & Subtracte

d.

And yes, tremendous amounts of concrete in the basement concourse. One sticky question.
Why was below ground concrete so pulverized? No big chunks of concrete came down, all materials were in smaller pieces except for this.

[Make7]

69. "425,000: Cubic yards of concrete used to build the World Trade Center"

GOVERNOR PATAKI, ACTING GOVERNOR DiFRANCESCO LAUD HISTORIC PORT AUTHORITY AGREEMENT TO PRIVATIZE WORLD TRADE CENTER
Date: July 24, 2001
Press Release Number: 101-2001

   <- snip ->

THE WORLD TRADE CENTER: BY THE NUMBERS

   <- snip ->

7: Buildings in the World Trade Center. In addition to One and Two World Trade Center (the Twin Towers), the complex includes Three World Trade Center (the World Trade Center Marriott Hotel); Four and Five World Trade Center (the Southeast and Northeast Plaza Buildings); Six World Trade Center (the U.S. Customs House); and Seven World Trade Center (a 47-story office building).

   <- snip ->

425,000: Cubic yards of concrete used to build the World Trade Center, or enough concrete to construct a 5-foot-wide sidewalk from New York City to Washington D.C.

http://www.panynj.gov/AboutthePortAuthority/PressCenter/PressReleases/PressRelease/index.php?id=80

[Christophera]

48. Concrete Volume Of 1 Tower x 2 = 420k CU. YD's-Close To 425k

I base the contention that the towers combined were what was referred to with the 425k CU. YD figure.

Yes, I forgot a word "made"

"According to my site plans there were 5 floors made of solid concrete at the center below the tower, outside its footprint which was acres." Meaning high strength aggregate concrete.

[jschurchin]

40. What area are you using......

Christophera to make this determination? Are you using the "bathtub area? My calculations provide me with some 55,278 sq. yds. of "bathtub" area. Assuming 12" thick decks (no ramps or walls) I figure some 104,445 cu. yds of concrete, 5 decks and the tub floor. A million is a lot. All of my calculations together are no where near that.

What am I missing, well besides a "normal" brain.

[Christophera]

55. Revised Estimate For Below Ground, Tower Foundation INCL. 200k CU. YD's

I did some rough calculations for the floors, walls, slurry wall and tower foundations. About 200k CU. YD.'s from a crude estimate seems to cover what may have been below ground.

A million total for the WTC was a wild guess. More like 650,000 total.

[Make7]

39. I always thought the 425,000 figure was for the entire WTC site. ( n/t )

[LARED]

14. I think the figures of

800,000 tons will be close.

Without knowing the scope of the concrete work it is hard to say where it went. We have very little knowledge about the foundations and lower level construction.

[Kevin Fenton]

21. What about the weight of the towers?

Several people have suggested that this weight was contained in the above-ground portions of the Twin Towers, i.e. each tower weighed 500,000 tons, of which steel accounted for 100,000 tons and concrete 400,000 (or a bit less if some of it were lighweight concrete). Do you agree with them or with NIST (which says each tower weighed 250,000 tons)?

If there were 800,000 tons of concrete in the towers and 200,000 tons of steel, then that would give us a steel: concrete ratio of 1:4, meaning that the towers were really heavy concrete structures, not lightweight steel ones. Even if we reduce the weight of some of the concrete (as Make7 suggests above), then we're not going to get a steel:concrete ratio below 1:3.

Vincent Dunn says, "The ratio of concrete to steel in the WTC is 40/60." (http://vincentdunn.com/wtc.html) That's just an estimate, but he was a Deputy Fire Chief in NY and seems to know quite a lot about the WTC and other NY buildings.
Also, every single other source describes the WTC as lightweight buildings, for example Wikipedia says the buildings had a "very light, economical structure". (http://en.wikipedia.org/wiki/World_Trade_Center)

As far as the basement goes, we should be able to get some ballpark figures using averages. The bathtub wall is 1,000 + 500 + 1,000 + 500 feet long, 3 feet thick and 70 feet high, that's not a difficult calculation, even for me. How thick do you think the various basement floors were? What about vertical (load-bearing) walls in the basement below the plaza?

[LARED]

26. If the NIST says the towers

weighed 250,000 tons each, I would assume that is the best number. The NIST did an extensive study of the towers, had access to available documents, hence would be in the best position to have accurate information.

It also seem to me if you go with 250,000 tons the math starts to add up a lot better.

[Kevin Fenton]

43. First of all...

What exactly do you mean by, "If you go with 250,000 tons the math starts to add up a lot better."

The NIST quote is:
"With no warning that could be discerned in WTC 1, WTC 2 collapsed. The shudder as the more than 250,000 tons of steel, concrete and furnishings hit the ground was felt well beyond the site." (p. 32/82 of the full report)
If the towers (or rather the above-ground portions of them, I assume this is what NIST is referring to) weighed approx. 250,000 tons, then each floor weighed about 22700 tons, right?
Obviously, there are issues with how the weight was distributed, for example there should be more steel at the bottom (because the columns were tapered), there should be more machinery on the technical floors (of which there were some at the very top of the towers) and above the elevators and there should be more concrete on the technical floors. However, this is horrendously complicated and they should cancel each other out to some degree, so let's leave them for now.
If we take the probable initial collapse floors (if it was a "natural" collapse, which I don't think it was) to be 96 for WTC 1 and 81 for WTC 2, then that gives us a maximum weight of 317,800 (14 x 22700) hitting floor 96 and 658,300 (29 x 22700) hitting floor 81. Right?

[jschurchin]

46. Kevin, I came up with a different.......

figure. Are you sure about 22,700?

[Kevin Fenton]

50. 22,700

is a number I derived from NIST's figure for the total weight of the above-ground portion of the South Tower. They say it weighed 250,000. I divided that by 110 and got 22,700.

The figure of 250,000 seems reasonably accurate to me. It probably works out at about 100,000 tons of steel, 100,000 tons of concrete and 50,000 tons of equipment and furnishings.

What number did you get?

[jschurchin]

52. 2,270, then I reversed the............

the calculation to read 110*2,270, to make sure my division was correct. The result was 250,470. I believe you may have just misplaced a zero. If you take 22,700 and multiply it by 110 the result is 2,497,000.

[Kevin Fenton]

53. Oh ****, sorry

You are right. Maybe I should do my calculations on paper too.

Yes, it is 2,270 - I added a zero.

Assuming the floors all weigh the same (they don't but nevermind for now), that gives us 31780 tons above the central impact floor in WTC 1 and 65830 tons above the central impact floor in WTC 2. Is that OK?

[jschurchin]

54. Doing my best Ed McMahon by.......

the late, great, Phil Hartman. "You are correct, Sir." Yeah, Kevin I got the same figures. I was searching last night and found a site, actually a forum where 2 engineer's where discussing that possibly the 500,000 may be for a "live load". Their calculations were metric and they figured 300,000 metric ton's as the towers gravitational weight, with the remainder as possibly being a live weight calculation. I will find it and post the link.

This is turning into a god damn science project.

[Christophera]

56. About Time To Clarify, Calculate Volume Issue W/Sources

Then of course you are talking load, tons, wherein we have to subtract the concrete weight from the steel because the concrete core was self supporting, then later took 20% at finish with an expected transfer of 10 to 20 percent more over time.

[Kevin Fenton]

59. Concourse, basement

Here is a plan of the concourse:


It covers the entire plaza area, not just the bathtub. I've no idea how much concrete they used in (floor, ceiling, supports), but we can add it to the "list of areas with concrete to be quantified".

What about the walls in the basement? If there were walls every 100 feet running east-west and north-south (meaning plan north, not true north) then that would give us four walls running north-south 1000 feet x 6 inches x 70 feet x 4 walls = 5180 cubic yards of concrete and 9 walls running east-west 500 feet x 6 inches x 70 feet x 9 walls = 5928 cubic yards of concrete. I'm not at all sure about this, what do you think?

[Christophera]

60. Best Reason For 425k CU YD's As Towers Only Figure, Where Do You Stop?

The same goes for the excavations. Do they consider part of the path tunnels as that?

BTW, I came up with a similar figure of concrete volume for the basement concourse, 500 x 100

[jschurchin]

15. I believe that's a fair estimate.

We all know structures are over-engineered. In other words, if you calculate a dead load at 200 psf you will design it to handle 300 psf. All of a vehicles weight is distributed thru the four tires at rest. Say an average vehicle weighs 2,500 lbs, the tires footprint is less then 1 sq. ft. each. The structure should be able to withstand 625 psf to support the vehicle. Agreed? Or am I making an error.

[LARED]

17. I would not be surprised in the least if it was 12"

I just don't understand how the comment about reinforced concrete being 12" thick and the comments that were posted are related.

[jschurchin]

18. I understand.

[Kevin Fenton]

22. Where does that leave us?

Doubling the thickness of the basement floors (from 4 to 8 inches) brings the amount of concrete there up from 37,000 to 74,000 cubic yards. I didn't go the whole hog and increase the thickness to 12 inches, because I don't think all the basement area was used as a garage (the concourse certainly wasn't). I'm assuming that the whole area of the bathtub was used, though.

Anyway, WTC 4
Some info can be found here: http://www.foxnews.com/story/0,2933,34255,00.html
The floor area is 84,500 square feet, if the floors were 4 inches thick, then that's 28167 cubic feet, divided by 27 gives us 1043, multiplied by 9 (floors) is 9387 cubic yards of concrete used in the above-ground floors.

WTC 6
Some info can be found here:
http://en.wikipedia.org/wiki/6_World_Trade_Center
Floor area of 537,693 square feet, divided by three gives us 179,564 cubic feet, divided by 27 is 6651 cubic yards of concrete used in the above-ground floors.

My running total is now 250125 - 175,000 cubic yards to go.

We haven't counted the roof of any building yet. What were they made of?
Also, there must be some vertical load-bearing (and also perhaps non-loading bearing) elements (presumably made of concrete) in the basement under the plaza. The area of the bathtub (and therefore presumably the basement under the plaza) is 500,000 square feet, but the towers were only 86528 square feet. The other 413472 feet have to be supported by something.

[jschurchin]

30. IMO this is where we stand.

We have given quantity's of material, and dimensions of the area, and structures, were we know that they fit. Some members have put forth theory's (concrete core) that people have ridiculed and called baseless. Until it can be proven to a reasonable certainty thru the study of the available materials and calculations of the structures and area along with certain variables i.e. concrete thickness, nothing can be ruled out.

This much I can say with certainty, we have a lot of research ahead of us. I want to thank everyone for their input to this thread. It is enlightening and stimulating to see people, who may disagree at times, that can also work together to find a solution to a puzzle.

One last thing, going with quantity is fine by me, I figure 50,192 cubic yards in the towers,including the sub-levels(towers only).
Thanks Again,

John

[Make7]

31. I think that may be a typo.

50,192 cubic yards?

-Make7

[jschurchin]

32. So it is Make..........

hey cut me a break, I'm doin this shit on paper. How about 60,192 per tower, dont forget including the tower lower levels. Sorry.

[Make7]

33. I just thought that number was odd.

It was less than what you had for each tower in your opening post.

In that post you calculated 528.471 cubic yards per floor. So if you take 110 floors above ground + 6 basement levels + the roof, you get 117 concrete slabs of 528.471 cubic yards. The product of those two numbers equals 61,831 cubic yards. As far as I can tell, your latest figure does not include any of the following: concrete walls in the basement, concrete encasement of columns in the basement, fireproofing of some of the steel beams throughout the building.

Estimating all of this is by no means an easy task. If it was, I probably would have done it long ago. As it is, there are still a lot of unknowns to try and resolve, but with everyone giving their input to the problem perhaps we can come up with something useful.

- Make7

BTW - Don't you have Excel or some other spreadsheet application on your computer? It would make things a whole lot easier.

[jschurchin]

35. Well to answer this .......

"BTW - Don't you have Excel or some other spreadsheet application on your computer? It would make things a whole lot easier."

Yeah it would make it easier. My brother is a CPA, I asked him one day what 81*9 was, I got this look like, Duh!!!!!! It took him a couple minutes to give me an answer. You see he forgot how to do math without a machine. Call me a dweeb but, I never want to get into that habit. That is why I do my calculations longhand.

[AZCat]

36. I try to do them longhand first...

but when I'm making lots of iterations it is far easier for me to implement the algorithm in a program like Excel. Fortunately I have lots of practice - I do a lot of this at work every day.

[Name removed]

23. Deleted message

Message removed by moderator. Click here to review the message board rules.

[Make7]

27. Directions.

This building:

Seen in the upper left hand corner of that picture, is the "Transportation Building" at 225 Broadway. It is on the corner of Barclay and Broadway - indicated by the green X in the upper right of the map shown below.

X

This would make the WTC building seen in the foreground of the picture WTC 5. So the camera is basically looking almost due east.

I see that you have taken it upon yourself to change the North indicator of the map shown above. While originally found on page 5 of the first chapter of FEMA's WTC report (link), that one looks like the map mirrored on the 911research.wtc7.net (link) analysis of the FEMA report. Here is the map as shown on that site:



Interesting.

- Make7

[Christophera]

19. Observations Of Parking Garages, Average Depending On Span

There are some diagrams of the parking garage in a set of plans I have that were 1964 preliminaries. I estimated by the ramps depicted the spans and guessed at their thickness. No sections or minor dimensions are given, but just knowing the spans will give us an idea of thickness in floors and walls. I'll check them out closer.

[LARED]

24. So what does this have to do with the

story about the guys in the WTC basement?

[Christophera]

28. The Walls Blowing At Impact In The Basement Were About Likely 12" And

our efforts to determine volumes in the basement need some basis.

[rman]

8. if there's disinfo out there regarding the core

(either way..)
then there's probably also disinfo regarding the rest of WTC construction - ie thickness and strengthening of the floors.

[jschurchin]

16. Here's the thing about the material.....

If you are the owner of a building under construction, you will pay for the material received, agreed? Say I own a supply company and I have a contract to supply you with 425,000 yds of concrete but I only deliver 350,000 yds. Would you still pay me for the 425,000? If, yes, whats your number? I got some stuff to sell you. If, no, it's safe to assume the material and quantities quoted were used in the structures.