What was the weight of a WTC Tower?

What was the weight of a WTC Tower?

If you really want to get into the physics of the collapse of the WTC Twin Towers, sooner or later you will need to know the weight (or mass) of a WTC Tower, or at least a Tower block of 15 to 30 floors. After all, the potential energy of a structure ( = Mgh) and the kinetic energy of a falling block ( = 1/2 Mv^2) are both functions of mass…......See, for example, the calculations presented at :

http://www.911myths.com/html/other_contributions.html

If you search for published values of the mass of WTC 1 or 2, the number quoted is invariably close to 500,000,000 kg or 500,000 tonnes. But where does this number come from?

I have certainly never seen a detailed calculation of the mass of WTC 1 or 2; but there are plenty of references on the web for the weight of the materials used in the construction of the WTC Towers. For example, the weight of structural steel used in each Tower is generally reported to be 96,000,000 kg and the weight of concrete is said to be 48,000,000 kg per Tower. I have also seen the weight of aluminum cladding reported to be 2,000,000 kg, and the weight of wallboard quoted at 8,000,000 kg per Tower, giving a total weight of structural materials of 154,000,000 kg per Tower.

Now let’s add in reasonable “guesstimates” for plumbing fixtures (5,000,000, kg), air conditioning (5,000,000 kg), electrical and telecommunication wiring (5,000,000 kg) and we have an additional 15,000,000 kg of structural mass that civil engineers always include as part of the “dead load” of a building. Thus combining all these contributions, we arrive at a weight, or dead load, of 169,000,000 kg for one WTC Tower. Surprisingly this accounts for only about 1/3rd of the oft-quoted 500,000,000 kg, so where is the missing mass?

The answer would appear to be in what civil engineers call the “live load” of the building, which in the case of one WTC Tower would have to be (500,000,000 - 169,000,000) kg or 331,000,000 kg, i.e., twice the dead load! We will show that this result leads to major problems …..

But first, let’s convert our load data in to more familiar engineering units based on floor areas. Building codes usually express loads in pounds per square foot (psf) or kilograms per square meter (kg/m^2). For example, the specification for a high live-load capacity floor is typically about 150 psf or 750 kg/m^2.

From the dimensions of a WTC Tower we estimate the available floor area per Tower was about 320,000 square meters. Hence, the live load was 331,000,000 kg divided by 320,000 m^2 which is equal to 1034 kg/m^2 or 212 psf. We see from the live load example given in the previous paragraph that 212 psf represents a very high live loading. But let’s look at just how high this load is…..

If the live loading within one WTC Tower really was 331,000,000 kg (more or less), that equals 3,009,091 kg per floor or about 3000 tonnes per floor!! I believe each WTC Tower employed about 15,000 people so we have an average of 136 people per floor. This means that each person working in the Twin Towers contributed about 22 tonnes of live load!!! That's an awful lot of office furniture, computers, printers, telephones..... or am I missing something?

NEU-FONZE

From Bazant-Zhou paper

Thanks for the reply!

If we assume that "the upper part of the North Tower" was 15 floors, then the mass of one floor is 1/15 x 58 x 10^6 kg = 3.87 x 10^6 kg, so the mass of 110 floors is 425 x 10^6 kg -quite a bit lower than the 500,000,000 kg figure I discussed in my post.........

By the way, I have recently found these building weights on various skyscraper websites:

Empire State Building, NYC = 365,000,000 kg
Woolworth Building, NYC = 223,000,000 kg
John Hancock Tower, Chicago = 174,500,000 kg

Looking at these numbers I would say that 500,000,000 kg is definitely too heavy for one WTC Tower. Bazant and Zhou's number is a bit more reasonable, but once again I ask: "Where does B&Z's number come from?" Are people just guessing!?!

NEU-FONZE

The mass of the flooring of all floors would be pretty much the same but the vertical structural columns are thicker nearer the bottom than they are higher up so the total weight of the top 15 floors (flooring and columns) would be less than say the 1st to 15th floor since the columns are much bigger and heavier there.

Yes, this is a good point, so Bazant's number would tend to give a low value based on my simple ratioing..... I have done some more digging on all this and found that the EXPERTS can't agree on this one. There are many values given for the total POTENTIAL ENERGY of one Tower, which is another way of expressing the mass of the Tower. FEMA give 4 x 10^11 Joules while the Civil Engineering Magazine (put out by the ASCE) give the PE of one Tower as 3 x 10^12 Joules, or almost 10 times higher than FEMA. At the other extreme, Prof. Frank Moscatelli of Swarthmore College tells us the PE of one Tower was only 3.4 x 10^11 Joules. So, as I say, I think the mass of the WTC is not known with any certainty .... Neufonze

Quite true. If one simply wants to know the energy released by the upper section and assume a free fall rate this is easier since we have a total mass falling a set distance. However in calculating even this one must add up not only the mass of steel and concrete but also the mass of the walls, the desks, the computers, the file cabinets and their contents, the furnishings and of course the people. At an average of 75 kilograms each, if a floor had 50 people on it that is another 3750 kg.

Then if one wants to calculate the total PE of the entire tower you have to take into account the fact that not all the mass is falling the same distance. The mass of material that makes up all of the tenth floor will only fall ten floors while the mass of the eleventh floor will be falling 3.7 meters farther.

Thus all calculations of this sort(for total mass or PE) will invlove estimation and/or various methods of integration(calculus)

Yes, you can correct for the pile-up of material if you want. For example if you allow for the thickness of each floor, material at the top of a Twin Tower cannot fall the full 416 meter distance to the ground, especially if the Tower falls entirely into its own footprint. That is why it is better to use a height of say 406 meters to calculate the free-fall time of the WTC, in which case the free fall time is 9.1 seconds. The actual collapse had to be longer than this because the structure offered some resistance. At this point the MASS of the building is critical and Aristotle not Galileo had the right answer... heavier bodies fall faster. NF

Well the piling up is one thing but in calculating PE I was refering to the fact that any specifac chunk of the building could only fall as far as it was above the ground.

Think of it this way. You have two full steel file cabinets with the same mass, one on the 100th floor and the other on the 50th. The one on the 100th floor has a potential gravitation energy that is twice that of the one on the 50th floor. When the building collapses the portion of PE represented by the file cabinet on the 50th floor is still the same.

The piling up of material reducing the recorded collapse time is something I have mentioned before on another thread.

Well, you can also allow for the fact that g, the acceleration due to gravity, is a function of h if you want to! But I would say that to take PE =1/2Mgh, with h ~ 400 meters, is a pretty good first approximation to the total PE of one Tower. The uncertainty in the mass is still a big problem however .... All I am looking for is a scientific evaluation of the mass of the Twin Towers (and the mass of WTC 7). WTC 7 was specially reinforced on a number of floors and probably had higher dead and live loads per floor than the Twin Towers. You need to know these numbers for a momentum transfer calculation of the respective collapse times........... NF

There is a huge building in Japan that has been the source of earthquakes by putting pressure on a nearby fault. The weight of water in new resevoirs has been shown to cause earthquakes in some instances. The shock waves from the collapse of the World Trade Center towers must have exceeded the force on the fault resulting from the weight of that skyscraper in Japan. If there was a nearby fault near Manhatten it might have triggered an earthquake. The is a fault somewhere in the Northeast that has not been active for 200 years. Sceintists should be looking at for signs of chnage from the collapse of thrd trade towers.

Yes, I have read something similar about the current "tallest building in the world" Taipei 101. It's been suggested it could cause an earthquake from the localized pressure its putting on a fault line. I believe Taipei 101 weighs in at a staggering 700,000,000 kg.

Manhattan Island is crisscrossed by earthquake faults, and twice in its history — 1737 and 1884 the nation's biggest city has been jolted by relatively mild quakes in the 5.0 range. Whenever the next one strikes, scientists worry that it could be far bigger. Much of Manhattan sits on a deep layer of soft, post-Ice Age sediment over extremely hard rock, a juxtaposition of geological extremes that bodes ominously. A 6.0 quake could shake the city's buildings with nearly the intensity of the 6.8 quake in Kobe. Inexplicably, the city dragged its feet about adding earthquake-mitigating requirements to its building codes until the mid-1990s. The generally well-designed towers in the Manhattan's skyline most likely would survive a 6.0, but the unreinforced masonry townhouses where most residents live might not fare so well. A 1989 study estimated that a quake would cause more than 130 simultaneous blazes, which could put the fire department under severe strain.

http://tlc.discovery.com/convergence/quake...satrisk_04.html

27 October 2001

At 5:42 AM EST a magnitude 2.6 tremor struck the west side of Manhattan (40.76°N latitude and 73.98°W longitude). The epicenter of the quake plots near the vicinity of 55th Street and Eighth Avenue and rang in at a depth of only 1 km. These events are significant because they mark the first recorded on-land earthquakes to occur within the confines of New York City. Incidentally, for comparison purposes only, the collapse of the first and second towers of the World Trade Center on 11 September 2001 registered 2.1 and 2.3 on the Richter scale according to seismologists at Lamont-Doherty Earth Observatory.

http://www.dukelabs.com/NYC%20Quake/NYCQuake.htm

That building makes use of a lot of concrete in its core columns so it could be heavier than the towers.

The actual mass of the twin towers is going to be an estimate unless someone actually did the calcs fot the completed , occupied building.

You posted

Given your numbers for those other buildings I have no problem accepting a 500,000,000 Kg mass for one tower. That would make it twice as massive as the Woolworth's building and a little over a third again as massive as the ESB. Considering the difference in construction materials and sizes this sounds about right.

Are these numbers including or excluding the foundation? My feeling is that this is only the above ground component of the structure.

I, too, would think that all the published weights of these buildings are for the above ground structures. That is certainly the number of interest for potential energy calculations. And, yes, I think 500,000,000 kg each for WTC 1 and 2, may not be too bad a number, but I still wonder about the live load vs. the dead load. With over 30 years of continuous operation, the Twin Towers were being loaded up with more and more junk all the time. Desk top computers wern't even invented when the Twin Towers were built! Was anybody keeping track of the increasing floor loading? NF

There is another way to estimate the mass of one WTC Tower. That is from the mass of the rubble pile. Because ground zero clean-up contracts were based on a specific WEIGHT REMOVED, there are good records of the mass of material removed from the WTC site after 9-11......

Values ~ 1.7 million tons for the entire site are usually quoted, but this includes WTC 1, 2, 3, 4, 5, 6 and 7. If we let the mass of WTC 1 = x and assume:

Mass WTC 2 = x
Mass WTC 3 = 1/4x
Mass WTC 4 = 1/4x
Mass WTC 5 = 1/4x
Mass WTC 6 = 1/4x
Mass WTC 7 = 1/2x,

we have:

Mass of all the buildings at the WTC site = 1.7 million tons = 3.5x,

in which case x, the mass of a Twin Tower = 485,700 tons