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NEU-FONZE
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
yesitdid
From Bazant-Zhou paper

QUOTE
m = mass of the upper part (of North Tower)  58·10^6 kg,
NEU-FONZE
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
yesitdid
QUOTE (NEU-FONZE+Jan 6 2006, 02:56 PM)
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.
NEU-FONZE
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
yesitdid
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)
NEU-FONZE
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
yesitdid
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.
NEU-FONZE
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
Neil Farbstein
QUOTE (NEU-FONZE+Jan 14 2006, 01:18 PM)
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.
NEU-FONZE
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.
Common Sense
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
yesitdid
QUOTE (NEU-FONZE+Jan 14 2006, 09:45 PM)
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.
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
 QUOTE Empire State Building, NYC = 365,000,000 kgWoolworth Building, NYC = 223,000,000 kgJohn Hancock Tower, Chicago = 174,500,000 kgLooking at these numbers I would say that 500,000,000 kg is definitely too heavy for one WTC Tower.
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. NEU-FONZE 15th January 2006 - 07:19 PM 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 NEU-FONZE 17th January 2006 - 12:43 AM 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 = xMass WTC 3 = 1/4xMass WTC 4 = 1/4xMass WTC 5 = 1/4xMass WTC 6 = 1/4xMass 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 NEU-FONZE 18th January 2006 - 01:07 AM The following information is available at a number of websites - try disaster.pandj.com for example: The initial debris estimate (at ground zero) included 125,000 tons of glass, 250,000 tons of steel, 450,000 cubic yards of concrete..... By July, 2002, 1,462,000 tons of debris had been removed. Could this figure for the amount of glass possibly be correct? Huddy 25th August 2006 - 07:23 PM I'm not an engineer or physics major, but...with the information below, my question would be: What is the maximum live weight load the building couldactually sustain.....remove the central core and then calculate the load based on the remaining square footage....And what's reasonable??? Albers 31st August 2006 - 01:31 PM I watched the towers being built as I went back and forth every few months from Long Island to Princeton, and was struck by the relatively spindly central column structure. I remember seeing the entire steel skeleton on central tubes. newton 7th September 2006 - 01:18 AM QUOTE (NEU-FONZE+Jan 15 2006, 07:19 PM) 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 towers have in-house engineers for this.old typewriters are not lighter than computers.in fact, if you recall, the standard case was cast iron, before plastic came into vogue.old cheque cutting machines were very heavy, old adding machines were quite heavy....steel filing cabinets used to be MUCH more massive than they are now(i have an old 4 drawer one,and HOLYCRAP, it must weigh two hundred pounds!), and all records were on paper back then, whereas now, you can fit an entire library in the palm of your hands, and paper records are nowhere near as voluminous as they once were, because of magnetic storage.i don't buy that they were more loaded than thirty years ago, and considering all the vacancies in the towers, i think they were far less loaded. newton 7th September 2006 - 01:23 AM oh yeah, and those standard old office desks made of thick hardwood weighed MUCH more than your run of the mill tube metal, tin and chipboard desk of today. Albers 7th September 2006 - 01:25 AM Yah, reams of paper are and were heavy. CRT monitors are dinosaurs. I think the point is the dynamic crunch, a momentum crunch, of several, or more than several, floors. Npolian 7th September 2006 - 02:54 AM Hi all,I'm not a theorist who is linked with any of the usual "conspiracies" movements or theories, but there is a paper I read a while back which carried some weight in its professionally published explanations and doubts, remaining unanswered publically and professionally, as far as I know, by the relevant bodies with the authority, time and need to.I am quite surprised that this topic remains in continuation on peoples mind, nevertheless, here are the links and sources, that I hope can come in handy to this discussion of yours:Why Did the World Trade Center Collapse? Science, Engineering, and SpeculationPublished in JOM by Thomas Eagar and Christopher Musso, 2001Feature: Special Reporthttp://www.tms.org/pubs/journals/JOM/0112/...Eagar-0112.htmlAn Initial Microstructural Analysis of A36 Steel from WTC Building 7Published in JOM by J.R. Barnett, R.R. Biederman, and R.D. Sisson, Jr., 2001http://www.tms.org/pubs/journals/JOM/0112/...erman-0112.htmlAnother site I frequented:http://www.iti.northwestern.edu/research/wtc/index.htmlWikipedia:http://en.wikipedia.org/wiki/Collapse_of_t...ld_Trade_CenterWorld Trade Center - Some Engineering Aspects - Civil Engineering - The University of Sydney [info about the WTC's]:http://www.civil.usyd.edu.au/wtc.shtml911 Research:http://911research.wtc7.net/mirrors/guardian/WTC/WTC_ch1.htmNew Jersey Institute of Technology Civil Engineering Professor Details How the Towers Collapsed; the Impact of 9/11 on Civil Engineers, Professors, Students:http://www.njit.edu/v2/News/Releases/254.htmlNow I've tried to register, but at the place I'm in, I think the IP address given out has already been taken from someone else registered here, so I can't I'm afraid (don't posses Internet at home).From the first paper (I've seen general acceptance of) some quotes and not so of others.[i]"skyscrapers in that they were to be very lightweight ""With a 700 Pa floor design allowable, each floor should have been able to support approximately 1,300 t beyond its own weight. The total weight of each tower was about 500,000 t. ""The floor below (with its 1,300 t design capacity) could not support the roughly 45,000 t of ten floors (or more) above crashing down on these angle clips. ""a 500,000 t structure has too much inertia to fall in any direction other than nearly straight down.""To a structural engineer, a skyscraper is modeled as a large cantilever vertical column. Each tower was 64 m square, standing 411 m above street level and 21 m below grade. This produces a height-to-width ratio of 6.8. The total weight of the structure was roughly 500,000 t, but wind load, rather than the gravity load, dominated the design. The building is a huge sail that must resist a 225 km/h hurricane. It was designed to resist a wind load of 2 kPa—a total of lateral load of 5,000 t.""lightweight “perimeter tube” design consisting of 244 exterior columns of 36 cm square steel box section on 100 cm centers""In the upper floors there is as much as 40,000 square feet of office space per floor. The floor construction is of prefabricated trussed steel, only 33 inches in depth, that spans the full 60 feet to the core, and also acts as a diaphragm to stiffen the outside wall against lateral buckling forces from wind-load pressures.""Since the mass of the combined towers is close to 1000000 tons, finding evidence will be an enormous task.""First tenant occupancy of the 110-story north tower (WTC 1) was in December 1970, and occupancy of the 110-story south tower (WTC 2) began in January 1972. The other WTC buildings were constructed during the 1970s and into the 1980s, with WTC 7 constructed just north of the WTC site in 1985. WTC 3, located immediately west of the south tower, was a 22-story hotel operated by the Marriott Corporation. WTC 4 and 5 were nine-story office buildings, and WTC 6 was an eight-story office building. WTC 7 was a 47- story office building. The seven-building complex provided approximately 12 million square feet of rentable floor space occupied by a variety of government and commercial tenants""Height: 1,368 and 1,362 feet (417 and 415 meters)Owners: Port Authority of New York and New Jersey.(99 year leased signed in April 2001 to groups including Westfield America and Silverstein Properties)Architect: Minoru Yamasaki, Emery Roth and Sons consultingEngineer: John Skilling and Leslie Robertson of Worthington, Skilling, Helle and JacksonGround Breaking: August 5, 1966Opened: 1970-73; April 4, 1973 ribbon cuttingDestroyed: Terrorist attack, September 11, 2001""There is no question that an important, yet overlooked, hero of 9/11, was the structural redundancy built into the framing of the Twin Towers," says Schuring. "Structural redundancy means there are multiple load paths to sustain the building weight. This redundancy provided precious time for thousands of workers to escape. And although it's not technically feasible to design a skyscraper to be invulnerable from impact by fully fueled jetliners, as design professionals we must develop improved details and systems that provide ever-greater protection against progressive collapse such as what occurred at the WTC site""On September 13, 2001, the cover of the New Civil Engineer in the UK consisted of a picture 1 WTC during its collapse with a single word written across it: "unthinkable". "Just hours earlier, it had been genuinely inconceivable that structures of such magnitude could succumb to this fate.""Leslie E. Robertson, the lead structural engineer on the team that designed the towers, wrote that "The events of September 11 are not well understood by me . . . and perhaps cannot really be understood by anyone." As NIST would also conclude""It was estimated by the Port Authority that the population of the WTC complex on September 11, 2001, was 58,000 people. ""It was assumed in the 1960s design analysis for the WTC towers that an aircraft, lost in fog and seeking to land at a nearby airport, like the B-25 Mitchell bomber that struck the Empire State Building on July 28, 1945, might strike a WTC tower while low on fuel and at landing speeds.""Boeing 707 considered by the designers, weighed 263,000 pounds and the Boeing 767s that hit the towers weighed about 274,000 pounds. This is a difference of 4%. ...Incidently, the maximum takeoff weight for a Boeing 707 is 336,000 pounds. The maximum takeoff weight for a Boeing 767-200ER is 395,000 pounds.""1,000,000 t of rubble will require 20,000 to 30,000 truckloads to haul away the material. The asbestos fire insulation makes the task hazardous for those working nearby. Interestingly, the approximately 300,000 t of steel is fully recyclable and represents only one day’s production of the U.S. steel industry. Separation of the stone and concrete is a common matter for modern steel shredders. The land-filling of 700,000 t of concrete and stone rubble is more problematic. "I've heard many allegations that people are just "making up" facts here, and have no evidence, method or support at all- (such as mass).As I can already see, I bet theres many individuals who've been at this, bickering, contending or otherwise defending certain views since 9/11 itself, that are on here thus should be very well educated in all its information.Some aspects seemed contradictory, however, on a general search, around the University websites, in the Departments of Civil Engineering, the figure taught, quoted and told to students was usually 500,000t.I realize on the Internet, people can often feel very bold, unchalant and emotionless to be able to act recklessly in any manner that suits them to others, usually vitriolic.. BUT I don't want to be a part of that thankyou, as I'm not here for gain, fame, blaming and hating.Hope it helps somewhere in your figures required. Lord Kelvin: “I often say . . . that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.” GregoryUrich 28th May 2007 - 10:05 PM Previously, many have used the 500,000 t mass without checking it.I have done a preliminary calculation of the mass and PE in wtc1. I am working on better supporting calculations and references. I am aware of a number of issues but I believe my preliminary result to be very close. Please see my paper published as a letter at the Journal of 911 Studies....journalof911studies.com/letters/wtc_mass_and_energy.pdfCan't post a link. Guest 11th December 2012 - 11:23 PM if it wasn't for the weight of the antiquated computers that was left in the walls of the Trade Center it never would have fell with the crashes of the Planes PhysOrg scientific forums are totally dedicated to science, physics, and technology. Besides topical forums such as nanotechnology, quantum physics, silicon and III-V technology, applied physics, materials, space and others, you can also join our news and publications discussions. We also provide an off-topic forum category. If you need specific help on a scientific problem or have a question related to physics or technology, visit the PhysOrg Forums. Here you’ll find experts from various fields online every day. To quit out of "lo-fi" mode and return to the regular forums, please click here.