Scientists examine the World Trade Centre Collapse
The Ghost in the Machines: The Mystery of the WTC Hard Drive Recoveries
by Michael Fury
Many are aware of the surge in put options purchased on American and United Airlines
as well as several major tenants of the WTC in the days preceding 9/11, purchases the
9/11 Commission Report waves away in a footnote on pg. 499 as having no connection
with the events of 9/11 since there were no ties to al Qaeda. More obscure, and nowhere
mentioned in the Commission Report, are the facts of the WTC computer data recovery
operation undertaken in late 2001 by Convar GmbH, a German firm. Under conditions of
hermetic secrecy, Convar used its proprietary technology to salvage data from the
damaged hard drives of WTC tenants, as reported in December 2001 by Reuters and
CNN.
http://www.rediff.com/money/2001/dec/17wtc.htm
http://archives.cnn.com/2001/TECH/industry/12/20/wtc.harddrives.idg/
From the Reuters article:
"The suspicion is that inside information about the attack was used to send financial
transaction commands and authorisations in the belief that amid all the chaos theby Michael Fury
Many are aware of the surge in put options purchased on American and United Airlines
as well as several major tenants of the WTC in the days preceding 9/11, purchases the
9/11 Commission Report waves away in a footnote on pg. 499 as having no connection
with the events of 9/11 since there were no ties to al Qaeda. More obscure, and nowhere
mentioned in the Commission Report, are the facts of the WTC computer data recovery
operation undertaken in late 2001 by Convar GmbH, a German firm. Under conditions of
hermetic secrecy, Convar used its proprietary technology to salvage data from the
damaged hard drives of WTC tenants, as reported in December 2001 by Reuters and
CNN.
http://www.rediff.com/money/2001/dec/17wtc.htm
http://archives.cnn.com/2001/TECH/industry/12/20/wtc.harddrives.idg/
From the Reuters article:
"The suspicion is that inside information about the attack was used to send financial
criminals would have, at the very least, a good head start," said Convar director Peter
Henschel.”
“Richard Wagner, a data retrieval expert at the company, said illegal transfers of more
than $100 million might have been made immediately before and during the disaster.”
"There is a suspicion that some people had advance knowledge of the approximate time
of the plane crashes in order to move out amounts exceeding $100 million," Wagner said.
"They thought that the records of their transactions could not be traced after the
main frames were destroyed."
“Henschel said the companies in the United States were working together with the FBI to
piece together what happened on September 11 and that he was confident the destination
of the dubious transactions would one day be tracked down.”
Convar’s website features a video confirming that Convar GmbH did in fact process the
WTC hard drives. http://www.datarecovery-europe.com/welcome.htm The widely disseminated claim that Kroll Associates--the powerful private-intelligence firm responsible for some elements of WTC security on 9/11--acquired Convar in June 2002 remains
unsubstantiated. What can be verified is that Kroll purchased Ontrack Data Recovery, a
U.S.-based rival of Convar with offices in Germany.
After the CNN article of December 20, the U.S. media were stricken mute on the Convar
investigation. Of the media blackouts shrouding 9/11, none has been more absolute.
Notice that Convar, its unnamed WTC clients and the FBI possessed these data, and that
the FBI would have no reason to withhold the results of its investigation had they proven
benign or consistent with the Commission’s account of the attacks.
It is worth remembering what Sibel Edmonds told Jim Hogue: “I can tell you that the
issue, on one side, boils down to money--a lot of money. And it boils down to people and
their connections with this money…”
http://baltimorechronicle.com/050704SibelEdmonds.shtml
Consider again Wagner’s inference: “They thought that the records of their transactions
could not be traced after the main frames were destroyed." The locations of the
computers in question within the towers is unknown, but if Wagner is correct, two
possibilities emerge: (1) either the “insiders” had foreknowledge of the precise impact
points of the aircraft (otherwise why assume that the main frames would be destroyed?)
or (2) they had foreknowledge of the total destruction of the towers. Upon reflection,
for numerous reasons the first possibility recedes into remote improbability. But why
would the “insiders” assume the total collapse of the towers when there was no historical
precedent for such an event and the towers had been designed to survive the impact of
fuel-laden 707s at 600 mph? http://911research.wtc7.net/wtc/analysis/design.html If in fact the
WTC towers were demolished by explosives, incendiaries or other means, whoever
initiated these transactions should be considered suspect for complicity in those acts.
No legitimate reason—in fact no reason whatsoever--for withholding the Convar data has
to date been offered.
http://journalof911studies.com/letters/MysteryofWTCHardDriveRecoveries.pdf
================
The Sustainability of the Controlled Demolition Hypothesis for the Destruction of the Twin Towers
Tony Szamboti, mechanical engineer April 24, 2007
Abstract: In the past year there has been an exponential growth in the number of people questioning the explanations we have been given, by official U.S. government bodies, concerning the collapses of the three WTC buildings in NYC on 9/11/2001. It is probably safe to say that much of this growth can be attributed to the Internet publishing of a paper by Physics Professor Steven Jones in November 2005, which put forth the hypothesis that the Twin Towers and WTC7 were actually demolished with prepositioned cutter charges.3 This hypothesis is in tension with the present government explanation of aircraft impact damage and/or fires being the causes for the complete collapses of the buildings. My intent here is to show that any honest and objective look at all of the theories, for the destruction of the twin towers, including the present government explanation, will cause one to realize that only the controlled demolition hypothesis is sustainable. I believe an honest look at the evidence will convince anyone that the controlled demolition hypothesis provides the best explanation for the complete collapses of the towers, as well as the damage to the buildings and objects surrounding them. The remarkable collapse of WTC7 seems to have had a separate cause in its own controlled demolition. Video of the collapse of WTC7 can be viewed quickly at http://www.journalof911studies.com/beginners.html before continuing, as it plays a part in understanding what probably occurred in NYC on Sept. 11, 2001.
It can be shown that due to the design and volume of the towers, the aircraft impacts and fires could not have been enough to cause them to collapse. The link below will provide an idea of how the towers were constructed, with photos seen in articles from the Engineering News Record at the time they were built. http://911research.wtc7.net/mirrors/guardian2/wtc/eng-news-record.htm
The following points then need to be understood to follow this line of reasoning:
• The twin towers were designed to handle multiple loads: their own weight (dead loads), live loads (due to people, furnishings, and equipment), wind loads, ice loads, and seismic loads. The dead and live loads are normal gravity loads. The central core was designed to handle 60% of the normal gravity loads of the building and the perimeter beams to take the remaining 40% of the normal gravity loads, and all of the wind, ice, and seismic loads.1 While wind loads are usually quite low, tall structures need to be designed to handle extremes. The towers where designed to handle the overturning moment and shear stresses generated by 100 mph winds acting on their considerable surface area and height. 2 Although heavy icing would be rare, the towers would still need to withstand the extra weight, which glaze ice would bring at 56 lbs./ft3, not insignificant on a structure with approximately 1.3 million square feet of outside surface area. Seismic loads can generate horizontal accelerations, which would cause high overturn moments, similar to those caused by high wind loads. Due to the need to withstand rare high wind, ice, and seismic loads, the tower’s perimeter beams had a minimum factor of safety of 5.00, when considering normal gravity loads only. The central cores were designed with the more standard factor of safety of 1.67, since they took normal gravity loads only. Prior to the attacks, on a low wind, warm sunny day, with no earthquakes, such as Sept. 11, 2001, the beams in each tower would have had no more than 33% of their total load sustaining capacity used.
• Upon impact with the buildings, the wings, tail, and engine fan assemblies of the aircraft would have certainly been shredded prior to completely entering the buildings. This would leave only the fuselage, center portions of the engines, and the landing gear, with greatly diminished energies, to cause damage to the central core columns.10,11 The central cores were comprised of 47 large steel columns interconnected at every floor in a three-dimensional matrix, encompassing a plan area of 137 feet x 87 feet. The fuselages of both Boeing 767-200ER aircraft, which hit the towers, were 16.5 feet in diameter.4 The spacing of the central core columns ranged from approximately 11 to 21 feet apart,11 so by volume alone there would be a limited number of columns which the remains of the fuselage, could contact.
The aircraft engines were approximately 9 feet in diameter, much of which was the fragile fan assemblies, which would have been decimated going through the outer wall. Only the much smaller diameter turbojet portions of the engines and their rigid shafts would have had much ability to cause additional damage to the central core columns. The damage to the perimeter columns is visible in photographs. It is known that no more than 20% of the perimeter columns were affected in either tower. It is the damage to the core columns, which was not visible, that needs to be scrutinized. Analyses can be done to show what the remaining energies and volumetric probabilities would be for impact damage to occur to the core columns. NIST did analyses of this type and in their base cases, for both towers, less than 20% of the central core columns were severed or heavily damaged.
• The towers were designed as virtual structural pyramids, with the wall thickness of the beams thicker at the bottom and thinning with greater vertical height location. The bottom beams were thicker due to heavier loading, and the top beams thinner due to lighter loading. Since the tower beams varied in wall thickness, depending on their vertical location, it could be ascertained which beams were in the aircraft impact and fire affected areas. With it being important to know the actual temperatures that the beams experienced, in the fire affected areas, NIST used the known microstructure characteristic of spheroidization to determine those temperatures.8 Temperature will change the spheroidization of the steel microstructure in a linear, predictable, and permanent way. In their testing of the beams it was found that only a few percent of them ever experienced temperatures above 250° C (482° F) and none above 600° C (1,112° F). None of the central core columns tested showed they experienced temperatures above 250° C (482° F). The chart below, which shows the proportional loss of strength in steel, as it’s temperature is increased, is from Corus Construction, with temperatures in degrees C.
As the chart shows, steel does not lose any of its strength until its temperature rises above 350° C (662° F), and only loses half of it at 600° C (1,112° F). So the evidence shows that no more than a few percent of the beams lost any of their strength due to the fires. While NIST includes this data in their report it is essentially ignored and an argument attempted that higher steel temperatures existed, even though there is no physical evidence for it. The amount of jet fuel, which actually entered the towers, could not have been any more than half of the 10,000 gallons on board each aircraft. Spreading the remaining 5,000 gallons, in each case, over an acre (one floor of one tower) results in a jet fuel film thickness of .015 inch. This film would have burned up quickly, leaving nothing more than office materials to fuel the fires. The fact that high temperature effects were not found in the microstructure of the steel should not be surprising.
To summarize, it can only be shown that approximately 20% of the beams, in the cases of both towers, had their strength significantly affected by the aircraft impacts and fire. That leaves approximately 80% of the beams, in both cases, with their full strength intact. Grid like structures, such as the twin towers, redistribute loads when individual beams are damaged. This occurs in a bridge like fashion, since the vertical beams are interconnected horizontally at every floor. In the reference section of this article, I show that if 20% of the central core and perimeter columns were totally incapacitated, 9 or 10 central core and 48 perimeter, the perimeter would have maintained a factor of safety of 4.00, and the central core a factor of safety of 1.34. The remaining factor of safety of 1.34 for the central core is not insignificant. What it means is that for the yield point of the steel to even be reached, and collapse to be incipient, an additional 20% of the core strength needed to be lost due to fire. In terms of the number of beams needing to be affected, an additional 19 out of the remaining 38 core columns would need to reach 600° C (1112° F) to lose half of their strength. This is not a likely scenario and there is no physical evidence for it, as shown above in the discussion of the beam temperature testing data gathered by NIST. It would appear that the initiation of vertical collapse, due to fire weakening and gravity, was improbable. So how then did the towers collapse?
The answer is obviously that another mechanism must have caused the collapses. The fact that the twin towers both collapsed due to a cause, which must obey the laws of physics, cannot be disputed. It is that cause which some claim is in dispute at the moment. The alternative collapse causation theories, which have been proposed to counter the insufficient U.S. government theory, are
1. A directed energy weapon was used to destroy the towers.
2. Mini-nukes were used to destroy the towers.
3. The towers were destroyed via controlled demolition with the use of incendiaries and explosives.
The first and second proposed causes have been shown not to be serious hypotheses, by scientifically based papers. These papers show that these two theories have no basis. These papers also explain away any perceived anomalies, and provide reasons for the observations, which are more natural and consistent with the controlled demolition hypothesis for the destruction of the towers. To date these papers have not been challenged in writing, or shown to be incorrect in any way, by those who have supported these first two theories. These papers can be found at http://www.Journalof911Studies.com The physical evidence for the third theory, controlled demolition, is due to the characteristics of the twin tower collapses. In one of his many writings on the subject of Sept. 11, 2001, Dr. David Ray Griffin lists the eleven characteristics of controlled demolition, which both of the towers exhibited in their respective collapses.
Sudden Onset Dust Clouds Molten Steel
Straight Down Horizontal Ejections Sliced Steel
Almost Free-Fall Speed Sounds Produced by Explosions Demolition Rings
Total Collapse Pulverization of Concrete and Other Materials
Dr. Griffin’s full article ‘The Destruction of the World Trade Center: Why the Official Account Cannot Be True” can be found at http://911review.com/articles/griffin/nyc1.html
Any close viewing of video, of the collapses of the towers, will physically show most of the characteristics of controlled demolition listed above. Witnesses, photos, and taped audio from that day, have attested to, molten metal, demolition rings, sliced steel, and sounds produced by explosions.
It was the revelation of the presence of molten metal, in the rubble of all three buildings which collapsed in NYC on Sept. 11, 2001, which caused Dr. Jones in 2005 to begin to question whether the present U.S. government explanation for the collapses was sufficient. It is provable that the molten metal in the rubble was not aluminum and that diffuse flame fires cannot achieve temperatures sufficient to melt steel. Steel can only be melted in the controlled environment of a blast furnace or with the use of incendiaries. There is very credible witness testimony of seeing, hearing, and feeling explosions, in many areas of the towers, both before and during the collapses. This testimony can be found in the Oral Histories of the 503 NYC firefighters and emergency personnel, who were on the scene that day and survived. Their testimony was taken and transcribed in late 2001 and early 2002 by order of the NYC fire commissioner. However, afterward the mayor of NYC repeatedly refused to release these testimonies to the public. They were only released by a court order from the New York State Court of Appeals in August of 2005, after earlier court challenges had failed to gain their release. There was no testing done for explosive residue on the beams during either the NIST or FEMA investigations of the building collapses. An article by Dr. David Ray Griffin discussing and quoting these Oral Histories can be found at
http://www.911truth.org/article.php?story=20060118104223192
It is also worth mentioning the fact that the buildings were designed to take an impact by a fully loaded Boeing 707 at 334,000 lbs. and moving at it’s cruise speed of 607 mph. While the NIST report mentions this, it claims that documentation supporting this contention could not be found. However, the late John Skilling, who was the head structural engineer on the tower design project, is quoted in 1993 as saying that a white paper was done on this design feature. The towers were actually hit with Boeing 767-200ER aircraft, which had only 10,000 gallons of fuel on board for their trips to the West Coast of the U.S. from Boston. While the 767-200ER is rated at a 395,000 lb. max takeoff weight, this is for a full fuel load of 23,980 gallons, which would be used for a longer flight as the aircraft had a 7,700 mile range4. Subtracting the weight of 14,000 gallons (at 6.825 lbs./gallon) from the max takeoff weight gives an aircraft weighing approximately 300,000 lbs. The 767-200ER had a cruise speed of 530 mph (there are various estimates by radar, and other timing methods, which put the actual speeds of the aircraft at impact at lower values). However, even using the higher 530 mph value and the equation
K = 1/2mv2
where K = kinetic energy
m = mass
v = velocity
it is found that the designed for 707 impact would have contained at least 1.4 times or 40% more kinetic energy than what the 767-200ER aircraft could have provided. The buildings obviously survived the impacts and thus the present theory we are given is that fire caused the collapses. The fact that fires have never in history caused the complete vertical collapse of a steel framed structure, let alone any built as robustly as the twin towers, has been amply documented. Serious doubt of the present government explanation has been emanating from qualified credible people for the last several years.
Editor Bill Manning wrote in Fire Engineering magazine in 2002 that: “Fire Engineering has good reason to believe that the ‘official Investigation’ blessed by FEMA… is a half-baked farce that may already have been commandeered by political forces whose primary interests, to put it mildly, lie far afield of full disclosure… Respected members of the fire protection engineering community are beginning to raise red flags, and a resonating [result] has emerged: The structural damage from the planes and the explosive ignition of jet fuel in themselves were not enough to bring down the towers….”. A letter was sent by a C. Thurston to Tucker Carlson of MSNBC, after he hosted Dr. Steven Jones on one of his nightly shows in November of 2005. In it he lists ten withering reasons for not believing the gravity driven collapse theory. It can be found at http://www.911research.com/letters/msnbc/index.html The NIST report wants to tell us that it was the perimeter columns that buckled and caused the collapses. The report says this was due to their deflection and bowing, caused by fire affected sagging floor trusses pulling on them, and the central core itself sagging due to plasticity and creep.6 The probable collapse sequences, as hypothesized by the NIST report, were issued at a press conference in NYC in April 2005.
That press release is available here.
http://www.nist.gov:80/public_affairs/releases/wtc_briefing_april0505.htm
It appears the press release and report want to say that the entire interior structure was sagging. It is interesting that the NIST press release and report don’t seem to concern themselves much with the fire testing of the floor deck and supporting truss assembly models, done under contract for them by Underwriters Laboratories. Full scale models of the floor deck and supporting truss assemblies were fire tested, under load for two hours, per ASTM E119. These tests did not produce a collapse and the 35 foot long trusses only sagged 3 inches at midspan, not likely enough to buckle the perimeter wall columns. In fact, NIST needed a non-evidence supported 42 inch floor truss deflection in their computer model to cause buckling of the perimeter columns. Their large heat capacity and ability to transfer heat to other areas of the building would have certainly made the core columns even less susceptible to weakening than the trusses. The lack of high temperature evidence on the core columns is a testament to this point. Curiously, the press release does not mention either the floor assembly fire testing or the low percentage of beams found to have experienced high temperatures in the microstructure testing. Both the press release and the report attempt to point towards a theory of dislodged fireproofing materials as the reason for the alleged interior steel weakening. Although they don’t say it out loud, it is a virtual certainty that NIST did floor assembly fire testing without fireproofing.9 If the trusses, in this case, had much more significant sagging or collapsed it would have proven their hypothesis. However, there is no mention of failure, so apparently the tests didn’t produce the results which would back up their theory. It is important to note that NIST has not been able to cause physical models to fail with their fire induced collapse theory.
It is instructive that the first visible signs of failure on the North Tower are when the antenna mast moves downward by ten to twelve feet before the perimeter roof line moves. This is indicative of the central core suddenly and completely failing first. If you haven’t seen this watch it frame by frame at the link below.
http://911research.wtc7.net/wtc/evidence/videos/wtc1_close_frames.html
These frames don’t show slow creep, they show sudden failure of the central core itself. They certainly don’t show the perimeter walls failing first. If the central core failed first it would cause the trusses not to sag, but to follow them downward, applying a tremendous bending moment on the perimeter beams, which would certainly cause them to bow inwardly. Even with their high factor of safety against vertical loads, the perimeter beams would be dragged down with bending moments much more severe than the wind load induced moments they were designed to withstand. By demolishing the core, the destruction of the building could also be done with the added advantage of the demolition being mostly hidden from view. It appears that the central core failed first and that is what caused the floor trusses to move downward and pull on the perimeter beams, causing them in turn to fail. The central core needed to have a minimum loss of 40% of its total strength before collapse could begin to occur. Since the evidence for column damage, due to aircraft impact and fire, can only account for a maximum 20% loss of strength in the central core, it does not appear collapse initiation can be accounted for without controlled demolition being involved.
It would seem that any honest and objective look at; the design of the buildings, the true damage potential of the aircraft impacts, the physical evidence of the low beam temperatures, the physics of the collapses, the evidence of molten metal in the rubble, and the witness testimony, should cause one to conclude that the towers must have been destroyed via controlled demolitions. In addition to the evidence mentioned so far, there is also evidence of the presence of incendiaries, in the chemical analysis of the dust from an apartment near the towers, and slag from a monument using salvaged twin tower steel, which have both been analyzed by Dr. Jones and others.
The present U.S. government explanation, for the collapses of the buildings in New York City on Sept. 11, 2001, is simply not sustainable. The evidence, which has surfaced in support of the controlled demolition hypothesis, in the last two years, is overwhelming. The obvious controlled demolition of WTC7, at 5:20 PM on Sept. 11, 2001, proves that charges were pre-positioned, as there would not have been time to rig the building that day, especially with fires in it. With this in mind, the demolition of WTC7 lends considerable weight to the notion that charges could also have been pre-positioned in the twin towers. The spectacular collapses of the twin towers, which were in reality caused by controlled demolitions, shocked us all, and caused us to demand action against the entities who we were told supported the hijackers. It is very plausible that the aircraft impacts were used as causal ruses, to allow the collapses to be blamed on outsiders, as the placing of the charges, which actually caused the spectacular collapses of the twin towers, would have required access that outsiders simply would not have. One may wonder who would want people in Afghanistan and Iraq to be blamed if they didn’t do it. A good hard look at the soon to be built U.S. oil company controlled gas pipeline in Afghanistan, and the virtual takeover of Iraq’s oilfields by U.S. oil companies, would be a start at solving that puzzle for oneself. Neither of these situations would have been possible, without the support of the American people, for the use of the U.S. military, to overthrow the previous governments of these countries. Endnotes and References:
1. Determination of the minimum factor of safety against gravity caused vertical collapse of the Twin Towers after sustaining aircraft impact and fire damage. While the actual detail drawings of the twin tower design have been withheld from the public (the recent release of blueprints was for architectural floor plan views only), the size of the central core’s largest beams are known, from magazine articles published in the Engineering News Record during the time the towers were being built. A link to these articles is provided at the beginning of this paper.
Below is a depiction, from one of those articles, of the base of the largest of the core columns. What the architectural plan views do tell us is that there were a total of sixteen of these size columns, with eight along each outside edge of the long span of the 137 foot x 87 foot central core. The remaining thirty-one columns were most probably 36” x 16” columns. Below is a sketch of the cross section of a 36” x 16” column, also from the Engineering New Record, which was located approximately half way up the tower.
It can be inferred that the bases of the 36” x 16” columns would have been built proportionally to the 54” x 22” columns, with 4” plates in lieu of 5” plates and a 5” plate in the center in lieu of the 6.25” plate on the larger beam. This would be done to increase the cross section to gain the needed resistance to the vertical compressive load.
Using the dimensioned pictorial view above, the total cross sectional area of the 54” x 22” columns is approximately 898 in.2. The total cross sectional area of a proportional 36” x 16” column, built with 4” plates, would be approximately 467 in.2. With sixteen columns at 898 in.2 and thirty-one columns at 467 in.2 the total cross sectional area of the base of the central core, to resist compressive loading and vertical collapse, would be 28,845 in.2.
The AISC manual,7 used for the design of steel framed structures in this country for the last eightyfive years, has specified, since long before the erection of the twin towers, that the allowable compressive stresses on vertical columns not exceed 0.60Fy, and thus have a factor of safety of 1.67. This means the actual stress cannot exceed 60% of the compressive yield strength of the material used for the column. The central core columns at the base were made from ASTM A36 steel which has a compressive yield strength of 36,000 psi. 60% of this strength gives an allowable stress of 21,600 psi. Coupling this allowable stress with the total cross sectional area of the forty-seven core columns shows that, as a group, they could support a vertical load of 311,526 tons. This is approximately 60% 8 of the reported 500,000 ton gravity load of each of the twin towers. The remaining 200,000 tons of gravity load would need to be supported by the perimeter columns.
On the far right of the pictorial below, is a dimensioned sketch of the cross section of the lowest 60 per side perimeter columns, which were actually located at five floors above the ground level on the buildings. These columns transitioned three into one near the fifth floor level and thus there were 20 larger perimeter columns per side, which would have actually went down to the base. Since no cross section sketches of the 20 per side perimeter columns exist in the public domain, of which I am aware, this sketch can serve as the cross sectional reference, to find a minimum total cross section of the perimeter columns at the base. The actual total cross sectional area of the perimeter columns, at the base, twelve stories down, would only be larger, so the analysis here can be considered conservative. The center view is of the cross sectional dimensions further up on the towers and the view on the left is of fireproofing on the steel with aluminum cladding over the fireproofing. Judging from the sketch on the right, the cross sectional area of one of the 60 per side columns at its base was approximately 88 in.2. There were 240 perimeter columns of this size in each tower so the total cross sectional area of the perimeter columns at their base would have been no less than 21,120 in.2. The compressive stress induced by 200,000 tons of gravity load on this area provides an actual stress of 18,939 psi. These perimeter columns were made from steels ranging in yield strength up to 100,000 psi. The lowest of the 60 per side columns would have had the highest strength, as that is where the maximum overturning moment and shear stress, from wind and seismic loads, would have existed. When considering gravity loads only, the perimeter columns would have provided a minimum factor of safety of approximately 5.00 against vertical collapse since Factor of safety = yield strength/actual stress
Although only the base loads and their stresses are considered here, it can be inferred that this would be true for all of the beams, over the full height of the towers, as they would be designed to maintain the same factor of safety throughout. The core columns would have had a factor of safety of 1.67 and the perimeter columns a factor of safety of 5.00, against vertical collapse, throughout the full height of the building, when considering gravity loads only.
The vertical load capacity of the beams, at their base, due to compressive loads only, was
Central core 300,000 tons x 1.67 = 500,000 tons
Perimeter 200,000 tons x 5.00 = 1,000,000 tons
Using the base as a reference, the actual load vs. the beam capacity, during a low wind day like Sept. 11, 2001, would have been
Actual Load/Beam Capacity = 500,000/1,500,000 = 33%
If 80% of the base central core columns had their strength unaffected by damage and/or fire they would have provided a remaining factor of safety and load capacity of 0.80 x 1.67 = 1.34 for a 300,000 ton load = 402,000 ton remaining capacity If 80% of the base perimeter columns had their strength unaffected by damage and/or fire they would have provided a remaining factor of safety and load capacity of 0.80 x 5.00 = 4.00 for a 200,000 ton load = 800,000 ton remaining capacity The remaining unaffected 80% of the tower structure would still have been capable of supporting 1,202,000 tons or 2.4 times the actual 500,000 ton load.
Standard design practice dictates that the beams in the upper part of the building would have had the same factor of safety as the beams at the base of the towers. So knowing the design of the columns at their base, the total gravity load of the buildings, and the percentage of damaged beams, we have deduced what the remaining factor of safety was for the beams at the aircraft impact and fire sites. The remaining factor of safety against vertical collapse in the aircraft impact and fire affected areas would have been at least
1.34 for the central core columns
4.00 for the perimeter columns
This is with the assumption that 20% of the central core columns were lost, which is improbable.
Buckling can occur at stresses below the compressive yield strength of a material. The critical buckling stress is dependent on the slenderness ratio of a column and whether its ends are fixed or free. The slenderness ratio is related to the stiffness of the cross section of the column and the unsupported length between the column’s connections to supports. The end condition for the best buckling resistance is fixed at both ends, which the columns were in the aircraft impact and fire affected areas. The design of the tower columns would have precluded buckling as an earlier mode of failure, due to the short vertical length of the columns between horizontal supports and the stiffness of the cross section of the beam. The design would have followed AISC guidelines, which would have required that the critical buckling stress not be less than the compressive yield strength.7
2. NIST NCSTAR 1-1A, WTC Investigation, Chapter 2, page 34, paragraph 2.3.2. http://wtc.nist.gov/NISTNCSTAR1-1A.pdf
3. “Why Indeed Did the WTC Buildings Completely Collapse” by Physics Professor Steven Jones http://www.journalof911studies.com/volume/200609/WhyIndeedDidtheWorldTradeCente rBuildingsC ompletelyCollapse.pdf.
4. Boeing Technical characteristics for the 767 family of aircraft. See tables for the 767-200ER. http://en.boeing-me.com/ViewContent.do?id=2404
5. Executive Summary of the Final Report of the National Construction Safety Team on the Collapses of the World Trade Center Towers, extracted from NIST NCSTAR 1.
http://wtc.nist.gov/pubs/NCSTAR1ExecutiveSummary.pdf
6. Final Reports of the Federal Building and Fire Investigation of the World Trade Center Disaster http://wtc.nist.gov/reports_october05.htm
7. Manual of Steel Construction, 8th edition, 1980 printed by the American Institute of Steel Construction Inc.
8. Examples of microstructure of steel which has been heated and cooled. At bottom of page. http://wtc.nist.gov/media/gallery.htm#sim
9. NIST photos of fire experiment setups. See uninsulated truss setup in next to last picture at bottom. http://wtc.nist.gov/media/gallery2.htm
10. Photo of the aircraft impact damage to the exterior of the North Tower As the aircraft was at an angle, the wings would have had to go through the perimeter beams plus 60 feet of floor decking of multiple floors edge on. The tail would have also had this situation due to its height.
11. Graphic of central core column spacing vs. fuselage and central engine
diameters
87 feet
137 feet
North Tower aircraft
approximate orientation to the central core
Perimeter Beams
Central Core
208 feet
Wings, engine fan assemblies, and the tail would have been shredded after going through perimeter beams and multiple floors edge on, leaving only parts of the fuselage, landing gear, and 4 foot diameter center portions of engines, with greatly diminished energies, having any chance of causing damage to the Central Core 4 foot dia. central portion of engine South Tower aircraft approximate orientation to the central core with fuselage and central portion of engine shown in relative sizes
Relative size of 16.5 ft. dia. fuselage
ORIGINAL WITH GRAPHICS:
http://journalof911studies.com/letters/SzambotiSustainabilityofControlledDemolitionHypothesisfortheDestructionofTwin%20Towers.pdf
================
Analysis of Mass and Potential Energy in the World Trade Center Twin Towers
Gregory H. Urich
B.S. Electrical and Computer Engineering
Abstract
The mass of one of the Twin Towers is calculated based on available data and estimated live loads. The potential energy for one of the Twin Towers is calculated based on the mass of the tower distributed over the various floors. The mass for each floor is established based on the average mass per floor adjusted for differences in mass due to stronger steel structures lower in the tower. All floors including mechanical floors and the basement floors are treated equally with regard to superimposed dead-loads.
Introduction
Many references can be found with different values for the mass of and the amount of potential energy stored in the WTC twin towers. A number of references are shown in Table 1 below. None of these references provide any data or calculation method on which the mass and potential energy are based. The purpose of this paper is to establish a substantiated value for the mass and potential energy of one tower.
Table 1: Different values for mass and potential energy given by references
Source Mass Potential Energy
Ashley 7 500,000 tons
Bazant and Zhou 6 = 480,000 tons (metric)*
Hamburger, et al. (FEMA) 4 4 E+11 J
Tyson 2 500,000 tons
Wikipedia 5 500,000 tons
* calculated based on mass given for upper part of North Tower = 58 E+6 kg
Analysis
In the design documentation for WTC1 and WTC2 the structural loads are divided into deadloads, super-imposed dead-loads, and live-loads. These divisions are also used here. Dead-loads
Foundation
The mass of the foundation is provides no load on structural components other than itself and contributes a negligible amount to potential energy. The mass of the foundation is nonetheless approximated based on the film footage from the Port Authority of New York and New Jersey.1 Dimensions are established by comparison to objects of known size, i.e. humans. The foundation for the core columns was comprised of steel reinforced concrete footers and steel grillages built up out of I-beams. One steel grillage is made up of 17 I-beams with approximate dimensions 0.75m x 0.2m x 2m with a plate thickness around 0.03m. Each grillage also had a base plate for the core column with approximate dimensions 1m x 1m x 0.3m. It is assumed that there is one grillage per core column. Using a density of 7.784 metric tons per cubic meter for the density of A35 steel, the total mass for the grillages is approximately 484 metric tons. Each grillage was placed on a concrete footer with approximate dimensions 2.5m x 2.5m x 2m. Using a density of 2.4 metric tons per cubic meter, the total mass for the concrete footers is approximately 1410 metric tons. The foundation for the external columns was comprised of a continuous, steel reinforced, concrete footer and base plates ranging from 7 to 9 square feet (approx. 0.74 m2). The reference for this value is unsure but it is most likely from FEMA or NIST. The thickness of the base plate is unknown but a thickness of 3 cm is assumed. Using a total number of 80 exterior columns (transition to 238 columns at 7th floor), the total mass of the base plates is approximately 14 metric tons. The concrete footer for the external columns had a perimeter of 252 meters. The other dimensions of the footer are unknown but are approximated using 2 meters for depth and 2 meters for width. The total mass for the concrete footer is thus 2420 metric tons.
Table 2: Mass of foundation
Component Mass (short tons)
Mass (metric tons)
Core steel grillage w/ base plate 534 484
Core concrete footer 1555 1410
External column steel base plates 15 14
External column concrete footer 2670 2420
Total mass foundation 4774 4328
Structural steel
NIST’s value for the mass of steel used in one tower is 100,000 short tons.3 A simplified approximation based on averaging component dimensions provided by NIST demonstrated that this value is reasonable.
The actual mass of the upper floors is less than the lower floors due to heavier supporting structures lower in the building. FEMA describes a variation in thickness of exterior column plates from 4 inches at the base to ¼ inch in the upper stories.4 This indicates a ratio of 16 to 1 for structural steel from bottom to top. The mass of the steel can be scaled linearly as a function of floor number from the bottom to the top as follows: msteel (f) = mavg • (-30f + 3710)/1955
f is the floor number, mavg is the average mass of steel per floor (= 99,451 tons/116 floors; foundation components are subtracted)
Mass above grade:
Mass below grade: . mavg • (-30f + 3710)/1955 = 10,035 short tons 6 . mavg • (-30f + 3710)/1955 = 89,416 short tons
116
f = 7
f = 1
Table 3: Mass of structural steel per floor in short tons (Note: floor 116 has been transposed
to 110 to correspond to the normal floor numbering. Also, 549 tons has been used for floor 0,
i.e. steel in the foundation.)
floor mass floor mass floor mass floor mass floor mass floor mass
110 101 90 364 70 627 50 890 30 1153 10 1416
109 114 89 377 69 640 49 903 29 1167 9 1430
108 127 88 390 68 653 48 917 28 1180 8 1443
107 140 87 403 67 667 47 930 27 1193 7 1456
106 153 86 417 66 680 46 943 26 1206 6 1469
105 167 85 430 65 693 45 956 25 1219 5 1482
104 180 84 443 64 706 44 969 24 1232 4 1495
103 193 83 456 63 719 43 982 23 1245 3 1509
102 206 82 469 62 732 42 995 22 1259 2 1522
101 219 81 482 61 746 41 1009 21 1272 1 1535
100 232 80 496 60 759 40 1022 20 1285 0 1548
99 246 79 509 59 772 39 1035 19 1298 -1 1561
98 259 78 522 58 785 38 1048 18 1311 -2 1574
97 272 77 535 57 798 37 1061 17 1324 -3 1587
96 285 76 548 56 811 36 1074 16 1338 -4 1601
95 298 75 561 55 824 35 1088 15 1351 -5 1614
94 311 74 574 54 838 34 1101 14 1364 -6 549
93 325 73 588 53 851 33 1114 13 1377
92 338 72 601 52 864 32 1127 12 1390
91 351 71 614 51 877 31 1140 11 1403
Concrete floor slabs above grade (Floors 1-110)
Floor slabs outside of the core were constructed primarily of light concrete. The mass of light concrete can be calculated using the floor area outside of the core (approx. 28,225 sq ft), the floor thickness (4 in. 8), and the density of light concrete (109.3 lb/ft3). 28,255 sq ft/floor x 0.33 ft x 109.3 lb/ft3 x 110 floors x 1 ton/2000 lbs = 56,600 short tons Floor slabs inside the core were constructed primarily of normal concrete. The mass of normal concrete used in these floors can be calculated using the floor area (11,745 sq ft), the floor thickness (5 in. 8), and the density of normal concrete (150 lb/ft3). 11,745 sq ft/floor x 0.4167 ft x 150 lb/ft3 x 110 floors x 1 ton/2000 lbs = 29,400 short tons Concrete floor slabs below grade (Floors B1-B6)
Floor slabs below grade were constructed primarily of normal concrete. The mass of normal concrete used in these floors can be calculated using the floor area (40,000 sq ft), the floor thickness (8 in. 8), and the density of normal concrete (150 lb/ft3). 40,000 sq ft/floor x 0.6666 ft x 150 lb/ft3 x 6 floors x 1 ton/2000 lbs = 8,700 short tons
Superimposed Dead-loads
Superimposed dead-loads are considered permanent non-varying loads from non-structural components such as wiring, plumbing, heating and cooling aggregates, elevators, etc. Unfortunately the dead loads are very difficult to approximate due to the lack of information about what elements comprised them. Superimposed dead-loads in the WTC towers are considerably higher in the so called mechanical floors. This is however ignored for simplicity and an average superimposed dead-load is approximated and distributed throughout all floors. The design documents give a superimposed dead-load of 8 psf for most floors outside of the core. 8 This value is most likely larger than the actual loads but is used for all floors to take into account the much larger actual loads of the mechanical floors.
Mass of superimposed dead-loads above grade:
40,000 sq ft/floor x 8 lb/ft2 x 110 floors x 1 ton/2000 lbs = 17,600 short tons
Mass of superimposed dead-loads below grade:
40,000 sq ft/floor x 8 lb/ft2 x 6 floors x 1 ton/2000 lbs = 960 short tons
Live-loads
Live-loads are approximated using 1/4 (as used by NIST) the maximum design loads. Above grade, the most predominate design load outside of the core was 100 lbs/sq ft.8 25 lbs/sq ft x 28,255 sq ft/floor x 110 floors x 1 ton/2000 lbs = 38,850 short tons Above grade, the most predominate design load inside the core was 50 lbs/sq ft. 8 12.5 lbs/sq ft x 11,745 sq ft/ floor x 110 floors x 1 ton/2000 lbs = 8,075 short tons Below grade, the most predominate design load inside the core was 500 lbs/sq ft. 8 125 lbs/sq ft x 40,000 sq ft/ floor x 6 floors x 1 ton/2000 lbs = 15,000 short tons
Total Mass
The total mass is 279,000 short tons or 254,000 metric tons.
Table 4: Mass above grade
Component Mass (short tons) Mass (metric tons)
Concrete floor inside core area 29 400 26 671
Concrete floor outside core area 56 600 51 347
Structural steel 89 416 81 117
Live-load inside core 8 075 7 326
Live-load outside core 38 850 35 244
Superimposed dead-load 17 600 15 966
Total mass above grade 239 941 217 671
Table 5: Mass below grade
Component Mass (short tons) Mass (metric tons)
Concrete foundation 4 221 3 829
Concrete floor 8 700 7 893
Structural steel 10 035 9 104
Live-load 15 000 13 608
Superimposed dead-load 960 871
Total mass below grade 38 916 35 304
Potential Energy
The potential energy (u) due to gravity (close to earth) of any object can be calculated as:
u = mgh
m = mass, g = acceleration due to gravity, h = height
A reasonable approximation for potential energy relative to ground level (above grade) can be made using:
mnon.steel is the average mass (converted to metric) of one floor excluding structural steel, msteel (f) is the value for the mass of steel for a particular floor from Table 3 (converted to metric), g = acceleration due to gravity, f is the floor number, 414,53 is the height of the tower above grade in meters
The sum is from 1 to 110 to include all floors above ground and the roof and their underlying support structure. Potential energy per floor is show in Table 6 below. The total potential energy is 3.98 x 1011 J.
Table 6: Potential energy per floor (above grade)
floor PE(MJ) floor PE(MJ) floor PE(MJ) floor PE(MJ) floor PE(MJ) floor PE(MJ)
110 5415 90 5223 70 4680 50 3783 30 2534 10 933
109 5413 89 5205 69 4643 49 3729 29 2463 9 844
108 5411 88 5185 68 4606 48 3674 28 2390 8 753
107 5408 87 5164 67 4568 47 3618 27 2317 7 662
106 5405 86 5143 66 4529 46 3562 26 2242 6 570
105 5400 85 5121 65 4489 45 3504 25 2167 5 477
104 5394 84 5097 64 4448 44 3446 24 2091 4 384
103 5388 83 5073 63 4406 43 3386 23 2014 3 289
102 5380 82 5048 62 4363 42 3326 22 1936 2 194
101 5372 81 5022 61 4320 41 3265 21 1857 1 97
100 5363 80 4996 60 4276 40 3203 20 1778
99 5353 79 4968 59 4230 39 3140 19 1697
98 5342 78 4939 58 4184 38 3076 18 1616
97 5330 77 4910 57 4137 37 3012 17 1534
96 5318 76 4880 56 4089 36 2946 16 1450
95 5304 75 4849 55 4040 35 2880 15 1366
94 5290 74 4817 54 3991 34 2812 14 1281
93 5275 73 4784 53 3940 33 2744 13 1196
92 5258 72 4750 52 3889 32 2675 12 1109
91 5241 71 4715 51 3836 31 2605 11 1021
. (mnon-steel + msteel (f) ) • 9.8m/s2 • (414,53m • f/110) = 398,000 MJ
f = 1
110
Discussion
One difficulty in approximating the potential energy is that the dimensions for core columns
are unknown. Since the structural components are stronger (i.e. heavier) lower in the building,
it is necessary to know how these components varied over the height of the building. Some
dimensions for core box columns given by NIST are not correct. For example, the dimensions
“as large as 12 in. by 52 in., comprised of welded plates up to 7 inches thick” must be
incorrect. It can be seen from the photographic evidence that the thickest plates are used for
the larger dimension of the rectangular box columns. Thus, the width dimension would need
to at least 14 inches to accommodate the 7 inch thick plates.
Accuracy of the calculation
Due to certain limitations of available information and also the method of calculation, the
values for mass and potential energy are not perfectly accurate. Factors which may affect the
accuracy are listed in the below along with estimated effects caused by reasonable deviation.
Factor Deviation Effect on mass
and PE
A significant part of the floor
space inside the core was used
for elevator shafts and such so
the actual floor space could be
reduced.
- 10% - 1%
Structural steel was mostly
below the level of the floor
rather than at floor level as
used in the calculation.
<< 1% of the
height
(PE only)
negligible
Mass of structural steel per floor
could vary more or less than
93.75% with height.
± 5% (PE only) < 1%
Value given for steel by NIST
could be inaccurate.
± 10% ± 3%
Estimated live-load and
superimposed dead-loads could
be inaccurate.
± 10% ± 3%
Floors 1-6 were special purpose
floors so dead-loads, live-load
and superimposed dead-loads
are probably inaccurate.
± 10% < 1%
Conclusion
The calculated mass of one tower is 253,000 metric tons. The total potential energy above grade is 3.98 x 1011 J. This indicates that the value for mass given by Ashley, Bazant and Zhou, and Wikipedia are nearly 80% more than the actual mass of one tower. The value for potential energy given by FEMA is probably correct. It is interesting to note that the mass of the upper part of the North Tower (i.e. above floor 96) given by Bazant and Zhou is nearly three times higher than if calculated by this method. References
1. Port Authority of New York and New Jersey, “Building the World Trade Center.” (1983) http://www.pbs.org/wgbh/amex/newyork/sfeature/sf_building.html
2. Tyson, P., “Towers of Innovation.” PBS/NOVA http://www.pbs.org/wgbh/nova/wtc/innovation.html
3. Gayle, F.W., et al., “NIST NCSTAR 1-3 Mechanical and Metallurgical Analysis of Structural Steel.” NIST Federal Building and Fire Safety Investigation of the World Trade Center Disaster http://wtc.nist.gov/reports_october05.htm
4. Hamburger, R., et al., (May 2002) “World Trade Center Building Performance Study, Chapter 2: WTC1 and WTC2.” FEMA 403 http:/www.fema.gov/rebuild/mat/wtcstudy.shtm
5. Wikipedia, “World Trade Center.” Wikipedia http://en.wikipedia.org/wiki/World_Trade_Center
6. Bazant, Z.P., Zhou, Y., (in press 9/13/01, Expanded 9/22/01, Appendices 9/28/01) “Why Did the World Trade Center Collapse?—Simple Analysis.” Journal of Engineering Mechanics ASCE
7. Ashley, S., (October 09, 2001) “When the Twin Towers Fell.” Scientific American
8. Lew, H.S., Bukowski, R.W., Carino, N.J., “NIST NCSTAR 1-1 Design, Construction, and Maintenance of Structural and Life Safety Systems.” NIST Federal Building and Fire Safety Investigation of the World Trade Center Disaster http://wtc.nist.gov/reports_october05.htm
ORIGINAL WELL FORMATTED DOCUMENT:
http://journalof911studies.com/letters/wtc_mass_and_energy.pdf
Henschel.”
“Richard Wagner, a data retrieval expert at the company, said illegal transfers of more
than $100 million might have been made immediately before and during the disaster.”
"There is a suspicion that some people had advance knowledge of the approximate time
of the plane crashes in order to move out amounts exceeding $100 million," Wagner said.
"They thought that the records of their transactions could not be traced after the
main frames were destroyed."
“Henschel said the companies in the United States were working together with the FBI to
piece together what happened on September 11 and that he was confident the destination
of the dubious transactions would one day be tracked down.”
Convar’s website features a video confirming that Convar GmbH did in fact process the
WTC hard drives. http://www.datarecovery-europe.com/welcome.htm The widely disseminated claim that Kroll Associates--the powerful private-intelligence firm responsible for some elements of WTC security on 9/11--acquired Convar in June 2002 remains
unsubstantiated. What can be verified is that Kroll purchased Ontrack Data Recovery, a
U.S.-based rival of Convar with offices in Germany.
After the CNN article of December 20, the U.S. media were stricken mute on the Convar
investigation. Of the media blackouts shrouding 9/11, none has been more absolute.
Notice that Convar, its unnamed WTC clients and the FBI possessed these data, and that
the FBI would have no reason to withhold the results of its investigation had they proven
benign or consistent with the Commission’s account of the attacks.
It is worth remembering what Sibel Edmonds told Jim Hogue: “I can tell you that the
issue, on one side, boils down to money--a lot of money. And it boils down to people and
their connections with this money…”
http://baltimorechronicle.com/050704SibelEdmonds.shtml
Consider again Wagner’s inference: “They thought that the records of their transactions
could not be traced after the main frames were destroyed." The locations of the
computers in question within the towers is unknown, but if Wagner is correct, two
possibilities emerge: (1) either the “insiders” had foreknowledge of the precise impact
points of the aircraft (otherwise why assume that the main frames would be destroyed?)
or (2) they had foreknowledge of the total destruction of the towers. Upon reflection,
for numerous reasons the first possibility recedes into remote improbability. But why
would the “insiders” assume the total collapse of the towers when there was no historical
precedent for such an event and the towers had been designed to survive the impact of
fuel-laden 707s at 600 mph? http://911research.wtc7.net/wtc/analysis/design.html If in fact the
WTC towers were demolished by explosives, incendiaries or other means, whoever
initiated these transactions should be considered suspect for complicity in those acts.
No legitimate reason—in fact no reason whatsoever--for withholding the Convar data has
to date been offered.
http://journalof911studies.com/letters/MysteryofWTCHardDriveRecoveries.pdf
================
The Sustainability of the Controlled Demolition Hypothesis for the Destruction of the Twin Towers
Tony Szamboti, mechanical engineer April 24, 2007
Abstract: In the past year there has been an exponential growth in the number of people questioning the explanations we have been given, by official U.S. government bodies, concerning the collapses of the three WTC buildings in NYC on 9/11/2001. It is probably safe to say that much of this growth can be attributed to the Internet publishing of a paper by Physics Professor Steven Jones in November 2005, which put forth the hypothesis that the Twin Towers and WTC7 were actually demolished with prepositioned cutter charges.3 This hypothesis is in tension with the present government explanation of aircraft impact damage and/or fires being the causes for the complete collapses of the buildings. My intent here is to show that any honest and objective look at all of the theories, for the destruction of the twin towers, including the present government explanation, will cause one to realize that only the controlled demolition hypothesis is sustainable. I believe an honest look at the evidence will convince anyone that the controlled demolition hypothesis provides the best explanation for the complete collapses of the towers, as well as the damage to the buildings and objects surrounding them. The remarkable collapse of WTC7 seems to have had a separate cause in its own controlled demolition. Video of the collapse of WTC7 can be viewed quickly at http://www.journalof911studies.com/beginners.html before continuing, as it plays a part in understanding what probably occurred in NYC on Sept. 11, 2001.
It can be shown that due to the design and volume of the towers, the aircraft impacts and fires could not have been enough to cause them to collapse. The link below will provide an idea of how the towers were constructed, with photos seen in articles from the Engineering News Record at the time they were built. http://911research.wtc7.net/mirrors/guardian2/wtc/eng-news-record.htm
The following points then need to be understood to follow this line of reasoning:
• The twin towers were designed to handle multiple loads: their own weight (dead loads), live loads (due to people, furnishings, and equipment), wind loads, ice loads, and seismic loads. The dead and live loads are normal gravity loads. The central core was designed to handle 60% of the normal gravity loads of the building and the perimeter beams to take the remaining 40% of the normal gravity loads, and all of the wind, ice, and seismic loads.1 While wind loads are usually quite low, tall structures need to be designed to handle extremes. The towers where designed to handle the overturning moment and shear stresses generated by 100 mph winds acting on their considerable surface area and height. 2 Although heavy icing would be rare, the towers would still need to withstand the extra weight, which glaze ice would bring at 56 lbs./ft3, not insignificant on a structure with approximately 1.3 million square feet of outside surface area. Seismic loads can generate horizontal accelerations, which would cause high overturn moments, similar to those caused by high wind loads. Due to the need to withstand rare high wind, ice, and seismic loads, the tower’s perimeter beams had a minimum factor of safety of 5.00, when considering normal gravity loads only. The central cores were designed with the more standard factor of safety of 1.67, since they took normal gravity loads only. Prior to the attacks, on a low wind, warm sunny day, with no earthquakes, such as Sept. 11, 2001, the beams in each tower would have had no more than 33% of their total load sustaining capacity used.
• Upon impact with the buildings, the wings, tail, and engine fan assemblies of the aircraft would have certainly been shredded prior to completely entering the buildings. This would leave only the fuselage, center portions of the engines, and the landing gear, with greatly diminished energies, to cause damage to the central core columns.10,11 The central cores were comprised of 47 large steel columns interconnected at every floor in a three-dimensional matrix, encompassing a plan area of 137 feet x 87 feet. The fuselages of both Boeing 767-200ER aircraft, which hit the towers, were 16.5 feet in diameter.4 The spacing of the central core columns ranged from approximately 11 to 21 feet apart,11 so by volume alone there would be a limited number of columns which the remains of the fuselage, could contact.
The aircraft engines were approximately 9 feet in diameter, much of which was the fragile fan assemblies, which would have been decimated going through the outer wall. Only the much smaller diameter turbojet portions of the engines and their rigid shafts would have had much ability to cause additional damage to the central core columns. The damage to the perimeter columns is visible in photographs. It is known that no more than 20% of the perimeter columns were affected in either tower. It is the damage to the core columns, which was not visible, that needs to be scrutinized. Analyses can be done to show what the remaining energies and volumetric probabilities would be for impact damage to occur to the core columns. NIST did analyses of this type and in their base cases, for both towers, less than 20% of the central core columns were severed or heavily damaged.
• The towers were designed as virtual structural pyramids, with the wall thickness of the beams thicker at the bottom and thinning with greater vertical height location. The bottom beams were thicker due to heavier loading, and the top beams thinner due to lighter loading. Since the tower beams varied in wall thickness, depending on their vertical location, it could be ascertained which beams were in the aircraft impact and fire affected areas. With it being important to know the actual temperatures that the beams experienced, in the fire affected areas, NIST used the known microstructure characteristic of spheroidization to determine those temperatures.8 Temperature will change the spheroidization of the steel microstructure in a linear, predictable, and permanent way. In their testing of the beams it was found that only a few percent of them ever experienced temperatures above 250° C (482° F) and none above 600° C (1,112° F). None of the central core columns tested showed they experienced temperatures above 250° C (482° F). The chart below, which shows the proportional loss of strength in steel, as it’s temperature is increased, is from Corus Construction, with temperatures in degrees C.
As the chart shows, steel does not lose any of its strength until its temperature rises above 350° C (662° F), and only loses half of it at 600° C (1,112° F). So the evidence shows that no more than a few percent of the beams lost any of their strength due to the fires. While NIST includes this data in their report it is essentially ignored and an argument attempted that higher steel temperatures existed, even though there is no physical evidence for it. The amount of jet fuel, which actually entered the towers, could not have been any more than half of the 10,000 gallons on board each aircraft. Spreading the remaining 5,000 gallons, in each case, over an acre (one floor of one tower) results in a jet fuel film thickness of .015 inch. This film would have burned up quickly, leaving nothing more than office materials to fuel the fires. The fact that high temperature effects were not found in the microstructure of the steel should not be surprising.
To summarize, it can only be shown that approximately 20% of the beams, in the cases of both towers, had their strength significantly affected by the aircraft impacts and fire. That leaves approximately 80% of the beams, in both cases, with their full strength intact. Grid like structures, such as the twin towers, redistribute loads when individual beams are damaged. This occurs in a bridge like fashion, since the vertical beams are interconnected horizontally at every floor. In the reference section of this article, I show that if 20% of the central core and perimeter columns were totally incapacitated, 9 or 10 central core and 48 perimeter, the perimeter would have maintained a factor of safety of 4.00, and the central core a factor of safety of 1.34. The remaining factor of safety of 1.34 for the central core is not insignificant. What it means is that for the yield point of the steel to even be reached, and collapse to be incipient, an additional 20% of the core strength needed to be lost due to fire. In terms of the number of beams needing to be affected, an additional 19 out of the remaining 38 core columns would need to reach 600° C (1112° F) to lose half of their strength. This is not a likely scenario and there is no physical evidence for it, as shown above in the discussion of the beam temperature testing data gathered by NIST. It would appear that the initiation of vertical collapse, due to fire weakening and gravity, was improbable. So how then did the towers collapse?
The answer is obviously that another mechanism must have caused the collapses. The fact that the twin towers both collapsed due to a cause, which must obey the laws of physics, cannot be disputed. It is that cause which some claim is in dispute at the moment. The alternative collapse causation theories, which have been proposed to counter the insufficient U.S. government theory, are
1. A directed energy weapon was used to destroy the towers.
2. Mini-nukes were used to destroy the towers.
3. The towers were destroyed via controlled demolition with the use of incendiaries and explosives.
The first and second proposed causes have been shown not to be serious hypotheses, by scientifically based papers. These papers show that these two theories have no basis. These papers also explain away any perceived anomalies, and provide reasons for the observations, which are more natural and consistent with the controlled demolition hypothesis for the destruction of the towers. To date these papers have not been challenged in writing, or shown to be incorrect in any way, by those who have supported these first two theories. These papers can be found at http://www.Journalof911Studies.com The physical evidence for the third theory, controlled demolition, is due to the characteristics of the twin tower collapses. In one of his many writings on the subject of Sept. 11, 2001, Dr. David Ray Griffin lists the eleven characteristics of controlled demolition, which both of the towers exhibited in their respective collapses.
Sudden Onset Dust Clouds Molten Steel
Straight Down Horizontal Ejections Sliced Steel
Almost Free-Fall Speed Sounds Produced by Explosions Demolition Rings
Total Collapse Pulverization of Concrete and Other Materials
Dr. Griffin’s full article ‘The Destruction of the World Trade Center: Why the Official Account Cannot Be True” can be found at http://911review.com/articles/griffin/nyc1.html
Any close viewing of video, of the collapses of the towers, will physically show most of the characteristics of controlled demolition listed above. Witnesses, photos, and taped audio from that day, have attested to, molten metal, demolition rings, sliced steel, and sounds produced by explosions.
It was the revelation of the presence of molten metal, in the rubble of all three buildings which collapsed in NYC on Sept. 11, 2001, which caused Dr. Jones in 2005 to begin to question whether the present U.S. government explanation for the collapses was sufficient. It is provable that the molten metal in the rubble was not aluminum and that diffuse flame fires cannot achieve temperatures sufficient to melt steel. Steel can only be melted in the controlled environment of a blast furnace or with the use of incendiaries. There is very credible witness testimony of seeing, hearing, and feeling explosions, in many areas of the towers, both before and during the collapses. This testimony can be found in the Oral Histories of the 503 NYC firefighters and emergency personnel, who were on the scene that day and survived. Their testimony was taken and transcribed in late 2001 and early 2002 by order of the NYC fire commissioner. However, afterward the mayor of NYC repeatedly refused to release these testimonies to the public. They were only released by a court order from the New York State Court of Appeals in August of 2005, after earlier court challenges had failed to gain their release. There was no testing done for explosive residue on the beams during either the NIST or FEMA investigations of the building collapses. An article by Dr. David Ray Griffin discussing and quoting these Oral Histories can be found at
http://www.911truth.org/article.php?story=20060118104223192
It is also worth mentioning the fact that the buildings were designed to take an impact by a fully loaded Boeing 707 at 334,000 lbs. and moving at it’s cruise speed of 607 mph. While the NIST report mentions this, it claims that documentation supporting this contention could not be found. However, the late John Skilling, who was the head structural engineer on the tower design project, is quoted in 1993 as saying that a white paper was done on this design feature. The towers were actually hit with Boeing 767-200ER aircraft, which had only 10,000 gallons of fuel on board for their trips to the West Coast of the U.S. from Boston. While the 767-200ER is rated at a 395,000 lb. max takeoff weight, this is for a full fuel load of 23,980 gallons, which would be used for a longer flight as the aircraft had a 7,700 mile range4. Subtracting the weight of 14,000 gallons (at 6.825 lbs./gallon) from the max takeoff weight gives an aircraft weighing approximately 300,000 lbs. The 767-200ER had a cruise speed of 530 mph (there are various estimates by radar, and other timing methods, which put the actual speeds of the aircraft at impact at lower values). However, even using the higher 530 mph value and the equation
K = 1/2mv2
where K = kinetic energy
m = mass
v = velocity
it is found that the designed for 707 impact would have contained at least 1.4 times or 40% more kinetic energy than what the 767-200ER aircraft could have provided. The buildings obviously survived the impacts and thus the present theory we are given is that fire caused the collapses. The fact that fires have never in history caused the complete vertical collapse of a steel framed structure, let alone any built as robustly as the twin towers, has been amply documented. Serious doubt of the present government explanation has been emanating from qualified credible people for the last several years.
Editor Bill Manning wrote in Fire Engineering magazine in 2002 that: “Fire Engineering has good reason to believe that the ‘official Investigation’ blessed by FEMA… is a half-baked farce that may already have been commandeered by political forces whose primary interests, to put it mildly, lie far afield of full disclosure… Respected members of the fire protection engineering community are beginning to raise red flags, and a resonating [result] has emerged: The structural damage from the planes and the explosive ignition of jet fuel in themselves were not enough to bring down the towers….”. A letter was sent by a C. Thurston to Tucker Carlson of MSNBC, after he hosted Dr. Steven Jones on one of his nightly shows in November of 2005. In it he lists ten withering reasons for not believing the gravity driven collapse theory. It can be found at http://www.911research.com/letters/msnbc/index.html The NIST report wants to tell us that it was the perimeter columns that buckled and caused the collapses. The report says this was due to their deflection and bowing, caused by fire affected sagging floor trusses pulling on them, and the central core itself sagging due to plasticity and creep.6 The probable collapse sequences, as hypothesized by the NIST report, were issued at a press conference in NYC in April 2005.
That press release is available here.
http://www.nist.gov:80/public_affairs/releases/wtc_briefing_april0505.htm
It appears the press release and report want to say that the entire interior structure was sagging. It is interesting that the NIST press release and report don’t seem to concern themselves much with the fire testing of the floor deck and supporting truss assembly models, done under contract for them by Underwriters Laboratories. Full scale models of the floor deck and supporting truss assemblies were fire tested, under load for two hours, per ASTM E119. These tests did not produce a collapse and the 35 foot long trusses only sagged 3 inches at midspan, not likely enough to buckle the perimeter wall columns. In fact, NIST needed a non-evidence supported 42 inch floor truss deflection in their computer model to cause buckling of the perimeter columns. Their large heat capacity and ability to transfer heat to other areas of the building would have certainly made the core columns even less susceptible to weakening than the trusses. The lack of high temperature evidence on the core columns is a testament to this point. Curiously, the press release does not mention either the floor assembly fire testing or the low percentage of beams found to have experienced high temperatures in the microstructure testing. Both the press release and the report attempt to point towards a theory of dislodged fireproofing materials as the reason for the alleged interior steel weakening. Although they don’t say it out loud, it is a virtual certainty that NIST did floor assembly fire testing without fireproofing.9 If the trusses, in this case, had much more significant sagging or collapsed it would have proven their hypothesis. However, there is no mention of failure, so apparently the tests didn’t produce the results which would back up their theory. It is important to note that NIST has not been able to cause physical models to fail with their fire induced collapse theory.
It is instructive that the first visible signs of failure on the North Tower are when the antenna mast moves downward by ten to twelve feet before the perimeter roof line moves. This is indicative of the central core suddenly and completely failing first. If you haven’t seen this watch it frame by frame at the link below.
http://911research.wtc7.net/wtc/evidence/videos/wtc1_close_frames.html
These frames don’t show slow creep, they show sudden failure of the central core itself. They certainly don’t show the perimeter walls failing first. If the central core failed first it would cause the trusses not to sag, but to follow them downward, applying a tremendous bending moment on the perimeter beams, which would certainly cause them to bow inwardly. Even with their high factor of safety against vertical loads, the perimeter beams would be dragged down with bending moments much more severe than the wind load induced moments they were designed to withstand. By demolishing the core, the destruction of the building could also be done with the added advantage of the demolition being mostly hidden from view. It appears that the central core failed first and that is what caused the floor trusses to move downward and pull on the perimeter beams, causing them in turn to fail. The central core needed to have a minimum loss of 40% of its total strength before collapse could begin to occur. Since the evidence for column damage, due to aircraft impact and fire, can only account for a maximum 20% loss of strength in the central core, it does not appear collapse initiation can be accounted for without controlled demolition being involved.
It would seem that any honest and objective look at; the design of the buildings, the true damage potential of the aircraft impacts, the physical evidence of the low beam temperatures, the physics of the collapses, the evidence of molten metal in the rubble, and the witness testimony, should cause one to conclude that the towers must have been destroyed via controlled demolitions. In addition to the evidence mentioned so far, there is also evidence of the presence of incendiaries, in the chemical analysis of the dust from an apartment near the towers, and slag from a monument using salvaged twin tower steel, which have both been analyzed by Dr. Jones and others.
The present U.S. government explanation, for the collapses of the buildings in New York City on Sept. 11, 2001, is simply not sustainable. The evidence, which has surfaced in support of the controlled demolition hypothesis, in the last two years, is overwhelming. The obvious controlled demolition of WTC7, at 5:20 PM on Sept. 11, 2001, proves that charges were pre-positioned, as there would not have been time to rig the building that day, especially with fires in it. With this in mind, the demolition of WTC7 lends considerable weight to the notion that charges could also have been pre-positioned in the twin towers. The spectacular collapses of the twin towers, which were in reality caused by controlled demolitions, shocked us all, and caused us to demand action against the entities who we were told supported the hijackers. It is very plausible that the aircraft impacts were used as causal ruses, to allow the collapses to be blamed on outsiders, as the placing of the charges, which actually caused the spectacular collapses of the twin towers, would have required access that outsiders simply would not have. One may wonder who would want people in Afghanistan and Iraq to be blamed if they didn’t do it. A good hard look at the soon to be built U.S. oil company controlled gas pipeline in Afghanistan, and the virtual takeover of Iraq’s oilfields by U.S. oil companies, would be a start at solving that puzzle for oneself. Neither of these situations would have been possible, without the support of the American people, for the use of the U.S. military, to overthrow the previous governments of these countries. Endnotes and References:
1. Determination of the minimum factor of safety against gravity caused vertical collapse of the Twin Towers after sustaining aircraft impact and fire damage. While the actual detail drawings of the twin tower design have been withheld from the public (the recent release of blueprints was for architectural floor plan views only), the size of the central core’s largest beams are known, from magazine articles published in the Engineering News Record during the time the towers were being built. A link to these articles is provided at the beginning of this paper.
Below is a depiction, from one of those articles, of the base of the largest of the core columns. What the architectural plan views do tell us is that there were a total of sixteen of these size columns, with eight along each outside edge of the long span of the 137 foot x 87 foot central core. The remaining thirty-one columns were most probably 36” x 16” columns. Below is a sketch of the cross section of a 36” x 16” column, also from the Engineering New Record, which was located approximately half way up the tower.
It can be inferred that the bases of the 36” x 16” columns would have been built proportionally to the 54” x 22” columns, with 4” plates in lieu of 5” plates and a 5” plate in the center in lieu of the 6.25” plate on the larger beam. This would be done to increase the cross section to gain the needed resistance to the vertical compressive load.
Using the dimensioned pictorial view above, the total cross sectional area of the 54” x 22” columns is approximately 898 in.2. The total cross sectional area of a proportional 36” x 16” column, built with 4” plates, would be approximately 467 in.2. With sixteen columns at 898 in.2 and thirty-one columns at 467 in.2 the total cross sectional area of the base of the central core, to resist compressive loading and vertical collapse, would be 28,845 in.2.
The AISC manual,7 used for the design of steel framed structures in this country for the last eightyfive years, has specified, since long before the erection of the twin towers, that the allowable compressive stresses on vertical columns not exceed 0.60Fy, and thus have a factor of safety of 1.67. This means the actual stress cannot exceed 60% of the compressive yield strength of the material used for the column. The central core columns at the base were made from ASTM A36 steel which has a compressive yield strength of 36,000 psi. 60% of this strength gives an allowable stress of 21,600 psi. Coupling this allowable stress with the total cross sectional area of the forty-seven core columns shows that, as a group, they could support a vertical load of 311,526 tons. This is approximately 60% 8 of the reported 500,000 ton gravity load of each of the twin towers. The remaining 200,000 tons of gravity load would need to be supported by the perimeter columns.
On the far right of the pictorial below, is a dimensioned sketch of the cross section of the lowest 60 per side perimeter columns, which were actually located at five floors above the ground level on the buildings. These columns transitioned three into one near the fifth floor level and thus there were 20 larger perimeter columns per side, which would have actually went down to the base. Since no cross section sketches of the 20 per side perimeter columns exist in the public domain, of which I am aware, this sketch can serve as the cross sectional reference, to find a minimum total cross section of the perimeter columns at the base. The actual total cross sectional area of the perimeter columns, at the base, twelve stories down, would only be larger, so the analysis here can be considered conservative. The center view is of the cross sectional dimensions further up on the towers and the view on the left is of fireproofing on the steel with aluminum cladding over the fireproofing. Judging from the sketch on the right, the cross sectional area of one of the 60 per side columns at its base was approximately 88 in.2. There were 240 perimeter columns of this size in each tower so the total cross sectional area of the perimeter columns at their base would have been no less than 21,120 in.2. The compressive stress induced by 200,000 tons of gravity load on this area provides an actual stress of 18,939 psi. These perimeter columns were made from steels ranging in yield strength up to 100,000 psi. The lowest of the 60 per side columns would have had the highest strength, as that is where the maximum overturning moment and shear stress, from wind and seismic loads, would have existed. When considering gravity loads only, the perimeter columns would have provided a minimum factor of safety of approximately 5.00 against vertical collapse since Factor of safety = yield strength/actual stress
Although only the base loads and their stresses are considered here, it can be inferred that this would be true for all of the beams, over the full height of the towers, as they would be designed to maintain the same factor of safety throughout. The core columns would have had a factor of safety of 1.67 and the perimeter columns a factor of safety of 5.00, against vertical collapse, throughout the full height of the building, when considering gravity loads only.
The vertical load capacity of the beams, at their base, due to compressive loads only, was
Central core 300,000 tons x 1.67 = 500,000 tons
Perimeter 200,000 tons x 5.00 = 1,000,000 tons
Using the base as a reference, the actual load vs. the beam capacity, during a low wind day like Sept. 11, 2001, would have been
Actual Load/Beam Capacity = 500,000/1,500,000 = 33%
If 80% of the base central core columns had their strength unaffected by damage and/or fire they would have provided a remaining factor of safety and load capacity of 0.80 x 1.67 = 1.34 for a 300,000 ton load = 402,000 ton remaining capacity If 80% of the base perimeter columns had their strength unaffected by damage and/or fire they would have provided a remaining factor of safety and load capacity of 0.80 x 5.00 = 4.00 for a 200,000 ton load = 800,000 ton remaining capacity The remaining unaffected 80% of the tower structure would still have been capable of supporting 1,202,000 tons or 2.4 times the actual 500,000 ton load.
Standard design practice dictates that the beams in the upper part of the building would have had the same factor of safety as the beams at the base of the towers. So knowing the design of the columns at their base, the total gravity load of the buildings, and the percentage of damaged beams, we have deduced what the remaining factor of safety was for the beams at the aircraft impact and fire sites. The remaining factor of safety against vertical collapse in the aircraft impact and fire affected areas would have been at least
1.34 for the central core columns
4.00 for the perimeter columns
This is with the assumption that 20% of the central core columns were lost, which is improbable.
Buckling can occur at stresses below the compressive yield strength of a material. The critical buckling stress is dependent on the slenderness ratio of a column and whether its ends are fixed or free. The slenderness ratio is related to the stiffness of the cross section of the column and the unsupported length between the column’s connections to supports. The end condition for the best buckling resistance is fixed at both ends, which the columns were in the aircraft impact and fire affected areas. The design of the tower columns would have precluded buckling as an earlier mode of failure, due to the short vertical length of the columns between horizontal supports and the stiffness of the cross section of the beam. The design would have followed AISC guidelines, which would have required that the critical buckling stress not be less than the compressive yield strength.7
2. NIST NCSTAR 1-1A, WTC Investigation, Chapter 2, page 34, paragraph 2.3.2. http://wtc.nist.gov/NISTNCSTAR1-1A.pdf
3. “Why Indeed Did the WTC Buildings Completely Collapse” by Physics Professor Steven Jones http://www.journalof911studies.com/volume/200609/WhyIndeedDidtheWorldTradeCente rBuildingsC ompletelyCollapse.pdf.
4. Boeing Technical characteristics for the 767 family of aircraft. See tables for the 767-200ER. http://en.boeing-me.com/ViewContent.do?id=2404
5. Executive Summary of the Final Report of the National Construction Safety Team on the Collapses of the World Trade Center Towers, extracted from NIST NCSTAR 1.
http://wtc.nist.gov/pubs/NCSTAR1ExecutiveSummary.pdf
6. Final Reports of the Federal Building and Fire Investigation of the World Trade Center Disaster http://wtc.nist.gov/reports_october05.htm
7. Manual of Steel Construction, 8th edition, 1980 printed by the American Institute of Steel Construction Inc.
8. Examples of microstructure of steel which has been heated and cooled. At bottom of page. http://wtc.nist.gov/media/gallery.htm#sim
9. NIST photos of fire experiment setups. See uninsulated truss setup in next to last picture at bottom. http://wtc.nist.gov/media/gallery2.htm
10. Photo of the aircraft impact damage to the exterior of the North Tower As the aircraft was at an angle, the wings would have had to go through the perimeter beams plus 60 feet of floor decking of multiple floors edge on. The tail would have also had this situation due to its height.
11. Graphic of central core column spacing vs. fuselage and central engine
diameters
87 feet
137 feet
North Tower aircraft
approximate orientation to the central core
Perimeter Beams
Central Core
208 feet
Wings, engine fan assemblies, and the tail would have been shredded after going through perimeter beams and multiple floors edge on, leaving only parts of the fuselage, landing gear, and 4 foot diameter center portions of engines, with greatly diminished energies, having any chance of causing damage to the Central Core 4 foot dia. central portion of engine South Tower aircraft approximate orientation to the central core with fuselage and central portion of engine shown in relative sizes
Relative size of 16.5 ft. dia. fuselage
ORIGINAL WITH GRAPHICS:
http://journalof911studies.com/letters/SzambotiSustainabilityofControlledDemolitionHypothesisfortheDestructionofTwin%20Towers.pdf
================
Analysis of Mass and Potential Energy in the World Trade Center Twin Towers
Gregory H. Urich
B.S. Electrical and Computer Engineering
Abstract
The mass of one of the Twin Towers is calculated based on available data and estimated live loads. The potential energy for one of the Twin Towers is calculated based on the mass of the tower distributed over the various floors. The mass for each floor is established based on the average mass per floor adjusted for differences in mass due to stronger steel structures lower in the tower. All floors including mechanical floors and the basement floors are treated equally with regard to superimposed dead-loads.
Introduction
Many references can be found with different values for the mass of and the amount of potential energy stored in the WTC twin towers. A number of references are shown in Table 1 below. None of these references provide any data or calculation method on which the mass and potential energy are based. The purpose of this paper is to establish a substantiated value for the mass and potential energy of one tower.
Table 1: Different values for mass and potential energy given by references
Source Mass Potential Energy
Ashley 7 500,000 tons
Bazant and Zhou 6 = 480,000 tons (metric)*
Hamburger, et al. (FEMA) 4 4 E+11 J
Tyson 2 500,000 tons
Wikipedia 5 500,000 tons
* calculated based on mass given for upper part of North Tower = 58 E+6 kg
Analysis
In the design documentation for WTC1 and WTC2 the structural loads are divided into deadloads, super-imposed dead-loads, and live-loads. These divisions are also used here. Dead-loads
Foundation
The mass of the foundation is provides no load on structural components other than itself and contributes a negligible amount to potential energy. The mass of the foundation is nonetheless approximated based on the film footage from the Port Authority of New York and New Jersey.1 Dimensions are established by comparison to objects of known size, i.e. humans. The foundation for the core columns was comprised of steel reinforced concrete footers and steel grillages built up out of I-beams. One steel grillage is made up of 17 I-beams with approximate dimensions 0.75m x 0.2m x 2m with a plate thickness around 0.03m. Each grillage also had a base plate for the core column with approximate dimensions 1m x 1m x 0.3m. It is assumed that there is one grillage per core column. Using a density of 7.784 metric tons per cubic meter for the density of A35 steel, the total mass for the grillages is approximately 484 metric tons. Each grillage was placed on a concrete footer with approximate dimensions 2.5m x 2.5m x 2m. Using a density of 2.4 metric tons per cubic meter, the total mass for the concrete footers is approximately 1410 metric tons. The foundation for the external columns was comprised of a continuous, steel reinforced, concrete footer and base plates ranging from 7 to 9 square feet (approx. 0.74 m2). The reference for this value is unsure but it is most likely from FEMA or NIST. The thickness of the base plate is unknown but a thickness of 3 cm is assumed. Using a total number of 80 exterior columns (transition to 238 columns at 7th floor), the total mass of the base plates is approximately 14 metric tons. The concrete footer for the external columns had a perimeter of 252 meters. The other dimensions of the footer are unknown but are approximated using 2 meters for depth and 2 meters for width. The total mass for the concrete footer is thus 2420 metric tons.
Table 2: Mass of foundation
Component Mass (short tons)
Mass (metric tons)
Core steel grillage w/ base plate 534 484
Core concrete footer 1555 1410
External column steel base plates 15 14
External column concrete footer 2670 2420
Total mass foundation 4774 4328
Structural steel
NIST’s value for the mass of steel used in one tower is 100,000 short tons.3 A simplified approximation based on averaging component dimensions provided by NIST demonstrated that this value is reasonable.
The actual mass of the upper floors is less than the lower floors due to heavier supporting structures lower in the building. FEMA describes a variation in thickness of exterior column plates from 4 inches at the base to ¼ inch in the upper stories.4 This indicates a ratio of 16 to 1 for structural steel from bottom to top. The mass of the steel can be scaled linearly as a function of floor number from the bottom to the top as follows: msteel (f) = mavg • (-30f + 3710)/1955
f is the floor number, mavg is the average mass of steel per floor (= 99,451 tons/116 floors; foundation components are subtracted)
Mass above grade:
Mass below grade: . mavg • (-30f + 3710)/1955 = 10,035 short tons 6 . mavg • (-30f + 3710)/1955 = 89,416 short tons
116
f = 7
f = 1
Table 3: Mass of structural steel per floor in short tons (Note: floor 116 has been transposed
to 110 to correspond to the normal floor numbering. Also, 549 tons has been used for floor 0,
i.e. steel in the foundation.)
floor mass floor mass floor mass floor mass floor mass floor mass
110 101 90 364 70 627 50 890 30 1153 10 1416
109 114 89 377 69 640 49 903 29 1167 9 1430
108 127 88 390 68 653 48 917 28 1180 8 1443
107 140 87 403 67 667 47 930 27 1193 7 1456
106 153 86 417 66 680 46 943 26 1206 6 1469
105 167 85 430 65 693 45 956 25 1219 5 1482
104 180 84 443 64 706 44 969 24 1232 4 1495
103 193 83 456 63 719 43 982 23 1245 3 1509
102 206 82 469 62 732 42 995 22 1259 2 1522
101 219 81 482 61 746 41 1009 21 1272 1 1535
100 232 80 496 60 759 40 1022 20 1285 0 1548
99 246 79 509 59 772 39 1035 19 1298 -1 1561
98 259 78 522 58 785 38 1048 18 1311 -2 1574
97 272 77 535 57 798 37 1061 17 1324 -3 1587
96 285 76 548 56 811 36 1074 16 1338 -4 1601
95 298 75 561 55 824 35 1088 15 1351 -5 1614
94 311 74 574 54 838 34 1101 14 1364 -6 549
93 325 73 588 53 851 33 1114 13 1377
92 338 72 601 52 864 32 1127 12 1390
91 351 71 614 51 877 31 1140 11 1403
Concrete floor slabs above grade (Floors 1-110)
Floor slabs outside of the core were constructed primarily of light concrete. The mass of light concrete can be calculated using the floor area outside of the core (approx. 28,225 sq ft), the floor thickness (4 in. 8), and the density of light concrete (109.3 lb/ft3). 28,255 sq ft/floor x 0.33 ft x 109.3 lb/ft3 x 110 floors x 1 ton/2000 lbs = 56,600 short tons Floor slabs inside the core were constructed primarily of normal concrete. The mass of normal concrete used in these floors can be calculated using the floor area (11,745 sq ft), the floor thickness (5 in. 8), and the density of normal concrete (150 lb/ft3). 11,745 sq ft/floor x 0.4167 ft x 150 lb/ft3 x 110 floors x 1 ton/2000 lbs = 29,400 short tons Concrete floor slabs below grade (Floors B1-B6)
Floor slabs below grade were constructed primarily of normal concrete. The mass of normal concrete used in these floors can be calculated using the floor area (40,000 sq ft), the floor thickness (8 in. 8), and the density of normal concrete (150 lb/ft3). 40,000 sq ft/floor x 0.6666 ft x 150 lb/ft3 x 6 floors x 1 ton/2000 lbs = 8,700 short tons
Superimposed Dead-loads
Superimposed dead-loads are considered permanent non-varying loads from non-structural components such as wiring, plumbing, heating and cooling aggregates, elevators, etc. Unfortunately the dead loads are very difficult to approximate due to the lack of information about what elements comprised them. Superimposed dead-loads in the WTC towers are considerably higher in the so called mechanical floors. This is however ignored for simplicity and an average superimposed dead-load is approximated and distributed throughout all floors. The design documents give a superimposed dead-load of 8 psf for most floors outside of the core. 8 This value is most likely larger than the actual loads but is used for all floors to take into account the much larger actual loads of the mechanical floors.
Mass of superimposed dead-loads above grade:
40,000 sq ft/floor x 8 lb/ft2 x 110 floors x 1 ton/2000 lbs = 17,600 short tons
Mass of superimposed dead-loads below grade:
40,000 sq ft/floor x 8 lb/ft2 x 6 floors x 1 ton/2000 lbs = 960 short tons
Live-loads
Live-loads are approximated using 1/4 (as used by NIST) the maximum design loads. Above grade, the most predominate design load outside of the core was 100 lbs/sq ft.8 25 lbs/sq ft x 28,255 sq ft/floor x 110 floors x 1 ton/2000 lbs = 38,850 short tons Above grade, the most predominate design load inside the core was 50 lbs/sq ft. 8 12.5 lbs/sq ft x 11,745 sq ft/ floor x 110 floors x 1 ton/2000 lbs = 8,075 short tons Below grade, the most predominate design load inside the core was 500 lbs/sq ft. 8 125 lbs/sq ft x 40,000 sq ft/ floor x 6 floors x 1 ton/2000 lbs = 15,000 short tons
Total Mass
The total mass is 279,000 short tons or 254,000 metric tons.
Table 4: Mass above grade
Component Mass (short tons) Mass (metric tons)
Concrete floor inside core area 29 400 26 671
Concrete floor outside core area 56 600 51 347
Structural steel 89 416 81 117
Live-load inside core 8 075 7 326
Live-load outside core 38 850 35 244
Superimposed dead-load 17 600 15 966
Total mass above grade 239 941 217 671
Table 5: Mass below grade
Component Mass (short tons) Mass (metric tons)
Concrete foundation 4 221 3 829
Concrete floor 8 700 7 893
Structural steel 10 035 9 104
Live-load 15 000 13 608
Superimposed dead-load 960 871
Total mass below grade 38 916 35 304
Potential Energy
The potential energy (u) due to gravity (close to earth) of any object can be calculated as:
u = mgh
m = mass, g = acceleration due to gravity, h = height
A reasonable approximation for potential energy relative to ground level (above grade) can be made using:
mnon.steel is the average mass (converted to metric) of one floor excluding structural steel, msteel (f) is the value for the mass of steel for a particular floor from Table 3 (converted to metric), g = acceleration due to gravity, f is the floor number, 414,53 is the height of the tower above grade in meters
The sum is from 1 to 110 to include all floors above ground and the roof and their underlying support structure. Potential energy per floor is show in Table 6 below. The total potential energy is 3.98 x 1011 J.
Table 6: Potential energy per floor (above grade)
floor PE(MJ) floor PE(MJ) floor PE(MJ) floor PE(MJ) floor PE(MJ) floor PE(MJ)
110 5415 90 5223 70 4680 50 3783 30 2534 10 933
109 5413 89 5205 69 4643 49 3729 29 2463 9 844
108 5411 88 5185 68 4606 48 3674 28 2390 8 753
107 5408 87 5164 67 4568 47 3618 27 2317 7 662
106 5405 86 5143 66 4529 46 3562 26 2242 6 570
105 5400 85 5121 65 4489 45 3504 25 2167 5 477
104 5394 84 5097 64 4448 44 3446 24 2091 4 384
103 5388 83 5073 63 4406 43 3386 23 2014 3 289
102 5380 82 5048 62 4363 42 3326 22 1936 2 194
101 5372 81 5022 61 4320 41 3265 21 1857 1 97
100 5363 80 4996 60 4276 40 3203 20 1778
99 5353 79 4968 59 4230 39 3140 19 1697
98 5342 78 4939 58 4184 38 3076 18 1616
97 5330 77 4910 57 4137 37 3012 17 1534
96 5318 76 4880 56 4089 36 2946 16 1450
95 5304 75 4849 55 4040 35 2880 15 1366
94 5290 74 4817 54 3991 34 2812 14 1281
93 5275 73 4784 53 3940 33 2744 13 1196
92 5258 72 4750 52 3889 32 2675 12 1109
91 5241 71 4715 51 3836 31 2605 11 1021
. (mnon-steel + msteel (f) ) • 9.8m/s2 • (414,53m • f/110) = 398,000 MJ
f = 1
110
Discussion
One difficulty in approximating the potential energy is that the dimensions for core columns
are unknown. Since the structural components are stronger (i.e. heavier) lower in the building,
it is necessary to know how these components varied over the height of the building. Some
dimensions for core box columns given by NIST are not correct. For example, the dimensions
“as large as 12 in. by 52 in., comprised of welded plates up to 7 inches thick” must be
incorrect. It can be seen from the photographic evidence that the thickest plates are used for
the larger dimension of the rectangular box columns. Thus, the width dimension would need
to at least 14 inches to accommodate the 7 inch thick plates.
Accuracy of the calculation
Due to certain limitations of available information and also the method of calculation, the
values for mass and potential energy are not perfectly accurate. Factors which may affect the
accuracy are listed in the below along with estimated effects caused by reasonable deviation.
Factor Deviation Effect on mass
and PE
A significant part of the floor
space inside the core was used
for elevator shafts and such so
the actual floor space could be
reduced.
- 10% - 1%
Structural steel was mostly
below the level of the floor
rather than at floor level as
used in the calculation.
<< 1% of the
height
(PE only)
negligible
Mass of structural steel per floor
could vary more or less than
93.75% with height.
± 5% (PE only) < 1%
Value given for steel by NIST
could be inaccurate.
± 10% ± 3%
Estimated live-load and
superimposed dead-loads could
be inaccurate.
± 10% ± 3%
Floors 1-6 were special purpose
floors so dead-loads, live-load
and superimposed dead-loads
are probably inaccurate.
± 10% < 1%
Conclusion
The calculated mass of one tower is 253,000 metric tons. The total potential energy above grade is 3.98 x 1011 J. This indicates that the value for mass given by Ashley, Bazant and Zhou, and Wikipedia are nearly 80% more than the actual mass of one tower. The value for potential energy given by FEMA is probably correct. It is interesting to note that the mass of the upper part of the North Tower (i.e. above floor 96) given by Bazant and Zhou is nearly three times higher than if calculated by this method. References
1. Port Authority of New York and New Jersey, “Building the World Trade Center.” (1983) http://www.pbs.org/wgbh/amex/newyork/sfeature/sf_building.html
2. Tyson, P., “Towers of Innovation.” PBS/NOVA http://www.pbs.org/wgbh/nova/wtc/innovation.html
3. Gayle, F.W., et al., “NIST NCSTAR 1-3 Mechanical and Metallurgical Analysis of Structural Steel.” NIST Federal Building and Fire Safety Investigation of the World Trade Center Disaster http://wtc.nist.gov/reports_october05.htm
4. Hamburger, R., et al., (May 2002) “World Trade Center Building Performance Study, Chapter 2: WTC1 and WTC2.” FEMA 403 http:/www.fema.gov/rebuild/mat/wtcstudy.shtm
5. Wikipedia, “World Trade Center.” Wikipedia http://en.wikipedia.org/wiki/World_Trade_Center
6. Bazant, Z.P., Zhou, Y., (in press 9/13/01, Expanded 9/22/01, Appendices 9/28/01) “Why Did the World Trade Center Collapse?—Simple Analysis.” Journal of Engineering Mechanics ASCE
7. Ashley, S., (October 09, 2001) “When the Twin Towers Fell.” Scientific American
8. Lew, H.S., Bukowski, R.W., Carino, N.J., “NIST NCSTAR 1-1 Design, Construction, and Maintenance of Structural and Life Safety Systems.” NIST Federal Building and Fire Safety Investigation of the World Trade Center Disaster http://wtc.nist.gov/reports_october05.htm
ORIGINAL WELL FORMATTED DOCUMENT:
http://journalof911studies.com/letters/wtc_mass_and_energy.pdf
Earth's magnetic field:
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