Since a cubic
foot of steel weights 490 pounds, it is
enough to deal with volumes rather than weights. We will calculate
the volume of steel on a per floor basis.
To calculate the per floor volume of steel used in the construction
of the twin towers, we will divide the calculation into three
parts, namely, the volume of steel in the perimeter wall, the
volume in the central core and the volume used in the floor support
system.
The perimeter
wall was comprised of box columns
welded to large spandrel plates. Two typical prefabricated sections
are illustrated below. Each consists of three spandrel plates
welded to three box columns and each is three floors high.
The first figure below shows the cross section of one of the
perimeter box columns and its surrounds. The second and third
figures detail the dimensions of two actual perimeter columns that
were salvaged from the rubble.
The numbers in the figure denote:
To obtain an
estimate of the "typical" perimeter
column, the dimensions of the perimeter columns listed in the
WTC Steel Data Collection
documentation were
averaged. Whether this accurately reflects the true distribution of
perimeter column thickness, is unclear, but it is all one has to go
on (till those who hold the architectural details release
them).
So, our "average" perimeter column has dimensions:
d = 13.4, t_w = 0.48, b_f = 12.9, t_(tf) = 0.32 and t_(bf) =
0.32.
and cross-sectional area:
2 x (13.4 x 0.48) + (12.9 x 0.32) + (14 x 0.32) = 21.5 square
inches,
The parameters d, t_w, b_f, t_(tf) and t_(bf) are as in the
following diagram from Appendix D
which is part of the report found at
http://www.house.gov/science/hot/wtc/wtcreport.htm.
For the time being we will ignore the column end plates and the
spandrel beams. Since each floor is 12 feet high, the per floor
volume of steel in an average perimeter box column is:
12 x 21.5/144 = 1.792 cubic feet.
In total there are 240 such columns, so the volume of steel so far
is
240 x 1.792 = 430 cubic feet.
Now lets deal with the volume of steel in the column end plates.
Each end plate is 14 inches wide by 11.75 inches deep and 1.375
inches thick, giving a volume of
14 x 11.75 x 1.375 = 226.2 cubic inches = 226.2/1728 = 0.130896
cubic feet.
Since, on each floor, one third of the columns are joined, and each
join involves two end plates, the per floor volume of steel in the
end plates is
2 x 0.130896 x 240/3 = 20.9433 cubic feet.
The spandrel plates are large, being 52 inches high and 3/8 inches
thick. Each floor has the equivalent of one spandrel beam that
stretches 4 x 207 = 828 feet right around the building. The volume
is easily calculated to be
828 x 12 x 52 x 3/8 = 193752 cubic inches = 193752/1728 = 112.125
cubic feet.
So the overall per floor volume of steel in the perimeter wall
is
430 + 21 + 112 = 563 cubic feet.
Now, we wish to calculate the per floor volume of steel in the core
section
of the building. To do this, we first need to calculate the volume
of steel in each of the core columns. This is complicated by the
fact that the dimensions of the columns reduced in size with
increasing height. For example, at the base of the WTC some of
these columns were 36 inches wide by 16 inches deep and 4 inches
thick, whereas at the top, these box columns had transitioned to
H-sections (I-sections) fabricated from 3/4 inch steel (the
transition to H-sections occurred at floor 85). We will ignore the
reduction in width and breadth of the columns, and only take into
account the reduction in column thickness by assuming an average
thickness of 2 inches (this roughly corresponds to a reduction in
thickness of one quarter of an inch, every seven floors, up to
floor 85). In reality, the column width and breadth decreased quite
considerably and we only make this very generous assumption as the
actual reductions in the width and breadth are unknown. So, we
assume each core column has the following cross-section:
The cross-sectional area is (36 + 12 + 36 + 12) x 2 = 192 square
inches = 192/144 = 1.333 square feet. Since each floor is 12 foot
high, the per floor volume of steel in one such column is 12 x
1.333 = 16 cubic feet. Reports as to the number of core columns
vary from 44 to 47. Once again, we will be generous in our
assumptions and choose the higher figure of 47. Thus, the total
volume of steel (per floor) in the core columns is
47 x 16 = 752 cubic feet.
On each floor, the core columns were bound together by a
rectangular grid of beams. As the dimensions of these beams are not
known we will assume they were, 14 inch by 14 inch box sections
fabricated from 3/4 inch steel. Again, this is a very generous
assumption. The cross-sectional area of such a box section is:
( 2 x 14 x 0.75 ) + ( 2 x 12.5 x 0.75 ) = 39.75 square inches =
39.75/144 = 0.276 square feet.
The core section is 137 feet wide x 87 feet deep. Hence, our
rectangular grid comprises six 137 foot sections and eight 87 foot
sections, for a total length of 822 + 696 = 1518 feet.
Additionally, the outer two 137 foot sections have to extend to the
perimeter wall (to give support for the trusses). Actually, the
"official" version has a much smaller U shaped beam, but as I have
mentioned above, we are being very generous. This adds another 140
feet to the length. The volume of the 1518 + 140 = 1658 feet of box
section is:
1658 x 0.276 = 458 cubic feet. Thus the overall volume of steel in
the core section is:
752 + 458 = 1210 cubic feet.
We now turn our attention to the floor support system.
The floor slab was poured on 1.5 inch corrugated 22-gauge steel
decking. Now, 22-gauge steel is 0.0336 of an inch thick. The
corrugations lead to 1.25 square feet of steel decking for every
square feet of floor slab. Hence, the volume of steel involved
is
207 x 207 x 1.25 x 0.0336/12 = 150 cubic feet.
To complete our calculations, we need to calculate the volume of
steel used in the system of trusses which supposedly supported the
concrete floor slabs. The following graphic illustrates the truss
system. The double trusses (of which, in this graphic, we only have
an end view) ran perpendicular to the transverse trusses, and were
essentially two transverse trusses bound together.
Consider one of the 3 foot four inch (40 inch) sections illustrated
in the above graphic. The diagonal rod has a diameter of 1.09
inches (radius 0.545 inches) and a length of twice the square root
of 20 squared plus 30 squared, that is, a length of
2 x srt( 20^2 + 30^2 ) = 2 x srt( 1300 ) = 72 inches.
Here, srt stands for the square root.
The cross-sectional area of the rod is 3.14 x 0.545 x 0.545 = 0.933
square inches. Hence the volume of rod in this segment is 72 x
0.933 = 67.2 cubic inches.
This gives a volume of 67.2 x 12/40 = 20.16 cubic inches per foot
of truss.
Pictured above, is the connection of one of the double trusses to
the perimeter wall. The cross section marked X--X in this graphic,
is pictured below. Note that the original graphic
from the WTC-report was so out
of scale, that it was necessary to stretch it somewhat.
The first image below is apparently the real life version of the
above graphic (supposedly obtained from the WTC wreckage). The
second image shows the gusset plate and seat connection.
The dimensions quoted in the following section were made by taking
measurements from these two photos. Standard adjustments for
perspective had to be made for measurements from the second
photo.
The gusset plate is 4 x 2 x 3/8 and has a volume of 3 cubic inches.
The seat angle has a volume of roughly 2 x ((9 + 4) x 14.5 x 3/8) =
141 cubic inches and the "stiffeners" add another 9 x 1.5 x 3/8 = 5
cubic inches. Since there were (at most) 120 gusset plates and seat
angles, these add in 120 x 149 = 17880 cubic inches. The 76
horizontal diagonal brace plates add in another 76 x 90 x 3/2 x 1/2
= 5130 cubic inches for an addition of
(17880 + 5130)/1728 = 13.3 cubic feet of steel to our total.
The upper chord (top section) of one of the double trusses
consisted of four pieces of 1/8 inch thick angle iron, as
illustrated below (it is circled in red).
Below, is a more detailed view of the cross section of the top
chord of a transverse truss (left) and double truss (right).
So, the upper chord has a cross sectional area of
((2 + 1.25) + (1.25 + 2))/8 = 0.8125 square inches for a transverse
truss and,
((2 + 1.25) + (1.25 + 7 + 1.25) + (1.25 + 2))/8 = 2 square inches
for a double truss.
Since we have no information concerning the lower chord (and the
"official" pictures are inconsistent and nowhere near to scale) we
will assume it has the same dimensions as the upper chord.
Now summing the volume of steel in the top and bottom chords and
diagonal rods, we have the following per foot volumes:
2 x 0.8125 x 12 + 20.16 = 39.7 cubic inches per foot for the
transverse trusses, and
2 x 2 x 12 + 2 x 20.16 = 88.3 cubic inches per foot for the double
trusses.
Now we need to calculate the total length of double and transverse
trussing. There were apparently, 60 double trusses spanning the 60
feet from the perimeter wall to (a beam attached to) the core and
24 double trusses spanning
the 35 feet from the perimeter
wall to the core. They are pictured in the following graphic:
The overall length of double trussing was thus 60 x 60 + 24 x 35 =
4440 feet. Transverse trusses ran perpendicular to the double
trusses as illustrated:
The overall length of transverse trussing was thus 8 x 207 + 4 x 87
= 2004 feet.
There was also a lesser supporting feature called "intermediate
support angle". Since all we know about the intermediate support
angle, is that its support capabilities were inferior to the double
and transverse trusses, we shall be generous and assume that it was
similar in nature to the transverse trusses. This adds another 1764
feet, to give a total of 2004 + 1764 = 3768 feet of transverse
trussing.
Hence, the volume of steel in the double trusses was 4440 x
88.3/1728 = 227 cubic feet.
And the volume of steel in the transverse trusses was 3768 x
39.7/1728 = 86.6 cubic feet.
So the overall per floor volume of steel in the floor support
system was
150 + 13.3 + 227 + 86.6 = 477 cubic feet.
The total per floor volume of steel, is now the sum of that in the
perimeter wall, the central core section and the floor system. This
is 563 + 1210 + 477 = 2250 cubic feet.
So why have we gone to all this trouble to calculate the per floor
volume of steel? Well, we know that 96,000 tons of steel was used
in the construction of each of the WTC towers. The WTC towers had
117 floors (110 above and 7 below the Plaza level) so an average
floor contained 96,000/117 = 820 tons of steel. Since the density
of steel is 490 pounds per cubic foot, we see that each floor
contained about 820 x 2000/490 = 3347 cubic feet of steel.
Now, according to the above calculations, the per floor volume of
steel in each of the towers, is (a very generous) 2250 cubic feet.
But this is only 67 percent of the volume of steel that we know was
used in the construction of the tower. So, the big question is:
Where is the other 33 percent? Where are the missing 32,000 tons of
steel? What features of the building are being left out of the
"official" explanations?
Could it
be that each concrete floor was actually
supported by weighty steel beams and not by the very flimsy trusses
of the "official" story?
Well, the following picture, taken during the construction of the
WTC, may hold the answer.
Here, one can see what appear to be large steel girders laid out
according to the plan for the positioning of the supposed double
trusses (this plan
is pictured here). To make
things clearer, the position of the
girders have been marked in white in the photo below. Remember,
that the perimeter columns which appear like a row of toothpicks in
the visible sections of the wall, are actually 14 inches wide. Thus
the floor joists do indeed appear to be quite large steel girders.
One thing is certain though, they are not the claimed double
trusses.
In this photo the vertical red lines correspond to visible core
columns. The white lines (apart from the outer perimeter lines)
correspond to visible floor joists.
Above, is a photo of early construction work on the South Tower.
Behind, is the North Tower and further back, the Verizon building.
The photo was taken from the old extention of Greenwich Street
(which was ripped up to make way for WTCs 4 and 5) looking north
west. Some interesting aspects of the construction are presented in
the following enlargements of the red-boxed regions.
In this enlargement one can see eight perimeter box columns at ten
foot intervals (further up the structure these columns split into
three smaller box columns at 40 inch intervals). Of course, what is
of interest here are the eight (seven on the lower level and one on
the upper) quite solid looking beams spanning the 35 foot gap
between the perimeter wall and the central core, where the
"official line" promised us there were only flimsy trusses.
In the foreground of this enlargement one can see eighteen
perimeter box columns of the South Tower (those in the background
are of the North Tower). If you look closely, you can just make out
a single quite large beam spanning the 60 foot gap between the
central core and the perimeter wall. Remember, that the corner core
column to which this beam is attached is some 3 foot wide (and 16
inches deep). However, one floor below this, workers are working on
a section of flooring held up by what appears to be trussing. One
supposes that this is temporary flooring. If one looks carefully
one can see a barrier rail to prevent workers from falling off the
area supported by the trusses. This tends to support the case that
this is temporary flooring.
Assuming that all the missing steel is contained in these beams we
can estimate their cross-sectional area (the assumption that all
the missing steel is contained in these beams is somewhat dubious,
as I suspect that the sample of perimeter columns has been
deliberately biased toward columns with thin cross-sections, and
hence, that a significant percentage of the missing steel, is
missing from the perimeter columns). Still, using this assumption,
we have 1100 + 227 = 1327 cubic feet of steel to play with (the 227
comes from the no longer necessary double trussing). The total
length of double trussing to be replaced is 4440 feet. Hence, the
desired estimate of the cross-sectional area is:
1327/4440 x 144 = 43 square inches.
So, we have enough steel to replace the double trusses by H-beams
(or I-beams, depending on how you view them) that are 24 inches
deep, 10 inches wide and fabricated from one inch thick steel.
These would be very, very strong beams, and would be much, much
stronger than necessary to span the 35 and 60 foot spans from the
central core to the perimeter wall.
It is
worth emphasizing that these beams, plus the
thicker stronger perimeter columns, would mean that WTC One and Two
were actually traditional steel-framed buildings, that also
incorporated extra thinner perimeter columns, to attain the
rigidity necessary to resist wind loading.
Above are pictures taken during the construction of the WTC. On the
right is a picture of some 30 feet of trussing, which one supposes
was temporary flooring. Note the vertical gaps in the box columns
of the perimeter wall. Gaps in the box columns do not seem to be a
sensible feature in a supposedly load bearing wall. Is this because
the perimeter wall was not actually meant to be a load bearing wall
as such, but a feature designed to give the WTC its required
rigidity (against wind loading)? In the left photo note the yellow
and red lines in the concrete. In the right photo note the three
parallel light-colored lines (about 4 inches wide) in the concrete.
One also wonders why the pile of steel in the foreground was
hoisted up the building, unless it was to be incorporated in the
structure. An answer to this question may be provided by the
following photo.
Between the workers cutting up a couple of WTC core columns, is a
column with concrete still attached to the beams that are
welded/bolted to it. These U-shaped beams look suspiciously like
the lengths of steel in the foreground of the picture of the
trussing. Is it possible that floor slab was some eight inches
thick and laced with significant steel beams? Was the slab poured
in situ and not prefabricated as some claim? Was the temporary
flooring only necessary till the concrete in the floor slabs had
set? And where does the following piece fit in the whole
affair?
Design architecture for the World Trade Center was provided by
Minoru Yamasaki & Associates. Emery Roth & Sons served
as
the architect of record. Since these people have nothing to hide,
they should provide the architectural plans of the World Trade
Center, for all to see. This will enable any misunderstandings
regarding the facts of the collapse to be established and
corrected. In fact, Minoru Yamasaki & Associates, Roth
&
Sons, or their descendent companies, should put the entire set of
architectural plans on the internet.
Home Page (an assortment of
articles on September 11 and Palestine).
Detailed Analysis of the Crash at
the Pentagon and the FAKED Explosion Pictures.
Large 1.4
megabyte file.
The most extensive presentation of the official line is the 21
pdf-documents to be found at
www.house.gov/science/hot/wtc/wtcreport.htm
The most pertinent of
these to this article are
www.house.gov/science/hot/wtc/wtc-report/WTC_toc.pdf
(Table Of Contents).
www.house.gov/science/hot/wtc/wtc-report/WTC_ch2.pdf
www.house.gov/science/hot/wtc/wtc-report/WTC_apndxB.pdf
www.house.gov/science/hot/wtc/wtc-report/WTC_apndxB.pdf
www.house.gov/science/hot/wtc/wtc-report/WTC_apndxB.pdf
html-versions of these
documents (with comment) can
be found at:
Table
Of Contents For The
Report.
WTC_ch2.htm
Large 2
megabyte file.
WTC_apndxB.htm
WTC_apndxD.htm
WTC_apndxD_sheet.htm
Other sites of interest
are:
Testimony
of Dr. Abolhassan
Astaneh-Asl.
Professor, Department of
Civil
and Environmental Engineering University of California, Berkeley
before the Committee on Science of the U.S. House of
Representatives, April, 2002.
Microsoft
software used to simulate the
crash of a Boeing 747 into the World Trade Centre.
911review.org/Wget/www.serendipity.li/wtc.html
serendipity.magnet.ch/wot/psyopnews2.htm
911review.org/Wget/www.public-action.com/911/jmcm/physics_1.html
hera.org.nz/PDF%20Files/World%20Trade%20Centre.pdf
hera.org.nz/PDF%20Files/Elaboration%20on%20WTC%20Paper.PDF
html-version
of the above HERA
article.
tms.org/pubs/journals/JOM/0112/Eagar/Eagar-0112.html
Article
on the World Trade Center collapse from
Scientific American.
tenlinks.com/NEWS/special/wtc/index.htm
civil.usyd.edu.au/wtc.htm
serendipity.magnet.ch/wot/psyopnews1.htm
http://www.serendipity.li/wtc.html
http://www.serendipity.li/wot/wtc_demolition.htm(mirror
of this site)
http://members.fortunecity.com/911/
Evidence of Explosives in the World Trade Center Towers collapse (0.7 MB).
Why did the World Trade Center Towers Fall? A Review of Thomas Eagar's (of MIT) Article (0.7 MB).
Collapse of the World Trade Center Towers. A Review of Charles Clifton's Article (0.7 MB).
The Jet Fuel; How hot did it heat the World Trade Center?
Proof the Twin Towers were Deliberately Demolished.
The FEMA Report into the World Trade Center 7 Collapse is a Total Joke.
Multi-Storey Buildings in Steel: The World Trade Center (0.4 MB).
Some Articles from Engineering News Record (0.8 MB).
Comments on the World Trade Center Demolition (0.4 MB).
Microsoft Software used to simulate the crash of a Boeing 747 into the World Trade Center.
University of California, Berkeley Professor, Abolhassan Astaneh-Asl Testifies.
The World Trade Center 7 Explosion Myth.
The World Trade Center Towers collapse as an Enormous Insurance Scam.
What went wrong with the investigation? By Eric Hufschmid (with comment).
Sixty State Street and the World Trade Center towers: A Comparison (0.7 MB).
Was Thermite used to Melt Sections of the World Trade Center Core Columns.
Calculations Say at Least 14 Tons of High Explosive Needed to Bring Down Each Tower.
Table Of Contents for the FEMA World Trade Center Report.
Chapter 1 of the FEMA WTC Report: Introduction (with comment) (0.9 MB).
Chapter 2 of the FEMA WTC Report: The Twin Towers (with comment) (2.2 MB).
Chapter 3 of the FEMA WTC Report: WTC 3 (0.4 MB).
Chapter 4 of the FEMA WTC Report: WTC 4, 5, and 6 (1.2 MB).
Chapter 5 of the FEMA WTC Report: World Trade Center Seven (with comment) (1.3 MB).
Chapter 6 of the FEMA WTC Report: Bankers Trust Building (0.6 MB).
Chapter 7 of the FEMA WTC Report: Peripheral Buildings (0.8 MB).
Appendix A of the FEMA WTC Report: Overview of Fire Protection in Buildings (0.5 MB).
Appendix B of the FEMA WTC Report: Structural Steel and Steel Connections (0.6 MB).
Appendix D of the FEMA WTC Report: WTC Steel Data Collection (0.8 MB).
The FEMA World Trade Center Collection in PDF-document format.
Download 45 Megabytes of Information Concerning 9-11.http://guardian.250free.com/
If you like the articles presented on guardian.150m.com then you can download them, and many more like them, by clicking on the following link.
Click here to download the September 11 2003 update of the nerdcities.com/guardian site (45 MB)
Save the archive file guardian11Sep03.tar to a directory on your hard-drive.
We will assume that you have chosen C:\ but any directory will do.
Extract the archive using WinZip, Stuffit or tar -xf to the directory C:\
This will automatically place the contents of the archive into the directory C:\guardian (and sub-directories).
Microsoft users will use WinZip to extract the files.
Linux/Unix users will use the command tar -xf guardian11Sep03.tar and
Apple users will use Stuffit.
Now point your web browser at C:\guardian\index.html.
That is, type C:\guardian\index.html in the address/location bar (where you usually enter a web-sites URL) of Internet Explorer.
This will bring up the main index page (don't forget to bookmark it for easy return). Now just follow the links.
If you wish you can also download a collection of full-sized photos from the MIT report - Sixty State Street - A Case Study.
Click here to download the collection of photos from the MIT report (15 MB)
Thumbnail versions of these photos are already available in the archive guardian11Sep03.tar
Save the archive file sixty-state-street.tar to the same directory that you saved guardian11Sep03.tar
Similarly, extract the archive using WinZip, Stuffit or tar -xf to the directory C:\
This will automatically place the contents of the archive into the directory C:\guardian\sixty-state-street
THE COMPLETE FEDERAL EMERGENCY MANAGEMENT
AGENCY
(FEMA) REPORT IN WEBPAGE FORMAT.
The Government FEMA WTC
"investigations"
- TWIN TOWERS - Part 1.
The Government FEMA WTC
"investigations"
- TWIN TOWERS - Part 2.
The Government FEMA WTC
"investigations"
- WORLD TRADE CENTER THREE.
The Government FEMA WTC
"investigations"
- WORLD TRADE CENTER FOUR, FIVE AND SIX.
The Government FEMA WTC
"investigations"
- WORLD TRADE CENTER SEVEN.
The Government FEMA WTC
"investigations"
- THE BANKERS TRUST BUILDING.
The Government FEMA WTC
"investigations"
- PERIPHERAL BUILDINGS.
The Government FEMA WTC
"investigations"
- APPENDIX A - THE FIRES.
The Government FEMA WTC
"investigations"
- APPENDIX B - THE STEEL Part 1.
The Government FEMA WTC
"investigations"
- APPENDIX D - THE STEEL Part 2.
WTC-7: The Improbable Collapse 9/11
Building 7 Collapse WTC - 9/11 Review
Barry Mawn - 9/11 Encyclopedia
WTC building 7 collapse or missile ? September 11
Building 7 Collapse - 9/11 Encyclopedia
Jerome Hauer - 9/11 Encyclopedia
Clouds of Concrete - 911review
9/11 Rescuer Saw Explosions Inside WTC 6 Lobby
Jeff King - WTC collapse video controlled demolition 9/11
Bin Laden Not Wanted for 9/11!
bin laden confession 9/11 review
Expose on Bush, bin Laden and the Carlyle Group
Blackstone Group - 9/11 Encyclopedia
Meet Jerome Hauer, 9/11 Suspect Awaiting IndictmentComparisons of the wall damage and plane images,
Photoshop overlay of the wall damage vs the FEMA report.
Other pics of the wall and damage...september 11
The FEMA report shows little damage to the structures of the WTC's.