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9.11 investigation

FDNY : Major Building Collapse! Whose turn was it to watch Dick Cheney?

was thermite used?
Former President Bush was seen escorting the families of those responsible to the gate at LaGuardia to fly to Saudi Arabia!

I have a steel frying pan and it doesn't melt when I put on the stove so how come this building collapsed??

We want answers!!!

Maybe you should try an experiment 26.Mar.2015 18:01

Mike Novack

"I have a steel frying pan and it doesn't melt when I put on the stove so how come this building collapsed"

Are you willing to wreck your frying pan? Who said anything about MELTING.

You will need the frying pan, a couple of sturdy bricks, and a heavy hammer or small maul.

You first carefully measure the frying pan in all dimensions. Place the bricks outdoors spaced apart a little less than the width of the pan and put the maul nearby.

Now put the pan on the gas stove and turn the fire on and let it get hot, real hot. Oh, I forgot, you'll want heavy leather gloves, stove/fire gloves. It will help if you can turn off all the lights in the room because when I say "hot" I mean glowing red. True, the pan hasn't melted, would need to be hotter than you'd get on top of a gas range, but it is annealed.

Grab it off the stove and quickly take it outdoors and place over those bricks. Now give it a good whack with that maul. The beams of the building weren't just "sitting there", they had the weight of the structure on them acting as a force. When the pan has cooled, measure it again. You see any change in shape? (bending, bulging, etc.)

Or save your frying pan and just go watch where a blacksmith is giving a demonstration. The iron he (or she) is working is NOT melted. But notice how it can be deformed by hammer blows or bent by sticking an end in a hole on the anvil and applying some force.

How do you think we make things out of steel? Did you imagine it was melted and cast into shape? No, just heated to red hot and then it cam be pulled through dies into wire as if it were taffy or rolled into sheets by being passed through a series of rollers closer and closer together or formed into beams by being passed through rollers of more complex shape.

everybody knows heat doesn't bend metal! 27.Mar.2015 06:16

i

All superior intelligent and enlightened people know that heat won't bend steal. 911 is a cover up!

 https://www.youtube.com/watch?v=IiTUjZR1gdU


The sad part is you may be serious 27.Mar.2015 13:09

Mike Novack

"All superior intelligent and enlightened people know that heat won't bend steal"

Not the heat but the load.

When a building is designed, the size of the beams is such that they will support the required load with a safety factor of 3 to 5 (in other words, the beam would actually support say three times the load without bending, buckling, etc.)

But that is with the metal in its hard state (work hardened, stress hardened by rapid cooling in the case of a metal* like steel (iron with some carbon in it). In its soft/annealed state the beam would support only a relatively small fraction of the load.

So not melted, just annealed. Say in its hard state the beam would be good for a load of 300 tons but in its annealed state just 60 tons. If the building had been designed with a safety factor of three, it would be loaded with 100 tons. If heated to above the annealing temperature the beam will fail, bend, sag, buckle, etc. because still loaded with 100 tons but only good for 60.



* Many other metals only care that they were heated to above the annealing temperature and remain in that state whether cooled fast or slow. Copper, for example.

RE: beams of the building weren't just "sitting there" 28.Mar.2015 07:08

-

Problem with the WTC tower collapses is - they occurred at free fall speeds. i.e. Even if deformation occurred (in any part of the structure), the actual mass of materials in the lower parts of the towers still were not removed quickly enough in order to satisfy Newton's laws, based on observed collapse velocities / total collapse times.

The mass of the materials themselves i.e. the thousands of tons of structural steel in the lower parts of the WTC skyscrapers, had to be removed quickly enough and in exact sequence, in order for the collapses to have occurred at the speed they did. It's not enough for them to (supposedly...) "pancake" or "push" the bottom materials, merely by 'collapse', 'crushing' or sheer weight - they won't occur fast enough.

The entire structure of a skyscraper, apart from its structural tensile/compressive strengths which 'keep it up' / maintain it standing upright, has basic mass which offers a physical impediment to anything — no matter how huge/massive — that might 'fall on to' it, or 'crushes' / impacts it. Those requisite physical forces take __time__ to accomplish.

That is why we have demolition engineers and controlled demolition.

Yes, all structures of any constituent material, or design, are subject to stresses and deformation (of varying degrees according to loads, incipient temperatures, and type of materials used).



Recommended Viewing :

9/11 Experiments: The Great Thermate Debate
 http://portland.indymedia.org/en/2014/11/428610.shtml

 http://www.youtube.com/watch?v=5d5iIoCiI8g

physicsandreason
Uploaded on Nov 10, 2010

What's wrong with mainstream experts?

http://www.youtube.com/watch?v=5d5iIoCiI8g
9/11 Experiments: The Great Thermate Debate

they occurred at free fall speeds. 28.Mar.2015 18:20

i

no they did not.

Watch the videos (listed above). its all explained.

Yes, the 9/11 NYC skyscraper collapses occurred at free fall speeds. 29.Mar.2015 01:21

.

Towers 1 and 2 of the World Trade Center (each over 1,300 feet tall) collapsed into their own footprints at what is essentially free fall velocity —

in less than 10 seconds.


Building 7 (not even struck by an airliner) collapsed in under 7 seconds flat.



All three buildings collapsed symmetrically, into their own foundation footprints.



It is impossible for a steel framed skyscraper to collapse at or near these speeds (< 10 seconds, < 7 seconds), and moreover in symmetrical fashion with all major support columns-structures within the building failing in precise, rapid and sequential orchestration (so as to prevent toppling).

As seen, for example in a controlled demolition.

Not only is it impossible, but (aside from NIST/U.S. government's explanation for the 3 skyscrapers on 9/11) has never occurred in the entire history of steel framed high rise structural engineering/architecture, anywhere in the world.

Of course, only NIST and its parent government cling to their official pronouncement that these collapses were caused by "office fires".


Ah, of course 29.Mar.2015 07:04

Garth

. wrote "Towers 1 and 2 of the World Trade Center (each over 1,300 feet tall) collapsed into their own footprints at what is essentially free fall velocity..."

Yes, "essentially." A weasel word if ever there was one. In other words, they did not fall at free fall velocity, but what the hell, I have a theory and it must be true because I start from my conclusion anyway (and also, as is the backbone of the conspiracy theorists, brown people are too stupid to have done this).

RE: " weasel word if ever there was one " 29.Mar.2015 10:49

.

Quote:
------
" and also, as is the backbone of the conspiracy theorists, brown people are too stupid to have done this "
------

Yeah that weasel trope's long outdated (and never was even worthy of 'debunking') Garth. "backbone"?? Lol.

Nothing to do anyway with the collapse of 3 steel framed skyscrapers — one of which wasn't struck by an airliner — in New York City on 9/11.


"done this" :

Precisely what do you mean by, "this" ?

We're discussing the physics of skyscraper collapses in NYC on 11 September 2001, here.


Hopefully you, Garth, aren't "too stupid" to understand basic math —

see below.



Quote:
------
" In other words, they did not fall at free fall velocity "
------

Math, how does it work ?

(let's go thru it, just for Garth... what the hell. Hopefully he won't weasel out.)


Below is linked a simple, basic Free Fall Calculator program so that we can crunch the numbers.

Pic attached shows the basic equations.


from t0 to t (beginning time to end time, 10 seconds)
calculates

v = gt

and

h = 1/2gt^2

where

v = velocity (m/sec)
g = acceleration of Earth's gravity (m/sec^2)
t = time
h = height


We're inputting the time it took (10 secs for WTC Towers 1 and 2) for collapse, from which it calculates the free fall distance and velocity.

Free fall (distance and velocity)
Free fall time t = 10 sec

[ Gravity g 9.80665 m/s2 ]

Free fall distance h = 490.3325 m
Free fall velocity v = 98.0665 m/s


Result is a Distance h = 490 meters

= 1600ft

Height of the towers within a couple hundred feet; they were 1,368 feet high.

With the 360-foot tall antenna/mast, the highest point of the North Tower reached 1,728 feet.



** NOTE : For purposes of sensitivity testing / calibration, we can input a collapse time of

t = 9.5 seconds

and the resulting Distance h = 442 meters = 1450 feet

Using

t = 9.2 seconds

resulting Distance h = 415 meters = 1361 feet

**> which is the actual height of the Towers.


Therefore only shaving __fractions of a second__ off of the collapse time, we match the height of the towers exactly.


Now, input the time it took for World Trade Center Building 7 to collapse into its own footprint (6.5 secs) :

t = 6.5 seconds

and the resulting Distance h = 207 meters = 679 feet


Building 7 was 610 feet tall.

Using

t = 6.2 seconds

resulting Distance h = 188 meters = 616 feet


Again, shaving only mere fractions of a second from the input collapse time gives the exact building height.

But even NIST was operating from external film/video evidence of collapse timings (to input into their models) for all 3 buildings.

See below — they also used far more than "fractions of a second" to "adjust" their timing of the "phased collapse" of Building 7.

i.e. NIST fabricated their model of the collapse, using Orders Of Magnitude greater timing adjustments to "make it fit".

Here's what's crucial about these calculations, particularly with regard to Building 7.

NIST used a dodgy, arbitrarily lengthened measurement of the actual vertical collapse time in concocting its "three phase collapse sequence" model for Building 7.

This is one of the main reasons NIST's report is so unreliable.

See the article previously ^posted,  link to www1.ae911truth.org


And see :

Clocking WTC7
 http://www.youtube.com/watch?v=pP4_8s-2Gmc

WTC7 in Freefall: No Longer Controversial
 https://www.youtube.com/watch?v=rVCDpL4Ax7I


Reference
 http://rememberbuilding7.org/7-facts-about-building-7/


Anyway, even (of course) a controlled-demolitioned building of any type doesn't actually fall at the exact free fall velocity in 100% conformance with the mathematics of gravitational acceleration as shown above. But it's close enough/within a few percentage points.

And that is absolutely necessary, in order for the engineering and physics of any controlled demolition to work properly.
(i.e. the building doesn't collapse sideways, or in a non-uniform manner.)



Quote:
------
" I have a theory and it must be true because I start from my conclusion anyway "
------

It is of course, interesting that 'Garth' has chosen to eventually pile on to this thread over 7 comments in, symphonically coordinated with his buddies 'anon' and 'i' on these purportedly "irrelevant" 9/11 topic articles.

RE: theory.

The official Theory, as explained by Conclusion of NIST and U.S. government —

and which 'Garth', 'anon' and 'i' seem so eager to bolster/defend at apparently even the horrific cost of "wasting time on Indymedia" every time 9/11 related topics appear —

is that 19 hijackers were able to cause the free fall collapse of 3 of the world's tallest steel framed skyscrapers — one of which wasn't struck by an airliner — into their own footprints (an event which has never before or after been replicated in engineering history) on that day.

NIST, furthermore in the case of their eight-years-delayed/fudged Building 7 report, most definitely started with their Conclusion and adjusted data and modeling to fit just so.

now there's a theory, for ya.


Those ^ pics, again 29.Mar.2015 11:22

resize / reformat

>

The Missing Jolt: Simple Refutation Of NIST-Bazant Collapse Hypothesis 29.Mar.2015 13:30

Graeme MacQueen and Tony Szamboti

The Missing Jolt: A Simple Refutation of the NIST-Bazant Collapse Hypothesis

Prof. Graeme MacQueen and Tony Szamboti, January 2009

PDF link \\\_with Figures\\\_ :
 http://www.journalof911studies.com/volume/2008/TheMissingJolt7.pdf

Journal of 9/11 Studies - Articles page
 http://www.journalof911studies.com/articles.html

-----------------

The Missing Jolt:

A Simple Refutation of the NIST-Bazant Collapse Hypothesis

Graeme MacQueen
Tony Szamboti

April 22, 2009*

In its Final Report on the Collapse of the World Trade Center Towers, the National Institute of Standards and Technology summarizes its three year study and outlines its explanation of the total collapse of WTC 1 and WTC 2. [1]

Readers of the report will find that the roughly $20 million expended on this effort have resulted in an explanation of the total collapse of these buildings that is so vague it barely qualifies as a hypothesis. But it does have one crucial feature of a hypothesis: it is, in principle, falsifiable. In fact, it is easy to demonstrate that it is false.

In this paper we will, concentrating on the North Tower, offer a refutation that is:

• easy to understand but reasonably precise
• capable of being stated briefly
• verifiable by any reader with average computer skills and a grasp of simple mathematics.

NIST's Hypothesis of Total Collapse:

Three essential elements of NIST's hypothesis of total collapse are made explicit in the Final Report and the companion volumes of the study:

1. Because of damage to stories 93 to 98, and especially because of column buckling due to fire, the top 12 stories of the North Tower (99-110) plus the roof were, in effect, separated from the rest of the Tower and began to behave as a unit. [2]

2. This "rigid block" of 12 stories plus the roof began to move. First it tilted, and then it abruptly fell onto the stories beneath it. [3]

3. The fall of the rigid block caused such damage to the lower structure that "global collapse began."[4]

The rigidity of the upper block of stories is crucial to this explanation. If the upper block were to break, disintegrate or flow on impact it would certainly not threaten the 92 intact floors beneath it.

In addition, the rigid block had to fallonto the rest of the building. Although this seems obvious, the NIST authors are often shy about saying it. We hear about the rigid block's "descent."[5] We hear of tilting and "downward movement."[6] We have to look carefully to find the NIST authors using the language of falling. Whatever the reasons for their reticence, it is clear that it will not do for the upper block to ease itself onto the building beneath it, with a gradual creaking of buckled columns and sagging floors. If this were to happen, why would the structure beneath collapse\\\?

There was nothing special about the weightof the upper block, rigid or otherwise. The lower part of the Tower had held up this weight without difficulty since 1970. The lower block had 283 cold steel columns, with less than 30\\\% of their total load capacity being utilized for gravity loads, because of the factors of safety designed into the structure and the need to withstand high winds—and gravity loads were essentially the only loads the columns would have been subject to on a day such as 9/11 with little wind. The lower block was not weak, nor (excluding stories 93-98) was it damaged by plane impact or fire. The weight of the upper block posed no threat to it. If there were to be a threat, it had to come from the momentumof the upper block. But momentum is a product of mass and velocity, and since the upper block could not increase its mass it had to increase, if it were to become a threat, its velocity. Since NIST's theory assumes the only energy at play at this stage of events was gravitational, the upper block had to fall, and the greater its velocity the greater its momentum. The longer and the less impeded its fall, the greater would be its impact on the lower structure. So it is no surprise that the NIST authors, however shy they are about affirming it, eventually come out in favour of the fallingof the upper block. [7]

Zdenek Bazant and Yong Zhou, with whose September 13, 2001 back-of-the-envelope theory (with subsequent revisions and additions) NIST largely agrees, have never hesitated to say that the upper block fell. [8] Bazant has likewise been frank about the need for severe impact as the upper and lower structures met: he believes the impact may have been powerful enough to have been recorded by seismometers. [9] In his view, collapse initiation of the lower structure required "one powerful jolt."[10] Of course, if there was a powerful jolt to the lower structure there must also have been a powerful jolt to the upper falling structure, in accord with Newton's Third Law.

In order to keep a sense of reality as we discuss NIST's theory it may be useful to label the three interacting parts of the North Tower, as theyare pictured by NIST, as RB-12+, DS-6 and RB-92.

Where RB stands for rigid block, DS stands for damaged structure, and the numbers following the letters refer to the number of stories ineach structure. The upper block comprised the 12 stories of 99-110 as well as the roof structure with antenna and hat truss; the intermediate area was damaged by plane impact and fire and was six stories high (93-98 inclusive); and the lower block was rigid and comprised, in addition to subterranean levels, the first 92 stories of the building.

These designations actually underestimate the contrast between RB-12+ and RB-92, because the latter was not only largely undamaged by fire butwas more massive per story. It was also stronger: the Tower's columns tapered as theyascended. [11] Yet the fall of RB-12+, we are supposed to believe, put a catastrophic end to DS-6 and RB-92.

What NIST essentially says, agreeing with Bazant, is that the lighter and weaker part initially fell with a powerful jolt onto the heavier and stronger part, which could not withstand its momentum, and that this caused a progressive collapse to initiate smashing the lower block to bits all the way to the ground.

The NIST Final Report does not tell us what happened to RB-12+ after its impact with the two structures beneath it. Did it fall through them all the way to the ground (that is, to the rubble heap on the ground), maintaining considerable mass and rigidity the whole time--as Bazant argued in 2001 and has continued to argue\\\? [12]

On this the NIST authors are silent.

NIST also does not tell us how far RB-12+ fell beforeits impact with intactstructure. Did it fall one story (roughly 12 feet), or several stories\\\? We are left in the dark. Once again Bazant comes to the rescue. It fell "at least one story," he says. [13]

To his credit, Bazant is willing tostate the essential elements ofthe hypothesis. If this hypothesis is to hold any water at all there must be substantial impact: RB-12+ has a lot of work to do, so it had better fall at least one story.

As we will show, for the purposes of the present refutation it does not matter whether RB-12+ fell one story, six stories, or somewhere in between.

The Necessary Jolt:

As Bazant has said, when the top part fell and struck the stories beneath it, there had to be a powerful jolt. While a jolt entails acceleration of the impacted object it requires deceleration of the impacting object. Even a hammer hitting a nail decelerates, and if the hammer is striking a strong, rigid body fixed to the earth its deceleration will be abrupt and dramatic.

Although NIST does not explicitly speak, like Bazant, of a "jolt", and may therefore be thought to evade this paper's refutation, it is impossible for NIST to escape the implications of its own assertions. The NIST report speaks of a strong, rigid structure (the upper structure or rigid block) falling freely onto another strong, rigid structure (the intact part of the building below the damaged area): the jolt cannot be avoided. [14]

This was a necessary jolt. Without it the required work could not have been done.

Testing for Deceleration:

If a jolt occurred there would have been high short-term deceleration of the upper block. Why not simply check for this deceleration\\\? It is not difficult. We will:

• examine a video clip of the North Tower's collapse
• find a point on the upper block of the North Tower, the progress of which can be observed and measured in the early stages of the collapse
• plot the progress of this point on a graph
• check for evidence of deceleration

We have chosen a well known video clip of the collapse associated withFrench film maker, Etienne Sauret. [15] The Sauret clip has advantages over many others. It is a single, continuous sequence with no changes in camera angle and no zooming in and out. There is a very slight shift in the camera position relative to distant objects caused by a trembling of the camera several seconds prior to the collapse, but this is irrelevant to us since all our measurements are taken after the shift. The camera is very steady throughout the time we are making our measurements, as we can confirm by measuring the position of the picture frame relative to stationary objects. In addition, the image of the north face of the North Tower is exceptionally clear in these images.


Here is how we proceed: [16]

1. We save the Sauret footage to our hard drive.

2. We break the 1 minute, 56.53 second clip into 3497 equal segments or "frames." Each frame is approximately 0.033 seconds in length (33 thousandths of a second).

3. We find two points associated with the roof of the upper block of the North Tower whose progress we can measure. Two points are necessary since neither one is consistently visible but one of the two is always visible. The point whose fall we shall use in our computations is at the tip of a white device on the roof. (The distance between this point and the upper frame is called Distance A in Figure 1 below.) The other point is located at the interface of the upper white section of the roof and the lower dark section. (Thedistance between this point and the upper frame is called Distance B in Figure 1.) The difference between Distance B and Distance A is approximately 28 pixels. Where the white device on the upper right-hand corner of the roof is obscured by smoke, measurements of the roof interface have been taken and the position of the device has been obtained by subtracting 28.

4. We choose a set of frames that stretches fromFrame 929, before the discernible beginning of the roof's fall, to the last frame in which our point can be recognized before it disappears into the dust cloud, Frame 1024.

5. We measure the number of pixels separating the white device from the fixed upper edge of the video frame, computing the position of the device when necessary by measuring the position of the roof interface. We take one measurement at each five frames in the progress of the Tower's collapse, ending up with 20 points.

6. Our measurement stretches from 30.93 seconds into the clip to 34.1 seconds into the clip, giving us a total interval of 3.17 seconds.

7. We find that during this interval the white device on the roof has fallen a distance represented by 130 pixels.

8. In order to get an approximation of the realdistances at issue; we find a known vertical distance on the north face of the North Tower. (The Tower's proportions have been distorted as it has been rendered into frame-by-frame format. See Appendix A for a description of our method of determining the known vertical distance and the ratio of pixels to feet.) We discover that in our frame-by-frame version ofthe Sauret video 1 pixel = 0.88 feet. We now know that the point on the roof has fallen approximately 114.4 feet. The figure is not precise--there are the effects of foreshortening to consider (the roof and device are higher than the camera and the upper block, as it moves downward, tilts away from us)--but the figures are close enough for our purpose because we are looking for changes in acceleration over time, not exact velocity values.

Figure 1: Sauret Video: Representative Frame with Key Points for Measuring the Roof's Fall

Distance
A
Distance
B

9. We know that

d = ½ ×g ×t^2

where d stands for distance, gstands for acceleration due to gravity, which is 32.174 ft./s^2 at sea level, and tstands for time. Using this formula, we discover that a freely falling object would travel 161.6 feet in the time it took the roof to drop 114.4 feet.

10. We create two graphs. In the first the roof's descent is given in pixels. In the second the roof's fall is given in feet.

Figure 2: The Roof Fall: Pixels

Roof Fall in Pixels

0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3 3.5

Time (sec)
Pixels

Data:
Frame
from clip
start
Distance
of device
(pixels)
Distance
of inter-face
(pixels)
Distance of
device (pixels)
adjusted to 0
Distance of device
(feet) adjusted to 0
(1 pixel = 0.88 ft.)
Time
(seconds)
from clip
start
Time (seconds)
adjusted to 0

929 109 0 0.00 30.93 0.0000
934 110 1 0.88 31.10 0.167
939 111 2 1.76 31.27 0.334
944 113 4 3.52 31.43 0.500
949 115 6 5.28 31.60 0.667
954 118 9 7.92 31.76 0.834
959 122 13 11.44 31.93 1.000
964 126 17 14.96 32.10 1.167
969 132 23 20.24 32.27 1.334
974 138 29 25.52 32.43 1.500
979 146 37 32.56 32.60 1.667
984 (153) 181 44 38.72 32.76 1.834
989 (161) 189 52 45.76 32.93 2.000
994 (170) 198 61 53.68 33.10 2.167
999 (180) 208 71 62.48 33.27 2.334
1004 (190) 218 81 71.28 33.43 2.500
1009 (201) 229 92 80.96 33.60 2.667
1014 (213) 241 104 91.52 33.76 2.834
1019 (226) 254 117 102.96 33.93 3.000
1024 (239) 267 130 114.40 34.10 3.167


Figure 3: The Roof Fall: Distance

Roof Fall Distance
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3 3.5

Time (sec)
Distance (feet)

Data:

Time (sec.) Roof Fall Distance (ft.)
0.000 0.00
0.167 0.88
0.334 1.76
0.500 3.52
0.667 5.28
0.834 7.92
1.000 11.44
1.167 14.96
1.334 20.24
1.500 25.52
1.667 32.56
1.834 38.72
2.000 45.76
2.167 53.68
2.334 62.48
2.500 71.28
2.667 80.96
2.834 91.52
3.000 102.96
3.167 114.40


Knowing the distance the roof fell, in equal timeintervals, from our measurements, we can now determine its actual velocity, at each measured point through its fall, using symmetric differencing. The equation is

Vn= (Dn+1- Dn-1) / (Tn+1- Tn-1)

where V = velocity
D = distance
T = time
n = point in question

Data:

Time (sec) Roof Fall Distance (ft.) Velocity (ft./sec)
0.0000 0.00 0.00
0.1667 0.88 5.28
0.3334 1.76 7.92
0.5000 3.52 10.56
0.6667 5.28 13.20
0.8334 7.92 18.48
1.0000 11.44 21.12
1.1667 14.96 26.39
1.3334 20.24 31.68
1.5000 25.52 36.96
1.6667 32.56 39.59
1.8334 38.72 39.60
2.0000 45.76 44.88
2.1667 53.68 50.15
2.3334 62.48 52.81
2.5000 71.28 55.45
2.6667 80.96 60.71
2.8334 91.52 66.01
3.0000 102.96 68.65

It may be noticed that the last point measured at 3.167 seconds is left off of the data table above and the velocity graph below. The reason for thisis that each point the velocity is found for needs to have a point ahead of it as well as behind it, so this method cannot calculate the velocity for the last point measured. As it is known that the measurements were taken every five frames with a 30 frame per second video, the actual time can be resolved fairly precisely. The use of four places for time increments, of 0.1667 seconds between measurements, in the velocity calculation above, is done for accuracy.

Below is a graph of the actual velocity of the roof at each measurement point over the same time frame in which the distance was measured.

Figure 4: The Roof Velocity

y = 22.81x
R2
= 0.9961
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5 2 2.5 3 3.5

Time (sec)
Velocity (ft./sec)
Regression analysis (least squares curve fit)

The velocity of the roof increases in a relatively linear way and is 68.65 ft./s after 3.00 seconds, which is about 71\\\% of the free fall velocity of96.52 ft./s for this fall time. At the actual measured distances and calculated velocities, the initial fall through one story would have taken place in approximately 1.0 second.

If the upper block, RB-12+, were rigid, as Bazant and NIST claim, the powerful jolt, required by Bazant to generate an impulsive load and explain the collapses of the Twin Towers, would show itself as an abrupt negative deviation in the otherwise positively sloped and virtually linear velocity graph.

For readers unfamiliar with the concept of an impulsive load, the impulse-momentum change equation is shown below and essentially shows that the change in momentum with respect to time provides the force involved in a collision.

ma
t
v
m
t
vmvm
Force
ffii
=
\\\?
\\\?
=
\\\?
-
=

As stated earlier, it is only the velocity that changes with respect to the duration of the impulse, as the mass of an object is constant at all times everywhere in the universe. A change in velocity with respect to time is defined as either an acceleration or deceleration, depending on whether it is positive or negative. This acceleration or deceleration is then multiplied by the mass of the impacting object and provides the force involvedin the collision, so the impulse equation ultimately reduces to the well known relation F = ma.


It is useful to refer to accelerations and decelerations in terms of the acceleration due to gravity, which is defined as 1g. The static weight of any item on earth is measured as the force due to the mass of the item multiplied by the acceleration of earth's gravitational pull or 1g. An acceleration or deceleration of 1g is equal to 32.174 ft./s^2, so if the deceleration of an impacting object during a collision is greater than this then the weight or force applied by the impacting object is amplified. To find the number of g's involved one merely needs to divide the actual deceleration by 32.174 ft./s^2.

Bazant claims that a minimum force amplification of 31g, or 31 times the static weight of the upper stories, could have occurred in a collision between the upper and lower blocks of the Twin Towers after a fall of one story. [17] With the 98th story columns completely collapsing, a distance between floor slabs of approximately 11.44 feet, and the actual measured velocity of 22.81 ft./s of the upper block at this point, the first collision would haveoccurred approximately one second into the fall.
Regardless of the actual amplification, any impulse at the impact zone between the 98th and 99th story floor slabs capable of causing collapse continuation would have had to cause the columns on at least the first stories on either side of the impact to deform elastically, and plastically, and then to buckle. The deformations and buckling of the columns of the impacting stories, on both the lower and upper blocks, would cause a kinetic energy drain, which would reduce the velocity of the rigidly attached falling mass above them. Using energy methods we have calculated what effect these energy drains would have on the velocity of the upper block. Since the upper block would pick up the mass of the 98th floor in the impact there would also be a conservation of momentum component to the velocity reduction. From Appendices D and E we find the reduced velocity (Vreduced) of the upper block, after impact, considering the three energy drains and conservation of momentum, and it is
Vreduced= 22.81 ft./s - (15.63 ft./s + 1.75 ft./s)
= 22.81 ft./s - 17.38 ft./s
= 5.43 ft./s

Since the roof was part of the rigid upper block it would have displayed this momentary abrupt change in its velocity, from 22.81 ft./s to 5.43 ft./s,if the collapse were a natural occurrence. It should also be noted that the energy losses and conservation of momentum we have calculated and used here, to determine the velocity loss, are a minimum. We do not consider energy losses due to vibration of the building, heat, and sound, during the initiating impulse, all of which would have required energy from the impulse to produce and thus have anadditional effect on velocity loss. The intent here is only to show that, even with a quantifiable minimum energy loss and conservation of momentum, the velocity loss would be quite dramatic,and should have been readily observed if an impulse capable of causing collapse had indeed occurred.

The graph below shows what the upper block velocity change would look like if a 31g impulse had occurred one story into the fall, with its velocity at least momentarily reduced in a significant way after impact.

Figure 5: Roof Velocity Curve with a hypothetical 31g deceleration

The fact that a 31g impulse requires a deceleration of 997.4 ft./s^2 is unassailable, and it does not matter whether the collision is elastic or inelastic. With a velocity reduction of 17.38 ft./s and a 997.4 ft./s^2 deceleration, the duration of this impulse would have been 17 milliseconds. This rapid deceleration associated with the 31g impulse would necessarily show itself as an abrupt negative slope change in the velocity curve.

We have shown the curve starting upward again after the impact, on the generous assumption that the impacting object (the upper block) is now free to accelerate. We have also only charted what the effect on the velocity would have beenfor an initiating impulse between the first two floors to collide.

The measurements of the roof's actual fall do not show any abruptnegative change in velocity, so it appears that there was no impulse and thus no amplified load. It seems that Dr. Bazant was simply theorizing that there had tobe one to make sense of the collapse in a natural way. It is also important to note here that Dr. Bazant was off by a factor of ten in his calculation of the stiffness of the columns, with his 71 GN/m estimate. [8] The actual stiffness, calculated here using the actual column cross sections, is approximately 7.1 GN/m. (see Appendices B and C) [19][20] This error caused Dr. Bazant to significantly overestimate the potential amplifying effect of the impulse or jolt, which he claims occurred after a one story fall of the upper block.

In an effort to refute the argument put forth in this paper, some may claim that plastic deformation of the lower stories of the upper block could have created a crush wave below the upper block and kept the roof fromexperiencing a discernable impulse. If that were true then the impulse durations would have increased dramatically, absorbing the energy over a longer period of time and eliminating any significant amplification of the upper block's weight. But without the amplification of the upper block's weight why would the lower block have collapsed\\\?

0
10
20
30
40
50
60
70
80
00.5 11.5 22.5 33.5

Time (sec)
Velocity (ft./sec)
Actual measured velocity
31g impulse with abrupt negative slope and velocity loss
Pre-impact velocity recovery
700 msec

There are those who might argue that the tilt of the upper block to the south could have kept an impulse from being discernable—that there may have been impulses on the south face or further inside the Tower, in the central core, that werenot visible on the north face. Impulses at these locations could not have caused the collapse of the north face of the Tower and its corner columns in the observed vertical manner. The corner columns of the east and west faces, in conjunction with the columns of the north face, formed a structural channel (a stiff structural element with support in two orthogonal directions) and, barring planned demolition, would have collapsed as observed only if they were struck impulsively, in a vertical manner by the upper block.

In reality, the upper block could not have tolerated the potential 31g impulse theorized by Dr. Bazant. To get this overload he claims was possible, all of the mass of the upper block would have had to participate, and if it did so it would have come apart completely.

Perhaps the impulse was of a lower value but still high enough to cause an overload of the lower structure and bring about global collapse\\\? Consider a velocity graph with a 6g deceleration, very likely the minimum load amplification necessary to overcome the reserve capacity of the perimeter columns, which had a minimum factor of safety of 5.00 to 1.

Figure 6: Roof Velocity Curve with a hypothetical 6g deceleration

0
10
20
30
40
50
60
70
80
0 0.5 1 1.5 2 2.5 3 3.5

Time (sec)
Velocity (ft./sec)
6g impulse with abrupt negative slope and velocity loss
Pre-impact velocity recovery
800 msec
Actual measured velocity

A 6g impulse requires a deceleration of 193 ft./s^2. With a velocity reduction of 17.38 ft./s and a 193 ft./s^2 deceleration, the duration of this impulse would have been 90 milliseconds. As the graph shows, there would still bea quite obvious abrupt negative slope change, which is not seen in the velocity curve determined from the measured data.

The measurements were taken every five frames, or 167 milliseconds apart. The recovery to the pre-impact velocity is shown to occur in the dashed graphs in the approximate times of 700 milliseconds for the 31g case and 800 milliseconds for the 6g case. In both cases there are four data points taken well within this recovery window, so it is apparent that a negative change in the velocity of the roof would have been captured if an impulse had indeed occurred.

Findings:

As the figures and graphs above clearly show, any impulsive load would have required a high deceleration, which would have shown itself very prominently in the velocity curve derived from the measured data. The fact that no such negative change exists in the roof's actual velocity curve reveals that no major interruption or significant abrupt deceleration, and therefore no amplified load, could have occurred during the fall of the upper block. How can this be\\\? If RB-12+ fell with a jolt on the rest of the building after a 12 foot drop (one story), the deceleration, as shown above, would have revealed itself clearly, and if RB-12+ fell more than one story, the deceleration would have been even more dramatic. If RB-12+ fell 72 feet—all the way through the six damaged stories—we would see powerful evidence of a jolt during the measured 114.4 foot fall of the roof. It would be dramatic precisely because the velocity and therefore the momentum would be high, and any change more discernable. But there isno evidence of major impact and deceleration either early or late.

In the main, these findings confirm the earlier research of Dr. Frank Legge. [18] In 2006 Legge, using a different video clip and measurement technique, carried out detailed measurements of the fall of the roof of the North Tower and calculated its acceleration rate. Although his purposes were different from ours, he discovered similarly smooth curves. There is no more trace of deceleration in his graphs than in ours.

What happened to RB-12+ during its fall\\\? It would appear, based on the Sauret video and other
video recordings of the event, that a substantial portion of the bottom of RB-12+, along with DS-6, was violently destroyed amidst clouds of ejected matter at the same time the top portion of RB-12+, containing the rooftop, was falling. Since the clouds of matter in the videos obscure many details of the event, it is easy to see why someone might try to make the case that the fall of the upper portion of the rigid block was accompanied by a fall of its lower portion. But we do not see a fall of its lower portion: we simply see violent destruction in the vicinity of the lower portion and fall of the upper portion.

To repeat: if RB-12+ had fallen as a rigid block, there would be impact, and the impact would have caused abrupt interference with the fall of its upper part, including the roof. No such interruption has occurred, and therefore no such impact has taken place. Evidently, the violent destruction that occurred--presumably through planted explosives or other means of demolition--effectively destroyed the structural integrity of the lower part of the upper block as well as DS-6, permitting the upper block to fall at speed whilemeeting minimal resistance and experiencing neither major impact nor abrupt deceleration.

Conclusions:

We have tracked the fall of the roof of the North Tower through 114.4 feet, (approximately 9 stories) and we have found that it did notsuffer severe and sudden impact or abrupt deceleration. There was no jolt. Thus there could not have been any amplified load. In the absence of an amplified load there is no mechanism to explain the collapse of the lower portion of the building, which was undamaged by fire. The collapse hypothesis of Bazant and the authors of the NIST report has not withstood scrutiny.


NOTES

Thanks are offered to members of the discussion forum of Scholars for 9/11 Truth & Justice, especially to Alfons, who initiated the discussion and provided a number of interesting ideas. Thanks are also due to Zoran Bilanovic for a critical reading of the paper and to Paul Bouvet for early software advice. Crucial software assistance was obtained from Joe Terrien, who gave freely of his time and expertise. We are enormously grateful to Civil Engineering Professor Robert Korol for help with the calculations inthe appendices. All measurements, calculations, and conclusions are the sole responsibility of the authors.

1. NIST NCSTAR 1. Federal Building and Fire Safety Investigation of the World Trade Center Disaster. Final Report on the Collapse of the World Trade Center Towers. National Institute of Standards and Technology, U.S. Department of Commerce, September 2005.
 http://wtc.nist.gov/NISTNCSTAR1CollapseofTowers.pdf

2. There is some ambiguity in the NIST study on which stories are included in the upper rigid block, but the analysis given in this paper appears to represent NIST's best estimate. See, e.g., NIST NCSTAR 1, p. 150-151.

3. NIST NCSTAR 1, p. 151.

4. NIST NCSTAR 1, p. 151.

5. NIST NCSTAR 1, p. xxxviii.

6. NIST NCSTAR 1, p.151.

7. NIST NCSTAR 1, 145 ("the falling building section");146 ("the falling building mass," "the falling mass"). See also the companion volume: NIST NCSTAR 1-6. Federal Building and Fire Safety Investigation of the World Trade Center Disaster. Structural Fire Response and Probable Collapse Sequence of the World Trade Center Towers. National Institute of Standards and Technology, U.S. Department ofCommerce, September 2005, p. liv ("the building section began to fall downward") and p. 156 ("the building section began to fall vertically").
 http://wtc.nist.gov/oct05NCSTAR1-6index.htm

8. Bazant, Zdenek and Yong Zhou, "Why Did the World Trade Center Collapse\\\?—Simple Analysis". Journal of Engineering Mechanics, vol. 128, no. 1 (Jan. 2002), p. 2-6 See also the Addendum to this article in the same journal, vol. 128, no. 3 (March 2002), p. 369-370.
 http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/405.pdf
Note: when we refer in the article to Bazant, we include his co-authors.
For NIST's reference to the Bazant paper, see NIST NCSTAR 1-6, p. 323.
Journal of 911 Studies January 2009/Volume 24 15

9. Bazant, Zdenek and Jie-Liang Le, Frank Greening, David Benson, "Collapse of the World Trade Center Towers: What Did and Did Not Cause It\\\?" Structural Engineering Report No. 07-05/C605c. Department of Civil and Environmental Engineering, Northwestern University. May 27, 2007. Revised December 15, 2007. p. 11.
 link to www.civil.northwestern.edu
Jim Hoffman challenged Bazant's claim some time ago in his article "Seismic Records of the Twin Towers' Destruction: Clarifying the Relationship Between Seismic Evidence and Controlled Demolition Theories." Version 0.9, Oct. 31, 2006.
 http://911research.wtc7.net/essays/demolition/seismic.html#evidence\\\_of

10. Addendum, Bazant and Zhou, 2002, p. 369.

11. See Gregory Urich, "Analysis of the Mass and Potential Energy of World Trade Center Tower 1." Journal of 9/11 Studies, vol. 18 (Dec. 2007).
 http://www.journalof911studies.com/
See also NIST NCSTAR 1-1. Federal Building and Fire Safety Investigation of the World Trade Center Disaster. Design, Construction, and Maintenance of Structural and Life Safety Systems. National Institute of Standards and Technology,U.S. Department of Commerce, September 2005.
 http://wtc.nist.gov/oct05NCSTAR1-1index.htm

12. Bazant and Zhou, 2002; Bazant et al, 2007.

13. Bazant et al, 2007, p. 1.

14. The following four points commit NIST to impact and jolt:
(a) NIST speaks of the core ofthe building as consisting of three sections, which correspond closely to the sections we have spoken ofwhen discussing the building as a whole: "At this point, the core of WTC 1 could be imagined to be in three sections. There was a bottom section below the impact floors that could be thought of as a strong, rigid box, structurally undamaged and at almost normal temperatures. There was a top section above the impact and fire floors that was also a heavy, rigid box. In the middle was the third section, partially damaged by the aircraft and weakened by heat from the fires." (NIST NCSTAR 1, p. 79)
(b) The section of the building above the damage zone NIST calls a "rigid block." This rigid block first manifests its independent movement when it tilts to the south. ("The section of the building above the impact zone (near the 98th floor), acting as a rigid block, tilted... " NIST NCSTAR 1, p. 201.) NIST also refers to this rigid block with terms such as "upper section," "building section above the impact zone," "building mass," "upper building section" and "structural block." See NIST NCSTAR 1, pp. 83, 195, 196, 201
(c) NIST acknowledges that this rigid block then falls. NIST says that "the building section began to fall downward," "the building section began to fall vertically." Indeed, we are told that this falling rigid block goes through all or part of the damaged area "essentially in free fall."
("Since the stories below the level of collapse initiation provided little resistance to the tremendous energy released by the falling building mass, the building section above came down essentially in free fall, as seen in videos.") See NIST NCSTAR 1-6, pp. 416, 238; NIST NCSTAR 1, p. 196.
(d) After falling through all or part of the damaged area of the tower, the rigid block or falling building mass encounters "intact structure." ("The potential energy released by the downward movement of the large building mass far exceeded the capacity of the intact structure below to absorb that through energy of deformation.") See NIST NCSTAR 1, p. 196. This "intact structure," has, of course, already been referred to as including the core of the building, described as "a strong, rigid box, structurally undamaged and at almost normal temperatures."

15. A version of the Sauret video clip can be found at:
 http://www.youtube.com:80/watch\\\?v=xGAofwkAOlo
For our purposes we have used the footage from Etienne Sauret's film, "WTC: the first 24 hours."

16. Readers wanting to get a rough approximation ofthe measurements in this paper without
expense may acquire from the internet the software, Vdownloader:
 http://www.softpedia.com/progDownload/VDownloader-Download-51327.html
Once the on-line version of the Sauret video clip (see note 15) is downloaded it can be broken into 0.033 second frames using VirtualDub:
 http://www.virtualdub.org/
A pixel measurement device (several are available free or for a minimal charge on the Internet) can be used for measurements.
For our paper we found we were able to get more accurate measurements by ripping the Sauret video (from the DVD) using DVD Decrypter. Then the raw video files were converted to mpeg2 using Xilisoft Video Converter 3.The converted files were thenimported into Adobe Premiere Pro CS3. The timestamp was added and the entire segment was exported as a still frame sequence in .gif format.
For pixel measurements, we used Screen Calipers:
 http://iconico.com/caliper/

17. Bazant and Zhou, 2002, p. 3.

18. Frank Legge, "9/11-Evidence for Controlled Demolition: a Short List of Observations."
Journal of 9/11 Studies, vol.1 (June 2006).
 link to www.journalof911studies.com

19. The cross sectional areas of the central core columns on each story were released by NIST in
2007 and are publicly available. This information can be found at  http://wtcmodel.wikidot.com/nist-core-column-data

20. The exterior column cross sectional area for each story was determined using the WTC1 mass analysis cited in reference [11], which gives the total mass of the columns on each story. Knowing the length of the columns and the densityof steel, the area could be determined.

21. See Section 2.6 on pages 5 through 7 of the below link for an explanation of column cross section classifications for resistance to local buckling.
 http://www.nottingham.ac.uk/civeng/H23S07/Design\\\%20of\\\%20SHS.pdf


* This paper has been revised to use symmetric differencing to calculate instantaneous velocity. The initial method used the equations of motion to calculate velocity, which are only valid with constant acceleration, causing smoothing of the data and inflation of the pre-impact velocity. Since the energy requirements do not change, the actual lower pre-impact velocity results in a larger percentage of kinetic energy drained at impact with a correspondingly more dramatic change in velocity.
An arithmetic error in the velocity reduction calculation on page 26 was also corrected.


AUTHORS

Graeme MacQueen received his Ph.D. in Asian religion and literature fromHarvard University. Now retired, he taught at McMaster University in Canada for almost thirty years. He was founding Director of McMaster's Centre for Peace Studies and directed peace-building projects in several war zones, including Sri Lanka and Afghanistan. He is a member of Scholars for 9/11 Truth & Justice.

Tony Szamboti received his Bachelor's degree in Mechanical Engineering from Villanova University. Prior to that he workedas a machinist and tool engineer in industry, and as an aircraft mechanic in the U.S. Navy. Since 1990 he has worked as a design engineer in industry, performing structural and thermal design, analysis, and testing to ensure survivability of antennas and equipment for use on ships, aircraft, spacecraft, and communication towers. He is a member of Scholars for 9/11 Truth & Justice and Architects & Engineers for 9/11 Truth.




APPENDIX A
DETERMINING THE PIXEL-FOOT RATIO FOR THE SAURET VIDEO

1. In order to correct any possible vertical distortion of the image of the North Tower that might affect our measurements (such distortions are common), we decided to find a vertical distance on the north face of the Tower that can be measured accurately in pixels. We took a measurement from a horizontal line of damage caused by the plane to a line on the roofof the NT, where the upper white part of the roof meets a darker, lower part of the building.

2. We then chose five excellent still photos of the North Tower. The perspective from which they were taken seemed unlikely to create severe foreshortening effects. These photographs are from the NIST report (NIST NCSTAR 1.5A, Chapter 8), and are grouped conveniently on the forensic website "WTC Demolition Analysis" found at:
 link to www.sharpprintinginc.com
&PHPWS\\\_Photo\\\_op=view&PHPWS\\\_Photo\\\_id=909

The photographs were taken at different times and by several different photographers, and they are reproduced below with added red arrowsshowing the two distances measured.

Our aim was to measure, in pixels, the horizontal distance xand then the vertical distance yso that we could work out the ratio of xto y. If consistency could be found, we could be confident that we had the correct ratio. Then, knowing the value of x(the width of the tower) in feet, we could determine the value, in feet, of y.

3. Here are the measurements made for the originalfive photos, marked A, B, C, D, and E. (Note that the measurements will be different on the photos as reproduced below, but the proportions will remain constant.)

Photo x y x:y ratio
A 231 pixels 211 pixels 1: .91
B 373 pixels 340 pixels 1: .91
C 379 pixels 354 pixels 1: .93
D 373 pixels 343 pixels 1: .92
E 327 pixels 302 pixels 1: .92

4. There is little variation in the figures found for the ratio of x: y. The average is 1:92, which corresponds to the ratio in what is arguably the photograph with the least apparent distortion from foreshortening, photo D,

5. Various figures, from 207 to 210 feet, have been suggested for the external width of the Towers. We chose 210 feet as our best estimate. The figure is from NIST NCSTAR 1, p. 5. See also Gregory Urich, "Analysis of the Mass and Potential Energy of World Trade Center Tower 1" (Journal of 9/11 Studies), p. 8. Bear in mind that the perimeter columns were covered in insulation and aluminum cladding, which added to their external dimensions.

6. This means that the value of the vertical distance measured (y)is 210 x .92 = 193.2 feet.

7. Measuring yin our frame-by-frame version of the Sauret video we found it to be 220 pixels.

The ratio of pixels to feet for vertical measurements in this version of the Sauret video is: 1 pixel = 0.88 feet.


A
B
C
D
E


APPENDIX B
CORE AND PERIMETER COLUMN CROSS SECTIONS ON THE 97TH STORY CORE COLUMNS 97TH story

Yield Flange Flange Web Web Cross sectional strength width thickness height thickness area

Column No. Designation (ksi) (in.) (in.) (in.) (in.) (in.^2)

501 14WF426F42 42 16.695 3.033 12.624 1.875 124.942
502 14WF264F42 42 16.025 1.938 12.624 1.205 77.325
503 14WF264F42 42 16.025 1.938 12.624 1.205 77.325
504 14WF246F36 36 16.945 1.813 12.624 1.125 75.645
505 14WF219F36 36 15.825 1.623 12.624 1.005 64.055
506 14WF287F42 42 16.13 2.093 12.624 1.31 84.058
507 14WF264F42 42 16.025 1.938 12.624 1.205 77.325
508 14WF426F42 42 16.695 3.033 12.624 1.875 124.942
601 12WF106F42 42 12.23 0.986 10.908 0.62 30.881
602 14WF150F36 36 15.515 1.128 12.624 0.695 43.776
603 14WF158F36 36 15.55 1.188 12.624 0.73 46.162
604 12WF106F36 36 12.23 0.986 10.908 0.62 30.881
605 12WF120F36 36 12.32 1.108 10.908 0.71 35.046
606 14WF150F36 36 15.515 1.128 12.624 0.695 43.776
607 14WF142F36 36 15.5 1.063 12.624 0.68 41.537
608 12WF106F36 36 12.23 0.986 10.908 0.62 30.881
701 12WF161F42 42 12.515 1.486 10.908 0.905 47.066
702 14WF176F36 36 15.64 1.313 12.624 0.82 51.422
703 14WF103F36 36 14.575 0.813 12.624 0.495 29.948
704 14WF53F50 50 8.062 0.658 12.624 0.37 15.280
705 14WF43F45 45 8 0.528 12.624 0.308 12.336
706 14WF111F36 36 14.62 0.873 12.624 0.54 32.343
707 14WF167F36 36 15.6 1.248 12.624 0.78 48.784
708 12WF161F42 42 12.515 1.486 10.908 0.905 47.066
801 12WF161F42 42 12.515 1.486 10.908 0.905 47.066
802 14WF176F36 36 15.64 1.313 12.624 0.82 51.422
803 12WF133F42 42 12.365 1.238 10.908 0.756 38.862
804 12WF79F36 36 12.08 0.736 10.908 0.47 22.909
805 14WF111F42 42 14.62 0.873 12.624 0.54 32.343
806 14WF167F36 36 15.6 1.248 12.624 0.78 48.784
807 14WF167F42 42 15.6 1.248 12.624 0.78 48.784
901 12WF120F36 36 12.32 1.108 10.908 0.71 35.046
902 14WF150F36 36 15.515 1.128 12.624 0.695 43.776
903 14WF193F36 36 15.71 1.438 12.624 0.89 56.417
904 12WF92F36 36 12.155 0.856 10.908 0.645 27.845
905 12WF99F36 36 12.19 0.921 10.908 0.56 28.562
906 14WF142F36 36 15.5 1.063 12.624 0.68 41.537
907 14WF150F36 36 15.515 1.128 12.624 0.695 43.776
908 12WF120F36 36 12.32 1.108 10.908 0.71 35.046
1001 14WF426F42 42 16.695 3.033 12.624 1.875 124.942
1002 14WF264F42 42 16.025 1.938 12.624 1.205 77.325
1003 14WF342F36 36 16.365 2.468 12.624 1.545 100.282
1004 14WF219F36 36 15.825 1.623 12.624 1.005 64.055
1005 14WF202F36 36 15.75 1.503 12.624 0.93 59.085
1006 14WF314F42 42 16.235 2.283 12.624 1.415 91.992
1007 14WF287F36 36 16.13 2.093 12.624 1.31 84.058
1008 14WF426F42 42 16.695 3.033 12.624 1.875 124.942

Total area (in.^2) = 2,621.657


PERIMETER COLUMNS

The perimeter columns were uniform in cross section on a given floor. While their exact cross sections have not been made publicly available they are discernable due totheir height, number, material density, and total weight per floor being known. The NIST NCSTAR 1-3D report states that "As the elevation in the building increased, the thickness of the plates in the columns decreased, but the plates were always at least 0.25 thick".

The height of a floor of perimeter columns in WTC 1 can be calculatedby dividing the building height of 1,368 feet by 110 stories to get a height of 12.44 feet or 149.24 inches per story.

The weight of the 236 perimeter columns at the 97th story was approximately 78.71 tons or 157,420 lbs..

Dividing the weight by the 0.283 lbs./in.^3 density of steel and the number of columns gives a volume for each column of 2,357 in.^3
.
Dividing this volume by the 149.24 inch height of each floor gives a cross sectional area for each column of 15.79 in.^2.

With 236 columns this gives a total cross sectional area for the perimeter columns at the 97th story of 3,726 in.^2.

As the perimeter columns can be approximated as 14 inch square columns, the wall thickness can be estimated. For the 97th story it would be approximately 0.289 inches. This comports well with the NIST statement that the plate thickness was never less than 0.25 inches thick, and since the 97th story was 13 floors down from the top ofthe building it appears reasonable.


APPENDIX C
CALCULATION OF THE AXIAL STIFFNESS OF THE COLUMNS FROM THE 97TH STORY DOWN TO GROUND LEVEL IN THE TOWERS

The axial stiffness of a structural column can be determined knowing the modulus ofelasticity of
its material, the cross sectional area, and the length of the column, with the equation K = AE/L.

The problem for determining this for the tower columns below the 97th story is that the cross sectional areas change with elevation. One way toestimate the cross section is to use a median, which we will do here using the cross sectional area of the columns at the 55th story since it is the midpoint in the tower above ground level.

The core column cross sectional area at the 55th story was 8,777 in.^2 and the perimeter column cross sectional area 10,784 in.^2 giving a total column cross sectional area of 19,561 in.^2 at the 55th floor.

Steel was used for all of the columns and the modulus of elasticityof steel is 30 x 10^6 psi.

The length of the columns from the 97th story down to ground level was 149.24 inches per story multiplied by 97 stories, giving a length of 14,476 inches.

Using K = AE/L = (19,561 in.2)(30 x 10^6 psi)/14,476 inches, the stiffness is found to be

40,538,132 lb./in. or 7.1 GN/m.

While one could make the case that the stiffness used should have been that from the 97th story down to the foundation, and considering the six sub-levels, the stiffness in that case would be nearly the same. The median floorin that case would be the 52nd story and the columns on that floor were only slightly larger incross section than those on the 55th, which would be offset in the calculation by the additional length of the six sub-level floors.


APPENDIX D
CALCULATION OF VELOCITY CHANGES DUE TO ENERGY DRAINS DURING THE COLLISION OF THE UPPER AND LOWER BLOCKS

It is assumed that there are 3 parts to the energy dissipation fromthe collision for a given story.

These are:

1) Uniform elastic spring action compression inthe core and perimeter columns.

2) Compressive plastic yielding of core and perimeter columns in columns of the 97th and 99th stories.

3) Plastic hinging action (buckling) ofall columns, in the two stories.

1) Calculations show that an average spring constant for the tower columns is 40,500 kips/in or 7.1 GN/m, i.e. if the columns were of uniformcross section over the 110 stories of the building, and using values found at mid-height for the 55th story. If the cross sections were uniform the tops of the columns of the 97th story would axially compress elastically 19.84 in.

However, the column sections are not uniform, since the cross sections get smaller with increasing height, as one would expect with decreasing load. Thus the 97 stories of columns can only be shown to compress elastically the amount consistent with the least cross sectional area, i.e. those of the 97th story. To calculate the maximum resistance offered by the core and perimeter columns in the 97th story we need to take intoaccount the fact that some columns are very stocky while some have thin elements that will buckle locally before they yield. All 47 core columns plus 236 perimeter columns are categorizedinto classes 1, 2, 3 and 4 (with 4 being the thinnest-walled and 1 being the sturdiest), where class 4 columns do not reach yield before local buckling occurs. [21] Approximately half of the core columns were 36 ksi yield strength with the remaining half at 42 ksi or above, resulting in an average yield strength of approximately 40 ksi. 14 of the core columns are class 4 and we conservatively use 50\\\% yield resistance before buckling for these columns. With the remaining 33 columns being given 40 ksi credit, weget a total core column load resistance of 94,900 kips. The 236 perimeter columns at the 97th story are considered class 4, but all have a yield strength of 65 ksi. Using the 1/2 factor and multiplying by the total area of perimeter columns we get 121,600 kips. The total sustainable load, before plastic deformation occurs, for the 97th story columns = 216,500 kips. As expected, the columns of the 55th story have a significantly larger overall cross section and their sustainable load, before plastic deformation occurs, is 821,600 kips. The elastic displacement of the tops of the 97th story columns can then be found using the ratio of (216.5/821.6) times 19.84 inches = 5.22 inches.

Using the equation E = ½Kx2, the elastic energy absorbed by axial deformation of the columns can be calculated using the figures above as

½ (40,500 kips/in.)(5.22 in.)^2 = 552,000 in-k.
(Note: in-k is an accepted abbreviation for in-kip).

2) The 216,500 kip elastic strain limit value, that was used to calculate the elastic axial strain energy above, is also used to calculate the plastic axial strain energy. When the columns as a group reach their elastic limit, many will be able to sustain the value of A x Fy, i.e. cross sectional area times the yield stress. The thinner walled columns will not. A 3\\\% axial strain limit is commonly assumed for class 1 sections, and lesser proportional amounts for classes 2, 3 and 4. Taking an average between 3 and zero (zero for class 4 since they will buckle locally before reaching yield), we get 1.5\\\% strain. The shortening of a column in a given story will thus be the height of the column of 149 inches times 0.015 = 2.24 inches. It follows that the axial plastic energy is 216,500 kips x 2.24 inches = 485,000 in-k.

3) After the 2.24 inch plastic strainoccurs, rather than continuingto squash like a pancake, the columns will deform by forming plastic hinges atthe top, bottom and at mid-height within the story and then buckle. The energy dissipation here is calculated in the same manner used in the Bazant model, in which the total rotations summed at the three locations = 2 pi. There will be fully plastic moments for the stockier sections that can maintain Mpfor several degrees of rotation before the bending capacity diminishes. For the less stocky columns (classes 2 and 3) Mpis initially reached and then degradation sets in. For the class 4 thin-walled columns, Mpis never reached, but a value of 0.5 Mpis likely. Finally, a scissors shape will occur in all columns of the 97th story with the 98th floor squashing the space between it and the 97thfloor slab with a corresponding energy drain of 2,103,000 in-k.

Adding these up, a total energy drain of 552,000 + 485,000 + 2,103,000 = 3,140,000 in-k is realized. However, this is only a part of the energy drain that needs to be considered. Since the lower columns of the upper block would be subject to equal but opposite forces, these columns would also be expected to suffer axial elastic and plastic deformation and buckling. The forces applied to the upper block will, in fact, be exerted on the columns of the 99th story, at the bottom of the upper block. With the forces being equal and opposite, the total damageto the structure of the upper block, if calculated, would show an equivalent total energy drain to that occurring in the structure of the lower block. However, here we are only quantifying the energy required to deform and buckle the columns on the 99th story, as we did for only the columns on the 97th story of the lower block. Since the 99th story columns had 93\\\% of the size of the columns on the 97th story, they result in 93\\\% of the energy drain found for the columns on the 97th story, with the difference being accounted for by stress wave propagation to points further up in the upper block structure.

The total amount of energy dissipation for the columns on both the 97th and 99th stories is thus 1.93 times that for the 97th story and it calculates as 1.93 x 3,140,000 in-k = 6,060,000 in-k.

As shown earlier, the weight of the upper 12 stories plus the roof had a value of 69,303 kips and the velocity determined by the regression analysis, at 1 second into the collapse and just prior to impact, is V1= 22.81 ft./s. The kinetic energy of the upper 12 stories plus the roof, dropping a height of 11.44 feet to the 98th floor slab below, can befound using the equation ½MV1^2, while also dividing the weight by the acceleration dueto gravity to get mass. A value of 6,725,860 in-k is found for the kinetic energy of the upper block, at the time of impact of the 99 th and 98th story floor slabs. The after impact velocity V2 can be found by subtracting the dissipated energy from the kinetic energy just prior to impact and solving the equation below for velocity.

6,725,860 in-k - 6,060,000 in-k = ½MV2^2

The value of V2 is 7.18 ft./s, reflecting a velocity reduction of 15.63 ft./s due to the three calculated energy drains of axial elastic deformation, axial plastic deformation, and plastic hinge buckling of the columns on the 97th and 99th stories.


APPENDIX E
CALCULATION OF VELOCITY REDUCTION DUE TO CONSERVATION OF MOMENTUM

The upper block consists of the 99th through 110th stories plus the roofwith an approximate weight of 69,303 kips, the mass of which we will designate as M ( = 2,152 k-slugs).

The measured velocity of the upper block, when it contacts the floor slab of the 98th story, was 22.81 ft./s (based on a height between floor slabs of h = 11.44 feet), which we will designate here as V1.

If the masses of the 98th story columns and floor slab are added to the original mass of the falling upper block, the new mass becomes 13/12M.

A velocity drop will occur due to conservation of momentum and can be found using the equation

M x V1= 13/12M x V1'

As mass drops out of the equation we are left with

12/13V1= V1'

Knowing V1 from the actual measurements and solving we find the new velocity V1'= 21.06 ft./s
reflecting a reduction in velocity due to conservation of momentum of 1.75 ft./s.