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What did and did not Cause Collapse of WTC Twin Towers in New York. Anders Björkman, M.Sc., explains why the Bazant ... NIST ... theory is wrong! . Discussion to Paper (3 February, 2009 - final 3 June, 2009) by A. Björkman, M.Sc. .
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Anders Björkman, M.Sc., explains why the Bazant ... NIST ... theory is wrong!
The below Discussion to Paper was submitted to ASCE - Journal of Engineering Mechanics, JEM, on 3 February 2009 and approved for publication 3 June 2009, apparently awaiting a reply or Closure by Messrs. Bazant, Le, Greening and Benson, that had not come forward 15 December 2009. As ASCE/JEM delayed publication, I decided to publish it 15 December, 2009, at http://heiwaco.tripod.com/blgb.htm. Comments are always welcome at email@example.com.
The illustrations, the figures, did not form part of the original submission to ASCE-JEM but are added here for easy verification of observations.
ASCE-JEM has informed 25 January 2010 that a Closure has finally been written by Messrs. Bazant, Le, Greening and Benson and given to JEM mid-January 2010 to be published with this Discussion of Paper in JEM at some future date.
Discussion of "What did and did not Cause Collapse of WTC Twin Towers in New York" by Bazant, Le, Greening and Benson, Journal of Engineering Mechanics, ASCE, Vol. 134 (2008), , http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/WTC%20Collapse%20-%20What%20Did%20&%20Did%20Not%20Cause%20It%20-%20Revised%203-31-08.pdf:
I have read subject article by Bazant, Le, Greening and Benson (BLGB) with great interest and would like to make the following observations:
There is no need to describe the destruction of WTC 1 using differential equations. Simple math + observations of videos prove the BLGB model and paper wrong.
BLGB suggests that upper part C (of WTC 1) drops on the lower structure of WTC 1 - part A - that is one-way crushed in 97 steps until ground. During crush of the first, the uppermost storey of part A (floor 97) a layer of debris is formed - part B - that grows thicker as more storeys are crushed by parts B and C.
Fig. 1 - The Bazant & Co crush-down theory applied to a structure consisting of five assemblies of structural elements - one upper part C and four lower parts A; All parts consists 95% of air. Each part has height h. Thus total structure has height 5 h.
(1) Lower parts A carries upper part C of the structure statically with a FoS >1 (actually >3 so that part C will not collapse by itself before start). Primary load bearing elements make up <1% of the structure volume. Upper part C is then dropped on top part A and one way crush-down, suggested by Bazant & Co, starts. The suggested reason is that upper part C can apply sufficient energy to destroy elements in part A and compress them into rubble part B without destroying itself. It is of course crazy! Part C cannot apply energy to destroy part A without destroying itself!
(2) Upper part C has crushed top part A into rubble part B A/4; The density of part B rubble is 4 times the density of C and A according Bazant. Part C has dropped 3/4 h. Part C remains intact according to Bazant & Co. In reality it cannot happen but Bazant & Co suggest otherwise!
(3) Upper part C has crushed two top parts A into rubble part B A/2; Part C has dropped 1.5 h! The rubble B assists the crushing of part A.
(4) Upper part C has crushed three top parts A into rubble part B 3A/4; Part C has dropped 2.25 h. The rubble B assists the crushing of part A.
(5) Upper part C has crushed all four parts A into rubble part B = one part A; Part C has dropped 3 h. The rubble B assists the crushing of part A.
(6) Rubble part B (!) has crushed up (?) upper part C into rubble from below. Parts A and C with density 0.25 have become 100% rubble of height 1.25 h and 'rubble' density 1.
(7) The rubble then spills out on the ground, according Bazant & Co (and is more compressed to density >1?).
Steps 2 to 6 go very fast according to Bazant & Co; Upper part C decends down/crushes parts A and produces rubble part B at acceleration about 0.7 g (g = 9.8 m/s²). If the structure A+C is only 1 meter high (and the top part C 0.1 meter), A should disappear in a fraction of second like a POUFF! What kind of structure is that?
The Bazant theory can evidently not be verified in a laboratory or in reality for any structure of any size. Actually the whole theory is complete garbage: Upper, structural part C would either bounce or get locally damaged (partly or completely) when contacting structural top part A after a gravity drop and would then get stuck up on top of what remains of parts A.
Fig. 2 - Figure 2 bottom from . The suggestion by Bazant & Co that a small upper top part C of any structure can crush down a bigger same structure bottom part A into rubble, part B, only by gravity is not possible. Upper top part C can never apply sufficient force and energy on the bottom part A and the result should always be that upper top part C remains stuck up top. The Bazant theory can not be verified in a laboratory for any structure.
What happens using the BLGB model is easily calculated by simple calculations, step by step. Differential equations are not really required.
1. Mass and Density of Part C
Near the top, the specific mass (of WTC 1) (mass per unit height) µ = 1 020 000 kg/m or 1 020 ton/m according BLGB. With a storey height of 3.6 m, the mass of a storey is thus 3 672 ton. Assuming the upper part C is 53 m high (14.7 storeys) as suggested by BLGB, total mass of part C above the initiation zone for collapse is 54 060 tons. Part C is supposed to drop down and to one-way crush all 97 storeys of part A, while part C only suffers 'negligible damages'. Part A is quite similar structural wise to part C even if the columns get stronger lower down.
Using a floor area of 4 000 m² the volume of part C is 212,000 m3, thus the uniform (which it is not) density of the upper part C is 0.255 ton/m3 or 255 kg/m3 according BLGB. It is not very much. Reason is that there is plenty of air inside a storey structure. BLGB assumes that the upper part C has some sort of homogeneous structure/density.
Note that upper part Chas volume 212,000 m3and uniform density 255 kg/m3, like balsa tree! Very light Lower part A has same density.
Fig. 3 - Upper part C prior "crush down". It is 53 meters high. Floor levels 85 and 75 of Lower part A are indicated in red.
2. Density of Rubble - part B
The known typical (sic) density (sic - mass per unit height) of rubble, µc = 4,100 000 kg/m or 4 100 ton/m according BLGB. The density of this rubble is then exactly 1 025 kg/m3 (as the floor area is 4 000 m²), which is the density of salt water (that ships float in).
Thus, when one typical storey structure of WTC 1 part A is homogeneously crushed according the BLGB model, it becomes 0.896 m high/thick. As it was originally 3.6 m high, it has been compressed 75.1%.
Note that rubble part B has density 1 025 kg/m3, i.e. 4X the density of parts A and C. Every storey s0= 3.6 meters is compressed into 0.896 m rubble, part B, by factor ʎ=0.2489 during ‘crush down’ by part C of part A according BLGB.
3. Initiation of Collapse - the first Crush - Formation of Part B
According BLGB, at initiation - part C - 54 060 tons (actually the lowest floor 98 of part C) - crushes the uppermost storey of part A - floor 97 of the lower structure of WTC1 and compresses it into a 0.896 m thick layer of debris/rubble that becomes part B. Air/smoke is ejected sideways. BLGB suggests that the local failures are generally buckling of columns between floors 96/98 requiring little energy. Energy to compress the rubble is not considered by BLGB.
This layer, part B, is then resting on the second uppermost floor of part A - floor 96. This compression takes place at increasing velocity of part C. Only air is ejected sideways out. The mass of the rubble - 3 670 tons - is uniformly distributed on the floor below - 918 kg/m² - and the floor should be able to carry that uniform load according general building standards.
What about the part C and its mass 54 060 tons? Is it acting on the debris layer part B? Not really - part C is intact according BLGB but only its bottom floor is now in contact with part B. The columns of part C are now not in contact with the columns of part A below due to the layer of rubble, but it must be assumed that part C columns contact the columns of part A below as suggested by BLGB, so that crush-down destruction can continue.
The roof line of part C has now dropped 2.704 m after first crush (i.e. storey height 3.6 m minus part B height 0.896 m).
z0= 53 meters,
ʎs0= 0.896 meters after first ‘crush’.
Roof line has dropped 2.704 meters!
4. The second Crush - Part B doubles in Thickness
Then the part C + part B (the layer of rubble/debris) crush the second uppermost floor (no 96) of part A and compresses it into another 0.896 m thick layer of debris that is added to part B. Part B is thus 1.792 m high or thick after two storeys of part A have been crushed. The part C columns now crush the columns of part A again (how?) so that the destruction can continue.
The roof line has then dropped 5.408 m after two crushes! The velocity is increasing. More air/smoke is ejected sideways but only from the storey being crushed.
And so on!
Both the first and second crush is strange in many ways. You would expect the columns in part C between floors 97/99 to fail first at impact! The part C columns are weaker than the part A columns below.
z0= 53 meters,
ʎs0= 1.792 meters after second ‘crush’,
Roof line has dropped 5.408 meters!
Do you think that upper part C remains intact during ‘crush down ’?
Fig. 4 - Upper part C just after initiation of ‘crush down’ and when roof
line has dropped about 35 meters. There is no sign of a Part B.
Rubble/debris below the Upper part C. You can actually see ejections of
debris through windows at floor #85 and, on other videos/photos, local
destructions of other kind higher up. Upper part C is evidently not
5. The Displacement of the Roof Line of Part C during Destruction
According to paper The Missing Jolt: A Simple Refutation of the NIST-Bazant Collapse Hypothesis  by Graeme MacQueen, Tony Szamboti, January, 2009 (http://journalof911studies.com/volume/2008/TheMissingJolt4.pdf ) and careful observations of videos of the alleged crush-down we now know that the roof line of part C dropped (displaced downwards) 35 metres in 3.17 seconds at increasing velocity. This 'drop' of part C is also verified by BLGB. However, it is not part C moving down we see. It is part C becoming shorter, while part A remains intact.
Fig. 5 - from  - Upper part C roof line downward displacement versus time. The curve is very smooth. If Upper part C had really ‘crushed down’ 13 intact storeys below into Part B – 47 736 tons of Rubble/debris in 3.2 seconds, the curve should be staggered. The smooth curve suggests that Upper part C is simply destroyed.
Every time a storey is crushed, part C drops 2.704 meters and an 0.896 meters layer of debris is formed according BLGB, and the part C columns also destroy the columns below - how is not clear as there is a thick layer of rubble - part B in between.
Thus, when the roof line has dropped 35 meters, 12.94 storeys, total height 46.6 meters (!) of part A have been crushed and have been replaced by an 11.56 meters thick layer of debris - part B. 46.6 meters of columns of part A have been crushed at perimeter and core, the latter being mixed in the debris. I assume the wall columns are dropping down to ground outside the building.
MacQueen & Szamboti believe that only 9 (or 9.72) storeys of part A have been crushed after 3.17 seconds, but according BLGB it should be 12.94 storeys! MacQueen & Szamboti forget that there should be an 11.56 meters thick layer of debris on part A and below the upper part C, when its roof line has dropped 35 meters.
When roof line has dropped 35 meters,
part B, i.e.ʎ s0 = 11.56 meters after ‘crushes’ of 13 storeys into 47 736 tons of rubble in 3.2 seconds.
6. Verification of Parts A and B using Video Recordings of the Destruction
Regardless - does anybody see an 11.56 meters thick layer of debris - part B - on any video of WTC1 destruction after a 35 meters drop of the upper part of WTC1, part C according BLGB? Or that 46.6 meters of wall columns have disappeared?
And does anybody believe that an upper part C with density 255 kg/m3 can produce an 11.56 meters thick layer of rubble/debris in 3.17 seconds? Only BLGB suggests so, but there is no evidence for it. Reason is that BLGB ignore the energy required to compress the rubble. Simple calculations show that this energy doesn't exist.
This layer of debris is then moving at a velocity of >20 m/s and increasing. The acceleration of parts C and B becomes rather uniform 0.65-0.7g, i.e. very little force is applied on part A. Only air/smoke should be ejected from the next storey below being crushed, where more debris is formed.
7. Situation when Part C Roof Line has dropped 100 and 200 meters
Now - when part C has dropped 100 meters and 37 storeys (floors 97-60) have been crushed, the layer of debris - part B - should be 33 meters thick on top of which a 53 meters high part C should be visible (forgetting the mast). 133 meters of walls should be missing. You do not need differential equations to calculate this. Simple math suffices.
Fig. 6 – ‘Crush down’ between floors 85 and 75. Upper Part C is evidently not visible, nor is Part B - Rubble/debris. It should be clear to everybody that WTC 1 is now blown apart by energy released inside the tower.
And when part C has dropped 200 meters and 74 (floors 97-23) storeys of WTC1 have been crushed, the layer of debris should be an impressive 66 meters thick with part C still riding on top of it.
Imagine a layer of debris - density 1,025 ton/m3 - 66 meters high. Over 4 000 m² floor area it is almost a big cube of 264 000 tons of rubble. On top of which part C - 54 060 tons floats. Part C is 53 meters high. Add the rubble - part B - and we have a moving mass that is 119 meters high, when the part C roof line has dropped 200 meters.
Below this 119 meters high pile, a storey of part A - floor 23 - is just being crushed. How the columns of part C - 66 meters above floor 23 - can crush the columns there is not clear. 266 meters of walls should also be gone. There are another 23 storeys still to crush. About 83 meters of WTC 1 remains to be crushed. Can it be seen on any video? Note also that upper part C is still accelerating at 0.7g at this time. The speed is of the order 45 m/s.
Fig. 7 – ‘Crush down’ below floor 75. Upper Part C is evidently not visible, nor is Part B - Rubble/debris. Smoke is ejected upwards indicating energy release other than that of gravity.
When roof line has dropped 262.3 meters, only ʎ(H- z0) + z0 = 133 meters of structure parts B + C remain according BLGB. ‘Crush up’ of part C can now commence!
Schematics of a ‘crush down’ of WTC 1 part A (getting crushed) on 9/11 by upper part C
(remaining intact) and rubble part B (growing bigger), according BLGB. When roof line of part C has
dropped 200 meters, 266 meters (74 storeys) of part A have been destroyed and replaced by 66
meters of rubble, part B. When all 97 storeys have been crushed, the roof line has dropped 262.3
meters. Part B is then about 87 meters tall!
When all 97 floors of WTC 1 - part A - have been crushed, there should be an 83 meters thick layer of debris on the ground + upper part C on top of it - 53 meters. This is also confirmed by BLGB - see fig. 3 (b) in their paper: just before the end of crush- down the 53 meters high part C rests on a 92 meters thick layer of debris (density 1.025 ton/m3) - the crush down has also penetrated the basement 22 meters below ground! The roof line of part C should be 133 meters above ground then.
An instant later upper part C is destroyed in a crush-up according BLGB and should form another 13 meters thick layer of rubble (according another differential equation). The total thickness of rubble should be 92 + 13 = 105 minus 22 meters of rubble in the basement = 83 meters of rubble above ground but only 20 meters is suggested by BLGB.
Fig. 8 - figures 3 (a) and 3 (b) from 
Evidently some rubble is spread outside the 4 000 m² foot print, but it seems the density of the rubble must have increased 3 times - 3.075 ton/m3. But it is not possible - it is too dense. So where did all the rubble go?
Actually no rubble could be produced at all by dropping upper part C, as the destruction should have been stopped up top due to all local failures developing, when part C contacts part A and friction between all partly damaged parts develops at floor 98 level. Only by ignoring local failures and friction at first contact between parts C and A, the BLGB model is initiated. If any further columns would fail, they would have been in part C.
But what the BLGB theory and model postulate cannot be seen on any videos of the WTC1 destruction. Simple observations of any video of the WTC 1 destruction prove the BLGB model wrong.
Anders Björkman, M.Sc., Heiwa Co, European Agency for Safety at Sea, Beausoleil, France
When roof line has dropped 262.3 meters, only
ʎ(H- z0) + z0 = 133 meters of structure parts B + C remain! ‘Crush up’ of part C can now commence!
After crush up WTC consists of 104 m of rubble!
 What Did and Did not Cause Collapse of WTC Twin Towers in New York, Zdenek P. Bazant, Jia-Liang Le, Frank R. Greening and David B. Benson (2008) http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/WTC%20Collapse%20-%20What%20Did%20&%20Did%20Not%20Cause%20It%20-%20Revised%203-31-08.pdf
 The Missing Jolt: A Simple Refutation of the NIST-Bazant Collapse Hypothesis, Graeme MacQueen, Tony Szamboti, January 14, 2009 http://journalof911studies.com/volume/2008/TheMissingJolt4.pdf
More by A. Björkman at
The message is always the same. A small top part of a structure, i.e. an assembly of structural elements joined together, cannot crush down from above a much bigger bottom part of the same structure into rubble only by the force of gravity. It is physically impossible. So what happened to WTC 1 & 2 on 911 was not due to top parts of towers dropping down and crushing the towers below as suggested by NIST.