Anders Björkman, March 16, 2010
"Merely to get convinced of the inevitability of gravity driven progressive collapse, further analysis is, for a structural engineer, superfluous. Further analysis is nevertheless needed to dispel false myths, and also to acquire full understanding that would allow assessing the danger of progressive collapse in other situations."
Zdenek P. Bazant, Hon.M. ASCE, Jia-Liang Le, Frank R. Greening, and David B. Benson, March 31, 2008
"Some (stupid) people believe that actual size or scale plays a part of the dynamics of a relatively lightweight falling object. They think that when the weight of the falling top object, part C, is great enough (?), it will prevent a rebound against bottom part A below at contact and that the contact area between parts C and A gets crushed only in the bottom part A area. Such ideas are wrong because parts C and A are of same structure and material and will thus be equally affected. When top part C is smaller than bottom part A, top part C is always relatively more affected than A. Little top C can never crush down A below from above by gravity."
Anders Björkman, March 21, 2010
The below Discussion to Paper was submitted to ASCE - Journal of Engineering Mechanics 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 has not come forward 15 December 2009.The illustrations, figures 1-8 did not form part of the original submission to ASCE-JEM but are added here for easy verification of observations. As ASCE/JEM are delaying publication, I have decided to publish it here today, 15 December, 2009. Comments are always welcome at anders.bjorkman@wanadoo.fr .
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.
On 16 March 2010 ASCE has advised:
Date: 03-16-2010
Manuscript #: EMENG-296R1
Re: Discussion of "What Did and Did Not Cause Collapse of World Trade Center Twin Towers in New York" by Bazant, Le, Greening and Benson
Authors: Anders Björkman, M.Sc.
Dear Mr Anders Björkman,
Your article EMENG-296R1 entitled, "Discussion of "What Did and Did Not Cause Collapse of World Trade Center Twin Towers in New York" by Bazant, Le, Greening and Benson" by Anders Björkman, M.Sc. has been through a final check and is now scheduled for publication in the July 2010 issue of the Journal of Engineering Mechanics.
We are very pleased to be publishing your paper, and we look forward to receiving manuscripts from you in the future.
Sincerely,
ASCE Journals Department
So it looks as if ASCE will finally publish my paper + Bazant's 'Closure'.
Anders Björkman, M.Sc., Heiwa Co - European Agency for Safety at Sea
Discussion to Paper (3 February, 2009 - final 3 June, 2009) - To be published in ASCE:s Journal of Engineering Mechanics (July - 2010)
(Also as Power Point presentation + nice figures)
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), [1]
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 WTC1 using differential equations. Simple math + observations of videos prove the BLGB model and paper wrong.
BLGB suggests that upper part C (of WTC1) drops on the lower structure of WTC1 - part A - that is one-way crushed in 97 steps until ground.
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% b =" one">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 0.2 meter), 0.8 meter A should disappear in a fraction of second like a POUFF! What kind of magic structure or material 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 fantasy: 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.
No structure of any size can be crushed by an upper part of itself from top down by gravity.
It is quite elementary! Part C and the rubble part B cannot ever apply sufficient force/pressure/energy to crush part A from above. It is quite easy to calculate the pressure applied and energy released by falling upper part C and any rubble B and compare it with the energy required to break all elements in part A. The pressure applied and energy released by C and B is small ... and difficult to apply on A ... so A will never be crushed down. Question remains why Bazant & Co suggest the opposite? It is insane! Is Bazant & Co part of the conspiracy to destroy the WTC at NY?
Fig. 2 below shows Bazant & Co's original crush-down/up phases:
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. 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.
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) 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%.
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 WTC 1 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).
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.
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 [2] 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 m 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.
Every time a storey is crushed, part C drops 2.704 m and an 0.896 m 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 m, 12.94 storeys, total height 46.6 m (!) of part A have been crushed and have been replaced by an 11.56 m thick layer of debris - part B. 46.6 m 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 m thick layer of debris on part A and below the upper part C, when its roof line has dropped 35 m.
6. Verification of Parts A and B using Video Recordings of the Destruction
Regardless - does anybody see an 11.56 m thick layer of debris - part B - on any video of WTC1 destruction after a 35 m drop of the upper part of WTC1, part C according BLGB? Or that 46.6 m of wall columns have disappeared?
And does anybody believe that an upper part C with density 255 kg/m3 can produce an 11.56 m 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 become 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 m
Now - when part C has dropped 100 m and 37 storeys (floors 97-60) have been crushed, the layer of debris - part B - should be 33 m thick on top of which a 53 m high part C should be visible (forgetting the mast). 133 m 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 as described here.
And when part C has dropped 200 m and 74 (floors 97-23) storeys of WTC1 have been crushed, the layer of debris should be an impressive 66 m thick with part C still riding on top of it.
Imagine a layer of debris - density 1,025 ton/m3 - 66 m 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 m high. Add the rubble - part B - and we have a moving mass that is 119 m high, when the part C roof line has dropped 200 meters.
Below this 119 m high pile, a storey of part A - floor 23 - is just being crushed. How the columns of part C - 66 m above floor 23 - can crush the columns there is not clear. 266 m of walls should also be gone. There are another 23 storeys still to crush. About 83 m 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.
When all 97 floors of WTC 1 - part A - have been crushed, there should be an 83 m thick layer of debris on the ground + upper part C on top of it - 53 m. This is also confirmed by BLGB - see fig. 3 (b) in their paper: just before the end of crush- down the 53 m high part C rests on a 92 m thick layer of debris (density 1.025 ton/m3) - the crush down has also penetrated the basement 22 m below ground! The roof line of part C should be 133 m above ground then.
An instant later upper part C is destroyed in a crush-up according BLGB and should form another 13 m thick layer of rubble (according another differential equation). The total thickness of rubble should be 92 + 13 = 105 m minus 22 m of rubble in the basement = 83 m of rubble above ground but only 20 m is suggested by BLGB.
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.
And when part C has dropped 200 m and 74 (floors 97-23) storeys of WTC1 have been crushed, the layer of debris should be an impressive 66 m thick with part C still riding on top of it.
Imagine a layer of debris - density 1,025 ton/m3 - 66 m 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 m high. Add the rubble - part B - and we have a moving mass that is 119 m high, when the part C roof line has dropped 200 meters.
Below this 119 m high pile, a storey of part A - floor 23 - is just being crushed. How the columns of part C - 66 m above floor 23 - can crush the columns there is not clear. 266 m of walls should also be gone. There are another 23 storeys still to crush. About 83 m 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.
When all 97 floors of WTC 1 - part A - have been crushed, there should be an 83 m thick layer of debris on the ground + upper part C on top of it - 53 m. This is also confirmed by BLGB - see fig. 3 (b) in their paper: just before the end of crush- down the 53 m high part C rests on a 92 m thick layer of debris (density 1.025 ton/m3) - the crush down has also penetrated the basement 22 m below ground! The roof line of part C should be 133 m above ground then.
An instant later upper part C is destroyed in a crush-up according BLGB and should form another 13 m thick layer of rubble (according another differential equation). The total thickness of rubble should be 92 + 13 = 105 m minus 22 m of rubble in the basement = 83 m of rubble above ground but only 20 m is suggested by BLGB.
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.
Fig. 8 - figures 3 (a) and 3 (b) from [1]
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 WTC1 destruction prove the BLGB model wrong.
Anders Björkman, M.Sc., Heiwa Co, European Agency for Safety at Sea Beausoleil, France
References
[1] 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)
[2] The Missing Jolt: A Simple Refutation of the NIST-Bazant Collapse Hypothesis
Graeme MacQueen, Tony Szamboti, January 14, 2009
Anders Björkman, M.Sc., Heiwa Co, European Agency for Safety at Sea Beausoleil, France
References
[1] 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)
[2] The Missing Jolt: A Simple Refutation of the NIST-Bazant Collapse Hypothesis
Graeme MacQueen, Tony Szamboti, January 14, 2009
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