WTC 1 - the case for collapse/crush down arrest
A thin roof of a skyscraper cannot crush the skyscraper below! What you saw is just an example of media fakery propaganda and it is not a conspiracy theory
Welcome. This article of mine about the 911 WTC 1 collapse is in 39 sections for easy reference. If you still believe that a skyscraper collapses from top down (the weak top crushing the strong bottom) after having studied them, please tell me.
1. WTC 1/2 - Learning from ship collisions by Anders Björkman (M.Sc),
The WTC 1/2 Towers could not have been one-way crushed down and destroyed by its weak, light weight upper part C dropping on the much heavier and stronger bottom part A keeping part C in place on 9/11/2001 as reported by NYT and seen 'live on (faked) TV'. A light, weak top part crushing a heavy, strong bottom part of a structure as suggested by evil magicians in the USA cannot happen in the real world. It is also explained at 1.18.50 in DVD2 - a film about the 911 incident.
Can actually hijacked jets making holes in the weak tops of towers, destroy the complete, stronger, intact, not on fire towers below as suggested by evil people in the USA? Or was NYT publishing a lie? More faked photos were published by the NYT Staff ... and they got a prize!
According basic structural damage analysis no structure can destroy itself by its light top part dropping on the lower stronger part. Why did NYT suggest the contrary? Watching TV?
It is very easy to fake a plane crashing into a skyscraper! Like this! It is just a question of various layers on a video! And to add some scripted comments! It is like composing music. But when a plane collides with a skyscraper there should be plenty of plane parts bouncing off the skyscraper ... but there were none!
It appears that all videos and pictures showing the destruction of WTC and the rubble afterwards are simply faked by the terrorists!
I am convinced that the POTUS 2001 ordered the falsifications of all 911 investigations of all kind, incl. the structural analysises done by NIST, and that the fakery should be kept secret forever by an Executive order to this effect backed up by laws to prevent any whistle blowers to tell the truth as described below.
I am convinced that the United States and key allies and partners 2017 use disinformation and other propaganda tools to undermine the national security objectives of Sweden, France and other countries deemed vulnerable to foreign propaganda and disinformation campaigns.
Upper small part C crushing big A = ridiculous! Prove me wrong and win €1.000.000:- (Note - photos are fakes! Smoke and debris are just added by Photoshop.)
This presentation explains why a structure cannot destroy itself from top down by gravity, i.e. there is too little energy available to destroy the lower, stronger structure ... and the bottom part of WTC1 is 10 times stronger than the top part.
That's why houses and towers never globally collapse from top down. The USA is simply fooling the world. It will take 30 minutes to read the presentation!
Analysis of the seismic waves emitted near the time of the plane impacts and at the moments of the collapses and recorded at stations in New York and four neighboring states on September 11, 2001, indicate that WTC1 and WTC2, respectively were brought down by controlled demolition.
The author is a naval architect with 40 years of steel structural design experience including structural damage analysis and maintenance and repairs of steel structures. He has investigated the structural damage from many ship collisions. The destruction of WTC 1, a plane colliding with a steel framed tower (as described here) and what follows, e.g. weak upper part of WTC 1 dropping on/impacting lower, stronger structure, is in many respects similar to a collision between two steel ships - one small and one big!
At the moment of contact of A) the 'WTC 1 upper part and lower structure' or B) 'two ships in collision', a certain momentum (mass times velocity), kinetic energy (momentum times velocity divided by 2) and forces (energy divided by displacement) have to be considered.
All structural elements involved are subject to displacements and local failures due to the forces applied; energy is absorbed and consumed, friction forces between failed/displaced elements in contact develop, forces and loads are re-distributed, momentums are reduced as outer forces are applied on the parts and the environment and the destruction is always arrested after a while. All kinetic energy of the collision is transformed into heat and the momentum is transmitted to ground/Earth (very big mass part of the collision).
Many people ask how were the towers destroyed if they were not crushed from top down by gravity. The top down crush seen on TV was just an animation of computer generated images, CGI, done by Hollywood. The 110 floors steel frame WTC1&2 towers were brought down by controlled demolition, like the 28 floors tall Biltmore Hotel, October 1977:
"Seconds after the final warning signal blared Sunday afternoon at a downtown redevelopment site in Oklahoma City, precisely placed explosive charges dropped a 28-story building almost in its tracks. When it fell, the 245-ft-high structure became the tallest steel-frame building to be demolished with explosives.
The result was a big heap of steel frames showing that explosives had been used, so all footage of the rubble was faked too using CGI.
2. Structural damage analysis
It is not a static or dynamic solid mechanics problem! It is a structural damage analysis problem easy to solve! The upper part of WTC 1 and its roof can only apply forces on the lower structure elements that the upper part can itself withstand in the first place. As the upper part and the lower structure of WTC 1 have identical structures, the upper part cannot destroy the lower structure of WTC1 in a top-down collapse. In ship collisions, where different types of structure come into contact, the situation is slightly different but identical principles of analysis apply. Both structural parts deform and maybe damage each other. A roof remote from the collision interface cannot just disappear!
What happened to the smaller upper part and its roof of WTC 1 colliding with/dropping on (?) the bigger lower part on 911 can be seen on photos below (origin of photos is Internet videos and reliability cannot be guaranteed; footage is obviously manipulated). Try to follow the roof that does not contactr anything:
Fig. A1 - The upper part C (floors 97-110 + roof + mast) rests on the lower part! Destruction has not started. Roof is intact. At right insert is shown upper part C in original position.
Fig. A2 - Destruction and collision (!) have started!! The upper part C (floors 97-110 + roof + mast) (95% air) is destroyed (using Photoshop!), while roof line and mast move down 5 floors or 18-19 meters. It, the upper part C incl. roof, should however remain intact and not get smaller and it should now crush down intact, strong WTC 1 lower structure according US authorities! The animators are doing a lousy job!
Fig. A3 - The upper part C (floors 97-110 + roof + mast) is completely destroyed and turned into dust, i.e. removed by Photoshop, but mast can still be seen. But where is the roof? It should be intact!! Debris is ejected sideways at high velocity. This is obvious fake animation - top Photoshopped and smoke added!
Fig. A4 - The WTC 1 lower, intact, strong structure top part explodes (LOL) in a cascade of debris and dust! The upper part C roof, and mast is fully destroyed or removed/turned into dust and cannot produce what we see! It looks as if a bomb has gone off inside WTC 1 blowing debris sideways. No upper part C with intact roof is crushing down anything here, i.e. what you see is a Photoshopped (computer graphic image) animation.
Fig. A5 - More debris is thrown out sideways (more bombs go off!) and smoke is ejected upwards! Evidently not a result of the upper part C + roof being intact and crushing down lower structure as per US authorities. It, the upper part C + roof, has already disappeared or gone up in Photoshopped smoke and dust. The animators add more smoke and dust for effect!
Fig. A6 - There is no sign of an intact upper part C crushing WTC 1! Why does US authorities suggest that a skyscraper can be destroyed by a small top upper part C one-way crushing down (!) much stronger, bigger structure below by gravity and fire up top? Anybody can see on animated photos above that WTC1 is blown apart from top down in a simple animation and that the upper part C is turned into dust first. It cannot happen in reality, i.e. what we see is an animation, Hollywood style. It was also shown 'live on TV' in USA on all five major TV channels. Imagine that! Fake footage was shown live on TV on 911!
Actually an upper part C and its roof crushing anything would have been impossibe, because Björkman's axiom (see below) regarding structural damage analysis of identical structures in collision says:
3. The Björkman axiom explained
The Björkman axiom can be better understood by looking at what happens when two objects C and A collide inelastically, i.e. the objects are deformed/damaged in an isolated space (in some simple, numerical examples):
We start with two objects C and A of same mass (and other structural properties). Note how the velocity of the moving part C changes (is reduced) at collision!
C has mass m = 1 kg and is moving at velocity v = 10 m/s and its kinetic energy (mv²/2) is 50 J and its momentum (mv) is 10 kgm/s. A has mass 1 kg but is stationary (0 energy and momentum). After inelastic collision C with A in a closed space we assume both objects move at velocity 5 m/s - momentum 10 kgm/s is conserved - and then we observe that the kinetic energy of A+C is only 25 J. Note that moving part C slowed down from 10 to 5 m/s in this inelastic collision! Where did the 25 J go? (In an elastic collision A gets velocity 10 m/s and C becomes stationary and no energy and momentum is lost).
If an inelastic collision really can take place in a closed, isolated space as suggested; mass C 1 kg/10 m/s/ 50 J/ 10 kgm/s hits stationary mass A 1 kg/0/0/0 and both (C+A) proceeds at 5 m/s (glued together?) after collision thus with constant momentum 10 kgm/s but only with 25 J kinetic energy, the missing 25 J energy evidently was transformed into, e.g. heat, deformations, failures and gluing of C and A at the inelastic collision. 12.5 J/kg can really locally transform/modify/glue C and/or A in many ways, but it depends on the structural and material properties of C and A.
The difference between an elastic and inelastic collision in closed space is that, in the latter, structure is modified and kinetic energy is transformed into heat. Momentum is always conserved.
Now lets study an example of the axiom. C is the smaller part and remains at 1 kg and A becomes the bigger part!
Let's say that A is 9 times bigger - 9 kg - than C and that C+A (10 kg) proceeds at only 1 m/s after collision/glued together in a closed space (momentum 10 kgm/s is conserved) and that you lose 45 J in the collision or only 4.5 J/kg on A+C together. Note that moving part C now reduces speed from 10 to 1 m/s in order to transmit energy.
However, if the 45 J energy used to transform/glue the objects is split 50/50 between C and A, then 22.5 J/kg is applied on small part C and only 2.5 J/kg is applied on big part A. Reason for this is that the contact forces between C and A are equal at contact.
In this case and, if C and A, has same structure/material/properties and are subject to identical forces, actually pressures or stresses, C breaks up long before A in an inelastic collision, as small C must absorb 9 times more energy than big A. The axiom suggests that similar things happens when two objects collide in an open space, where A may be fixed to, e.g. ground, e.g. like WTC 1 on 911.
It means that you cannot crush an isotropic or composite 3-D structure A by a part C of itself (C = 1/9 A) by dropping part C on A using gravity. Part C either bounces (elastic collision) on A or gets damaged (inelastic collision) in contact with A and is stopped by A that is also damaged a little. It is quite basic and all due to forces/pressures/energy applied and that the two parts have identical structure and material. Actual materials, size and particulars of the elements of the structure A doesn't matter the least. Part C of A cannot destroy A, as C must absorb much more energy per mass unit than A in the inelastic collision.
Thus no structures, 1, 2 or 5 meters tall, or 100, 200 or 500 meters tall exist that will one-way crush down, when a small part C is dropped on the bigger part A below.
And everytime a small, upper part C collides with a stationary big, lower part A, small C loses most of its velocity and stops! If C does not lose velocity at all, as seen on 911, there is no collision! (It is a controlled demolition of some sort - C is destroyed first followed by A -from top down - and impossible to show on video/photo).
However, various people, i.a. Bazant and Seffen (apart from Usama Bin Laden, Condoleezza Rice, GW Bush and similar clowns), which will be further described below in parts I , III and V of this paper propose otherwise.
They suggest that what they describe as one-way crushing or progressive collapse takes place as follows: First, after impact, upper part C of a building A does not lose any velocity but increases it due gravity (!) and during the collapse there is a transfer of mass (?) from the stationary building, lower part A, to the moving top section, part C, due to deformation and local failures of structural elements in part A only - a layer of rubble, part B, attached to part C is formed, which is a function of displaced distance downwards. Second, the stationary building, lower part A, lamely resists the motion of the top, upper section, part C, and its rubble layer, part B, but cannot stop it. C and B just increase (!) their speed. After a few seconds the building C+A is just rubble B from top down. Or in other words; just drop a little piece C of a structure A you want to destroy on A and C destroys A.
4. After a few seconds the building parts C+A are just rubble B from top down!
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) POUFF!! 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) POUFF!! 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) POUFF!! 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) POUFF!! 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.
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 POUFF!!,
according Bazant & Co (and is more compressed
to density >1?). Evidently no structure
POUFF!! POUFF!! POUFF!! POUFF!!
from top down when
you drop a small top piece on it. The basic errors with these
suggestions are simply that no transfer of mass can
occur between parts A and C due to a rubble layer,
part B, being formed and accelerated and that part
A evidently can arrest the motion of C in various
ways. Bazant and Seffen are like the stalinist
scientist (!) Lyssenko
in the 1930's. Their theories cannot be verified
scientifically by laboratory and field experiments
under controlled conditions; they just make up
fantasy theories (to support
terrorism!). Actually, you can fly in as
many planes as you like in the tops of WTC 1 and 2
but the lower structure of WTC 1 and 2 will not be
crushed down by the tops ever! Structures like WTC
1 and 2 cannot collapse from top down! To destroy a
structure you have to do it from bottom up
(controlled/planned demolition) removing elements
at the bottom or step by step applying energy
locally. Fig. A7 -
top part C
due to progressive collapse and crush down of A by
C according to false theories of Bazant and Seffen
developed after 11 September 2001. Evidently a
small top part cannot crush a bigger bottom part of
same structure only due to
(6) POUFF!! 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 POUFF!!, according Bazant & Co (and is more compressed to density >1?).
Evidently no structure goes POUFF!! POUFF!! POUFF!! POUFF!! POUFF!! from top down when you drop a small top piece on it.
The basic errors with these suggestions are simply that no transfer of mass can occur between parts A and C due to a rubble layer, part B, being formed and accelerated and that part A evidently can arrest the motion of C in various ways. Bazant and Seffen are like the stalinist scientist (!) Lyssenko in the 1930's. Their theories cannot be verified scientifically by laboratory and field experiments under controlled conditions; they just make up fantasy theories (to support terrorism!).
Actually, you can fly in as many planes as you like in the tops of WTC 1 and 2 but the lower structure of WTC 1 and 2 will not be crushed down by the tops ever! Structures like WTC 1 and 2 cannot collapse from top down! To destroy a structure you have to do it from bottom up (controlled/planned demolition) removing elements at the bottom or step by step applying energy locally.
Fig. A7 - A building A with a top part C becomes rubble B due to progressive collapse and crush down of A by C according to false theories of Bazant and Seffen developed after 11 September 2001. Evidently a small top part cannot crush a bigger bottom part of same structure only due to gravity!
Finally drop anything weak (an egg or a lemon?) on something strong! PLAFSH! The weak anything (the egg or lemon!) is crushed against the strong something! It's velocity becomes zero!
Don't forget that! This is what happens when different structures collide.
Try to compress a lemon with another lemon. What happens? Both lemons compress. This happens when identical structures collide.
Drop rubble on a structure and the structure doesn't collapse. Rubble cannot crush down any structure.
Now you have learnt a little what can happen when you drop anything on something and try to compress something. Contact forces develop temporarily and the velocity of the striking object changes! This basic knowledge is used in this paper.
And then you have to work from there. Do the analysis step by step! In A) a vertical drop, gravity is always at work and produces forces acting on the various parts in contact and you have to include that, in B) a horizontal collision, the propulsion force of the ship may still be active and you have to consider that.
6. What is a drop?
If the upper, 53 meters tall, 13-15 storeys upper part of WTC 1 above floor 97 actually dropped on the structure below is a matter of semantics. Drop suggests that it was not being held at all. I prefer that it came into contact after local structural failures and downward displacement and that it was prevented from dropping by the connecting elements between the two parts. Only the velocity at contact is of interest and it was not high in the WTC 1 case. Assuming a 'drop' of 3.7 metres, it does not produce a big velocity; it is around 8 m/s. If the 'drop' is dampened by intermediate connections the velocity is much less.
Assuming in A) above (WTC 1 upper part drops on the lower structure with perfect alignment columns/columns) that the two parts act as springs (disregarding local failures), the upper part would just bounce as described in one of my other articles. No global one-way collapse would ensue! This article is a follow-up of this conclusion.
In B) above (ships colliding or running aground like M/T Exxon Valdez) the contact velocity may be up to 10 m/s and the masses up to 200 000 tons, so it should be clear that in B) 8 times bigger momentums and 10 times more energies may be involved compared with A).
According Prof Bazant & al.
 the following happens - one way
crushing - when an
part C, with
initial constant (!) height
z0, of WTC 1, with total
height H, above say floor #97, falls
on the similar structure,
part A, below
floor #97 and crushes floors ##97-0, part A,
part B: During the
Crush-Down, the falling
C of tower (C in
Fig. 2 bottom (fig. 1
right)), having a
of debris at
its bottom (zone B), is crushing
A) with negligible damage to
itself. During the
Crush-Up, the moving
of tower is being crushed at bottom by the
resting on the ground.
According Prof Bazant & al.  the following happens - one way crushing - when an upper part C, with initial constant (!) height z0, of WTC 1, with total height H, above say floor #97, falls on the similar structure, bottom part A, below floor #97 and crushes floors ##97-0, part A, into rubble, part B:
During the Crush-Down, the falling upper part C of tower (C in Fig. 2 bottom (fig. 1 right)), having a compacted layer of debris at its bottom (zone B), is crushing the lower part (zone A) with negligible damage to itself. During the Crush-Up, the moving upper part C of tower is being crushed at bottom by the compacted debris B resting on the ground.
Or - first upper part C one-way Crushes-Down bottom part A top into a thin layer of debris B with thickness ls0 and then the complete bottom part A into a thick layer of compacted debris B with thickness l(H-z0) and then the thick layer of compacted debris B Crushes-Up upper part C bottom into a thin layer of debris B' with thickness r=lr0 and then the complete upper part C into a thick layer of debris B' with thickness lz0 and then there is only a tick layer of debris B+B' with thickness lH left of bottom part A and upper part C. l is the compaction ratio! Very nasty Greek letter! Apply it to any structure and l will compact it. First down, then up. And then there is nothing left but rubble!
It is very simple according Bazant [5}:
"When the upper floor crashes into the lower one, with a layer of rubble between them, the initial height h of the story (below) is reduced to lh, with l denoting the compaction ratio (in finite-strain theory, l is called the stretch). After that, the load can increase without bounds."
Nothing happens to the upper floor element or any other structural elements in upper part C! Its height z0 is constant during the complete Crush-Down Phase!
This is evidently impossible as we know from above that when two parts of identical structures come into contact in an impact, both parts are affected. One small part, e.g. weak upper part C cannot transform a bigger part, e.g. stronger bottom part A, into dust, smoke and rubble ... and remain intact! Bottom part A is stronger than weak upper part C.
Fig. 1 - Figure 2 bottom from 
Since the initial Crush-Up phase terminates at very small axial deformation, it must be concluded that the simplifying hypothesis of one-way crushing is perfectly justified and causes only an imperceptible difference in results.
This new phenomenon one-way crushing of a 3-D structure has never taken place before and after 9/11 as it is physically impossible! Note no mention of forces! So how could one-way crushing of a 3-D structure suddenly occur on 9/11? Check again photos above!
Answer is that one-way crushing of any structure from top down is not possible under any circumstances. What is seen on videos and photos of the 911 WTC destructions is all faked! It is simulations type Hollywood, Dreamworks & Disney. And Bazant & Co fake it by assuming that big bottom part A is weaker than small top part C. In reality A is 100 times stronger than C (as A carries C before) and C can never crush A. C will always bounce on and remain on top of A that remains intact!
NIST has slightly different description of the one-way crushing down of part A by upper part C! From NIST report - NIST NCSTAR 1-6D chapter 5.2:
"The aircraft impacted the north wall of WTC 1 at 8:46 a.m. between Floor 93 and Floor 98. The subsequent fires weakened structural subsystems, including the core columns, floors and exterior walls. The core displaced downward At 100 min (at 10:28:18), the north, east, and west walls at Floor 98 carried 7 percent, 35 percent and 30 percent more gravity load loads and the south wall and the core carried about 7 percent and 20 percent less loads, respectively., At 10.28 a.m., 102 min after the aircraft impact, WTC1 began to collapse. The release of potential energy (PE) due to downward movement of the building mass above the buckled columns exceeded the strain energy (SE) that could be absorbed by the structure. Global collapse ensued."
can only apply forces/energy limited to its own
strength and then it will break up. No
one-way crushing can take
place! No rubble of steel elements is
generally produced, when failures occur, as
all elements, even broken ones, are still
connected to other elements. Only rubble is
damaged furniture and similar inside the steel
structure and it is of no importance.
C of a structure cannot crush down a bigger part
A of the same structure assisted only by
gravity. No global collapse can ensue for that
The upper part can only apply forces/energy limited to its own strength and then it will break up. No one-way crushing can take place! No rubble of steel elements is generally produced, when failures occur, as all elements, even broken ones, are still connected to other elements. Only rubble is damaged furniture and similar inside the steel structure and it is of no importance.
A smaller upper part C of a structure cannot crush down a bigger part A of the same structure assisted only by gravity. No global collapse can ensue for that reason!
8. Just watch the videos (they are all fakes) of the destruction and the rubble on the ground
The global collapse (sic!) or one-way crushing that ensued at WTC 1 can be seen here! Or just the start of it, the collision of the upper part C with the lower structure here as also shown below on two snap shots - fig. 2. All videos/pictures are fake animations! You can slide the video fwd/aft and see how the upper part C is first turned into dust and smoke, while everything below remains intact as shown below - there is no impact or collision:
Fig. 2 - Upper part C is destroyed! Note - the pictures are fakes!
The upper part C of WTC 1 is above the yellow lines applied on the photos (from Internet - reliability not guaranteed) of the WTC 1 tower at say floor 95 and the lower structure is below. Snap shot left above (fig. 2) is just before destruction of upper part C starts and snap shot right a few seconds later. It should be clear to anybody that the upper part C above the yellow lines simply disappears in the smoke and dust, while nothing has happened to the lower structure of WTC 1.
The aircraft impact point in the North Tower was between the 95th (yellow lines) and 96th floors with the aircraft nosed down at 10 degrees, but the North Tower collapse initiates 30 feet above at the 98th floor, where there was very little aircraft impact damage.
The first floors to collapse afterward are the 99th through the 102nd, which in addition to having no aircraft impact damage had little fire if any. In other words intact structure above the aircraft impact zone and main fire affected areas is actually collapsing first.
These observations alone should make it clear that the building was demolished and that the aircraft impacts were a cover for the demolitions to allow the collapses to be blamed on outsiders.
Evidently gravity alone cannot destroy, shorten, the upper part C before it, the upper part C is supposed to impact and collide with and crush down WTC 1 below!
Why is there so much smoke, debris and vertical deformation of the upper part C only?
It, the upper part C, is simply destroyed by some energetic material devices and there is no collision with the lower part. Same devices are apparently used to destroy the lower structure of WTC 1 a few seconds later. In the official accounts of the destruction of WTC 1 the upper part C is supposed to remain intact - its height z0 is assumed constant - and produce one-way crushing until the end of destruction and be crushed against the ground.
9. Rigid blocks, boxes or sponges
NIST speaks of the core of WTC 1 as consisting of three sections - NIST NCSTAR 1, p. 79:
"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 (i.e. below floor 93) that could be thought of as a strong, rigid box, structurally undamaged and at almost normal temperatures. There was a top section (the upper part C above floor 97) 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."
The section of the building above the damage zone, the upper part C, NIST calls a "rigid box."
This rigid box first manifests its independent movement, when it tilts to the south - NIST NCSTAR 1, p. 201: "The section of the building above the impact zone (near the 96th floor), acting as a rigid block, tilted ". Do you see that on photos above?
NIST also refers to this rigid block or box with terms such as "upper section", "building section above the impact zone", "building mass", "upper building section" and "structural block." - NIST NCSTAR 1, pp. 83, 195, 196, 201.
However, you have to treat the upper part C structure/stiffness in 3-D and then it becomes very springy - like a sponge; light structure of elastic material full of holes. It is quite difficult to destroy a sponge dropping another sponge on it. The other sponge bounces.
NIST acknowledges that this rigid block or box, upper part C, then falls. NIST says that "the building section began to fall downward", "the building section began to fall vertically". Do you see that on photos above?
It is suggested that this falling rigid block goes through all or part of the damaged area or initiation zone "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" - NIST NCSTAR 1-6, pp. 416, 238; NIST NCSTAR 1, p. 196. Do you see that on photos above?
And seen in videos? Where? None of above is seen anywhere!
After falling through all or part of the damaged area of WTC 1, the rigid block or falling building mass - the upper part C - encounters "intact structure". And, no surprise: "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." - NIST NCSTAR 1, p. 196. This is very strange! The intact structure was previously described as a rigid box! And there is no evidence for the suggestion!
Energy of deformation is the same as strain energy!
10. What is strain energy and can you calculate it?
Strain energy (SE) is simply speaking a measure of the strength of the elements of the structure that holds it together and can resist deformation and damage. Apply outside energy (force times displacement) on the structure that exceeds the strain energy that can be absorbed and the structure deforms or an element fails locally. If it fails, it fails in the highest stressed area only and the structure changes! Evidently the strain energy of the structure at every floor above, the upper part C, and in the structure below the initiation zone was about the same. However, in all official explanations of the collapses it is assumed that the upper part C is rigid with height z0 is constant and infinite strain energy from start and therefore will not deform and will absorb no amounts of extra strain energy at all! All free energy (or forces!) at impact is therefore assumed being directed down (?) into the lower non-rigid structure by NIST and its supporting experts. No forces are directed upwards!
The upper part C is however not rigid and can only absorb very limited strain energy during a crush down prior it self-destructs to forces acting on it and the destruction is arrested. To assume the opposite in various papers described below and indirectly by NIST is simply to mislead the public. The upper part C has a very limited capability to absorb strain energy - it will get destroyed - and that is the main reason why it cannot crush down the structure below and produce rubble. On the contrary - the upper part C structure should be subject to serious structural failures at impact and absorb the energy released and arrest further destruction. Not so difficult to grasp. That's why steel buildings of any type are not crushed down one-way by gravity acting on a loose top part due to local failures of some elements.
Bazant, like NIST, also assumes that the WTC 1 upper part C was rigid (!). Its height z0 is constant! A rigid object is indestructible and will destroy anything non-rigid. But ships and WTC 1 upper part C structures are not rigid and break up at impact or collisions (unless they just bounce) due to local forces developing.
The structural damage analysis are quite similar for A) and B). Very few mechanical, civil or building engineers have studied the subject (99.9% concentrate on design of new, intact structures) but there is nothing new about structural damage analysis . No need to write scientific papers about it, as it was a new event that had never happened before and needed explanation. Structural damages (ship collisions) occur every day. Steel structure tower collapses are much more rarer.
The Bazant papers described below are therefore very suspect. Enjoy this article. Comments are always welcome. And thanks for comments already given.
The thin, weak floors of the upper part C are in turn locally punched or sliced by the part A strong walls/columns below and will soon be jammed inside the part A walls/columns below. No walls or columns are dropping on other walls or columns producing an impact! Do not believe that the upper part C is solid, rigid, strong or anything like that! It is quite weak. Local failures - weak floors punched and sliced - will be produced at contacts. No crush down will ever start!
One way of demolishing a structure is to horizontally cut off vital connections of primary structure holding the structure together at the bottom, i.e. to reduce its strain energy in its strongest elements. The structure above will then drop straight down due to gravity and be damaged. It is called Controlled Demolition! You can try the same thing starting from the top, cutting structure horizontally up top!, but then you will create a fountain of rubble, when blowing broken structure sideways. See figure 22. Gravity only failures without further assistance do not produce rubble. Controlled demolition on the contrary produces plenty of rubble in the process of destruction.
To demolish WTC 1 with controlled demolition is very simple. As 37.4% of the total mass of the tower is carried by only 24 outer, albeit very strong, core columns of various thickness, it would appear that by cutting them at say 10 floors intervals, load transfers to the perimeter walls would break the walls and the tower would come down. Big sheets of intact perimeter wall columns assemblies, 10 floors high, would then be pushed out and drop to ground! You can see it on all videos of the destructions.
Access to these outer core columns appears very easy. How to quickly cut a 25 mm plate at very low cost is explained here. Similar devices can cut and burn steel columns.
14. The major NIST Problem - Lack of evidence!
The major problems with the NIST cause - a one-way crush down from top to bottom - are that fires normally only cause visible, local structural failures, deformations, fractures and displacements of steel structure elements that are soon arrested, when any energy released is absorbed by intact structure above and below the contact points and local failures - no global collapse or rubble . There is
(1) no evidence that the core structure displaced downward, as it could not be seen,
(2) no evidence of any simultaneously buckled visible, outside wall columns in the fire zone - no such damaged, buckled, columns have been retrieved from the rubble;
(3) no sign (evidence) of drop of the building mass above the buckled columns - the upper part C - at near free fall acceleration a certain height and time as a rigid, solid mass and associated release of potential energy, PE, and
(4) no indication (evidence) of an impact (the PE is now kinetic energy, KE) between the rigid, upper part C and the non-rigid structure below at which perfect alignment is necessary, which would be seen as a bump/deceleration on any video.
These four conditions are according NIST required for the upper part C to commence destroying, crushing down, the structure below, but there is no evidence for them. Evidence to the contrary will be produced below.
The upper part C is not really one part. It is a steel structure and an assembly of elements; columns and floors.
There is further
(5) no calculations by NIST of the potential energy, PE, released and the strain energy, SE, or lack of it, of the structure below (and above!) that could be absorbed proving it was less than the PE or KE transmitted to it by the upper part C permitting a gravity only driven global collapse/one-way crush down to progress or ensue,
(6) no mention or calculation of forces, deformations, fractures in and friction between locally and partly damaged floors and other elements that would absorb further energy after initiation,
(7) no explanation how the solid, intact columns below were overloaded by gravity only, what loads were actually applied on the columns after initiation and why the columns would rupture/fracture horizontally in 1 000's of pieces about 10-12 meters long,
(8) no explanation (or evidence) why the upper part C would remain intact at the (4) impact (except that it is rigid, which it is not), and
(9) no explanation why so much rubble (broken, fractured elements), smoke and dust were produced.
Evidently the potential energy released is transmitted to both the upper part C structure and the structure below - always as walls/columns punching/slicing floors - a fact that NIST conveniently forgets or ignores or intentionally censors. Actually 50% of any energy released should be absorbed by the smaller upper part C floors at impact and following deformation and local structural failures.
15. Evidence contradicting the NIST cause
All videos of the WTC 1 destruction show that the upper part C telescopes into or shortens itself or implodes for about 3-4 seconds (like the bottom structure below floor 16 of WTC 7 10 hours later), while the steel columns of the structure below are still intact prior any invisible impact! Gordon Ross has described this clearly 2007. The deformation of the upper part C cannot be produced by gravity forces alone. The upper part C is not very strong and you wonder how it can crush down anything - except itself - later? David Chandler explains clearly what happens in his video analysis 2009.
Fig. 1 - Figure 2 bottom from 
According Bazant  upper part C shall be 100% intact during these 3.1 seconds (and later of course) and produce an 11.7 meters rubble layer and destruction shall only take place below it and the rubble part. No destruction can take place above the rubble part, where upper part C shall remain intact!
What we are really seeing on above three pictures (fig. 7 A, B and C) is local destruction of both parts A and C and not a one-way crush down of part A by an intact part C producing rubble. In above picture right (fig. 7 C) it is obvious that the upper part C is being destroyed just after initiation of destruction and that there is no rubble below. No smoke and debris shall be expelled from an undamaged upper part C structure.
There are 1 000's of photos of the crush down that follows but unfortunately some are missing, e.g. those during the 0.8 - 0.9 seconds, when the alleged indestructible upper part C supposedly near free falls 3.7 meters - all columns fail there and disappear at one storey - and then collides/impacts with the structure below transmitting the total upper block KE.
Actually no such photos exist as no free fall or impact took place! And no intact upper part C is seen during the crush down destruction of the structure below that follows. The upper part C was simply destroyed prior to any impact.
The upper part C of WTC 1 is a problem for NIST. Its weight was not massive, only about 33 000 tons and the uniform density was <0.18! It consisted of 95% air. The load bearing columns - the primary structure carrying this weight - occupied only 0.13% of the total foot print or floor area in the initiation zone - the rest was air, floors and furniture, which is an indication how strong the lower steel structure columns were! The compressive static forces and associated stresses in the steel columns were low; <32% of the yield stress, i.e. a Factor of Safety, FoS, of elements against yield more than 3. And the built in strain energy, strength, to keep the upper part C together was exactly the same as for the structure below.
The American professor Z P Bazant, already mentioned above, published (13 September 2001) soon (2 days only!) after the WTC destructions an early explanation of his ostensible and passionate theory  that was adopted by the authorities, FEMA and NIST, as true. Bazant suggested that there were five stages until the doom/one-way total crush down of a structure as illustrated in Fig. 8.
Stage 4 (First one-way crush):
The vertical impact of the mass of the upper part onto the structure below applies enormous vertical dynamic load on the underlying structure below, far exceeding its load capacity, even though it is not heated.
(Actually 50% of the energy (the dynamic load) is transmitted to the upper part, if an impact and visible deceleration of the upper part would have taken place, and the upper part would have been destroyed very quickly; compare the rubber ball bouncing on a floor described above).
Stage 5 (Compression and more one-way crushing):
This causes failure of an underlying multi-floor segment of the tower, in which the failure of the connections of the floor-carrying trusses to the columns is either accompanied or quickly followed by buckling of the core columns and overall buckling of the wall columns!
(Not proven, of course. The upper part should simply bounce on the lower structure, while there are some local failures. Just buckling one column requires; first to deform it elastically vertically and sideways, then to produce three plastic hinges in the column, then to produce fractures in the hinges that must cut through the column; as soon as one fracture cuts off the column, there is no longer any contact and the top part slides off the lower part, etc).
Stage 6 (One-way crush down):
The part of building lying beneath, i.e. the structure below, is then impacted again by an even larger mass falling with a greater velocity and the series of impacts and failures then proceeds all the way down.
(This is impossible! Each column has now been cut off by one fracture at one plastic hinge and the upper part of a column can no longer impact a lower column. It will therefore contact something else - a floor! - and cause local failure there or just slide against other structure. Friction between loose parts absorbing energy should now start).
This Stage 6 is the famous 'one-way crush down' of a 3-D steel structure that nobody in serious structural engineering circles had ever heard of before 911, when it was invented by Bazant. Or after! Compare with the global collapse (sic!) that ensued that can be seen here!
In  Bazant (2007) points out errors in his previous paper and develops some new ideas about Stage 6:
"The kinetic energy of the top part of the tower impacting (sic - highlight by AB) the floor below was found to be about 8.4X larger than the plastic energy absorption capability of the underlying storey, and considerably higher than that if fracturing were taken into account. This fact, along with the fact that during the progressive collapse of underlying stories the loss of gravitational potential per story is much greater than the energy dissipated per story, was sufficient for Bazant and Zhou to conclude, purely on energy grounds, that the tower was doomed once the top part of the tower dropped through the height of one story or even 0.5 m. It was also observed that this conclusion made any calculations of the dynamics of progressive collapse after the first single-story drop of upper part superfluous."
"When the upper floor crashes into the lower one, with a layer of rubble between them, the initial height h of the story is reduced to lh, with l denoting the compaction ratio (in finite-strain theory, l is called the stretch). After that, the load can increase without bounds."
Does really the kinetic energy of the upper part C after a drop of only 0.5 m exceed the plastic energy absorption capability of the underlying storey and by a factor of 8.4, if the drop is 3.6 m, and is it relevant? Well, the upper part C is 53 meters tall and an underlying storey is only 3.6 meters tall and if you assume that the upper part C is like a solid hammer head and the underlying storey is a nail, then the hammer head will deform the nail. But no rubble will be produced. The hammer head, the upper part C will then slip off. Bazant assumes it hits again. To produce rubble you must hammer several times, repeatedly.
If, one the other hand you assume that the nail consists of 97 storeys, i.e. consider the whole structure below, then the underlying structure can elastically absorb 97 times more energy than just one storey and then the upper part will just bounce on the lower structure. The kinetic energy of the upper part C is just 0.086 of the plastic absorption capability of the total structure. And let's face it - the upper part C is not a solid like a hammer head! It is as flexible as the lower structure and will absorb 50% of the energy applied at alleged impact.
The kinetic energy of the upper part C was too small to do any real harm or initiate a crush down. The only result will be lots of local failures up top.
17. Upper part C is destroyed by forces acting on it
It is furthermore not the total kinetic energy of the upper part C that is applied to the underlying storey - only the forces applied by upper part C columns are locally damaging, fracturing the underlying floor. At the same time the columns below apply forces on and start to destroy the upper part C bottom floor in the same manner. To fracture, punch through or slice a floor requires energy. Locally damaged floors would then get entangled into one another, huge friction forces would develop and arrest further destruction. No impact! To suggest that the load can increase without bounds due to a layer of rubble is nonsense. Bazant ignores local damages to the floors, all fractures that develop and the huge friction between these locally failed floors as the main factors arresting structural destruction. The loads and forces are actually reduced, mostly by friction! And collapse arrest should soon follow!
18. Obvious contradictions
Regardless - Bazant 100% contradicts what NIST says about the system that supports the upper part C (repeat from above):
"The subsequent fires weakened structural subsystems, including the core columns, floors and exterior walls. The core displaced downward At 100 min (at 10:28:18), the north, east, and west walls at Floor 98 carried 7 percent, 35 percent and 30 percent more gravity load loads and the south wall and the core carried about 7 percent and 20 percent less loads, respectively., ." (NIST report - NIST NCSTAR 1-6D chapter 5.2).
Imagine an upper part C supported by a core and four walls and that the core below it (not seen of course) displaces downwards! Then the core cannot support anything above, unless the upper part C starts to deform, but why should it? It is undamaged. So, if the core displaced downwards as suggested by NIST, the core would then carry 100% (!) less load, i.e. nothing at all; actually the core must have been disconnected from the upper part C and the load on the core should be transmitted to the walls.
Furthermore, Bazant assumes in  that the lower structure can be regarded as a spring (while the upper part C is rigid and not a spring at all!) and wonders what its spring constant C can be:
"According to this hypothesis, one may estimate that C =71 GN/m (due to unavailability of precise data, an approximate design of column cross sections had to be carried out for this purpose)".
This results in an extremely stiff spring that does not really compress at all as a spring (more like a solid rod) and is easily locally overloaded, i.e. breaks in one point (at the top) but does not globally collapse. But if a big force, or 4F in figure below, would suddenly be applied to the top of a lower tower structure with flexible vertical columns supported by horizontal floors pin joint to the columns by an upper part from above (let's forget that the core has already displaced downwards), you would expect the whole lower tower structure to deform as shown below in fig. 9, i.e. bulge in/out between floors, before any failures occur! Simple Finite Element Analysis, FEA, or rather beam analysis shows this. The forces are evidently balanced by reaction forces at ground supports and the energy E applied to the structure, now stored as elastic compression d, is simply E = 4 F d.
Fig. 9 - Elastic, vertical deformation of of steel beam tower
19. The WTC # 1 and 2 towers were flexible
The WTC towers were in fact very flexible. Apply a very strong wind load sideways and the roof may deflect transversely 2-3 meters relative the ground. Assuming that a plane suddenly impacted horizontally at floors 95-96, the whole WTC 1 tower must have been displaced sideways (south) at least 1 meter or more there and then have been swinging back to vertical and 1 meter or more in the opposite (north) direction in say 10 seconds and more at roof level (not seen on any film of the collision). The mast on top must have been swaying a lot. People in the top floors should have been thrown into walls and furniture or on the floor due such a big, sudden impact from the side. Wind loads are less sudden but must have been felt earlier in the history of the building. Wave impacts on ships are described here. WTC 2 was impacted lower down and would only displace sideways (north) 0.5 meter at floor 77, then back to vertical and 0.5 meter backwards (south) but more higher up. Total displacement between extremes is >1 meter, which should be seen on any video, e.g. the Scott Meyers video of the west and east walls (distance between wall columns is 1 meter and maybe you will see them swaying? The author could not!) The tower would be oscillating for one or two minutes after impact and NIST has apparently analysed that. So much for transverse flexibility.
Regarding the lateral impact - e.g. an aluminium wing structure, the ax, chopping through a steel box wall column, the log - the pressure between aluminium and steel parts and energy applied at a very small contact area at high velocity (>200 m/s) must have been extreme causing high temperatures virtually melting the metal instead of fracturing it. The chop must have taken <0.002 seconds! The wing is then destroyed and cannot chop, e.g. internal steel core columns! However, the vertical impact later, upper part C dropping by gravity on part A, should have taken place at much lower velocity allowing the structures to deform.
A realistic value for WTC 1 as a vertical spring - vertical flexibility- being suddenly loaded from above is C = 0.5-1.0 GN/m at top and little more further down, the lower structure is also quite flexible, and then the upper part C should just bounce  on the lower structure at hypothetical impact disregarding local failures at contact points. You should in fact be able to see a big compression of the lower part A, if the upper part C actually impacted and then local failures would follow.You wonder why Bazant estimates spring constants 140 times bigger than a realistic one and that the upper part C remains intact and no elastic deformation of the lower part. To prove global collapse? His whole theory seems to be based on this estimate. However, David B. Benson, co-author of  with Bazant has 27 January 2009 explained to the this author:
"That result applies, strictly speaking, only to a one-dimensional homogenous crush down. Since the top portion was tilted and the sturcture (!) was not homogeneous, no damage to the top portion is only an approximation to reality."
The WTC1 destruction is evidently not a one-dimensional homogeneous one-way crush down of a homogenous rod and approximations should be avoided.
David B. Benson has also informed he has seen no videos and pictures of WTC 1!! His PC is too slow!
If any column would fail and not produce a bounce before that - Stage 2 in the Bazant theory - you would expect the following to happen to it in 3-D, when a compressive load is applied:
Fig. 10 - Five steps of buckling of a column due to vertical, compressive load
First, A, a plastic hinge develops in the middle of the compressed column due to lack of strain energy there, then, B, two more plastic hinges develop above and below the first hinge, then, C and D, the column 'kneels' and finally, E, a severely deformed part of the column may punch a hole in the floor below it. The column will never fracture in any location and it will never rupture due to fractures at the hinges into several pieces, i.e. it will always be connected, albeit very deformed. To suggest that 'buckling' of a column will result in free fall of the load it carries is not correct! The above deformation takes time and would be seen on any video, if it took place! Thus, Stage 3, of Bazant in not possible! It is an invention!
20. Strange explanations and real verifications
More strange explanations/inventions were given by Bazant (2008) in  with Frank Greening and David B. Benson joining.
In  WTC 1 is split into three parts during destruction; part A - lower structure to be crushed, part B - a layer of rubble being formed by a part C - the upper part - that remains intact and drives the destruction.
21. Mass and density of upper part C
23. Initiation of collapse - the first crush - formation of rubble part B
Thus at initiation upper part C 54 060 tons crushes the uppermost floor - say it is floor no. 96 - of part A, the lower structure of WTC 1, and compresses it into a 0.9 m thick layer of debris that becomes part B. This layer is resting on the second uppermost floor of part A. This compression takes place at increasing velocity. Only air/smoke is ejected sideways out between floors 96/95. The mass of the rubble - 3 670 tons - is uniformly distributed on the floor no. 95 below - 918 kg/m² - and this floor no. 95 floor should be able to carry that load according NIST FAQ.
Note that part C only compresses the storey floors 96/95 into a rubble layer - part B. It does not accelerate the rubble layer/part B. No solid parts are ejected sideways. The compression should be associated with a noticable deceleration of upper part C. Not seen of course.
What about the upper part C and its 54 060 tons? Is it acting on the rubble layer part B? Not really - upper part C is intact and only its bottom thin floor, floor no. 97, is in contact with rubble part B. The columns of upper part C are now not in contact with the columns of part A below due to this layer of rubble, but let's assume that upper part C columns crushes the columns below as suggested in , so that destruction can continue!
Then the upper part C + part B (the layer of rubble ) crushes the second uppermost floor of part A. This event can hardly be associated with a second impact by part C as it had just compressed floors 96/95. Regardless, now storey floors 95/94 is compressed into another 0.9 m thick layer of rubble that is added to part B. Part B rubble is thus 1.8 m high/thick after two floors of part A have been crushed.
If a typical storey of part A is 3.6 m tall, it then becomes a 0.9 m thick layer or rubble at crush down. This layer has a mass of 3.67 × 106 kg (or 3 670 tons) and uniform density 1 025 kg/m3.
It is suggested that the first crush down can be initiated by a 0.5 m drop of upper part C, thus the initial potential energy, PE0, applied is 0.5 x 54.06 × 106 x 9.82 = 265.44 × 106 J.
Then upper part C drops another 3.6 m and compresses one storey into 0.9 m of rubble, thus more potential energy, PE1, is applied; 3.6 x 54.06 × 106 x 9.82 = 1 911.13 × 106 J.
Total energy E applied is PE0 + PE1 = 2 176.57 x 106 J or simply 2.18 GJ to crush down the top storey of part A.
Bazant & Co suggest  that
the total energy dissipation per unit height, which represents the resisting force Fc, consists not only of energy Fb dissipated by the inelastic hinges formed during column buckling, but also of energy Fs required for comminuting concrete floor slabs, energy Fa required for expelling air from the tower, and energy Fe required for ejecting particles and fragments.
However, it seems Bazant & Co in their 1-D model miss the friction force required to compress and accelerate the rubble.
Anyway if total energy E = 2.18 GJ is used to buckle the columns, to comminute one floor, to expel air, eject particles and fragments and to compress the rubble into a 0.9 m layer, then after this second crush and compression part C and the rubble would have stopped. 2.18 GJ corresponds to about 606 kWh.
The total volume of rubble is after crushing one storey is 3 700 m3 with a mass of 3 760 tons. The unit amount of energy to compress one ton of rubble is thus only 0.161 kWh/ton. This may be compared with the amount of energy to shred a scrap steel stripped car that is about 36.8 kWh/ton in a very modern recycling factory, or 240 times more. Crushing grapes into wine also requires a lot of energy, the author is being told.
It is realized that shredding a thin steel plate car cannot be compared with compressing a composite steel columns/concrete floor tower, but in the author's the amount of energy to compress one storey into 3 670 tons of rubble seems very low.
The roof line has then dropped 5.4 m! The velocity of the roof line apparently is increasing - but why? It should slow down by so much sudden compression. More air/smoke should be ejected sideways from between floors 96/95, i.e. only from the storey being crushed. Can you see it on any video?
Furthermore,  suggests that part C and the rubble do not stop after the first crushes. On the contrary part C continues to accelerate and the rubble is also accelerated, while part A is being crushed again.
Thus we have to deduct the energy required to keep part C accelerating and to accelerate the static rubble to same speed as part C in above calculations to find the energy dissipated only to produce - part B - the rubble of crushing the first or second storey of part A. To accelerate 3760 tons of rubble to 20 m/s requires about 209 kWh, to 30 m/s it is 470 kWh, etc.
If, say, upper part C is not stopped after crushing one storey but continues to accelerate at say 0.65 g and that part B - the rubble - should be brought up from speed 0 to the speed of upper part C, then maybe only 30% of total energy E is available to buckle columns, comminute concrete, expel air, eject particles and fragments and compress the rubble, thus unit amount of energy to compress one ton of rubble becomes only 0.05 kWh/ton or 736 times less than shredding a car. In the author's opinion that is much too little to produce a crush down of any kind of 3-D structure. To crush one ton of grapes into wine requires more than 0.05 kWh. Try! It is a healthy exercise!
A more detailed energy balance is shown here when upper part C has dropped 31.38 meters. The potential energy applied to (lost in) the process is upper part C moving down 31.38 meters and 41.84 meters of part A crushed down 15.69 meters (53 000 000 x 31.38 + 41 840 000 x 15.69) x 9.82 = 22.8 GJ, which means that only 22.8 - 20.4 = 2.4 GJ of energy is used to compress 41 840 000 kg of part A into rubble B or 2 400 000 000/41 840 000 = 57.4 J/kg or 57 kJ/ton or only 0.016 kWh/ton WTC 1 structure.
And so on!
25. The displacement of the roof line of part C during destruction of 13 storeys
According careful observations in  we know that the roof line of upper part C dropped 35 m in 3.17 seconds at increasing velocity. We also know that upper part C roof line is accelerating at about 0.64-0.7g ! This means that upper part C, or what remains of it, as it is shortened and disappears, can only apply a force of 0.3 g or 30% of its own weight to crush floors of part A and build up the rubble layer - part B - ignoring the fact that it is upper part C that actually implodes.
Every time a storey is crushed, upper part C drops 2.70 m and an 0.9 m layer of rubble is formed according  and upper part C is remaining intact according Bazant & Co.
Thus, when the roof line has dropped 35 m, 12.94 storeys (!!), total height 46.6 m (!) of part A should have been crushed, and should have been replaced by an 11.66 m thick layer of rubble part B - with the upper part C still on top.
Writers of  believe that only 9 (or 9.72) storeys have been crushed but according  it should be 12.94 storeys! Writers of  forget that there should be an 11.66 m thick layer of rubble below the upper part C, when it has dropped 35 m after 3.17 seconds.
26. Verification of parts A and B using video recordings of the destruction of 13 storeys
Fig. 11 - Upper Part C being destroyed - No rubble Part B being formed (same as fig. 7 above)
Regardless does anybody see (fig. 11) an 11.56 m thick layer of compressed rubble part B on any (fake!) video after a 35 m drop of the upper part of WTC 1, part C according ? And that 46.6 m of part A - floors 96-85 - has been destroyed after 3.17 seconds?
It would appear that at least floors 85-93 are still intact!
And does anybody believe that an upper part C with density 255 kgs/m3 can produce an 11.56 m thick layer of rubble during 3.17 seconds and at the same time accelerate at 0.64-0.7g? Only  suggests so, but it is just an invention to suit a false 1-D mechanics model/theory of a one-way crush down.
This layer of rubble - part B - should then be moving at a velocity of >20 m/s and increasing as acceleration seems to be rather constant 0.64-0.7g. Only air should be ejected from the next storey below being crushed, where more rubble is formed. But upper part C cannot possibly both compress and accelerate part B at the same time! Ah, what funny model  invents! Don't they see that upper part C is destroyed?
28. Correspondence with G
After having published above G, Frank Greening, who co-authored  asked:
So, Heiwa (that's me), tell me what you see after a 35 m drop!
And I replied:
"Thanks for asking. There is plenty to see on the videos of the WTC1 destruction apart from a 'jolt' that nobody sees. Lately I have concentrated on those features that you postulate in your paper What Did and Did not Cause Collapse of WTC Twin Towers in New York  that I found in the Journal of Engineering Mechanics, ASCE, Vol. 134 (2008). And there are plenty features I do not see.
Of course, the title of your paper is misleading. WTC 1 never collapsed! It was crushed down from the top according to you. It - part A/lower structure below floor 97 - was crushed by a layer of rubble - part B - that was created when part C - the upper part floor 98 and above - dropped down. Part A never collapsed - each and anyone of its 97 storeys were crushed, one after the other.
According your paper - as I understand it - part C suddenly dropped (its support were weakened by fire/heat and buckled) and impacted on floor 97 of part A. This impact allegedly destroyed the columns between floor 97/96 and floor 97 dropped down on floor 96. I do not see that on any video.
It is now the crush down of part A starts. When floor 97 drops down it becomes a 0.896 m thick layer of rubble - that you call part B - that contacts floor 96 of part A. This rubble is volume vise about 3 600 m3! The uniform (!) density of structure floors 97/96 was originally 0.255 according you (plenty of air). The density of the rubble is 1.025 according you so compression takes place. It is part C that compresses structure floors 97/96 75.1%.
I do not see that on any video.
To compress rubble requires energy applied by part C and it seems you do not consider that in your differential equations. To compress rubble you must overcome friction in the rubble. As the solid parts of the rubble have density 7.8 (columns) and 2.5-3.0 (concrete) there must still be plenty of air in part B - the rubble layer.
I do not see this rubble layer on any video. To compress 14 400 m3 of structure with density 0.255 to 3 600 m3 of rubble with density 1.025 requires plenty of energy! I would expect the destruction to stop then. But I do not see that! Instead upper part C soon after accelerates constantly a 0.7g due gravity. Not possible if part C shall compress rubble at the same time.
Anyway, next crush is floors 96/95. Now it is a layer of rubble - part B - with part C on top that damages part A. An impact between parts C and A is impossible with so much rubble in between. You suggest that parts B and C now overloads floor 96 (pancake theory?) so floor 96 drops down.
Fair enough! I don't agree and I do not see it, but this is what you suggest. According videos (and your own paper) acceleration of part C is now 0.65-0.7g.
Part B - the rubble layer doubles in thickness - and the crushing continues another 11 floors of part A at constant acceleration 0.7g.
So after a 35 m drop of part C - it takes 3.17-3.3 seconds according your differential equations and acceleration given above - total 13 floors of part A have been crushed (should be floors 97-84), 46.6 m of perimeter walls have failed in pieces and part B has become 11.56 m thick and part C should remain intact on top of the rubble !
Frankly speaking nobody can see that on any video.
What I see is that part C - the upper part - explodes in its lower part - floors 98-105. Controlled demolition no doubt! That's why the roof line has dropped 35 m. I do not see an 11.56 m thick layer of rubble on top of floor 84! Actually I can clearly see that floors 84-96 are undamaged!
So much for your model and theory, G.
So what do I see, when there is 36 floors to crush (61 floors of part A have been crushed)?
It is always nice with reader contacts! I will update this page when G clarifies his motives.
29. More funny explanations and air jets clarified
The authors of  suggest (fig. 15):
"The 53 meters high upper part C, intact, rigid and of uniform density at start of crush down remains INTACT after the global crush down ... on top of all rubble that the upper part has produced of the structure below ... and only then finally destroys itself in crush up as illustrated in figure ... left. The destruction of the upper part is the last event of the gravity driven global crush down."
All these assumptions, apart from being ridiculous, are false. A rigid body, an upper part C, does not exist! By definition a rigid body destroys anything non-rigid it touches. But the upper part C is destroyed before the destruction of the lower structure commences.
Note, e.g. the Bazant explanation for air jets. The upper part C intact, with an air tight bottom floor (with a thick layer of compressed rubble below it - part B) is supposed to compress the air in the top remaining storey below - part A - and blow out (?) the debris and rubble before the wall columns are affected. The crush down has changed in character. No compression - now it is blow out! To compress this storey takes 0.07 seconds according , i.e. the velocity of part B - the rubble - is 51.4 m/s! Ask yourself what produces these air jets, if there is no upper part C or rubble layer part B, and when the air jets can be mistaken for smaller air jets seen preceding the destruction - fig. 5 - by 10 storeys. And where does the rubble being ejected come from? It is ejected horizontally! Local failures due to gravity do not produce the big amount of rubble ejected horizontally as seen on the videos! And according  the rubble should just be compressed to form part B.
No, photo fig. 16 above of smoke and dust outside a crumbling tower and air jets below from intact floors is just from a stupid animation of computer generated images done by Hollywood.
Another 'expert', K. A. Seffen, in a paper  suggests that the potential energy released by the mass above - the upper part - resulted in dynamical "over-loading" of the undamaged columns of the structure below by a factor of 30 compared to their static load capacity at impact and transmits it to the complete structure below and shakes it into pieces. Seffen also treats the problem in 1-D: a line that becomes shorter!
Seffen assumes that during a gravity driven collapse (or crush down or over-loading) a tower of height L and uniform density ro consists of three parts (fig. 17):
These are the false assumptions of K.A. Seffen:
(1) the tower has uniform (<0.18) density ro, while it is not uniform at all; it consists of solid steel columns 0.13% of the floor area (with density 7.8), weak reinforced concrete floors 99.87% of the floor area (with density about 3 but spaced 3.7 meters apart) and 3.6 meters of air (density <0.02) between floors and columns,
(2) the lL upper part begins to accelerate downwards as a rigid, undamaged body with uniform density ro, while it is seen to self-destruct on all faked animations,
(3) the initial load imposed onto the structure below was exceptionally high, while is not established how and when it contacts the structure,
(4) the damage, no new failures seen of course in the smoke, was bound to propagate, and
(5) fractures in and friction between locally damaged parts in contact with one another can be ignored.
Alignment of upper part with columns below is conveniently forgotten. According to Seffen the rigid lL upper part drives the crush down. And the upper part is not slipping off the structure below.
31. Unproven assumptions and collapse arrest
There are many unproven assumptions by terrorists like Bazant & Co. associated with the WTC 1 crush down destruction apart from treating the process in 1-D, i.e. lack of evidence for, e.g:
1. All support columns suddenly disappear/buckle in the fire zone below the upper part C (they should just 'kneel').
2. The upper part C near free falls or drops 3.7 meters (it cannot as it is connected via deformed columns to the structure below - part A).
3. The upper part C impacts the structure below, part A, with perfect alignment (it cannot happen!) and produces a layer of rubble, part B.
4. The upper part C and its bottom thin floor are still intact due to massive strain energy in it (it is assumed rigid and remains so for while - compare 7. below).
5. The upper part C (mostly air - uniform density <0.18 or 0.255 ) assisted by gravity only destroys the solid steel columns below (the columns break/fracture horizontally every 10-12 meters like spaghetti) and produces 0.9 meter rubble and débris of every storey.
6. Friction between parts, floors, of the upper part C rubbing against parts, floors, of the lower structure does not exist.
7. The upper part C and the rubble part B produce air jets in the structure, part A, below, that blow out the débris and throw out the rubble 200 meters!
8. The upper part C lands intact on a 70-80 m high heap of soft rubble after a successful one-way crush-down of the tower.
9. The upper part C finally self-destructs in a crush-up (!) of the soft rubble, i.e. suddenly it is not rigid anymore!
As with all real conspiracy theories there are no evidences for them.
Bazant's & Co's crush down theory is based on a rigid, intact upper part C that is not damaged by local failures, when first losing its supports and later, when in contact with the structure below. The upper part C bottom floor (no. 97) remains air tight, flat and solid, etc, like the rest of the upper part C! It thus has massive strain energy built in and is supposed to be much stronger than the structure below (but not stronger than rubble on the ground). But it does not really matter -  suggests that a layer of rubble - part B - increasing to 70-80 m thickness destroys WTC 1.
"I admit my model calculation is very crude, but it shows that a gravity-driven collapse of WTC 1 & 2 was physically possible without the help of explosives! My model may not see everything that happened; you, on the other hand, see things that never happened ".
Exactly the Bazant 1-D solid mechanics model is very crude and has nothing to do with reality! The nine invented events or assumptions listed above cannot be seen and never happened. Local deformations, failures, fractures and friction alone of the elements of the 3-D structure would have stopped the destruction very early. Part C would have got stuck up on top of part A. No rubble layer part B would have been formed. And why say that the structure below collapsed, when it was just crushed down one-way by the upper part C producing a rubble layer, part B, and throwing out loose parts sideways according a new phenomenon never seen before? Nobody has ever heard of steel 3-D structures being crushed down by an upper part above with equivalent strength as the structure below, but everything must happen a first time. Twice - within an hour.
32. Collapse Arrest - Happens all the time!
Bazant, Greening, Benson and Seffen incorrectly assume that the upper part C can absorb massive amounts of strain energy to remain intact during any local failures, i.e. the upper part C is indestructible. That is a puerile assumption and apparently intended to fool people.
What a reasonable person using clear thinking would expect after local failures of supporting structure in the initiation zone - even very serious ones - is that the forces in the structure of the upper part C would be redistributed and cause failures there and that gravity would just slowly (no free fall, no sudden release of PE) pull the upper part C assembly down, i.w.o. local failures. The upper part C is always connected to the structure below albeit by deformed columns. Some parts may then contact the structure below and cause further damages or get damaged like in a soft collision (no impact!), and after that primary and secondary structural parts of the upper part and the structure below would get entangled into one another and friction develops.
33. No rubble would be produced!
Evidently the structure below will cause serious damages to the upper part C structure above at once, when the upper part C displaces downwards and makes contact with the static structure below. It means that the Bazant, Seffen, NIST assumption of an undamaged upper part C during the whole destruction or crush down is proven wrong ... at once. This strange misty assumption - that the upper part C remains intact - is suspicious. Very suspicious. Has nothing to do with reality.
If the upper part C masses drop or move, their PEs become KEs. Each part mass has its own PE/KE due to gravity. And each part mass starts at a different location and will drop on a different location by gravity on the structure below.
The structure below of WTC1 is fairly complex - 280+ columns, 94 floors, etc. The columns only occupy 0.13% of the total cross area of the tower. What loads are applied on them at an impact? Probably none as they are small and any load will slip off.
The uppermost floor of the structure below thus occupy 99.87% of the cross area. What loads are put on it and where and when? There are different masses dropping down or moving. And what parts will rub against each other and what are the frictional forces?
In order to analyze the damage initiation you evidently apply the loads to the structure below and see what happens! Does global collapse or crush down or whatever starts and is rubble produced or is it just local failures that are arrested and no rubble?  The analysis is based on experience from ship collisions.
34. No rubble is produced by local failures!
So let's assume (see fig. 19 below) that the upper part gets lose (A). It means that the potential energy available in a one-story drop was greater than the local strain energy to be overcome in the initiation zone, i.e. crushing all columns there. It is furthermore assumed that the compressive force, necessary for a descent was available; otherwise the motion would not start, i.e. no initiation. If these assumptions are not fulfilled, the conclusion is that the motion will be arrested already during the damage of the initiation zone and the building will stand.
What happens then?
In this funny simulation complete upper part (floors are not bolted to the columns) first bounces on the lower structure as expected, upper part perimeter wall then becomes disconnected from core (no bolts assumed) and will drop down outside while upper part core gets entangled in the lower structure core and is arrested there. Lower structure perimeter wall remains in place! Nothing is resting on it!
However, let's assume that the upper part gets misaligned (exaggerated in fig. 19 below) and is shifted outside the lower structure on two wall sides and inside on the two other wall sides of the lower structure (B) and goes down (C). Similar misalignment takes place at the core. The original interface between upper part and lower structure changes. Before the primary load bearing solid steel columns were connected. Now they are only in contact with secondary structure; the thin, mainly concrete floors or with nothing outside the building! It is now the 'impact' or collision or contact starts.
If the upper part columns are not misaligned with the lower structure columns and there is perfect contact of all columns of upper part and lower structure at collision/impact, the upper part would be subject to a visible jolt and deceleration  at contact. As such perfect contact is impossible to take place under any circumstances - the columns will slide off - here it is thus assumed that the solid columns contact the thin floors or air outside the structure.
The upper part walls steel columns (right in C above), misaligned on the inside of the lower structure, will now punch or slice through the first red floor below the initiation zone - the red floor hinges down on the red floor below as it is only bolted to the core column/beam - while the upper part walls steel columns (left in picture C above) misaligned on the outside will drop in the air and hit nothing! Actually only half the mass/walls of the upper part carried by the walls participate in the local failures/crashes that follow and results in tilting of the upper part.
;;;;;;;;;;;;;;;;;; xxxxxxx;A ;;;;;;;;;;;;;;;;;;;;;;;;;;B ::::::::::::::::::::::;;;;;;C:::::::::::::::::::::::::::::D xxxxxxxxxxxxxxxxxxE
On the other hand the steel columns of the structure below (left in C above) on the inside of the upper part will slice/punch through the first, lowest green floor of the upper part - and it hinges down too on the red floor below! You do not need much energy for that. And the walls steel columns of the structure below on the outside of the upper part (right in picture C above) will remain ... intact, as they are not contacted by anything!
Similar floor failures occur at the core but there the steel columns are fewer and spread around and interconnected by horizontal beams to which the floors are bolted. These latter connections will shear off and the floors will hinge down around the opposite edge.
Does anyone believe that the upper part will fall vertically - at near free fall speed - under these circumstances of local floor failures - and crush down parts below - which is the fundamental assumption of Bazant, Greening and Seffen? No free rubble (lose structural parts) can be produced that would provide extra energy and drive the destruction further!
What a free fall drop is, is explained at web site http://uk.youtube.com/watch?v=gC44L0-2zL8 . Or try to click here! The WTC 1 collapse can be seen at web site http://www.youtube.com/watch?v=dtx_GcFCs6c&feature=channel_page . Or try to click here here! Internet is funny. Sometimes the link doesn't work! I wonder why?
Progressive local failures of structural parts have however started in the little example due to the original energy input and local failures! Thus we have to see what happens at the next floors above and below applying all the relevant contact loads there in proper order as per [4.1, 4.2 and 4.3].
The upper part is thus assumed to continue moving down due to gravity, but there is no free fall, only local failures and fractures in the floors and friction between bent and punctured parts in contact producing friction and absorbing energy and slowing the downward movement. No rubble is produced! No air jets are produced! And no débris can be ejected as there is no loose débris produced!
In D the upper part right wall solid steel columns inside the structure below are assumed to have sliced three red floors in the structure below and these floors have hinged down below the green floors of the upper part that have also been cut by the strong wall columns of the structure below inside the upper part. Similar failures take place at the core.
35. Massive frictional forces develop
Evidently this asymmetric destruction pattern of local failures will tip the upper part against the intact (right in D above) steel wall of the structure below held together by spandrels and the upper part will soon be jammed, e.g. in E when outside walls of the upper part (left in E above) has been sliced off by the columns below and dropped to the ground. All the floors of the upper part however remain jammed in the top of the structure below.
Fig. 20 - from 
If the upper part drops and accelerates at 0.75 g  and the punching of holes in the floors by the columns and hinging down of the locally failed floors take no time, the upper and lower floors themselves, spaced 12 feet apart, will contact each other after about 1.0, 1.4, 1.75, 2.08, 2.3, 2.53, 2.75,2.88, 3.17 and 3.3 seconds, i.e. after 3.3 seconds 10 floors of the upper part would be entangled in 10 floors of the lower structure ... and the WTC1 would be 120 feet shorter as per above fig. 20. It is very likely that the destruction would be stopped earlier.
logical local pattern of destruction is not
considered by NIST, Bazant or
This logical local pattern of destruction is not considered by NIST, Bazant or Seffen.
36. Other possibilities
There are other possibilities of serious local structural failures and what may happen. In fig. 21 below it is assumed that three green floors in the upper part fail in their bolted connections to the wall columns (B) due to fire/heat in the initiation zone and that the green floors hinge down on the red top floor of the structure below. The green floors are still connected/bolted to the core acting as a hinge.
xxxxxxxxxxxx A xxxxxxxxxxxxxxxxxxxx B xxxxxxxxxxxxxxxxxxxx C xxxxxxxxxxxxxxxxxxxx D
Fig. 21 - Upper part wall panels dropping off due to failures below
The result would be that the walls in the fire zone buckle inwards on top of the green floors that dropped down previously (C). The walls of the upper part are then hanging on the hat truss in the roof that is assumed to deform downwards. The walls above do not transmit any forces to the walls of the structure below!
The outside floors in the upper part are thus pulled down by the unsupported walls of the upper block. The extra load in the hat truss is transmitted to the core columns at the top that buckle locally at the weakest areas just below the hat truss due to overload. The roof and the mast on top displace downwards (C) a couple of meters. Due to these deformations and displacements of the upper block parts the floor bolts shear off at the walls (it is assumed they remain intact at the core), the walls of the upper block gets loose and falls down (D) and slips off on parts off the walls previously buckled inwards acting as a damper on top of the damaged green floors in the initiation area and drops to the ground ... and the collapse is arrested. Or the green floors hanging on the upper part core pull down the upper block core more until they contacts the inwards buckled wall below and are diverted outside the tower ... when further destruction or collapse is arrested. No crush down will occur! No free rubble is produced.
It should be noted that in this second example, fig. 21, the local failures at the fire zone - the green floors dropping down and the walls buckle bending inwards - result in further local failures 58 metres higher up due to local forces in the upper part structure being transferred there due to the first failures below. The upper part is evidently not just one 'parts' but consists of many parts, and the weakest ones will fail, when any supports below fail. Thus the upper part will be part destroyed prior anything can happen to the structure below! This is a fundamental part of collapse arrest analysis of steel structures.
38. Dangerous Sect at Work
In the struggle against great, organized, sectarian forces of intolerance and insane self-assertion it is important that scientific reports, papers and analysis of damaged and destroyed steel structures are done by honest people using correct thinking, right feeling and proper estimating of facts. Confused thinking, bad passions, dishonesty, corrupt manners, erroneous assumptions and haste do not contribute to a better understanding of the world around us. They are only normal parts of dangerous sects that threathen us.
quite basic and all due to forces and that part
C has identical structure as part A.
size and particulars of the elements of the
structure A doesn't matter the least. Part C of
A cannot destroy A. Flying
planes into weak tops of skyscrapers or towers
will not destroy the intact strong skyscraper or
tower below the top. No
skyscraper or tower can collapse from top.
happens in stupid Hollywood
It is quite basic and all due to forces and that part C has identical structure as part A.
Materials, size and particulars of the elements of the structure A doesn't matter the least. Part C of A cannot destroy A.
Flying planes into weak tops of skyscrapers or towers will not destroy the intact strong skyscraper or tower below the top.
No skyscraper or tower can collapse from top.
It only happens in stupid Hollywood animations.
Zdenek P. Bazant, F.ASCE, and Yong Zhou (2001)
Zdenek P. Bazant, Jia-Liang Le, Frank R. Greening and David B. Benson (2008)
K. A. Seffen, Cambridge University
Professor Ted Krauthammer, Protective Technology Center, The Pennsylvania State University, Robert L. Hall, PhD, Stanley C. Woodson, PhD, James T. Baylot, PhD, John R. Hayes, PhD, US Army Engineer Research and Development Center, Young Sohn, PhD, Defense Threat Reduction Agency
10 engineers think structures collapse from above!
"Recent dramatic collapses of buildings due to blasts exemplified by the World Trade Center Towers in New York City on September 11, 2001, may not be examples of progressive collapse."
Zdenek P. Bazant, F.ASCE, and Mathieu Verdure (2007)
Graeme MacQueen, Tony Szamboti, January 14, 2009