The mass/load above a column evidently compresses it. The columns act as springs. As long as the compressive stress is less than yield stress, the compression is elastic and hardly noticeable. As seen above the actual compressive stresses were only <30% of yield stress and it is assumed this was common practice in steel tower construction in US and elsewhere in the 60's.
How is the yield stress of steel affected by heat? In this writer's opinion it is not affected very much at about 500°C. This is confirmed by any fire test - the test chamber and what's in it never collapses due to the heat inside up to 1000°C. The heat inside is normally by kerosene set on fire.
English authorities concur: "Although the formulae cannot provide perfect fitting with the test data at all temperatures, the correlation at temperatures above 400°C is in good agreement. Generally, the lack of accuracy at low temperatures below 400°C will not hinder the accurate prediction of fire resistance of steel structures in practice. This is because the actual loads applied to most buildings are commonly below 60% of the ultimate loads they are designed for at ambient temperature. That means the structures will generally have a minimum inherent fire resistance of 500°C."
As noted above the stresses in the WTCs were less than 30% of the yield stress. But let's assume the yield stress is reduced 20% due to heat. The compressive stress in the allegedly heated core columns is still then less than 40% of the yield stress. The wall columns are lesser stressed.
The purpose of fire proofing of steel is not to prevent collapse or melting (!) of the steel. The purpose is only the delay transmission of heat and to allow the heat to dissipate to adjacent structure. In the WTCs no structure was heated >500°C at any time according NIST even if the fire proofing were missing. Fire proofing of subdivisions/walls delays the fire to spread. Fire proofing of internal steel structure elements delays, e.g. thermal expansion and deformation of the structure. That fire/heat can produce local structural failures of steel elements that in turn produce a complete collapse of the steel structure involved is unheard of. 911 was the first time it happened. Trice! Anybody suggesting that open fire can melt steel is a charlatan. Plenty of steel ships have caught fire and not one part of them has ever melted. Boilers and engines are made of steel - and do not melt!
It is very easy to check in a fire test chamber how a steel column under compression at 30% the yield stress resists collapse due to heat at 500°C allegedly existing in the Towers. The answer is that it does not collapse. You can verify this yourself - see 8.1 below.
Applied to WTC1 what you would expect due to a fire around the core columns is that they only compress and that their cross areas expand due to heat and the downward movement of the core is a few centimeters! It may put some extra tension in the floor trusses and their bolted connections pulling the perimeter walls inwards a few centimeters - and that is all! The wall perimeter columns, 80% of them are intact and free of soot and marks of fire as shown on many videos and subject to little heat as they are cooled by fresh air, will then further stabilize the core.
7.2 The columns cannot bend 180°, twist or crumple up
Remember that the outer core columns are extremely solid, e.g. no. 501. It is an H-beam with two flanges 17x3.5 inch connected by a 2.2x12.6 inch web. In metric terms the flanges are 430x90 mm and the web is 56x320 mm. Such thick plates, 56 and 90 mm cannot buckle under any circumstance when the compressive stress is only 30% of yield stress, even if the temperature is 500°C. The (smallest) moment of inertia I of this section is about 120 000 cm4, area A is 953.2 cm2 and its radius of gyration r is thus of the order 11 cms. With a free length l of 350 cms the slenderness ratio (l/r) is 32! Such a column will not buckle! Same for the wall columns that have a radius of gyration r of abt 15 cms and a slenderness ratio of 24, when supported by spandrels and floors. We know how the core columns were joined bolts or welding and that it seems most failed at their weld planes or with bolts ripped apart, with little to no buckling involved.
Therefore there will be no downward movement. And no impact!
7.3 There is no release of potential energy
NIST does not calculate the amount of potential energy released due to downward movement in their report, which is therefore incomplete. The simple reason is that no potential energy is released. In fact, no downward movement of a mass above is even possible due to heat inside the cage and there should be no sudden release of potential energy.
This is easily verified at any fire test laboratory. NIST has never done such tests! NIST should be encouraged to do such tests, e.g. 8.1 below.
The 236 off wall columns are, never seen to deflect at all prior to the sudden, initial dropping down of the roof. If the core columns collapse, as alleged, by release of potential energy above, the wall columns should remain intact as no release of potential energy is acting on them! Weakening is inherently a GRADUAL process and CANNOT BE SIMULTANEOUS EVERYWHERE throughout a given 4 000 m² large floor area! It will always be local and topple the mass above in the direction of the local collapse.
But let's assume that potential energy is released vertically as all low stressed columns wall/core collapse simultaneously and are removed allowing a free drop.
When 33 000 tons of mass above in WTC 1 falls down 3.7 metres due to gravity during and crushes all the columns abt 340 kWh (1.22 GJ) of potential, PE, or kinetic energy, KE, is produced by gravity force and a fair part of that energy is consumed to crush the columns. Let's assume that this event by gravity takes 5-6 seconds based on video clips (it should only take 0.8-0.9 seconds at near free fall acceleration) and that there is a certain velocity when the upper part impinges the lower structure. In reverse - to first stop and second pull the upper block back up again you need a very big engine with power 204 000 kW that pulls up the mass above. Let's assume this engine is very effective and that you require 120 grams of diesel oil to produce 1 kWh. It means that 40 800 grams or 40.8 kgs of diesel oil is required to stop and pull the mass up again! It takes 6 seconds! It can be done. It shows how much energy was released when the top fell. 40.8 kgs of diesel oil.
But is this what we see on this (faked) video or this (faked) video of the fall of the mass above? That all the columns at the initiation zone crumple up during 6 seconds? Evidently not! We can see the roof of the top of the mass above starting to move and that nothing happens at the initiation zone = no crumbling of columns there. After 2-3 seconds the mass above seems to disintegrate and after 4-5 seconds smoke and dust spew out through the windows at the initiation zone, where the wall columns are still intact. They have not crumbled! This will be further shown in 7.7 below.
It is interesting to compare the energy released by the top of WTC 1 at impact of the bottom part of WTC 1, i.e. 1.22 GJ, with the energies applied on the Towers by the aircrafts earlier. The mass of each aircrafts was about 150 000 kgs and the impact velocities were estimated at 211 m/s and 265 m/s. So at impacts about 3.34 GJ and 5.27 GJ energies were applied sideways and caused some local failures to the Towers and shredded the aircrafts. Thus 2.74 and 4.32 times more energy was involved in the sideways plane impacts than in the vertical impact of WTC 1 later. As the Towers were much weaker sideways than vertically, you really wonder why WTC 1 suddenly collapsed by a vertical impact of much less energy than the planes had applied sideways!
The authorities suggest that the energy released by the WTC 1 top part was enormous, but in fact it was 3-4 times less than what the aircrafts applied earlier!
It is in fact a very strange
release of potential energy due to alleged downward
movement of an
part mass above! The
wall columns at the initiation zone did not buckle,
deform or crumple up, when the mass above (the
roof) has allegedly been falling down for 4-5
seconds. Evidently the wall columns in
the initiation zone should buckle, deform and
collapse synchronized - at the same time and
speed - as the movement of the mass
release of potential energy due to
downward movement of the building mass
above the buckled columns
exceeded the strain energy that could
be absorbed by the structure. Global collapse
It is in fact a very strange release of potential energy due to alleged downward movement of an upper part mass above! The wall columns at the initiation zone did not buckle, deform or crumple up, when the mass above (the roof) has allegedly been falling down for 4-5 seconds.
Evidently the wall columns in the initiation zone should buckle, deform and collapse synchronized - at the same time and speed - as the movement of the mass above.
"The release of potential energy due to downward movement of the building mass above the buckled columns exceeded the strain energy that could be absorbed by the structure. Global collapse ensued."
But let's again assume that the mass above drops down 3.7 meters due to gravity acceleration 9.8 m/s². It means that the speed after 3.7 meters displacement is abt 8 m/s or 30 kms/h. It is not a significant speed. A collision at such low speed is not an impact! It is a bump and the velocity should be considerably reduced. And do really 280+ columns of the upper part really simultaneously impact the 280+ columns of the lower structure? Or do they slip off?
7.6 The timetable - time for cause and time for effect
In order to establish what happened to WTC1 we need to know two times for two events that allegedly occurred: the time Tcause, when the potential energy, PE, was released due to all columns in the initiation zone collapsing simultaneously, i.e. the time of the cause of the disaster, and the time Teffect when this energy was applied to the structure below at an impact, i.e. the time of the effect. NIST and Z P Bazant do not advise these times. Nothing should evidently happen to the WTC1 before Tcause. If anything strange happens before Tcause, e.g. the roof is moving, the upper part becomes shorter or smoke suddenly erupts, it cannot be due to the columns in the initiation zone collapsing releasing potential energy. Also the time difference (Tcause - Teffect) cannot be more than 0.8-0.9 seconds, because that is the time for the potential energy to reach and impact the columns of the tower below, if we assume that the distance of fall is one floor level = 3.7 m without obstructions. During this time also nothing strange can happen. The global collapse that ensued after Teffect according NIST has still not started. The lack of a proper time table in both the NIST report and the Bazant report is very disturbing. The times are evidently available from all videos of the incident. Can anybody provide a time for the alleged impact?
NIST and Bazant talk about an upper solid, rigid part above the initiation zone that suddenly falls down as a hammer on all columns below and causes global collapse at a crushing front - actually 280+ crushing fronts - one in each column! This is the second assumption of Bazant:
(2) Energy is dissipated only at the crushing front! This implies that the separate parts of the upper and lower part of the collapsing tower may be treated as rigid, i.e., the deformations of the parts away from the crushing front may be neglected.
There are many fake videos (animations) of the WTC1 incident but NIST and Bazant never show us the famous upper rigid part at times Tcause (hammer/upper part starts to fall) and Teffect (hammer/upper part hits all the columns below)!
It is evidently quite easy to sketch in the rigid upper part at time Tcause, when it starts to drop, on any fake video or fake photo, so that we know what they talk about, and then to do the same at time Teffect, when the same upper part impacts the columns below, to show that the upper part above actually remains rigid, intact and unchanged all the time, while the columns are deformed below it. In below pictures of the initial collapse the assumed initiation zone at around floor 98 is indicated with a blue line. The upper red line is the original roof level. The lower red line is around floor 93. A green vertical line has been added beside the right wall. The upper part is originally between the upper red line and the blue line. Note that all pictures below are from fake, animated videos.
In Bazant's theory the upper part above floor 98 is supposed to be rigid and intact until the end of global collapse about 12-14 seconds after Teffect.
Same thing from another angle, where the disappearance of the upper part is clearer (!):
In Bazant's theory the upper part above floor 98 is, as already stated, supposed to be rigid and intact until the end of global collapse about 12-14 seconds after Teffect.
Want to see more faked animations? Notice how the upper part between floors 110 and 98, height abt 50 meters, drops down from floor 98 to floor 92, a 25 meters drop, and nothing happens below floor 92. The upper part is compressed 50% ... and nothing happens below it.
You wonder why NIST and Bazant cannot show us in their reports a time table for the 33 000 tons upper rigid part and its potential energy first initiating by impacting the columns below and then producing global collapse - all columns fail. It seems that the upper part is disappearing (!) at Teffect and a few seconds later in the animations before global collapse of the structure below starts. The terrorists got it all wrong in the animations.
Thus we can conclude that the Bazant second assumption -
"Energy is dissipated only at the crushing front! This implies that the separate blocks of the upper and lower part of the collapsing tower may be treated as rigid, i.e., the deformations of the blocks away from the crushing front may be neglected"
- is not true. Both parts are flexible. Furthermore only 50% of any energy released is transmitted to the structure below. The other 50% is transmitted to the upper part. Back to Summary! While reflecting about this lack of easy to understand photo evidence in the official reports and university papers ...
4 off steel pipes, length 750 mm, dia 20 mm wall thickness 1 mm (each cross area 62.83 mm²). Yield stress 23.5 kgs/mm²
2 off 1000 x 1000 x 5 mm steel plates (weight about 40 kgs)
4 off 1000 x 1500 x 5 mm steel plates (each weight about 60 kgs)
4 off 960 x 4 x 3 mm steel flat bars (spandrels)
4 off plywood sheets 995 x 920 x 5 mm. Make some holes in them to allow air to enter and smoke to escape! One hole can look like as if a model air plane has made it.
You weld the pipes to the corners of the square steels plate and you get a steel 'table' with four legs. Each leg has slenderness ratio abt. 75 with fixed upper ends at the top. Weld the spandrels between the legs at about half height.
Put table on firm ground, e.g. cement floor.
Then weld the four other plates on the top of this table to form a 'water tank'.
Fix the four plywood sheets between the legs of the table as a skirt.
Decorations: The 'water tank' on the table is the 'upper mass' of WTC1. You can paint it to look like it. The four plywood sheets - the skirt - are the walls of the initiation zone of WTC1. You can paint that too to look like it. It is in fact a 1/20 model of part of WTC1 'mass above' and 'initiation zone'. The legs are four of the columns!
Load on table: In order to compress the table legs in the WTC1 model initiation zone at say 30% yield we need abt 1 500 kgs of weight on the table top! Thus you fill the water tank to level about 1.5 meters and there you are: 1 500 kgs of water + 280 kgs of steel plates = 1 780 kgs are carried by four legs each cross area 63 mm². Stress in columns = 7.06 kgs/mm² = 30% of yield stress.
Table, 0.755, m and tank, 1.5 m, make a 2.255 m high model of WTC1 mass above and initiation zone! .
Then you fit a suitable thermometer to record the temperature inside the initiation zone.
The volume of the initiation zone is only 0.75 m3 and it is quite easy to heat it up to 500°C!
Cost of model is not too much: 7 m² of 5 mm steel plate (280 kgs) - say $400:- Pipes $20:-, Skirt $80:- welding rods, paint and misc. $100:- . Labour $ 0:-, if you ask daddy to assemble it.
Now the fun starts! We are going to put this model of WTC1 on fire! Or at least the initiation zone.
Put a high edged tray of some flammable liquid on the cement floor between the legs of the model and fill the rest of the initiation zone with paper, rugs and similar. Ensure that the liquid cannot spill out or damage the cement floor! Have a fire extinguisher available. Call your parents to ensure that safety is maintained! Call visitors to attend and witness your 9/11 show from a distance. Why not invite the local Fire Brigade and your Senator and Congress person (if you live in USA)?
Now put the flammable liquid on fire! See how the initiation zone heats up, air is drawn in and smoke escapes through the holes. Very soon the temperature is 500°C uniformly inside the initiation zone and the table legs are heated up to same temperature. The plywood will burn very slowly.
The purpose of the model test is of course to establish the stiffness of the table leg pipes (the columns of the initiation zone) under heat and to see if suddenly, at, e.g. temperature 500° C, the mass above (luckily most water in this test for children) drops down, at a significant speed and with an enormous kinetic energy, and impacts on the cement floor with an enormous dynamic load.
Or does nothing of that sort happen? Maybe the table legs will just bulge. You will find out (the latter)! Back to Summary!
It should thus be clear that the only primary structure below our wall cage bars are the wall cage bars and it is very easy to calculate what elastic strain energy they can absorb before plastic deformation and rupture when any of them is compressed above 30% of yield stress.
The total strain energy our wall
and core columns and attached spandrels and floors
can absorb is evidently the energy required to
first strain them to 100% yield - the elastic
strain energy - and second to
plastically deform or buckle or rip them apart -
the buckle or rupture or plastic strain
energy. In order to rip a column apart, the
stresses in the structure must exceed the
rupture/break stress of the steel that is much
higher than the yield or buckling
stress. But you have to understand how
the wall cage bars deform under compression before
failure. They will not only compress vertically but
also deflect transversely, bulge in/out between the
pin (bolted) joint supports of the floors to the
columns as shown in figure 9.9.1 right: Fig. 9.9.1 - Deformation
of structure under load
The total strain energy our wall and core columns and attached spandrels and floors can absorb is evidently the energy required to first strain them to 100% yield - the elastic strain energy - and second to plastically deform or buckle or rip them apart - the buckle or rupture or plastic strain energy. In order to rip a column apart, the stresses in the structure must exceed the rupture/break stress of the steel that is much higher than the yield or buckling stress.
But you have to understand how the wall cage bars deform under compression before failure. They will not only compress vertically but also deflect transversely, bulge in/out between the pin (bolted) joint supports of the floors to the columns as shown in figure 9.9.1 right:
Fig. 9.9.1 - Deformation of structure under load
You may argue that the core structure, with less cross area and higher static stresses, may act as one spring and the wall perimeter columns structure, less stressed, as another spring - the structure is one spring in another spring . These two springs are then connected by floors acting as horizontal springs. The deformation of such a structure with a unit load applied on the top can easily be calculated using standard beam analysis and therefore the spring constant C of it can be established. It is interesting to note that NIST does not compute it!
As shown above in 7.4 the theoretical energy E input to compress the 'spring' is only 340 kWh or 1.22 GNm, when the upper part hits the 'spring' instantaneously at Teffect. This is the KE explained above.
Let's assume only half this energy KE is used to compress the 'spring' and that the other half was lost destroying the remaining columns in the initiation zone, which were not damaged by heat, and sweeping them out of the way and that the upper part was also absorbing energy, was deformed as another spring, at impact. In reality the energy involved must be much less as there is no free fall or impact.
Let's assume the 'spring' below is suddenly compressed by 0.5 KE = E = 0.61 GNm at time Teffect.
The maximum compression d of the 'spring' due to energy E then becomes 156 centimeters (because d² = 2 E/C) and after that all the 0.61 GNm or 170 kWh of energy is absorbed as compression! And any motion has stopped! And as the force F is then maximum the upper part will be pushed up again! It will bounce! This is a good indication of the elastic strain energy that could be absorbed by a 'spring' without any permanent deformations, failures or local buckling. The total length (or depth) of the 'spring' is abt 370 meters all the way down to the basement and it is thus temporarily compressed 0.42%. In the basement the energy is also transmitted into the ground and will be recorded as such by any seismograph in the vicinity.
To compress the 'spring' d = 156 centimeters you need a force F corresponding to 0.78 GN (because F = d C) and as the spring cross area at the top is 5.64 m², the compressive stress in the spring becomes temporarily 138 MPa at maximum compression, which is well below yield stress (248 MPa).
It must be noted that the compression of the stress is not pure, vertical compression of a solid steel rod (column), but that the steel rod (column) can also deflect transversely (between pin joint supports - the floors) due to shear and associated bending that assist the compression. In the WTC case the columns can easily deflect 0.1 m transversely at mid-length between supports/floors 3.7 m apart without buckling, which then corresponds to about 0.5% total vertical compression. The WTC1 tower structure was in fact very flexible. It will not collapse like a house of cards as suggested by NIST, Bazant and Seffen (see below) due to a vertical impact by an upper part.
NIST does not calculate the elastic strain energy that can be absorbed in the total primary structure after Teffect below the initiation zone and the time of such compression in their report, which is therefore incomplete.
Evidently the lower part of WTC1 does not react as one 'spring'. There are 280+ vertical 'springs' at every floor held together by horizontal 'springs' (spandrels, beams, floors, etc). There are 1000's of springs to compress! And in reality local failures will occur at the impact interface changing the structural configurations.
This is further evidence that Bazant's second assumption is wrong:
"(2) Energy is dissipated only at the crushing front! This implies that the separate parts of the upper and lower part of the collapsing tower may be treated as rigid, i.e., the deformations of the blocks away from the crushing front may be neglected." Sorry, Bazant. All WTC1 structures are very flexible and cannot be regarded as rigid. They are on the contrary very flexible and will break at the impact interface.
The advanced reader of this article should try to calculate the total (elastic, plastic, rupture) strain energy, SE, built into the structure of one intact floor only!
The lower part is thus not rigid, it is very flexible. Like the upper part. Furthermore the assumed impact energy is not loaded instantaneously - there is no real sudden impact, only a bump over a some time after Teffect when various masses are loaded - so the compression force never becomes 0.78 GN or the max compression 156 centimeters. The compression takes time and should be associated with a jolt - sudden bump - DECELERATION - of the upper part masses above - normally followed by arrest. No such jolt is recorded on any video. It actually means that no upper part ever impacted the lower structure.
The compression, if it takes place, is evidently in the elastic range of the 'spring' and takes place when it is completely unloaded except by its own weight! Or is it? Prove me wrong and earn € 1 000 000:- !!
Unloaded? Was the tower unloaded before impact? It is like children jumping in a bed! The child is in the bed and compresses the springs in the mattress. That is WTC1 under static load. The child is the upper part. The mattress is the bottom part. Then the child jumps up a little - the columns are suddenly removed - the mattress is not under load then - and then the child falls down at Tcause on the mattress with a certain velocity and momentum that compresses at Teffect. Very funny! The child bumps.
Because the spring unloads and pushes the weight above up again. The downward velocity of the mass above becomes first zero and then changes direction, upwards. Nothing should break!
Another 'expert', K. A. Seffen, in a paper 'Progressive Collapse of the World Trade Centre: a Simple Analysis' suggests that
"both towers survived until the intense fire compromised the ability of the remaining (!), intact columns close to the aircraft impact zones to sustain the weight of the buildings above them. The subsequent near free-falling of these upper parts over the height of just one storey resulted in dynamical "over-loading" of the relatively undamaged lower columns by a factor of 30 compared to their static load capacity ..."
i.e. 30-40 wall columns were initially cut, then later fire compromised the remaining 240-250+ columns close to the impact zones so that potential energy was released by the mass above - the upper part - near free falling that resulted in dynamical "over-loading" of the undamaged lower columns by a factor of 30 (!) compared to their static load capacity at impact and transmits it to the structure - 'spring' - below and shakes it into pieces. How is that possible? According Seffen:
"... studies usually deal with progressive collapse of structures, where damage accrues in a prescribed fashion following an initiation phase. Depending on the local collapse behaviour inveigled by the instability sweeping through the initially undamaged structure, it becomes possible to ascertain the level of loading required to sustain its propagation, or conversely, to quantify the ability of the structure to resist or comply with collapse, thereby defining its "residual capacity". In the case of the WTC towers, it is clear that the initial loads imposed by both parts falling onto the undamaged buildings beneath were exceptionally high (!) due to the unforeseen preceding events, and that damage was bound to propagate (!) into the floors below: this is the initiation phase."
Note that Seffen, like Bazant, suggests unscientifically that the initial load applied was exceptionally high! Seffen avoids carefully to explain that for the initial loads to be applied on the undamaged building, actually its columns, the upper and lower parts must be 100% aligned, so that the columns actually meet in the impacts, and that the impact surfaces - broken columns - must be 100% flat, so that the upper part does not slip off the lower part. Further:
"... In order to assert the potential for progressive collapse (!), it is essential to consider the deformation of the next "unit" of structure. This unit is taken to be a single storey (!) whose top and bottom floors laterally restrain the outer columns: compression of the storey follows from the plastic buckling of these columns, as proposed by Bazant and Zhou (2002). All columns are assumed to deform axially and in unison, in a linear one-dimensional way (!), and the behaviour of a single column is sufficient to characterise the complete response of a storey: the initial softening during buckling of a given column, predicted momentarily via Fig. 2, would suggest a redistribution of load paths into any of the stronger, undeformed columns, which guarantees their buckling and some sense of synchronicity of deformation throughout the storey."
Note that the 'initial load' is instantaneously applied to the columns of only one (?) flexible, weak storey at a time and that the rest of the lower structure (90+ floors of WTC1) are ignored or is assumed solid, rigid, while the complete upper part remains rigid, and that the initial load is re-distributed to be uniform over 280+ columns spread over 4 000 m², which requires 100% alignment. Maybe the one poor storey gets crushed under those unrealistic assumptions, but the upper storey is part of a bigger structure below that cannot be ignored! It cannot be rigid one moment and weak another! It is by cheating in this way that virulent metaphysics is produced.
This 'initial load' then
produces a bL
part according Seffen that has developed below the
part cannot be rigid and aligned with the structure
below except if you assume a one-dimensional way
... of buckling! Actually Bazant assumes a two
dimensional way! A number of hinges are assumed to
develop in the columns so that they can bend ...
sideways! Not possible in Seffen's 1-D world!
Further: "... The linear,
one-dimensional collapse (!)
of a homogeneous multi-storey
building is shown schematically in Fig. 4. Lateral
stability is not considered in view of the
near (!) vertical collapse of
both WTC towers. Initially, the overall height is L
and the uniform density is
Thereafter, the horizontal level at which the first
columns lose strength, due to fire or otherwise, is
located at a distance
from the top, where
1, see Fig. 4(a). The building everywhere above
this floor (i.e.
part) begins to
accelerate downwards as
(!) when, at time t =
0, (i.e. Teffect) it
are assumed to fail in the manner proposed in the
This 'initial load' then produces a bL part according Seffen that has developed below the rigid upper part. This bL part cannot be rigid and aligned with the structure below except if you assume a one-dimensional way ... of buckling! Actually Bazant assumes a two dimensional way! A number of hinges are assumed to develop in the columns so that they can bend ... sideways! Not possible in Seffen's 1-D world! Further:
"... The linear, one-dimensional collapse (!) of a homogeneous multi-storey building is shown schematically in Fig. 4. Lateral stability is not considered in view of the near (!) vertical collapse of both WTC towers. Initially, the overall height is L and the uniform density is ro (i.e.0.18 ton/m3). Thereafter, the horizontal level at which the first columns lose strength, due to fire or otherwise, is located at a distance lL from the top, where l< 1, see Fig. 4(a).
The building everywhere above this floor (i.e. the lL upper part) begins to accelerate downwards as a rigid undamaged body (!) when, at time t = 0, (i.e. Teffect) it impinges on the floor (?) and columns beneath, which are assumed to fail in the manner proposed in the previous section."
1. A rigid upper part lL that is rigid and intact and perfectly aligned with the columns below all the time during collapse.
2. A moving intermediate block bL between the upper part and a crush front that apparently consist of semi-broken parts and produces a crush front, actually 280+ crush fronts that are perfectly applied to the 280+ columns at every stage of the collapse.
3. A static, rigid lower, intact part (1-a-b-l)L below the crush front that produces resistance to motion. It is in fact only the 280+ flexible columns that produce resistance ... if a load is actually applied on them from above.
Actually the static lower, intact part (1-a-b-l)L below the crush front is complex structure that gets stronger further down as it is supports all structure/mass above. K.A. Seffen completely ignores that the big lower, intact part gets stronger further down and cannot be crushed from above by anything. The lowest bottom part is 100 times stronger than the top part! It appears that K.A. Seffen is a supporter of terrorists! MI5/6 should investigate!
l is constant during the collapse, which is not observed during the WTC collapses. What b is, is completely incomprehensible but should be 0 just before impact at t = 0 and then be variable until the collapse is completed at t = t(end), thus b is a function of time t.
9.3 The uniform density
How the uniform density ro behaves between t = 0 and t = t(end) is also a mystery. It is evidently assumed constant in the rigid upper part and rigid lower, intact part, but what about density ro of the intermediate block bL?
Apparently the original uniform density ro increases in the bL part according Seffen during collapse - to another uniform but higher density as a function of time - a new phenomenon!
The pulverization of the floors is one curious aspect of the collapse, where the tower with height L and the upper part lL starts to collapse at an initiation zone below the upper part. The tower is assumed to have uniform density, i.e. no floors! During collapse (tower compressed aL) the solid upper part lL part is intact, an intermediate block bL has developed below the lL part and a crush front below the bL part and above what still remains of the rigid lower, intact part.
Let's say that the uniform density ro at start is 0.2 (in lieu of 0.18) and that l is 0.1.
Let's then assume that a is 0.5, half the tower L is crushed, and that b is 0.1 and therefore the lower, intact part below is 0.3L.
At this time 0.5L of the previously solid and rigid building is compressed into bL and the uniform density of the bL part has increased to 1.2 i.e. 600%. Total mass of tower is constant, as Seffen assumes no loss of mass from the bL part. No parts are being thrown out sideways or falling down beside the tower.
So the uniform density of the mass in the bL part has increased 600% from 0.2 to 1.2, reason being that it was not uniform from the start but mostly air, say 90% + 10% solid parts; columns and floors. Uniform density?
When a is 0.5, all the solid parts of the 'collapsed' aL part are in the bL part, where the air pressure must have increased (unless the air escapes, which is more logical but not considered by Seffen) as the solid parts can hardly compress (just be ripped apart by brute force into smaller pieces).
Actually, when a is 0.5, the bL part consists of 60% solid parts (now rubble due to lack of strain energy according NIST) and only 40% air.
What has caused this mess? Well it is only the solid upper part lL (0.1L) that has dropped through solid (!) aL (0.5L), so we know the potential energy, PE, released by the lL block, when a is 0.5. And this block lL has ripped apart the 280+ columns in half the building aL, because they lacked sufficient built in strain energy, SE. The lL block is perfectly aligned with the columns all the time, so that the PE can be applied to still undamaged structure.
Photos of the WTC collapses show that material, dust and smoke are pushed outwards at high speed of the intermediate block, which is not explained by Seffen. There cannot be any uniform density of any type in this area of damaged core columns and falling off walls.
Thus - during collapse according Seffen a rigid upper part lL floats on a mysterious intermediate block bL of broken, compressed material with a uniform (?) density that increases >600% with time that in turn floats on the lower, intact part below a strange crush front. It is quite magic actually and could only have been invented by a blind scientist in an ivory tower supporting terrorism. No mention that the flexible columns must be perfectly aligned.
These are the false assumptions of K.A. Seffen! That (1) the tower has uniform density ro, while it is not uniform at all, (2) the upper part begins to accelerate downwards as a rigid undamaged body with uniform density ro= 0.18 ton/m3, while it is seen to self-destruct, (3) that the initial load imposed onto the structure beneath was exceptionally high, while it was only that of a big bale of cotton, and (4) that the damage, no new damage seen of course in the smoke, was bound (?) to propagate. Alignment of columns is conveniently forgotten.
You wonder what kind of structure bL is? Solid? No! Damaged? Yes! How is the upper part connected and aligned with the undamaged structure below via the mysterious structure bL zone?
As shown in 7.7 the upper block disappears, implodes before it even reaches the floor below to impinge it, and, if it impinged, it should only bounce! But according to Seffen the upper block drives the collapse.
You need kinetic energy, KE, for that and it can only be provided by an intact, rigid, uniform density upper part that remains intact, rigid, with uniform density during the whole destruction of the lower structure. The upper part is the only part that can provide KE during the alleged global collapse. The lower structure does not add any extra KE to the collapse or contribute to the collapse - it is being destroyed (lack of strain energy according NIST).
part, intact, rigid and
of uniform density at start of collapse, should
according to Seffen's theory also remain INTACT
after the global collapse ... on top of all
part has produced of the
below. Nothing could
destroy a rigid
part of uniform density
- not even the final impact with the ground
forgetting that the rubble is there to dampen the
final impact. The lack of the
part on top of the
rubble after collapse proves Seffen
wrong. That is one reason why there is
no figure of final collapse in Fig. 4 above! It
should evidently show the
part on top of the
rubble of the
then resting on ground
as in figure left! You can easily calculate the
uniform density of that
Actually, the upper part, intact, rigid and of uniform density at start of collapse, should according to Seffen's theory also remain INTACT after the global collapse ... on top of all rubble the upper part has produced of the structure below. Nothing could destroy a rigid upper part of uniform density - not even the final impact with the ground forgetting that the rubble is there to dampen the final impact. The lack of the upper part on top of the intermediate block bL rubble after collapse proves Seffen wrong.
That is one reason why there is no figure of final collapse in Fig. 4 above! It should evidently show the upper part on top of the rubble of the intermediate block bL then resting on ground as in figure left! You can easily calculate the uniform density of that rubble heap!
The only gravity driven collapses or destructions known to mankind are snow or soil avalanches (or similar), i.e. an upper part with uniform density of snow/soil that gets lose on a slope at a transverse initiation zone due to the gravity force exceeding the friction between the upper part and ground. In spite of its low uniform density the upper part is pretty stiff during the collapse that starts at an initiation zone in the snow. Then the upper part releases potential energy and pushes a lot of lighter snow in front of it with density much less than the upper part that piles up and compresses in the crush zone (density is increased there but the strain energy is small - snowflakes!) until it runs out of potential energy ... and the upper part is compressed. Evidently lose snow is thrown up in the air, when the crush zone advances down the slope.
A snow avalanche evidently can only take place, if the upper part snow is denser and more compact than the lower part snow!
Such a snow avalanche has nothing in common with the WTC1 destruction, even if the upper part of WTC1 had a uniform density similar to that of compressed snow (180 kgs/m3) that sticks together - snow crystals interacting. But this is what the authorities and university professors want us to believe. Upper part is stronger/denser than lower part and potential energy is always potential energy. But are they?
Say that you drop 33 000 tons of snow (or wool or water for that matter) on the intact structure below the initiation zone of WTC1. It has the same potential energy as the upper part but it will probably just be pushed away by the strong intact structure below. No global collapse will ensue due to release of such potential energy. Is the real upper part any different?
The big difference is that the upper part of WTC1 is a cage of primary structure steel columns and secondary structure floor trusses of very high density (7 800 kgs/m3) but very little volume, concrete floors of less density while the rest of the upper block was air.
Such an assembly of steel parts does not behave like a solid block of snowflakes sliding down a mountain slope, even if the potential energy is same.
Reason is that the potential energy released in the snow avalanche can reasonably be assumed to be as uniformly distributed as the density (snowflakes or crystals only). In WTC1 most potential energy is in the solid parts - the primary structure - and throwing a narrow steel part with its potential energy on another steel part below is not easy. High probability that it misses the other part! Then there are less solid parts - the secondary structure (e.g. floors with their potential energies and concrete crystals) but when they are thrown against more solid parts (e.g. steel beams), the former will be crushed (concrete dust) ... and the latter will remain.
It can be argued that a snow avalanche will break trees, etc in its way (when enough snow piles up and compresses against a tree in the way of the avalanche) but you should then note that the tree is only broken in one piece at that time.
The WTC1 upper part avalanche and its potential energy could therefore never break all the 'trees' (= steel columns) below in small pieces at the columns' weld seams. Most of this energy would only be applied to secondary structure (floors) that would deform or be overloaded, hinge and get sloping or would detach itself from the primary structure that would remain intact. Loose masses from above would get deflected sideways and get jammed inside the perimeter structure or be pushed out and fall to the ground. The collapse would be arrested.
Another difference is the foot print! All material in an avalanche is afterwards always located just below the transverse initiation zone above (everything just drops right down), while in the WTC1 collapse only broken core columns and some floor pans were found within the WTC foot print. Complete sections of primary structure perimeter wall columns were thrown 100+ meters outside the foot print, while most concrete seems to have been mysteriously pulverized already during the collapse and was blown away by the wind. The foot print of WTC1 with its steel rubble only is prima facie evidence that it was not a gravity driven collapse. Back to Summary!
NIST or Bazant or Seffen does not consider the elastic strain energy of the primary structure and masses above or the upper block. It is in fact another 'spring'! It consists of a number of solid weights - the floors - connected to columns - each a 'spring'. Such a contraption is evidently neither rigid nor solid as assumed by NIST, Bazant and Seffen and in the unlikely case that it actually drops down free fall on a structure below; it will only transmit a sequence of energy pulses divided by finite times, each of which cannot overload the structure below. Furthermore, this upper part multiple 'springs' contraption is not very solid. It implodes before it can do any harm!
Only the steel columns (10% of the upper part) and floor steel trusses (another 10% of the upper part) contribute to the elastic strain energy of the structure above. The weakest steel parts are the bolted connections of the floors to the columns.
If the steel structure above is deformed, e.g. the core columns move downwards relative the wall columns, you would expect the floor truss bolts to shear off - see 3.3 - and the floor trusses to hinge down.
As soon as a floor truss hinges down and the loose edge contacts another floor, its concrete will break up in small pieces. There is no strain energy to resist bending and tension in concrete.
The result is then that the principal weight of the upper part - when it starts to slowly fall down at time Tcause - consists of broken concrete (70%) and glass and miscellaneous (10%) in small parts and disappears, as seen, on all videos. It is a broken 'spring'. Evidently these small parts cannot destroy the intact steel structure below particularly when the final speed is only 30 km/h. The upper part is neither rigid nor solid at all and the potential energy released is split into 1 000's of small pieces - mostly concrete - that will just become dust! And this is what we may have seen on the faked pictures and videos above.
It should therefore be clear that 1.22 GNm energy cannot suddenly impact the structure below at time Teffect. It is in fact only a small, broken spring hitting a bigger intact spring. What you would expect is that the steel columns of the upper part would remain attached the steel structure below - no ruptures - after any heat deformation - no collapse, only local failures with some structure entangled and jammed together at some damaged floors, so that the NYFD could extinguish the fires in the normal manner. Dangerous job, though. Concrete and similar lose items could detach from the upper block and fall down beside it. Anything else is apparently caused by some other energy input.
10.2 Rupture strain energy - plastic deformation - ruptures
The elastic strain energy of a
steel primary structure is only a small part of the
total inherent strain energy of the steel structure
required to plastically deform and break it. The
elastic strain energy will only elastically deform
it as shown above and dampen any motion. To break
all the parts of the primary structure you
need to further deform, rip them apart and buckle
them until 'total collapse ensues' and for
that extra energy is required that far exceeds the
elastic strain energy. NIST or Bazant has never
calculated that extra energy and the total energy
required for 'global collapse'. "The release
of potential energy due to downward movement of the
building mass above supposedly buckled columns
is only sufficient to elastically deform
the primary structure below. Ruptures
require much more energy. Global collapse cannot
The elastic strain energy of a steel primary structure is only a small part of the total inherent strain energy of the steel structure required to plastically deform and break it. The elastic strain energy will only elastically deform it as shown above and dampen any motion. To break all the parts of the primary structure you need to further deform, rip them apart and buckle them until 'total collapse ensues' and for that extra energy is required that far exceeds the elastic strain energy. NIST or Bazant has never calculated that extra energy and the total energy required for 'global collapse'.
"The release of potential energy due to downward movement of the building mass above supposedly buckled columns is only sufficient to elastically deform the primary structure below. Ruptures require much more energy. Global collapse cannot ensue."
But how and why would 6 or 11 floors in the initiation zone and above suddenly drop down? Does anybody believe that? Does the picture right look like some floors falling down?
On the faked video and pictures above we see that the roof falls before any floors and that the upper part disappears before destruction of the lower structure commences! Gordon Ross has made similar calculations using another approach and using a mass above - the upper part - of 58 000 tons in lieu of 33 000 tons here and finds that vertical movement of the falling section would be arrested prior to completion of the 3% shortening phase of the impacted columns, and within 0.02 seconds after impact. A collapse driven only by gravity would not continue to progress beyond that point. If you redo the Ross calculations using a mass of 33 000 tons it becomes even more obvious.
Jim Hoffman has an explanation what actually happened and why you should not believe that some floors fell down (You have to click on the sub-links to see his video presentation).
In the writer's view the picture above looks as if a bomb has hit the tower with enormous energy, structural joints vaporize and mass murder is committed (but that is beside the topic of this article). And where did the upper part go? Back to Summary!
This means that we can conclude the following:
The Twin Towers structure was very simple and its primary structure wall and core columns can be likened to steel bars in a bird cage full of air ... and humans. The compressive stress in the bird cage bars due to mass incl. floor loads is very small (<30% of yield stress). The Towers' structure was very strong!
You can heat up the bars under compression in the cage to, say 500°C, and nothing dramatic happens and particularly not that the bird cage suddenly collapses in 1000's of pieces. The stress in a 500°C heated column may increase to 40% of yield. It will not buckle due to that. As soon as the fire moves away to another area the column cools again. Local deformation may take place. But in this article we assume that the upper part gets detached and suddenly falls down on the bottom part; release of potential energy.
NIST has not produced any
"buckled" columns of the initiation zones, be
it bent 180° or crumpled up, that would have produced
downward motion and release of potential energy. We are
talking about 566 columns that must have
"buckled" for the effect ... and none is
presented as evidence that potential energy was released for
that cause. But it is assumed here
anyway. The suggestion that the Tower
cages collapsed due to release of potential energy
of a rigid
part at an unknown time
Tcause exceeding the total strain
energy of the cage structure in the initiation zone
and later below after an impact at time
Teffect is not demonstrated by
NIST, Z P Bazant and Seffen and not supported
by any evidence what so ever or any serious
structural analysis. Simple calculations show that
the potential energy released in such a case would
only elastically strain the structure temporarily.
The picture above does not show a global collapse
due to floors falling down or a hammer hitting a
nail ... or a child jumping on a mattress in a
cause of global collapse according
The suggestion that the Tower cages collapsed due to release of potential energy of a rigid upper part at an unknown time Tcause exceeding the total strain energy of the cage structure in the initiation zone and later below after an impact at time Teffect is not demonstrated by NIST, Z P Bazant and Seffen and not supported by any evidence what so ever or any serious structural analysis. Simple calculations show that the potential energy released in such a case would only elastically strain the structure temporarily. The picture above does not show a global collapse due to floors falling down or a hammer hitting a nail ... or a child jumping on a mattress in a bed!
Impossible cause of global collapse according NIST
Reason why a steel building cannot collapse due to release of potential energy is, in simple terms, that the potential energy will mainly be applied to secondary structure - the floors - that will be overloaded and detached from the primary structure - the columns! The potential energy will then be deflected and will not be applied to the primary structure ... that will remain intact! The collapse is arrested.
That is one reason why there are no figures of final collapse in Fig. 2.1.1 (Bazant) and Fig. 9.2.1 (Seffen) above! It should evidently show the upper part on top of the rubble then resting on ground!
Nothing could destroy a rigid block of uniform density - not even the final impact with the ground forgetting that the rubble is there to dampen the final impact. The lack of the upper part on top of the intermediate block bL rubble after collapse proves Bazant and Seffen wrong.