AE911 New Collapse Hypothesis

[Jeffrey Orling]

Interesting. But were elements able to fall faster within the ROOSD mass than the crushing front itself progressed to the ground? That is, can we imagine pieces of the hat truss moving to the bottom (or even middle) of the ROOSD mass before the crushing front (the bottom edge of the mass) gets to the ground? And can we imagine the hat truss outpacing (and outmaneuvering) pieces of the floor trusses of the, e.g., 101st floor?

As the top blocks descended onto/into the lower intact parts... they broke apart...including all steel and all concrete. both inside and outside the core. There was no impact on the facade of the top blocks so they remained intact until they were broken apart upon impact with the lower block. The break up was not uniform and so the ROOSD "front" was not uniform.

 

[Thomas B]

The break up was not uniform and so the ROOSD "front" was not uniform.

In my model (if I may call it that) the front has a range of about 60 meters (in terms of its location along the height of the building at any given moment) as it nears the ground.

But I'm still curious about how materials on the 110th floor get mixed up with materials from, say, the 95th floor while the whole mass is falling with an average acceleration of 2/3s g. Wouldn't the different elements maintain their relative position even if they've been structurally broken apart?

 

[Thomas B]

Legit question: why the focus on the hat truss? Why would we expect it to ride the collapse downward without breaking apart, when very clearly no other major assembly did?

I began with the idea that it would be a discrete trackable element (unlike the very chaotic crushing front). But @Mendel got me to question this assumption and in the model I've drawn I've got it first tiliting (subjecting it to irregular forces) and then eventually breaking apart. This still seems to work, as long as we assume that the pieces fall at roughly the same rate and therefore track each other (more or less) vertically. They may not hit the ground at exactly the same time, but they arrive near the end, along with the other materials that started at the top of the of the building.

As @Mick West has demonstrated somewhere (I can try to find it) it is likely that some parts of the building peeled off and toppled off it sort of like a tree. In those cases components from higher on the building could fall "head over heels" and arrive at the ground before lower sections did. But I think, on the whole, we have to assume that most of the materials above the crushing front arrived on the ground after the crushing front had gotten there.

 

[Jeffrey Orling]

In my model (if I may call it that) the front has a range of about 60 meters (in terms of its location along the height of the building at any given moment) as it nears the ground.

But I'm still curious about how materials on the 110th floor get mixed up with materials from, say, the 95th floor while the whole mass is falling with an average acceleration of 2/3s g. Wouldn't the different elements maintain their relative position even if they've been structurally broken apart?

I suspect for the most part the materials top of the structure did end up on the top of the pile.... But must of the concrete was pulverized. Steel beams were composite with concrete floors and connected to 3 story. The break up of the steel was chaotic.... so there was "mixing"... rather than a neat collapse with everything in order or vertical position in the tower. I also suspect the beams from the lower floors largely were buried at the bottom. From the point of view of scale....the steel members were like toothpicks and subject to forces from multiple directions in the collapse. The hat trusses broke up was also attributed to the large super imposed mass of the large mech equipment which was on the floors of the hat truss. Key is that the hat truss broke up and did not survive to ride the collapse to the ground.

 

[Thomas B]

Key is that the hat truss broke up and did not survive to ride the collapse to the ground.

My model allows for that. I have it in three pieces hitting the ground in a 1-second window (i.e., not simultanesouly). But there's obviously no science behind those numbers. More pieces and a 2-second window is probably possible. But I don't think anything is possible. That's the point.

 

[Jeffrey Orling]

My model allows for that. I have it in three pieces hitting the ground in a 1-second window (i.e., not simultanesouly). But there's obviously no science behind those numbers. More pieces and a 2-second window is probably possible. But I don't think anything is possible. That's the point.

Why does this matter?

 

[Thomas B]

Why does this matter?

My aim is to try to clarify the difference between Schneider's model and ROOSD. Tracking the tilt and fall of the hat truss (as a whole or in pieces) is a way to transpose the three-dimensional ROOSD model into the single dimension of Schneider's curves.

 

[Jeffrey Orling]

My aim is to try to clarify the difference between Schneider's model and ROOSD. Tracking the tilt and fall of the hat truss (as a whole or in pieces) is a way to transpose the three-dimensional ROOSD model into the single dimension of Schneider's curves.

ROOSD in my opinion is a more accurate way to characterize what was called a pancake collapse. The math is "trivial"... that is to say... a typical floor slab could support X pounds per square foot... and then it would fails. The so called "over loads" were not uniform over the entire foot print... but more chaotic with some areas becoming over loaded before others... leading to local/partial collapse... and then other areas "followed" when they were similarly overloaded. Dropping mass was a dynamic load and rather destructive. Columns did not resist collapse... nothing actually fell "on" them... but for sure they became "involved" as the bracing was connected to the columns of course.
The columns were increasing thicker sections going from top to bottom and less subject to forces from the collapsing debris... and the beams/bracing were not increasing in size... they were more or less uniform top to bottom.
Pancakes makes no sense since this would required every support of a floor to fail at the same time... and this is virtually impossible given the variable nature of the collapsing material in space and time. The slabs were not designed to arrest a collapse of support more than a few static localized "floor loads"... so once started the collpase was unstoppable able.
There was some resistance offered by each slab and there was resistance offered by the air which is basically non compressible and "blew out" the windows. But neither of these "resistances" could stop or slow the collapse which seemed to progress at about 100' feet per second.
ROOSD was OBSERVED not calculated but basic statics/physics supports it.

 

[Thomas B]

ROOSD was OBSERVED not calculated but basic statics/physics supports it.

I still can't get my mind completely around it. At some point I'll draw my understanding of ROOSD as 15 second-by-second frames and run it by you and @econ41 to see if I'm getting it right.

Then I'll be able to update my Schneider-like curves too.

 

[econ41]

Why does this matter?

EXACTLY.

 

[econ41]

Legit question: why the focus on the hat truss?

It is a red-herring derail. The Thread Topic OPed by @arsyn raised the question of why the Schneider hypothesis is wrong compared with the real event. There is one fundamental reason >> Schneider repeats the error first made 16 years earlier and which misled debate until about 2009-10. There are several secondary errors in Schneiders hypothesis. The fundamental error arises from assuming a one-dimensional approximation that had the columns "in-line" with the descending debris and providing significant resistance. That did not happen. The real mechanism was first EXPLICITLY posted on-line as far as I am aware in Nov 2007 with this diagram:

... the issue was put into mainstream on-line truther v debunker debate in 2009 on what was then the JRE Forum by Major_Tom labelled by the acronym "ROOSD" ("Runaway Open Office Space Destruction") coined by femr2. Both those persons came from positions of neutrality but were ridiculed as "truthers" in the bigotted setting of one forum. The record of the resulting farcical discussions is still available for interested members to read. For those with a sense of humour the low point came when a couple of debunkers in effect said "Major_Tom, you are wrong because you are a truther BUT what you are saying is correct when we debunkers say it." AND those same debunkers had been denying "it" for months.

Now the OP Topic of THIS current thread was effectively resolved in the first page of posts.

What happened to the Hat Truss is a derail that is not relevant to that central issue of Schneider's false hypothesis.

However recent posts have focussed on the hat trust for reasons that have not been made clear. AND have resulted in debate which confuses and conflates abstract model concepts with the real event. ROOSD is an acronym that describes the real event. Schneider's hypothesis does NOT describe the real event. And the debate of the break up of the hat truss does nothing to address the difference between Schnieder's recycled fantasy and the real event described and labelled as ROOSD.

 

[econ41]

There is no evidence that the hat truss rides the collapse to the ground.

I confess that I have a vague recollection that some portions of the Hat Truss did "ride the debris" down to the ground. Haven't seen the evidence or any discussion for at least 10 years. And I have not tried to refresh my 80yo memory.

It broke apart like all the rest of the beams and bracing... and fell down WITHIN as part of the ROOSD mass.

That is closer to reality - as always I recommend understanding the four stages of the collapse mechanism. Because the "early progression" stage which saw the mutual break up of both Top Block and top of Lower Tower MUST have impacted Hat Truss. It is part of "Top Block".

And we are still a way off topic speculating about the demise of the hat truss as a process separate from the break up of Top Block.

AND it is irrelevant to the OP Topic "What is wrong with Schneider's hypothesis"?

 

[econ41]

(My position is not that the hat truss disintegrated on the way down, my position is that we don't know whether it did.)

AGREED. We don't know. We cannot know. And, more important, "So what"? The debate is pursuing an irrelevant derail AND making the fundamental error of conflating/confusing "What really happened" with "abstract modelling of a scenario which is NOT what really happened".

 

[Thomas B]

The fundamental error arises from assuming a one-dimensional approximation that had the columns "in-line" with the descending debris and providing significant resistance.

I think this is an (understandable) misinterpretation of Schneider's paper. It is true that he adopts Bazant's language about column failure. (Schneider says he is modelling the "upward directed resistance force of the crushing columns".) But I don't think his argument depends (as Bazant's did) on the alignment of the columns and a sequence of buckling failures.

His model is more general, applying to whatever resistance the lower section provided. He simply gives this resistance a numerical value. (We have previously talked about this as being about 1/3 g.) The actual collapse mechanism is not important to him because all he needs (for the sake of argument) is a homogenous structure being destroyed by a continuous process that unfolds from a set of specifiable initial conditions with no further inputs. It doesn't matter (as far as I can tell) whether that process is ROOSD or Bazant's CD/CU.

His conclusion is that the process can't have been continuous after all. Whatever the mechanism, there must have been further inputs of energy after the collapse initiated, he says. He finds an empirical discontinuity in the data that needs an "unknown phenomenon" to be explained (he's obviously alluding to controlled demolition).

So to dismiss his argument on the basis of the column alignment issue misses the mark, I think.

 

[econ41]

I think this is an (understandable) misinterpretation of Schneider's paper.

Noted.

It is true that he adopts Bazant's language about column failure. (Schneider says he is modelling the "upward directed resistance force of the crushing columns".) But I don't think his argument depends (as Bazant's did) on the alignment of the columns and a sequence of buckling failures.

1) The real event did not involve "crushing columns" in the progression stages which is the main focus of what we are debating.
2) Schneider includes the forces resulting from column crushing:

F (z) is the upward directed resistance force of the crushing columns (that is the quantity in which we are interested);

3) How do you get "crushing columns" other than by "alignment of the columns and a sequence of buckling failures"?

His model is more general, applying to whatever resistance the lower section provided. He simply gives this resistance a numerical value. (We have previously talked about this as being about 1/3 g.)

His model cannot conflate the real mechanism with a false assumed mechanism AND then pretend that they are somehow the same or equivalent.

The actual collapse mechanism is not important to him

It must be if he is attempting to draw valid explanations of OR comparisons with the real event.

because all he needs (for the sake of argument) is a homogenous structure

It wasn't. The assumption of "homogeneous" is false and it is the fundamental error we are disagreeing with. (i.e. @arsyn and I in this thread.)

being destroyed by a continuous process

It wasn't. There are four definable stages each with different mechanisms. The third of those stages - "early progression" - saw the Top Block breaking up in mutual destruction with the top of the lower tower. Bazant's assumption of CD before CU is false. And Schneider makes the same error when referring to his "Zo" remaining at a constant height. That is pure Bazant CD/CU and wrong.

that unfolds from a set of specifiable initial conditions with no further inputs.

The real event involved four stages - of which "ROOSD" is a subset of the "progression" stage and the ROOSD explanation pre-dated the clear distinction of the two sub-stages of progression. And each of those four stages has definable "initial conditions" and involves a change of mechanism at each step. Yes, there were "discontinuities. Neither Schneider's nor your smoothed graphs reflect the actual discontinuities of the real event. << And that is another nail in the coffin of the claim that: "The actual collapse mechanism is not important to him." The discontinuities identified by Schneider are not those of the real event because he does not work with the real event mechanisms.

It doesn't matter (as far as I can tell) whether that process is ROOSD or Bazant's CD/CU.

Define the objective as I have said many times.

His conclusion is that the process can't have been continuous after all.

It wasn't. So which "process"? The Real Event or his modified Bazant fantasy?

Whatever the mechanism, there must have been further inputs of energy after the collapse initiated, he says. He finds an empirical discontinuity in the data that needs an "unknown phenomenon" to be explained (he's obviously alluding to controlled demolition).

The "unknown quantity" is an artefact of his false model.

So to dismiss his argument on the basis of the column alignment issue misses the mark, I think.

Noted. Again.

 

[Thomas B]

Again, I am genuinely curious to see your corrections to my graph, Econ.

How do you get "crushing columns" other than by "alignment of the columns and a sequence of buckling failures"?

What I was trying to say is that the reference to columns in the paper just follows from Schneider's use of Bazant's language as a point of departure. He ends up just working with mass density and resistance force, irrespective of the structure and mechanism of the towers.

The assumption of "homogeneous" is false and it is the fundamental error we are disagreeing with.

I don't understand how you can describe the intact WTC towers as anything other than homogeneous structures. The load is more or less equally distributed across 110 floors and capacity increases as we get lower on the building in a regular way. The buildings are also symmetrical.

Modelling them in terms of smooth functions of mass density, resistance force, and height is perfectly reasonable.

Neither Schneider's nor your smoothed graphs reflect the actual discontinuities of the real event.

I think we mean different things by discontinuity here. My assumption (which I think has to be true) is that there were no additional inputs of destructive energy on the way down. (This is also Schneider's "for the sake of argument" assumption.) What that means is that you must be able to predict the collapse curves (roofline and front) from initial assumptions you make about the mass density and resistance force functions.

The real event involved four stages - of which "ROOSD" is a subset of the "progression" stage and the ROOSD explanation pre-dated the clear distinction of the two sub-stages of progression.

The stages have no explanatory, only descriptive, power. Since no new causes are introduced, the explanation for the transition from one stage to the next is simply the state of the structure at the (essentially arbitrary) end of one stage and begining of the next.

If you think describing the event in stages constitutes explaining it then we are not at all on the same page.

Neither Schneider's nor your smoothed graphs reflect the actual discontinuities of the real event.

And yet a blue and red line must be possible even in a ROOSD regime. Just draw them and specify the function that produces them from a set of initial conditions you prefer.

Since the whole buildings ultimately ended up on the ground, the lines must be "smooth" (i.e., there's no place where the crushing front "skips" ahead fifty meters, though it might steepen to freefall along the way, I guess.)

I would argue that someone who can't draw those curves at all, simply doesn't understand the collapses. And, yes, the deficiencies of my curves reveal deficiencies in my understanding.

Again, I'd love to see your corrections. Just draw your curves right on top of mine.

 

[Jeffrey Orling]

One has to see what took place to understand it.
Understanding is informed by accurate observations and the science to explain it.

The key feature of the collapse/destruction of the lower blocks was that it took place with NO INVOLVEMENT of the columns - core and perimeter/facade. It was a collapse of the floor slabs and the things on them. The slabs including their connections to the axial structure were "structurally" overwhelmed (overloaded) and failed.

Columns, the axial structures which support the floors and their contents were incapable of arresting the collapse and were in fact unloaded as the floors failed. The columns failed because they required the lateral bracing the floors and their beams provided. Without lateral bracing the columns were weakened and their slenderness ratio increased past the point of stability.

The collapse had nothing to do with the towers being homogeneous structures. They were not. They were composites and the elements of the composites failed. The key elements failing in the collapse of the lower blocks were the slabs. Each was designed to support normal superimposed office floor loads (including a factor of safety). Any engineer can understand that a single floor fails when it has to support multiple floors. One hardly has to do any math... as the collapse dynamic is actually intuitive or trivial engineering. There is nothing to debate about the collapse phase.

++++

There is "fog" concerning how the tops get moving and essentially became the slab destroying mass when freed from the axial support of the columns. So you can have several theories about how the tops' movement was "initiated". What IS accepted is that the energy input after the plane strikes was heat from fires. You had damaged frames ... obviously with decreased, but adequate capacity having that capacity eroded by the effect of heat. It is established what heat does to materials including steel... It lowers its strength in compression and tension. It causes it to expand. It cause it to become somewhat
"plastic" and deform. It can cause metals to melt, but the temps were not high enough in the case of steel. So you had a structural frame (composite) of decreasing capacity (locally where the heat was concentrated) and distortion, warping of the individual elements depending on the temperature and the cross section of the members. Members include both beams (bracing) and columns. Beams included the bar trusses outside the core and the rolled sections inside the core. The "systems" designed to mitigate heat had failed - sprinklers and to some extent spray on heat insulation. There was no active fire fighting. Over time the heat compromised the structure in the plane strike regions that capacity was forced below the "service" loads and the tops broke up and descended on the slabs beneath it... overwhelming and causing the UNSTOPPABLE rapid runaway floor collapse...which led to instability of all axial structures (columns) which likewise "failed".. toppled and or buckled.

The only calculation one needed was the ultimate capacity of a single floor slab. Once that was exceeded locally and then globally over its footprint.. the building collapse was inevitable.

Simply stated:
Structural plane damage - serious but not fatal
Weakening and frame distortion/warping from heat
Loss of integrity and capacity of columns to support upper blocks
Collapse of upper blocks onto lower cold intact lower slabs
runaway top to bottom sequence of collapse/crushing/pulverization of floor slabs
collapse causes columns loss of stability / integrity and floor destruction race to the ground
toppling of all columns weakened without the bracing of the floor slabs

The growing dynamic load of the unstoppable collapsing floor mass was almost unimpeded except for the slight resistance of each slab and the air inside the building which had to be pushed out of the way. This destruction took about 10-11 seconds once it started.

 

[Mendel]

I don't understand how you can describe the intact WTC towers as anything other than homogeneous structures. The load is more or less equally distributed across 110 floors and capacity increases as we get lower on the building in a regular way. The buildings are also symmetrical.

Modelling them in terms of smooth functions of mass density, resistance force, and height is perfectly reasonable.

But they're not homogenous, they're "lumpy", stronger at the edge and in the core, with mass density and resistance force also distributed unequally.
The initial failure at the top was not symmetrical, either, we see the top block tipping to one side.

And "capacity increases" holds for the columns, but not for the floors!

Schneider's process halts because of this increase!

And I explained this, with quotations, over a month ago, in post #8, so please stop flogging a dead horse. This is no longer up for discussion because your assertions have already been demonstrated to be false in this very thread, and you're just in denial about it. Unreasonably.

 

[Mendel]

1. The capacity of the floors doesn't increase, there is no increase of resistance as the floors get crushed, leaving the columns standing.

2. The facade columns mostly just fall over, they don't fail through crushing.

3. The core columns do get crushed initially, resistance increases, the process stops (and also because the top loads are no longer aligned with the columns because of the asymmetrical breakdown), the spire is seen to be standing because of that, and then also falls over.

You know about the floor destruction mechanics, Thomas, because we chewed through it in considerable detail, yet here you conveniently forget that we did. You keep holding on to your state of denial, no matter how much time and effort is directed at you, and you hijack other threads with this.

 

[Jeffrey Orling]

Truthers are confused (ignorant) about the column strength of the towers and their ability to resist collapse.

They don't understand the collapse.

As the floors collapsed/broke apart... the loads on the columns decreased. There was nothing "crushing" the columns. What happened was actually the reverse... the loads the columns had carried - floor slabs and contents - were removed (as the floor slabs were shattered and collapsed). Floors were attached to the sides of the columns... so removing the floors by "collapse" decreased the axial loads on the columns.

The spire columns were the strongest columns in the core and as such were the ones which could stand the "tallest" without bracing. However when the slenderness ratio was too large they too lost their ability to self support.... and self buckled or toppled. This turned out to be about 930 feet tall.

 

[Thomas B]

The spire columns were the strongest columns in the core and as such were the ones which could stand the "tallest" without bracing. However when the slenderness ratio was too large they too lost their ability to self support.... and self buckled or toppled. This turned out to be about 930 feet tall.

I've been trying to get someone to explain this to me. Here's the reason the slenderness ratio / self-buckling argument doesn't work for me. I found this "tallest column" calculation in an MIT textbook:

https://ocw.mit.edu/courses/mechani...-2013/course-notes/MIT2_080JF13_Lecture10.pdf

Notice the very thin tube and very small cross-sectional area of this mast when compared to the WTC core columns. But its slenderness ratio is 1/650! How does a much stronger column (and one that is tapered, not prismatic) self-buckle at under 1/200?

The math is a little beyond my working knowledge, but it would be great if someone would just do this calculation with the dimensions of (the various segments of) column 501.

 

[Jeffrey Orling]

I've been trying to get someone to explain this to me. Here's the reason the slenderness ratio / self-buckling argument doesn't work for me. I found this "tallest column" calculation in an MIT textbook:

https://ocw.mit.edu/courses/mechani...-2013/course-notes/MIT2_080JF13_Lecture10.pdf

Notice the very thin tube and very small cross-sectional area of this mast when compared to the WTC core columns. But its slenderness ratio is 1/650! How does a much stronger column (and one that is tapered, not prismatic) self-buckle at under 1/200?

The math is a little beyond my working knowledge, but it would be great if someone would just do this calculation with the dimensions of (the various segments of) column 501.

The math is above my pay grade. However the real world example is a tell. Col 501 was about 75 stories tall and it toppled. Clearly its form, mass and height could not self support.

 

[johnny plectrum]

The math is a little beyond my working knowledge, but it would be great if someone would just do this calculation with the dimensions of (the various segments of) column 501.

The fabricated core columns were welded together at every 36' below the 85th floor.

In this photo you can see one of primary core columns. The striking thing is the barely visible remains of the torn weld on the long faces that were used to secure each 36′ section. The welded connection between each column lift was typically a 25mm bevel-groove weld which, on the lower storeys, produced a column with very little bending capacity (relative to its section size).
Whilst the huge webs and flanges give the section massive compression resistance, its tiny connection welds leave it lacking in tensile capacity; the reduced radius of gyration leading to early buckling failure once unbraced.
The smaller column behind exhibits exactly the same issue.

The second moment of area used for the radius of gyration calculation would be that of the welds, not that of the 'theoretically' homogenous column. The actual column size is therefore not relevant for the buckling analysis.

The debris pile was littered with these neat column sections in various multiples of 36'.

 

[Thomas B]

The second moment of area used for the radius of gyration calculation would be that of the welds, not that of the 'theoretically' homogenous column. The actual column size is therefore not relevant for the buckling analysis.

Interesting. Thanks.

Do you know how the calculation would come out for the homogenous vs. welded versions? What would the maximum height of the unsupported column be in each case?

 

[Thomas B]

The math is above my pay grade. However the real world example is a tell. Col 501 was about 75 stories tall and it toppled. Clearly its form, mass and height could not self support.

Unfortunately, this begs the question when talking to truthers. They would argue that the columns should have remained standing, so the "real world" tell proves that demolition was involved. That's why I'd like to have the math worked out.

 

[Jeffrey Orling]

The fabricated core columns were welded together at every 36' below the 85th floor.

View attachment 48625

In this photo you can see one of primary core columns. The striking thing is the barely visible remains of the torn weld on the long faces that were used to secure each 36′ section. The welded connection between each column lift was typically a 25mm bevel-groove weld which, on the lower storeys, produced a column with very little bending capacity (relative to its section size).
Whilst the huge webs and flanges give the section massive compression resistance, its tiny connection welds leave it lacking in tensile capacity; the reduced radius of gyration leading to early buckling failure once unbraced.
The smaller column behind exhibits exactly the same issue.

The second moment of area used for the radius of gyration calculation would be that of the welds, not that of the 'theoretically' homogenous column. The actual column size is therefore not relevant for the buckling analysis.

The debris pile was littered with these neat column sections in various multiples of 36'.

Not only that... but the core column ends were unrestrained. Floor beam/brace connections were about 6' below the top of the 36' column, then 18' and then 30' from the top. The perimeter column panels had floors connected at 6' from bottom, then 18' then 30'. Facade was stiffer because of being staggered and composite with 3 spandrel panels.

 

[Jeffrey Orling]

Unfortunately, this begs the question when talking to truthers. They would argue that the columns should have remained standing, so the "real world" tell proves that demolition was involved. That's why I'd like to have the math worked out.

Tall columns need bracing to prevent buckling.

 

[Gamolon]

Truthers are confused (ignorant) about the column strength of the towers and their ability to resist collapse.

They don't understand the collapse.

As the floors collapsed/broke apart... the loads on the columns decreased. There was nothing "crushing" the columns. What happened was actually the reverse... the loads the columns had carried - floor slabs and contents - were removed (as the floor slabs were shattered and collapsed). Floors were attached to the sides of the columns... so removing the floors by "collapse" decreased the axial loads on the columns.

The spire columns were the strongest columns in the core and as such were the ones which could stand the "tallest" without bracing. However when the slenderness ratio was too large they too lost their ability to self support.... and self buckled or toppled. This turned out to be about 930 feet tall.
View attachment 48622

Jeffrey,

What criteria did you use to put each box column type into which floors they were present on? The reason I ask is this. According to a drawing of the column schedule for column 501, I see the following:

1. The 52" x 22" box column dimensions ended at floor 72 (the upper column splice was at floor 72). The box column between floors 72 and 75 (the upper column splice was at floor 75) was 46" x 22". The box column between floors 75 and 77 (the mechanical floors, this box column was only two floors in height, upper column splice at floor 77) and was 40" x 22". The box column between floors 77 and 80 was 34" x 22" (upper column splice was at floor 80) . The box column between floors 80 and 83 was 28" x 22" (upper column splice was at floor 83). Floor 83 and above were wide flanges decreasing in size every three floors.
2. You have the columns designated as 37 tons ending at floor floor 42. The column splice was at floor 43. The 35 ton column designation shows them ending at floor 78, The splice was at floor 77.

Here is the column schedule. Not sure if this affects your calculations or not.

Example column type (forth row in schedule above). Column type 354, majority of box columns for 501:

Link to above. WTC drawing book 3 is where I found them.
https://archive.org/details/fav-gerrycan

 

[Thomas B]

Tall columns need bracing to prevent buckling.

Yes, everyone understands that. At some height they need bracing or they will buckle. And that height can be calculated. To say "they buckled so they must have reached their maximum height" begs the question of whether they collapses naturally.

 

[Jeffrey Orling]

Yes, everyone understands that. At some height they need bracing or they will buckle. And that height can be calculated. To say "they buckled so they must have reached their maximum height" begs the question of whether they collapses naturally.

What is naturally? All the bracing was stripped off in the floor collapse. The lowest stories of the columns were buried (and braced) by debris to some extent. Column section DID decrease and end to end connections were fairly wimpy fillet welds. After the floors collapsed what motion do you observe? Does it look like explosions caused the toppling?

How does the survival and subsequent collapse of the core's columns support a CD theses?

 

[Thomas B]

What is naturally?

By "naturally" I just meant predictable with math from the known initial conditions.

 

[Gamolon]

They would argue that the columns should have remained standing, so the "real world" tell proves that demolition was involved.

Do you agree with them?

 

[Thomas B]

Do you agree with them?

I reject the last part for sure.

Until recently, I thought the columns must have been self-supporting at full height (but that this wouldn't have arrested the collapses.)

That was challenged a while back and I'm still trying to get my mind around it. (As I understand it, the ROOSD process destroyed the columns -- all the columns, the entire vertical structure of the building -- solely by removing their lateral support, never -- or only incidentally -- by buckling them from above. It sounds strange to me still.)

@johnny plectrum's suggestion with the welds is promising on this front, though. I just need to quantify it.

 

[Jeffrey Orling]

By "naturally" I just meant predictable with math from the known initial conditions.

Whatever the math... unbraced columns can only stand to a certain length and then they are unstable and self buckle by "gravity alone.

 

[Jeffrey Orling]

I reject the last part for sure.

Until recently, I thought the columns must have been self-supporting at full height (but that this wouldn't have arrested the collapses.)

That was challenged a while back and I'm still trying to get my mind around it. (As I understand it, the ROOSD process destroyed the columns -- all the columns, the entire vertical structure of the building -- solely by removing their lateral support, never -- or only incidentally -- by buckling them from above. It sounds strange to me still.)

@johnny plectrum's suggestion with the welds is promising on this front, though. I just need to quantify it.

ROOSD essentially bypassed columns... ALL columns. Columns fell because the floors were the critical bracing for the columns... so AS A RESULT of the floors collapsing... the columns that supported them... which those columns braced... collapsed from gravity.. self buckling.

 

[Thomas B]

Schneider's process halts because of this increase!

Does this mean that if the columns had stayed aligned (as Bazant's model assumes) then the collapses would have stopped (contra Bazant). I.e., as a criticism of Bazant, Schneider's paper is a good exercise, but as support for controlled demolition it fails, because ROOSD, and not Bazant's column failure model, is what actually happened?

 

[Thomas B]

Whatever the math... unbraced columns can only stand to a certain length

Well, my point is that the "certain length" can always be determined by math in advance. That's why buildings are so safe. We know they will stand at a "certain" height, using "certain" materials in a "certain" design, carrying a "certain" load, under "certain" wind conditions. And we build to that height. We're certain. But we even build in a safety margin to be sure.

We don't just build them and see what happens.

 

[Gamolon]

ROOSD essentially bypassed columns... ALL columns. Columns fell because the floors were the critical bracing for the columns... so AS A RESULT of the floors collapsing... the columns that supported them... which those columns braced... collapsed from gravity.. self buckling.

Just trying to understand this.

Are you saying you believe that ALL the columns (designated as 501, 502, 601, 602, etc.), from base to roof, self buckled due to their weight and being unbraced?

What about falling debris impacting a column and causing it to snap at a weld or causing it to buckle? Could some of those columns have been pulled horizontally due to falling debris impacting horizontal structural components connected to them causing them to snap ay a weld or buckle?

 

[Jeffrey Orling]

Well, my point is that the "certain length" can always be determined by math in advance. That's why buildings are so safe. We know they will stand at a "certain" height, using "certain" materials in a "certain" design, carrying a "certain" load, under "certain" wind conditions. And we build to that height. We're certain. But we even build in a safety margin to be sure.

We don't just build them and see what happens.

The so called experts completely missed why the tower collapsed and the columns had nothing to do with it. THEY collapsed because the floors did a runaway top to bottom collapse of the lower block.
A tower is a composite structure designed to support gravity loads including its own weight and the live loads imposed on the floors AND the lateral loads from wind.
Columns move ALL loads to the foundations/bedrock
Columns cannot self support when their unbraced length exceeds a calculated amount. The floor/beams reduce this length. When floors are gone... unbraced length is too long... columns are unstable and self buckle.
Columns could not and did not resist the floor collapse.
Floor collapse "unloaded" the columns... but "unbraced" them too and made them unstable
Note that the floor loads were applied to the sides of the columns... they were not resting on them.

There has been some discussion related to the failure of the slab to column connections. The main failure of the floors was likely the destruction of the integrity of the floors themselves...

If the floors had been "slowly" loaded to the point where the beam to column connections failed... all at the same time... then the entire floor would drop like a record on a changer. THAT DID NOT HAPPEN. The floors were not uniformly overloaded. Imagine a bunch of steel safes dropping on those floors... they would punch through and cause multiple local collapses. If there were enough safes the entire floor would be destroyed. NOTHING WAS FALLING AXIALLY ON THE COLUMNS. Floors broke up and collapse down... leaving columns behind. But the columns can stand without the floors bracing them and so the collapse of the columns from self buckling was the "final act".

 

[Thomas B]

The so called experts completely missed why the tower collapsed

This is something I can't agree with. Expert opinion on this must have converged on the truth by now. Engineering students are being correctly taught why the towers collapsed. They are not being misled by experts who still don't get it.

The truth about the collapses is not known only to amateurs.