# How high could the plane have hit, and still caused a total collapse?

No matter how solid and convincing your reasoning seems to you, it should be checked through experiment.
We-re not trying to discover new scientific principles.
We are applying established scientific principles to an observation.

Can you evaluate an experiment without reasoning (e.g. in quantum physics)?

The question is what part of this can be verified through physical experiments, or if you can't do that, a computer simulation
A computer simulation is reasoning, not an experiment.
all it does is apply logic and mathematics to a set of inputs

Forget about what "makes sense" for a moment. The question is what part of this can be verified through physical experiments, or if you can't do that, a computer simulation. Lots of people think it "makes sense" that the position of Saturn this week will affect their romantic pursuits, doesn't make it so.

So someone can think it "makes sense" that the columns missing would explain why there was no jolt, and be wrong. It should be checked through experiment. If you look at videos on the Tacoma bridge collapse, you will find that scientists did build physical scale models of the bridge and replicated its behaviour in wind. But it seems like that with the WTC towers, all you get is an endless barrage of excuses of why it can't be done, or wouldn't be worthwhile to do.
If you understand structural engineering you would know that materials have been "tested" and their physical characteristics recorded. For structural steel, concrete, wood etc... their are design load tables.

Composite systems are obviously more complex and can be structurally "indeterminate".

https://en.wikipedia.org/wiki/Statically_indeterminate.

Buildings are designed using load tables... and those tables have been derived empirically. Engineering is applied science.

Structures fail when elements of the structure... columns, beams, joints etc. are subject to loads which exceed their capacity.

It's been explained to you how the failure "progressed" and became runaway. There was no "arrest" feature designed in... other that the given factor of safety which is included in load tables.

Loads were not disappearing... but elements of the structure were "structurally disappearing" - failing... so equilibrium was lost and the entire structure failed... in a runaway progression of failures.

However, scientists are often permitted to start with experimentally-verified "A has a very high probability of leading to B", and "B has a very high probability of leading to C", and conclude "A has a high probability of leading to C". (You want to mix in a bit of "B leading to C shouldn't depend on whether A was the cause of B or not", of course, which can sometimes be a leap of faith.)
There is a fundamental difference between analysing a one-off past event that has in fact happened AND the more normal method of science. Which Feynman was referring to when he mentioned experiments.

For all the bits of science needed to explain WTC collapses the experiments have already been performed many times. Yield strength of steel. Reduction in strength due to temperature. The distribution of forces, moments, and loads between members of a structural frame. It has all been done many times.

The implied idea that we cannot understand how a lot of those known bits fit together in WTC collapse without building and testing a series of WTC buildings is ludicrous. If you don't know how much a piece of steel bends under loads - do the experiments. Bt experiments at that level have already been done many times. In fact many of them are replicated routinely in the manufacture of materials, in the assembly of sub-systems.

The only "experiment" needed is the multiple experiments that have also been performed in forming and testing explanatory hypotheses. Which is actually what we are trying to do here. Some irony in that

If you look at videos on the Tacoma bridge collapse, you will find that scientists did build physical scale models of the bridge and replicated its behaviour in wind. But it seems like that with the WTC towers, all you get is an endless barrage of excuses of why it can't be done, or wouldn't be worthwhile to do.
I agree with this. We can add other disasters like the Hyatt Regency and the Challenger and the Concorde. It's because I understand those disasters that I'm dissatisfied with the explanation of the WTC collapse.

It's easy to reject the conspiracy theories as implausible. But once that's out of the way, I need to make sense of the disaster on its own terms, and in a way that jibes with my (admittedly amateurish) understanding of physics and engineering. In the other cases, I learn something from my inquiries, and there always seems to be more learn. In this case, we keep arriving at things I shouldn't worry my pretty little head about.

Edit: in the interest of staying on topic, it's not clear to me what the people here who think it is totally obvious that the top, say, 10 floors could destroy the remaining 100 think would happen if the collapse had initiated at the 107th floor. I'm especially interested in the math.

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I agree with this. We can add other disasters like the Hyatt Regency and the Challenger and the Concorde. It's because I understand those disasters that I'm dissatisfied with the explanation of the WTC collapse.

It's easy to reject the conspiracy theories as implausible. But once that's out of the way, I need to make sense of the disaster on its own terms, and in a way that jibes with my (admittedly amateurish) understanding of physics and engineering. In the other cases, I learn something from my inquiries, and there always seems to be more learn. In this case, we keep arriving at things I shouldn't worry my pretty little head about.

Edit: in the interest of staying on topic, it's not clear to me what the people here who think it is totally obvious that the top, say, 10 floors could destroy the remaining 100 think would happen if the collapse had initiated at the 107th floor. I'm especially interested in the math.
What math?
Look up strength / span (design loads) for light weight concrete slabs.
I believe some of the slab strength issues were included in the Addenda to the NIST report.

++++

Twin Towers were built as economically as possible and therefore as light as possible using the least amount of material. The system chosen for the floor system was light weight steel bar trusses and light weight aggregate concrete on Q decking.
The floor strength was chosen the the anticipated loads.... and that included occupants, partitions and furnishings. Architects/engineers do this every time the design and spec a building.

What math?
Look up strength / span (design loads) for light weight concrete slabs.
This goes back to the simple calculation implied by FAQ#18. In that calculation the only "strength" is in the floor connections and the load is just a function of the amount of floors.

But the towers were not held up (and bound together) by the floors alone, and the loads were continously ejected outside the foot print and inside the core, where they didn't impact the lower floors and therefore didn't stress the column connections.

There's a lot of strength there that needs to be accounted for in the destruction. I wouldn't know where to begin. But someone must. And someone ought to have long ago.

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This goes back to the simple calculation implied by FAQ#18. In that calculation the only "strength" is in the floor connections and the load is just a function of the amount of floors.

But the towers were not held up (and bound together) by the floors alone, and the loads were continously ejected outside the foot print and inside the core, where they didn't impact the lower floors and therefore didn't stress the column connections.

There's a lot of strength there that needs to be accounted for in the destruction. I wouldn't know where to begin. But someone must. And someone ought to have long ago.
No... the towers were supported by the columns and the loads--- slabs and contents were applied to the "sides" of the columns where beams/trusses rested on and bolted or welded to "beam seats".
The over loading of the floor would cause the weakest "link" to fail. This may be the truss/beam to column connections of or the slabs themselves... or both depending. As the slabs were pretty much destroyed in the collapse it appears that most of the destructive impulse was from the "mass" of the floor(s) / contents dropping onto the floor below.
Each floor slab was a similar design... the columns however, were stronger at the base because the carried the loads from above as well as the attached floor.
A floor failing would collapse and cause all those below to sequentially fail.
Not much material ejected. However the slab driven down by mass falling on it compressed the air on the floor below and this air was pressurized and forced out through the windows taking with it floor contents, partitions etc.
Columns fell as a result of loss of bracing... becoming unstable. Floors and beams were the bracing and they came down in the runaway floor collapse.

No... the towers were supported by the columns and the loads--- slabs and contents were applied to the "sides" of the columns where beams/trusses rested on and bolted or welded to "beam seats".
The over loading of the floor would cause the weakest "link" to fail. This may be the truss/beam to column connections of or the slabs themselves... or both depending. As the slabs were pretty much destroyed in the collapse it appears that most of the destructive impulse was from the "mass" of the floor(s) / contents dropping onto the floor below.
Each floor slab was a similar design... the columns however, were stronger at the base because the carried the loads from above as well as the attached floor.
A floor failing would collapse and cause all those below to sequentially fail.
Not much material ejected. However the slab driven down by mass falling on it compressed the air on the floor below and this air was pressurized and forced out through the windows taking with it floor contents, partitions etc.
Columns fell as a result of loss of bracing... becoming unstable. Floors and beams were the bracing and they came down in the runaway floor collapse.
I understand all of these things.

For each hypothetical initiation floor (100, 101, 102 ... 107) all this qualitative language you're using -- "over loading", "weakest", "pretty much", "impulse", "mass", "stronger", "not much", "pressurized and forced" -- can be expressed in mathematical quantities. I'm just looking for the back-of-the-envelope version of it.

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The top of the North Tower accelerated down smoothly at about 65% of g as long as it was visible, it did not decelerate. Chandler will claim this is proof that the top is not crushing what's below, but is instead falling as its supports are being removed by something else.

I understand all of these things.

For each hypothetical initiation floor (100, 101, 102 ... 107) all this qualitative language you're using -- "over loading", "weakest", "pretty much", "impulse", "mass", "stronger", "not much", "pressurized and forced" -- can expressed in mathematical quantities. I'm just looking for the back-of-the-envelope version of it.
Why do you need math? If you understand the language and what the process of the collapse was...

Why do you need math?
Are you serious? I undertand that a structure could be built with particular loads and strenghts such that it would collapse completely from near the top but not from somewhat nearer to the top. I want to know how the math checks out on the WTC. I want to know that someone (eventually) did the math (rather than referring us to video evidence as John Gross did. See @Henkka's post #140.)

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Are you serious? I undertand that a structure could be built with particular loads and strenghts such that it would collapse completely from near the top but not from somewhat nearer to the top. I want to know how the math checks out on the WTC. I want to know that someone (eventually) did the math (rather than referring us to video evidence as John Gross did. See @Henkka's post #140.)
The "math" was done in the empirical testing of steel and concrete and so on for load tables).... The engineers use tables such as

and do calcs w/ super imposed live and dead loads and select the steel and slab thickness accordingly

For each hypothetical initiation floor (100, 101, 102 ... 107) all this qualitative language you're using -- "over loading", "weakest", "pretty much", "impulse", "mass", "stronger", "not much", "pressurized and forced" -- can be expressed in mathematical quantities. I'm just looking for the back-of-the-envelope version of it.

Enough.

Prove me wrong. Cite a real world example.

I understand all of these things.

For each hypothetical initiation floor (100, 101, 102 ... 107) all this qualitative language you're using -- "over loading", "weakest", "pretty much", "impulse", "mass", "stronger", "not much", "pressurized and forced" -- can be expressed in mathematical quantities. I'm just looking for the back-of-the-envelope version of it.
How many times do you want the "back of the envelope" version? There were only two significant "forces" involved in limiting the progression to approx 2/3rds "g". The purely structural resistance forces needed to shear off the floor joist or floor beam to column connections. And the force involved in the changing momentum as debris accumulated.

Whatever the numeric value of the joist shearing force - call it "f" - it was hit by a static minimum force of 6 times plus a dynamic impact several times that, NIST's conservative estimate (See FAQ #18) says it would survive about 6f. So whether it is 20f, 30f or 50f it beats the maximum resistance of 6f. Overwhelmingly so. And, there is no legitimate reason to argue about whether it was actually 24.738f OR 18.526f even if it was possible to legitimately do such a calculation. Anything over 10f "beats" 6f and by sufficient margin to accommodate a possible low side inaccuracy in the admittedly conservative NIST version.

I've always used the term "overwhelming" because it was. And the only counter claims from denialist truthers refer to their belief that it needed explosive "squibs". Utter nonsense.

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@Thomas B.... I suggest you write to Skilling or Robertson and ask them for their calculations for the various elements of the WTC buildings because you need to be convinced someone did the math.

And any calculation would need the weights of all the partitions, furniture and contents of the floors, mechanical equipment and so on.
Thomas B is just trolling because his request will prove nothing.

Far more than enough of this repetitive trolling. The impulse forces causing failure were somewhere in the order of 20 thru 50 times the design load. So, even allowing for 5 times "FoS", that is from 4 to 10 times what was needed for failure. There is no purpose in attempting the complex task of accurately determining the actual magnitude. It could only be an average anyway. There were bound to be variabilities between individual columns which could not be assessed but, like all such variances, would add to the assurance of failure. (And even THAT claim may be a challenge for understanding why it must be so. )

(Please note all the numerals I included. They constitute maths which is more than sufficient to show the legitimacy of the argument.)
Prove me wrong.
Reversing the "Burden of DISproof" is SOP for truthers and trolls. "They" cannot prove "their" claim. Usually, "they" cannot even define a legitimate claim. So "we" have to DISprove what "they" cannot prove or even clearly specify.
Cite a real world example.
You perrenial optimist.

If you look at videos on the Tacoma bridge collapse, you will find that scientists did build physical scale models of the bridge and replicated its behaviour in wind.
They did that because they had to devise and verify a new methodology to analyse structure stability with regard to vibrational stresses and modes of resonance.
In this, the Tacoma bridge collapse lead to new science.

The WTC collapses were not scientifically surprising.

There's a lot of strength there that needs to be accounted for in the destruction. I wouldn't know where to begin. But someone must.
Why?

....

There's a lot of strength there that needs to be accounted for in the destruction. I wouldn't know where to begin. But someone must. And someone ought to have long ago.
The collapse of the floors "unloaded" the columns. No extra loads were added to the columns.... except in the initiation phase in the core where columns were failing one by one (buckling) and their load was redistributed to other columns and this is the proximate cause for the top blocks dropping more of less as "intact structures"... until they collided with the lower block/floors below.

The WTC collapses were not scientifically surprising.
I'm sure you have some way of dismissing Bazant's take on this.
External Quote:

The destruction of the World Trade Center WTC on September 11, 2001 was not only the largest mass murder in U.S. history but also a big surprise for the structural engineering profession, perhaps the biggest since the collapse of the Tacoma Bridge in 1940. No experienced structural engineer watching the attack expected the WTC towers to collapse. No skyscraper has ever before collapsed due to fire. The fact that the WTC towers did, beckons deep examination.
http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/466.pdf

But I'm going to withdraw from this silliness for a while. As always, thanks for your time and energy.

No experienced structural engineer watching the attack expected the WTC towers to collapse.
Funny thing for him to say, considering how many people expected WTC 7 to collapse. I guess he's only talking about the Twins there though.

I'm sure you have some way of dismissing Bazant's take on this.
External Quote:

The destruction of the World Trade Center WTC on September 11, 2001 was not only the largest mass murder in U.S. history but also a big surprise for the structural engineering profession, perhaps the biggest since the collapse of the Tacoma Bridge in 1940. No experienced structural engineer watching the attack expected the WTC towers to collapse. No skyscraper has ever before collapsed due to fire. The fact that the WTC towers did, beckons deep examination.
http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/466.pdf
Why dismiss it? All three of his concluding assertions are realistic. Despite the first two having been misquoted and misrepresented by many truthers over the years.

BUT - as already identified by me for both you @Thomas B and @Henkka THIS is wrong:

And this comment in that Bazant & Verdure paper is probably wrong:
The subsequent progressive collapse was not simulated at NIST because its inevitability, once triggered by impact after col-
umn buckling, had already been proven by Bažant and Zhou's 2002a comparison of kinetic energy to energy absorption capa-
bility. The elastically calculated stresses caused by impact of the upper part of tower onto the lower part were found to be 31 times
greater than the design stresses note a misprint in Eq. 2 of Bažant and Zhou 2002a: A should be the combined cross section area of
all columns, which means that Eq. 1, rather than 2, is decisive.
Explanatory proof is available if needed.
But I'm going to withdraw from this silliness for a while. As always, thanks for your time and energy.
We are aware of your SOP.

Funny thing for him to say, considering how many people expected WTC 7 to collapse. I guess he's only talking about the Twins there though.
He was referring to "Twin Towers". The Bazant & Verdure paper was written and published in 2007. All the extensive debate up until that time had been Twin Towers focused. The NIST report on WTC7 was not released until late 2008 - so one year after Bazant made that comment.

All the extensive debate up until that time had been Twin Towers focused.
Really, there was not much debate on the first ever tall building to supposedly collapse from fire? If Bazant thought the collapse of the Twins was surprising, WTC 7 ought to have given him a heart attack.

Really, there was not much debate on the first ever tall building to supposedly collapse from fire? If Bazant thought the collapse of the Twins was surprising, WTC 7 ought to have given him a heart attack.
You do have a bad habit of taking quotations out of context.

Remember that Bazant was speaking as a professional with other professionals and honest lay-persons as his target. He holds Conspiracy Theorists in disdain - read his papers. It would be unthinkable for him to even consider CTs worthy of intelligent comment.

The Twin Towers both survived a massive trauma from aircraft impacts. And remained standing for about one hour before the unfought fires caused collapse. So the professionals knew that the towers withstood the impact. Most would have, in that hour, been wondering about the extent of fire. And expecting survival - remember the scale of fire was not fully obvious.

I never had that hour of professional doubt. I first saw the event on "breaking news" (BBC TV in Wales - I was on a tour.) So my first knowledge was based on two video "grabs" - plane impact and collapse. I never knew of the one-hour delay. So it was obvious "plane impact causes collapse". I never gave it another thought for 6 years till I first heard of the nonsense and stupidity of claims for CD from a work colleague who I had not been aware was a Conspiracy Theorist. Tho I had experienced many dealings with CTs in my professional career - public health engineering - so the CTs I experienced were health faddists. The same sort of characters who make up anti-vax and COVID CT claims.

THEN - again you take this comment also ignoring context:
WTC 7 ought to have given him a heart attack.
Why? It was 7 hours later. After fire had caused the collapse of both Twin Towers. And WTC7 was ravaged by unfought fires. And, even if he had earlier had any doubt, he now knew with certainty that fires could cause collapse.

Remember also he is a respected Professor of Engineering. Structural engineering. And, like every such engineer who is competent, he is well aware of the vulnerability of steel-framed high rises to heat weakening from fires. Fire resistance is a major factor in designing steel framed high rises.

Put bluntly he, like me, is one of the last who is likely to either be as ignorant or be impressed by the lies of conspiracy theorist claiming CD. And it only took him 2 days to put out the first professional assessment - that paper co-authored with Zhou "Why Did the World Trade Center Collapse?—Simple Analysis".
.

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Really, there was not much debate on the first ever tall building to supposedly collapse from fire? If Bazant thought the collapse of the Twins was surprising, WTC 7 ought to have given him a heart attack.
Debate about what? The cause??? Fires raged with no fire fighting and that level of heat is fatal to steel frames. Progressive floor collapse? Really basic engineering... a high rise with all floors of the same structural specs... column free floor space is subject to runaway floor collapse - pancaking (top down to bottom,)

Details of the initiation are "debatable" or subject to discussion. The heat cause is accepted but not the sequence of failures and precisely where and how the heat acted. NIST seemed to favor the floor trusses as the culprit. There are perhaps better arguments that the initiation took place in the core. Hard to know because data is scarce and the models are best guesses using physics / engineering.

It seems like the role the structural design played in the collapse (form) is something worthy of discussion / debate such as column free office space plans... massive transfer structures and so on.

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Debate about what? The cause??? Fires raged with no fire fighting and that level of heat is fatal to steel frames. Progressive floor collapse? Really basic engineering... a high rise with all floors of the same structural specs... column free floor space is subject to runaway floor collapse - pancaking (top down to bottom,)

Details of the initiation are "debatable" or subject to discussion. The heat cause is accepted but not the sequence of failures and precisely where and how the heat acted. NIST seemed to favor the floor trusses as the culprit. There are perhaps better arguments that the initiation took place in the core. Hard to know because data is scarce and the models are best guesses using physics / engineering.

It seems like the role the structural design played in the collapse (form) is something worthy of discussion / debate such as column free office space plans... massive transfer structures and so on.
Do others think the heat acted to:
lengthen steel
weaken steel

Obviously heated steel is weaker than room temperature steel.

Did columns lose so much strength that they were too weak to supported the loads?

Did lateral steel (bracing, girders, beams) expand and push columns? (7WTC supposedly had heated beams move from the columns seat... drop and start a local floor collapse)

Did sagging trusses pull in at exterior wall to cause buckling? Was the buckling local or all around the perimeter?

Was the top drop (tilt) caused / initiated by core column failure? Perimeter column failure? both?

Is the tilt of the tops explain by uneven heating of the fires?

Was the twin tower facade able to effectively redistribute load when locally damaged?

Were the falling/tilting top blocks largely intact when they dropped or had partially destroyed interiors?

Why? It was 7 hours later.
Because of what you said here:
So it was obvious "plane impact causes collapse".
Before 9/11, not a single tall building had ever collapsed from fire, no matter how severe. Yet not even 2 hours after the Twins were struck by planes, both had collapsed to the ground. The natural conclusion from that is that large planes going at high speeds striking buildings can cause collapse... Not that fire alone can cause collapse, since that goes against 100% of our previous experience of fires in tall buildings. It's completely logical to assume then that the plane impact played a huge role in causing the building the collapse, and not just by setting fires. (Is it your position that the WTC towers could have collapsed from fire alone, without plane impact?)

So Bazant was surprised that the Twins collapsed, but it was at least a brand new phenomenon. We may have assumed that the towers would survive a large plane impact, but we had never experienced that before, so it was ultimately just an assumption. But with WTC 7, we had experienced large fires in tall buildings many times, and never experienced a collapse. So Bazant should have been much more surprised then, that a third building collapsed with no plane striking it. It also had much larger implications for structural engineering in general, since fires are far more common than planes flying into buildings. So if he thought the Twins merited "deep examination", I wonder what he thought of WTC 7.

Because of what you said here:

Before 9/11, not a single tall building had ever collapsed from fire, no matter how severe. Yet not even 2 hours after the Twins were struck by planes, both had collapsed to the ground. The natural conclusion from that is that large planes going at high speeds striking buildings can cause collapse... Not that fire alone can cause collapse, since that goes against 100% of our previous experience of fires in tall buildings. It's completely logical to assume then that the plane impact played a huge role in causing the building the collapse, and not just by setting fires. (Is it your position that the WTC towers could have collapsed from fire alone, without plane impact?)

So Bazant was surprised that the Twins collapsed, but it was at least a brand new phenomenon. We may have assumed that the towers would survive a large plane impact, but we had never experienced that before, so it was ultimately just an assumption. But with WTC 7, we had experienced large fires in tall buildings many times, and never experienced a collapse. So Bazant should have been much more surprised then, that a third building collapsed with no plane striking it. It also had much larger implications for structural engineering in general, since fires are far more common than planes flying into buildings. So if he thought the Twins merited "deep examination", I wonder what he thought of WTC 7.
None of this is on topic.

@Henkka >> This is the essence of your "off-topic" claim dressed up as "JAQing":

(Is it your position that the WTC towers could have collapsed from fire alone, without plane impact?)
No. As I have made explicitly clear in many previous posts.

IF you want to discuss that topic please OP a thread and I will explain my position one more time.

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@Henkka are the shelves at the bottom sturdier than the shelves at the top?
or are they the same?

@Henkka are the shelves at the bottom sturdier than the shelves at the top?
or are they the same?
And, for a bookshelf, the "columns" do not need to be tapered.

And, for a bookshelf, the "columns" do not need to be tapered.
well, if you had 100 shelves in that bookcase....

well, if you had 100 shelves in that bookcase....
All fully loaded. Now if the adjacent "columns" bounding each module were joined by screws.

To me, it sounds like you're describing the floors being sort of stripped off of the core.

Yes.

You've implied that after the core columns lost lateral support of the floors, they would fail also, but I don't think you cited anything to back that up. The core columns were laterally braced between themselves.

First of all, the core columns were mostly 'braced' by floor beams and slabs. These things provide only limited bending resistance compared to the deep spandrel plates of the exterior walls.

With that said, let's demonstrate that the core could collapse without lateral bracing.

Consider a 40 storey, 480ft remnant whose base load is just 10% of normal at 1.5 to 2.1ksi. I don't know the gyradius, but it's probably in the range of 1-2ft. So let's use this handy derivative of the self-buckling equation

Slenderness² × base strain = 7.8373

Slenderness = 396 to 335

So gyradius = 1.4 to 1.6ft

FIORmTNOTES
1. Wikipedia gives self buckling equation

Length³ × density × gravity × area = 7.8373 × elastic modulus × area moment of inertia

Length × area = volume

Volume × density = mass

Area moment of inertia = gyradius² × area

Mass × gravity / area = base stress

Base stress) elastic modulus = base strain

Therefore we get

Skenderness² × base strain = 7.8373

2.Tge core columns were mostly made of 36 and 42 ksi steel, with a load factor of 50%. Hence the base stress values

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