[alancalverd]

Pretty much the point. Once one column has buckled, the weight of the floor around it and all the structure above and outside it will exert a torque on the neighbouring columns  and they will begin to bend. As soon as the next one has gone beyond its elastic limit you will have more floor area exerting torque on the next nearest neighbours....Hence the gentle initial acceleration building to near-free fall.

It's a mistake to think of modern buildings as composed of independently stable parts - the whole structure is only rigid if it retains full integrity. There were several instances of half-built "box girder" bridges collapsing in the Sixties: these structures were brilliant on paper and in the laboratory but only met their design strengths when complete - which by definition doesn't happen on a building site until the last day. And like office blocks, they were also vulnerable to serious weakening through minor damage. We live with stressed-skin aeroplanes and racing cars because they can be inspected easily, withdrawn from service if damaged, and repaired under non-stress conditions, but civil structures can't.   

[Aemilius (OP)]

Cool theory, but it doesn't add up. It seems to me that for your "aerostatic blowout" model to work here it would have to take into account how all the remaining perimeter and core columns could all have essentially failed at once (starting with the descent of the East Penthouse), rather than progressively like the scenario described above, over a span of about 8 stories in order to match the conditions that we know must have, or very nearly must have existed....

....beneath the falling visible part of the building during its observed descent at gravitational acceleration for 105 feet in 2.25 seconds....

The shockwave/air blast in your model that would have been created by the initial collapse of the West Penthouse within the building by the "piston effect" would not have been powerful enough (left) to account for the creation of those conditions (center), and even if it was powerful enough to have blown out all the cladding and windows and buckle all the remaining perimeter and core columns too (right), which I very much doubt it would have been powerful enough to do, the building still wouldn't have gone into free fall....

Buckling columns don't just go from a hundred percent to zero percent when they buckle, they go from a hundred percent to zero percent while they buckle and that takes time. Whether one column or a hundred, no free fall....

Control on the right, details....
http://picasion.com/pic76/ef2992a1bed34a1ad9d2e8f520c5ad7e.gif

[alancalverd]

Have it your way if you wish - magic?

The rate of stress propagation throughout the structure is the speed of sound, which in steel or concrete is 5 to 7 times its speed in air - about 1 mile per second. And remember that the video does not show immediate free fall but quite slow acceleration in the initial few seconds.

[Aemilius (OP)]

Have it your way if you wish - magic?

The rate of stress propagation throughout the structure is the speed of sound, which in steel or concrete is 5 to 7 times its speed in air - about 1 mile per second.

Right. Looks like you found a novel (if highly improbable) "Newtons cradle" effect to explain the failure/buckling of so many columns at once. Again though, even if that were possible the buckling of all the columns at once will still not result in free fall....

And remember that the video does not show immediate free fall but quite slow acceleration in the initial few seconds.

The initial few seconds? Unless I'm interpreting this improperly, it's not a "few seconds" but only about 1.75 seconds from the beginning of the descent of the East Penthouse to the entire building going into free fall like a rock being dropped off a cliff....

Anyway it wouldn't be when it went into free fall that's amazing, what's amazing is that it went into free fall at all. For example.... Is there some point during this collapse (below right) where one could say "The columns have all clearly buckled and the level of resistance offered by them to the upper part of the building that's descending should be roughly equivalent to that of air (below left) at this point in the collapse."....

I don't think the progressive collapse of a building (below right) can achieve gravitational acceleration (below left) over time through the path of greatest resistance in a manner indistinguishable from air.... Is there an equation that describes how that would work?

   

Thanks again for responding Mr. Calverd.

[Aemilius (OP)]

The rate of stress propagation throughout the structure is the speed of sound, which in steel or concrete is 5 to 7 times its speed in air - about 1 mile per second. And remember that the video does not show immediate free fall but quite slow acceleration in the initial few seconds.

Just thinking that's interesting. I was aware of the speed of sound in steel being greater than the speed of sound in air, but.... Stress propagation? Does that mean that if one bends a 5 foot long iron bar at one end that the other end will undergo some measurable similar type of stress a fraction of a second later? Maybe I'm not clear on the definition of "stress propagation".... Is that seen by physicists as being essentially synonymous with "sound propagation"?

[alancalverd]

The cross bracing and floor reinforcements of a modern building are such that there may be several "rigid" paths, allowing stress to be propagated by tension and compression, between any two points. Tension and compression forces are transmitted at the speed of sound - by definition.

Imagine a simple cubical box frame. It has tension and compression rigidity along the axes of the struts but is very weak in shear and torsion. So we add diagonal tensioners, or fill the faces with compressively rigid panels, and now any force applied to a corner will be transmitted rapidly to all the others.   

Bending a single bar beyond its elastic limit at one point won't transmit much stress to the other end, but in a real building the ends are connected  by a whole lot of other bits of rigid structure. Hence you have to look at your collapsing building as an entity, not a bunch of disconnected components.

[Aemilius (OP)]

Thanks Mr. Calverd.... understood.

[Aemilius (OP)]

Hi Mr. Calverd. As you outlined earlier....

Once one column has buckled, the weight of the floor around it and all the structure above and outside it will exert a torque on the neighbouring columns  and they will begin to bend. As soon as the next one has gone beyond its elastic limit you will have more floor area exerting torque on the next nearest neighbours....Hence the gentle initial acceleration building to near-free fall.

....in a progressive collapse due to buckling, the buckling of one column leads to the buckling of the next, and the buckling of that column leads to the buckling of the next and so on. In that scenario (starting with column 79 which would be on the left) we should, at least to some degree, expect to see some recognizable signature of that failure mode during the collapse. It should have progressed across the 300 foot wide facade of the building from left to right during the buildings descent, but we don't see anything like that. Buckling can't account for how the conditions required for free fall that we know must have existed, or very nearly existed, could have arisen beneath the visible upper part of the building as it descended either. That scenario doesn't match observations....

Post blowout (slower than free fall) progressive column
failure due to buckling.

The rate of stress propagation throughout the structure is the speed of sound, which in steel or concrete is 5 to 7 times its speed in air - about 1 mile per second.

With the "speed of sound stress propagation" approach, by which (theoretically) all the remaining columns throughout the building could've been buckled at roughly the same time following the buckling of column 79 and subsequent collapse of the West Penthouse, any "aerostatic shockwave" that resulted, just as with the first scenario, would only result in buckling at best which, though it may account to some extent for the initial uniform descent of the facade, again, doesn't account for the conditions required for free fall we know must have existed, or very nearly existed, or how those conditions could have arisen beneath the visible descending upper part of the building....

Post blowout (slower than free fall) simultaneous
column failure due to buckling.

 
In neither of those scenarios (or any scenario that only buckles the columns) would an aerostatic blowout have been powerful enough to have physically blown out all the remaining columns, and since they could at best only have caused the columns to buckle, knowing as we do that buckling columns cannot give rise to or match the conditions required for free fall to occur....

....neither the mechanism of buckling nor the outcome predicted by it can in any way account for or explain the prevailing conditions we know the upper part of the building must have fallen under....

In other words, it's inconsistent with the observation of free fall since we know buckling cannot give rise to the conditions required for free fall to occur, so the "areostatic blowout" model for how the building came down fails.

Nice try though!

[alancalverd]

the initial uniform descent of the facade,

not seen on the video. You can see the propagation of a shockwave diagonally across the front of the building and the roof accelerates up to near-free-fall for several seconds. The acceleration only decreases when the collapse is almost complete.

My concern is that you are unlikely to accept any explanation other than the sudden magical and simultaneous disappearance of all the steelwork, which would be a proud first for the demolition industry, especially if it rematerialised on the far side of the moon.

[Aemilius (OP)]

You can see the propagation of a shockwave diagonally across the front of the building and the roof accelerates up to near-free-fall for several seconds. The acceleration only decreases when the collapse is almost complete.

A moot point. Your catastrophic aerostatic blowout/speed of sound stress propagation shockwave (really reads more like it was hit by an asteroid!), as we discussed earlier, could have only buckled some of the columns, and even had it been powerful enough to buckle all the remaining columns, knowing as we do that buckled/buckling columns, whether weakened by heat (left) or by overloading (right), whether buckled in sequence or simultaneously, whether one or a hundred....

Control on the right, details....
http://picasion.com/pic76/ef2992a1bed34a1ad9d2e8f520c5ad7e.gif

....cannot give rise to or match in any way the conditions required for the observed period of free fall the building verifiably underwent. In other words, whatever this "shockwave" did, it couldn't have created the required conditions for gravitational acceleration "The condition under which a body is, literally, free to fall under the influence of the local gravitational field with no resistance to its acceleration."

The model still fails.

My overall impression (not trying to be rude) is that somehow you'd like to minimize the significance of free fall by referring to it as "near-free-fall" and similar, maximize the impression of suddenness of some modes of failure that can "come down very quickly" and emphasize the inherent lack of structural integrity/flimsiness of construction in this case but, except for progressive structural failure involving things like bridges that pass through the air over rivers and such, you'll not succeed at marrying progressive structural failure of any building to gravitational acceleration.... if I'm not mistaken, it's right up there with perpetual motion. Haven't you some equation or formula that would bear any of this out?

[alancalverd]

Nothing moot about it: the evidence is all on the video - or was that a fake?  Anyway here are the relevant equations

a = F/m  (Newton's Law, where F is the net force)

F -> mg (= GmM/r²) as the supporting structure fails in vacuo.

v = u + integral(at)dt  at any time

These equations describe the observed speed/time curve quite nicely. You can't "minimise the significance of free fall" because the curve pretty closely approximates to free fall over most of its length.

What, apart from structural failure and gravity, do you think could cause a structure to collapse at a rate approximating to free fall, apparently without damaging adjacent structures.? A giant vacuum cleaner, perhaps? 

[Aemilius (OP)]

My concern is that you are unlikely to accept any explanation other than the sudden magical and simultaneous disappearance of all the steelwork, which would be a proud first for the demolition industry, especially if it rematerialised on the far side of the moon.

Any explanation? We've only discussed one theory so far Mr. Calverd, yours, so I'm not sure how your "concerns" made it all the way out there into left field. If it was magic I was looking for though, I would have instantly accepted your catastrophic aerostatic blowout/speed of sound stress propagation shockwave model.... it's a beauty!

Nothing moot about it: the evidence is all on the video - or was that a fake?

Your model only buckles the columns, and since we know buckled/buckling columns can't account for or explain the creation of the conditions required for free fall, it's moot. You can buckle all the columns on every floor of the building at the speed of light if you wish.... no free fall. You must know this. 

Anyway here are the relevant equations

a = F/m  (Newton's Law, where F is the net force)

F -> mg (= GmM/r²) as the supporting structure fails in vacuo.

v = u + integral(at)dt  at any time

These equations describe the observed speed/time curve quite nicely. You can't "minimise the significance of free fall" because the curve pretty closely approximates to free fall over most of its length.

I get the free fall part. What I was really asking you for is some hypothetical scenario with a formula or equation, even a crude graph, anything that describes how any falling object, with a starting velocity of 0, could gently accelerate building to free fall speed while overcoming resistance in the process. For example.... How long would it take a 100 pound cannon ball dropped from a height of 1000 feet (with a starting velocity of 0) working against a resistance of 10 pounds to achieve (in vacuo if you prefer) gravitational acceleration? 

What, apart from structural failure and gravity, do you think could cause a structure to collapse at a rate approximating to free fall, apparently without damaging adjacent structures.? A giant vacuum cleaner, perhaps?

What apart from structural failure and gravity? My impression is that you're still including/considering gravity driven progressive structural failure as something that might be able to explain this.... it can't. There is no gravity driven progressive structural failure mode that can result in gravitational acceleration (except for bridges and other structures that pass through air), so I don't know. The only model I've seen so far that really displays a solid one to one behavioural correspondence with the video evidence is closer to your "brick shed gas explosion near the base of the structure", which you only touched on briefly. 

Originally the idea was to firmly establish what the conditions are that govern free fall and you did that.... "The condition under which a body is, literally, free to fall under the influence of the local gravitational field with no resistance to its acceleration."....

We agreed that this (below) was a fairly accurate and reliable empirical method of determining, by comparing distance travelled and rate of descent of the red marker with a control, that the scenario weight must have fallen under free fall conditions (nothing beneath it) despite not being able to see into the space it was falling through....

Control on the right, details....
http://picasion.com/pic76/ef2992a1bed34a1ad9d2e8f520c5ad7e.gif

....which naturally led to the comparison....

.... establishing the conditions (nothing beneath it) under which the visible upper part of the building must have fallen....

Now, you're asking me to believe that there are other conditions under which free fall can occur, and even suggesting that the two fall time scenarios below, under certain conditions, can actually be the same even though in the one scenario (left) there's considerable resistance/mass occupying the space beneath the falling object, and in the other scenario (right) there's nothing but air occupying the space beneath the falling object....

Even after agreeing about the improbability of your catastrophic aerostatic blowout/speed of sound stress propagation shockwave being able to do anything more than buckle a few columns (or even all the columns, it makes no difference) you're continuing to insist that buckling, a mode of structural failure we know doesn't create the conditions for or result in free fall....
 

Control on the right, details....
http://picasion.com/pic76/ef2992a1bed34a1ad9d2e8f520c5ad7e.gif

....somehow created the conditions for and resulted in free fall!

Control on the right, details....
http://picasion.com/pic76/ef2992a1bed34a1ad9d2e8f520c5ad7e.gif

Abracadabra.... Mr. Calverd.

[alancalverd]

I get the free fall part. What I was really asking you for is some hypothetical scenario with a formula or equation, even a crude graph, anything that describes how any falling object, with a starting velocity of 0, could gently accelerate building to free fall speed* while overcoming resistance in the process. For example.... How long would it take a 100 pound cannon ball dropped from a height of 1000 feet (with a starting velocity of 0) working against a resistance of 10 pounds to achieve (in vacuo if you prefer) gravitational acceleration? 

It can't. If F = mg - f, the mass can never accelerate* at g.

But then it didn't, so what's the problem?

I was very careful always to state "near free fall" because there was obviously always some resistance. Not a lot, but if you calculate the slope of the linear part of the velocity/time graph very carefully you will find that it is a bit less than g, and turns over at the top as the falling roof approaches a terminal speed with increasing f.   

No need for a hypothetical scenario - this is how loaded minimally stiff structures collapse: slowly at first, then more rapidly up to terminal speed. Try it with a house of cards! 

*Remember that free fall isn't a speed but an acceleration.

[Aemilius (OP)]

Thanks, my error.... meant to say acceleration not speed. 

[alancalverd]

OK, so your cannon ball weighs 100 lb = mg  (if you use the proper Imperial system of units, this gives the mass m of the cannon ball as 100/g, about 3.5 slug)

Resistance = 10 lb

So the accelerating force is a constant 90 lb

So from the instant is is released, the cannon ball accelerates at a constant 0.9 g.

In order to accelerate slowly at first, then gradually more rapidly, you need to replace the constant retarding force with a gradually decreasing one. Pretty much what happened to the roof of the building, in fact. The initial retarding force was obviously sufficient to prevent the roof from collapsing since the structure was built, then a bit of the structure gave way, the roof began to move, and the supporting structure progressively disintegrated, allowing the roof to accelerate more rapidly towards g, limited by increasing aerodynamic drag until it reached terminal speed or hit the ground, whichever came first.

[Aemilius (OP)]

Hi Mr. Calverd (hope you had a nice Christmas!)....

Your model seems to be growing more complicated, like a perpetual motion machine that really can work.... if we can just manage to add that one last gear!
 
Originally, we just had the brick shed "aerostatic blowout" gear to drive the whole thing, but when it came to light that the bursting event would not have been powerful enough to remove any of the columns creating the conditions required for free fall to occur, only buckling some of them at best....

The "speed of sound in steel stress propagation shockwave" gear is added to explain an even greater and more sudden weakening and subsequent near simultaneous buckling of all the columns, but when it came to light that even more forceful buckling of all the columns at once would not create the conditions required for free fall to occur....
 
"The roof began to move" gear is then added to explain how events occurring on the roof could have caused the columns to not only have buckled, but also to have "progressively disintegrated" (presumably fast enough to create the conditions required for free fall) 20 or more stories below where they would likely have been heavier and stronger....

And all of it, the whole "aerostatic blowout / speed of sound in steel stress propagation shockwave / roof began to move" contraption of catastrophic buildup of aerostatic pressure purportedly responsible for all this is powered by just the first 25 to 30 feet of descent of the West Penthouse, when as you say, the first evidence of a bursting event is seen along with an aerostatic shockwave texturally rippling across the buildings facade (apparently without much regard for any interior walls or flooring) along now with roof movement that purportedly causes immediate buckling and subsequent progressive disintegration (progressive disintegration?) of the columns many stories below....

It's almost as though you're attempting to conjure a nuclear explosion from a firecracker!
 
And we still have one more little gear left over that will help smooth things out.... We mustn't forget that the building was very badly designed (probably a junior architect at some nickle and dime outfit working out of a garage somewhere), and as anyone with eyes can see it was clearly a heavily loaded structure that was very poorly engineered and flimsily constructed (some say just barely able to stand!), and besides, free fall never really ocurred anyway making it all quite ordinary, so.... What is all the fuss about?
 
In a nutshell, the reason you're having to do all this is because of the inadequacy of the original precedent setting example you used for your model. The aerostatic blowout in the "brick shed" analogy, wherein an explosive aerostatic blowout following structural failure in the lower part of the walls can result in complete removal of support, allowing the structural components of the roof (without the shingles) to approximate free fall for a period of time under the conditions required for free fall to occur, ultimately couldn't be used to support an aerostatic blowout in the case of the building because, unlike the complete removal of support that could be expected to occur at some point in the case of the brick shed example, the same mechanism when applied to the building leaves the columns in place.... and you've been struggling with that ever since.
 
It is impossible for any period of free fall to occur in the case of the building in the same way it could be expected to occur in the case of the brick shed from an aerostatic blowout because the conditions required for free fall to occur are actually created at some point during the post blowout descent of the brick shed in the example, but the conditions required for free fall to occur are never actually created at any point during the post aerostatic blowout descent of the real building.
 
The aerostatic model fails.

I was very careful always to state "near free fall" because there was obviously always some resistance.

As far as whether or not it went into free fall, the NIST web page just says.... "Stage 2 (1.75 to 4.0 seconds): gravitational acceleration (free fall)" ....followed by.... "During Stage 2, the north face descended essentially in free fall, indicating negligible support from the structure below." I'm assuming they're as familiar with the precise use of language as you are so I'm going with that.

After your review of the graph though, how much less than g did you estimate it was.... Do you remember?

[alancalverd]

Not sure what you are getting at here. On the one hand you say it is impossible to create the conditions for free fall, and on the other you are claiming that it was observed.

NIST was properly circumspect in its language   

descended essentially in free fall, indicating negligible support from the structure below."

Qualifying adjectives are not zeroes.

Far from adding gears (not the way to build a PM machine - simpler is better) I'm just trying to explain what you can see in the video, using known physics and engineering. A real building is a very complicated and interconnected structure so the best we can achieve from a blurred external video is bound to be an approximation, and the real thing will have a lot more hidden gears.

Difficult to estimate the actual acceleration from the image I have of the NIST graph. g is around 32.2 ft/sec² and the maximum slope of the graph is certainly " a bit more than 30". I would be surprised if it exceeded 32, and the only way it could reach or exceed 32.2 would be if the air was being sucked out of the building. You could do that with an explosive but that would produce a different shockwave pattern from what we observe in the video.

[Aemilius (OP)]

I didn't say it's impossible to create the conditions for free fall (the brick shed is a good example), what I said was it's impossible for any period of free fall to have occurred in the case of the building in the same way it could be expected to occur in the case of the brick shed example you've constructed your theory around because free fall was observed (during the descent of the building), and that since nowhere in the course of your model playing out would the conditions required for free fall to occur be created, your model fails.

[alancalverd]

In what way? I haven't "constructed a theory around a brick shed" because we know that this was a steel frame building, and I've gone to a lot of trouble to explain how torsional stresses are incurred in a collapsing steel-and-concrete structure. The "brick shed blowout" is just a simple example of aerostatic collapse under an intact roof, which can result in loads beyond the design limit. A building with significant internal structure is bound to be a bit more complicated.

Nor have I criticised the design or construction of this building. "Just stiff" is optimal for civil structures and this one had presumably tolerated its design stresses of floor loading and windage. Building codes are particularly stringent with regard to fireproofing of steelwork precisely because it is prone to spectacular collapse under torsional load, which suggests that the initiating fire was particularly intense - sprinklers and passive protection should provide adequate time for evacuation under foreseeable conditions. 

[Aemilius (OP)]

In what way? I haven't 'constructed a theory around a brick shed' because we know that this was a steel frame building...."

Maybe I misunderstood (shouldn't surprise anyone, I'm an eighth grade dropout!), but I got the strong impression, at least at the time, that in reply 68 where I described my interpretation of your theory in some detail, including a schematic animated representation that very much resembles the brick shed example....

....and judging by your affirmative response in reply 69, it looked like that was exactly what you had in mind and had originally constructed your theory around, you even mentioned it as such in connection with the NIST graph in reply 58 saying that it was "....consistent with my aerostatic model of lower-floor blowout."
 
Apologies though.... if I was mistaken.