[alancalverd]

Something of a circular argument developing here. "Low speed" is presumably any speed at which the acceleration of the falling object is for practical purposes indistinguishable from its value in vacuo, and will obviously be different for a sycamore piano or a sycamore seed. We dealt with form factors (though admittedly not autorotational lift) several pages ago, and it turns out that the questioner was specifically interested in concrete buildings falling down on the earth's surface. Even an old pedant like me thinks that we can ignore relativistic corrections when trying to work out why the building collapsed. 

[Pmb]

"Low speed" is presumably any speed at which the acceleration of the falling object is for practical purposes indistinguishable from its value in vacuo, and will obviously be different for a sycamore piano or a sycamore seed.

I was trying to make the point that "low speed" was not an absolute but relevant to the particular scenario. The way he said it seemed to me that he was speaking in absolute terms. Let's leave it at that and not pit pick, shall we?

Even an old pedant like me thinks that we can ignore relativistic corrections when trying to work out why the building collapsed

I never mentioned a falling building. I was talking strictly about the statement In free fall, all objects fall at the same rate. and while true in Newtonian mechanics its not precisely true since GR has a correction for high speed motion. I'm not interested in whether you think I should make this point or not. It's a fact and we can't nor shouldn't say what people want to know.

[Aemilius (OP)]

Right.... sorry about all that Pmb. Thanks for the input (I need all the help I can get!).

[Pmb]

Right.... sorry about all that Pmb. Thanks for the input (I need all the help I can get!).

You're most welcome, sir! I was and will assume that you want to know as much as you can about this even when I know there's things you might have the knowledge to inquire about such as the corrections GR has to high speed free-falling like that around a black hole.

[Aemilius (OP)]

Are you a Ph.D too Pmb? You've both given me something to think about. What do you think of alancalverds aerostatic model of lower-floor blowout? I've read a number of theories about how this building collapsed, but this is the first I've heard of it.

Just a note to add that it was a steel frame building, not concrete Mr. Calverd.... wasn't sure if I'd mentioned that.   
 

[Pmb]

Are you a Ph.D. too Pmb?

Not yet. I started working on it but had to stop due to an illness in the family. I plan on going back to graduate school next fall. I have the equivalence of a masters degree in physics.

You've both given me something to think about. What do you think of alancalverds aerostatic model of lower-floor blowout?

I never saw it. He's in my ignore list for reasons I won't get into in open forum.

[evan_au]

Just noticed your "Profile". Telecommunications.... Electrical Engineer?

Yes, my formal education was in Electrical Engineering.

[alancalverd]

Just a note to add that it was a steel frame building, not concrete Mr. Calverd.... wasn't sure if I'd mentioned that.   
 

Steel frame, certainly, but apparently clad with concrete panels or something similar. Indeed a "concrete" building is essentially a combination of steel mesh to support tension loads and concrete in compression. A framework of rectangular steel lattice is not rigid. You need to brace it with triangulating beams (as in a bridge or a roof) or fill the spaces with panels made from something fairly incompressible like concrete - the usual procedure for large office blocks. Now if you blow out a few of those panels, the steels either side can buckle and the whole lot will collapse - as it did.

[Aemilius (OP)]

Hi Mr. Calverd....

The NIST graph shows velocity, not height, versus time. As Evan pointed out, free(ish) fall produces a linear increase of velocity with time, and this is only apparent after the first 2 seconds of collapse, which is consistent with my aerostatic model of lower-floor blowout.

I understand.... It's actually a pretty cool theory. Like I said I thought I'd seen them all. So in your theory, it would be in the first seconds 1 and 2 (approx.) that the building descended to one degree or another and a rapid pressure build up occurred as a result. Then in the next seconds 3 and 4 (approx.) the actual period of free fall following the blow out event occurs....

Am I close?

[alancalverd]

It certainly consists with the video and graph, and also explains why the graph turns over at the top. At some point the descending piston will be travelling faster than the air beneath can escape, so it slows down a bit until there is enough pressure to cause another blowout - and of course it's now falling through rubble as well as air. 

[Aemilius (OP)]

Hey evan_au....

Electrical engineering, interesting. So, about the aerostatic model of lower-floor blowout (replies 58 and 68).... What do you think?

[Aemilius (OP)]

So I still can't quite get the aerostatic blowout model to work.

The collapse of the "Penthouse", on the left, is the first sign (below) of any catastrophic progressive structural failure....

The rest of the rooftop structure to the right of the now collapsed "Penthouse" atop the building, however, remains stationary for about 4 seconds, and then it (the remaining rooftop structure) suddenly begins to descend largely intact, meaning the core columns must all have given way almost simultaneously (the dreaded horizontal "Newtons cradle" effect). As the remaining rooftop structure begins to descend, even before it reaches the roofline, the roofline also begins to descend, also largely intact, and they're seen afterwards essentially descending (below) together into the free fall period .....

So.... How could the brief 30 to 35 foot drop of the remaining rooftop structure on the right have developed the kind of pressure that would blow out 8 stories of glass, cladding and steel columns many stories below?

The initial collapse of the "Penthouse" above column 79 (on the left) couldn't have built up pressure to the point of being able to blow out 8 stories about the girth of the lower part of the building (required for the observed period of free fall) because the facade continues to stand afterwards for about 4 seconds.

If the symmetry of descent and free fall for 8 stories, or over 100 feet, of the building is to be explained by a symmetrical blowout about the girth of the building, it obviously can't have occurred prior to the blowout. In other words.... While the initial symmetrical descent can explain an eventual blowout, an eventual blowout cannot explain the initial symmetrical descent, which leaves unanswered the original question as to how any initial symmetrical descent could have started to begin with (the dreaded horizontal "Newtons cradle" effect).

Otherwise, if there were to be a blowout event, I would expect increasing pressure to find and then cause to burst only the weakest part of the facade as just part of a larger overall conventional progressive structural failure....

The debris field surrounding the post collapse zone doesn't reflect what one would expect to see from a blowout event of that magnitude (spanning 8 stories about the girth of the building) either....

If pressure had built up sufficiently to blow out all the glass, cladding and perimeter columns at once over a span of 8 stories (over 100 feet) we should expect to find a more substantial debris field, certainly greater than the reported 70 feet in any direction....

....and the way the walls all seem to have fallen inward rather than having been blown outward (notice the undamaged dust covered windows of a neighboring building)....

....and finally, as you noted earlier, "Very few buildings (apart from nuclear power stations and the like) are designed to withstand outward force." So, this obviously wouldn't be the expected post blowout/collapse appearance of a debris pile resulting from that scenario. I couldn't go with the aerostatic blow out model/theory of collapse at this point.

Thanks again Mr. Calverd, it's been very interesting..... I'll let you guys have the last word. Looking forward to chatting with you now and again about other things.

[alancalverd]

If you look carefully at the part just below the penthouse you can see the initial blowout happening about 5 floors below, and you can see the pressure wave propagating downwards and to the right. Now you have not only the roof but some 5 to 8 concrete floors descending as a piston so you don't need a lot of initial blowout to weaken the entire structure. As the collapse progresses, there will be an inward rush of wind behind the descending piston, so a fair quantity of outer wall debris will end up inside or close to the footprint of the original building.

The pressure wave doesn't have to propel the walls very far - a few feet will be enough to relieve the pressure but destroy the integrity of the structure.

[Aemilius (OP)]

Is this what you're referring to Mr. Calverd?

[alancalverd]

Indeed.

[Aemilius (OP)]

Hi Mr. Calverd....

So, let me see if I really understand your aerostatic blowout model....
 

The building has been damaged (the 12 columns toward the rear) and there are several fires continuing to burn on various floors, but it's still standing....

In the first visible stage of the collapse, column 79 (circled) weakens and buckles due to heating from one of the fires. The other 5 columns supporting the West Penthouse immediately follow, buckling/failing in rapid succession, leading to the collapse of the West Penthouse into the building....

For about the next 4 seconds, though nothing much appears to be happening from the outside, on the inside the West Penthouse is actually continuing to crash its way downward like a giant piston through floor after floor gaining both mass and momentum as it goes, and this leads to a sudden rapid aerostatic pressure build up in the lower part of the building (out of view)....
 
 

In the next visible stage of the collapse, as the West Penthouse continues to descend, the aerostatic pressure becomes great enough that a catastrophic bursting, spanning about 8 stories, in the lower part of the building (out of view) begins, starting with the core columns, and it literally blows them away, leading to the beginning of the collapse of the East Penthouse into the building....
   

As the bursting process continues, all the connections between the outer structure and the collapsing core columns are quickly severed by the sudden removal of 8 stories of core support. As a result, all at once within a second of the beginning of the descent of the East Penthouse, 8 stories of perimeter columns, cladding, glass and other materials making up the walls, unable any longer to withstand the increasing pressure and no longer restrained by any connections to the core suddenly expands and blows out, and it's this completion of a symmetrical blowout that breaks up/removes any remaining intact supporting perimeter columns, along with trusses, girders and other structural components, including interior/exterior walls, cladding, glass and other materials of the lower part of the building (out of view)....
 

Finally, in the last visible stage of the collapse, all the various structural components that might have resisted the descent of the upper part of the building have been thoroughly dismantled/largely removed by the completed blowout, allowing the upper part of the building to quite naturally go into free fall for about 8 stories with no apparent resistance from either the core columns or perimeter columns as they had already been largely dismantled/removed by the blowout.... Is that close?

[alancalverd]

You can't analytically separate the columns of a completed building from each other, the cladding, or the floors. The whole thing is designed to be just adequately rigid. If you blow out the cladding it will buckle some of the exterior columns to which it is attached, at which point the outer edge of the floor will fall, thus twisting the inner columns (because the concrete floors are floated on steel crossmembers bonded to the columns) . Steel columns are rigid in compression or tension, but not designed to withstand much torsion, and once buckled, they will collapse under their design compression load.

You can see the bursting on the video in your previous post. As the penthouse begins to fall, the texture of the face of the building changes as the windows bulge. The "texture wave" actually begins  fairly near the top and moves sideways (left to right) possibly quicker than downwards because corridors allow the air to move horizontally but the floors impede vertical propagation of the pressure wave.  If the building had a large atrium or substantial service shafts, this would allow quicker vertical propagation.

Remember that it isn't necessary to "blow away" the lower parts, only to get them to move outwards a couple of feet.     

[Aemilius (OP)]

So the failure was all due to buckling.... None of the columns were actually blown away?

[alancalverd]

Try sitting on a corrugated cardboard box, then get someone to kick the side of the box! Minimally stiff structures live up to their name.

[Aemilius (OP)]

So, none of the columns would have actually been blown away by the explosive pressure that had built up.... but some of the columns would certainly have been weakened and buckled by the blowout.