Acceleration of the falling top blocks.

[WTC Dust]

This falls into the "weak building" category of bandaids that hijack conspiracy theorists have to add to their story to make it work. Those buildings were strong! They weren't weak.

Originally Posted by DGM

Very true. A point ergo will never except is, the towers were incapable of standing without the floors.

[sheeplesnshills]

Originally Posted by WTC Dust

This is a silly concept. The mass of the upper floors did not increase at any point.

Ah, I assume you never covered "dynamics" at pharm school......

A little exercise you could try.......place a can of Diet coke on your toes......apart from having cold toes (assuming the can can out of your fridge) your toes are none the worse.

Now drop that can from above your head onto your toes..........

Notice any difference The mass is of course the same but the loading on your toes is much much greater for a short time.

[WTC Dust]

What you call the "normal" view doesn't account for the beginning moments of the final destruction of those buildings.

Originally Posted by leftysergeant

Let me bring it back to my original premise. The normal way of viewing the collapses is that the tops of the buildings did a pratfall on the lower, causing instant catastrophic destruction of joints at the point of impact, thus initiating a cascade of destruction. This concept may actually confuse some people because itis hard to understand how even a dynamic load would crush down the core columns.

What I see happening, rather, is that the top parts sort of sagged, putting strain on the core columns in ways that they were not designed to bear weight, forcing them apart. This same process, of course, also separates the top core columns from one another. This releases a lot of floor slabs to overload those below to cause a steady progressive collapse down the inside of the office areas and to force the perimeter columns outward.

That the crushing and wedging apart of the core columns would arrest is not really controversial. What is controversial, and it is a point on which we diverge from the twoofers, is that there are other forces at play. The lateral connections between many of the core columns at the top have now been deswtroyed and are standing there, shaking in the tumultuous upward stream of air and being pounds by collapsing floor slabs (which I think we can colclude spararted first fromm their outer connections. This has to have set up some serious vibrations or various sorts of resonnances to further stress the welds and joints.

The ability of a steel grid tower (as championed by ergo) depends on every part's moving and rebounding in unison. If there are columns of uneven lengths standing free at the top of that tower, this will not happen. Thus joints are strained even more, and the stress becomes greater as more joints at the top fail, allowing more chaotic and wider-ranging oscillations of the standing colmuns. We can see this in the final shot of the spires, as one column moves back and forth at least three times before falling. This is obviously inconsistant with CD, which requires simultaneous failure of all columns at any given level.

[sheeplesnshills]

Originally Posted by WTC Dust

This falls into the "weak building" category of bandaids that hijack conspiracy theorists have to add to their story to make it work. Those buildings were strong! They weren't weak.

And what in Pharm school would lead you to think you have the ability to "know" that?

The buildings were strong but they depended on the floor trusses as part of that strength. Each Floor was capable of carrying about 3X its maximum possible static load. However even one floor falling on the one below would apply a dynamic loading in excess of that strength. That floor would then too fail and the two floors would then hit the one below with a force that would instantly cause it too to fail and so on down all 80 plus floors below the impact point.
The floors were the building Achilles heel. The piledriver that destroyed it.

[WTC Dust]

So what destroyed the steel columns, under this theory of yours?

Originally Posted by sheeplesnshills

And what in Pharm school would lead you to think you have the ability to "know" that?

The buildings were strong but they depended on the floor trusses as part of that strength. Each Floor was capable of carrying about 3X its maximum possible static load. However even one floor falling on the one below would apply a dynamic loading in excess of that strength. That floor would then too fail and the two floors would then hit the one below with a force that would instantly cause it too to fail and so on down all 80 plus floors below the impact point.
The floors were the building Achilles heel. The piledriver that destroyed it.

[phunk]

Originally Posted by WTC Dust

I include the columns on the first floor to be a part of the first floor. Not just the "floor" itself, but the entire construction of the first floor. It was strong enough to hold the top 109 floors without a problem for 30+ years.

See, there's your problem. ONLY the columns are strong enough to hold up the building above, the rest is not. Looking down at a cross section of the building, those columns make up about 1% of the area of the building. Once the load above shifts off the columns, there's nothing to stop it from falling.

[phunk]

Originally Posted by WTC Dust

I'd like to know what you think broke apart all the steel columns. Not the floors. It's not like the floors went wackety wackety all the way down and the steel columns remained. They were broken apart.

The columns were built in 3 storey tall sections, bolted and/or welded together. They were designed to support vertical load, not horizontal. When the floors and beams attached to them were being broken apart and torn off the columns, they were exerting horizontal load that the columns weren't designed to handle, breaking the connections between the segments.

[phunk]

Originally Posted by WTC Dust

This is a silly concept. The mass of the upper floors did not increase at any point.

Poorly phrased, but not silly. Just replace mass with weight. For a demonstration of the effect, gently place a brick on one foot, then drop a brick on the other foot from 12 feet, and compare.

ETA: Lol, posted this before I saw sheeplesnshills coke can example.

[phunk]

Originally Posted by WTC Dust

Ewww. 2 pound babies are commonly known as fetuses.

You sure you know anything about biology? Two pounds is WAY past fetus.

[beachnut]

Originally Posted by WTC Dust

So what destroyed the steel columns, under this theory of yours?

Fire destroyed the strength of the steel. Steel columns did not turn to dust or foam as you claim with your idiotic fantasy.

Fire destroyed the strength of steel. You could try science instead of fantasy, but ...

Originally Posted by WTC Dust

I said this "At the relatively low speeds that gravity alone would produce". I never said gravity was a speed, rather, that it would produce a speed. Get it right.

You got it wrong; why can't you get it right?
This statement, along with your inability to grasp a momentum model is an indication you and physics are not on talking terms.

"low speeds". Oh? ZERO to 65.83 mph in three seconds is SLOW????!!!!!

Gravity will produce 60 mph in 2.735 seconds, making Gravity one of the top 8 fastest Cars in the world.

Name a car that does 0-60 in 3 seconds. There are 7 cars close or better than Gravity, a 2011 Ferrari 458 Italia gets close. These cars are not called the world's low speed cars, these are called the World's Fastest Cars. Most cars are "slower" than gravity, to put it in the language of woo.

The people who jumped on 911 were hitting the ground at 100-120 mph; you call this low speed. Good for you.

You don't understand physics.

[Sunstealer]

Honestly, someone who can't use the quote function properly doesn't deserve a response, it's rude, annoying and makes the forum hard to follow.

[WTC Dust]

Don't even try to school me on biomedical science. A fetus (pronounced /ˈfiːtəs/; also spelled foetus, fśtus, faetus, or fćtus, see below) is a developing mammal or other viviparous vertebrate after the embryonic stage and before birth.

Originally Posted by phunk

You sure you know anything about biology? Two pounds is WAY past fetus.

[WTC Dust]

I love it when detractors prove my points for me. See how the steel sagged? That's what steel does when exposed to extreme heat for a significant duration. It sags. It doesn't shatter.

Originally Posted by beachnut

Fire destroyed the strength of the steel. Steel columns did not turn to dust or foam as you claim with your idiotic fantasy.
http://i286.photobucket.com/albums/l...dsteelfire.jpg
Fire destroyed the strength of steel. You could try science instead of fantasy, but ...


You got it wrong; why can't you get it right?
This statement, along with your inability to grasp a momentum model is an indication you and physics are not on talking terms.

"low speeds". Oh? ZERO to 65.83 mph in three seconds is SLOW????!!!!!

Gravity will produce 60 mph in 2.735 seconds, making Gravity one of the top 8 fastest Cars in the world.

Name a car that does 0-60 in 3 seconds. There are 7 cars close or better than Gravity, a 2011 Ferrari 458 Italia gets close. These cars are not called the world's low speed cars, these are called the World's Fastest Cars. Most cars are "slower" than gravity, to put it in the language of woo.

The people who jumped on 911 were hitting the ground at 100-120 mph; you call this low speed. Good for you.

You don't understand physics.

[phunk]

Originally Posted by WTC Dust

Don't even try to school me on biomedical science. A fetus (pronounced /ˈfiːtəs/; also spelled foetus, fśtus, faetus, or fćtus, see below) is a developing mammal or other viviparous vertebrate after the embryonic stage and before birth.

Poor choice of words maybe, but I was replying to you saying "2 pound babies", and in the context, disgusting as it was, they were clearly out of the womb.

[WTC Dust]

Apology accepted.

Originally Posted by phunk

Poor choice of words maybe, but I was replying to you saying "2 pound babies", and in the context, disgusting as it was, they were clearly out of the womb.

[NoahFence]

Originally Posted by WTC Dust

Don't even try to school me on biomedical science. A fetus (pronounced /ˈfiːtəs/; also spelled foetus, fśtus, faetus, or fćtus, see below) is a developing mammal or other viviparous vertebrate after the embryonic stage and before birth.

Pick your science. Pick your topic.

A dumbass like me can school you on ANY of them.

[grandmastershek]

Originally Posted by NoahFence

Pick your science. Pick your topic.

A dumbass like me can school you on ANY of them.

I think the fact that Dr. Dusty had to copy-paste that definition directly from wiki speaks volumes about her competence in her alleged field of expertise.

[Oystein]

Originally Posted by leftysergeant

I have been thinking a great deal over the last couple of days about the rate of acceleration when the top blocks of the twin towers began collapsing.

Everybody seems to assume that the core columns all broke more or less at the same time, to allow the top block to fall more or less at free-fall acceleration. Has that actually been measured?

Only in the context of free-fall does Tony's "missing jolt" make the least bit of sense.

But the seems to me to be an alternate mode of failure that would not produce any jolt.

Think for a moment of the huge "horseshoe" column, smoothly bent with not much cracking. This can, of course, only occur in very hot steel. Is it possible that the columns just sagged enough to let the top blocks come to rest catawampus on the perimeter columns and start to break up, thus wedging the perimeter columns open?

Over at the911forum, I revived an older thread, which started out with someone's misbegotten hypothesis on something, which in turn caused OneWhiteEye to revisit some other thread where he (?) had derived from theoretical considerations of conversation of momentum (and, implicitly, energy) what the collapse acceleration will be if all collisions are inelastic, and asuming that no energy is dissipated beyond the work done in those inelastic collisions.

The result is, analytically, that acceleration will in the long run converge on 1/3 of g. It will start out faster if the initial mass ("top block") is larger, and then take somewhat longer to get near 1/3 g, but the difference is not large. It turns out that it doesn't matter how high the floors are or what their individual mass is.

I get approximately the same result through discrete iteration with a spreadsheet in which I compute each individual collision of "top block" with next floor below from the 95th (or 80th) down to the ground: Acceleration starts somewhat below 1g and above 2/3 g, and drops to not much above 1/3 g towards the end.



Acceleration of 1/3 of g means directly that only 1/3 of the potential energy is turned and sustained as kinetic energy, and the rest is dissipated in the inelastic collisions, mostly as deformation and fracture, and to a small extent as heat.



We are currently thinking hard about whether these close to 2/3 of available energy that gets converted into "destruction" already takes care of / includes all, most, some or none of the destruction of the structural supports that necessarily must be destroyed for collapse to continue^*). My intuition says that most of the energy required to break structural connections is already accounted for in the loss of kinetic energy due to inelastic collision, OWE seems to think otherwise, but I don't know how to model this, and he isn't there yet.

Any energy expended on top of (or temporally after) the inelastic collision to break connections would decrease the collapse acceleration. Again, my hunch is that this is not very significant.

The same is true for all energy (and momentum) that's transferred down the columns and into the ground and thus lost to planet earth. Here, too, my hunch is that this is not very significant.


Now this model that we are talking about seems too simple and unrealistic, but I think it does get us pretty close to true values. The reason is that I think that in the chaos of the collapse front, even though everything is not going smoot and uniform and all collisions have elastic components, it eventually all adds up to being insignificantly different from a total inelastic scenario: As some have said, the perimeter mesh helps to keep most of the material confined to the footprint so there isn't a lot of mass shedding; components that get kicked down elastically undergo further collisions with other floors to give them more chances to dissipate energy and get caught up with the bulk of the collapse front.


Anyway, expect any top-down collapse starting with a sufficient top mass to start above 2/3 g, drop quickly (after a few floors) below 1/2 g and soon converge near 1/3 g.



*) We don't show it in that thread, but we both know (from Bazant's limiting cases) that this amount of energy easily suffices to break enough connections (say: all long truss to column connections). Iirc, Bazant has shown that if the top 15 floors reach a velocity that is equivalent to a free-fall drop of 0.5 meters, then their kinetic energy will overwhelm the next floor worth of connections, and from then on the structure is doomed. (Notice that this scenario does not need to assume any actual free fall at collapse initiation!)

[DaveThomasNMSR]

Originally Posted by Oystein

...

The result is, analytically, that acceleration will in the long run converge on 1/3 of g. It will start out faster if the initial mass ("top block") is larger, and then take somewhat longer to get near 1/3 g, but the difference is not large. It turns out that it doesn't matter how high the floors are or what their individual mass is.

I get approximately the same result through discrete iteration with a spreadsheet in which I compute each individual collision of "top block" with next floor below from the 95th (or 80th) down to the ground: Acceleration starts somewhat below 1g and above 2/3 g, and drops to not much above 1/3 g towards the end.



Acceleration of 1/3 of g means directly that only 1/3 of the potential energy is turned and sustained as kinetic energy, and the rest is dissipated in the inelastic collisions, mostly as deformation and fracture, and to a small extent as heat.

...

Anyway, expect any top-down collapse starting with a sufficient top mass to start above 2/3 g, drop quickly (after a few floors) below 1/2 g and soon converge near 1/3 g.
...

Interesting! As I wrote in Skeptical Inquirer last year (July/August 2011),

Quote:

Second, Chandler argues that being a Newtonian action/reaction pair, the impact force of the upper section on the lower section was only a third of the upper part’s weight. However, I’ve found that his estimate of the downward impact force was too low by a factor of one hundred. In addition, I found that the actual process—a series of twelve-foot free falls punctuated by violent and brief collisions with each floor—would have resulted in an average acceleration of precisely what Chandler measured for the start of the collapse of WTC 1, namely 2/3 g. (By the end of the collapse, my calculations indicate an average acceleration of only 1/3 g, but this can’t be measured in dust-obscured videos.)

Cheers, Dave

[Oystein]

Dave, the interesting result is that this limit of 1/3 g is independent of the local spacial distribution of the mass, and of the absolute mass. It's the same if you multiply the mass of each floor slab by 100 or divide it by 100; it's the same if you have 110 floors or 1100 of 1/10 the actual height^*, and I dare say it is independent of the physical arrangement if the material into slabs, trusses, girders, columns, dead weight etc.

Now the answer to this question that we are still debating, whether an additional and significant amount of energy (and thus momentum) is dissipated to fracture support or not, will bear on the question if the "factor of safety" has a significant effect on collapse acceleration. My intuition is that as long as the energy needed to snap connections is very much less than the potential energy available, then the FoS makes hardly any difference, as I presume that that energy is mostly included in the inelastic-collision-only dissipation.




* In fact, OWE takes this idea to its infinitesimal limit where the building mass is continual - uniform density - as it is distributed over infinitely many floors of zero height.

[ozeco41]

Originally Posted by Oystein

... My intuition is that as long as the energy needed to snap connections is very much less than the potential energy available, then the FoS makes hardly any difference, as I presume that that energy is mostly included in the inelastic-collision-only dissipation...

It is interesting to see that this energy based approach is aligning with my historic (2007-8) explanations where I relied on the concept of "overwhelming" forces/impacts.

There are only two significant types of failures in the "global collapse" or "progression" stage. viz shear off of the OOS floor joists from perimeter and core columns AND shear off of horizontal beams in the core. And the energy to do that is orders of magnitude overwhelmed by the massive falling mass/momentum.

Hence the progressive and successive acceleration of overwhelmed floor structural materials becomes the limiting factor.

It would have been a different story if the columns had played any significant role in resisting collapse. But they didn't and the fact that they didn't is the key to the mechanism which actually occurred. Three parallel and nearly coincident mechanisms if we need to get pedantic at that level of detail.

[Oystein]

Originally Posted by ozeco41

...
Hence the progressive and successive acceleration of overwhelmed floor structural materials becomes the limiting factor.

It would have been a different story if the columns had played any significant role in resisting collapse. But they didn't and the fact that they didn't is the key to the mechanism which actually occurred. Three parallel and nearly coincident mechanisms if we need to get pedantic at that level of detail.

I doubt even that, as I seem to recall that even Bazant's most arrest-friendly limiting case of perfect column alignment predicted overwhelming forces energy. The difference would be measurably different from zero I guess, but still small.

[ETA]This would mean that if there was a terminal velocity observed, as some at the911forum seem to claim, rather than a terminal acceleration (or terminal acceleration = 0), then there would have been an additional and quite mysterious resisting force of (nearly) 1/3 mg up - the opposite of what CD proponents believe who insist that structural connections excerting resisting forces were artificially removed ahead of the collapse front.[/ETA]

And this is as far as I am going to speculate without doing any actual analysis and calculations. I am far out on a limb already.

[ozeco41]

Originally Posted by Oystein

I doubt even that, as I seem to recall that even Bazant's most arrest-friendly limiting case of perfect column alignment predicted overwhelming forces energy. The difference would be measurably different from zero I guess, but still small....

I get confused as to Bazant's initial starting point for global collapse. IIRC he initially assumed one storey drop then reduced it but still had a drop.

that is where Bazant and I part company. I don't comprehend any initiating scenario which somehow created a clear fall drop. And that puts me in a small minority - maybe a minority of 1. BUT the "initiation" was a progressing cascade. Where does that process produce a drop?? However if I press that line I will get dumped on from both sides - Bazantophiles and Bazantophobes.

Been there before.
BTW and IIRC that is also where Chandler and Szamboti got into water that was too deep.

Originally Posted by Oystein

...[ETA]This would mean that if there was a terminal velocity observed, as some at the911forum seem to claim, rather than a terminal acceleration (or terminal acceleration = 0), then there would have been an additional and quite mysterious resisting force of (nearly) 1/3 mg up - the opposite of what CD proponents believe who insist that structural connections excerting resisting forces were artificially removed ahead of the collapse front.[/ETA]

"They" do seem to get lost between V and A -- plus anything related to free body identification or mechanics. "They" are allowed to mix factors from two different scenarios. You and I are not allowed. So deal with them separately.

Originally Posted by Oystein

...And this is as far as I am going to speculate without doing any actual analysis and calculations. I am far out on a limb already.

There is one rule there - Saw the limb off outboard of where you are sitting.

[Oystein]

Originally Posted by ozeco41

I get confused as to Bazant's initial starting point for global collapse. IIRC he initially assumed one storey drop then reduced it but still had a drop.

that is where Bazant and I part company. I don't comprehend any initiating scenario which somehow created a clear fall drop. And that puts me in a small minority - maybe a minority of 1. BUT the "initiation" was a progressing cascade. Where does that process produce a drop?? However if I press that line I will get dumped on from both sides - Bazantophiles and Bazantophobes.

Been there before.
BTW and IIRC that is also where Chandler and Szamboti got into water that was too deep.

Forget any (free)fall drop. It doesn't matter much how the top starts moving, all that matters is that it does start moving and attains a downward velocity / momentum sufficient to overcome the "first collision". If that momentum is gained in 0.5 seconds of freefall at g or 1 second of acceleration increasing linearly from 0 to g or 2 seconds of 0.25g or whatever, all that matters is that a minimum momentum arises.

As soon as the moving block starts impacting major components at rest - we typically think "floor slabs", and if this initial momentum suffices, those components will be overwhelmed, and movement will continue at an average of 0 < a < g

So Bazant says "drop"? Maybe he doesn't mean that literally, or maybe he shouldn't.

That doesn't invaldidate the rest of his work.

Originally Posted by ozeco41

"They" do seem to get lost between V and A -- plus anything related to free body identification or mechanics. "They" are allowed to mix factors from two different scenarios. You and I are not allowed. So deal with them separately.

I don't actually know where this idea of a "terminal velocity" originated; it seems that the motion is difficult to observe at least for the lower third of the towers, for that is cloaked in dust plumes. Did they look at ejections from just below the collapse front disturbing the plumes?

Originally Posted by ozeco41

There is one rule there - Saw the limb off outboard of where you are sitting.

Different solutions are possible
- crawl back towards the trunk
- support the limb
- ...?

[ergo]

This thread is about the acceleration of the falling top blocks, not about cascading floor failures. Make up your minds, bedunkers.

[NoahFence]

Originally Posted by ergo

This thread is about the acceleration of the falling top blocks, not about cascading floor failures. Make up your minds, bedunkers.

how about you show me your evidence then I'll make up my mind

[MIKILLINI]

Originally Posted by WTC Dust

Ah, is this where the rumor started that I said something
"stopped in its tracks"? Because I will reiterate now that I
do not think this happened.

Nothing stopped. Once stuff started heading downward, it
kept going. Not all of the building was turned into foam at
the exact same moment, but once it turned into foam, it
started heading downward and didn't stop until it ploomped
onto the ground like a balloon filled with baby powder, or
actually like a balloon filled with foam, because the stuff
expanded once it hit the ground and rolled down the street.

Some of the building was aerosolized. After this happened,
the aerosol went up into the sky, not downward. But much
of the building did head in a downward direction AFTER it
had been foamed.

Collisions played no role in the destruction of the WTC.

The gravity collapse model is faulty on the numbers, yes,
as I'm sure you've at least heard me say. But it's also faulty
on the energy, as maybe I haven't emphasized enough.

I'll start another thread about the energy, because it isn't
acceleration.

You're so far away from reality with the fantasy weapon analogy, plus the lack of understanding/failing to apply physics and conservation of momentum. The seismic data verifies collision during each towers collapse, Tracy; You can't escape that fact.

[DaveThomasNMSR]

Originally Posted by ergo

This thread is about the acceleration of the falling top blocks, not about cascading floor failures. Make up your minds, bedunkers.

ergo, ergo, ergo.

The big kids have been talking about how the cascading floor failures indeed account most precisely for the acceleration of the falling top blocks.

Do try to keep up!

[DaveThomasNMSR]

Originally Posted by Oystein

Dave, the interesting result is that this limit of 1/3 g is independent of the local spacial distribution of the mass, and of the absolute mass. It's the same if you multiply the mass of each floor slab by 100 or divide it by 100; it's the same if you have 110 floors or 1100 of 1/10 the actual height^*, and I dare say it is independent of the physical arrangement if the material into slabs, trusses, girders, columns, dead weight etc.

Now the answer to this question that we are still debating, whether an additional and significant amount of energy (and thus momentum) is dissipated to fracture support or not, will bear on the question if the "factor of safety" has a significant effect on collapse acceleration. My intuition is that as long as the energy needed to snap connections is very much less than the potential energy available, then the FoS makes hardly any difference, as I presume that that energy is mostly included in the inelastic-collision-only dissipation.




* In fact, OWE takes this idea to its infinitesimal limit where the building mass is continual - uniform density - as it is distributed over infinitely many floors of zero height.

That agrees with most of what I've figured out, also. Plus, the impacts are enough to make collapse inevitable over a wide range of stiffness parameters, etc.

[MIKILLINI]

Originally Posted by ergo

This thread is about the acceleration of the falling top blocks, not about cascading floor failures. Make up your minds, bedunkers.

An ergo truther-operative credo: Separating the dynamics of physics to throw out an argument that these dynamics are separate.

It's not a choice of one or the other ergo; The law of physics is the dynamic of cascading floors and falling top blocks. You've been debunked.

[ozeco41]

Originally Posted by DaveThomasNMSR

ergo, ergo, ergo.

The big kids have been talking about how the cascading floor failures indeed account most precisely for the acceleration of the falling top blocks.

Do try to keep up!

Precisely.

We need some flags for "little kids stay outside - the big kids know what they are talking about..."

[WTC Dust]

Originally Posted by grandmastershek

I think the fact that Dr. Dusty had to copy-paste that definition directly from wiki speaks volumes about her competence in her alleged field of expertise.

That I copied the definition of fetus from wiki means I don't know what a fetus is?

[WTC Dust]

You seem to have given this subject some thought. Can you tell me, what began the first downward acceleration? What was the force that initiated the first movement downward?

Originally Posted by Oystein

Over at the911forum, I revived an older thread, which started out with someone's misbegotten hypothesis on something, which in turn caused OneWhiteEye to revisit some other thread where he (?) had derived from theoretical considerations of conversation of momentum (and, implicitly, energy) what the collapse acceleration will be if all collisions are inelastic, and asuming that no energy is dissipated beyond the work done in those inelastic collisions.

The result is, analytically, that acceleration will in the long run converge on 1/3 of g. It will start out faster if the initial mass ("top block") is larger, and then take somewhat longer to get near 1/3 g, but the difference is not large. It turns out that it doesn't matter how high the floors are or what their individual mass is.

I get approximately the same result through discrete iteration with a spreadsheet in which I compute each individual collision of "top block" with next floor below from the 95th (or 80th) down to the ground: Acceleration starts somewhat below 1g and above 2/3 g, and drops to not much above 1/3 g towards the end.



Acceleration of 1/3 of g means directly that only 1/3 of the potential energy is turned and sustained as kinetic energy, and the rest is dissipated in the inelastic collisions, mostly as deformation and fracture, and to a small extent as heat.



We are currently thinking hard about whether these close to 2/3 of available energy that gets converted into "destruction" already takes care of / includes all, most, some or none of the destruction of the structural supports that necessarily must be destroyed for collapse to continue^*). My intuition says that most of the energy required to break structural connections is already accounted for in the loss of kinetic energy due to inelastic collision, OWE seems to think otherwise, but I don't know how to model this, and he isn't there yet.

Any energy expended on top of (or temporally after) the inelastic collision to break connections would decrease the collapse acceleration. Again, my hunch is that this is not very significant.

The same is true for all energy (and momentum) that's transferred down the columns and into the ground and thus lost to planet earth. Here, too, my hunch is that this is not very significant.


Now this model that we are talking about seems too simple and unrealistic, but I think it does get us pretty close to true values. The reason is that I think that in the chaos of the collapse front, even though everything is not going smoot and uniform and all collisions have elastic components, it eventually all adds up to being insignificantly different from a total inelastic scenario: As some have said, the perimeter mesh helps to keep most of the material confined to the footprint so there isn't a lot of mass shedding; components that get kicked down elastically undergo further collisions with other floors to give them more chances to dissipate energy and get caught up with the bulk of the collapse front.


Anyway, expect any top-down collapse starting with a sufficient top mass to start above 2/3 g, drop quickly (after a few floors) below 1/2 g and soon converge near 1/3 g.



*) We don't show it in that thread, but we both know (from Bazant's limiting cases) that this amount of energy easily suffices to break enough connections (say: all long truss to column connections). Iirc, Bazant has shown that if the top 15 floors reach a velocity that is equivalent to a free-fall drop of 0.5 meters, then their kinetic energy will overwhelm the next floor worth of connections, and from then on the structure is doomed. (Notice that this scenario does not need to assume any actual free fall at collapse initiation!)

[WTC Dust]

Let's say there was enough energy in gravity to snap the connections between the floors and the support columns. Then, under this scenario, what destroyed the support columns?

Originally Posted by Oystein

Dave, the interesting result is that this limit of 1/3 g is independent of the local spacial distribution of the mass, and of the absolute mass. It's the same if you multiply the mass of each floor slab by 100 or divide it by 100; it's the same if you have 110 floors or 1100 of 1/10 the actual height^*, and I dare say it is independent of the physical arrangement if the material into slabs, trusses, girders, columns, dead weight etc.

Now the answer to this question that we are still debating, whether an additional and significant amount of energy (and thus momentum) is dissipated to fracture support or not, will bear on the question if the "factor of safety" has a significant effect on collapse acceleration. My intuition is that as long as the energy needed to snap connections is very much less than the potential energy available, then the FoS makes hardly any difference, as I presume that that energy is mostly included in the inelastic-collision-only dissipation.




* In fact, OWE takes this idea to its infinitesimal limit where the building mass is continual - uniform density - as it is distributed over infinitely many floors of zero height.

[DaveThomasNMSR]

Originally Posted by WTC Dust

Let's say there was enough energy in gravity to snap the connections between the floors and the support columns. Then, under this scenario, what destroyed the support columns?

The support columns fell last, after the floors surrounding them had collapsed. They are called "spires" for the brief time they tottered, before collapsing themselves (no support).

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[Oystein]

Originally Posted by WTC Dust

You seem to have given this subject some thought. Can you tell me, what began the first downward acceleration? What was the force that initiated the first movement downward?

Oh that is easy: Gravity.

[Oystein]

Originally Posted by WTC Dust

Let's say there was enough energy in gravity to snap the connections between the floors and the support columns. Then, under this scenario, what destroyed the support columns?

Again, that's easy: Gravity again. There was a lot (a huge lot) of excess energy to not just snap the necessary and sufficient connections, but also surplus connections, and crush concrete, bend things, and blow the toilets to smithereens.

Any columns still standing after the momentum-driven rubble went past were stripped of lateral support, became thus too slender, and failed mainly due to Euler buckling. Under gravity again of course.

[NoahFence]

Quote:

What was the force that initiated the first movement downward?

Gravity honey.

Gravity.

[ergo]

Originally Posted by DaveThomasNMSR

ergo, ergo, ergo.

The big kids have been talking about how the cascading floor failures indeed account most precisely for the acceleration of the falling top blocks.

Do try to keep up!

Ah, my mistake. Could you just remind me what/whose collapse model you're discussing? Thanks.

[ergo]

Originally Posted by DaveThomasNMSR

The support columns fell last, after the floors surrounding them had collapsed. They are called "spires" for the brief time they tottered, before collapsing themselves (no support).

Right. And again, where can we read the official version of this collapse model? Where, for example, can engineers find this explanation? Thanks.