Has anyone seen a realistic explanation for "Progressive Collapse"

[William Rea]

William, it's a paper written by engineers, for engineers. It's not intended for the general public. It's not on Oprah's book list. You'll have to ask engineers what they think of it.

It's a "paper" written to give the appearance that something is being done. Actually calling it a "paper" in the conventional sense is misleading because it doesn't advance or extend the body of knowledge, it just reiterates what is largely 1st Year Degree training.

Like I implied before, any Engineer not already doing what is in this "paper" should be so ashamed of themselves that they will already have left the profession!

 

[gumboot]

Of course, this fellow also thought those big power lines out in the country side were designed to walk (hence, their general bipedal appearance) in case of earthquake or other disasters...

That is so awesome...

Back onto the OP though...

As a layman... one thing that often bugs me. There is much talk of the energy required to crush the initial floors and get the party started.

Someone made a reference of several GJ of energy just for the first moments. It is also used in reference to the top section remaining intact at initiation of collapse.

This all works on the notion that the building is sitting there happily intact, and suddenly from some where enormous forces compress the top floors through those immediately beneath.

I would agree that such a thing was impossible. Had that been what happened to the towers, I'd be joining those in demanding an explanation.

But that's not what happened. As a layman, watching video and photographs, I can see that's not what happened. The experts who studied the collapses have never said that happened. The witnesses on the scene never said that happened.

The only people claiming that happened are the people who are also saying that COULDN'T have happened. Go figure.

Here's what I understand to have happened:

-Airliner crashes into building, severing columns, destroying floors, and exposing steel by stripping fire proofing.
-Extensive fires burn through many floors.
-Floor trusses heat up from the fires and begin to sag.
-Some floors partially or completely collapse under the loading. The remaining trusses sag further, pulling the exterior walls inwards producing shear stress (is that the right word?). Basically, the forces stops being compression.
-The hat truss transfers loading from severed core columns to exterior columns, further loading the bowing exterior walls.
-At some point the bowing of the exterior walls reaches a critical point at which the excessive loading becomes more than the material can resist. At this point the exterior wall, as a structural element, fails.

Now. What happens next?

Well, as we know, by this stage the floor trusses in the impact area have already structurally failed - they have either collapsed already, or are sagging. This means, once the exterior walls fail, the only structural integrity within the collapse zone is the core columns - many of which have ALSO been severed or damaged.

Remember, the sagging of the walls occured across the entire impact zone. That means failure was simultaneous across this entire zone. What happens if you instantly remove the exterior and floor trusses of 5 or 6 floors? Will the damaged core manage to keep the upper floors floating above?

Of course not. The upper section will immediately begin to fall through the collapsed space. It will meet no resistance until it comes into contact with the intact floors immediately below the impact zone.

So the issue is, how much energy does this upper section of floors have, after having free-fallen through the space of five or six floors? And is it enough magnitudes of energy greater than the dead load of the upper floors to overcome the redundancy of that first intact floor, resulting in continuation of the collapse?

Because the way I see it, logically, if that first intact floor did not stop the collapse, there's no way any other floor below it was going to stop the collapse. Unless anyone is capable of explaining how that first floor would stop the collapse, their cause is lost.

-Gumboot

 

[Muckar-duva]

Reading 9/11- an Oral History, from what survivors from upper floors say, the destruction was well underway almost immediately. Sagging floors, buckling walls, marble popped out from the elevators' walls- all in all, a lot of statements about the fact that the planes damaged the structure of the buildings quite severely.

 

[gumboot]

Reading 9/11- an Oral History, from what survivors from upper floors say, the destruction was well underway almost immediately. Sagging floors, buckling walls, marble popped out from the elevators' walls- all in all, a lot of statements about the fact that the planes damaged the structure of the buildings quite severely.

Yup. The New York Times article on those trapped in the North Tower indicates the same - widespread structural failures well before global collapse occured.

-Gumboot

 

[einsteen]

Einsteen, if I may try:

The failure propagation front progresses downward much faster than it progresses upward, because the "disintegrated" floors will continue to impel the downward propagating front, while actually reducing the upward propagating front. Capiche?

Let me say first that nothing goes upwards, I mean relatively upwards. Yes g is still working during that collapse, but if you want to separate the propagating fronts (of how you call them) and assume a part is going faster downward than a part upward then the upper part cannot contribute its kinetic energy.

 

[William Rea]

That is so awesome...

Back onto the OP though...

As a layman... one thing that often bugs me. There is much talk of the energy required to crush the initial floors and get the party started.
...Because the way I see it, logically, if that first intact floor did not stop the collapse, there's no way any other floor below it was going to stop the collapse. Unless anyone is capable of explaining how that first floor would stop the collapse, their cause is lost.

-Gumboot

Simple question, if the WHOLE of the impact floor zone was damaged and failed in unison, why did the top tilt? There would be no moment on the top if this was so, which proves from observation that the collision damage did not penetrate through the whole building.

It is possible for the falling portion of the tower to penetrate the first floor and stop at subsequent ones. The building can act as a brake on the PE to KE conversion process so the whole thing does not rely on the credibility of the first floor to collapse.

 

[einsteen]

In general if the collapse is natural the weakest storey will go first, from video observation and the fact that the plane hit more floors you see that the floors around the weakest floors are weaker than the stronger floors far from the impact zone.

The global collapse depends on the energy to break a storey. If the upper block does not integrate you can calculate a critical energy to break a storey, if the energy is equal to that energy then the block will travel downwards with constant speed (to be more precise it will fluctuate around a constant speed), if the critical energy is lower than the kinetic energy of the solid upper block it will travel down and accelerate, if the energy is higher than the critical value it will slow down and stop after some storeys.

It is easy to calculate that energy, if the block has mass Mblock and it got another distance of h_free to fall (v1 is initial velocity of the block and v2 the velocity of the block after travelling the distance h_floor) then you have

V2^2=v1^2+gh_floor-(2E_break/Mblock)

Then Ecritical=(1/2) Mblock g h_floor

ps. of course if you assume no mass is lost the model should be more precise because during the fall mass adds and then there is more kinetic energy for the next storey to break

 

[Shrinker]

V2^2=v1^2+gh_floor-(2E_break/Mblock)

Could you show your working for this?

 

[MRC_Hans]

Simple question, if the WHOLE of the impact floor zone was damaged and failed in unison, why did the top tilt?

I never get you people. First it is "Why didn't the towers topple, instead of collapsing straight down?". Now you ask why they tilted......

The top tilted because nothing is perfect. Weakening was not entirely uniform.

And, what this means is that not only did the floors just below the collapse zone have to withstand the impact of the falling top, but it was not uniformly distributed, something that would make collapse even more likely.

There would be no moment on the top if this was so, which proves from observation that the collision damage did not penetrate through the whole building.

Of course it didn't. It would have collapsed immidiately, if so.

It is possible for the falling portion of the tower to penetrate the first floor and stop at subsequent ones. The building can act as a brake on the PE to KE conversion process so the whole thing does not rely on the credibility of the first floor to collapse.

This is just your assumption. However, let us say that you are right; there might exist a scenario where only a few floors collapse and the building then holds. So what? Does this in any way indicate that it is impossible, or even unlikely, that a total collapse happens?

Hans

 

[MRC_Hans]

In general if the collapse is natural the weakest storey will go first, from video observation and the fact that the plane hit more floors you see that the floors around the weakest floors are weaker than the stronger floors far from the impact zone.

WOW! ... Try to read that again. What were you trying to say, if anything?

The global collapse depends on the energy to break a storey. If the upper block does not integrate you can calculate a critical energy to break a storey, if the energy is equal to that energy then the block will travel downwards with constant speed (to be more precise it will fluctuate around a constant speed), if the critical energy is lower than the kinetic energy of the solid upper block it will travel down and accelerate, if the energy is higher than the critical value it will slow down and stop after some storeys.

You are assuming that:

1) The energy needed to break each floor is constant.

2) The energy available to break each floor is constant.

#1 is probably wrong, and #2 is certainly wrong.

We can see from the videos that jets of air are expelled from windows a considerable distance below the collapse zone (CT'ers call this squibs). This could indicate that structural damage is happening inside the building in advance of the main collapse (for instance heavy parts falling through floors, steel supports being punched down ahead of the falling part). And of course, the structure has to transmit the downward forces from the collapse, as evidenced by the seismic record.

Thus, as the collapse progresses, the remaining structure is increasingly weakened, probably crumbling over an ever larger collapse zone (this is hidden by dust).

As for #2, you are deliberately ignoring the fact that an increasing amount of wreckage is coming down on each successive floor.

In conclusion, while it might be possible to imagine a scenario where the collapse stops, this is highly unlikely; once the first floor fails, the rest are almost certainly doomed.

Hans

 

[einsteen]

Hans,

Of course are the E's not constant, I'm again using F.R.Greening's argumentation and model. If I use his name he is the collapse HERO,
if I don't mention his name I'm attacked, the fact that v2<>v1 means that the energy available is not constant.

And that energy to break a floor is really really questionable. I think the energy needed to break a floor is over 1GJ even for the weakest floors, to be more precise I don't think that, it is video observation.

@Shrinker, multiply all terms by Mblock/2 and it looks more familiar.

 

[Shrinker]

@Shrinker, multiply all terms by Mblock/2 and it looks more familiar.

I recognise v^2 = u^2 + 2as but I don't follow you from there. I don't have a physics degree so please spell it out for me. PS are you aware this forum supports Latex for formulae. Don't know how to use it myself though...

 

[einsteen]

Hey didn't know that...direct latex....

What Greening in fact does is: for each floor that merges its mass with the next floor use conservation of momentum: P_before=P_after, for the first block of 14 floors collapsing onto #15 you then have a factor 14/15 decrease in speed for the falling block (the next time 15/16 and so on), this will slow down and slow down.

One big mistake is that some people apply conservation of momentum for the whole building as a whole, that is nice for die-hard debunkers, then they divide the block by the rest of the building concluding that the end speed is 14/110th of the initial speed,

this site does that for example

http://www.911dossier.co.uk/momentum.html

this is very wrong (although I like the story) because the conservation of momentum is valid during the impacts, between those floors the block got 3.8 meters to fall and during that fall it increases its speed, and that is a consequence of F=m*a.
It is fact no closed system, g is still working.

The v1 and v2 that I mean have nothing to do with the merging of blocks but is in fact the increase of velocity between the two merging phases.

If such a mass is Mblock (whatever it is at that moment) then you can write

E_kin_block_top+E_potential_released=E_kin_block_down+E_break

that is

(1/2)Mblock v1^2+Mblock*g*h_floor=(1/2)Mblock v2^2+E_break

or

v1^2+2*g*h_floor=v2^2+2E_break/Mblock

You can verify your formula, if E_break=0 and v1=0 (first floor removed completely) then v2=sqr(2*g*h_floor)=8.6 m/s

and again a typo at top, forgot factor 2..time to take a pencil + paper and isolate a while...this doesn't go together with working

 

[Shrinker]

Thank you einsteen, I follow it now.

For latex put latex and /latex tags around your equations. It will make them much more legible IMO.

 

[William Rea]

I never get you people. First it is "Why didn't the towers topple, instead of collapsing straight down?". Now you ask why they tilted......Hans

Tell me where I said that. My username says William Rea not "people".

 

[Augustine]

It's a "paper" written to give the appearance that something is being done. Actually calling it a "paper" in the conventional sense is misleading because it doesn't advance or extend the body of knowledge, it just reiterates what is largely 1st Year Degree training.

Like I implied before, any Engineer not already doing what is in this "paper" should be so ashamed of themselves that they will already have left the profession!

Clearly you have no experience in the practice of consulting structural engineering. The NIST paper, so far as I can tell, is intended to provide additional perspective on a phenomenon that is addressed only in the most general sense in the building codes, and attempt to provide some overarching guidance for practicing engineers. The paper addresses the indirect method and direct method of design for resisting progressive collapse, and touches on some practical details. The vast majority of buildings are likely designed for progressive collapse by indirect methods, such as incorporating typical details to enhance the ductility of the structure.

I would agree with you that the engineers most likely to read this paper are the ones who don't need to; and the ones least likely are the ones who should.

 

[Augustine]

It is possible for the falling portion of the tower to penetrate the first floor and stop at subsequent ones. The building can act as a brake on the PE to KE conversion process so the whole thing does not rely on the credibility of the first floor to collapse.

To halt the collapse, the plastically dissipated energy (the energy to form plastic hinges in the columns) in the impacted floor would have to be greater than the gravitational potential energy released from the fall of the floors above (converted to kinetic energy). In the WTC, the kinetic energy was on the order of 8 times greater than the energy required to form plastic hinges. Consequently, the collapse would accelerate from floor to floor.

 

[Augustine]

Let me say first that nothing goes upwards, I mean relatively upwards. Yes g is still working during that collapse, but if you want to separate the propagating fronts (of how you call them) and assume a part is going faster downward than a part upward then the upper part cannot contribute its kinetic energy.

I think you misunderstand. Your contention was that the upper block was being treated as an infinitely strong block and was not collapsing. On the contrary, Bazant very explicitly states that collapse will progress through the upper block; however, the collapsed floors will reduce the energy collapsing stories upward (relatively), while increasing the available energy for collapsing stories downward. Consequently, the rate of collapse WILL NOT be equal; the floors in the falling block will collapse at a slower rate than the building floors below the collapse.

 

[Augustine]

if the energy is equal to that energy then the block will travel downwards with constant speed (to be more precise it will fluctuate around a constant speed), if the critical energy is lower than the kinetic energy of the solid upper block it will travel down and accelerate, if the energy is higher than the critical value it will slow down and stop after some storeys.

ps. of course if you assume no mass is lost the model should be more precise because during the fall mass adds and then there is more kinetic energy for the next storey to break

These are correct statements. What you refer to as "critical energy" or the energy required to create plastic hinges and fail the columns, was about 8 times less than the kinetic energy available. So, yes the upper block traveled down and accelerated. Yes, more kinetic energy is available for the next floor, but the energy required to form plastic hinges has not increased appreciably (particularly at the upper floors).

 

[Augustine]

And that energy to break a floor is really really questionable. I think the energy needed to break a floor is over 1GJ even for the weakest floors, to be more precise I don't think that, it is video observation.

Drs. Wierzbicki and Bazant, through separate calculations, arrive at approximately 0.6 – 0.5 GJ. You use video and assert over 1 GJ….

Regardless, it’s irrelevant, even if you assume 1 or even 2 GJ, your gravitational potential energy converted to kinetic with the falling block is still an order of magnitude greater, meaning the collapse accelerates…