New guy here: Questions for official hypothesis

[Sizzler]

I'm not off to be yet. Had a bunch of emails and PMs to answer.
I'm not looking at the paper now, but those numbers represent a range of mass shedding (outside the footprint) from 5% to 50%, which would be in line with the seismic and video records. The paper shows how the collapse times would be affected by lower and higher numbers within that range for each tower. Interesting stuff, and somewhat counterintuitive, at least to me.

Thanks Gravy.

When I watch the collapse, you are right in that very little mass escapes in the beginning.

However, later on 'a lot' falls outside of the footprint. 50% satisfies my statement, of 'a lot'.

So what is his calculated fall time with K (out) = .5....?

(I'll try to find it too, but you guys are pretty fast so you may beat me)

 

[jhunter1163]

Calculating K(out) as 50% of the mass above the collapse zone might give a misleading result. As you pointed out above, very little mass escaped to the sides early in the collapse. The falling mass was increasing with every floor destroyed.

Also, in the pictures Gravy posted, you can see debris falling that is actually in free-fall (to the sides of the Tower). As you can see, that debris is ahead of the collapse front; therefore the collapse front must be moving somewhat slower than free-fall. This is in good accord with the previous posters' calculations.

 

[Thabiguy]

Thanks Gravy.

When I watch the collapse, you are right in that very little mass escapes in the beginning.

However, later on 'a lot' falls outside of the footprint. 50% satisfies my statement, of 'a lot'.

So what is his calculated fall time with K (out) = .5....?

(I'll try to find it too, but you guys are pretty fast so you may beat me)

There is a whole section discussing this; it's called "Effect of Uncertainty of Mass Shedding Fraction kappa_out". It's at page 12.

Quoting from this section to answer your question:

For the North Tower, ... if kappa(out) is varied between 0.05 and 0.5, the crush-down collapse duration is extended, but not by no more than 0.35 s, ...
For the South Tower, ... if kappa(out) is varied from 0.05 to 0.5, the crush-down collapse duration decreases by only 0.1 s.

 

[Architect]

Sizzler

You may be interested to learn that Edinburgh University and Ove Arup both published papers which disagreed with some aspects of the NIST findings regarding collapse initiation. In particular both believed that the fire on its own would have been sufficient to cause collapse due to a range of factors including creep and inadequate modelling of fire engineering issues at the time of design.

These opinions have been published and well known in engineering and architectural communities, as have the NIST findings, and represent the only substantive divergence in professional opinion on the issue.

You should also be aware that, following the collapse, key design documents such as the Eurocodes and national building regulatory codes were revised to introduce additional measures seeking to limit the scope for progressive collapse.

In short, the collapse itself has been widely studied by the professional community. The Truthers just don't seem to understand the scrutiny which what they call "the official consipracy theory" has undergone.

 

[Sizzler]

There is a whole section discussing this; it's called "Effect of Uncertainty of Mass Shedding Fraction kappaout". It's at page 12.

thanks.

So it seems the compounding of floors doesnt affect the collapse time much.

In fact, Bazant says;

Some lay critics claim that k-out should be about 95%, in the (mistaken) belief that this would give a faster collapse and thus vindicate their allegation of free fall. However, this would actually extend the duration of collapse of North Tower by about 5.78 s (and 3.03 s for k-out = 90%) because the aforementioned effect (b) would become dominant. The agreement with the seismic record would thus be lost. Therefore, values out > 0.5 are unrealistic.

So even if only 5% of the floors contributed to the mass, the collapse would still go to the ground, but 5.78 seconds slower.

So would the collapse have gone to the ground if k-out is 99 or 100?

i still can't satisfy the collapse time in my head.

All that steel structure only slowed the collapse by 4 seconds? And a 15 story chunk can cause 95 floors to collapse even though they are made of the same material? And according to Bazant, the collapse wasn't that dependant on a compunding weight as floors collapse.

I don't have the technical skills to describe my issues. But basically, all 85 floors or so offered almost no resistance to the falling top part. Is that expected?

Help me out guys.

 

[Apollo20]

Sizzler:

You really need to write a momentum transfer program and vary the key parameters which are the energy expended in collapsing one floor, which I call E1, the mass of the upper section and the amount of mass shedding per impact. If you do this you will find that the collapse of WTC 1 & 2 are going to be self-sustaining over a wide range of reasonable values for these parameters.

For E1 values up to 1 GJ a lot of mass shedding is permissable and the collapse accelerates at ~ 2/3 g all the way down. This means the descent velocity would be about 15 m/s after 5 floors have collapsed and ~ 40 m/s after 50 floors. The problem with comparing this calculated result with observations is that the top of each tower disappears into the dust and debris cloud generated by the collapse about 4 seconds into the collapse so you can't see what's going on! You can resort to comparisons with the seismic data available for each collapse if you wish, but I feel this approach is a little shaky (if you pardon the pun!). The bottom line is that each collapse was unstoppable once the upper section got moving. Even a controlled demolition works essentially the same way.... it too is largely a gravity-driven collapse.

 

[Sizzler]

Sizzler:

You really need to write a momentum transfer program and vary the key parameters which are the energy expended in collapsing one floor, which I call E1, the mass of the upper section and the amount of mass shedding per impact. If you do this you will find that the collapse of WTC 1 & 2 are going to be self-sustaining over a wide range of reasonable values for these parameters.

For E1 values up to 1 GJ a lot of mass shedding is permissable and the collapse accelerates at ~ 2/3 g all the way down. This means the descent velocity would be about 15 m/s after 5 floors have collapsed and ~ 40 m/s after 50 floors. The problem with comparing this calculated result with observations is that the top of each tower disappears into the dust and debris cloud generated by the collapse about 4 seconds into the collapse so you can't see what's going on! You can resort to comparisons with the seismic data available for each collapse if you wish, but I feel this approach is a little shaky (if you pardon the pun!). The bottom line is that each collapse was unstoppable once the upper section got moving. Even a controlled demolition works essentially the same way.... it too is largely a gravity-driven collapse.

Thanks for your explanation.

In layman terms, is E1 debatable? Or is it pretty easy to make a good estimation?

Also, is E1 for just the next floor, or is E1 a combination of all the floors?

 

[Thabiguy]

thanks.

So it seems the compounding of floors doesnt affect the collapse time much.

In fact, Bazant says;



So even if only 5% of the floors contributed to the mass, the collapse would still go to the ground, but 5.78 seconds slower.

So would the collapse have gone to the ground if k-out is 99 or 100?

i still can't satisfy the collapse time in my head.

All that steel structure only slowed the collapse by 4 seconds? And a 15 story chunk can cause 95 floors to collapse even though they are made of the same material? And according to Bazant, the collapse wasn't that dependant on a compunding weight as floors collapse.

I don't have the technical skills to describe my issues. But basically, all 85 floors or so offered almost no resistance to the falling top part. Is that expected?

Help me out guys.

"Almost no resistance" is relative. The 85 floors or so offered enormous resistance. So much resistance that it was capable of holding a whole (peacefully standing) skyscraper up. But this resistance was dwarved by the dynamic load of the falling upper section, which was even ... well, enormouser.

I could defer you to the calculations in the paper, but I sense that the problem you're having is that you can't reconcile the progressive collapse with your "gut feeling". So I'll try to explain with a very simple model that you could grasp more intuitively.

Let's say that one floor (floor A) fails and the upper section falls the distance of one floor. When it hits the next lower floor (floor B), it will have speed v_B-enter. Now, floor B either a) has enough strength to brake the upper section entirely to a halt, or b) it does not have enough strength. In case a), the falling section is halted and collapse is arrested.

In case b), floor B fails. It may have slowed down the fall of the upper section, but the section continues with non-zero speed, v_B-exit > 0. But this means that when it falls another one-floor distance and impacts C, it will have greater speed than it had when it impacted floor B. This is because the first fall began with zero speed, but the second fall began with greater speed, v_B-exit. So floor C will be hit with speed v_C-enter > v_B-enter.

Well, if floor B couldn't halt the upper section impacting with speed v_B-enter, floor C is likely not going to halt it impacting with speed v_C-enter > v_B-enter. So it will fail, and slow the fall down to v_C-exit. And, if floor B slowed down v_B-enter to v_B-exit, it's only logical that floor C will slow down v_C-enter > v_B-enter to v_C-exit > v_B-exit.

And so on. Note that we didn't even consider that the mass of the upper section was increasing; even if the floors vaporized upon being crushed, the collapse would still progress with increasing speed.

This is of course a very simplified model. It would, for example, be different if the initial falling distance was greater than one floor. In such case, it would be conceivable that the collapse could be halted even after several floor are crushed.

But basically, it shows that either the collapse is halted very early in its beginning, or it's not halted at all. Once the fall begins to accelerate, meaning that the floors fail to slow it from floor to floor, there is no way to stop it - until the upper section hits something much firmer, that will be able to halt it (such as the ground).

 

[Apollo20]

Sizzler:

E1 is difficult to calculate from first principles but it is a nice parameter to work with. All I can say is that if you set E1 ~ 0.6 GJ for the uppermost impacted floor you will have a collapse with an acceleration ~ 3/4 g for WTC 2 and ~ 2/3 of g for WTC 1 which matches the observed initial rates of collapse of these towers.

These days, (though not in my original paper!), I assume E1 is proportional to the effective column area per floor. Now there is data available on this which shows that the core column area varied from about 2 m^2 at floor 90 to about 10 M^2 at floor 20. For this reason I have run my progran with E1 increasing linearly down the tower so that it is 5 times larger at the bottom than at the top. Guess what? When you do this the collapses are still self-sustaining - they just take a few seconds longer!

 

[Sizzler]

"Almost no resistance" is relative. The 85 floors or so offered enormous resistance. So much resistance that it was capable of holding a whole (peacefully standing) skyscraper up. But this resistance was dwarved by the dynamic load of the falling upper section, which was even ... well, enormouser.

I could defer you to the calculations in the paper, but I sense that the problem you're having is that you can't reconcile the progressive collapse with your "gut feeling". So I'll try to explain with a very simple model that you could grasp more intuitively.

Let's say that one floor (floor A) fails and the upper section falls the distance of one floor. When it hits the next lower floor (floor B), it will have speed v_B-enter. Now, floor B either a) has enough strength to brake the upper section entirely to a halt, or b) it does not have enough strength. In case a), the falling section is halted and collapse is arrested.

In case b), floor B fails. It may have slowed down the fall of the upper section, but the section continues with non-zero speed, v_B-exit > 0. But this means that when it falls another one-floor distance and impacts C, it will have greater speed than it had when it impacted floor B. This is because the first fall began with zero speed, but the second fall began with greater speed, v_B-exit. So floor C will be hit with speed v_C-enter > v_B-enter.

Well, if floor B couldn't halt the upper section impacting with speed v_B-enter, floor C is likely not going to halt it impacting with speed v_C-enter > v_B-enter. So it will fail, and slow the fall down to v_C-exit. And, if floor B slowed down v_B-enter to v_B-exit, it's only logical that floor C will slow down v_C-enter > v_B-enter to v_C-exit > v_B-exit.

And so on. Note that we didn't even consider that the mass of the upper section was increasing; even if the floors vaporized upon being crushed, the collapse would still progress with increasing speed.

This is of course a very simplified model. It would, for example, be different if the initial falling distance was greater than one floor. In such case, it would be conceivable that the collapse could be halted even after several floor are crushed.

But basically, it shows that either the collapse is halted very early in its beginning, or it's not halted at all. Once the fall begins to accelerate, meaning that the floors fail to slow it from floor to floor, there is no way to stop it - until the upper section hits something much firmer, that will be able to halt it (such as the ground).

Your description helps a lot. Thanks for that.

But, is this ignoring that forces are working in both directions?

I mean, the force on the lower intact floors should also be equally transmitted up into into the falling section.

Wouldn't this significantly decrease the kinetic energy of the falling block? And wouldn't this also crush the upper section too?

Also, can we consider the strength of just one floor at a time, or should be consider the strength of the whole lower intact section together? Isn't this important considering the vertical core?

 

[MG1962]

Also, can we consider the strength of just one floor at a time, or should be consider the strength of the whole lower intact section together? Isn't this important considering the vertical core?

No, the trusses acted independently of the vertical load weight. Example floor 1 is not designed to hold the weight of the rest of the building.

From memory each floor was rated to hold three thousand tons plus its own construction weight.

 

[DGM]

Your description helps a lot. Thanks for that.

But, is this ignoring that forces are working in both directions?

I mean, the force on the lower intact floors should also be equally transmitted up into into the falling section.

Wouldn't this significantly decrease the kinetic energy of the falling block? And wouldn't this also crush the upper section too?

Also, can we consider the strength of just one floor at a time, or should be consider the strength of the whole lower intact section together? Isn't this important considering the vertical core?

Even if the upper block is being crushed the mass is still there. This mass is constantly being added to the mass at the collapse front that is only crushing one (or a few toward the end) floor at a time.

I like when people say that 20 floors destroyed 90. If you watch the video you see this is not true. The top block that was getting larger all the time destroyed one floor at a time all the way to the bottom.

 

[Sizzler]

Here's an analogy that might help.

Consider a bowling ball and a Styrofoam board.

If I suspend a single Styrofoam board in the air and drop a bowling ball on it, it will break.

If I suspend two Styrofoam boards in the air spaced apart, the bowling ball will break through one and then the other.

But if I suspend 85 Styrofoam boards in the air spaced apart, would the bowling ball continue through all 85?

Is it possible to create a situation where although a bowling ball can break through one Styrofoam board, it cannot progress though all of the boards? Meaning, as some point the progression will stop.

Or, as long as the bowling ball can break one board, it will naturally progress through all the boards no matter how many are suspended?

 

[Architect]

Sizzler

You talk about the steel structure offering no resistance as if this were a surprise, but bear in mind my comments above regarding how the structure was designed and worked. In short, it couldn't handle the differing load paths caused by a chaotic collapse and hence the resistance would be quite modest.

As regards your bowling ball analogy, you need to consider the relative weights and masses of the object before it becomes particularly helpful.

 

[Sizzler]

Even if the upper block is being crushed the mass is still there. This mass is constantly being added to the mass at the collapse front that is only crushing one (or a few toward the end) floor at a time.

I like when people say that 20 floors destroyed 90. If you watch the video you see this is not true. The top block that was getting larger all the time destroyed one floor at a time all the way to the bottom.

Right, but the compounding of the floors seems insignificant according to Bazant.

The collapse would have progressed even if the crushed floors just vapourized. It would have just been around 5 seconds longer.

 

[Sizzler]

No, the trusses acted independently of the vertical load weight. Example floor 1 is not designed to hold the weight of the rest of the building.

From memory each floor was rated to hold three thousand tons plus its own construction weight.

The trusses can be treated independantly, but can the vertical core columns be too?

They would have had to have been literally crushed, right? the rose vertically.

 

[Sizzler]

About the bowling ball.

Let ask this question then.

Is it possible to stop a bowling ball falling through Styrofoam boards by adding more boards?

Or will that ball continue to fall, as long as it can pass through the first board.

Weight and density, etc can be adjusted to anything as long as the bowling ball can break the first board.

 

[DGM]

Right, but the compounding of the floors seems insignificant according to Bazant.

The collapse would have progressed even if the crushed floors just vapourized. It would have just been around 5 seconds longer.

Actually he's right because if the initial mass was sufficient to destroy the floor below.

Like in your bowling ball example, as long as the ball could go though the first layer the second layer is not getting any help from the first (and so on) so it will continue.

ETA The only way to stop the ball is to make the boards stronger.

 

[Architect]

About the bowling ball.

Let ask this question then.

Is it possible to stop a bowling ball falling through Styrofoam boards by adding more boards?

Or will that ball continue to fall, as long as it can pass through the first board.

Weight and density, etc can be adjusted to anything as long as the bowling ball can break the first board.

With respect, that's a kind of peculiar question.

Even tissue paper would stop the ball fallling, as long as there's enough of it.

 

[Sizzler]

With respect, that's a kind of peculiar question.

Even tissue paper would stop the ball fallling, as long as there's enough of it.

I just trying to get my head around the physics of a progressive collapse. Humour me

If I raise a bowling ball 2 feet above a stryofoam board, and place hundreds of more styrofoam boards, spaced 2 feet a part, below the first board, the bowling ball will go through all the boards as long as they are all spaced 2 feet a part and the initial 2 foot drop broke the first board.

Right?

So it wouldnt matter how many boards I place below, the bowling ball would just continue to break through them all.