Possibility of twin towers collapse arrest

[Confuseling]

Bit of a spin off from R. Mackey's thread here.

I'm wondering whether anybody with a head for numbers and some spare time would be interested in calculating some limiting cases for the progressive collapse of the twin towers. I know I'd be interested in the answer.

To clarify, what I mean is that I've heard that NIST have said that the energy released by the collapse was orders of magnitude larger than that required to overcome the towers' structure.

What does this actually translate to in metal? Presumably a solid block of steel wouldn't collapse if a middle part of it vanished totally (would it? I don't know. Would it drop straight through the Earth's crust? ) So where is the tipping point? Can you offer meaningful estimates of how much overengineering would have been required to resist progressive collapse? Or how much stronger the 'adamantium' would have had to have been?

If, as must be assumed, it is the case that if the towers were strong enough to drop one floor but not collapse completely, then they would not have collapsed in the first place, I suppose we can just invoke magic, and ask the question with the collapse initiation as an assumed given.

Why ask this question? It seems to me that a lot of the belief about controlled demolition comes from basic incredulity that a structure of that magnitude could just disintegrate, and this is an invitation for somebody who understands how to do so to illustrate why this incredulity is mistaken. Experts sometimes forget how monumentally awful laypeople are at intuiting things like this. I realise that there are a lot of variables here, but sometimes throwing numbers around is interesting.

Gregory Urich, I believe you have a spreadsheet with some structural specifics in? Could this be adapted to this question?

 

[R.Mackey]

Bazant and Zhou provides this explicitly. We can quibble over certain assumptions so it won't be exact, but WTC 1 was somewhere between, say, 4 and 15 times too weak to absorb the falling upper block. And it only gets worse from there. If collapse isn't caught at once, additional collapses only get faster and heavier.

 

[X]

A related question, which I have pndered:

What would be the maximum size of upper block that would have allowed for collapse arrest?

Obviously, this is assuming the airplane hit somewhere other than where it hit.
And the situation would still require that the upper section (however large is the maximum) still be massive enough to initiate collapse from impact damage and fire.

 

[BenBurch]

See, the mechanism of the collapse as I view it does not require much energy!

I see it as a peeling process, not a crushing process. The walls were pushed away, and the floors detached from them and fell, pushing more wall away. That is why so many large wall segments had enough lateral velocity to damage all the surrounding buildings!

 

[boloboffin]

Ben, the lateral velocity thing is an assumption we don't need to make. Most of the pictures 9/11 CT advocates show of beams being hurled are actually of the aluminum cladding spinning in mid-air. The beams seen in buildings like the Financial Center and the Winter Gardens are there because the sides of the buildings peeled away and fell out.

As you can see, there's a path of perimeter column panels leading to the Winter Garden building and the WFC. There's video where you can see the leading edge of this side fall out through the smoke.

 

[Confuseling]

Bazant and Zhou provides this explicitly. We can quibble over certain assumptions so it won't be exact, but WTC 1 was somewhere between, say, 4 and 15 times too weak to absorb the falling upper block. And it only gets worse from there. If collapse isn't caught at once, additional collapses only get faster and heavier.

Thanks. That was easier than expected! I've found it...

http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/405.pdf

...here.

 

[BenBurch]

boloboffin, I think that is what I said!

 

[DC]

pfff pseudoscience.....

 

[Slayhamlet]

pfff pseudoscience.....

So do your own calculations, with your own, more accurate assumptions, and prove that collapse would have been arrested. Nobody's stopping you.

 

[peteweaver]

Wasn't there a stairwell in WTC 1 which survived intact with people trapped on it for several hours ?

I would say that counts as evidence that the collapse was eventually arrested - by the pile of debris.

 

[BenBurch]

Wasn't there a stairwell in WTC 1 which survived intact with people trapped on it for several hours ?

I would say that counts as evidence that the collapse was eventually arrested - by the pile of debris.

Yes! Like 7 stories survived. A segment of the stairs that they were on was saved for some future museum display.

 

[Hyperviolet]

Wasn't there a stairwell in WTC 1 which survived intact with people trapped on it for several hours ?

Yes.

Stairwell B in the North Tower.

 

[GregoryUrich]

At this point, I am pretty much in agreement with Mackey's statement above, but I think the upper bound might be a bit lower. The primary assumption in Bazant model was evenly distributed coaxial column impacts which is grossly in favor of survival of the structure. Using this assumption without idealization of the columns I get an overload ratio of around 2 (working on verifying this). Hopefully we will be able to do something to demonstrate this more rigorously in the near future.

Here's a new finding and another interesting point that I haven't seen much discussion about.

1. After a number of discussions regarding the load distribution between the core and exterior columns in WTC1, I did some analysis including applying the weights from my mass and PE paper. The results differ quite dramatically from NIST's conclusions in NCSTAR 1-6D. I get roughly 72% of the weight above floor 98 being supported by the core.

2. I haven't seen anyone bring up the fact that the tilting of the upper block would contribute to the vulnerability of the upper block. The fact that the upper block was tilted during the first impact would lead to all kinds of nasty moments and lateral forces (relative to the upper block). This makes alot of sense in the context of the question of why the upper block of WTC2 appeared to dissintegrate very early in the collapse.

Nonetheless, I think these two factors probably balance out somewhat as they have opposite effects on the outcome.

Does anyone have the amount of weight that could be supported by the floors or floor connections (and a reference please)? I think NIST calculated this.

 

[R.Mackey]

Here's a new finding and another interesting point that I haven't seen much discussion about.

1. After a number of discussions regarding the load distribution between the core and exterior columns in WTC1, I did some analysis including applying the weights from my mass and PE paper. The results differ quite dramatically from NIST's conclusions in NCSTAR 1-6D. I get roughly 72% of the weight above floor 98 being supported by the core.

That is quite a departure. How does it compare to NCSTAR1-2A, the undamaged load assessment? In 1-6D, the assumption is that the core is heavily damaged, and the perimeter takes more load through the hat truss. We expect the perimeter to load even more in that case. 1-6D will be tougher to compare since the damage makes it anisotropic, and more sensitive to details.

2. I haven't seen anyone bring up the fact that the tilting of the upper block would contribute to the vulnerability of the upper block. The fact that the upper block was tilted during the first impact would lead to all kinds of nasty moments and lateral forces (relative to the upper block). This makes alot of sense in the context of the question of why the upper block of WTC2 appeared to dissintegrate very early in the collapse.

We have discussed this before, in passing. Also very difficult to estimate.

Does anyone have the amount of weight that could be supported by the floors or floor connections (and a reference please)? I think NIST calculated this.

This is given as a function of temperature in Table 5-2 and 5-3 of NCSTAR1-6C. At STP, the strength is between 94 and 207 kip depending on which one we're talking about for the exterior connections. 194 to 395 kip for the interior connections.

I'll also respond to your PM shortly.

 

[Corsair 115]

pfff pseudoscience.....

You could advance your case by demonstating conclusively why it is pseudoscience. But that would likely entail mathematical engineering and physics calculations...

 

[GregoryUrich]

That is quite a departure. How does it compare to NCSTAR1-2A, the undamaged load assessment? In 1-6D, the assumption is that the core is heavily damaged, and the perimeter takes more load through the hat truss. We expect the perimeter to load even more in that case. 1-6D will be tougher to compare since the damage makes it anisotropic, and more sensitive to details.

We have discussed this before, in passing. Also very difficult to estimate.

This is given as a function of temperature in Table 5-2 and 5-3 of NCSTAR1-6C. At STP, the strength is between 94 and 207 kip depending on which one we're talking about for the exterior connections. 194 to 395 kip for the interior connections.

I'll also respond to your PM shortly.

I looked quickly at 1-2A to check if I remembered correctly. They only give the baseline performance for the original design loads (full design live load) as opposed to a more realistic in-service live load. They give 53/47 (core/exterior) for the basement.

I interpreted the values in 1-6D (p176) as baseline because they were considering construction sequence. Here they give 52/48 (core/exterior). I wondered why exterior loads for the exterior walls were so varied. The north and south walls of WTC1 are carrying much more load than the east and west and they give the opposite for WTC2. Now, I just realized it was due to the orientation of the core.

Anyway, in 1-6 (p242) NIST gives baseline loads and has the split 47/53 (core/exterior). This doesn't make sense and it is the most divergent value from my calc. See below:

The diagram below shows three different areas of a representative floor (96-100). Loads are distributed differently for each of the three areas.

The two-way truss areas in the corners outside the core (designated A) have a load distribution that is ¾ on the exterior columns and ¼ on the core columns. Basically, this can be deduced by considering a rectangular table with four legs, one at each corner. Each leg bears ¼ of the weight. If intermittent legs are added to two adjoining sides, the leg at the opposite corner (equivalent to the core connection) is unaffected. The “A” areas have a floor area that is 34.5’ x 60’. The total area is 4 x 34.5’ x 60’ = 8280 sq ft.

The core area (designated B) is supported entirely by the core columns as the exterior floor connections have no way of transferring this load to the exterior columns. The floor area of the core is 137’ X 85’ = 11,745 sq ft.

The one-way truss areas outside the core (designated C) the load is distributed equally between the core and exterior columns. The floor areas of the “C” areas are 60’ x 137’ and 30’ by 85’. The total area of the “C” areas is 2 x 60’ x 137’ + 2 x 34.5’ by 85’ = 22,305 sq ft.

The table below shows a calculation of load distribution for floor 96 which is representative for the building as a whole. The conclusion is that 63% of the load was supported by the core and 37% by the exterior columns. This is in opposition to NIST which states that the loads were distributed 50/50 and Heiwa who has stated that the distribution was 40% supported by the core and 60% supported by the exterior.

The result reduces the demand/capacity ratio in the core to roughly ½ or stated differently the in-service stress was 48% of the yield stress (250 MPa assuming all A36 steel).

Previously calculated: (0.5 x 32.8E+06 kg x 9.81 m/s^2) / 1.70 m^2 = 94.6 MPa (38 %)

New value: (0.63 x 32.8E+06 kg x 9.81 m/s^2) / 1.70 m^2 = 119 MPa (48%)​

Note that when I apply the loads from my mass/PE analysis, the distribution becomes 72/28 (core/exterior).

 

[twinstead]

pfff pseudoscience.....

In case you don't know, the definition of 'pseudoscience' isn't 'science I don't understand'.

Just keeping it real DC.

 

[R.Mackey]

I interpreted the values in 1-6D (p176) as baseline because they were considering construction sequence. Here they give 52/48 (core/exterior). I wondered why exterior loads for the exterior walls were so varied. The north and south walls of WTC1 are carrying much more load than the east and west and they give the opposite for WTC2. Now, I just realized it was due to the orientation of the core.

Anyway, in 1-6 (p242) NIST gives baseline loads and has the split 47/53 (core/exterior). This doesn't make sense and it is the most divergent value from my calc. See below:

[...] Note that when I apply the loads from my mass/PE analysis, the distribution becomes 72/28 (core/exterior).

I see where you're going. For Floor 96 etc., your calculation makes sense. However, the answer globally may be different. There are significant load transfer mechanisms in the Towers, i.e. the hat truss, the two sets of beam-framed floors, and the framing near the "column trees." I suspect that the much higher local loading of columns at typical floors, like you've shown here, gets ultimately fed back to the core at a lower level.

It's possible NIST's "50/50" estimate doesn't apply at the highest levels. We should probably look harder at the DCR calculations for individual elements at the highest floors to see if we can reconcile the two viewpoints.

 

[pomeroo]

pfff pseudoscience.....

But you like pseudoscience. Real science lends no support to your fantasies. Remember?

 

[GregoryUrich]

I see where you're going. For Floor 96 etc., your calculation makes sense. However, the answer globally may be different. There are significant load transfer mechanisms in the Towers, i.e. the hat truss, the two sets of beam-framed floors, and the framing near the "column trees." I suspect that the much higher local loading of columns at typical floors, like you've shown here, gets ultimately fed back to the core at a lower level.

It's possible NIST's "50/50" estimate doesn't apply at the highest levels. We should probably look harder at the DCR calculations for individual elements at the highest floors to see if we can reconcile the two viewpoints.

All the values I'm comparing are for either floor 96 or 98 with the exception of the values from 1-2A which are at the base.