Buckled Structural Steel in Building Fires

[Oystein]

Something fundamental:

A structural collapse is an event where many elements of a solid structure get severed (or otherwise severely deformed) under the force of gravity.

To sever structural elements, one needs to expend energy. Where does the energy come from? -> Wholly or in substantial part from the potential energy of the structure itself in the field of gravity.

The task here is to understand a collapse as an event that kicks off by some external (non-gravity) energy source having already damaged the structure somewhere such that it has started to move downward (possible lateral motion notwithstanding), following the direction of gravity.
And then to see that the potential energy freed by the mass of the structure descending is sufficient, and available, to continue severing structural elements and make more and more of the structure descend.

So, absolutely crucial in any fair modelling of a collapse is to ensure that the available potential energy is greater than the energy needed to sever enough of the structure for it to come apart and drop to the ground.
Or, put differently, you need to scale both the potential energy and the energy needed to break the model to the same scaling factor.

That is not practically possible. At all. Hopeless. Here is why:

The potential energy of a structure scales with the power of 4 relative to its one-dimensional expanse:
Pe = m * g * h, where h (height) scales 1:1 with the scale of the model, and mass (m) scales with the power of 3.

The general strength of structural elements is generally proportional to their cross-sectional areas and thus scales to the power of 2.

So, if you build a model to a scale of 1:1000, and use the exact same materials, and model every single element perfectly to scale - every splice, every bolt, every weld, everything, then its mass will be 1:1,000,000,000 that of the original, its available potential energy will be 1:1,000,000,000,000 that of the original, the sum of energies required to sever the elements required for total collapse will scale to be 1:1,000,000 - and because of that, because 1:1,000,000 is a MILLION times more than 1:1,000,000,000,000, this perfect scale model will be a MILLION times too strong to model a collapse.

So how to alleviate that?
You could go to a place (or engineer with kick-ass centrifuge) a gravity that's 1,000 times our gravity (g= 9805 m/s^2) PLUS use a material that is 1000 times weaker (requires a 1000 times less energy to sever at same dimensions) than steel, and build the model from foil of that extremely tender material 1,000 times thinner than the original plate steel from which columns were made, or 1,000 times thinner steel rods for the trusses.

So, your 1:000 model would have to be a thousand times more delicate than a to-scale model, PLUS it would have to stand in 1,000 times the gravitational force.


Do you understand this?

 

[Oystein]

Don't we just solve this by adjusting the dead loads *on* the structure. Is there a useful difference between being a 1000 times heavier and gravity being a thousand times stronger?

Yes, there is: Not only do you need to scale mass properly, you also need to scale the height differential correctly through which the mass falls. See my longer post just prior to this: Relative to material strength, potential energy is a million times too low in a 1:1000 model.

 

[Thomas B]

This is pretty much within the range of common gauges of houshold aluminium foils.

This isn't a bad idea. It's not a great material to work with because once it creases it becomes a lot weaker. But I can actually imagine an aluminum structure, with lead floors standing (even with a bit of shaking at the base) and then crumpling all the way down. Intuitively, it makes sense.

 

[Thomas B]

Do you understand this?

I probably don't understand all of it perfectly. But, yes, the general idea is what I'm working with.

It may be that you understand something (which makes all this impossible) that I will only really understand after some more experimenting. That's fine with me.

 

[Thomas B]

So, your 1:000 model would have to be a thousand times more delicate than a to-scale model, PLUS it would have to stand in 1,000 times the gravitational force.

I think the "thousand times more delicate" can be achieved with my paper facade (with cut outs). The 1000 times the gravitational force is of course harder to achieve. I'm guessing we'd go from the previous estimate of 280 grams to 280 kg? That's a lot for a paper model to bear.

But maybe the paper model can actually be made 100,000 times more delicate than the to-scale model?

 

[Thomas B]

Something fundamental:

You seem very knowledgeable about this. Do you have a back-of-the-envelope calculation of what the smallest possible structure would be that could demonstrate the actual mechanism of the WTC collapses? I get it that you think 1:1000 scale is out. But surely a building half the size could be (made to be) both strong and vulnerable like the WTC? How small can we go before your absurdities kick in?

 

[Thomas B]

This is pretty much within the range of common gauges of houshold aluminium foils.

This isn't a bad idea. It's not a great material to work with because once it creases it becomes a lot weaker.

I just had a thought. Make the perimeter structure out of crumpled (and then reflatened) aluminium foil. That will introduce a lot of the "chaotic" weaknesses needed during the collapse, but, if the load is properly calibrated, should let it stand in all directions before the initiating event.

 

[Landru]

I just had a thought. Make the perimeter structure out of crumpled (and then reflatened) aluminium foil. That will introduce a lot of the "chaotic" weaknesses needed during the collapse, but, if the load is properly calibrated, should let it stand in all directions before the initiating event.

How about just do something. You have been talking about this for a while. Do it, document it, open a new thread with your findings. This one is closed.