#### Oystein

##### Senior Member

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?