With regard to the horizontal force required to displace the immense upper block laterally...
Please note that an axial FOS of 5 as Tony claims for the perimeter means the columns at any point in the structure could supply (roughly) 5
mg of force in the vertical direction, where
m is the mass of the structure above that point.
If this force were directed horizontally, it would accelerate the entire upper block at 5g. (
this greatly exceeds the maximum acceleration of the fastest production cars).
This is all about proportion! An initially self-supporting structure is more than capable of supplying a side force suitably scaled to laterally displace what it formerly supported, just from a little eccentricity. Where would this eccentricity come from? Like Jazzy said:
Jazzy said:
...the co-ordinated lateral force of dozens of columns buckling in almost perfect simultaneity. That force.
Bingo. Like this:
and this:
...both which come from Tony's coauthor on
Some Misunderstandings.
Simple examination shows that the force vector at the end of a buckling column (which would've happened in the initial failure area) has both vertical and horizontal components. It is certainly not difficult to imagine getting an average horizontal force at least 1/353 of the vertical, is it?
If it were true that the orientations of the column ends were random or otherwise properly mixed in the azimuthal direction, it could be argued that the horizontal contributions would cancel and give no net horizontal force. To that, I reply:
1) the magnitude of horizontal force for an individual column evident in the FEAs above must FAR exceed a mere 1/300th of the vertical component. In fact, they may well exceed the vertical component entirely over a large travel. Those ends stay aligned as much as they do because of externally imposed constraints on the simulation, not because they would if the ends were free to move the load above.
2) Given #1, elimination of forces by opposing buckling orientations would require cancellation to within a very fine degree. I don't think an acre footprint crush tube could be
intentionally designed which would maintain axial alignment so well under
uniform applied axial force. To suggest that it could happen by accident in a collapsing heterogeneous structure with irregular damage boggles the mind.
3) The fact that there is already tilt and non-zero angular velocity at initiation requires there be a spatial asymmetry present from the get-go. This is not a pure axial crush; there is definitely a bias and preferred direction. Thus there is zero expectation that horizontal components will be oriented in such a way as to cancel themselves out virtually to perfection.
It requires a proportionally very small force to displace the upper section far enough in one story's drop to reduce nominal capacity by up to an order of magnitude.
It is unrealistic to expect anything else.