Originally posted by exponent
You seem to keep
making this mistake. The towers did not collapse because there was too much energy. It's not a question of the amount of energy, it's a question of
the forces and the geometry.
an effective FoS of around 0.3 is needed to make progressive axial collapse in less than 20 seconds possible.
You in turn keep saying this, and all I have to do is quote Bazant ("what matters is energy, not strength nor
stiffness") and point you to the fact that force is energy per distance. I have also provided a calculation based on the sum of forces alone,
comparing the top's stiction to its sliding friction and leaving the mass of theintact 95/80 stories out of the equation. You can't just keep saying
that this is false and wrong and meaningless, yet not propose a different calculation that is more meaningful, more correct and still describes what
is globally going on in a structure that falls through itself within seconds.
There's no trivial way to summarise this as an 'effective
factor of safety'. Please stop using it, it's meaningless.
I understand why it makes you cringe. Partly, because it is not very scientific
and partly because it brings matters to a head. I am fully aware this "effective FoS" thing is my own invention to describe a phenomenon that
doesn't occur very often - something being somewhat stable and static but be unstoppable once gone kinetic - and therefor has not its own SI unit
The best and most physically scientific approach would be to look at it as a compression
(in the sense of a volume change under an axial
force), however, my proposal was not very welcome - again, most probably because it brings matters to a head and sheds some light upon the question
under which pressure/tension
the towers stood.
Let me clarify right from the start, please. I would have a hard time explaining what I mean even in my mother's tongue, it's even harder in
English, so bear with me if I got the terminology wrong, you may want to help me. What I mean is this: when I stack my Jenga blocks on top of each
other, I will make sure they are well-aligned. That makes them stable. When there is an offset, the area
each block stands on - the contact
face - becomes smaller, so less force is needed to dislocate the center of mass beyond the contact face to cause the block's toppling (and less
height can be achieved). So, 5 blocks well-aligned are under less "inner tension" than 5 blocks alternately offset half an inch left and right -
although both stacks have the same height, one is less stable and prone to collapse than the other.
The isolated and iterative analyses are techniques used in FEAs to simplify the problems so they can be resolved by computers. I don't see you
doing an FEA or p-delta calculations. These are what are needed in order to support your point.
I understand your critique. Would you give me a
helping hand with the p-delta? I'm not too good with trigonometry and rheology. Let's say each tower had a sailing area of 64*400 meters and
withstood winds with 260km/h. So, in a sense, they were built like vertical cantilevers. This lateral force was transferred by momenta to act
vertically into the ground. Can we make any deductions from the fact the towers did not fail and buckle under the pressure of the first caribbean
hurricane? It may be another conspiracy nut rumour, but I heard the towers sometimes swayed so hard on windy days that pencils rolled off the tables;
elsewhere it was said that the dampers on the truss system were in place so they do
sway to a certain degree (so that some of the kinetic
energy is converted to heat, so to say).
There are several problems with a FEM. Firstly, I couldn't afford the software. Secondly, we would need the blueprints. Thirdly, there would have to
be a trade-off between transparency and complexity of the model. And fourthly, I don't have the computing power for this sort of stuff, I even had to
limit my processors to 90% so they don't overheat when rendering a POV-Ray scene.
I would prefer a most simple model with a simple core, simple slabs and a simple perimeter wall that actually explains
, not obscures, the
collapse mechanism for one simple reason. I believe - on the grounds of experience and my understanding of the findings of Newton, Galileo and
Archimedes - that the towers did not collapse accidentally, but being a good scientist, I know I could be wrong. In the case that I am wrong, it would
be one hell of a favor to architecture students around the world to show what mistake they want to avoid at all costs. So either way, much would be
gained with a model as simple as possible.
but you seem so confident there's something dodgy to find that you miss out all of the important
knowledge in your rush to the answer.
I am quite confident, therefor I welcome any new knowledge -- but it has become sparse.