Here is the first post from page 64, when M_T was still, and actually, attempting to provide a mathematical approach to ROOSD.
Mathematical approach to ROOSD as progressor
Let's pick up there and go bit by bit:
Fundamental conditions:
for rubblized driving mass > M(1) moving at a downward velocity > V(1) , the runaway process is assured. The threshold conditions require a minimum M(1) traveling downward at velocity V(1).
Assuming that you haven't determined any specific values (numbers) for M(1) and V(1) for both or either WTC1 or WTC2, do I take it that you hypothesize that for any suitable building there is such a set of values, and that this can in principle be found using either math or observation?
Does "fundamental condition" mean that with M < M(1)
or V < V(0), ROOSD will not happen?
How (or where - link will do) did you derive that the fundamental conditions are these two values and not, for example, their product (M*V) oder the kinetic energy implied by the numbers (0.5*M*V
2) - or some other such relationship?
The process requires progressive and runaway breakability of successive floor-to-column connections.
Not sure I understand this correctly.
What is "progressive and runaway breakability of successive floor-to-column connections"?
Does this mean that each successive connection must have a property called "runaway breakability" plus a a property called "progressive breakability"? And what on earth would that property mean??
Examination of available literature: None
Measurements and observations of a first known documented case: WTC1 and 2 (roofline and collapse front)
...
[snipped links and stuff with measurements. Result:]
...
I skip this longish part and just acknowledge it's there and has been carefully crafted. I accept for the moment without argument that your measurements are correct, relevant, sufficiently accurate and sufficiently complete (for whatever purpose you may have).
What are the characteristic features of the progressor (steady state) portions of the curves? (Measured along the OOSsw crush front)
- Tendency toward terminal velocity
- A steady state acceleration of zero
That's the same thing in two different wordings.
What are the characteristic features of the initiator (initial movement to steady state) portions of the curves? (Measured along 2 points: roofline and crush front)
- Crush front seems to start on floor 95
- Quick take off velocity
- Short transitory phase (reaches steady state velocity and acceleration rapidly)
That definition of "initiator" - do you use this consistently throughout your work?
Most people around here have a concept of a "collapse initiation phase" that begins with the first yielding piece of structure that starts an uninterupted chain of macro movement at the beginning of the final collapse, and ends roughly when something like your "fundamental conditions" as described above are fulfilled; in my words, when the vertical drop has progressed to a point where total collapse becomes inevitable.
This is (probably) a shorter time frame than your "initiator" here. Your initiator goes past the "point of no return" and through an additional phase where acceleration is > 0.
"Quick take off velocity" - really? I guess the whole thing takes off at V=0? Or do you mean that V(0) (from your fundamental condition above) has to be high? How high? By what criterion do you decide a take-off velocity is "high"?
Or do you mean high take-off acceleration, i.e. initial acceleration close to g?
I hope you find some questions helpful or at least legitimate.