Thanks to NoahFence, Oystein and ChrisMohr for attempting the thought exercise.
This was the exercise - a simplified model resembling the WTC Twin Towers situation - and I will overlay
<< the answers:
So just three rows of columns.
They are carrying loads of L=100, C= 200 and R=100.
Step #1
The Top Block we assume rigid. Cut out all of row "R"
Q 1A What happens to the loads in "L" and "C"?
<< L becomes ZERO C becomes 400
Q 1B Does the Top Block move?
<< No. It balances (precariously) on "C"
Step #2
The Top block is really slightly flexible as with any steel framed structure.
Again remove row "R"
Q 2A What happens to the loads in "L" and "C"?
<< As previously L becomes ZERO C becomes 400 fora brief instant then
Q 2B Does the Top Block move?
<< It topples to the right
Q 2C Why
(or why not)?
<< Because the Top Block "sags" over the pivot C causing the CoG to drift slighty right of C >> topple.
I will obtain 3 mini Mars Bars and hold the prizes for collection next time any of you three are down this way.
OK mark your own papers. I didn't overlay the issue with disclaimers about near enough. So Oystein did a good job of identifying what he sees as the second order issues.
I disagree slightly. I think he has picked the third order ones and skipped over second. Oystein - not making a big issue of it but my engineer’s gut feeling is that the (near enough) static explanation of elastic sagging would dominate over your dynamic interpretations. Second order over third order. The elastic nature of the top structure and the supports not sufficient to allow the movements and velocities you identify to have sufficiently large effects. I agree with your
qualitative assessments but suggest they are
quantitatively too small. Similarly your 600 IMO too optimistic.
However the exercise demonstrates clearly the points I wanted everyone to grasp.
Removal of a proportion of columns will almost always weaken the structure by more than the proportion of columns removed.
Removal of 25% of the overall load capacity has a 100% increase in load on the most affected columns. Obviously the sort of effect that would be critical in a cascading failure scenario.
Repeat it with 100-100-100 initial loads and the C load becomes 300.
Sure both of the examples are worst case scenarios BUT the point is the same.
Removal of a proportion of columns does not have a proportional effect on load redistribution.
It indirectly proves my secondary points - the real effect will NEVER be less than proportional and with one unlikely exception ALWAYS worse.
Now the challenge is to get Tony Szamboti, jay howard et al accepting that building block fact of physics as part of the overall real event.
And the next stage is to overlay heat effects and once again show why the columns which collapsed from axial overload all got "hot enough" to buckle/fail.