In lieu of a home for discussions of initiation, I will throw one thing in here.
I am not a structural engineer by a long shot. I understand a lot more than I did before falling in with this crowd, but it is only a thimble-full of knowledge. I am puzzled by the lack of resistance in the collapse continuation but much more so by the abrupt onset of global descent. I've not reviewed the NIST documents regarding the period of time between penthouse collapse and onset, and perhaps some answers lie there. Still, I have some theoretical hurdles to overcome before I can understand how such a thing is possible.
While collapse continuation can be modeled in 1D with the generalized coordinate in the vertical dimension, the initiation can also be modeled in 1D - but with the coordinate horizontal. The issue is lateral progression of instability. The question is, how did it get so far so fast? If the roofline kink is assumed to be downward displacement - and I'm becoming less confident that it is so exclusively - then the failure spread across two-thirds the width in about a second. This makes sense if an over-capacity load is suddenly added at the top but not so much from the perspective of removing strength at the bottom. While not necessarily simultaneous across the span, the velocity of propagation is startling to me in any case.
Dr. G had posted info about progression of instability in CDs over at physorg, I link to it early in this thread but physorg has been down for some time and I can't immediately refer to the post. As I recall, even with a CD
, it takes some time for the failure to propagate across the structure and commence global collapse. Not very much time, maybe, but these are buildings that are pre-weakened and conceivably have dozens of columns cut or kicked simultaneously. The Landmark CD, 41 stories, didn't drop this fast. How does a localized point of failure become a global failure in such a short time in such an extensive structure?
I try to imagine a cascading failure, like a zipper opening up. And it seems to me brittle materials may propagate very quickly but ductility ought to slow things down. The stiffer it is, the quicker the propagation, but the less likely to fail in the first place. If a beam can transmit downward deflection laterally so as buckle large numbers of columns below, then it's strong enough not to have failed in the first place, being that it so effectively redistributes load to columns which could hold the same weight in the previous second.
This is getting longer than I wanted it to without saying much of anything. Let me wrap it up with a hypothetical scenario which perhaps someone can explain to me, to help with my fundamentals. Load redistribution, very basic stuff.
Imagine a slab or beam supported by identical columns evenly spaced underneath. The columns and beam are geometrically ideal and perfectly rigid so do not deform in any way from their ideal shape. The figure labeled #1 below depicts such an arrangement with seven columns supporting the beam.
How much load does each column experience in #1? The OBVIOUS answer is one-seventh the mg
of the slab/beam, the total load being distributed equally amongst the columns. Now, magically remove the left three columns without disturbing the system, shown in #2. Since the objects are perfectly rigid, the redistribution of load in the now eccentric arrangement would be instantaneous, but what would that distribution be?
If the columns could deform, then the center column (now leftmost) would deflect downward somewhat from the load which has a cm directly above and would promote a tilt of the beam, which in turn would transfer even more of the load in that direction. But, if the columns can't
deflect? In this scenario, the beam is simply resting on the columns and is free to move but won't because it is adequately supported in balance by unyielding columns. Intuition is not such a good guide. My intuition says the three columns on the right are experiencing some load, after all, they're in contact. Perhaps the rightmost sees none, but surely the other two do. I think my intuition comes from real material that deforms, but is not applicable here.
Remove the right three columns and there is only the center column remaining, as in #3. Now I'm back in my comfort zone, it's clear that all the weight is on one column. The beam is balanced so still doesn't move. So, somehow, without displacement, the load has been redistributed from all to one. Since the beam is balanced in #3, I'm led to conclude that, without deformation, all the load is on the center column in #2 as well, and three columns experience no load.
So, then: if columns are removed from the left one at a time, does load come off columns on the right one at a time?
My lay concluson from all of this is that it's meaningless to talk about load distribution without deformation, that idealizations which do not include deflection are of no value in modeling propagation of yield location.