The second part of the statement, "proportional to its axial capacity or FoS in original configuration", is interesting in its own right. Again, it
does not matter what the capacity of the column is in terms of resisting collapse if the element it impacts is much weaker than it is. The point I
wanted to illustrate is the loading "impedance mismatch"; the capacity of the column-floor system is given by the floor, which is the weakest link.
But there are more interesting considerations.
I noticed you used the words "proportional" and "axial", and I applaud you for your precision. In doing so, you seem to be aware of two things: some
proportionality is involved in out-of-spec conditions, and out-of-spec geometry is also involved. I'm only guessing, but I'd bet if a single column
impacted an intact floor at a severe enough off-axial angle, it would bend instead of punching through. But a perimeter tree, which consists of
multiple columns and spandrels, would not do so or would require an even more severe angle.
More importantly, the issue of proportionality comes in. What if the impact is not axial, regardless of what the column impacts? Then the FOS rating
of the column does not apply. More than a few degrees off axial, and the failure mode shifts from hinge buckling under axial compression to bending
under applied moment. The force required to fail the column (i.e. irreversible deformation and further capacity loss until full compaction) is
reduced by one or even two orders of magnitudes. There goes your FOS, and that also serves to reinforce my point.
Which is (to beat a dead horse): the FOS of the as-built structure can be X, but the effective capacity during collapse is some value MUCH less than
X. That is, not even enough to support the static load. This is in response to the ABSURD (and yes, stupid) claims that the design FOS should apply
in a messy collapse. No more, no less.
Apparently the floor slabs would be stacking up thick and fast. A column end would not be getting very far punching through this stack and
would be able to apply a great deal of its axial capacity to the falling floors.
If you're going to change the context to columns abutting a stack of floors, it's a different story. My remarks apply to my context. It is fair to
shift the context if doing so presents a more realistic situation within the larger context of the collapse progression. Fair enough; the context I
described would apply mostly if not exclusively in the initial impacts between upper and lower, and is therefore quite a limited context.
Does not mean your context is more probable or even applicable.
You presuppose the context must necessarily be pancaking. Why? Why can't it be loose (uncompacted) rubble? Why can't it be an extent of perimeter
wall shearing (up or down) the floor pans off at their perimeter connections? But, okay, I'll go with pancaking.
You presuppose there is a nice stack of floor slabs one atop the other when it's far more realistic to expect pancaked floors to be fragmented,
therefore semi-permeable under concentrated impulse. Okay, I'll go with that.
There are two situations to consider. The first is a column(s) from above impacting a stack of floors below, the second is a stack of floors
impacting a column(s) below. In the first case, the stack may either be stationary or moving. If moving, the upper section must overtake at a higher
velocity for there to even be an impact. Upon impact, the column either fails and crush up begins on top of the pancake, or the column survives and
comes to rest atop the moving pancake, adding the full mass and transient impulse of the upper section to the moving pancake. If the pancake is
stationary, then the column can also either fail or survive. If it fails, crush up has started, if it survives, collapse is arrested - after some
arbitrary amount of pancaking! If you like, but that begs the question of what stopped the pancake, deferring it to the second situation.
The second situation, a stack of floors impacting a column below, can also result in failure or survival. If failure, game essentially over, it keeps
going. If survival, then can a column end punch through a stack of (e.g) 20 floors? No, I don't think so. One? Yes. Two, very likely. Three,
still probable. How then would floor slabs remain intact to accrue a 20-floor pancake? But, let's suppose 5 stacked, intact floors were effectively
impenetrable and manged to accumulate, THEN hit column ends below.
Arrest is possible, assuming the momentum of the integral pancake mass doesn't overload the columns. But, by definition, the pancaking mass is
detached from the rest of the structure. Only the pancaking mass is arrested. If interior pancaking collapse is all there is, then there is arrest.
But both upper sections go into motion at the start of the collapses, therefore pancaking is at most part of the picture, if any.
30-1-2012 by IrishWristwatch because: (no reason given)