Originally posted by ANOK
Originally posted by IrishWristwatch
Design FOS is meaningless in a messy collapse.
Again your opening statement shows you are confused.
FoS is NEVER meaningless, it is the structural capacity of the building. A 'messy' collapse doesn't mean physics is ignored.
I'm sorry, but this has long since moved past ridiculous.
One of my pet peeves is people who are obviously utterly and totally clueless about physics proclaiming their imaginary version of pseudoscientific
mumbo jumbo as fact. The stark contrast between boldly proclaimed falsehoods and reality sticks in my craw, probably because I had to work my ass off
with problems of this nature to get passing grades. You are just making stuff up.
Suppose the typical tower had a typical, average FOS of 5, when assembled according to print. Some scholarly estimates put it as low as 2.5, no
plausible estimate puts it above 6. Now, I'm going to guesstimate some things for an order of magnitude answer - don't ignore the disclaimer! The
widest short axis dimension in any core column is (to the best of my knowledge) 10 inches. The perimeter columns are roughly 14.5 inches square and
spaced 40 inches center to center. Therefore, if a tower were to be cut on a horizontal plane and displaced only 15 inches, all perimeter ends and
and least half the core ends will be in opposition to - AIR!
Since load was split equally between core and perimeter, that's a reduction in as-built capacity to 25% of the original value, NOT including loss of
contact surface in the assumed remaining 25% of columns. The FOS of the optimal configuration (by print) is reduced to 1.25, a mere 25% margin of
safety. This residual capacity is barely enough to support the static load, assuming a uniform distribution. It would not even withstand sudden
loading (defined to be bringing the load in CONTACT and releasing); that requires a minimum FOS of 2. Forget about arresting any finite drop height
Momentum counts, and it counts in exactly the way I think it does. It is encumbent on you to absorb this remedial physics, and pontificate less.
To reduce the residual capacity to FOS = 1.25, it was only necessary to displace the upper portion by 15", or about 0.6% of its width! Now, let's add
some tilt. Recall the article I posted above. Leslie Robertson was concerned with building collapse
due to a building undetectably out of
plumb. While it is difficult (not impossible) to put numbers on it, I'd say capacity reduces proportionally to eccentricity over a small range of
tilt, with at least a reduction in capacity by half at 20 degrees inclination. According to this very generous guess, a 10 degree tilt would would
lower the FOS to 1.
At that point, the upper section is on the threshold of overloading the capacity of the lower. If it does, it will descend, even though everything
above and below the imaginary cut is intact. The effective FOS is 1, and if overloaded, it will decrease dramatically - that's what steel does when it
fails. The first significant resistance the hypothetical collapse will encounter is entanglement of spandrels after 1 - 2m. Of course, it has
acquired MOMENTUM by that point, so the resistance is going to have to arrest that motion AND support the static load.
But the spandrels were designed to mediate loads between the perimeter columns in the manner of a Vierendeel truss. This does not equate to an FOS
where surfaces which were never meant to be the load bearing regions are impacted. It wouldn't be unreasonable to claim these suboptimal load paths
could not even support the static load. The load imposed is is unstable and immediately degenerates to a bending moment. Where spandrel meets in
knife-edge orientation, St. Venant's principle dictates deformation until adequate load distribution, which will allow the upper section to drop
further, lose more potential energy and, in turn, acquire more kinetic energy and MOMENTUM. Good luck finding equilibrium and arrest.
FOS is meaningless in messy collapse. Get over it.
edit on 30-1-2012 by IrishWristwatch because: (no reason given)