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I'm not aware of how you can use the UBC directly to make your overturning
evaluation.  But, you may be able to use an energy method to predict
whether or not overturning will occur.  Basically, assume the structure is
a 2D rigid body rotating about a corner.  Calculate the potential energy
for the position where the center of gravity is directly over the pivot
point.  Compare this value to the kinetic energy imparted by the ground
motion.  The trick is to get the maximum ground velocity which I would
estimate by converting the design acceleration spectra to velocity spectra
(V = A/w and w = 2*pi*f) and picking the maximum velocity.  I think this
would be a conservative approach.

Nels Roselund mentioned using the method described in Housner's paper
titled "The Behavior of Inverted Pendulum Structures During Earthquakes".
In order to use this method you will still need to know something about the
excitation frequency (or period).  Also, if you read Housner's paper
carefully, his analysis predicts the maximum amplitude (or duration) of an
acceleration pulse that would cause the body to reach the point of
instability.  Since the ground motion is random, the next pulse that comes
along may cause the body to tip over or drive it back down.  In other
words, Housner's method will be able to tell you the maximum acceleration
you can tolerate with 50% confidence.  But I still recommend that you take
a look at Housner's paper.  It will give you some good insight.  This is
one of those classical papers that generated lots of discussion and follow
on papers.

I would be surprised if you found overturning is predicted to occur for the
type of structure you're analyzing.  Sliding off the supports seems like it
would be more of a concern.

Walter Sawruk
EQE International, Inc.
Shillington, PA