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Re: Factor of Safety against Uplift

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John MacLean,

Structures in seismic events do not fail due to overturning instability
unless a structural element fails.  Foundations do not get rooted out of the
ground.  That is because earthquake loads are dynamic -- they are cyclic.

Stability under earthquake shaking is not like stability under soil pressure
or other constant loading.  Earthquake loads are cyclic.  A building with a
period of, say, 0.2 seconds and any significant amount of overturning
resistant mass will not have time to progress toward instability due to
earthquake loads before the loads reverse.  The structure's period of
response that we use for design is much shorter than the period of the
overturning response.  While the maximum design loads may develop due to a
cyclic response in a small fraction of a second, it will take a much longer
period of time for any significant overturning displacement to develop in
the system.

The overturning resistance mass in the foundation of a structure need be no
more than enough to provide the structural system with a polar moment of
inertial that has a long period compared with the response period of the
structure.  Our seismic codes may still be conservative on this issue
because we don't compare the structural system's overturning response
period with its flexural response period -- for simplicity we arbitrarily
require static stability based on unfactored service loads.

Nels Roselund
Structural Engineer
South San Gabriel, CA

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