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The problem you are facing is that it takes a quantum leap
going from modal superposition to history-type analysis.
Unfortunately, when you use SAP type FEA, there is not
much else you can do having discrete dampers in the system.
For such a set up the damping matrix becomes unsymmetric,
therefore making the problem unsolvable for SAP.
I haven't done a complex seismic in years, but I remember that in more
advanced codes, like ANSYS, for example, there is a provision for such
a situation, I.e. you can run it without resorting to time-history.
Sincerely, Gregory
On Jan 11, 2005, at 12:06 PM, Gerard Madden, SE wrote:

> Model the structure, using the damper properties (use etabs, sap, or
> the
> like). It's a dual system with CBF's... use 100% of load. Then run the
> analysis with the braces/dampers inactive with 25% of the lateral
> force.
> Probably should do a dynamic analysis if you are going to the trouble
> of
> using dampers to really get the behavior down.
There are a few caveats here. For the most part structural analysis
programs don't extract damped eigenmodes or frequencies because
structural damping is small and the overall results won't be
significantly affected. For seismic analysis damping is normally
included in the response spectra. Another problem with discrete dampers
is figuring out the damping coefficient, which is different than the
damping ratio of the structure, since the damping ratio includes the
equivalent mass associated with the applicable eigenmode.

If you're actually going to use discrete dampers, your best bet is to
run a time history analysis. It's going to be a huge pain in the ass if
you use a synthetic earthquake record, but you might have some luck if
you confine your attention to a few governing modes and see if you can
associate a damping ratio with the damping coefficients by running a
step load input and noting the amplitude decay. You can back-calculate
the damping ratio from the ratio of the amplitude of successive peaks.
The actual relationship is in most vibration handbooks.