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The fatigue results are independent of actual time. Consider a loading scenario that produces 2 result sets with fatigue damage caused by the stress difference between those sets. It does not matter if the stresses occur .2 seconds apart or 1 second apart (or any other time difference). The time between the result sets does not affect the calculated fatigue damage.
The static stress must be saved in a separate result set. It does not matter if that result set is from a unique system or from the same system as the acceleration loading. You could use 2 systems, or you could use 1 system with multiple result sets. DesignLife translates all imported results sets into one results file.