I have missed the stiffnesses in X, Y and Z direction you mentioned. You need to alocate those stiffnesses to the supports in case you are running analysis for an ordinary piping.
I guess modeling the structure will give you better picture rather than the assigning the stiffnesses.
In my analyses, for the compressor piping we needed to comply with the stiffness requirement of API 618 for the structural support members.
If you are running analysis for the compressor piping read this code carefully.

Regards,

Ibrahim Demir