I am currently working on a piping system running through a pipe bridge linking two platforms. to be able to asses the fatigue, I calculated the cycle numbers and of course, I have applied the platform displacements on proper spots of the piping.
I would like to know which one of the following is the correct way of fatigue analysis for this situation:

1- making a (EXP) stress case and incorporate the stress reduction factor as per the code graph (fig. 302.3.5 in B31.3)

L1: W+P+T+D
L2: W+P
L3: L1-L2 (EXP) (modified stress reduction factor)

2- making a (FAT) case and using a proper fatigue curve

L1: W+P+T+D
L2: W+P+T
L3: L1-L2 (FAT)

thanks in advance

I would figure both may be appropriate with #2 considered as "more rigorous analysis". But what will be your allowable stress for #2? Do you intend to use the criteria in ASME VIII-2?
I believe #1 should be fine but what do you mean by "modified" f? Is this the cycle adjustment for combining two or more cycle sets? (different cycles for T and cycles for D) If so, you would first have to run EXP for T and then EXP for D to find the controlling value and then determine the equivalent cycles to set the allowable for the higher calculated stress. - This can get complicated real fast.
If you can pass the total EXP (T+D) using the largest cycle set (D?), perhaps you can justify safe operation.

what about wave data with number cycle

You can evaluate fatigue by using equation (1d) in B31.3. That will be a lot of work if the highest stress at each node can be caused by either T or D.
A nice trick in CAESAR II is to build a fatigue curve based on (1a) and let the CAESAR II fatigue processor run its cumulative damage check. This will give the results expected in (1d).

Hi Dave,

What you point out in your second post starts to look a whole lot like a proper ASME VIII-2 check... Except your still checking with B31.3 allowables. When would one consider switching to ASME VIII-2 fatigue curve for these type of fatigue analyses?

ASME VIII-2 would be considered '"more rigorous analysis". See B31.3 paragraph 300(c)(3). But such use must be accepted by the owner.
Because of the added work, I believe this would be practical only for specific components in your piping system.