If I can summarize...
For fatigue analysis (for codes other than TD/12),
CAESAR II calculates a maximum 3D stress intensity. This is what's used for harmonic stress calculations where load cycles are defined. (I incorrectly stated previously that stresses are shown as (HAR) when load cycles are not defined; that's been changed to (OCC).)
CAESAR II on-line documentation has an awkward expression for that 3D stress intensity. I have a pdf posted on our web site that says it a little better. See
3D S.I. .
Now, for harmonic analysis on
CAESAR II, where pressure equals zero this gets real simple. Hoop and radial stress are zero so all you have remaining is longitudinal stress and shear stress. The maximum 3D stress intensity reduces to SQRT(SL^2+4T^2).
This is a stress amplitude as is goes both positive and negative. Compare this to the material fatigue curve that's based on amplitude (rather than peak-to-peak). Since we're probably talking high cycles here, instead of accumulating damage, just be sure the stress amplitude remains below the endurance limit. For that I'll point you back to API 618 or OM-3.
Yes, we are not considering paek stresses.