Hi,

You may find answers for your questions here:
https://www.pveng.com/origins-of-the-asme-fatigue-...
and here
https://pdfslide.net/documents/hinnant-asme-plant-...

The code reference is VIII-2 5.5.1.4. You can also refer to API579 14B.2 which allows you to define custom margins and mean stress correction. You should get a pretty close fit to the original work by Langer if you want to verify it for yourself. While there are lost of mean stress correction models, the main one of interest is the Goodman relation/diagram. The book and papers by N. Dowling are also very good if you are after further reading.

You can also find the discussion in ASME PTB-1 - in Section 5.5.3 under the discussion of "Resistance - Smooth Bar Fatigue Curve". That Section also references WRC 487 and NTIS report PB-151-987.

I will also note that the Structural Stress Method for the Fatigue of Weldments has an explicit mean stress correction.

Thanks for your reply, Idanpv and BJI.
Thanks, TSG4, i have learned so much from your posts before.

hi, Idanpv, i have read the post you advised. and i have a question which may be fundamental that, may i interpret that the effect of mean stress is incorporated into the safety factor of 20 on cycles for S-N curve in ASME VIII-2?

Thanks so much.

ASME VIII-2 permissible curves are obtained from the original design curves by adding factors of safety:
2 on stress
20 on cycles
I think that Chris Hinnant study, although it is very old, is a very good for understanding the basis for the ASME VIII-2 curves.

No, the factor of 20 on cycles is based on the effects of data scatter, size effects, surface finish and environment. It isn't really a safety factor. Regardless, this is applied after the curve is corrected for mean stress. Since mean stress has negligible effect above yield, the mean stress correction affects the higher cycle part of the curve, shifting is downwards.

THanks for your guidance,Idanpv,BJI.