WHAT IS THE DERIVATION OF THE ALLOWABLE EXPANSION STRESS RANGE FROM B31.3 Sa= f(1.25Sc + 0.25Sh)?
I was trying to derived this formula from the Soderberg criterion with my mean stress as zero and the alternating stress is [(0.5Sh+2.5Sc)/2]. Am I correct with this derivation? Thanks in advance.

See the classic paper Piping-Flexibility Analysis by A. C. Markl, published in the Transactions of the ASME, February 1955.

You can find this paper reprinted in a number of references, such as Piping Engineering, published by Tube Turns (1986).