The calculated reference displacement stress range, SE shall not exceed the allowable stress range, SA, calculated by eq. (1A)
SA = f(1.25Sc + 0.25Sh) (1A)
When Sh is greater than SL, the difference between them may be added to the term 0.25Sh in eq. (1A). In that case, the allowable stress range, SA, is calculated by eq. (1B)
SA = f(1.25Sc + 1.25Sh − SL) (1B)
where,
Sc and Sh are the basic allowable stresses for the cold and hot conditions.
f is cyclic stress range factor1 for the total number of equivalent reference stress range cycles, N, determined from eq. (1C)
f = 6N^-0.2 ≤ 1.0 (1C)
These equations were derived from the moment fatigue tests by A.R.C. Markle, H.H. George, E.C. Rodbaugh in 1940's-1950's, based on iS(N)^-0.2=245,000 for carbon steel at room temperature, 281,000 stainless steel at room temperature and 183,500 stainless steel at 1050 F, where i is the stress intensification factor and it is 1.0 for girth butt weld in straight pipe.
However, if the stress range is logically limited as follows:
SE+SLe <= f(1.25Sc + 1.25Sh)
where SLe shall be calculated using the stress intensification factor i for moments which is used in SE calculation.
This equation is not same as Eq.(1B), and it seems to be so called as "LIBERAL STRESS RANGE".
References
Fatigue Tests of Welding Elbows vs. Mitre Bends - A.R.C. Markl, 1947
Fatigue Tests of Flanged Assemblies - A.R.C. Markl and H.H. George, 1949
Fatigue Tests of Piping Components - A.R.C. Markl, 1951
Markle, A. R. C , "Fatigue Tests of Piping Components," Transactions of the American Society of Mechanical Engineers, Vol. 74, 1952
Piping Flexibility Analysis - A.R.C. Markl, 1953
Balanced Quality as a means of Attaining Maximum Economic Safety For Critical Piping - A.R.C. Markl, 1957
Amplitude - The maximum extent of a vibration or oscillation, measured from the position of equilibrium.
Range - The area of variation between upper and lower limits on a particular scale.