B31.3 does not provide an explicit equation for sustained stress calculations, but only requires that the engineer compute the longitudinal stresses in the pipe due to weight and pressure, and then ensure that these do not exceed Sh- This is most commonly interpreted to mean:
Fax = axial force due to sustained (primary) loads, lb Mj = in-plane bending moment due to sustained (primary) loads, in-lb Mo = out-plane bending moment due to sustained (primary) loads, in-lb ii, io = in-plane, out-plane intensification factors, as per Appendix D of B31.3 Code Sh = basic allowable material stress at the hot (operating) temperature, as per Appendix A of B31.3 Code. Sh is defined as the minimum of:
1/3 of the ultimate tensile strength of the material at operating tempera-ture;
1/3 of the ultimate tensile strength of the material at room temperature;
2/3 of the yield strength of the material at operating temperature (90% of the yield stress for austenitic stainless steels);
2/3 of the yield strength of the material at room temperature (90% of the yield stress for austenitic stainless steels);
100% of the average stress for a 0.01% creep rate per 1000 hours;
67% of the average stress for rupture after 100,000 hours; and
80% of the minimum stress for rupture after 100,000 hours.
Mj = range of in-plane bending moments due to expansion (secondary) loads, in-lb M0 = range of out-of-plane bending moment due to expansion (secondary) loads, in-lb
Mt = range of torsional moment due to expansion (secondary) loads, in-lb Sc = basic allowable material stress at the cold (installation) temperature, as per Appendix A of B31.3 Code.
The equation for calculating occasional stresses is undefined by B31.3, which simply states that the sum of the longitudinal stresses due to sustained and occasional loads shall not exceed 1.33Sh. The default interpretation of this requirement is to calculate the sustained and occasional stresses independently (as per the equation given for sustained stresses above) and then to add them absolutely.
Note the differences between these two codes:
B31.1 intensifies torsion, while B31.3 doesn't.
B31.3 calculation methods are undefined for sustained and occasional load cases, while they are explicit for B31.1.
In its most common interpretation, B31.3 neglects torsion in the sustained case, while B31.1 includes it.
B31.1 neglects all forces, while in the default interpretation, B31.3 includes Fax in the sustained case.
Allowable stresses are different for each code.
Stress increase for occasional loads are different for each code.
Note that both codes additionally cite a conservative value of SA» f (1.25Sc + 0.25Sh), which may be used instead of the more liberal allowable of f (1.25Sc + 1.25Sh - Si). This is a carry over from pre-computer days, when sustained stress calculations were rarely done, so Si was not known explicitly, and conservatively estimated to be at its maximum allowable level of Sh.
Specific requirements of other common codes are shown below as well.