The most difficult problem associated with the comprehensive ASME Section VIII Division 2 nozzle/vessel analysis involves the pressure calculation. Hoop and longitudinal pressure hand calculations are not considered reliable, and axial pressure loading on the junction is often miscalculated or omitted. Another issue with the comprehensive calculation is the amount of time it takes to organize and manipulate the stress data. For these reasons, an alternate simplified approach was developed using three checks.
The first check, Pm due to pressure, must be £ 1.0 Smh. To eliminate the concern for pressure, both the loading pressure term on the left side of the inequality and the allowable pressure term on the right side of the inequality cancel out.
This assumes that the area of reinforcement around the nozzle satisfies the pressure requirements. Also, let Pm equal the maximum value.
The second check, Pm + Pl + Pb, must be £ 1.5 Smh. Subtract the stress due to pressure, Pm, from both sides of the inequality and assuming Pm equals Smh. This reduces the check to: Pl + Pb £ 0.5 Smh (due to external sustained forces without pressure).
The third check, Pm + Pl + Q, is the root of the application controversy. There are three schools of thought:
-
Pm+Pl+Q is an operating loading condition, and as such, includes the loads due to pressure and weight.
-
Pm+Pl+Q is the range of loads or the expansion loading condition, and as such, excludes the effects of sustained, or primary loads. Also, exclude the primary sustained loads like weight and pressure.
-
Pm+Pl+Q is the range of loads and excludes the primary load weight, but includes the varying pressure load at least in those thermal load cases where the system goes from a startup ambient temperature and pressure condition to operating condition.
To simplify the calculation, assume that Pm, due to pressure, is included on both sides of the Pm+Pl+Pb+Q < 3Sm inequality. Also, assume that the area reinforcement requirements are exactly satisfied. Again, let Pm = Sm and subtract this term from the expansion allowable (Pm + Pl + Q < 3Sm) to provide a simplified allowable limit.
The expansion, operating, or both loads from the CAESAR II Restraint report must satisfy the computed stress requirement:
Pl + Pb + Q (operating or expansion excluding pressure) < 2Sm.
To summarize:
-
Ensure proper nozzle reinforcement for pressure and assume pressure stresses are at their maximum.
-
Compare primary stresses without pressure to ½Smh.
-
Compare stresses due to the sum of primary and secondary loads to 2Sm(avg); where Sm(avg) is the average of the hot and cold allowable stress intensities Smh and Smc.