As it is known, Caesar II performs the elastic analysis of the "Shell - Nozzle" junction through the WRC 107 and WRC 297 modules.
The piping stress analyses that I accomplished for several piping projects, requested the vessel stress assessment by the WRC 107 method. Following this procedure (implemented within the Caesar II software package - 4.00 and 4.20 versions), I have noticed a major inadvertence regarding the interpretation of the material strength safety criteria. The main problem is the WRC 107 stress summation routine.
As it is known, following the ASME Code (Section VIII, Division 2) provisions, Caesar II provides the following three well-known stress intensity checking criteria: 1) Pm < k Smh; 2) Pm + Pl < 1.5 k Smh; 3) Pm + Pl + Q < 1.5 (Smc + Smh), where the meaning of the involved notations may be found in the Caesar II documentation (Technical Reference Manual) or in the Pressure Vessel ASME Code, Section VIII, Division 2 (see Appendix 4, Article 4-1, par. 4-130...4-134, Fig. 4-130.1).
The major problem appears in connection with the first and the second stress intensity checking conditions. The first restriction involves the general primary membrane stresses (i.e. the normal hoop and the normal longitudinal primary membrane stresses for the cylindrical shells) developed in the unpenetrated vessel/shell wall, under the internal pressure loading exclusively. The nozzle orifice discontinuity and the shell-nozzle interaction are excluded.
The second restriction involves the (algebraic) sum of the general and of the local primary membrane stresses. The local primary membrane stresses are developed in the near vicinity of the "Shell - Nozzle" junction, as a result of the combined internal pressure and applied sustained forces&moments loading. The nozzle orifice discontinuity is taken into account, but the shell-nozzle interaction is excluded.
As a conclusion, we may say that the first and the second stress intensity checking conditions, involve the primary membrane stresses, or, in other words, the primary stresses that are uniformly distributed along the (shell) wall thickness.
Now, the WRC 107 analysis module (included in the Caesar II software package) contains the "Include Pressure Stress Indices" option. When this option is activated, the vessel stress analysis takes into account the stress indices provided by the Pressure Vessel ASME Code, Section VIII, Division 2 (see Appendix 4, Article 4-6, par. 4-612). The programme multiplies the general primary membrane stress components by these indices and the results are interpreted as being the effective general primary principal (hoop and longitudinal) membrane stresses. In the WRC 107 Stress Summation Report, the effective "general primary membrane stress" components (calculated with the ASME stress indices) are not the same for the inside and for the outside vessel wall surfaces, and, thus, these stresses don't satisfy the main membrane stress requirement: the invariance along the vessel wall thickness.
In my opinion, this approach manner is inadequate.
As the ASME Code (Section VIII, Division 2, Article 4-6) stipulates, the stress indices provided at par. 4-612, quantify the PEAK STRESS components induced by the internal pressure action, at the inside and at the outside "Shell - Nozzle" junction wall. Therefore, when we multiply the general primary membrane stress components by the ASME stress indices, we obtain the peak stresses developed under the internal pressure loading, in the near vicinity of the "Shell - Nozzle" junction.
The peak stresses quantify the following effects, developed under the internal pressure loading: a) the nozzle orifice discontinuity effect; b) the general stress concentration effect (i.e. the gross structural discontinuity effect, at the "Shell - Nozzle" junction level - the so-called "edge effect"); c) the local stress concentration effect (i.e. the local structural discontinuity effect, at the "Shell - Nozzle" junction level - small fillet radii, partial penetration welds, etc.). Briefly, the peak stress components quantify the result of the general and of the local stress concentration effects, developed under the internal pressure loading. These peak stresses deal with the fatigue analysis stress intensity checking condition: Pm + Pl + Q + F < Sa (see the ASME Code, Section VIII, Division 2, Appendix 4, Article 4-1, par. 4-135, Fig. 4-130.1). Thus, it's obvious that the peak stresses cannot be interpreted as being the effective general primary membrane stress components, because they contain the general and the local bending stress components, induced by the internal pressure action.
The consequence of this inadequate approach, is in erroneous overestimation of the general and of the local primary membrane stresses (i.e. the normal hoop and the normal longitudinal primary membrane stresses for the cylindrical shells), that may cause the unjustified failure of the membrane stress intensity checking criteria.
In my opinion, this inadvertence can be reasonably amended if the "Pressure Stress Indices" concept utilisation will be slightly modified. The most conservative, but acceptable approach of the "Pressure Stress Indices" utilisation, could be organised as follows:
1. The general and the local primary membrane stress components (i.e. the normal hoop and the normal longitudinal primary membrane stresses for the cylindrical shells) remain unmodified, as they have been assessed without applying the ASME stress indices. These stress components are: a) the hoop/circumferential general membrane stress - Circ/Pm(SUS); b) the longitudinal general membrane stress - Long/Pm(SUS); c) the hoop/circumferential local membrane stress - Circ/Pl(SUS); d) the longitudinal local membrane stress - Long/Pl(SUS).
2. The secondary/bending stress components, developed by the combined internal pressure and applied sustained forces&moments loading, have to be corrected in order to include the general and the local stress concentration effects, induced by the combined sustained actions. Therefore, instead of Circ/Q(SUS) and Long/Q(SUS) initial assessed values, we should have Circ/Q(SUS) + (Kcirc - 1) * Circ/Pm(SUS) and Long/Q(SUS) + (Klong - 1) * Long/Pm(SUS) values respectively, where Kcirc and Klong are the ASME pressure stress indices, for the hoop/circumferential and longitudinal normal principal stresses respectively (the inside and the outside wall surfaces).
3. All the other stress components remain unmodified.
In this way, although on the one hand, the total stress intensity (i.e. Pm+Pl+Q) includes the pressure peak stress components, and, on the other hand, the pressure local primary membrane stress components and the pressure secondary/bending stress components are somehow twice taken into account, this new alternative of the vessel stress summation is much closer to the ASME Code precepts than the existing procedure is.