The "WRC 107: Elastic Analysis vs. Fatigue Analysis" article, published in COADE's June 2000 Newsletter, brings some useful explanations regarding the Ceasar II WRC 107 module utilisation. However, in my opinion, some aspects remain unsettled and, somehow, inadequately interpreted.


The main problem is the Local Primary Membrane Stresses (Pl) assessment, in the near vicinity of the 'Shell-Nozzle" junction. The other problems are the "Pressure Stress Indices" calculation and the "Include Pressure Thrust" option.


In most of the engineer practical applications, the internal pressure loading of the Vessel accompanies the external mechanical local loadings of the Nozzle (consisting of external forces and moments). Therefore, the stresses due to external loadings have to be superposed over the stresses developed under the internal pressure loading. The nozzle quasi-circular orifice cutting up makes the effective bearing thickness of the vessel wall to decrease. The immediate consequence is that the membrane stress components (the stress components normal to the current plane of section especially) due to internal pressure loading increase (in many cases significantly) in the near vicinity of the nozzle orifice. The nozzle reinforcement only diminishes the proportions of this fact, but cannot prevent it. In such circumstances, the elastic local stress analysis has to assess realistically the local primary membrane stress components (Pl), taking into account this nozzle orifice discontinuity effect.
The calculation procedure recommended in the June 2000 Newsletter, neglects the nozzle orifice discontinuity effect (regarding the pressure loading membrane stress components increasing) and considers only the external loadings effect (including here the pressure thrust force eventually) on the local primary membrane stress components (Pl). In my opinion, this approach is inadequate and leads to an underestimation of the general plus local primary membrane stress intensity (i.e. an unjustified relaxation of the "Pm + Pl < 1.5 k Smh" stress intensity checking criterion). This drawback can be reasonably amended if the "Pressure Stress Indices" concept utilisation and the Stress Summation philosophy are slightly modified, as follows (these proposals supplement the corrections I suggested in the "An Inadvertence regarding Caesar II WRC 107 Module" intervention, posted on June 10 2000):


1. The general primary membrane stress components, developed in the unpenetrated vessel wall, under the internal pressure loading exclusively, 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), and b) the longitudinal general membrane stress - Long/Pm(SUS). These stress components are used to compute the general primary membrane stress intensity, that is equivalent to the hoop stress: Pm = Circ/Pm(SUS).


2. The local primary membrane stress components have to be assessed taking into account both the pipe sustained external loadings effects and the nozzle orifice discontinuity effect. First, the local primary membrane stress components due to the pipe sustained external loadings (i.e. external forces and moments) are assessed using the original WRC 107 algorithm, WITHOUT the "Include Pressure Thrust" option activated. In this way, the local primary membrane stress components [i. e. the hoop stress - Circ/Pl(SUS-F,M) and the longitudinal stress - Long/Pl(SUS-F,M)] developed under the pipe sustained external loadings are computed.
Second, the local primary membrane stress components due to internal pressure loading are assessed using the ASME stress indices values. So, if Kcirc/out , Kcirc/inn , Klong/out and Klong/inn are the ASME stress indices values (from ASME Code, Div. 2, Article AD-560.7 and Table AD-560.7, or Article 4-6, Par. 4-612), for the hoop/circumferential and longitudinal normal principal stresses, corresponding to the inside ("inn") and outside ("out") wall surface, then the local primary membrane stress components due to internal pressure loading can be assessed using the following formulas: a) the hoop pressure local membrane stress: Circ/Pl(SUS-p) = [(Kcirc/inn + Kcirc/out)/2]* Circ/Pm(SUS) - Circ/Pm(SUS); b) the longitudinal pressure local membrane stress: Long/Pl(SUS-p) = [(Klong/inn + Klong/out)/2]* Circ/Pm(SUS) - Long/Pm(SUS).

The b formula isn't wrong. Regarding the Stress Indices calculation (see ASME Code, Div. 2, Article AD-560.7 and Table AD-560.7, or Article 4-6, Par. 4-612), it should be reminded that BOTH for the longitudinal symmetry plane and for the transverse symmetry plane, for ALL the pressure stress components, the membrane reference stress used at the ratios denominator place, is the membrane HOOP stress in the unpenetrated and unreinforced vessel wall. Therefore, the existing Caesar II WRC 107 module contains another inadvertence: when the "Include Pressure Stress Indices" option is activated, the longitudinal pressure stress components are computed using the shell longitudinal primary membrane stress as the reference stress value. Hence, for the cylindrical shells, the computed longitudinal pressure stress components are twice smaller than their actual levels. If we examine the WRC 297 analysis results, for the same problem, we'll see this difference.

The pressure stress indices values quantify the nozzle orifice discontinuity effect, the general stress concentration effect and the local stress concentration effect, developed under the internal pressure loading, in the near vicinity of the "Shell-Nozzle" junction. Therefore, the pressure stress indices values have taken into account the pressure stress state developed in the nozzle wall. This stress state includes the pressure longitudinal stress that develops the axial (from the nozzle point of view) pressure force or, in other words, the nozzle pressure thrust. In such circumstances, it's obvious that the "Include Pressure Thrust" option doesn't need to be activated.

The total local primary membrane stress components are assessed using the following obvious formulas: a) the total local primary membrane hoop stress: Circ/Pl(SUS) = Circ/Pl(SUS-F,M) + Circ/Pl(SUS-p); b) the total local primary membrane longitudinal stress: Long/Pl(SUS) = Long/Pl(SUS-F,M) + Long/Pl(SUS-p).
These stress components are used to compute the general plus local primary membrane stress intensities (Pm + Pl), which have to satisfy the second stress intensity checking criterion: Pm + Pl < 1.5 k Smh.


3. The secondary stress components have to be assessed taking into account the following loadings and effects: a) the bending stress components developed under the pipe sustained external loadings (external forces and moments); b) the membrane and the bending stress components developed under the pipe expansion external loadings (external forces and moments); c) the bending pressure stress components due to the shell-nozzle interaction (the so-called "edge effect", due to the shell wall - nozzle wall stiffness difference)..
The bending stress components due to the pipe sustained external loadings (external forces and moments) are assessed using the original WRC 107 algorithm, WITHOUT the "Include Pressure Thrust" option activated. In this way, the bending stress components developed under the pipe sustained external loadings [i. e. the hoop stress - Circ/Q(SUS-F,M) and the longitudinal stress - Long/Q(SUS-F,M)] are computed.
The membrane and the bending stress components due to the pipe expansion external loadings (external forces and moments) are assessed using the original WRC 107 algorithm. In this way, the membrane and the bending stress components developed under the pipe expansion external loadings [i. e. the hoop stresses - Circ/Qm(EXP), Circ/Qb(EXP) and the longitudinal stresses - Long/Qm(EXP), Long/Qb(EXP)] are computed.
The bending pressure stress components due to the general stress concentration effect (the so-called "edge effect", due to the shell wall - nozzle wall stiffness difference) are assessed using the ASME stress indices values, as follows: a) the hoop pressure bending stress: Circ/Q(SUS-p) = [(Kcirc/inn - Kcirc/out)/2]* Circ/Pm(SUS); b) the longitudinal pressure bending stress: Long/Q(SUS-p) = [(Klong/inn - Klong/out)/2]* Circ/Pm(SUS). It has been assumed that a positive bending moment stretches the inside wall surface and compresses the outside wall surface.
The secondary stress components (Q) are added to the general plus local primary membrane stress components (Pm + Pl). The total (primary plus secondary) stress intensities (i. e. Pm + Pl + Q) have to satisfy the third stress intensity checking criterion: Pm + Pl + Q < 1.5 (Smc + Smh).

While the general and the local stress concentration effects due to the external loadings (i.e. forces and moments) can be differentiated (using the local stress concentration factors Kn and Kb), the general and the local pressure stress concentration effects cannot be discriminated, because the ASME pressure stress indices (which are equivalent to the total pressure stress concentration factors) quantify the both phenomena. This fact is the main drawback of this new approach. It could be amended only if we'd renounce at the ASME "Pressure Stress Indices" concept and we'd use more accurate methods in order to quantify separately the general and the local pressure stress concentration effects (i. e. the systematisation of a large number of extended finite element analyses results).
However, this modified approach yields conservative results, which satisfy acceptably ALL the ASME stress intensity checking criteria.


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Regarding the Caesar II WRC 297 module, I have noticed here an inadvertence concerning the assessment of the pressure stress components developed in the nozzle wall. The existing procedure calculates the normal principal pressure stresses, developed in the nozzle wall, in the near vicinity of the "Shell-Nozzle" junction, using the theoretical formulas for the thick wall cylindrical bodies. The nozzle orifice discontinuity effect, the general stress concentration (or the gross structural discontinuity) effect and the local stress concentration effect are neglected.
It's obvious that this approach is inadequate.
In my opinion, this drawback could be amended using the same "Pressure Stress Indices" concept. The ASME Code, Sect. VIII, Div. 2 (see Article AD-560.7 and Table AD-560.7, or Article 4-6, Par. 4-612) stipulates that the pressure stress indices are applied to the near vicinity of the "Shell-Nozzle" junction. The utilisation of these total pressure stress concentration factors has not been restricted only to the vessel wall, or only to the nozzle wall exclusively. In fact, the material continuity requires the pressure stress indices utilisation both for the vessel and for the nozzle.