(7) Stress Index Method. One of the reasons for selecting the
nozzle geometry for the 4.0 inch diameter nozzles as shown in Figure 2-10 was
that such a configuration could be analyzed by the "Stress Index Method"
described in Article 4-6. This method allows the determination of stress
intensification factors or "stress indices" for a select set of nozzle
configurations and only when such nozzles can be considered as single,
isolated openings. The term "Stress Index" is defined as the ratio of the
maximum stress found in such nozzles to the computed membrane stress
intensity, Pm in the unpenetrated and unreinforced vessel material.
Further, this method is applicable solely to vessels loaded by internal
pressure. Other types of load-induced stresses such as those induced by pipe
loads or thermal gradients must be determined by some other means. However,
if this is done, then the total stresses acting at certain given points in
the nozzle configuration may be obtained by superposition of results.
The 4.0 inch nozzles were carefully designed to meet all the specifications
of Paragraphs AD-540.1, AD-540.2 and Figure AD-540.1. This latter group of
paragraphs and the figure quoted assure that the nozzle shall meet all the
stress intensity limits except the PL + Pb + Q + F = 2 Sa limitation.
Thus for static internal pressure loading only, such nozzle configurations
require no further analysis. Paragraph 4-612 lists the Stress Indices for
such nozzles. For internal pressure loading, all the Stress Indices apply.
If the internal pressure is the sole load then the Stress Index, S, on the
inside corner is of prime importance as it sets the maximum stress intensity
in the nozzle. In Paragraph 4-612 (a) "Nozzles in Spherical Shells and
Formed Heads," S is equal to 2.2 on the inside corner. The calculated
membrane stress intensity in an unpenetrated and unreinforced sphere is
determined by
Pm = Sm - 0.5 P
if Equation (a) of Paragraph AD-201 was used to set the sphere's minimum
thickness. For the sphere in this case
Pm = 23,200 - 0.5 (1000.0)
22,750 psi.
The maximum stress intensity then is equal to
Smax =
2.2 (22,750) = 50,050 psi.
There are no PL, Pb, or Q stress components in an unpenetrated spherical
shell away from any other opening or other type of discontinuity. Thus
Pm < Sm
Pm (or PL) + Pb + Q = Smax 2.2 Pm < 3.0 Sm
PL + Pb + Q + F = Smax = 50,050 < 74,000 = 2 Sa.
As can be seen from the above, all the static stress intensity limits are
met. Further this evaluation shows that the maximum stress intensity in the
nozzle is lower than the 2 Sa limit imposed for 10,000 cycles of 0-1000 -O
psig load.
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