[sigma]1 - [sigma]2
S = greatest of [sigma]2 - [sigma]3
[sigma]3
- [sigma]1
Note carefully that the wording of the Code at this point may be misleading,
for Pm and PL may now represent not the sum of the stresses as defined
previously, but rather "stress intensities."
Figure 4-130.1 "Stress Categories and Limits of Stress Intensity" from the
Code is shown here as Figure 2-7. Note that for each class, and for the suc-
ceeding sums of each class, there is a "Stress Intensity Limit" (shown in a
circle), which is a multiple of the "Design Stress Intensity Value," Sm,
for the material as previously defined. The correct interpretation of Figure
2-7 is that the following conditions must be met for all points throughout
the body of the vessel.
(a)
Pm < / = Sm
(b)
PL < / = 1.5 Sm
(c)
Pm (or PL) + Pb < / = 1.5 Sm
(d)
PL - Pb + Q < / = 3.0 Sm
(e)
PL + Pb + Q + F < / = Sa.
For a vessel subjected to static loading only, the failure to meet any
condition except (e) means that the vessel is unacceptable. For a vessel
subjected to cyclic loading sufficient to require a fatigue analysis, the
failure to meet any condition including (e) means that the vessel is
unacceptable.
Appendix 5, Article 5-1, "Design Based on Fatigue Analysis." This article
presents the methods of determining the adequacy of a code vessel to sustain
a given number of load cycles. The application of its provisions are
mandatory if a fatigue evaluation is required. The requirement for a fatigue
analysis is established by examining the operational conditions of the vessel
from the viewpoint of the specifications of Paragraph AD-160, "Fatigue
Evaluation" in Article D-1, "General" of Part AD, "Design Requirements," of
Section VIII, Division 2. Before a fatigue analysis can be carried out, a
complete stress analysis of the vessel must be conducted and all the stress
intensity limits established. This means, in essence, that at this design
stage the vessel is adequate to sustain a static load condition.
The amplitude of alternating stress intensity must now be determined. This
is the portion of the quantity formed of PL + Pb + Q + F that is cyclic
in nature. There will be some conditions where the entire sum of these
quantities is cyclic as in start-up and shut-down operations. For most
conditions, only part of those quantities will be cyclic and the amplitude of
alternating stress intensity can be reduced by the amount of the steady
stresses. Thus in the nature of the operation of pressure vessels, there is
usually a history of operation at different amplitudes of alternating stress
intensities, each operating for a given number of cycles. For instance,
consider the following:
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