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# 3.4.2 Calculation of Vessel Stresses Due to Nozzle Loads

Loads from piping attached to vessels induce stresses in the vessel walls, in the form of membrane and bending stresses. These stresses normally must be evaluated against the requirements of the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2. Accurate calculation of stresses in a vessel wall is difficult without a finite element analysis; the best means of doing a calculation otherwise is to use a reference which parameterizes results of finite element analyses. The most common reference of this type is Welding Research Council Bulletin 107.

Section VIII Division 2 of the ASME Boiler and Pressure Vessel Code provides fairly detailed rules for allowed stress in nozzle junctions and vessels. A synopsis of the elastic code rules are outlined here in order to provide some rules of thumb by which to analyze stresses in the vessel, at a junction:

1 - Section AD-160.3 contains two conditions to determine if a fatigue analysis may be ignored for nozzles. The second of these, Condition BP is summarized below:

a) The expected design number of full-range pressure cycles does not exceed the number of allowed cycles corresponding to an Sa value of 4Sm on the material fatigue curve, where Sm is the allowable stress intensity for the material at the operating temperature. b) The expected design range of pressure cycles other than startup or shutdown must be less than 1/4 the design pressure times (Sa/Sm), where Sa is the value obtained on the material fatigue curve for the specified number of significant pressure fluctuations. c) The vessel does not experience localized high stress due to heating. d) The full range of stress intensities due to mechanical loads (including piping reactions) does not exceed Sa from the fatigue curve for the expected number of load fluctuations.

2 - If fatigue analysis is not required, then Appendix 4 states that the following limits must be satisfied:

a) General pressure membrane stress intensity must be less than Sm. b) Primary membrane plus primary bending stress intensity must be less than 1.5Sm. c) Primary plus secondary stress intensity must be less than 3Sm.

Note that the 3Sm limit applies to the range of stress intensity. The quantity 3Sm is defined as three times the average of the tabulated Sm values for the highest and lowest temperatures during the operation cycle. In the determination of the maximum primary-plus-secondary stress intensity range, it may be necessary to consider the superposition of cycles of various origins that produce a total range greater than the range of any of the individual cycles. The value of 3Sm may vary with the specific cycle, or combination of cycles, being considered since the temperature extremes may be different in each case.

In pipe stress terminology, this can be approximated as:

1 - The sum of the pressure stress intensity in the vessel and the local sustained stress intensity at the nozzle connection, computed using WRC 107, must be less than 1.5Sm. 2 - The sum of the pressure stress intensity in the vessel, the local sustained stress intensity at the nozzle connection, and the local expansion stress intensity at the nozzle connection, computed using WRC 107, must be less than 3Sm (where Sm is the average of the Sm at the operating and installed temperature).

Because it is often difficult to include pressure in the local loading condition in a WRC 107 analysis, and because the area reinforcement requirements are supposed to take care of the pressure stress requirement at the intersection, it may sometimes be convenient to simplify these requirements to the following:

1 - The local sustained stress intensity at the nozzle connection, computed using WRC 107, should be less than 0.5Sm. 2 - The sum of the local sustained stress intensity at the nozzle connection and the local expansion stress intensity at the nozzle connection, computed using WRC 107, must be less than 2.0Sm.

This is based upon the worst case assumption that the full value of Sm is used to satisfy the pressure stress; this leaves 0.5Sm to satisfy the local stresses from the sustained external loads. The same rationale can be applied to the second requirement as well, leaving 2.0Sm to satisfy the local stresses from the sustained and expansion external loads. If these reduced allowables are not satisfied then the engineer should review the magnitude of the pressure loading and revert back to considering it within the full local stress analysis.

Modeling And Analysis Of The Piping System

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