Local Stresses in Pressure Vessels Due to Internal Pressure and Nozzle Loadings

By Ray Chao

The subject of local stresses in the vicinity of nozzles in pressure vessels has been investigated for more than forty years. Indeed, the nozzle-to-shell intersection has been one of the most researched areas of pressure vessels. As a result of this effort, several practical approaches to this problem have evolved which enable the vessel designers to check the adequacy of nozzle designs in pressure vessels. However, very little direction has been given on the calculations on local stresses due to the combined internal pressure and external nozzle loadings. This article will address this problem and provide guidance to the vessel designers in the correct application of the available simplified calculation methods for local stresses in pressure vessels.

One of the most widely used methods has been that detailed in the Welding Research Council (WRC) Bulletin 107 published in 1965. In 1989, WRC Bulletin 297 was published as a supplement to WRC Bulletin 107. Together, they provide a simplified approach to the calculations of local stresses due to the combined internal pressure and external nozzle loadings. This article will address this problem and provide guidance to the vessel designers in the correct application of the available simplified calculation methods for local stresses in pressure vessels.

Local stresses, however, also occur in the vicinity of nozzles due to internal pressure. Therefore, a complete evaluation would require that these stresses be accounted for, in addition to those due to external loadings. The calculations of the total local stresses due to the combined internal pressure and external loadings have not, in general, been done correctly. It appears that the following two approaches have often been taken but neither of these will give correct answers.

* The nozzle is reinforced in accordance with the ASME Code, Section VIII, Division 1 based on the internal design pressure. This has been taken as being sufficient to nullify the effect of nozzle opening and only the general membrane stresses in the vessel due to internal pressure are calculated and superimposed to those due to external loadings.
* The internal pressure in the nozzle is converted into a radial outward thrust force on the nozzle and this is combined with the other nozzle loadings which are then used in the calculations of local stresses in the vicinity of the nozzle using the WRC Bulletins 107 and 297.

The local stress calculations using WRC Bulletins 107 and 297 have been incorporated in several commercially available engineering computer programs. In fact, the two approaches described above to account for the effect of internal pressure have been incorporated into at least one of such programs. The use of these approaches will give grossly incorrect results.

The first approach ignores the local stresses due to internal pressure which will result in an underestimate of the total local stresses due to the combined internal pressure and nozzle loadings. The second approach, on the other hand, will result in an overestimate of the local stresses, as has been shown in an earlier article (FEM Analysis of a Large Nozzle-to-Cylinder Shell Junction, by Doug Stelling, Carmagen Report, October 1996). It should be noted that WRC Bulletins 107 and 297 are intended for external nozzle loadings only and should not be used for pressure thrust loads on nozzles.

In 1991, WRC Bulletin 368 was published to fulfill the need for the determination of local stresses at nozzles due to internal pressure. The design formulas presented in this bulletin were based on the results of a parametric study performed using the computer program FAST2. Using these formulas, the maximum membrane and surface stresses in the vessel shell and nozzle at the nozzle-to-shell intersection may be computed. The resulting stresses due to internal pressure may then be combined with those due to external nozzle loadings by superposition.

A final evaluation of the acceptability of the design requires that the computed stresses be compared to an allowable stress basis. ASME Code, Section VIII, Division 1 provides no guidance on the evaluation of local stresses in pressure vessels. In fact, it does not specifically require a detailed stress analysis to evaluate the higher, localized stresses that are known to exist, but instead allow for these by lower basic allowable stresses and a set of design rules. Yet, it does require that loadings such as those acting on the nozzles be considered in designing a vessel. Therefore, local stresses due to nozzle loadings are often calculated and evaluated using the guidelines given in Division 2.

A calculated value of stress means little until it is associated with its location and distribution in the structure and with the type of loading which produces it. Different types of stress have different degrees of significance and must, therefore, be assigned different allowable values. Division 2 provides detailed guidance on the classification of stresses and also provides associated allowable stress limits. However, further discussions on the calculated local stresses due to internal pressure and external nozzle loadings using the WRC bulletins are warranted and this will be covered in a future article.

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