Vessels Subject to Combined Loading

Pressure vessels are subjected to other loads in addition to pressure (see Section 13.4.7) and must be designed to withstand the worst combination of loading without failure It is not practical to give an explicit relationship for the vessel thickness to resist combined loads. A trial thickness must be assumed (based on that calculated for pressure alone) and the resultant stress from all loads determined to ensure that the maximum allowable stress intensity is not exceeded at any point. 

Example 11.15. A cylindrical shell that is 84-in. ID by 1.0-in. nominal thickness contains a nozzle 8-in. ID by 1.0-in. nominal thickness. The design pressure is 400 psi and the allowable stress of the material is 17.5 ksi. The nozzle is subjected to an inward radial loading of 12,000 lb and an applied moment in the longitudinal direction of 150,000 in.-lb. What are the combined stresses on the longitudinal axis due to these two external loadings using the Mershon method and the curves in Appendix K The vessel is not subjected to cyclic loading, and therefore no stress concentration factors need be considered. 

A vessel will not be subject to all these loads simultaneously. The designer must determine what combination of possible loads gives the worst situation, and design for that loading condition. 

Two fundamentally different types of failure may occur in vessels operated under vacuum (as opposed to high pressure). The problem in vacuum operation is the elastic stability of the vessel shell when it is under an external pressure loading. In general, elastic instability is a problem that must be considered in all structures having limited rigidity when subjected to bending, torsion, compression or a combination of these loadings. In failure by elastic instability, the structure buckles or collapses like an evacuated thin-shelled vessel. 

Coils inside pressure vessels may be subjected to the internal pressure of the vessel acting as an external pressure on the coil. In addition, steam coils should be designed for full vacuum or the worst combination of external loads as well as the internal pressure condition. The coil must either be designed for the vessel hydrotest, externally, or be pressurized during the test to prevent collapse. 

A tall, vertically supported vessel which is subjected to external pressure and external loading contains stresses similar to fliose in a vessel with external pressure only. The method of combining loadings as developed by Bergman and described in Section I6.S is used to obtain used in the analysis. 

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