Pressure vessels 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. 

An elementary understanding of pressure vessel design is needed in the preliminary stages of design, as most correlations for pressure vessel costs are based on the weight of metal required, and hence require an estimate of the vessel wall thickness as well as its volume. In many cases the required wall thickness will be determined by the combination of loads acting on the vessel rather than internal pressure alone. 

Tlie shell thickness as computeil by Ciode formulas for internal or external pressure alone is often not sufficient to withstand the combined effects ol all other loadings. Detailed calculations consider the effects of each loading separately and then must be combined to give the total state of. stress in that part. The stres.ses that are present in pressure vessels are separated into various classes in accordance with the types of loads that produced them, and the hazard they represent to the vessel. Each class of stress must be maintained at an acceptable level and the combined total stress must be kept at another acceptable level. The combined stresses due to a combination of loads acting simultaneously are called stress categories. Plea.se note that this terininolo differs from that given in Division 2, but is clearer for the pui poses intended here. 

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. 

Division 1 and as a result will require more analysis. Part 4 clearly indicates that if rules are not provided for a specific detail, geometry, or loading, then an analysis in accordance with Part 5, or design-by-analysis , shall be performed. Most vessels designed to Part 4 wiU use both the rules in Part 4 as well as specific procedures in Part 5. Both Part 4 and Part 5 contain load combinations for the pressure envelope. The load combinations in Part 4 are based on the allowable stress design (ASD) load combinations from ASCE 7, with non-appUcable loads removed. 

Hechmer, J.L., and Hollinger, G.L. Three-dimensional stress criteria -summary of the PVRC project, /. Pressure Vessel TechnoL, 122, 105-109, 2000. Chattopadhyay, S., Allowable stresses for nonrectangular sections under combined axial and bending loads, /. Pressure Vessel TechnoL, 110, 188-193, 1988. 

In any computer package involving 2- and 3D finite-element technique, Table AIB.l giving analytical formulation can be simulated to analyse the liner between the studs, standpipes and cooling pipes. For the global analysis of the pressure and containment vessels, these local effects can form the worst case. The vessel can be analysed with and without the contribution of the liner. Under ultimate conditions the liner local areas must be thoroughly assesed prior to the final decision of the factor safety above the elastic conditions under (pressure + prestress + temperature) the combined loading ... 

Again, the viscoelastic solution for stress is exactly the same as the elastic solution stress. As stated earlier, in general, if the linear elastic solution for stresses for a given boundary value problem does not contain elastic constants, the solution for stresses in a viscoelastic body with equivalent geometry and equivalent loads is identical to that for the elastic body. This means that the stress analysis of most problems considered in elementary solid mechanics such as beams in bending, bars in torsion or axial load, pressure vessels, etc. will have the same solution for stress in a linear viscoelastic material as in a linear elastic material. Further, stress analysis of combined axial, bending, torsion and pressure loads can be handled easily using superposition. 

For a tall vessel under external pressure only, in addition to the basic consid erations for external pressure design given in Chapter 8, the effect of fluid pressure and dead load is considered. This is very similar to those conditions considered in Section 16.3 for the vessel under internal pressure only. When direct loads caused by the fluid pressure and dead load create a compressive loading, it has to be combined with the loading from the external pressure. 

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