The critical compressive stress (scr) for buckling (collapse) of a spherical shell has been experimentally determined to be approximated by: where R is the radius of the sphere, and E is the modulus of elasticity of the material.

Read More…## Cylindrical Shells Subjected to External Pressure

The critical collapse pressure (Pc) of a cylindrical shell under external pressure depends on two characteristic geometric ratios: t/Do and L/Do, where t is the shell thickness, L is the unstiffened length, and Do is the outside diameter. If L is short enough, the cylinder can fail by plastic yielding in compression at a stress […]

Read More…## Stresses in Pressure Vessel Shells Due to External Pressure

External pressure on a vessel most commonly occurs when a vacuum or partial vacuum is created inside of the vessel by (1) design, (2) discharge of its contents, (3) steam-out cleaning (condensation of steam), or (4) mechanical action, such as on a compressor suction, during off-design events. In these circumstances, the atmospheric pressure surrounding the […]

Read More…## Pressure Vessels Thermal Stresses

Thermal-expansion problems can occur whenever there is: (1) a considerable difference between the vessel operating temperature and the temperature of the environment surrounding the vessel; (2) restricted expansion or contraction; or (3) a temperature gradient within a vessel component that creates a differential expansion. Problems due to external constraint are solved differently than those due […]

Read More…## Stresses from Locally Applied External Loads

Most vessels are also subject to loadings at the supports, nozzles, and attachments. These loadings produce deflections, edge rotations, shears, bending moments, and membrane forces. The effect rapidly decreases with the distance from the point of application, where the maximum stress occurs. In practical applications, the number of variables is considerable, and some judgement must […]

Read More…## Pressure Vessels Reinforced Openings

Because stresses around openings are higher than the normal design stresses for the plate thickness, additional material must be provided to carry the additional stress in the shell around the opening. The additional material provided is referred to as reinforcement. The basic concept of reinforcement of openings is that the cross-sectional area of material removed […]

Read More…## Pressure Vessels Stresses at Openings

All pressure vessels must be provided with openings to get the process fluid in and out, and to provide entry for maintenance and inspection. When a circular opening is made in a plate subjected to uniform tension, a high concentration of stress occurs near the hole, with its maximum value at the edge of the […]

Read More…## Pressure Vessels Stress Concentrations

The normal equations for stresses in pressure vessels are based on the assumption that there is continuous elastic action throughout the member, and that the stress, for simple tension and compression, is uniformly distributed over the entire cross section. Abrupt changes in section geometries, however, can invalidate these assumptions, leading to great irregularities in stress […]

Read More…## Concentric Toriconical Reducers Discontinuity Stress

At high pressures (over 150 psi), where discontinuity stresses at the cone-to-cylinder junction can reach values above allowable limits, conical reducers having a knuckle radius at the large cylinder and a flare (reintrant knuckle) at the small end are preferred, as shown in Figure 100-13. Although more expensive to fabricate, toriconical reducers have the advantage […]

Read More…## Shell-to-Cone Junction Without Knuckle Discontinuity Stress

The thickness of a conical head or sections under internal pressure, with a half-apex angle smaller than 30°, is calculated by simple ASME Code membrane-stress equations and the ASME Code rules for reinforcement at the junction. No special analysis of discontinuity stresses is normally required. When, in addition to internal pressure, there are external loads, […]

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