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 vessel becomes greater than the internal pressure.

Theoretically, the equations for internal pressure could be used to calculate the membrane compressive stresses in the shell of a pressure vessel under external pressure, if the pressure (P) is replaced by (-P). Thin wall vessels under external pressure, however, fail at stresses much lower than predicted by the equations, because of elastic or plastic instability, or buckling of the shell. In addition to the properties of the material and the operating temperature, the principal governing factors are geometrical: the unstiffened shell length, the shell thickness, and the outside diameter. Buckling or collapse is assumed to occur at a critical strain, when the potential energy of the external pressure exceeds the strain energy, caused by bending, that the cylinder can accommodate.

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