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 hole. Away from the opening, the stress decreases until the nominal stress (stress in the unperforated plate) is reached. The ratio of the maximum stress at the edge of the opening to the nominal stress is the stress intensity, or concentration factor.
Figure 100-14 illustrates the concentration of stress for an opening of radius r in cylindrical and spherical shells. This figure shows that at a distance from the hole edge equal to the radius of the hole, the effect of the opening on the stress becomes negligible. This distance is usually accepted as the boundary limit for effective reinforcement.
Occasionally, an elliptical opening is used for special purposes, such as a manway or handhole. For elliptical openings, the maximum stress occurs at the end of the minor axis. Because the hoop stress is always greatest in a cylindrical shell (see Section 120), the most favorable alignment for an elliptical opening is to have the minor axis of the ellipse perpendicular to the hoop direction (or parallel to the longitudinal axis of the vessel). Otherwise the stress concentration factor will be greater than for a circular opening. The minimum stress concentration is obtained by making the elliptical opening with the lengths of the axis inversely proportional to the applied stresses: for a cylindrical vessel subjected to internal pressure, where the hoop stress is double that of the meridional (longitudinal stress), this requires an ellipse with an axis ratio of 1:2.
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