## Pressure Vessel Torispherical Heads Under Internal Pressure

A torispherical head, sometimes referred as a “dished head,” simulates an elliptical head with a compound curve composed of a crown radius that is a spherical segment and a knuckle, as shown in Figure 100-7. The knuckle radius should be large enough to minimize the latitudinal stress in this region. For this reason, the ASME Code specifies a minimum knuckle radius of 6% of the crown radius. The maximum inside crown radius for a torispherical head equals the outside diameter of the cylindrical shell it caps. Under internal pressure the maximum membrane stress in the crown region is the same as in the cylindrical shell it caps. The type of heads using the radii values approved by the ASME Code are usually called “ASME 6% Flanged and Dished Heads.”

The abrupt change in radius from L to r in torispherical heads introduces large discontinuity stresses which are absent in elliptical heads. This factor makes dished heads suitable for use only in low pressure applications (under 150 psi), where their shallower depth and lower fabrication costs make them a desirable shape.

Figure 100-8 gives the equations for calculating the meridional stresses (sx) and latitudinal stresses (sj) in torispherical heads. The maximum calculated compressive latitudinal stress in the knuckle occurs at point “a.” In the spherical cap the meridional and latitudinal stresses are both tensile stresses. The actual compressive stress in the knuckle is reduced by the tensile stress in the spherical segment, with a resulting lower membrane stress at point “a.”

As with the design of semiellipsoidal heads, the ASME Code uses a simplified procedure for stress calculations, introducing an empirical correction factor “M” into the equation for membrane stress in the crown region. This correction factor compensates for the discontinuity stresses at the shell-to-head junction. In practical applications it has been found that the ASME Code equation for the thickness of a torispherical head under internal pressure gives conservative results for the majority of head designs, but is not adequate for large ratios of R/t.

During hydrotests, large, thin-wall torispherical heads have collapsed as a result of elastic buckling, plastic yielding, or a combination of both. ASME Code, Section VIII, Division 2, Appendix 4, provides a method of checking the plastic collapse pressure of torispherical heads against the hydrotest pressure of the vessel.

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