Pressure Vessel Conical Sections Under Internal Pressure
Conical shapes are used mainly as bottom end closures, or as transition sections between cylinders with different diameters. The circumferential stress (Qt) and longitudinal stress (QL) in a conical section, as shown in Figure 100-10, are calculated by essentially the same equations as for cylindrical shells, in which R has been replaced by R/cosa:
The largest stresses, however, will occur at the junction of the cone to the cylinder, which must always be considered as part of the cone design. The end supporting force at section “a-a” (Figure 100-10) is actually sustained by the cylindrical shell, as shown in Figure 100-11. This arrangement will produce an unbalanced force (PRtana)/2 pointing inward, which develops a compressive stress at the junction. This force increases with the angle a and therefore, the ASME Code limits this angle to 30° and sets special rules (UA-5b and c) for reinforcement of the junction. Otherwise, the Code uses the membrane-thickness formula to determine the maximum stress and the minimum thickness of a conical shell.
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