Design Equations for Preventing Buckling in Fabricated Torispherical Shells Subjected to Internal Pressure

Abstract

Design rules to prevent buckling in thin fabricated torispherical shells subjected to internal pressure are not yet available in either the American or the British pressure vessel Codes. They are the subject of the present paper and some possible design equations are suggested. The equations were obtained from the buckling equations for perfect torispheres after considering all known experimental results on fabricated models. The empirical constants in the proposed design equations depend on the type of head construction used, i.e. whether crown and segment or pressed and spun. For both types of head the equations give a factor of safety of at least 1.5. The design equation proposed for the crown and segment heads was also checked on several large vessels which had failed in service. The safety factors found for these cases were all greater than 1.7, which means that the vessels would not have buckled if the design equation had been available at the time.

The other failure mode of these torispherical heads, i.e. large axisymmetric deformations leading to through-thickness yielding, is also discussed briefly. Curves are given which show that, for 300 < D/t < 500, buckling controls the failure mode in some cases and axisymmetric yielding in others. Neither the American nor the British codes recognize that buckling can occur in this D/t range but the theoretical predictions have been confirmed by experiments. However, the amount of test data is limited and more work is needed on the topic.

It is also shown in the paper that, for torispherical shells with D/t ratios in the range 300 < D/t < 500, the axisymmetric limit pressures, p_DS, are lower than both the internal buckling pressures and the large deflection axisymmetric yielding pressures. From this, one would expect the failure modes to be axisymmetric in this D/t range. However, as some non-symmetric buckling failures have occurred, the limit analysis predictions for the failure mode are thus not always correct.

One feature of the experimental results on stainless steel torispherical shells which are reviewed in the paper is the relatively poor buckling performance of the heads tested by Kemper in comparison with similar heads tested by Stanley and Campbell. As the values of the empirical constants in the design equations are controlled by the lowest test results, the higher bucking pressures obtained by Stanley/Campbell cannot be utilized unless an adequate explanation for the difference in the two sets of results is forthcoming.