Torispherical Shells—A Caution to Designers

Abstract

It has recently become apparent, through a rigorous stress analysis of a specific case that designing torispherical shells by the current edition of the ASME Code on Unfired Pressure Vessels can lead to failure during proof-testing of the vessel. The purpose of the present paper is to show in what respects the Code fails to give accurate results. As an illustrative example, a hypothetical pressure vessel with a torispherical head having a diameter-thickness ratio of 440 was selected. The supports of the vessel were considered to be either on the main cylinder or around the torus. The vessel was subjected to internal pressure and the elastic stresses in it were determined rigorously and by the Code. A comparison of the two revealed that the Code predicted stresses in the head which were less than one half of those actually occurring. Furthermore, the Code gave no indication of the presence of high compressive circumferential direct stresses which exceeded 30,000 psi for practically the entire torus. If the head had been fabricated using a steel with a yield point of 30,000 psi, then a limit analysis shows that it would have failed or undergone large deformations, whereas the Code would have predicted that it was safe. The Code’s rules for torispherical heads are thus in need of revision for certain geometries. The implications of the foregoing results are currently being studied by the ASME; in the interim, however, designers should exercise care in applying the Code to torispherical shells. It is also shown in the paper that the use of the membrane state as a particular solution of the differential equations is not a good approximation for toroidal shells of the type considered.