The present study is the continuation of an extensive investigation aimed at the development of rational design rules for formed pressure vessel heads. The program was sponsored and coordinated by the Pressure Vessel Research Committee. This problem was one of the first research projects the Design Division of PVRC selected for study and by maintaining its interest stimulated an increasing amount of work on the diverse behavior of seemingly similar head shapes. In the course of this work, not only new analysis techniques were developed but also a number of new failure modes unique to these deceivingly simple looking geometrical shapes were uncovered. Many of the details of the problem have been studied, and while much remains to be done, enough data became available to assemble a consistent set of design rules for the more common dished heads. This report is an attempt to summarize the present state-of-the-art and to provide the background information for the recommended changes in the present design rules.

The study proceeds as follows: first the geometry of torispherical heads is discussed and the dimensionless parameters governing the stress distribution and failure modes are described. Next, the current status of the design codes in the U. S. and abroad is summarized and a brief historical background of the code development is presented. Following this, the available analysis results supporting experimental evidence are presented and the structural behavior and corresponding failure concepts for the elastoplastic and buckling regions are described. The analysis methods are critically evaluated and design criteria based on a uniform margin of safety are proposed for the ideal geometrical shapes. From this, the dominating geometry parameters are identified and the effects of deviations from the perfect shape are evaluated. Finally, the numerical values for the failure pressures are assembled in tabular and graphical forms which are adaptable for code design rules. In conclusion, the reliability of the proposed revisions of the design procedure is reassessed and the scope of future work is discussed.