A METHOD OF DETERMINING THE SECONDARY STRESSES IN CYLINDRICAL SHELL ROOFS.

Abstract

Synopsis. The membrane theory for the stresses in thin shells is based on the fundamental assumption that there is no change of shape of the shell on loading. In shell-roof construction, however, there must be a deflexion of the edge tie-beam, with resultant secondary stresses in the shell. Some solutions have been given for this problem (outstanding being those of Dischinger, Finsterwalder, Schorer, and Jenkins), but many of them are very difficult to follow and are of doubtful value to engineers because of the lack of numerical examples. The first part of this Paper is devoted to a summary of the work of those previous investigators. Dischinger's solution of the problem shows that the longitudinal stress-distribution in the cylindrical portion of the shell is almost equal to that obtained by considering the complete shell as a beam spanning between the columns at the gable ends. The Author has utilized this stress distribution as a means of determining the constants of integration in Schorer's method of analysis. The “beam” method described in the Paper entails less work than other methods and has the advantage that a slide-rule can be employed for most of the calculations. The Paper concludes with a section giving an example which shows the application of the method to the design of a roof.