Symmetrical Bending of Thin Circular Elastic Plates on Equally Spaced Point Supports

The determination of bending moments, tWlstmg moments, and shearing forces in a thin circular elastic plate subjected to symmetrical bending is a problem which is often encountered in the design and analysis of structural elements or systems. This study deals.,with the solution of this problem for a thin circular elastic plate supported at points equally spaced along a concentric support c ircle and subjected to a transverse load which is symmetrically distributed over a concentric circular area. These structures may be typified as end closures, bulkheads, and diaphragms. UsualJy the analysis of such a structure is simplified by the introduction of engineering approximations which pertain to the particular structural system under examination. However, this paper presents a special application of a more general solution developed by Bassali [1]' which more closely represents the cond itions realized in practical structures and obviates the necessity for some of the approximations. This specialized treatment of Bassali's theory provides the equations necessary to calculate moments, shearing forces, and associated stresses anywhere within the plate. It also shows that the expressions for maximum bending stresses at the center are independent of the angular orientation and the number of supports. Further reduction of these expressions result in the Grashof [2] equations. A comparison between a limited amount of experimental results and the theoretical predictions of tangential strains along the concentric support circle show good agreement. This good agreement for strains along with that for deflections [3] tend to substantiate the theory.