The Bending of the Clamped Sectorial Plate

Abstract

Abstract The problem of evaluating the bending moments, existing in a uniformly loaded clamped plate having the form of a sector of a ring, is one which arises in connection with the stress analysis of reinforced piston heads and in other design problems. In this paper, expressions are derived for the bending moments along the edges of such a plate. Similar problems, i.e., those of the clamped rectangular plate under uniform pressure, under a central concentrated load, and that of the simply supported sector of a disk under uniform pressure, have been discussed by previous authors. The general approach used in the foregoing problems is adopted in the present case; a considerable reduction in the computational work is achieved, however, by the use of an integral-equation method of solving the boundary-condition equations. Numerical results are obtained for plates of various dimensions, and the edge moment distributions are plotted for these cases. Curves are also plotted which indicate the relationship existing between the maximum bending moments derived for sectorial plates and those previously obtained for clamped rectangular plates of similar size.