Several solutions on circular cylindrical shell roofs have been obtained up-to-date, but they are rather complicated for practical eingineers. Solutions presented here are obtained from the ordinary differential equations which are developed from the fundamental partial equation by using the finite difference method in one direction. The shell is divided into a number of strips in one direction, and in another direction, the solution of each strip is got by the Fourier sieries. The solutions, as an example shown in this paper, were obtained by dividing the shell into six strips in the circumferential direction along the longitudinal direction. Since they are expressed as the simple formulae, the displacements and stresses of the shell roof, simply supported on the boundaries under concentrated, uniform and one side loads, can be computed easily. As a numerical example, the deflections of a cylindrical shell roof, 20m long and 10m in span with 60° of the open angle, obtained by the formulae for given loads, are shown in the figure together with the values of some stresses computed from them. In some cases, errors due to the finite difference cannot be neglected, but they can be reduced by dividing the shell into smaller strips. The author believe that the method used in this paper is applicable to other problems, for instance, the bending of plates or eigen-value problems in two dimensions.
