NACA Technical Note No. 1341

NACA Technical Note No. 1341 - A Simplified Method of Elastic-Stability Analysis for Thin Cylindrical Shells, I - Donnell's Equation was issued by the United States National Advisory Committee for Aeronautics in June 1947. It described a mathematical approach for estimating the bearing strength and deflection under load of thin-walled cylindrical structures.

Introduction
The equation for the equilibrium of cylindrical shells introduced by Donneli in NACA Report No. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. It is shown that by this method solutions may be easily obtained, with results expressed in terms of two nondimenslonal parameters, one dependent on the critical stress and the other essentially determined by the geometry of the cylinder. The influence of boundary conditions related to edge displacements in the shell median surface is discussed. The accuracy of the solutions found is established by comparing them with previous theoretical solutions and with test results. The solution to a number of problems concerned with buckling of cylinders with simply supported edges on the basis of a unified viewpoint are presented in a convenient form for practical use. The continuing emphasis on aircraft designed for very high speed has resulted in a trend toward thicker skin and fewer stiffening elements. As a result, more of the aerodynamic load is being carried by the skin, and thus ability to predict accurately the behavior of thin molded sheets under load has become more important. Accordingly, it was considered desirable to provide the designer with more information on the buckling of curved sheet than has been available in the past. In carrying out a theoretical research program for this purpose, a method of analysis was developed which is believed to be simpler to apply than those generally appearing in the literature. The specific problems solved as a part of this research program are treated in detail in other papers. The purpose of the present investigation, which is discussed in two papers, is to present the method of analysis that was developed to solve these problems. In the present paper the method is briefly outlined and applied to a number of the simpler problems in the buckling of cylindrical shells. In reference 1 the method is generalized for application to more complicated problems.

Conclusions
The use of Donnell's equation to find the buckling stresses of cylindrical shells leads to simpler results and involves less labor than the use of equations in which second-order terms are retained. The buckling stresses found by use of Donnell's equation are in reasonable agreement vdth results based on other theoretical calculations. Except for the case of axial loading, they are also in reasonable agreement with test results. Boundary conditions having to do with axial and circumferential displacements cannot be handled directly by use of Donnell's equation. This disadvantage is not considered serious, however, because the boundary conditions on axial and circumferential displacement, which are implied by the simple solutions given, correspond approximately to those that are most likely to occur in practical constructlon and because in many cases the buckling stress is not very sensitive to these boundary conditions.