and Kendrick's Part I solution give pressures as much as 35 percent higher than the Part III 

 solution. In such cases use of the more exact solution in design work is desirable, but it is 

 impractical because of the extensive calculations required. 



In view of these difficulties, it seemed worthwhile to look for a short method of approx- 

 imating Kendrick's Part III solution. Accordingly, an extensive program was begun at the 

 Model Basin to obtain numerical solutions over a wide range of geometries, the objective be- 

 ing to summarize the results in some graphical form which would be of practical use to the de- 

 signer. Such a presentation would not only provide a quicker and more accurate means of 

 determining the general-instability strength of a structure but would present a better picture 

 of how variations in the scantlings affect this strength. Because of the very large amount of 

 computation involved, this program would have been virtually impossible without the aid of 

 the high-speed computer UNIVAC* 



The results of the calculations are summarized in this report in the form of graphs 

 which relate general-instability strength to variations in frame size, frame spacing, shell 

 radius and thickness, and compartment length. All calculations were for externally framed 

 steel cylinders with a Young's modulus of 30 x 10^ psi. Since the elastic general-instability 

 pressure is directly proportional to the modulus, these results are readily applicable to other 

 elastic raaterials having Poisson's ratio v - 0.3. Moreover, since internal frames theoreti- 

 cally provide slightly higher general-instability strength than external frames of the same 

 dimensions, the results can be safely applied to internally framed cylinders. The accuracy 

 of the graphical results is demonstrated by a comparison with numerical solutions of Ken- 

 drick's Part III theory for a wide range of geometry. The use of the graphs is illustrated in 

 Appendix A by a numerical example. In Appendix B, approximate formulas are given whereby 

 a frame strength parameter can be determined, and several numerical examples are provided 

 to demonstrate the accuracy of the formulas. 



METHOD 



Since Kendrick's Part III analysis cannot be reduced to a simple algebraic expression, 

 the problem of presenting the theory in graphical form must be approached somewhat indirectly. 

 The method adopted consisted of plotting the results of many numerical calculations against 

 various geometrical parameters until, 'by a process of trial and error, a system of coordinates 

 was found in which the points followed closely a set of single-valued curves. 



In attempting to define general-instability strength in terms of the shape and size of 

 the structure, at least five quantities must be considered, i.e., shell radius, shell thickness, 

 compartment length, frame spacing, and some measure of frame size. This situation is further 

 complicated by the variability of frame shape and the fact that the number of circumferential 



* Numerical results for more than 200 different geometries were obtained on UNIVAC through the solution 

 of a fifth-order matrix by iteration methods. 



