occurs between the first two asymptotes corresponding to Dj^ = and 



D3 = is the elastic buckling pressure for a stiffened cylinder with 



elastically restrained edges which buckles in a single-wave configuration. 



A more complete discussion of all the possible solutions of Equation (62) 



together with their physical interpretation is given in Reference 27. 



SEMI- EMPIRICAL FORMULA FOR INELASTIC 

 BUCKLING BETWEEN RING FRAMES 



Before we get into the rigorous formulation of the inelastic panel- 

 buckling problem, it is instructive to consider the derivation of a semi- 

 empirical formula for cylindrical shells which follows along the same 

 general development as for columns. The assumptions and underlying 

 concepts are not new, but the order and emphasis given them should help 

 to clarify a number of questions which have arisen in regard to this 

 formula. The basic approach has been given by Trilling and Windenburg 

 in an obscure reference in which they review the development of column 

 formulas for inelastic buckling and suggest the extension of the same 

 concepts for inelastic buckling of ring -stiffened cylindrical shells under 

 hydrostatic pressure. 



We start out first with a consideration of the column-buckling for- 

 mulas. The well-known Euler formula for the buckling of columns in the 

 elastic range is 



p. = '-^ (72) 



57 



