By assuming a deflection function corresponding to simple supports at the 



ring frames, i.e., 



w (x) = w__sin (48) 



^ L 



Lunchick was able to derive the following expression for the buckling 



pressure: 



2 



= Tr^(^-^4r>Mir;^^-a) - 



^^ (l-v^) 



where 



C^.-^ (50) 



^ Rh 



In order to carry out numerical caluclations to find p^-j. from Equa- 

 tion (49), a graphical solution must be resorted to. First, for a given 

 geometry, the membrane state of stress at midbay defined by ^-^^^^ and 

 ^(£m '^^ determined using Equations (15) and (16), respectively, with <^xbm 

 set to zero therein. These stresses are then used in the Huber-Hencky- 



Von Mises theory of failure to compute a stress intensity d ^, i.e., 



-.1/2 

 4m+ 4m - ^Xm^^mJ (51) 



Next, the uniaxial stress-strain curve for the material which comprises 

 the cylinder is entered with the value of stress given by Equation (51), and 

 values of Eg and E^. are found for this stress level. A value of p^-j. can 

 then be computed from Equation (49), with the aid of all the other equations, 

 (43) through (47), needed to first find A^, A2, A12.I/ , • • • etc. By repeat- 



42 



