the Polytechnic Institute of Brooklyn, Salerno and Pulos around 1950 modi- 

 fied the earlier analyses to properly include the complete effect of the 

 pressure load. What has come to be accepted as the most up-to-date 

 solution and discussion of this problem is given in Reference 8. For our 

 purposes here, it suffices to give the governing differential equation and 

 its general solution, the boundary conditions invoked, and finally, the 

 expressions for the shell and frame stresses which are later used in 

 formulating some of the accepted and often used collapse criteria. 



The differential equation governing the axisymmetric elastic defor- 

 mations of a thin-walled circular cylindrical shell of finite length and 

 under the action of uniform external hydrostatic pressure (see Figure 11) 



4 2 



D^-^-H -P5_iJ5L+ _Eh_ w . -p(i-i//2) ^^. 



dx^ 2 dx2 r2 ^'^ 



where the necessary nomenclature and definitions used here and in the 

 equations to follow are indicated in the Notation. A derivation of Equation 

 (1) may be found in either References 8 or 9. 



The termi pR d_w ^hi^h renders the solution of Equation (1) to be a 

 2 dx2 



nonlinear function of the pressure is the "beam-column effect" which was 

 not considered in the analyses of References 6 and 7. The importance of 

 this term is further emphasized by the fact that it is the necessary in- 

 gredient for extracting a criterion for axisymmetric elastic buckling of a 



19 



