structure may be obtained by requiring that the displacements become in- 

 finitely large at buckling. It is on this basis that Salerno and Pulos arriv- 

 ed at the criterion of Equation (39). Since Von Sanden and Gunther, and 

 later Viterbo, omitted the beam-column term in the basic differential 

 equation, Equation (1), then this would correspond to y = in the more 

 complete formulation of Reference 8. In such a case, Equation (39) would 

 no longer have any meaning because the pressure p would not appear. 



A more complete analytical development and discussion of the 

 axisymmetric elastic buckling problem is given by Short and Pulos in 

 Reference 20. 

 AXISYMMETRIC INELASTIC BUCKLING BETWEEN RING FRAMES 



The collapse criteria which were developed earlier and were identi- 

 fied by the pressures p^^, p^3, P(,5, p^^, p^y, and p^Q are, strictly speak- 

 ing, valid only for an elastic-perfectly plastic material. As it has already 

 been stated, the axisymmetric collapse mode is in reality associated with 

 the phenomenon of buckling at a reduced modulus, so that the strain-hard- 

 ening characteristics as reflected by the secant (Eg) and tangent (E^) 



modulii must be considered. 



2 1 



On the basis of the deformation theory of plasticity, Gerard de- 

 veloped a general set of differential equations of equilibrium for cylin- 

 drical shells in which the coefficients reflect the plasticity or state-of- 



stress effects. Lunchick, specializes these equations for the case of 



22 

 short-length cylindrical shells subjected to hydrostatic pressure. In 



40 



