given by 



'^G = Tn'^Xm- Om) + Xm+ cj-mj (33) 



However, since according to this theory inelastic action at any point in a 

 body under any combination of stresses begins only when the octahedral 

 shear-stress T becomes equal to (v[2"/3)<3 then Equation (33) leads to the 

 following: 



2 2 



a + c - a ^ 6 

 Xm Om Xm Oin 



- % (34) 



Essentially two distinct criteria can be derived from Equation (34) 

 depending upon whether the outer-fiber stresses or mid-fiber (membrane) 

 stresses at midbay are used. For yielding on the outer surface of the 

 shell plating, when the appropriate stresses x°m^^^'^<5°m from 

 Equations (15) and (16), respectively, are substituted into Equation (34), 



the following criterion is obtained: 

 Pc6 



%h/R (35) 



If it is assumed that axisymmetric collapse is precipitated by the 

 yield zone having penetrated through the shell thickness, when the approp- 

 riate stresses ^Xm ^^^ % m. f^^orn Equations (15) and (16) with '^xbm ^^*- 

 equal to zero therein, respectively, are substituted into Equation (34), the 

 following criterion is obtained: 



