design should be directed. Of course, if the shell is much thicker than 

 R./R = 0.9, then the interaction loads will not be adequately predicted by 

 the use of a classical shell theory. 



The problem of predicting the ultimate load-carrying capacity of a 

 thick-walled pressure hull may be somewhat simpler than that associated 

 with the shallower depth designs. This latter question has been adequately 

 answered in an earlier section and the pertinent formulas used for pre- 

 dicting axisymmetric collapse, of relatively thin cylinders, precipitated by 

 yielding have been given as Equations (29), (31), (32), (35), (36), . . . etc. 

 For the case of the thicker walled hulls required to withstand the greater 

 pressures of deep depth, the following simple equations provide the 

 necessary means for predicting collapse strength: 



pE pR pR 



^ =_2 -^ ^ 2 -^ = 2_ (178) 



X 2h • <)) h(l + A /Lh) • r (R +R.) 

 f f o 1 



The stresses given by Equations (178) appropriately define the three- 

 dimensional state of stress in the shell wall; the stress '^^ results from 

 considerations of equilibrium in the eixial direction, whereas the stresses 

 d and d^ in the circumferential and radial directions, respectively, 

 result from integrating the Lame stresses through the thickness of the 

 shell. The added thickness A^fLr reflected by the term in the denominater 

 for d represents the stiffening action of the ring frames and is a conse- 

 quence of "spreading" the frame area Ar out over a frame spacing L(£. The 

 stresses. Equation (178), can then be used in conjunction with the Huber- 



120 



