thickness h just reached the yield stress o of the material. 



Pbz'^yh/R (28) 



Equation (28) does not reflect in any way the strengthening effect of the 

 transverse ring frames on the average circumferential stress. However, 

 an estimate of this effect can be found by assuming that the cross- section- 

 al area of the frames is spread out and its orthotropic stiffness effect is 

 "felt" in the form of a thicker unstiffened cylindrical shell. This requires 

 that the actual thickness h in Equation (28) be replaced by 



SO that we now get the following modified boiler formula: 



Pel r <^yh(l+Aeff/Lfh)/R (29) 



From the theory of Salerno and Pulos outlined earlier, the maLximum 

 stresses occur in the circumferential direction on the outside surface of 

 the shell plating midway between adjacent ring frames, and in the longitu- 

 dinal direction on the inside surface of the shell plating at a frame; these 

 stresses can be determined from Equations (16) and (17), respectively. 

 Which of the two stresses is the larger depends upon the geometry of the 

 cylindrical shell and the reinforcing ring frames, but in most cases of 

 interest, it turns out that ^X-f-^ "^ffjOm- However, extensive Model Basin 

 tests have shown that the stress '^^Oj^ is determinative in precipitating 



axisymmetric collapse. Application of the maximum principal stress 



17 

 theory of Rankine to this stress, i.e., 



32 



