discussed in detail by Howell et al. (1992). The waist ratio results, shown 

 in Figure 8, can be summarized with a quadratic fit of the fractional change 

 in stress as a function of waist ratio as follows: 



k z = a x + a 2 r + a 3 r 2 + a^r 3 

 where a x = 5.139 , a 2 = -28.738 , a 3 = 66.071 , and a r = -52.083. 

 1.25 

 1.2 



(5) 



0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 



Waist Ratio, r=B/C 



Figure 8 . Dolos waist ratio versus fractional stress 



49 . The layer modification can be thought of as a constant shift in 

 the stress for each layer added. This shift can be represented by the 

 following formula: 



SrC 



°sl = ~fc(N L - 1) 



where 



(6) 



o sL = the nondimensional increase in stress per added layer 

 S L =0.53 psi/in. , the dimensional layer coefficient 

 N L = the total number of layers 

 Note that S L assumes that C is in inches and 7 is in pounds per cubic 

 inch. Equation 6 assumes that the maximum static stress will be in the lowest 

 layer. 



26 



