50. The Crescent City static PDF can now be generalized using these 

 two stress modification relationships. The generalized nondimensional random 

 stress variable for the static stress distribution can be expressed as 



= k. 



yC 



-Je. 



yC 



+ k r 



yC 



(N L - 1) 



(7) 



where k r and k rL are the waist ratio modification factors. The additional 

 waist ratio modification factor, k rL , is required because k r does not in- 

 clude the effect of added layer stress with changing waist ratio. The added 

 stress per layer should decrease as the waist ratio increases due to the de- 

 crease in unsupported length. In Equation 7, the first term is the non- 

 dimensional Crescent City static stress modified for the design waist ratio, 

 the second term is the reduction in stress due to removal of the second layer 

 of dolosse, and the third term is the increase in stress due to the added 

 layers of the design dolos . Note that the subscript cc on the first and 

 second terms indicates that all of the variables in that term are for the 

 Crescent City dolosse. The third term variables are those of the new design 

 dolos . 



51. Assuming that 



K r . * K (8) 



Equation 7 becomes 



°* = K 



1±\ + S L U(N L -1) --L 



which can be reduced to 



a' s = k z (o' scc + a) 

 where the shift parameter is given by 



a = S T 



1 {Nr - i) _ _L 



(9) 



(10) 



(11) 



52. Now the design static distribution in terms of the generalized 

 random variable given in Equation 10 is 



27 



