

500 



750 

 1 



1000 

 1 



Variation in 

 2000 

 1 1 



.ongitudinal Bendir 

 3000 4000 

 1 . 1 



% Moment 

 5000 

 1 1 



Hog to 

 1 1 



Sag, foot-tons 

 10,000 15,000 

 1 I - 



20,000 



30,000 

 « 1 ■ ■ 



40,000 



0.05 

 0.1 

 0.2 



0.5 



' 



1 



1 



1 



1 





1 









1 1 



1 1 





1 



/ 



/ 



1 

































/ 



/ 





































/ 





































/ 







































/ 















1 









o Fractiles taken from Tabic 11 





/ 



^ 





































^ 



/ 

















> 



1 '° 

 1 

 1 20 



^ 30 



;t *o 



150 

 £60 























y/ 

































/ 



/ 



\ 































t 



/ 



































P 



/ 





































/ 





































/ 





































/ 



/ 

































80 

 90 







/ 





































/ 



/ 









































































98 















































































99.9 

 99.8 



99.5 

 99 



95 z 



> 



90 I 



'"O.! 0.2 0.5 1 2 5 10 



Variation in Stress, Main Decl(, Amidships, Ifips/in^, Hog to Sag 



Figure 10 - Long-Term Cumulative Distribution of Longitudinal Bending Moment, 

 Amidships, for Wartime Service, North Atlantic Ocean 



This log-normal distribution is computed on the basis of the data represented by the plotted points and it cor- 

 responds to the following parameters: ' 



Mean value of \o%.^ (variation in stress in kips/in. ) = 1.6016 

 Standard deviation of log (variation in stress in kips/in. ) = 0.3229 

 It is probably valid up to 40,000 ft-tons. 



conditions of ship speed, heading, speed, and sea are steady. The following is a more general 

 approach which may be applied to any distribution provided that its cumulative distribution 

 function P {x) is known. 



The following formula, developed in Reference 3, gives the fraction / of all samples of 



24 



