Table 6 SS Esso Asheville — Basic Data on Wave-Induced Stresses for the Period Septem- 

 ber 1, 1953 to April 3, 1954 











j= Sf 





E 



Number of Stress Cycles Falling between Stated Limilst(fo< a 30-Day Pe 



1 

 iod at Sea) { 



s 



II 

 ""1 



•< « 



1 



T3 B 



O J3 



1 1 



e 1 



i— ^ 



1 







1 



For a Sample of 2 min Taken Every Hour 



For a Sample of 2 min Taken Every Fourth Hourft 



5" u- 



i- 



1 S. 



f 



is 



§ 



g 



as 

 o 



.1 ^" 

 If 



1 



|. 



§ 



g a. 



5 S. 



1" 



S 



i 



stress 



A 



L 



75 



59 



79 



2,832 





1,208 



221 



31 



3 

























Stbd 



E 



L 











15.25 



18,422 



3,370 



473 



46 



















-^ 









A 



L 



CT 



40.9 



60 



2,136 



















1,226 



758 



206 



95 



.'43 



4 





E 



L 

























80.89 



99,171 



61,315 



16,663 



7,685 



iM 



324 



Stress 



A 



B 



69 



65 



94 



3,120 





1,690 



142 



14 





























Stbd 



E 



B 











13.85 



23,406 



1,967 



194 































A 



B 



61.9 



61.9 



100 



3,304 



















1,409 



1,336 



427 



115 



17 



5 





E 



B 

























52.3 



73,691 



69,873 



22,332 



6,015 



889 



262 



Stress 



A 



L 



75 



65 



87 



3,120 





1,767 



343 



55 



8 



4 





















Port 



E 

 A 



E 



L 

 L 

 L 



68 



34.8 



51 



1,888 



13.85 



24,473 



4,751 



762 



111 



55 







91.53 



987 

 90,340 



706 

 64,620 



222 

 20,320 



77 

 7,048 





 



1 

 92 



Stress 



A 



B 



69 



58 



84 



2,784 





1,442 



280 



38 



2 

























Port 



E 



B 











15.52 



22,380 



4,345 



590 



31 



























A 



8 



61.9 



35.2 



57 



1,922 



















785 



685 



280 



125 



48 



IB 





E 



B 

























89.90 



70,752 



61,582 



25,172 



11,238 



4,315 



1,618 



•The factors K and A'j are Hie lac 

 cycles that woulahave been obtained 



tors by which the cycles measured on the oscillogram samples are multiplied in order to estimate the number of stress | 



if continuous measurements had been talien over a period of 30 days at sea. 







tPeak-to-peak variation. 









ft€very fourth sample recorded was 



utilized in this analysis. 







Mathematical Synthesis of Cumulative Long- 

 Term Distribution of Wave Heights Based on As- 

 sumption of a Log-Normal Distribution of Sig- 

 nificant Wave Height. Let the instantaneous dis- 

 tribution of the wave heights pertaining to a 

 particular sea, be definerd by the Rayleigh dis- 

 tribution, thus 



pix) = 



2x 



where" Ei is the mean square value of all the 

 individual wave heights comprising the ith sea. 

 Let E — cE'^' be the significant wave height 

 where c is a constant. The distribution of E is 

 log normal, thus 



1 



p (log E) = —-y= e 2,« 



where c^ is the variance, and ii is the mean value 

 of log E. Therefore 



" £ is also equal to the total area under the power spectrum. See 

 references (14, 15) for a discussion of the power-spectrum concept. 



P{£) = g P(log E) 

 and the probability P that x take on a value < Xj 



P{- 



"^^= f ;it^ 



V27 



I -^ e E 

 J E^ 



E' dx dE 



The second integral is integrable, thus 



E = « 



-(log£ - u)' 



''('■'- / vrvY.' 



[i - r?'] 



dE 



The integral may be evaluated numerically by 

 a summation, thus 



P{xi) ^ 'e /, [1 - e- -Vfi,] 

 i = l 



20 



