Table 9 Hull-Girder Strain Variations Measured on Strength Deck or Keel Amidships 



■s 



1 



|l 



Q 



1 



1 g 



i||| 



Frequency Distribution of Stress 



■5 = 

 1 II 



t^umber of Stress Variations per 30 Day Period of Sea Duty 

 (The class limits are given in kips per square inch) 



<=" > 



11 



1<4 



1 Sep 53 ■ 3 Apr 54 



- 



220,000 



K-1 



1-2 



2-3 



3-4 



4-5 



5-6 



6-8 



8-10 



10-12 



Class 

 Limits 



18.4 



83,488 



64,348 



21,122 



7996 



3035 



573 



505 



48 



13 





Average of Load and Ballast Conditions 



This distribution is based on 10,580 measured stress variations. The average of the port and starboard 

 gage data was used. 



ll_ 



1 " 

 1^ 



74 



Dec 52 -Apr 53 

 Oct 53 ■ Nov 54 











2-4 



4-8 





8-10 



10-14 



>14 



Class 



Limits 



13.9 







121.706 



39,215 





2381 



176 



39 





This distribution is based on 403,343 measured stress variations 



|i 



5 i 



50 



5 Feb 54- 15 May 54 



7 Sec 



362,000 







2-4 



4-6 



6-8 



8-10 



10-12 



12-20 



>20 



Class 

 Limits 



97.6 







- 



7784 



966 



100 



19.5 



1.8 



0.65 





This disliibulion is based on 17,747 measured stress variations. The average of the port and starboard 

 gage data was used. 



o > 



Q 



- 



2(4 Years 



8 Sec. 



324,000 







2.2-4.5 



4.5-6.7 6.7-9.0 



9.0-11.2 



11.2-13.4 



13.4-15.7 



>15.7 



Class 

 Limits 



94.6 





16,690 



773 46 



3 



0.17 



0.08 1 





This distribution is based on 210,177 measured stress variations. 



o 



1° 



46 



Winter 55-56 



- 



- 







2-4 



4-6 



6-8 



8-10 



10-20 



>20 





Class 

 Limits 



6.4 





1 109,2601 40,660 



2000 



1213 



127 



0.3 







This distribution is based on 235,010 measured stress variations. 



< " 



S C3 



17 



Winter 55-56 



- 



- 



li-1 



1-lfe 



114-2 



2-214 2k-5 



>i 









Class 

 Limits 



16.6 



62,122 



31,733 



13,126 



5868 3198 



65 











This distribution is based on 65,797 measured stress variations. 



1 



il 



61 



Winter 54-55 







0.67-1.34 



1.34-2.01 



2.01-2.68 



2.68-3.35 



3.35-6.7 >6.7 









Class 

 Limits 



14.8 



64,603 34,617 



9444 



5365 



2480 2 











This distribution is based on 236,905 measurements of stress variation. 



♦The 

 VULC 



percenta 

 Mi. For 



ge of truncation was computed by l)ie mettiod proposed by R.A, Fisher (see chapter 6 of Reference 12) for alt cases except the GOPHER MARINER and the OCEAf^ 

 the tatter ships the percentage of truncation was estimated on the basis of an average period of stress variation. 



It has been shown in the literature (6, 19), 

 that, if a distribution is normal or log normal, 

 the largest values in repeated large samples from 

 this distribution have a cumulative distribution 

 F{x) of their own (18, 19, 20) which approaches, 

 as the sample size becomes larger and larger, the 

 form 



F{x) = exp [ — e" 



F{y) 



exp 



[1] 



where y = {x — Ui)a and is called the reduced 

 variate. 



In the present case x is a possible value of the 

 extreme of the stress, and Mi and a are constants 

 for a particular distribution. Special co-ordinate 

 paper has been devised. Fig. 17, on which such 

 a distribution will plot as a straight line. Gumbel 

 (19) has devised a method for estimating the 

 parameters Ui and a of the distribution of ex- 



tremes on the basis of measurements of extremes. 

 The method is applied here to the extreme sea- 

 induced stress variations measured in 2-min 

 samples taken at hourly intervals during 19 

 trips, each averaging 121 hr underway. 



The resulting extreme-value distributions for 

 the port and starboard strain gages are plotted in 

 Fig. 17. If all values of x are different, F(x) for 

 each observed point equals i/{n +1) where i is 

 the order number of the observed value when they 

 are arranged in order of increasing magnitude and 

 n is the total number of observed extremes. The 

 plotted points represent the individual meas- 

 ured extremes whereas the straight line in Fig. 17 

 represents the best fit to the measured data, 

 utihzing the method of Gumbel (19) under the 

 assumption that the underlying distribution is 

 of the log-normal type. 



On this assumption, F{x) represents the frac- 



27 



