Miner's Dule fot Estimation of "Cumulalive Damage" D 



0=. "1 + ^ + 3+...." ; D = 1 Corresponds lofailure 

 Ni Nj Nj N„ 



where iij denotes the number of stress cycles applied at stress i 



N| denotes the number of stress cycles of magnitude i, which if applied alone woirld cause a fatigue failure. 



10 10^ 10^ 10' 10^ 10' 



n = Number of Stress Cycles per Year (or Load Cycles) 



Percent Damage Per Year 



Fig. 22 Illustration of the Application of a Load Spectrum to the Design for Endurance 



Strength 



Thus / is given approximately by the expression 

 shown in Equation [2]. This result is inde- 

 pendent of the form of P. As a first example of 

 the application of Equation [2] let it be required 

 to estimate the extreme stress variation that 

 would be exceeded by one half of all ships" 

 (/ = y^i if 10,400 random stress measurements 

 (TV = 10,400) were made on each of many ships. 

 Assume that the underlying distribution appli- 

 cable to these ships is that given for the port side 

 of the main deck amidships in Fig. 16. 



/= M, 

 From Equation [2 ] 



N = 10400 



f = 14 = I — e - 10400 [1-P(a:„,)1 



- 10400 [1 - P{x„^] = -0.6931 



1 - P(a;„,) = 6.66 X 10-5 



The corresponding value of the stress variation 

 Xjn^ is read from Fig. 16 as 16,000 psi (from hog to 

 sag). Similarly an estimate of the stress vari- 

 ation which will be exceeded in 20 winter seasons 

 (26,700,000 stress variations) in one half of all 

 ships (/ = )/2) is about 50,000 psi (from hog to 

 sag). 



Not much confidence can be placed in the ac- 

 curacy of this last prediction because the meas- 

 urements on which the prediction is based did not 

 include magnitudes of the order of the estimate; 



i.e., the estimates are not expected to be reliable 

 if the estimated extreme value lies far outside 

 the range in which experimental data are avail- 

 able. 



A better method for making an estimate of the 

 probable extreme stress is by use of the experi- 

 mentally obtained distribution of extreme values; 

 this being the most direct method. 



Prediction of Life Expectancy of Structures 



The results of the study of hull-girder stresses 

 (bending moments) given here can contribute to 

 the rational design of ship structures on the basis 

 of the prediction of the life expectancy of such 

 structures. 



The information that is necessary to make such 

 a prediction is as follows : 



1 It is necessary to know the service loads or 

 stresses that the ship structure is required to with- 

 stand throughout its service life. The statistical 

 distributions given in this paper provide the wave- 

 induced load data in a convenient form. The 

 more or less steady stresses such as dead load 

 stresses, temperature-induced stresses, and built-in 

 stresses also must be estimated. 



2 Adequate data on the endurance strength of 

 the ship's structural components are necessary. 

 Probably such data will only be needed for typical 

 components as well as for those portions of the 

 structure in which a failure, could be disastrous. 



3 Finally, it will be necessary to have a suita- 

 ble method or theory available which relates the 

 applied service loads to expected structural dam- 



36 



