F£)(9) is an even function, and F^CSJ is an odd function, hence 



F^(0) = F^(-9), (7-53) 



and 



F,. id) = -F,.(-0). (7-54) 



and calculations need only be done for <_ Q <_ -n radians. Equations 

 7-53 and 7-54 are true for any wave that is symmetric about its crest, 

 and are therefore applicable if the wave tables of Skjelbria, et al. (1960) 

 and Dean (1973) are used. When these tables are used, the wavelength 

 computed from the appropriate finite amplitude theory should be used 

 to transform 6 into distance from the wave crest, x. 



The procedure is illustrated by the following examples. For sim- 

 plicity. Airy theory is used and only maximum horizontal force is con- 

 sidered. The same computation procedure is used for calculating maximum 

 moment . 



************** EXAMPLE PROBLEM 



*************** 



GIVEN : A design wave with height, H = 35 ft, and period, T = 12 sec, in 

 a depth, d = 85 ft, acts on a pile with a diameter, D = 4 ft, (assume 

 Airy theory to be valid). 



FIND ; The variation of the total force on the pile as a function of 

 distance from the wave crest, 



SOLUTION : From an analysis similar to that in Section 7,315, 

 Co - 0.7, 



and 



Cm = 1-5 • 



From Figures 7-43 and 7-44 using the curve for Airy theory with 



d 85 



— : = r = 0.0183 , 



gT^ 32.2(12)2 



^im= 0-378; K^^ = 0.195, 

 and from Equations 7-30 and 7-31, 



7^(4)2 

 Pfm = 1.5 (2) (32.2) -y- (35) (0.378) = 16,100 lbs., 



^Dm " 0.7 (0.5) (2) (32.2) (4) (35)2 (0.195) = 21,500 lbs. 

 Combining Equations 7-22 and 7-26 gives 



