material at the bottom and the amount of moment induced at the lower end 

 of the pile by horizontal loads. The top supports of the single-pile 

 bents were treated as elastic supports with their top reactions taken by 

 the adjacent bents through the superstructure. For expansion, the cause- 

 way was divided into three longitudinal sections. Battered-pile frames, 

 set longitudinally, provide necessary support in the longitudinal 

 direction. 



Many sources were investigated for applicable drag coefficients. 

 What appears to be a logical approach to the problem of waves breaking on 

 piles with relatively small £. ratios was given by Reid and Bretschneider 

 (1953). " 



Using the Berkeley-Monterey field data, which consisted of measure- 

 ments of moments on piles subjected to breaking or near-breaking waves, 

 the drag coefficient was obtained from the relation. 



Cn = 



M 



W/ DH' Kn„ Sn/, d 

 /2g ^"^ Vd 



where 



Cq = drag coefficient, 



M = measured moment at ocean bottom on 

 cantilever pile, 



w = unit weight of water, 



D = diameter of pile, 



H = wave height, 



K = maximum value of wave force factor 

 for drag effect of pile applicable 

 to nearly breaking waves , 



Sq = vertical position of action of total 



drag force on pile above ocean bottom, 



d = Stillwater depth 



Total forces and their centers of gravity were computed. The forces 

 were ten distributed along the pile. Instead of using a smooth curve for 

 this dynamic force distribution, the loading was simplified to an equiva- 

 lent straight line distribution which gave the same or slightly higher 

 results . 



The basic uncertainty in the correct value of the drag coefficient and 

 the fact that pile-frame analysis using the more refined smooth curves for 



44 



