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AprwoH >mate Weight . SO t 



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ELEVATION 



Figure 55. 



Geometry of barge under consideration as sloping-float 

 breakwater for protection of dredges, sand bypassing, 

 or cargo loading (after Raichlen and Lee, 1978). 



The equations of motion of the moored barge may be deduced after approxi- 

 mating the change in the buoyancy and the elastic restraint associated with 

 the mooring line. The restraining force due to buoyancy depends primarily on 

 the unit weight for resistance to small motions; for an elastic mooring, the 

 developed force is of the form 



T = C 



m 



(47) 



where As/s is the strain, and C and m are constants unique to the type 

 of mooring line. To define the tension in the mooring line, the strain, 

 As/s, which is related to the tension at breaking, must be determined. 

 Hence, the tension, T, can be determined from the characteristics of the 

 mooring lines. 



When the restoring forces have been defined in terms of the motion of 

 the barge, the equations of motion can be expressed in terms of surge (x- 

 direction) , heave (y-direction) , and pitch (^direction). Raichlen and Lee 

 (1978) noted that because of the analogous nature of the resulting expres- 

 sions, only the x-component should be considered. This is a balance of the 

 mass of the barge times the acceleration equated to the summation of six force 

 terms acting on the body: (a) effect of the weight of the body; (b) effect of 

 and change in buoyancy (a form of interaction among motions in the three 

 directions — surge, heave, and pitch); (c) stress in the mooring line; 

 (d) normal force acting on the bottom; (e) friction forces acting on the 

 bottom; and (f) the forcing function (the integrated pressure force acting in 



97 



