The scales for wave forces, and the weights of the structure and of 

 the mooring cables, when modeled by Froude's law, are 



m m \ /m / 



m I m 

 P 



^p"^"H ^LJ • (6-10) 



The elastic properties of the mooring cables are modeled by the Mach- 

 Cauchy law; i.e., for elongation, 



F„ F„ 



(EA)j^ (EA) (6- 11a) 



where A is the cross-sectional area of the cable and E is the modulus 

 of elasticity of the cable. Thus, 



In equation (6-llb), it was assumed that both the weight and the 

 elasticity of the cable are important variables. However, if the cables 

 were heavy steel chain links, then the elastic effects would be negligi- 

 ble, but flexibility of the linkages and the weight per unit length of 

 the chain must be scaled correctly. The flexibility would be modeled by 

 using small chain links as in the prototype, and the weight of the chain 

 mooring line would be modeled by equation (6-10). However, if the proto- 

 type mooring cable were a relatively lightweight elastic rope, the weight 

 scale would only be approximated, and the elastic, elongation properties 

 would be modeled by equation (6-llb). If a relatively heavy, stiff steel 

 cable were used as mooring line, the weight and bending forces could be 

 appreciable. In this case the weight of the cable would be scaled by 

 equation (6-10) , and the bending properties would be scaled from the 

 force scale (eq. 6-10), and the deflection formula 



A = ^ (6-12) 



where I is the area moment of inertia of the cable cross section, and 

 k is a constant that depends on the end restraints and the distribution 

 of loading forces along the cable length, which distribution is assumed 

 to be equal in model and prototype. Based on these considerations, and 

 that Aji,/Ap = L^/Lp, since the model is geometrically similar to the 

 prototype, the transference equation for cable bending is 



m m \__^_m I 

 (Tw) 



v^^T^li:/ • f^-i^) 



329 



