p = S ' - S AE (1) 



S 



where E = Young's modulus of elasticity 

 A = Cross sectional area 



Phillips and Costello developed [2] the twisting and bending moments 

 due to changes in torsion and curvature as: 



Jl = * Er (T' - T) (2) 



C 4(1 + v) 



4 



H = * E r (<• - k) (3) 



b / 



and 



where r = radius of wire 

 v = Poisson's ratio 



A force in the binormal direction is generated by this geometrical 

 change. 



B = 



= M k' - K, t' (4) 



Thus, knowing the change in S and a, one can calculate the wire tension p, 

 torque Mt, bending moment Mb, and binormal force B. With given external 

 boundary conditions, these internal stresses are computed and used in 

 the equilibrium equations to solve for the external deflections of the 

 whole strand. All external and internal forces and moments are shown in 

 Figure 2. A minimum helical radius Rm is reached when adjacent wires of 

 the same helix radius touch each other. This condition has been derived by 

 Phillips and Costello [2]. 



rn. 2 tt 2,1/2 ,_> 



R = r [1 + cot —esc a] (5) 



m m 



where m = number of wires in a strand. 



This radius is used as the minimum radius of a wire helix in the 

 numerical calculations. For a strand with solid core, if the core 

 helical radius is larger than the calculated minimum radius, then the 

 core radius is used in the calculations. For double-armored cables, the 

 outer wire must conform with the inner wire in helical radius. In complex 

 multistrand cables, such as 3x19, the minimum radius of various wire 

 layers becomes difficult to determine due to their complex geometrical 

 arrangements. Fortunately, the strand has a solid core so that the 

 minimum radius of each wire can be computed without using Equation 5. 



