cable there are six variables to be determined: a-j ' , 02', 3', S-| ' and S2 ' 

 and S s '. In order to simplify the equations, the double helical wires 

 were treated as single helical wires. Uniform elongation of all wires 

 in a strand gave the following condition. 



S ' sin a ' = S ' (12a) 



1 1 s 



S ' sin a • = S ' (12b) 



2 2 s 



The consistency of rotation requires that the end rotation of all wires, 

 (4>i) must be equal to the strand rotation 41 . For a specified end 

 rotation <\> , the condition is: 



♦l = *2 = *s = * 

 where 



S 1 



V 



V 

 V 



S ' 

 s 



R ' 



1^ - 2im 1 (13a) 



2™ 2 (13b) 



cos 3' + 2to (13c) 



Subscripts 1, 2, and s indicate inner layer, outer layer, and core or 

 strand, respectively. 



The last equation needed to solve for the six unknowns is the axial 

 force equilibrium equation: 



F = m g fm 1 C 1 + m 2 C 2 + ?c 1 sin 3' + B g sin ^ + 6 • ) (14) 

 where C = p sin a ' + B. sin ( ~x + a^'J 



C 2 = P 2 sin a 2 ' + B 2 sin ("2 + a 2/ 



The binormal forces in the wires, B-| , B2 and B s , caused by the 

 change in wire curvature and torsion are computed from Equation 4. The 

 wire stresses p^ and p s are related to wire lengths S-j/ and S s ' by Equation 

 1 . 



From equations 12a, 12b, 13a, 13b, 13c, and 14, the values of 



a„ , a„ ' , and 3' and S ' , S_ ' and S ' may be obtained by iteration. 

 12 12s 



