The end torque T is calculated based on the external torque-balance 

 equation: 



T = m 1 (M a1 - M c1 + M t1 sin o^ ' + M^ cos a 1 ') 



+ m„ (M _ - M + M . sin a ' + M, cos a.') (10) 

 2. az cz tz z dz z 



where M = p R' cos a' 

 a 



M = B R' sin a' 

 c 



The torsional and bending moments, M . and M^, caused by the change in 

 wire helix are computed from Equations 2 and 3. Elongation is calculated from 



AL = L^ - L 1 = L 2 ' - L 2 (11) 



Double-armored Cable With Specified Tension and Torque 



The two external variables to be determined are elongation and end 

 rotation, both of which can be expressed again in terms of cu ' , a^ ' , S.. ' 

 and S2'. The four equations for solving the four unknowns are: 



1. Uniform elongation: Equation 6 



2. Uniform rotation: From Equations 7 and 8, eliminating $ , 



S 1 ' cos a 1 ' S 9 ' cos a 9 ' 



J L _ 2 Trn 1 = — 2to 2 



R r R 2' 



3. Axial force equilibrium: Equation 9 



4. Axial torque equilibrium: Equation 10 



After solving for a ' , a ' , S ', and S„', by iteration the rotation is 



calculated by Equation 7 or 8 and the elongation is calculated by Equation 11. 



Multistrand Cable With Specified Tension and Rotation 



Based on the same principle used in solving the double-armored cable, 

 the helix geometry after loading is determined first . 



The variables needed to determine the unknown end conditions of a 

 multistrand cable are the wire pitch lengths S± and pitch angles a-^ 

 as well as the strand pitch length S and pitch angle 3. For a 3x19 



