moment. As the torque continues to increase, the resisting moment also 

 increases and finally reaches a maximum. This is the point for the onset 

 of kinking. Further increase in torque will result in a rapid formation 

 of a complete loop with one or more turns (Figure 16). Thus, the exterior 

 torque is relieved somewhat. The configuration of the loop formed depends 

 mainly on the tension and torque on the cable. When a homogeneous elastic 

 rod is subjected to low tension and high torsion, the ends of the rod rotate 

 opposite to one another and the axis of the rod gradually becomes helical. 

 After a certain number of turns, a loop with a small radius and a helical 

 twist will form at a weak point in the rod. Such a loop may be called a 

 kink. A rope or cable behaves in a similar way when it is under low tension 

 and high torsion. Such deformations have been observed in 3x19 cables in 

 both rotational directions and in 1x48 cables during negative rotation. 

 When the 1x48 double-armored cable is subjected to low tension and high 

 torsion in positive rotation, the outer layer contracts whereas the inner 

 layer expands resulting in high contact stresses between the layers. 

 Further, torsional loading increases these stresses and eventually the 

 wires in the inner layer buckle and push through a weak opening in the 

 outer layer (Figure 17). Such buckling of the inner wires causes considerable 

 reduction in torsion. Further increases in torsion produce additional 

 failures, usually distributed at equal intervals, until finally a kink is 

 formed at one of the failure points. Thus, the positively rotating 

 1x48 cable does not behave like the 3x19 cable or the negatively rotating 

 1x48 cable. 



The results of the twist experiment are presented in nondimensional 

 form. The tension is divided by the Euler compression force, which has 

 no physical meaning here. The torque is divided by the Greenhill torque, 

 which is the torque required to buckle a cylinder by twisting alone. 

 With the assumption that the cable behaves like a solid rod, the value of 

 EI may be derived from the torque-versus-rotation curves obtained during 

 the twist tests, assuming that I = I p /2 where I p is the polar moment of 

 inertia of the cable cross section. The criteria for kinking of the 1x48 

 and 3x19 cables are summarized in Figure 18. Most data points follow the 

 theoretical buckling criterion (Equation 18a) except those for the positive 

 twist of the 1x48 cable. This is expected since the kinking mechanism for 

 the 1x48 cable in the positive direction is different from the rest of 

 the cable-twisting tests as discussed previously. Therefore, for cables 

 that do not fail prematurely due to the construction of the cable or other 

 factors, the following empirical formula describes the average kinking 

 criterion: 



3T 



c (19) 



F = 



c 8EI 



Note that if I = I p /3 instead of I = I p /2 for a cable cross section, the 

 empirical formula would match Timoshenko's buckling criterion exactly. 



12 



