or yarn kinking. The buckling criterion for a circular rod according 

 to Timoshenko is: 



tt 2 EI 



= 1 



(17) 



where T = end torque 



c 



L = length of rod 



E = Young's modulus of elasticity 



I = Moment of inertia about diameter, I = I /2 



I = Moment of inertia about rod center 



P 



C = axial compression force. 



Since, for cable kinking, tension F (instead of compression C) is 

 applied, the equation becomes 



= 1 + 



TT 2 EI 



where F = -C 

 c 



Now, the axial force restrains the buckling action. In actual use, the 

 cable is long enough and the tension large enough that 



2 



F L 

 c 



u 2 EI 



» 1 



(see Figure 11), and the buckling criterion becomes 



2 

 T \ F 

 c 



2ttEI 



t\ EI 



(18) 



The term 2ttEI/L is the Greenhill torque T g , the torque at which a 

 rod will buckle under torque alone. The term (tt/L) 2 EI is the Euler 

 compression force F e , the axial force needed to buckle a rod. For cable 

 kinking, the Greenhill torque still provides a buckling criterion, but 

 the Euler compression has little meaning as the axial force is now in 

 tension. Since the terms (2tt/L)EI and (tt/L) 2 EI embody the torsional and 



10 



