;-— 4 - — n 



i v v 1 

 . — y i i-p(t) 



- ds '< — £ + d£ ->j 



Figure 1 - Deformation of Cable Element 



It is seen that the point s moves to s + % and the point 3 + ds 

 moves to (s + 6.3) + {i + d£) as a result of applying some force 

 F(t) to one end of the cable. Then at some time t, the lengtn 

 ds becomes ds + (d^/ds) ds. If ;!oo':e ' s law 2 is assumed for the 

 relationship between the applied force and the resulting strain, 

 the elongation, o?,/os, oroduces a tensile stress at section s 

 which Is given by E d^/ds. 



Consider a cable element of length ds as shown by the sketch 

 in Figure 2. 



AE •- 

 ds 



HH « [£ + B <•■] 



Figure 2 - Forces Acting on Cable Element 

 Summing forces on the element and applying Newton's Law yield: 



S ? 4 d 2 £ s 

 AE -— f ds = p. — -vu< 

 ds 2 dt a 



[1] 



and dividing Equation [1] by ds gives 



AE 



ay 



(2] 



