The cable segment BC forms a portion of a catenary whose loading 

 conditions are calculated for point B. In order to use standard catenary 

 analysis, the segment can be extended to include an imaginary portion of 

 cable which would form a single continuous catenary with the same resultant 

 loads at point B. This concept is illustrated in figure 12. 



The segment A'B is the imaginary portion with arclength s', horizontal 

 length x' and horizontal tension H'. The vertical displacement for the 

 catenary coordinate system is c'. Figure 13 depicts a free-body diagram 

 of this segment. The parameters in this figure are calculated as follows. 

 The value of y' is: 



y- = 11 (9) 



The horizontal tension H' is: 



H' - T'cos (10) 



(11) 



The coordinate displacement c' is: 

 H' 



^ce is then: 



The height d' is given by: 



d' - y' - c' (12) 



The horizontal distance is thenj 



x' = c' Ir 

 The arclength s' is: 



s' = Vy'^ - c'^ (14) 



The weight of the imaginary segment is: 



W = s'w (15) 



For the entire catenary A^ in figure 12 , we have: 



D' = D + d' - d (16) 



and 



Y' = D' + c' (17) 



The horizontal distance is: 



# 



ml^ ^\l(Vrf - 1) (18) 



