Page 336 - Civil Engineering Formulas

BRIDGE AND SUSPENSION-CABLE FORMULAS 267

T
d c (10.60)
w
Then
2
2 0.5
S
c (d c) 2 (10.61)
Sag d c ft (m) (10.62)

Span length then is L 2c, with the previous same symbols.

GENERAL RELATIONS FOR SUSPENSION CABLES

Catenary
For any simple cable (Fig. 10.3) with a load of q per unit length of cable, kip/ft
o
(N/m), the catenary length s, ft (m), measured from the low point of the cable
is, with symbols as given in Fig. 10.3, ft (m),
H q o x 1 q o 2
s sinh x x (10.63)
3
q o H 3! H
Tension at any point is

2
2 2
T 2 H q o s H q o y (10.64)

y
L
a b
L L
2 2 V R T R

T L h/ 2 RH
h V L
Cable H L s f R
L y
M y M
P x
C x
(a) (b)
FIGURE 10.3 Simple cables: (a) shape of cable with concentrated load; (b) shape of
cable with supports at different levels.