Page 338 - Civil Engineering Formulas

BRIDGE AND SUSPENSION-CABLE FORMULAS 269

where l span, or horizontal distance between supports L and R a b; h
vertical distance between supports.
The distance from the low point C to the right support R is
1 Hh
b (10.71)
2 w o l

Supports at Different Levels
The horizontal component of cable tension H may be computed from

w o l 2 h f L f R w o l 2
f
H 2 R (10.72)
h 2 8f
where f vertical distance from C to L
L
f vertical distance from C to R
R
f sag of cable measured vertically from chord LR midway between
supports (at x Hh/w l)
o
As indicated in Fig. 10.3(b),
h
f f L y M (10.73)
2
2
2
where y Hh /2w l . The minus sign should be used when low point C is
M o
between supports. If the vertex of the parabola is not between L and R, the plus
sign should be used.
The vertical components of the reactions at the supports can be computed
from
w o l Hh
V L w o a (10.74)
2 l
w o l Hh
V r w o b (10.75)
2 l
Tension at any point is
2
T 2 H w o x 2 (10.76)
2
Length of parabolic arc RC is
b w o b 2 H w o b
L RC 1 sinh (10.77)
2 B H 2w o H
1 w o 2
b b (10.78)
3
6 H