Page 339 - Civil Engineering Formulas

270 CHAPTER TEN

Length of parabolic arc LC is
a w o a 2 H w o a
L LC 1 sinh (10.79)
2 B H 2w o H
1 2
w o
3
a a (10.80)
6 H
Supports at Same Level

In this case, f f f, h 0, and a b l/2. The horizontal component of
R
L
cable tension H may be computed from
w o l 2
H (10.81)
8f
The vertical components of the reactions at the supports are
w o l
V L V R (10.82)
2
Maximum tension occurs at the supports and equals
w o l l 2
T L T R 1 (10.83)
2 B 16 f 2
Length of cable between supports is

1 w o l 2 H w o l
L 1 sinh (10.84)
2 B 2H w o 2H
8 f 2 32 f 4 256 f 6
l 1 (10.85)
3 l 2 5 l 4 7 l 6
If additional uniformly distributed load is applied to a parabolic cable, the
change in sag is approximately
15 l L
f (10.86)
2 2
16 f 5 24 f /l
For a rise in temperature t, the change in sag is about

2
15 l ct 8 f 2
f 2 2 1 2 (10.87)
16 f (5 24 f /l ) 3 l
where c coefficient of thermal expansion.