Page 335 - Civil Engineering Formulas

266 CHAPTER TEN

L
A B
d
C

Unit load = w
T (a)

A
C
H
(b)
FIGURE 10.2 Cable supporting load uniformly distributed along
the horizontal.

horizontal, the cable assumes the form of a parabolic arc. Then, the ten-
sion at midspan is
wL 2
H (10.57)
8d
where H midspan tension, kip (N)
w load on a unit horizontal distance, klf (kN/m)
L span, ft (m)
d sag, ft (m)
The tension at the supports of the cable is given by
2 (10.58)
2 0.5
wL
T H 2
where T tension at supports, kip (N); and other symbols are as before.
Length of the cable, S, when d/L is 1/20, or less, can be approximated from
8d 2
S L (10.59)
3L
where S cable length, ft (m).

Catenary Cable Sag and Distance between Supports
A cable of uniform cross section carrying only its own weight assumes the
form of a catenary. By using the same previous notation, the catenary parame-
ter, c, is found from