CIVIL ENGINEERING FORMULAS

266 CHAPTER TEN

horizontal, the cable assumes the form of a parabolic arc. Then, the ten-
sion at midspan is

(10.57)

whereHmidspan tension, kip (N)
wload on a unit horizontal distance, klf (kN/m)
Lspan, ft (m)
dsag, ft (m)

The tension at the supports of the cable is given by

(10.58)

whereTtension at supports, kip (N); and other symbols are as before.
Length of the cable, S, when d/Lis 1/20, or less, can be approximated from

(10.59)

whereScable 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

SL

8 d^2

3 L

TH^2 

wL

2 

2



0.5

H

wL^2

8 d

A

A

(b)

C

H

(a)

Unit load = w

B

C

L

d

T

FIGURE 10.2 Cable supporting load uniformly distributed along

the horizontal.