CIVIL ENGINEERING FORMULAS

268 CHAPTER TEN

The distance from the low point Cto the left support is

(10.65)

wherefLvertical distance from CtoL, ft (m). The distance from Cto the right
supportRis

(10.66)

wherefRvertical distance from CtoR.
Given the sags of a catenary fLandfRunder a distributed vertical load qo, the
horizontal component of cable tension Hmay be computed from

(10.67)

wherelspan, or horizontal distance between supports LandRab. This
equation usually is solved by trial. A first estimate of Hfor substitution in the
right-hand side of the equation may be obtained by approximating the catenary by
a parabola. Vertical components of the reactions at the supports can be com-
puted from

(10.68)

Parabola

Uniform vertical live loads and uniform vertical dead loads other than cable
weight generally may be treated as distributed uniformly over the horizontal
projection of the cable. Under such loadings, a cable takes the shape of a
parabola.
Take the origin of coordinates at the low point C(Fig. 10.3). If wois the
load per foot (per meter) horizontally, the parabolic equation for the cable
slope is

(10.69)

The distance from the low point Cto the left support Lis

a (10.70)

l

2



Hh

wol

y

wox^2

2 H

RLH sinh

qoa

H

RRH sinh

qob

H

qol

H

cosh^1 

qofL

H

 (^1) cosh^1 
qofR
H
 (^1) 
b

H

qo

cosh^1 

qo

H

fR (^1) 
a

H

qo

cosh^1 

qo

H

fL (^1)