CIVIL ENGINEERING FORMULAS

BRIDGE AND SUSPENSION-CABLE FORMULAS 271

Elastic elongation of a parabolic cable is approximately

(10.88)

whereAcross-sectional area of cable
Emodulus of elasticity of cable steel
Hhorizontal component of tension in cable

If the corresponding change in sag is small, so that the effect on His negligible,
this change may be computed from

(10.89)

For the general case of vertical dead load on a cable, the initial shape of the
cable is given by

(10.90)

whereMDdead-load bending moment that would be produced by load in a
simple beam; and HDhorizontal component of tension due to dead load.
For the general case of vertical live load on the cable, the final shape of the
cable is given by

(10.91)

where vertical deflection of cable due to live load
MLlive-load bending moment that would be produced by live load in
simple beam
HLincrement in horizontal component of tension due to live load

Subtraction yields

(10.92)

If the cable is assumed to take a parabolic shape, a close approximation to HL
may be obtained from

(10.95)

(10.94)

where d^2 /dx^2.



3 l

32 f

loge

4 f

l



B

1 

16 f^2

l^2 

Kl

1

4 

5

2



16 f^2

l^2 B

1 

16 f^2

l^2

HL

AE

K

wD

HD



1

0

dx

1

2



1

0

 dx



MLHLyD

HDHL

yD

MDML

HDHL

yD

MD

HD

f

15

16

Hl^2

AEf

1  16 f^2 /3l^2

5  24 f^2 /l^2

L

Hl

AE

1 

16

3

f^2

l^2