Page 340 - Civil Engineering Formulas

BRIDGE AND SUSPENSION-CABLE FORMULAS 271

Elastic elongation of a parabolic cable is approximately
Hl 16 f 2
L 1 2 (10.88)
AE 3 l
where A cross-sectional area of cable
E modulus of elasticity of cable steel
H horizontal component of tension in cable
If the corresponding change in sag is small, so that the effect on H is negligible,
this change may be computed from
2
15 Hl 2 1 16 f /3l 2
f (10.89)
2
16 AEf 5 24 f /l 2
For the general case of vertical dead load on a cable, the initial shape of the
cable is given by
M D
y D (10.90)
H D
where M dead-load bending moment that would be produced by load in a
D
simple beam; and H horizontal component of tension due to dead load.
D
For the general case of vertical live load on the cable, the final shape of the
cable is given by
M D M L
y D (10.91)
H D H L
where vertical deflection of cable due to live load
M live-load bending moment that would be produced by live load in
L
simple beam
H increment in horizontal component of tension due to live load
L
Subtraction yields
M L H L y D
(10.92)
H D H L
If the cable is assumed to take a parabolic shape, a close approximation to H L
may be obtained from
1 1
H L w D 1 (10.95)
K dx dx
AE H D 0 2 0
2
5 16 f 2 16 f 2
1
K l 4 2 l B 1 l 2 (10.94)
3l log e 4 f 16 f 2
1 2
32 f l B l
2
2
where d /dx .