Suspension bridges - Computational Analysis and Design of Bridge Structures - page 382

2

H
L d

H
L

1
2

1

2

L = L + + − d (12.12)

1

L

3

and Equation 12.6 becomes

2

H
L d

H
L

1
2

1

2

ε = + − d (12.13)

2

L

2 4

Follow the same procedure to derive Equation 12.10 from Equations
12.8 and 12.9; a polynomial equation with unknown variable of d can be
obtained:

3 2

a d + a d + a d a + = (12.14)

0 3 2 1 0

where:

2

2

EA
L L

H
L

1

a = − (12.15)

3

3

2

EA
L

H
L

3 1

a = H L − (12.16)

2

2 4

2

2

EA
L

H
L

+

H
L

2 1

a = − T (12.17)

1 0

L

3

and

H
L T

a = − P (12.18)

0 0

By resolving Equation 12.14, the displacement under external load P with
consideration of initial stress and large displacement can be obtained.
By comparing Equation 12.14 with Equation 12.10, which only illustrates
how an existing stress in cables influences their behavior, it is clear that it is
easier to consider only initial stress. If the initial stress is the predominant
issue, for certain purposes of analyses, only initial stress issue may be con-
sidered to save analysis time and cost. During the preliminary design, for
example, initial stress due to dead loads can be estimated first and further be
considered in live load analysis so as to quickly estimate extreme deflections.

12.3.2 Basics of suspension bridge analysis
Like suspension bridges, the analytical theories of them have a long history
of development. They can be classified as elastic theory starting from the