Arch bridges - Computational Analysis and Design of Bridge Structures - page 287

Figure 9.16 Demonstration of dynamic testing instrument on a hanger cable.

When using the second-order natural frequency f 2 , cable tension T 0 is

EI
l

2 2

T = 0 8207 . ml f − 167 9 . (9.14)

0 2

2

Because the second-order vibration function is an approximated function,
the result of Equation 9.14 is also an approximation.
Eliminating bending stiffness in Equations 9.13 and 9.14, cable force
can be calculated from the first and second natural frequencies as given in
Equation 9.15, in which the effect of bending stiffness EI is considered but
not needed to measure directly.

T ml =

2

( . 4 3865 f

2

− 0 2742 . f

2

) (9.15)

0 1 2

Instead of measuring the bending stiffness of a cable, which is not practical in
testing on-site, the second order of natural frequency can be obtained at the
same time when the first-order frequency is analyzed from a frequency spec-
trum analyzer as shown in Figure 9.16. Therefore, Equation 9.15 has a great
advantage of when to include the bending stiffness effect on cable forces.

9.4 ModeLIng of Arch brIdges

As high-strength hangers and/or tied cables are part of the structure, an arch
bridge is usually considered as a cable structure with the same consideration as
a cable-stayed bridge. The principle and modeling of an arch bridge is similar
to a cable-stayed bridge in many aspects. For example, the analyses of an arch