Dynamic/earthquake analysis - Computational Analysis and Design of Bridge Structures - page 512

y ( t )

k

f ( t )

m

c

Figure 17.1 Dynamic forcing system.

In comparison with the static equation 3.3, forces due to acceleration and
damping are introduced in dynamic analysis.
The damping ratio, or damping coefficient, ξ, is defined as c / c r = c /2

where steel bridges normally have a low damping coefficient ξ ≤ 0.02. Most
commonly used experimental method to determine the damping in a struc-
ture is the half-power (bandwidth) method by two frequencies shown in
Figure 17.2 and can be calculated by Equation 17.2 as

km

f −

+

f

ξ =

2 1

(17.2)

f f

2 1

where two frequency points f 1 and f 2 (in cycle/sec) are on either side of the
curve in Figure 17.2.

R d

R 2 R 2

f 1 f 2

Figure 17.2 Half-power method to estimate damping by experiment.