Loads and Forces on Steel Railway Bridges - Design of Modern Steel Railway Bridges - page 139

C n

Natural period, T n (seconds)

FIGURE 4.25 Typical actual response spectrum.

C n

T r T 0 T s

Natural period, T n (seconds)

FIGURE 4.26 Typical design response spectrum.

coefficient. This is essentially a pseudo-acceleration ∗ response spectrum normalized
by the natural period of vibration, T n . The actual pseudo-acceleration response spec-
trum for a given earthquake and the design pseudo-acceleration response spectrum
will typically look like the plots of Figures 4.25 and 4.26, respectively.
AREMA (2008) recommends the following with respect to the normalized design
response spectra: T r is the maximum natural vibration period for essentially rigid
response, T 0 = ( 0.48 S) 3 / 2 .

However, dynamic analyses of railway bridges typically underestimate the actual
natural vibration period and, therefore, the response of the bridge for low period
structures.AREMA (2008) recommends a design response spectrum without reduced
response (or C n ) below T 0 ( Figure 4.27 ) unless the effects of foundation flexibility,
foundation rotational movement, and lateral span flexibility were included in the
dynamic analysis. In some cases, the development of the response spectra from the
seismic response coefficient is inappropriate and consideration of loading based on
site-specific response spectra is required. †
The response spectrum must be calculated in each orthogonal and uncorrelated
direction (longitudinal and transverse) and, therefore, must be combined for design
purposes.AREMA (2008) recommends either the square root sum of squares (SSRC)

0.096 S , and T s =

∗ For steel bridge superstructures with low damping and short vibration periods the pseudo-acceleration
response is a close approximation the actual acceleration response.
† For example, where A ≥ 0.2 and T n ≥ 0.7 for bridges on very soft clays and silts, and for bridges on
soft clays and silts where vibration modes greater than the fundamental mode have periods of less than
0.3s and bridges near faults or in areas of high seismicity. In these cases, alternative equations, available
in seismic design standards and guidelines, for C n may apply.