Civil Engineering Reference
In-Depth Information
superstructure,
A
is the base acceleration ratio determined from appropriate geo-
logical sources
∗
for the design return period,
†
S
is the site coefficient between 1.0
and 2.0 depending on foundation soil conditions,
‡
D
is the
damping adjustment factor to account for the actual superstructure percentage of crit-
ical damping,
=[
1.5
/(
0.4
ξ +
1
)
+
0.5
]
,
§
T
n
is the natural period of the
n
th mode of vibration and is equal to
ξ
2
and
4.3
and
Figure 4.8)
.
However, in some cases, the development of the equivalent static distributed lateral
force based on the seismic response coefficient is inappropriate and consideration of
loading based on site-specific information is required.
∗∗
The equivalent static lateral distributed force,
p(x)
, is calculated in two orthogonal
directions(longitudinalandtransverseforordinarybridges).Followingalinearelastic
analysis
††
in each direction, forces are distributed to superstructure members based on
load path, support conditions, and stiffness. Since these member loads are orthogonal
and uncorrelated, they must be combined
‡‡
for design purposes. AREMA (2008)
recommends the method often referred to as the 100%-30% rule (Equations 4.50a
and b) to combine the seismic loads for member design.
π
/
ω
n
, and
EQ
=
1.00
F
T
+
0.30
F
L
,
(4.50a)
EQ
=
0.30
F
T
+
1.00
F
L
,
(4.50b)
where EQ is the combined seismic design force,
F
T
is the absolute value of the seismic
force in the transverse direction, and
F
L
is the absolute value of the seismic force in
the longitudinal direction.
4.4.4.2
Response Spectrum Analysis of Steel Railway Superstructures
The response spectrum used to represent the seismic loading of more complex steel
superstructures is a plot of the peak value of the response as a function of the natural
period of vibration of the superstructure. These are typically plotted for a particular
dampingratio
§§
andresponse(deformation,velocity,oracceleration).AREMA(2008)
recommends the use of a normalized spectral response based on the seismic response
∗
For example, the U.S. Department of the Interior Geological Survey maps.
†
The design return period depends on the earthquake event frequency and the limit state under
consideration (serviceability, ultimate, or survivability).
‡
Rock, soil type, stratigraphy, depth, soil stiffness, and shear wave velocity are considered in the site
coefficient.
§
Established from tests or other sources in the literature of structural dynamics. The percentage of
critical damping for steel superstructures is often less than 5% and depends on materials, structural
system/foundation, deck type and whether the structural response is linear elastic or post yield.
∗∗
For example, some bridges on soft-clays and silts where vibration modes greater than the fundamental
mode have periods of less than 0.3 s 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.
††
Linear elastic analysis is used for the equivalent lateral force method at the serviceability limit state.
‡‡
These combined forces account for the directional uncertainty and simultaneous occurrence of the
seismic design forces in members.
§§
Often established for a damping ratio (percentage of critical damping) of 5%.
