Civil Engineering Reference
In-Depth Information
Fixed bearing force at the abutment
:
Substitution into Equation 4.47 yields
t
α
0
Δ
C
1
)
T
X
F
=
N
3
(
0
)
−
N
2
(
0
)
=−
EA
αΔ
t
(C
2
−
=−
131,250
(C
2
−
C
1
)
,
2
αΔ
e
−λ
L
C
1
=
=
0.52,
C
2
=
λ
d
L
C
1
e
−λ
L
+
=
0.61
=
0.61,
X
F
=
131,250
(
0.61
−
0.52
)
=
11,585 lb for both bearings.
4.4.3.4
Design for the CWR on Steel Railway Bridges
Based on similar considerations,AREMA (2008) and many railway companies estab-
lish standard practice for anchoring CWR to long open deck steel spans. In general,
the recommended practice is to use longitudinal rail anchors on approaches, and near
fixed ends of spans, allowing some movement near expansion ends of spans.
∗
4.4.4 S
EISMIC
F
ORCES ON
S
TEEL
R
AILWAY
B
RIDGES
The level of seismic dynamic analysis required depends on the location and
characteristics of the bridge.
An equivalent static analysis is often used in the analysis of ordinary steel rail-
way bridges where the response to seismic forces is depicted primarily by the first or
fundamental vibration mode. Steel railway bridges that may be analyzed by an equiv-
alent static analysis are typically simply supported, not (or only slightly) skewed
or curved, and have spans of almost equal length and supporting substructures of
almost equal stiffness. Seismic forces in an equivalent static analysis are developed
based on a period-dependent coefficient and the weight of the bridge.AREMA (2008)
recommends the use of a seismic response coefficient and the uniform load method.
†
The seismic forces on complex steel railway bridges are generally determined for
use in a dynamic structural analysis.
‡
These loads are typically represented by an
elastic design seismic response spectrum. AREMA (2008) recommends the use of a
normalized response spectrum based on the seismic response coefficient.
4.4.4.1
Equivalent Static Lateral Force
The equivalent static distributed lateral force,
p(x)
, applied to the steel superstructures
of a railway bridge is
p(x)
=
C
n
w(x)
(4.49)
(
1.2
ASD/T
2
/
3
where
C
n
=
≤
2.5
AD
is the seismic response coefficient for the
n
th
mode of vibration and 5% damping ratio;
w(x)
is the distributed weight of the
)
n
∗
Rail expansion joints are sometimes used on very long bridges or bridges with unusual bearing
configuration (i.e., adjacent expansion bearings on long spans).
†
For some bridges it may be appropriate to consider the multimode dynamic analysis method.
‡
AREMA Chapter 9 indicates that a modal analysis is appropriate for such railway bridges.
