Civil Engineering Reference
In-Depth Information
Fundamental frequency of bridges
100
80
60
40
20
0 0
20
40
60
80
Length (ft)
100
120
140
160
Railway steel truss spans
Railway open deck girder spans
Railway ballasted girder spans
Highway bridges
FIGURE 4.8 Unloaded fundamental frequencies of various steel bridge types.
(Inglis, 1928) as
1
ω L1 = ω 1
x/L) .
(4.18)
( 2 P/mgL) sin 2 (
1
+
π
Example 4.4
Estimate the loaded natural frequency of the bridge in Example 4.3.
Unloaded natural frequency
= ω 1 =
66.58 rad/s
=
10.6 Hz.
Loaded natural frequency
= ω L1
66.58
1
=
+ 2 ( 400,000 )/( 103.6 )( 32.17 )( 45 )
1
=
26.45 rad / s
=
4.2Hz.
It is evident that many of the parameters affecting the dynamic behavior of a
steel railway bridge are complex and stochastic in nature. Deterministic solutions
are difficult, even with many simplifying assumptions. Modern dynamic finite ele-
ment analysis (FEA) methods and software enable incremental, mode superposition,
frequency domain, and response spectra analysis of structures. FEA is of particular
use in the dynamic analysis of long-span, continuous, and complex superstructures.
However, the dynamic effects of moving concentrated live loads on ordinary railway
Up to three modes of vibration should be considered for continuous and cantilever bridges (Veletsos and
Huang, 1970).
 
 
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