Geology Reference
In-Depth Information
RESEARCH BACKGROUND
Foundations for Dynamic Behavior
in Bridges
Description and FEM
Model of RSB Bridge
The dynamic force equilibrium equation for
bridges can be written as:
The RSB is a single-span hinged and simply sup-
ported steel box girder bridge with a main span
of 1490 m, shown in Figure 1. It is the longest
suspension bridge in China and ranks the third
in the globe. In addition, the central buckle is for
the first time used in suspension bridges in China.
The control of seismic responses involved in this
striking bridge under earthquakes is undoubtedly
crucial.
A 3-dimensional model for the bridge is es-
tablished on finite element program ANSYS, with
reference to design drawings of the RSB, to study
the structural seismic response. In the FE model,
the beam element with six degrees of freedom for
each node is employed to simulate the girder, the
central buckle and the towers. The massless rigid
element placed perpendicular to the spine which
is intended for modelling the main girder is to
simulate the connections between the suspenders
and the girder. The 3-dimensional linear elastic
truss element is to simulate main cables and the
suspenders whose nonlinear stiffness character-
istic due to gravity effect is approximately simu-
lated by linearizing the cable stiffness by the Ernst
equation of equivalent modulus of elasticity (Ernst,
1965). In addition, the pavement and the railings
on the steel box girder were simulated by mass
elements without stiffness.
The main girder and the relevant tower cross-
beams are coupled in three DOFs including vertical
displacement, lateral displacement and rotation in
longitudinal direction. The central buckle, applied
in China for the first time, is precisely simulated,
and the main girder and cables at the central buckle
are also coupled with references to the practical
design. The main cables are fixed at both the top
of towers and anchorages and towers are fixed at
their foundations (Wang, Li, & Mao, 2005). The
spatial FE model of RSB is shown in Figure 2.
J
∑
1
Mu t
( )
+
Cu t
( )
+
Ku t
( )
=
F t
( )
=
f g t
j
( )
j
j
=
(5)
All possible types of time-dependent loading,
including wind, wave and seismic, can be repre-
sented by a sum of “J” space vectors
f
j
, which
are nit a function of time and J time functions
g t
( )
, where J cannot be greater than the number
of displacements N. To combat the above equa-
tion, the following three methods are generally
employed.
j
1.
Static or Quasistatic Analysis Tools:
In
many cases of seismic analysis it is most
convenient to apply the seismic actions in
the form of an equivalent static force to
the bridge model, particular when seismic
distributions or likely deformation modes
can be estimated. The equivalent earthquake
force is:
F Wa
s
=
(6)
s
where
W
s
is the total seismic weight,
a
s
is
the absolute acceleration coefficient. The
equivalent force is lumped at the centroid
of seismic mass, or distributed proportional
to the expected fundamental mode force.
2.
Response Spectrum Analysis:
Analysis
models used for modal spectral analysis
are linear elastic models based on effec-
tive stiffness prosperities and on assumed
equivalent viscous damping ratios. Many
modal analysis programs provide an effec-
tive mass or mass participation factor for
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