Civil Engineering Reference
In-Depth Information
1.4
Interpretation of the Experiments and a Preliminary FE Model
The objective of the interpretation of dynamic tests was to determine a FE model of the bridge able to accurately predict its
dynamic behavior within the frequency range of interest for seismic analysis. A 2D-version of this FE model is used in [
13
]
to carry out a seismic analysis of the bridge.
A 3D Preliminary FE model was constructed based on the geometric details of the structure, see Fig.
1.6
. The simulations
are performed within the SAP2000 package. The FE model is created using solid FEs to model the deck and the pier. Typical
FE dimension for deck structure is of order 0.25 and 0.50 m in the transverse and longitudinal direction of the bridge,
respectively. The FE mesh has been refined to model the change in geometry of the deck near the central pier and near the
lateral footway.
The inertial/stiffening effects of the footways were neglected in this model. The abutments are considered as non-
deformable (rigid foundations), whereas the pier is assumed to be rigidly connected to the foundation, ignoring soil-structure
interaction effects to the dynamics of the bridge system.
Concerning the effect of prestressing, many studies agree that it tends to decrease the natural frequencies. Other
researches report that prestressing has no or negligible effect on the natural frequencies, see [
14
] for a recent account on
this issue. Here, the prestress force effect has been neglected in the eigenvalue analysis.
Base on material tests carried out during construction, the Young modulus of the concrete Ec was assumed equal to
43.20 GPa, both for deck and pier. The mass density of concrete was 2,500 kg/m
3
.
Bearing devices were modeled by 3D solid FEs, see Fig.
1.6
. In order to ensure a perfect correspondence between nodes
of the bearing devices and deck FE mesh, each isolator has been described by a parallelepiped with base dimension
1.20
4 FEs in plan and 6 FEs in thickness has been introduced. Bearing devices are assumed to
be made by an “equivalent” linearly elastic orthotropic material, with Young moduli E
x
,E
y
, shear moduli G
x
,G
y
, and
Poisson coefficient
1.00 m, and a mesh of 6
ν ¼ ν
x
¼ ν
y
, where X and Y are the transverse and longitudinal directions of the bridge deck. The
identification of effective elastic characteristics of the isolators represents a crucial point of identification. It is well known,
in fact, that nominal value of the (global) stiffness supplied by the manufacturer generally is significantly less than the
effective shearing stiffness under testing or ordinary traffic conditions. The reason for this large difference lies in the fact that
the strain experienced by the bearing during testing was much lower than the one associated with the mechanical
characterization under static or quasi-static load conditions in the laboratory, see, for example, [
9
].
A first mechanical characterization of the bearing devices, leading to the Preliminary FE Model of the bridge, has been carried
out assuming rigid-body motion of the deck. Therefore, isolator stiffness K
x
,K
y
associated to transverse (X-direction) and
longitudinal (Y-direction) shear displacements, have been determined by imposing a perfect matching between analytical
and experimental natural frequency values associated to RB Transverse and RB Longitudinal modes. Considering a total mass
of the deck equal to M
137.8MN/m.Basedonthese
values, the Young and shear moduli of the material forming each isolator have been determined and insert into the FE model.
Note that the nominal value of the shearing stiffness of the isolator is K
nom
¼
1,612 t, the stiffness turn out to be equal to K
x
¼
98.8 MN/m, K
y
¼
¼
71.25 MN/m. The axial stiffness of the bearing was
taken coincident with the nominal value K
z
¼
7631 MN/m.
Table
1.2
lists the values of the natural frequencies predicted by the Preliminary FE model of the bridge. A direct
comparison between vibration modes obtained experimentally and analytically revealed that all the measured mode shapes
have their counterparts in the Preliminary FE model, with the exception of EMA Modes 10 and 12. As it can be seen in
Table
1.2
, the order of the sequence is partially changed since EMA Modes 6,7,8,11 have correspondence to the set of
analytical Modes 7,8,10,16, respectively. The lack of correspondence to FEA Mode 6, which is the first horizontal “elastic”
Fig. 1.6
Preliminary FE model: (
a
) FE mesh of deck; (
b
) modeling of transversal cross section; (
c
) detail of the isolator
