Civil Engineering Reference
In-Depth Information
Table 12.1
Identified modal
frequencies versus updated FEM
frequencies
Modal frequency (Hz)
Identified
Mode
Description
FEM
1
Vertical - girders
1.77
1.76
2
Vertical - girders
3.10
3.13
3
Vertical - girders
3.90
4.06
4
Vertical - stringers
13.68
13.69
5
Vertical - stringers
15.03
16.38
6
Vertical - stringers
18.44
17.74
Fig. 12.6
Overview of three
dimensional sub-structured
finite element model with
overall dimensions. The
model is composed of frame
elements representing girders,
floor beams, stringers, rigid
and flexible links as well as
shell elements to model the
reinforced concrete slab
width of the concrete road deck and additional line mass to approximate the additional dead weight associated with
non-structural elements. Adding the concrete deck to the girder cross-section introduced composite action in the analysis.
The second model is a sub-structured finite element model of the structure that was generated using 1,141 frame elements
and 10,341 shell elements. The model represents approximately 20 % of the length of bridge and contains the instrumented
portion of the bridge. Figure
12.6
displays an overview of the detailed FEM. This model focuses primarily on the local
vibration modes mostly engaging the stringers. Coupled stiffness matrices were placed at the free end of the model at the
centroid of the exterior girder to include the stiffness of the remaining 80 % of the bridge (not being modeled explicitly).
Horizontal springs were placed at the roller supports to model the elastic effect of the expansion joint at the abutment.
Massless link elements connected the concrete deck shell elements to the frame elements of the model. Since the composite
global girder model correlated well with the identified global modal frequencies the rigid links connecting the deck to the
girders were taken as rigid. The link elements connecting the deck elements to the stringer frame elements were updated to
better correlate with the identified local modal frequencies. The compressive strength of the concrete deck was kept constant
at 4 ksi. Table
12.1
depicts the comparison between identified modal frequencies from the data and finite element models.
The free parameters in the FEM to be updated were: (1) support springs (2) stiffness of link elements between stringers and
slab (3) stiffness of link elements between girders and slab.
12.7 Conclusions
Based on the measured acceleration and strain data we can preliminarily conclude that even though the structural drawings
do not specify any explicit member for shear transfer at the interface of girder and the concrete slab, vibration data suggests
that the bridge main girders are acting completely composite with the concrete slab. One possible mechanistic explanation
for this phenomenon might be the fact that bridge built-up girders possess rivets that protuberate on the top flange, thus
creating a rugged interface which allows for significant shear transfer. In the case of the steel stringers, we have found that
even though these do not possess any shear transfer members they are acting partially composite (at around 70%). These
estimates allow engineers to estimate the member capacity under normal traffic loads and to compute upper bounds on the
member ultimate bending capacity. Table
12.2
presents preliminary relative LDF values for the three stringers under two
recorded load tests and three FEMs results considering various loading positions in the transverse direction. We have also
found as other researchers in the past have, that AASHTO load distribution factors for the stringers are overly conservative,
in our case by a factor of approximately 40%.
