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Department of Civil and Environmental Engineering
University of California, Berkeley
Experience with OpenFresco: Reinforced Concrete Bridge
Vesna Terzic
Objective Can a damaged bridge carry a heavy truck after
an earthquake?
It is very difficult to physically model the
bridge with the (moving) truck on it
hybrid simulation is
the way to go
2
Components of a Hybrid Simulation
3
Schellenberg, 2008
Five span, single column bent overpass bridge
Prototype Bridge
4
Ketchum et. al., 2004
Hybrid Model of the Bridge
5
Analytical model (full scale)
Physical model (SF=4.6875)
Geometry of the Specimen
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Diameter
Longitudinal reinforcement
Transverse reinforcement
Concrete
16’’ (40 cm)
12#4 Gr60 ( l=1.2%)
[email protected] in ( t=0.75%)
fc=5 ksi (34.5 MPa)
Calibration of the Analytical Model Bridge columns – nonlinear elements
Damage is concentrated at plastic hinges
To calibrate analytical model (used in HS)
bi-lateral quasi-static test was performed
Identical specimens
7
Quasi-Static Test
8
Experimental Setup
Load Pattern
Material Calibration
Lateral Hystereses
X direction Y direction
Analytical Portion of the Hybrid Model
Modeled in OpenSees (3D model)
Deck: linear elastic elements
Columns: force based nonlinear beam-
column elements (calibrated based on quasi-static test)
Abutments: rollers in both directions
Integration scheme: Alpha-OS ( =0.9)
9
Physical Portion of the Hybrid Model
Scaled model (SF=4.6875)
OpenFresco was used for hybrid simulation
10
Experimental beam-
column element
Loads Applied on the Bridge Gravity load
Earthquake load in X and Y direction
11
Truck load
What are we going to control?
12
There are 6 DOFs that could be controlled at the
top node of the column:
ux , uy , uz , x , y , z
We are controlling 4 DOFs:
ux , uy , x , y
Assuming that rotation ( z ) and displacement (uz ) are small enough that they can be neglected.
ExpSetup: Lateral Displacements To control the 4 chosen DOFs we will use 4 actuators:
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Rigid Body
ExpSetup: Axial Load
14
Geometric Transformations: Displacements
15
d1 d2
d3 d4
x
y
Nonlinear Transformation in
ESFourActuators3d
ux
uy
x y
X direction Y direction
Geometric Transformations: Forces
16
Px Py Note: Axial force will
also create moments at CP
Deformed configuration
Initial configuration
f1 f2
f3 f4
Nonlinear Transformation in
ESFourActuators3d
qx
qy
mx my
f6 f5
x
y
OpenFresco Interaction with OpenSees
In FE model (OpenSees framework):
loadPackage OpenFresco
Define experimental control
Define experimental setup
Define experimental site
Define experimental element
17
OpenFresco Interaction with OpenSees
In FE model (OpenSees framework):
loadPackage OpenFresco
Define experimental control
Define experimental setup
Define experimental site
Define experimental element
18
OpenFresco Experimental Setup ESElementName.h
ESElementName.cpp
TclExpSetupCommand.cpp
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OpenFresco: ESFourActuators3D.h
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OpenFresco: ESFourActuators3D.h
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OpenFresco: ESFourActuators3D.cpp
OpenFresco: ESFourActuators3D.cpp
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OpenFresco: ESFourActuators3D.cpp
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OpenFresco: ESFourActuators3D.cpp
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OpenFresco: ESFourActuators3D.cpp
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OpenFresco: ESFourActuators3D.cpp
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OpenFresco: ESFourActuators3D.cpp
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OpenFresco: ESFourActuators3D.cpp
Definition of ExpSetup in TCL Script
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Units in analytical model: kN, m Units in experimental setup: kips, in
Scaling factors: Sd=4.6875 Sf=1/Sd
2
Sm=1/Sd3
Results: Displacements
31
Results: Forces
32
Four truck positions on a bridge
Department of Civil and Environmental Engineering
University of California, Berkeley
Questions? Thank you!
http://openfresco.neesforge.nees.org
The development of OpenFresco has been sponsored in parts by the
National Science Foundation through grants from the NEES Consortium, Inc.
