1. Hybrid Simulation of Structural Collapse
Andreas Schellenberg, Tony Yang and Bozidar Stojadinovic
University of California, Berkeley
Ken Elwood
University of British Columbia

2. Hybrid Simulation
Hybrid simulation is an experimentally based testing method for investigating the response of a structure to dynamic excitation using a hybrid model
A hybrid model is an assemblage of one or more physical and one or more numerical, consistently scaled, partitions of a structure
The equations of motion of a hybrid model under dynamic excitation are solved during a hybrid simulation test

3. Response Simulation with Second-Order Effects
Dynamic loading excites a structure:
Inertia
Energy dissipation (damping)
Resistance
Second order effects are included in the resistance of the structure
However, they may be simulated in the computer

4. Outline of Talk Second-Order Effects and Structural Collapse
Implementation in OpenSees and OpenFresco
Structural Collapse of Portal-Frame Example
Summary and Conclusions

5. Second-Order Effects
Definition: effect of loads on the deformed geometry
P-D: change of global geometry
P-d: change of member geometry
P-MM interaction (section level) also local buckling

6. Simulation to Structural Collapse
Second order effects are essential for simulating collapse of structures that displace substantially
Typically civil structures are tested using shaking tables
However, structural collapse is difficult and expensive to investigate using shaking table tests

7. Advantages of using Hybrid Simulation
Gravity loads and resulting geometric nonlinearities are modeled analytically
Therefore, no complex active or passive gravity load setups are necessary
Actuator movements will limit displacements
Thus, there is no need to protect expensive test equipment from specimen impact
Only critical, collapse-sensitive elements of a structure need to be physically modeled

8. Corotational Formulation (2D)

9. Implementation in a Hybrid Model
Provide the geometric transformations such that the effect of axial loads is accounted for in the computer part of the hybrid model
Physical part of the model:
Model material and cross-section level response
Computer part of the model:
Model the second-order effect of axial load
Provide the rest of the structure

10. Implementation at nees@berkeley
Using:
OpenSees to provide the nonlinear geometric transformation facilities
OpenFresco to provide the hybrid simulation framework
OpenSees Navigator to graphically build the model, run the test and post-process the hybrid simulation results

11. Geometric Transformations
Experimental BeamColumn
Global System
Basic System A
(simply supported beam)
Basic System B
(cantilever beam)
geometric transformation in OpenSees (Linear, PDelta, Corotational)

12. OpenFresco Components
local
deployment
FE-Software
OpenFresco
interfaces to the
FE-Software, stores data and facilitates distributed testing
Experimental Site
transforms between the experimental element degrees of freedom and the actuator degrees of freedom (linear vs. non-linear transformations)
Experimental Setup
interfaces to the different control and data acquisition
systems in the laboratories
Experimental Control
Control System
in Laboratory

13. OpenFresco Components
network
deployment
FE-Software
OpenFresco
ShadowExpSite
ShadowExpSite
NTCPExpSite
NTCPExpSite
Exp.Setup
Exp.Setup
TCP/IP
TCP/IP
NTCP
NTCP
OpenFresco
OpenFresco
ActorExpSite
ActorExpSite
NTCP Server
NTCP Server
Exp.Setup
Control Plugin
with
transformation
Control Plugin
without
tranformation
Exp.Control
Exp.Control
Control System
in Laboratory
Control System
in Laboratory
Control System
in Laboratory
Control System
in Laboratory

14. OpenSees Navigator User Interface

15. OpenSees Navigator User Interface
gravity loads modeled analytically

16. OpenSees Navigator User Interface
Defining experimental components (OpenFresco)

17. Example: Portal Frame Test
Properties of Model:
num. DOF = 8 (2 with mass)
Period: T1 = sec
Damping: z1 = 0.02
P = 50% of fPn
Crd-Trans: P-Delta, Corotational
ExpElements: EEBeamColumn2d
ExpSetups: ESOneActuator
ExpControl: ECxPCtarget
SACNF01: pga = 0.755g

18. Response Animation w/o Gravity Load

19. Response Animation with Gravity Load

20. Response Comparison: Global Level

21. Response Comparison: Element Level

22. Findings Benefits: Shortcomings:
Second-order effects can be simulated without applying the axial force on the physical specimen
The specimens and test setups are less expensive
The physical setups are protected from falling structural elements
Shortcomings:
Interaction of axial force and element resistance at the local level is not accounted for properly (local buckling, P-MM interaction)
Rate effects are not accounted for

23. Conclusions
Second-order effects can be effectively simulated using a hybrid model:
The effect of axial load can be modeled in the computer using appropriate geometric transformations
Collapse of structural systems due to second-order effects can, thus, be simulated
OpenSees and OpenFresco implementation has been successfully demonstrated

24. Future Work Conduct large-scale simulations
Conduct simulations where the axial load will be physically applied on the specimen

25. Download OpenSees Navigator

26. Thank you!
Development and operation of the equipment site is sponsored by NSF
Special thanks to Dr. Eiji Kohama for all the help with the portal frame tests