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

Hybrid Simulation
of Structural Collapse
Andreas Schellenberg, Tony Yang and Bozidar Stojadinovic
University of California, Berkeley
Ken Elwood
University of British Columbia
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
2
Response Simulation with
Second-Order Effects
Dynamic loading excites a structure:



Inertia
Energy dissipation (damping)
Resistance
M  u(t )  C  u(t )  Pr (u(t ), geom)  P(t )
Second order effects are included in the
resistance of the structure

However, they may be simulated in the
computer
3
Outline of Talk
1. Second-Order Effects and Structural
Collapse
2. Implementation in OpenSees and
OpenFresco
3. Structural Collapse of Portal-Frame
Example
4. Summary and Conclusions
4
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
5
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
6
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
7
Corotational Formulation (2D)
v1  L f  L

 L  u4  u1    u5  u2 
2
2
L
v2  u3  
 u5  u2 
 u3  arctan 

 L  u4  u1 
v3  u6  
 u u 
 u6  arctan  5 2 
 L  u4  u1 
8
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
9
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
10
Geometric Transformations
U5, P5
v1, q1
U4, P4
v3, q3
j
d3, q3
j
j
Experimental
BeamColumn
Dy
Dy
Dy
U6, P6
controlled displacements
and acquired forces
d2, q2
d1, q1
U2, P2
U1, P1
U3, P3
v2, q2
i
i
i
Dx
Dx
Dx
Global System
Basic System A
Basic System B
(simply supported beam)
(cantilever beam)
geometric transformation in
OpenSees (Linear, PDelta,
Corotational)
1 0 0 
T  0  L 0 
0 1 1 
11
OpenFresco Components
FE-Software
interfaces to the
FE-Software, stores
data and facilitates
distributed testing
Experimental Site
Experimental Setup
interfaces to the different
control and data acquisition
systems in the laboratories
local
deployment
OpenFresco
transforms between the
experimental element
degrees of freedom and the
actuator degrees of freedom
(linear vs. non-linear
transformations)
Experimental Control
Control System
in Laboratory
12
OpenFresco Components
network
deployment
FE-Software
OpenFresco
ShadowExpSite
ShadowExpSite
NTCPExpSite
Exp.Setup
TCP/IP
NTCPExpSite
Exp.Setup
TCP/IP
NTCP
NTCP
ActorExpSite
NTCP Server
NTCP Server
Exp.Control
Exp.Control
Control Plugin
with
transformation
Control Plugin
without
tranformation
Control System
in Laboratory
Control System
in Laboratory
Control System
in Laboratory
Control System
in Laboratory
OpenFresco
ActorExpSite
OpenFresco
Exp.Setup
13
OpenSees Navigator User Interface
14
OpenSees Navigator User Interface
gravity loads modeled
analytically
15
OpenSees Navigator User Interface
Defining experimental
components (OpenFresco)
16
Example: Portal Frame Test
Properties of Model:
W6x12
4
Experimental
BeamColumn
S4x7.7
S4x7.7
54”
3
P
1
2
108”
num. DOF = 8 (2 with mass)
Period: T1 = 0.291 sec
Damping: z1 = 0.02
P = 50% of fPn
Crd-Trans: P-Delta, Corotational
ExpElements: EEBeamColumn2d
ExpSetups: ESOneActuator
ExpControl: ECxPCtarget
SACNF01: pga = 0.755g
Ground-Acceleration-Time-History (SACNF01 (1978 Tabas))
300
200
Ground Acceleration [in/sec 2]
P
•
•
•
•
•
•
•
•
•
100
0
-100
-200
-300
0
2
4
6
8
10
Time [sec]
12
14
16
18
20
17
Response Animation w/o Gravity Load
18
Response Animation with Gravity Load
19
Response Comparison: Global Level
SACNF01
SACNF01
16
4
14
Test 1 w/o Gravity Load
Test 2 with Gravity Load
3
12
Base Shear [kips]
Story Drift Ratio [%]
2
10
8
6
4
1
0
-1
2
0
-2
-2
Test 1 w/o Gravity Load
Test 2 with Gravity Load
0
2
4
6
8
10
12
Time [sec]
14
16
18
20
-3
-2
0
2
4
6
8
10
Story Drift Ratio [%]
12
14
16
20
Response Comparison: Element Level
SACNF01: Element 2
1.5
1
1
Shear in Basic-System [kips]
Shear in Basic-System [kips]
SACNF01: Element 1
1.5
0.5
0
-0.5
-1
0.5
0
-0.5
-1
Test 1 w/o Gravity Load
Test 2 with Gravity Load
Test 1 w/o Gravity Load
Test 2 with Gravity Load
-1.5
-1
0
1
2
3
4
5
6
Deformation in Basic-System [in]
7
8
9
-1.5
-1
0
1
2
3
4
5
6
Deformation in Basic-System [in]
7
8
9
21
Findings
Benefits:



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
22
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
23
Future Work
Conduct large-scale simulations
Conduct simulations where the axial load
will be physically applied on the
specimen
24
Download OpenSees Navigator
http://peer.berkeley.edu/OpenSeesNavigator
25
Thank you!
Development and operation of the nees@berkeley
equipment site is sponsored by NSF
Special thanks to Dr. Eiji Kohama for all the help with
the portal frame tests