Hybrid Simulation of Structural Collapse Andreas Schellenberg, Tony Yang and Bozidar Stojadinovic...
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Transcript of Hybrid Simulation of Structural Collapse Andreas Schellenberg, Tony Yang and Bozidar Stojadinovic...
Hybrid Simulationof Structural Collapse
Andreas Schellenberg, Tony Yang and Bozidar StojadinovicUniversity of California, Berkeley
Ken ElwoodUniversity 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 modelA hybrid model is an assemblage of one or more physical and one or more numerical, consistently scaled, partitions of a structureThe 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
( ) ( ) ( ( ), ) ( )t t t geom t rM u C u P u P
4
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
5
Second-Order Effects
Definition: effect of loads on the deformed geometry
P-: change of global geometryP-: change of member geometryP-MM interaction (section level) also local buckling
6
Simulation to Structural Collapse
Second order effects are essential for simulating collapse of structures that displace substantiallyTypically civil structures are tested using shaking tablesHowever, 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 analyticallyTherefore, no complex active or passive gravity load setups are necessary Actuator movements will limit displacementsThus, there is no need to protect expensive test equipment from specimen impactOnly critical, collapse-sensitive elements of a structure need to be physically modeled
8
Corotational Formulation (2D)
2
1
2
4 5
2
1
f
u uL u
v L L
u L
6
56
1
3
2
4
arctan
u
uu
u
v
L
u
u
3
53
1
2
2
4
arctan
u
uu
u
v
L
u
u
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 modelPhysical 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
i
j
x
y
d1, q1d2, q2
d3, q3
controlled displacementsand acquired forces
Geometric Transformations
i
j
x
y
U4, P4
U5, P5
U6, P6
U1, P1
U2, P2
U3, P3 i
j
x
y
v1, q1
v2, q2
v3, q3
Global System
Experimental BeamColumn
Basic System A(simply supported beam)
Basic System B(cantilever beam)
geometric transformation in OpenSees (Linear, PDelta, Corotational)
1 0 0
0 0
0 1 1
T L
12
OpenFresco ComponentsFE-Software
Experimental Site
Experimental Setup
Experimental Control
Control Systemin Laboratory
interfaces to theFE-Software, stores data and facilitates distributed testing transforms between the
experimental element degrees of freedom and the actuator degrees of freedom (linear vs. non-linear transformations)
interfaces to the different control and data
acquisitionsystems in the laboratories
OpenFresco
localdeployment
13
OpenFresco Componentsnetwork
deployment
FE-Software
Exp.Setup
Exp.Control
Control Systemin Laboratory
NTCP Server
Control Pluginwith
transformation
Control Systemin Laboratory
TCP/IP
NTCP Server
Control Systemin Laboratory
ActorExpSite
Exp.Control
Control Systemin Laboratory
ActorExpSite
ShadowExpSite NTCPExpSite
Control Pluginwithout
tranformation
TCP/IP
NTCP
NTCP
OpenFresco
OpenFresco OpenFresco
Exp.Setup
ShadowExpSite
Exp.Setup
NTCPExpSite
14
OpenSees Navigator User Interface
15
OpenSees Navigator User Interface
gravity loads modeled analytically
16
OpenSees Navigator User Interface
Defining experimental components (OpenFresco)
17
S4x7
.7
P P
4
2 1
3
54”
108”
Experimental BeamColumn S4
x7.7
W6x12
Example: Portal Frame TestProperties of Model:• num. DOF = 8 (2 with mass)• Period: T1 = 0.291 sec• Damping: = 0.02• P = 50% of Pn• Crd-Trans: P-Delta, Corotational• ExpElements: EEBeamColumn2d• ExpSetups: ESOneActuator• ExpControl: ECxPCtarget• SACNF01: pga = 0.755g
0 2 4 6 8 10 12 14 16 18 20-300
-200
-100
0
100
200
300
Time [sec]
Gro
und
Acc
eler
atio
n [in
/sec
2]
Ground-Acceleration-Time-History (SACNF01 (1978 Tabas))
18
Response Animation w/o Gravity Load
19
Response Animation with Gravity Load
20
Response Comparison: Global Level
0 2 4 6 8 10 12 14 16 18 20-2
0
2
4
6
8
10
12
14
16SACNF01
Sto
ry D
rift
Rat
io [
%]
Time [sec]
Test 1 w/o Gravity Load
Test 2 with Gravity Load
-2 0 2 4 6 8 10 12 14 16-3
-2
-1
0
1
2
3
4SACNF01
Story Drift Ratio [%]
Bas
e S
hear
[ki
ps]
Test 1 w/o Gravity Load
Test 2 with Gravity Load
21
Response Comparison: Element Level
-1 0 1 2 3 4 5 6 7 8 9-1.5
-1
-0.5
0
0.5
1
1.5SACNF01: Element 1
Deformation in Basic-System [in]
She
ar in
Bas
ic-S
yste
m [
kips
]
Test 1 w/o Gravity Load
Test 2 with Gravity Load
-1 0 1 2 3 4 5 6 7 8 9-1.5
-1
-0.5
0
0.5
1
1.5SACNF01: Element 2
Deformation in Basic-System [in]S
hear
in B
asic
-Sys
tem
[ki
ps]
Test 1 w/o Gravity Load
Test 2 with Gravity Load
22
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
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 simulationsConduct simulations where the axial load will be physically applied on the specimen
25
Download OpenSees Navigator
http://peer.berkeley.edu/OpenSeesNavigator
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