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Distributed Online Hybrid Test to Trace the Collapse of a Four-Story Steel Moment Frame
Tao Wang, IEM, ChinaAndres Jacobsen, Kyoto University, JapanMaria Cortes-Delgado, University at Buffalo, USAGilberto Mosqueda, University at Buffalo, USA
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223/04/20
1. Distributed hybrid test framework (P2P)
2. Flexible test scheme and implementation
OutlineOutline
3. Specimen design and measure scheme
4. Test results
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323/04/20
Substructure A
Substructure B
Substructure C
Substructure D
Concept of Hybrid Test SystemConcept of Hybrid Test System
==
==
== ==Force
Force
ForceForce
Coordinator
Partner
Partner
Partner
Partner
Displ.
Displ.
Displ.
Displ.
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423/04/20
dndndndnd2d2d2d2d1d1d1d1
Analysis Substru. Test Substru.Coordinator
R
R1
R2
R1
R2
…
…
…
R1
R2
System ImplementationSystem Implementation
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523/04/20
Two Challenges for System RealizationTwo Challenges for System Realization
(1) How to determine the boundary displacement? Satisfy equilibrium and compatibility at boundary Only use standard I/O, i.e., boundary force & displacement
(2) How to avoid iteration for physical loading? One physical loading in one time step Compatibility with trial and error procedure
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623/04/20
P
d
1nP
nP
nd 1nd
01nK
11nd
21nd
31nd
41nd
01n
11n
21n
31n
11nK
21nK
31nK
11 nd
21 nd
31 nd
41 nd
Procedures of Quasi-Newton Method:Procedures of Quasi-Newton Method:1. Equilibrium equation: 0}{}]{[}{ PdK
2. BFGS iteration:
}{][}{}{ 1111 iiii Kdd
1 1 1{ }{ }[ ] ([ ] )[ ]
{ } { }
{ }{ } { }{ } ([ ] )
{ } { } { } { }
i i Ti i
i T i
i i T i i T
i T i i T i
dK I K
d
d d dI
d d
}{}{}{ 1 iii ddd }{}{}{ 1 iii
Quasi-Newton ProcedureQuasi-Newton Procedure
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723/04/20
Analysis Substru. Test Substru.Coordinator
Predicting-Correcting SchemePredicting-Correcting Scheme
Displ.
A
For
ce
dn
Fn
B
dn+1
Fn+1
Displ.
A
For
ce
dn
Fn
B
dn+1
Fn+1
f
d
f
dC
dn+1
dn+1Wait…Wait…
dd dd
R1R1 R2R2
dd dd
R1R1 R2R2
Predicting
Loading
Correcting
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823/04/20
Target Structure
Target StructureTarget Structure
5,000 5,0004
x 3,
500
Planar ModelPlanar Model
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923/04/20
Substructures
5,000 5,000
4 x
3,5
00
Original Model Original Model Target SubstructuresTarget Substructures
Mass
1
2
31
4
51
6
7
2
3
4
5
1
6
7
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1023/04/20
Substructures with Overlapping Domain
5,000 5,000
4 x
3,5
00
Original Model Original Model Overlapped SubstructuresOverlapped Substructures
2
Mass
Mid-node
1
4 63 5 7
2 4 63 5 7
1
Overlapping DomainOverlapping Domain
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Flexible Implementation at Boundaries
Final SubstructuresFinal Substructures
Coordinator predict displacement of 1
Numerical sub. Tested sub. with linear assumption
Return reaction forces of 1Return reaction force using the initial stiffness Ki
Calculate unbalanced force of 1
NoBalanced or not?
Physical loading
Yes
I-Modification to erase undershoot
Calculate unbalanced force of 1
Coordinator correct displacement of 1
Numerical sub. Tested sub. with linear assumption
Return reaction forces of 1Return reaction force using the initial stiffness Ki
NoBalanced or not?
Calculate unbalanced force of 1
Yes
Next step
Targets: axial forces of 2, 4, 6, & horizontal displ. of 1, 3, 5, 7
3,5
00
3,5
00
3,5
00
Lumped mass
Lin
k
3,5
00
2,500
1,7
50
Lin
k
5,000 2,500
3,5
00
1,7
50
First story columns
Extended members
First story column
Extended members
Numerical substructure
Tested substructure at UB Tested substructure at KU
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Numerical Demonstration
First StoryFirst Story Roof LevelRoof Level
-50-40-30-20-10
01020304050
0 200 400 600 800 1000
Dis
pla
cem
en
t (m
m)
Step
Flexible scheme
Entire
-200
-150
-100
-50
0
50
100
150
200
0 200 400 600 800 1000
Dis
pla
cem
en
t (m
m)
Step
Flexible scheme
Entire
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Overseas Collaboration
University at BuffaloKyoto University
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System Configuration
Proxy PC
Sub1
Matlab xPC
Local LAN
Buffalo
ControlPC1
SC
RA
Mn
et
StationUB R
S23
2C
Coordinator
StationKU ControlPC2
ControlPC3
RS
232C
RS232C
Inte
rnet
Internet
Inte
rnet
Internet
Local LAN
Kyoto
1423/04/20
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1523/04/20
Specimen Setup
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Specimen Instrumentation (Kyoto)40
040
040
074
4
500
1(3)
24
5(7)
68
910
1112131415
510
600
640
304
800
1617
1819
2524
2322
2120
26
27
Strain gaugesDigital displacement transducers
1623/04/20
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Specimen Instrumentation (Buffalo)
CE1
400
400
400
CE2
CE3
CW1
400
400
400
CW2
CW3
900
B1
Strain gauges
900 900
B2 B3
1723/04/20
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Specimen Instrumentation (Buffalo)
PCE1
549.
3
PCE2
990.6
Potentiometers
50.8
549.
319
0.5 PB1T
PB1B
PCW1
549.
3
PCW250.8
549.
3
990.6 990.6
PB2T
PB2B
PB3T
PB3B
1823/04/20
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1923/04/20
Structure Responses
1. The story deformation remains uniform before collapse. The story drifts before collapse is close to 0.02.
2. It finally collapsed in the story mechanism, the first story drift is close to 0.12 rad.
-600
-500
-400
-300
-200-100
0
100
200
300
0 100 200 300 400 500 600
Step
Dis
pla
cem
en
t (m
m)
Dof1Dof2Dof3Dof4
-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0 1 2 3 4 5
Story
Pe
ak
dri
ft (r
ad
)
Peak1
Peak2
Peak3
Peak4
Peak5
Peak6
Peak7
-0.14
-0.12
-0.1
-0.08
-0.06-0.04
-0.02
0
0.02
0.04
0 100 200 300 400 500 600
Step
Sto
ry d
rift
(ra
d)
Dof1Dof2Dof3Dof4
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2023/04/20
Buffalo Specimen
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Kyoto Specimen
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2223/04/20
-800
-700
-600
-500
-400
-300
-200
-100
0
100
0 5 10 15 20
Time (s)
Dis
pla
cem
en
t (m
m)
Shaking Table
Online Test
-80
-60
-40
-20
0
20
40
60
0 500 1000 1500
Steps
Dis
pla
cem
en
t (m
m)
Shaking Table
Online Test
Comparison with Shaking Table Test
-25
-20
-15
-10
-5
0
5
10
15
20
25
0 200 400 600 800 1000
Steps
Dis
plac
emen
t (m
m)
Shaking Table
Online Test
-50-40-30-20-10
01020304050
0 200 400 600 800 1000
Steps
Dis
pla
cem
en
t (m
m)
Shaking TableOnline Test
20%
100%60%
40%
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2323/04/20
Comparison with Shaking Table Test
-800
-600
-400
-200
0
200
400
600
800
1000
-200 0 200 400 600
Displacement (mm)
Re
sto
rin
g F
orc
e (
kN)
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2423/04/20
Summaries
2. The hybrid test framework is able to implement multiple tested substructures, and it is demonstrated to be stable even though the tested substructures have significant unstable behavior.
1. The hybrid test framework encapsulates each substructure by a standard I/O interface. Only boundary displacements and forces are exchanged between substructures and the coordinator program.
3. The hybrid test framework has a capability to reproduce the dynamic behavior of a structure in a collapse stage.