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

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

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.

423/04/20

dndndndnd2d2d2d2d1d1d1d1

Analysis Substru. Test Substru.Coordinator

R

R1

R2

R1

R2

…

…

…

R1

R2

System ImplementationSystem Implementation

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

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

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

823/04/20

Target Structure

Target StructureTarget Structure

5,000 5,0004

x 3,

500

Planar ModelPlanar Model

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

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

1123/04/20

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

1223/04/20

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

1323/04/20

Overseas Collaboration

University at BuffaloKyoto University

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

1523/04/20

Specimen Setup

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

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

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

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

2023/04/20

Buffalo Specimen

2123/04/20

Kyoto Specimen

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%

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)

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.