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

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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

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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

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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

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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

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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

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OpenSees Navigator User Interface

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OpenSees Navigator User Interface

gravity loads modeled analytically

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OpenSees Navigator User Interface

Defining experimental components (OpenFresco)

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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))

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Response Animation w/o Gravity Load

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Response Animation with Gravity Load

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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

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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

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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

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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

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Future Work

Conduct large-scale simulationsConduct simulations where the axial load will be physically applied on the specimen

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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