Structural Dynamics Laboratory Department of Engineering Science, University of Oxford First European Conference on Earthquake Engineering and Seismology,

Structural Dynamics Laboratory

Department of Engineering Science, University of Oxford

First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006

Real Time Hybrid Earthquake Simulation of a Steel Column in a

20-Storey Building

Paul Bonnet, Martin S Williams, Anthony Blakeborough & Mobin Ojaghi

Department of Engineering Science

University of Oxford




Structure of talk• Structural Dynamics Laboratory at Oxford• Real time substructuring

– concept, technical issues• 20-storey building

– prototype, natural frequencies, physical/numerical substructuring

• Implementation• Results




Scale-model tests

Offshore wind turbine

Guyed mast

Structural Dynamics LaboratoryJenkin Building

Real-time hybrid tests mass/spring systems dissipative devices2-storey column




Hydraulic Installation

Oil reservoir

Pressure line

Instron actuators

Two100kN

Two250kN

Return line

Pump1

Pump2

Pump3

Accumulators

Hydraulic mains

Flexiblepressure andreturn hoses

Connectionmanifolds

Two Instron10kN hydraulicactuators

Instronsubstations




Structural

Dynamics

Lab




Control Installation

IBM compatible PCInstron8050

controller

IBM compatible PC

IEEE interfaceInstron RS-

plus program

ControlDeskprogram

IEEE bus

dSPACEboardSensor signals

Command signals

Actuatorsignals




Substructure testing

• Split the structure under test into two or more components– Full (or nearly full) scale physical model for ‘difficult’

bits

– Computational model of remainder




Displacement Control Loop Physical substructure

Measure forces andactual displacements

of test specimen

Numerical substructure

Calculatedisplacementsat interfacebetweenphysical andnumericalsubstructures

Apply measuredforces to numerical

substructure

Command actuatorsto apply interfacedisplacements to

physical substructure

External loads(eg. earthquake)

Delay/lag in displacement response

Calcu

lation

delay

Problems




Delay error

1.0

1.2

1.4

1.6

1.8

2.0

0 2000 4000 6000 8000

Actuator Load (N)

De

lay

Std

De

v. (

ms

)

5.0

5.2

5.4

5.6

5.8

6.0

0 2000 4000 6000 8000

Actuator Load (N)

Av

era

ge

De

lay

(m

s)




Chang explicit integration

1

0121

2

11

0121

1

11111

11

2211

4

1

2

1

2

1

2

1

4

1

2

1

2

KMCMIβ

CMIKMCMIβ

FfRvCaM

aavv

aβvβdd

TT

TTT

T

TT

nnnnn

nnnn

nnnn




Delay compensation

t (ms)

d (mm)

tn+1tntn-3tn-7tn-11

24ms 8ms

Integration step = 2msEstimated delay varies between 7.5ms & 8.5ms3rd order polynomial extrapolation used time integration calculation step results step calculations used for extrapolation at step n+1 extrapolated command signal for step n+1




Prototype structure

• Single braced bay• 20 stories - 3m per storey• 230 Mg/floor• Chevron braces (only tension brace

active)

• f1=0.46 Hz, f2=1.42 Hz, f20=12.4 HzFloor #1

Floor #2

Floor #3

Floor #18

Floor #19

Floor #20

Earthquake ground acceleration




Physical Scaling• Full scale is too large to fit into laboratory

• Scale to 40% on column height

• Adjust properties to keep natural frequencies the same

Full scale structure 40% model

Storey mass (T) 230 21

Lateral stiffness (kN/mm) 350 32

Lateral viscous damping (kN.s/m) 4700 434




Physical / Numerical

PartitioningFloor #1

Floor #2

Floor #3

Floor #18

Floor #19

Floor #20

PhysicalSubstructure

NumericalSubstructure

load_19

load_20

x 4

Earthquake ground acceleration

Actuator #1

Actuator #2

Specimen127x76x13 UB section

1.2m

1.2m

Rig bracing

Reaction floor

disp_19

disp_20

load_act 1

load_act 2x 4




Physical Substructure




Actuator coupling

Fl

dl

Fu

du

l

u

l

u

d

d

F

F

21

11




Numerical substructure

• Chang integrator• Stiffness proportional damping

– 2% for 1st mode• Integrator time steps

– 10ms, 20ms & 30ms• Measured actuator time delay• Horiuchi or Laguerre extrapolator




El Centro NS component




Displacement @ level 2 (upper actuator)

40% El Centro




Numerical – physical

displacement comparison

Upper actuator

Max error: 0.46%




Floor displacements @40%




Lower storey shear hysteresis

-20 -15 -10 -5 0 5 10 15 20-1.5

-1

-0.5

0

0.5

1

1.5x 10

4

Lower storey deflection (mm)

Low

er

sto

rey s

hear

forc

e (

N)

40% Earthquake input

Regression: F= -702 . D

-20 -15 -10 -5 0 5 10 15 20-1.5

-1

-0.5

0

0.5

1

1.5x 10

4

Lower storey deflection (mm)

Low

er

sto

rey s

hear

forc

e (

N)

60% Earthquake input

Regression: F= -684 . D




0 5 10 15 20 25 30 35 40-0.2

-0.1

0

0.1

0.2

Time (s)

RT

S d

isp

erro

r ac

t #1

(m

m)

0 5 10 15 20 25 30 35 40-0.4

-0.2

0

0.2

0.4

Time (s)

RT

S d

isp

erro

r ac

t #2

(m

m) std20

10ms

p60bsc

0 5 10 15 20 25 30 35 40-40

-20

0

20

40

Time (s)

RT

S d

esire

d di

sp a

ct #

1 (m

m)

0 5 10 15 20 25 30 35 40-20

-10

0

10

20

Time (s)

RT

S d

esire

d di

sp a

ct #

2 (m

m)

0 5 10 15 20 25 30 35 400

1

2

3

Time (s)

Rel

ativ

e ab

solu

te e

rror

act

#1

(%)

Mean abs relative error = 0.48469% (std = 0.62389%) (rms = 0.50302%).

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Time (s)

Rel

ativ

e ab

solu

te e

rror

act

#2

(%)

Mean abs relative error = 2.601% (std = 3.0161%) (rms = 2.4162%).




Comparison with Emulation and Test

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

Emulation (mm)

Tes

t (m

m)

Upper actuator

Max error: 1%




Main findings

• Small local processor perfectly adequate to perform simple numerical simulation and control of 20 dof model

• Errors increased with length of computational time step• Chang’s algorithm was best in terms of accuracy and

speed of execution• At larger time steps Horiuchi extrapolation was less good

the Laguerre method




Further work

• Extend tests to higher frequencies

• More plasticity in the physical specimen

• Non-linear numerical model

Documents

Structural Dynamics Laboratory Department of Engineering Science, University of Oxford First European Conference on Earthquake Engineering and Seismology,