structural dynamics laboratory department of engineering science, university of oxford first...
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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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
Scale-model tests
Offshore wind turbine
Guyed mast
Structural Dynamics LaboratoryJenkin Building
Real-time hybrid tests mass/spring systems dissipative devices2-storey column
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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 Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
Structural
Dynamics
Lab
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
Control Installation
IBM compatible PCInstron8050
controller
IBM compatible PC
IEEE interfaceInstron RS-
plus program
ControlDeskprogram
IEEE bus
dSPACEboardSensor signals
Command signals
Actuatorsignals
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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)
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
Physical Substructure
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
Actuator coupling
Fl
dl
Fu
du
l
u
l
u
d
d
F
F
21
11
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
El Centro NS component
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
Displacement @ level 2 (upper actuator)
40% El Centro
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
Numerical – physical
displacement comparison
Upper actuator
Max error: 0.46%
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
Floor displacements @40%
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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%).
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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%
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
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
Structural Dynamics Laboratory
Department of Engineering Science, University of Oxford
First European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006
Further work
• Extend tests to higher frequencies
• More plasticity in the physical specimen
• Non-linear numerical model