Hybrid Experimental Analysis of Semi-active Rocking Wall Systems K.J. Mulligan, M. Fougere, J.B. Mander, J.G. Chase, G. Danton,
R.B ElliottDepartments of Mechanical and Civil Engineering, University of
Canterbury, Christchurch
B.L DeamLeicester Steven EQC Lecturer in Civil Engineering, University
of Canterbury, Christchurch
Sponsor: EQC Research Grant # 03/497
Why use Semi-active system?
• Provide a broad range of control
- respond to changes in structural behaviour
• Provide supplemental damping for all rocking cycles, not only subsequently larger cycles
• Provide resistive forces when most benificial to system
Device DynamicsValve
PistonCylinder
Two chambered design:
-Utilises each side independently
-Resetting can occur at any prescribed point of piston displacement
-Portions of motion may dictate both valves to be open
Valve and valve controller
ResetableDevice
Test Machine
TestJig
Rocking Wall Dynamics
Fd
Wr Fd
O
b
h
Wr
Roof
R
OO’
F(t)2HBFMgBMgHθθI d
Hybrid TestingPhysical system
Measured Force and Displacement
Displacement command
Valve Control
Virtual System
Hybrid Testing Procedure
• Wall model calculations determine rotation of wall depending on applied forces
• Rotation of the wall converted into linear displacement for actuator, signal sent to the dynamic test rig
• Valve control determined for current time step • Dynamic test rig supplies displacement to
physical semi-active device• Force developed in device returned to virtual
system and used in subsequent time-step calculation.
Analysis Procedure
• Normalised to uncontrolled case
• Presented as:
-peak reduction factors, R.F
-equivalent viscous damping, ξ
• Suite of ground motions used to analyse efficacy of semi-active system to a variety possible events.
Results0 5 10 15 20 25 30
-1.5
-1
-0.5
0
0.5
1
1.5
2
time (sec)
m/s
2
Imperial Valley (1979)
0 5 10 15 20 25 30-0.03
-0.02
-0.01
0
0.01
0.02
0.03
time (sec)
theta
(rad)
uncontrolled
controlled
Rotation about point 0’
Rotation about point 0 Uncontrolled
Controlled
Device Reponse
-0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02-1500
-1000
-500
0
500
1000
1500
Act
ua
tor
Fo
rce
(N)
linear displacement (m)Displacement (m)
Dev
ice
F
orc
e (
N)
Change in Structural Period
15 20 25 30 35-3
-2
-1
0
1
2
3
time (sec)
m/s
2
Loma Prieta, Gilroy
15 20 25 30 35-0.015
-0.01
-0.005
0
0.005
0.01
0.015
time (sec)
thet
a (
rad
)
rocking towardscentre position
rocking away fromcentre position
uncontrolled
controlled
subsequent cycles are larger for controlled casecompared to uncontrolled case
large pulse
Comparison with Analytical Model
0 5 10 15 20-5
0
5
time (sec)
m/s2
Loma Prieta, Gilroy
0 5 10 15 20-0.02
0
0.02
time (sec)
theta
(ra
d)
0 5 10 15 20-0.02
0
0.02
time (sec)
theta
(ra
d)
a) hybrid result
b) analytical result
Full Scale Rocking Wall
Metric K=1000 kN/m K = 5000 kN/m
K= 10000kN/m
R.Fgeometric mean
1.01 1.14 1.21
R.Fmultiplicative variance
1.10 1.27 1.43
ξgeometric mean
5.11 5.47 7.12
ξmultiplicative variance
1.15 2.13 2.30
Summary
• Significantly reduce peak rotations of seismically excited rocking wall systems
• Provide additional restoring forces to the system when it is most benifical
• Model accurately predicts test results allowing scaling to a variety of applications
• Results are dependent on ground motion, hence important to examine using a suite of ground motions