Hybrid Experimental
Analysis of Semi-active
Rocking Wall Systems
K.J. Mulligan, M. Fougere, J.B. Mander, J.G. Chase, G. Danton,
R.B Elliott
Departments of Mechanical and Civil Engineering, University of
Canterbury, Christchurch
B.L Deam
Leicester 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 Dynamics
Valve
Cylinder
Piston
Valve and valve controller
Test
Jig
Resetable
Device
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
Test
Machine
Rocking Wall Dynamics
Roof
Wr
Fd
Wr
R
h
b
O’
O
O
Fd

I θ  MgHθ  MgB  Fd B  F(t)2H
Hybrid Testing
Physical system
Displacement command
Virtual System
Valve Control
Measured Force and
Displacement
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.
-1
-1.5
0
Rotation about point 0
5
0.03
Results
10
15
time (sec)
20
25
30
15
time (sec)
20
25
30
Uncontrolled
uncontrolled
Controlled
theta (rad)
0.02
controlled
0.01
0
-0.01
Rotation about point 0’
-0.02
-0.03
0
5
10
Device Reponse
1500
1000
Actuator Force (N)
Device
Force (N)
500
0
-500
-1000
-1500
-0.015
-0.01
-0.005
0
0.005
displacement (m)
linear
Displacement
(m)
0.01
0.015
0.02
Change in Structural Period
Loma Prieta, Gilroy
3
2
m/s
2
1
0
-1
-2
large pulse
-3
15
20
25
time (sec)
30
35
0.015
theta (rad)
0.01
0.005
uncontrolled
rocking towards
centre position
controlled
0
-0.005
rocking away from
centre position
-0.01
-0.015
15
20
subsequent cycles are larger for controlled case
compared to uncontrolled case
25
30
time (sec)
35
Comparison with Analytical Model
Loma Prieta, Gilroy
m/s
2
5
0
theta (rad)
-5
0.02
5
10
time (sec)
15
20
5
10
time (sec)
15
20
5
10
time (sec)
15
20
a) hybrid result
0
-0.02
theta (rad)
0
0.02
0
b) analytical result
0
-0.02
0
Full Scale Rocking Wall
Metric
K=1000 kN/m K = 5000 kN/m
K= 10000kN/m
R.F
geometric mean
1.01
1.14
1.21
R.F
multiplicative variance
1.10
1.27
1.43
ξ
geometric mean
5.11
5.47
7.12
ξ
multiplicative 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