Semi-active Management of
Structures Subjected to High
Frequency Ground Excitation
C.M. Ewing, R.P. Dhakal, J.G. Chase and J.B. Mander
19th ACMSM, Christchurch, New Zealand, 2006
The Scene
• Structures can be highly vulnerable to a variety of environmental loads
• These days, man-made events can also have significant impact on the
life, serviceability and safety of structures, and must be accounted for
in new designs
– i.e. blast loads
• However, what do you do about already existing and potentially
vulnerable structures?
– In particular, how do you manage to protect the structure without
overloading shear or other demands?
– Particularly true for relatively older structures
• Semi-active methods offer the adaptability to reduce response energy
without increasing demands on the structure, but add complexity
• Passive methods offer simplicity and ease of design, but are not
adaptable or as effective.
Characteristics of BIGM
Typical Seismic excitation
Typical BIGM
2
Horizontal
50 m
50m distance (horizontal)
1000
Acceleration, m/s
Acceln, m/s2
1500
500
0
-500
-1000
-1500
0.00
0.05
0.10
0.15
0.20
Time, sec
0.25
0.30
4
2
0
-2
-4
20
25
30
35
40
45
50
55
Time, sec
Large amplitude (~100 g)
May cause sudden collapse.
Short duration (<0.05 sec)
Impulsive nature. Post-BIGM
response is also important.
60
65
70
Characteristics of BIGM
Typical Seismic excitation
Typical BIGM
x 10
4
30
Horizontal 50 m
8
Fourier Amplitude
Fourier amplitude
Acceleration
spectra
10
Fourier
FourierSpectrum
transform
6
4
25
20
15
10
5
2
0
0
0
200
400
600
800
Frequency, Hz
High frequency (~200 Hz)
1000
0
2
4
6
8
10
Frequency, Hz
May excite high frequency vibration
Modes during major shock duration.
Max response factor, Rmax
Impulse Shock Spectra
2.0
1.6
1.2
Sine
2.0
0.8
1.6
Rect
1.2
0.8
0.4
Tri
0.4
0.0
0.0
0.1
0.2
0.3
0.4
Tri2
0.5
0.0
0.0
0.4
0.8
1.2
1.6
Ratio t1/T
•
If t1/T < critical (0.4-0.5),
- The maximum response of a linear structure depends on t1/T.
2.0
Max response factor, Rmax
Impulse-Response Relationship
2.0
1.6
T = 1 sec
1.2
Sine
2.0
0.8
1.6
0.4
1.2
Rect
0.8
Tri
0.4
Tri2
0.0
0.0
0
0
300
100 200 300 400 500
600
900
1200
1500
Impulse/mass, gal-s
•
If t1/T < critical (0.4-0.5),
– The maximum response factor is proportional to the total energy applied,
regardless of the impulse shape.
A Simple Structure & Damage
450kN live
•
Loads are impulsive
•
Excite higher order modes
•
Plastic first peak response
is not unusual
•
Plastic deformation on
return or second peak
response may also occur
•
After initial pulse the
response is transient free
response from a large
initial value
•
Main forms of damage:
–
–
Residual deformation
Low cycle fatigue
Blast load based on
pressure wave and face
area
630kN live
1000kg/story
E = 27GPa
General Dynamic Response
Fundamental
global mode
Higher order
global mode
Frequency increases
Acceleration increases
Displacement decreases
Fundamental
local modes
More Detailed Model
Basic Elements:
•
Multiple elements per column to capture higher
order responses [Lu et al, 2001]
•
Mass discretised over all elements in column
•
Blast load discretised to each storey based on
pressure wave and face area
•
Simple frame used to characterise basic solutions
available for something more complex than a
SDOF analysis
•
Non-linear finite elements (elastic-plastic with 3%
post yield stiffness)
•
Fundamental Period = 1 sec
•
Main structure model captures all fundamental
dynamics required for this scenario
P
Typical Load
•
•
•
•
•
Short duration impulse (< T1/5)
Any shape will give the same result, as the basic input is an applied
momentum
Provides an initial displacement
Pblast = 350kPa pressure wave
Triangular shaped pulse of duration Dt = 0.05 seconds or 5% of
fundamental structural period
Typical Uncontrolled Response
•
•
•
•
A first large peak that is plastic
Second and third peaks may also have permanent
deformation
Free vibration response after initial pulse (not linear)
Residual deformation
Permanent deflection may be larger
or even negative depending on size
of the load
Possible Solutions
•
Passive = Tendons
–
–
–
–
•
Tendon in shape of moment diagram
Semi-Active = Resetable devices using 2-4 control
law
–
–
•
Restrict first peak motion = initial damage
Add slightly to base shear demand on foundation
Match overturning moment diagram [Pekcan et al, 2000]
Tendon yields by design during initial peak
Do not increase base shear
Reduce free vibration response = subsequent damage
Therefore, in combination these devices are designed
to reduce different occurrences of damage in the
response
Resetable device 1st floor
•
However, can devices hooked to story’s manage
damage for this case characterized by higher column
mode response?
•
Paper also considers device on 2nd story and from
ground to 2nd story
Becoming A Proven Technology
End Cap
Seal
Cylinder
Piston
More later in conference from Mulligan et al, Rodgers et al and Anaya et al
on resetable devices and semi-active applications/experiments
Semi-Active Customised Hysteresis
Resist all velocity
Viscous Damper
Resist all motion
Reset at peaks
1-4 Resetable
1
Resist motion
away from 0
From 0Peak
Resist motion
toward 0
From Peak0
1-3 Resetable
3
4
2-4 Resetable
2
Only the 2 - 4 control law does not increase base-shear
The Very Basic Ideas
a)
b)
Valve
Valves
Cylinder
Piston
Cylinder
Piston
Independent two chamber design allows broader range of control laws
Specific Results
Device on first floor and tendon versus uncontrolled
First peak and free vibration reduced ~40-50%
1st story response
Displacement
•
•
•
Time
Device Stiffness is Critical
•
•
•
Results normalised to uncontrolled response
Device stiffness in terms of column stiffness k
50-100% of column stiffness = good result in free vibration per [Rodgers et al, 2006]
Response Energy 2-norm
1st Peak
2nd Peak
Parameter Uncontrolled
||Y||
1
F12
1
F11
1
F22
1
F21
1
Parameter
0.1k
||Y||
0.53
F12
0.712
F11
0.564
F22
0.644
F21
0.569
tendon
only
0.568
0.712
0.564
0.663
0.585
0.5k
0.43
0.712
0.564
0.563
0.492
0.01k
0.564
0.712
0.564
0.663
0.585
k
0.364
0.712
0.564
0.446
0.385
0.05k
0.548
0.712
0.564
0.654
0.579
2k
0.304
0.712
0.564
-
Conclusions
• Blast can be completely represented by the applied momentum
rather than shape, pressure or other typically unknown values
• Simple robust system shows potential in this proof of concept
study on an emerging problem of importance for structural designers
• Complexity added is minimal
• Results show that significant improvements that could be critical to
safety and survivability can be obtained
• Minimal extra demand on foundations makes it particularly suitable
for retrofit of existing (relatively older) structures