Semi-active Management of Semi-active Management of Structures Subjected to High Structures Subjected to High Frequency Ground ExcitationFrequency Ground Excitation

C.M. Ewing, R.P. Dhakal, J.G. Chase and J.B. Mander

19th ACMSM, Christchurch, New Zealand, 2006

The Scene 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 BIGMCharacteristics of BIGM

Typical BIGM

Large amplitude (~100 g)

Short duration (<0.05 sec)

May cause sudden collapse.

Impulsive nature. Post-BIGM response is also important.

50m distance (horizontal)

-1500

-1000

-500

0

500

1000

1500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Time, sec

Acc

eln

, m/s

2

Horizontal 50 m

-4

-2

0

2

4

20 25 30 35 40 45 50 55 60 65 70Time, sec

Acc

eler

atio

n,

m/s

2

Typical Seismic excitation

Characteristics of BIGMCharacteristics of BIGM

High frequency (~200 Hz)

May excite high frequency vibrationModes during major shock duration.

0

5

10

15

20

25

30

0 2 4 6 8 10Frequency, Hz

Fo

uri

er

Am

plit

ud

e

Typical BIGM Typical Seismic excitation

0 200 400 600 800 10000

2

4

6

8

10x 104

Frequency, Hz

Acc

eler

atio

n s

pec

tra Fourier transform

Fo

uri

er

am

pli

tud

e Fourier Spectrum

Horizontal 50 m

0.0

0.4

0.8

1.2

1.6

2.0

0.0 0.4 0.8 1.2 1.6 2.0

Ratio t1/T

Max

res

po

nse

fac

tor,

Rm

ax

Sine

Rect

Tri

Tri2

0.0

0.4

0.8

1.2

1.6

2.0

0.0 0.1 0.2 0.3 0.4 0.5

• If t1/T < critical (0.4-0.5),

- The maximum response of a linear structure depends on t1/T.

Impulse Shock SpectraImpulse Shock Spectra

0.0

0.4

0.8

1.2

1.6

2.0

0 300 600 900 1200 1500Impulse/mass, gal-s

Max

res

po

nse

fac

tor,

Rm

ax

Sine

Rect

Tri

Tri2

0.0

0.4

0.8

1.2

1.6

2.0

0 100 200 300 400 500

T = 1 sec

• If t1/T < critical (0.4-0.5),

– The maximum response factor is proportional to the total energy applied, regardless of the impulse shape.

Impulse-Response RelationshipImpulse-Response Relationship

A Simple Structure & DamageA Simple Structure & Damage

• 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 facearea

630kN live

450kN live

1000kg/storyE = 27GPa

General Dynamic ResponseGeneral Dynamic Response

Fundamentalglobal mode

Higher orderglobal mode

Fundamentallocal modes

Frequency increasesAcceleration increases

Displacement decreases

More Detailed ModelMore 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 LoadTypical 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 t = 0.05 seconds or 5% of fundamental structural period

Typical Uncontrolled ResponseTypical 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 largeror even negative depending on size of the load

Possible SolutionsPossible Solutions

• Passive = Tendons – 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

• Semi-Active = Resetable devices using 2-4 control law– 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

• 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

Resetable device 1st floor

Tendon in shape of moment diagram

Becoming A Proven TechnologyBecoming A Proven TechnologyEnd Cap

Cylinder

Piston

Seal

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 HysteresisSemi-Active Customised Hysteresis

Only the 2 - 4 control law does not increase base-shear

Viscous Damper

1-4 Resetable

1-3 Resetable

2-4 Resetable

Resist all motionReset at peaks

Resist motionaway from 0

From 0Peak

Resist motiontoward 0

From Peak0

Resist all velocity

4

2

1

3

The Very Basic IdeasThe Very Basic Ideas

Valvea)

Valves

Cylinder Piston

b)

Cylinder Piston

Independent two chamber design allows broader range of control laws

Specific ResultsSpecific Results• Device on first floor and tendon versus uncontrolled

• First peak and free vibration reduced ~40-50%

• 1st story response

Time

Dis

pla

cem

ent

Device Stiffness is CriticalDevice 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]

Parameter Uncontrolled tendon only 0.01k 0.05k

||Y|| 1 0.568 0.564 0.548 F12 1 0.712 0.712 0.712 F11 1 0.564 0.564 0.564 F22 1 0.663 0.663 0.654 F21 1 0.585 0.585 0.579

Parameter 0.1k 0.5k k 2k ||Y|| 0.53 0.43 0.364 0.304 F12 0.712 0.712 0.712 0.712 F11 0.564 0.564 0.564 0.564 F22 0.644 0.563 0.446 - F21 0.569 0.492 0.385 -

Response Energy 2-norm

1st Peak

2nd Peak

ConclusionsConclusions

• 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