Re-Shaping Hysteretic Behaviour Using Re-Shaping Hysteretic Behaviour Using Resetable Devices to Customise Structural Resetable Devices to Customise Structural

Response and ForcesResponse and ForcesGeoffrey W RodgersGeoffrey W Rodgers, John B Mander, J Geoffrey Chase, Kerry J Mulligan,, John B Mander, J Geoffrey Chase, Kerry J Mulligan,

Bruce L Deam, and Athol J CarrBruce L Deam, and Athol J Carr

End Cap

Cylinder

Piston

Seal

Device DesignDevice Design

Valvea)

Valves

Cylinder Piston

b)

Cylinder Piston

Independent two chamber design allows broader range of control laws

Overall Customised HysteresisOverall 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 motion

Resist motionaway from 0

Resist motiontoward 0

Resist all velocity

Semi-Active Resetable Device ModelSemi-Active Resetable Device Model

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Experimental Test Results

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Simulink Models

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Simplified Linear ModelSimplified Linear Model

Less computationally expensive, with no anticipatedloss of accuracy or generality

1-3 control 2-4 control

1-4 control

Response SpectraResponse Spectra

Average response spectra for different control laws

How do the different control laws perform relative to one another?

Reduction FactorsReduction Factors

More clearly represent reductions achieved with each control law

Note the apparent invariance to the type of ground motion encountered

Divide results with additional stiffness by the uncontrolled case

Largest reductions seen for the 1-4 device – This device acts over a larger percentage of each cycle and will consequently

have longer active strokes

Suite DependenceSuite DependenceNormalise the average reduction factor from each suite

to the reduction factors for all ground motions to investigate suite dependence

Values close to unity across the spectrum indicates an invariance to the type of ground motion (near field vs. far field) encountered – indicating a robustness of this form of control

Spread of ResultsSpread of Results

Log-normal co-efficient of variation or dispersion factor- Indicates the spread of the results within a ground motion suite- Largest spread is seen for the 1-4 device indicating more variability- Both the 1-3 and 2-4 device show a tighter spread

Structural ForceStructural ForceThe base-shear force for a linear, un-damped structure - Gives an indication of the required column strength

Largest reductions for the 1-4 device – consistent with other metricSimilar performance for the 1-3 and 2-4 devices

Base-ShearBase-ShearThe sum of the structural force and the resetable device force - Gives an indication of the required foundation strength

Only the 2-4 device reduces base shear across the entire spectrum

The 1-3 and 1-4 devices increase base-shear by as much as 60%

The 2-4 device provides similar reductions in displacement and structural force as the 1-3 device, and also reduces base-shear

Control laws comparedControl laws comparedAveraging across suites more clearly indicates

the relative advantage of the control laws

Structural Force Base-Shear Force

1-3 and 2-4 show similar reductions in structural force, but are outperformed by the 1-4 device

Only the 2-4 device reduces base-shear, whereas both the 1-3 and 1-4 increase base-shear by as much as 60%

Displacement Spectral AreaDisplacement Spectral AreaNumerically integrate the area under the response spectra in the seismically

important T = 0.5 to 2.5 second range.

An indication of the average displacement reduction factor in the constant velocity region of the spectra

Fit empirical equations to estimate damping reduction factors

BR /1 wherestructural

resetable

K

KCB 1

where C = 1.43, 1.59, and 5.75 for the 1-3, 2-4 and 1-4 devices

How accurate are these equations?How accurate are these equations?

Re-plot the displacement reduction factors, with the reduction factors from the empirical equations

Although variations can be seen above T = 3.0seconds, equations are appropriate over the constant velocity region from T = 0.5 – 3.0 secs

Black Line is Empirical Equation

ADRS ADRS Acceleration-Displacement Response Spectra

Relate additional resetable stiffness to design guidelines

Empirical reduction factor equations create a “standard design platform” for a structural engineer to safely and

effectively add resetable devices to their design.

SummarySummary

• The 1-4 device outperforms both the 1-3 and 2-4 device for displacement response and structural force as it acts over the full response cycle, has longer active strokes, and consequently higher energy dissipation

• Both the 1-3 and 1-4 devices provide a reduction in structural force and displacement response, but increase base-shear up to 60%

• The 2-4 device reduces both structural force and base-shear

• All three control laws are suite invariant indicating a robustness to the type of ground motion encountered

• Empirical equations to approximate reduction factors allow incorporation into accepted performance based design metrics

ConclusionsConclusions

• Semi-active control enables customisation of overall structural hysteresis in novel ways not available with passive systems

• The most applicable control law (of the selected few presented) depends on the application

• New purpose designed structure • Retrofit application with limited foundation strength• Thus, device selection and implementation is a structural design problem rather

than a control systems problem

• The overall approach presented can be used to develop standard design metrics for any similar novel semi-active or passive systems/devices, thus creating a bridge to the design profession and a greater likelihood of uptake.

AcknowledgementsAcknowledgements

Special thanks to Ms Kerry Mulligan and Professors Special thanks to Ms Kerry Mulligan and Professors Chase and Mander for their assistance with this research, Chase and Mander for their assistance with this research,

as well as to our co-authorsas well as to our co-authors

This research was funded by the NZ Earthquake Commission This research was funded by the NZ Earthquake Commission (EQC) Research Foundation and the New Zealand Tertiary (EQC) Research Foundation and the New Zealand Tertiary Education Commission (TEC) Bright Futures Top Achievers Education Commission (TEC) Bright Futures Top Achievers

Doctoral Scholarship SchemeDoctoral Scholarship Scheme

SATMD ConceptSATMD Concept

Upper or new stories added as Upper or new stories added as segregated masssegregated mass

Connections are of resetable Connections are of resetable devices and/or rubber bearingsdevices and/or rubber bearings

Use 1-4 devices to resist all motion Use 1-4 devices to resist all motion of upper stories and dissipate max of upper stories and dissipate max energyenergy

Goal 1: use upper stories as tuned Goal 1: use upper stories as tuned massmass

Goal 2: reduce displacements and Goal 2: reduce displacements and thus shears in lower storiesthus shears in lower stories

How to tune?How to tune?

Tuning and MethodTuning and Method Easy assumptionEasy assumption = tune to 1 = tune to 1stst mode as with passive TMD (PTMD) mode as with passive TMD (PTMD) Better assumptionBetter assumption = tune lower than first mode to enhance motion = tune lower than first mode to enhance motion

of device and thus the energy dissipatedof device and thus the energy dissipated Set SATMD stiffness to PTMD/5 (one fifth of stiffness)Set SATMD stiffness to PTMD/5 (one fifth of stiffness) Anything under PTMD/2 works pretty much equally wellAnything under PTMD/2 works pretty much equally well

MethodMethod:: Run suites of earthquakes and develop spectra (SAC project motions)Run suites of earthquakes and develop spectra (SAC project motions) Compare PTMD with SATMD using 100% resetable devicesCompare PTMD with SATMD using 100% resetable devices Use 20% of lower stories as SATMD/PTMD massUse 20% of lower stories as SATMD/PTMD mass Present 16Present 16thth, 50, 50thth and 84 and 84thth percentile results percentile results Assume optimal tuning in PTMD for most conservative comparisonAssume optimal tuning in PTMD for most conservative comparison All results presented as All results presented as reduction factorsreduction factors of base structure (y1) motion of base structure (y1) motion

as compared to uncontrolled case and presented as a percentage (%)as compared to uncontrolled case and presented as a percentage (%) Re-run some suites with Re-run some suites with non-linearnon-linear structure for more realistic case structure for more realistic case

Linear Spectra ResultsLinear Spectra Results

SATMD is much narrower than PTMDSATMD is much narrower than PTMD All SATMD values < 100%All SATMD values < 100% PTMD highly variable over suitesPTMD highly variable over suites Differences are greatest in 1-3 second Differences are greatest in 1-3 second

range of greatest interest for earthquakesrange of greatest interest for earthquakes Again, optimal PTMD tuning is usedAgain, optimal PTMD tuning is used

Low

High

Medium

Non-Linear ResultsNon-Linear Results Only low suite for most Only low suite for most

common eventscommon events Use Bouc-Wen model for Use Bouc-Wen model for

structural non-linearitystructural non-linearity

Similar results overall to Similar results overall to linear spectra caselinear spectra case

PTMD even wider over PTMD even wider over suite with realistic structuresuite with realistic structure

SATMD only a little widerSATMD only a little wider SATMD < 100% still even at SATMD < 100% still even at

8484thth percentile percentile

SATMD SummarySATMD Summary Concept shows significant promise in an area that may grow as Concept shows significant promise in an area that may grow as

developers and others seek to go upwardsdevelopers and others seek to go upwards Provides a novel way to obtain TMD like results without added massProvides a novel way to obtain TMD like results without added mass SATMD tuning does not require knowledge of exact masses or SATMD tuning does not require knowledge of exact masses or

exact first mode frequency, as with standard passive PTMD. exact first mode frequency, as with standard passive PTMD. Therefore, it is very easy to design tuningTherefore, it is very easy to design tuning

PTMD results are very wide and do not always reduce response – PTMD results are very wide and do not always reduce response – even with optimal tuning to first mode!even with optimal tuning to first mode!

Reduction factor results, as presented for spectra over suites of Reduction factor results, as presented for spectra over suites of events can be modelled to obtain design equations and integrate events can be modelled to obtain design equations and integrate into standard design methodsinto standard design methods

Approach is basically the same as presented for directly controlled Approach is basically the same as presented for directly controlled structures in prior workstructures in prior work