Vibration Control and Vibration Control and

Benchmark Problems on BridgesBenchmark Problems on Bridges

Suhasini Madhekar Suhasini Madhekar

College of Engineering PuneCollege of Engineering Pune

Faculty Development Program onFaculty Development Program on

Fundamentals of Structural Dynamics and Application to Fundamentals of Structural Dynamics and Application to

Earthquake EngineeringEarthquake Engineering

1212thth December 2015December 2015

Sanjay Sanjay GhodawatGhodawat Group of InstitutionsGroup of Institutions

AtigreAtigre, Kolhapur, Kolhapur 11

Golden Gate Bridge, USAGolden Gate Bridge, USA

Firth of Forth Bridge, ScotlandFirth of Forth Bridge, ScotlandSunshine skyway Bridge, USASunshine skyway Bridge, USA

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Bridges on Konkan RailwaysBridges on Konkan Railways

Catastrophic Failures of ‘LCatastrophic Failures of ‘Lifeline’ifeline’ structure !!!structure !!!

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Catastrophic Failures..Catastrophic Failures..

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Seismic Design Approach

Traditional

••Fixed to groundFixed to ground

••Amplification of Amplification of

AccelerationAcceleration

With controllers

••Seismic demand reducedSeismic demand reduced

••Reduced deck Reduced deck

accelerations and driftsaccelerations and driftsAccelerationAcceleration

••Structural and NonStructural and Non--

structural Damagestructural Damage

••Capacity is Capacity is

increased to meet the increased to meet the

demanddemand

accelerations and driftsaccelerations and drifts

•• Deck is decoupled from Deck is decoupled from

substructuresubstructure

••No nonNo non--structural damagestructural damage

••Seismic and wind controlSeismic and wind control

••Suitable for retrofittingSuitable for retrofitting66

Conventional Design Approach..Conventional Design Approach..

Structures : To resist earthquake through strength, ductility Structures : To resist earthquake through strength, ductility

& energy absorption & energy absorption

Earthquake / Wind Excitations : Inelastic deformation of a Earthquake / Wind Excitations : Inelastic deformation of a

structure by formation of plastic hingesstructure by formation of plastic hinges

Emphasis on increasing strength of structure to resist Emphasis on increasing strength of structure to resist

earthquake induced forces. earthquake induced forces.

Allow damages.. prevent collapse.Allow damages.. prevent collapse.

Design forces considered are very small compared to the Design forces considered are very small compared to the

actual Earthquake forces.actual Earthquake forces.

ΔΔdesign << design << ΔΔ actual. Permanent deformations through actual. Permanent deformations through

yieldingyielding77

Bridge : Lifeline structureBridge : Lifeline structure

0.2 0.2 ≤≤ T T ≤ ≤ 1.2 sec. 1.2 sec. -- Close to the preClose to the pre--dominant periods of dominant periods of

earthquake induced ground accelerations : results in earthquake induced ground accelerations : results in

amplification of response. amplification of response.

Bridges: Extremely vulnerable to damage Bridges: Extremely vulnerable to damage –– Relatively large Relatively large Bridges: Extremely vulnerable to damage Bridges: Extremely vulnerable to damage –– Relatively large Relatively large

deck mass supported by slender columns. Large deck mass supported by slender columns. Large

displacements displacements -- large shear forces in the piers large shear forces in the piers

Effort of protection of bridges against earthquakes: Focused Effort of protection of bridges against earthquakes: Focused

on minimizing shear forces transmitted to piers.on minimizing shear forces transmitted to piers.

Vibration Control of StructuresVibration Control of Structures

�� Dynamic loading on Bridges due Dynamic loading on Bridges due to Earthquakes, to Earthquakes, highhigh--wind, wind,

barge impact , blast, floodbarge impact , blast, flood

��MasonryMasonry, concrete , concrete (RCC & PSC) and (RCC & PSC) and steel steel provide provide a large a large

amount of structural stiffness. amount of structural stiffness.

��Provide very little Provide very little dampingdamping

��An alternate seismic design philosophy ensuring lifeAn alternate seismic design philosophy ensuring life--safety safety

during strong earthquakes, minimum damage to the during strong earthquakes, minimum damage to the

structural structural system : Vibration controlsystem : Vibration control

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�� Transfer Transfer the vibration energy of the main structural system the vibration energy of the main structural system

to an auxiliary oscillator to an auxiliary oscillator system (Isolator/ Damper / STU) system (Isolator/ Damper / STU)

��Reduce Reduce the flow of input excitation energy in to the main the flow of input excitation energy in to the main

structural system.structural system.

Structural Control PrinciplesStructural Control Principles

structural system.structural system.

��Subject Subject the structure to additional damping.the structure to additional damping.

��Prevent Prevent the the Bridge Bridge from exhibiting resonance due to an from exhibiting resonance due to an

external excitation.external excitation.

��Provide Provide a structural system with a structural system with controllable controllable forces forces

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Classification of controlled structuresClassification of controlled structures

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��LimitationsLimitations ofof existingexisting internationalinternational codescodes andand

standardsstandards forfor VibrationVibration controlcontrol onon structurestructure..

��IfIf MassMass (Ms)(Ms) && StiffnessStiffness (Ks)(Ks) areare bothboth doubled,doubled,

responseresponse isis halvedhalved approximatelyapproximately..

��OnOn thethe otherother handhand AnAn auxiliaryauxiliary damperdamper withwith aa massmass

Md=[MsMd=[Ms // 300300]] cancan reducereduce thethe responseresponse byby 5050%%..

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Merits:Merits:

��Simple, stable, with fixed properties.Simple, stable, with fixed properties.

��Forces developed at the location of the device.Forces developed at the location of the device.

��No energy added to the structure No energy added to the structure

��Independent functioning without external power supplyIndependent functioning without external power supply

� Isolation systems : Elastomeric and friction typeIsolation systems : Elastomeric and friction type

Passive Control Devices : IsolatorsPassive Control Devices : Isolators

� Isolation systems : Elastomeric and friction typeIsolation systems : Elastomeric and friction type

Demerits:Demerits:

��Control force depends only on the local information.Control force depends only on the local information.

��Unable to adapt to structural changes and varying loading Unable to adapt to structural changes and varying loading

conditions conditions

��Limited effectiveness when the structure is founded on soft groundLimited effectiveness when the structure is founded on soft ground..

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Base Isolation : Aseismic design philosophy Base Isolation : Aseismic design philosophy

Seismic isolation : separation of upper structure from base

(Buildings) or from down structure (substructure of bridges /

staging of ESR)

Flexibility is increased by inserting additional elements in

structure, known as IsolatorsIsolators..

Time Period of the total System is Elongated

The structure remains operational after a major earthquake

The isolator behaves as Rigid system under Wind or Minor

Earthquake and as Flexible system under severe earthquake

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Merits of Seismic Isolation Merits of Seismic Isolation

Seismic isolation system absorbs larger part of seismic

energy.

Therefore, vibration effects of soil to upper structure are

drastically reduced.

Forces, accelerations and drifts are substantially reduced

During a Richter 8 Earthquake, a seismically isolated bridge During a Richter 8 Earthquake, a seismically isolated bridge

will behave as if it was experiencing a 5.5 earthquake. will behave as if it was experiencing a 5.5 earthquake.

Safest or most cost effective ways of designing a structure in

a highly seismic zone. 1515

The American River Bridge installed with FPS

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II--40 Mississippi River Bridge : Memphis, Tennessee40 Mississippi River Bridge : Memphis, Tennessee

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1818

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Infinity bridgeInfinity bridge--Tuned Mass DampersTuned Mass Dampers

2020

Lead rubber bearing (1975) Lead rubber bearing (1975) New Zealand BearingNew Zealand Bearing

�Steel Shims: Provide high

vertical stiffness to support

structure weight while limiting

lateral bulging of rubber

�Provide 10 to 30 % damping

�Large shear deformation

capacity

�Self – centering

�Life ~ 50 years

�Rubber Layers: Provide

lateral flexibility - Low

horizontal stiffness

�Lead plug: Provides source of

energy dissipation

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FullFull--Scale Bearing Prior to Dynamic TestingScale Bearing Prior to Dynamic Testing

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Shear Deformation of Elastomeric BearingShear Deformation of Elastomeric Bearing

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Linear Mathematical Model forLinear Mathematical Model forRubber Rubber BearingsBearings

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Elastomeric Bearing Hysteresis LoopsElastomeric Bearing Hysteresis Loops

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Spherical Sliding Bearing:Spherical Sliding Bearing:Friction Pendulum System (FPS)Friction Pendulum System (FPS)

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Idealized FPS Idealized FPS : Hysteresis : Hysteresis LoopLoop

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Computer Computer Software forSoftware forAnalysis of BaseAnalysis of Base--Isolated StructuresIsolated Structures

��ETABS : Linear ETABS : Linear and nonlinear analysis of buildingsand nonlinear analysis of buildings

��SAP2000 : General SAP2000 : General purpose linear and nonlinear purpose linear and nonlinear

analysisanalysis

��DRAINDRAIN--2D : Two2D : Two--dimensional dimensional nonlinear analysisnonlinear analysis

��3D3D--BASIS : Analysis BASIS : Analysis of baseof base--isolated buildingsisolated buildings

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��ConsistsConsists ofof describingdescribing thethe structurestructure inin termsterms ofof ‘system‘system

parameters’parameters’ suchsuch asas massmass andand stiffnessstiffness..

��TheThe mathematicalmathematical formulationformulation toto calculatecalculate thethe responseresponse ofof

systemsystem isis donedone usingusing STATESTATE SPACESPACE methodmethod..

Mathematical FormulationMathematical Formulation

systemsystem isis donedone usingusing STATESTATE SPACESPACE methodmethod..

��ThisThis methodmethod analyzesanalyzes thethe responseresponse ofof thethe systemsystem usingusing

bothboth displacementdisplacement andand velocityvelocity asas independentindependent variablesvariables ::

calledcalled asas statesstates..

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��ConsistsConsists ofof aa pistonpiston inin thethe damperdamper housinghousing filledfilled withwith

compoundcompound ofof siliconesilicone..

��TheThe damperdamper dissipatesdissipates thethe energyenergy throughthrough thethe movementmovement ofof

aa pistonpiston inin highlyhighly viscousviscous fluid,fluid, usingusing thethe conceptconcept ofof fluidfluid

orificingorificing ..

Viscous Damper : STUViscous Damper : STU

orificingorificing ..

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Piston Head

with Orifices

Accumulator HousingCylinderPiston Rod

Chamber 1Chamber 2

Rod Make up

Accumulator

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��SemiSemi--active control uses the building’s response active control uses the building’s response

and a feedback feature to develop control forcesand a feedback feature to develop control forces

��Requires a small power sourceRequires a small power source

��

Semi Semi –– Active ControlActive Control

��Variable stiffnessVariable stiffness

��Variable damperVariable damper

�� FrictionFriction

�� FluidFluid

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��Variable Stiffness DevicesVariable Stiffness Devices

��Controllable Friction DevicesControllable Friction Devices

�� Variable Orifice DampersVariable Orifice Dampers

Semi Semi –– Active Control DevicesActive Control Devices

�� Variable Orifice DampersVariable Orifice Dampers

�� Controllable Fluid Dampers and Controllable Fluid Dampers and

��Controllable Tuned Mass/Tuned Liquid DampersControllable Tuned Mass/Tuned Liquid Dampers

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Hydraulic dampersHydraulic dampers--ArasuArasu BridgeBridge--FukuokaFukuoka

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Magnetorheological DamperMagnetorheological Damper

��MajorMajor partpart ofof SASA ControlControl systemsystem..

��UseUse MRMR fluidsfluids forfor producingproducing controlcontrol forceforce..

��MRMR fluidsfluids consistconsist ofof micronmicron--sized,sized, magneticallymagnetically polarizablepolarizable

particlesparticles disperseddispersed inin aa carriercarrier mediummedium (silicon(silicon oil)oil)..

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��WhenWhen exposedexposed toto magneticmagnetic field,field, alignalign alongalong thethe magneticmagnetic

fluxflux..

��VeryVery lowlow powerpower requirementrequirement (less(less thanthan 5050W)W)

�� LowLow voltagevoltage ((55--1212V)V)..

Iron Particles

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Objective : To identify most promising control strategy for Objective : To identify most promising control strategy for

alleviating dynamic response of structure alleviating dynamic response of structure

Direct comparison of effectiveness of competing control Direct comparison of effectiveness of competing control

strategies applied to the test strategies applied to the test -- bed structure bed structure

(Building / Bridge)(Building / Bridge)

Benchmark Problems : IntroductionBenchmark Problems : Introduction

(Building / Bridge)(Building / Bridge)

Response : Measured to standardized set of loads : In terms Response : Measured to standardized set of loads : In terms

of defined performance indices. of defined performance indices.

Provide systematic way to evaluate newly developed control Provide systematic way to evaluate newly developed control

strategiesstrategies

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��Seismically excited nonlinear buildings Seismically excited nonlinear buildings

((OhtoriOhtori et al., 2004) et al., 2004)

��WindWind--excited tall buildings (Yang et al., 2004) excited tall buildings (Yang et al., 2004)

Benchmark Problems Benchmark Problems

��EarthquakeEarthquake--excited Cableexcited Cable--Stayed bridge Stayed bridge

(Dyke et al., 2003) (Dyke et al., 2003)

��Benchmark Highway Bridge (Agrawal et al., 2005)Benchmark Highway Bridge (Agrawal et al., 2005)

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Choice of Control SystemChoice of Control System

Important Features of the structure Important Features of the structure

Height, plan dimensions, symmetry / asymmetry Height, plan dimensions, symmetry / asymmetry

of the buildingof the building

Total span of the bridge, continuous / simply Total span of the bridge, continuous / simply Total span of the bridge, continuous / simply Total span of the bridge, continuous / simply

supported spanssupported spans

Number of continuous spansNumber of continuous spans

Seismic Zone Seismic Zone

Frequency of vibration: Past recordsFrequency of vibration: Past records4141

Benchmark Highway BridgeBenchmark Highway Bridge

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Case I: Bridge deck fixed to outrigger and isolated at the Case I: Bridge deck fixed to outrigger and isolated at the

abutments (16 control devices); Case II: Bridge deck also abutments (16 control devices); Case II: Bridge deck also

isolated at the outrigger (20 control devices) isolated at the outrigger (20 control devices)

Located near two major faults (~ 20 km) : strong seismic Located near two major faults (~ 20 km) : strong seismic

considerationsconsiderations

Benchmark Highway BridgeBenchmark Highway Bridge

considerationsconsiderations

Two spanTwo span--four lane continuous PC Highway bridge with four lane continuous PC Highway bridge with

skewed abutmentsskewed abutments

Six real biSix real bi--directional earthquake ground motionsdirectional earthquake ground motions

Evaluation criteria : Deck displacement and acceleration, Pier Evaluation criteria : Deck displacement and acceleration, Pier

base shear etc.base shear etc. 4343

Phase I: Bridge deck fixed to outrigger and isolated at the abutments.

(control devices =16)

Phase II: Bridge deck also isolated at the outrigger (control devices=20)

Located near two major faults (~ 20 km)

Two span - four lane continuous Highway bridge with abutments skewed

at 330

Bridge deck : 3 cells PC box girder , Central bent : PC outrigger

Total mass of the bridge = 4,237,544 kg , Mass of deck = 3,278,404 kg

Benchmark Highway BridgeBenchmark Highway Bridge

Total mass of the bridge = 4,237,544 kg , Mass of deck = 3,278,404 kg

Actual bridge : At each abutment : 4 traditional non-seismic elastomeric

pads and 4 viscous fluid dampers

Effect of Soil structure interaction is considered

Nonlinear Evaluation model : 430 DOFs (Phase I); 442 DOFs (Phase II)

Uncontrolled response : Bridge with LRBs at each deck end-abutment

junction

T= 0.813 sec

Six real bi-directional earthquake ground motions

Sample Passive ControlSample Passive Control : Nonlinear fluid viscous dampers : Nonlinear fluid viscous dampers

Sample SemiSample Semi--active Controlactive Control : MR dampers : MR dampers

Sample Active ControlSample Active Control :Ideal hydraulic actuators :Ideal hydraulic actuators

Maximum device capacity = 1000 Maximum device capacity = 1000 kNkN

16 Dampers ~ 50% control force of the deck mass16 Dampers ~ 50% control force of the deck mass

Various controllers Various controllers

16 Dampers ~ 50% control force of the deck mass16 Dampers ~ 50% control force of the deck mass

20 Dampers ~ 62% control force of the deck mass20 Dampers ~ 62% control force of the deck mass

Other isolators used :Other isolators used : FPS, VFPS,VFPI,FPS, VFPS,VFPI,

Other dampers used :Other dampers used : Viscous dampers, Variable dampers, Viscous dampers, Variable dampers,

PiezoPiezo--electric friction dampers, Pseudoelectric friction dampers, Pseudo--negative stiffness negative stiffness

dampers.dampers.4545

��Nonlinear fluid viscous dampers (1000 kN)Nonlinear fluid viscous dampers (1000 kN)

��8 Dampers provide ~ 50% control force of the deck mass8 Dampers provide ~ 50% control force of the deck mass

��10 Dampers provide ~ 62% control force of the deck 10 Dampers provide ~ 62% control force of the deck

massmass

Sample Passive Controllers Sample Passive Controllers

��Due to additional control devices at the center :Due to additional control devices at the center :

��Substantial reduction in pier base shear, base Substantial reduction in pier base shear, base

moment and midmoment and mid--span acceleration span acceleration

��Large increase in midLarge increase in mid--span deck displacement and span deck displacement and

isolator displacement isolator displacement 4646

�� Defined to evaluate functionality of the controller Defined to evaluate functionality of the controller

�� [ Controlled response / Uncontrolled response ] smaller values : [ Controlled response / Uncontrolled response ] smaller values :

superior performance of the device superior performance of the device

�� Evaluated in the Longitudinal (EW) and Transverse (NS) direction Evaluated in the Longitudinal (EW) and Transverse (NS) direction

�� Peak responses and Peak responses and NormedNormed responsesresponses

Evaluation Criteria and Earthquake Ground MotionsEvaluation Criteria and Earthquake Ground Motions

( )21

• = •∫ft

dtt

�� Six earthquake ground motions : Six earthquake ground motions : Represent global spectrum in Represent global spectrum in

terms of PGA , PGV and soil properties. terms of PGA , PGV and soil properties.

��North Palm Springs (1986) ChiNorth Palm Springs (1986) Chi--Chi (1999)Chi (1999)

��El Centro (1940) Northridge (1994)El Centro (1940) Northridge (1994)

��Turkey (1999) Kobe (1995) Turkey (1999) Kobe (1995)

( )0

• = •∫f

dtt

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FPS : SIMULINK model FPS : SIMULINK model

(Hysteretic model of frictional force of a sliding system)4848

Sliding isolators: Schematic diagram and Mathematical model Sliding isolators: Schematic diagram and Mathematical model

FPS VFPS VFPI FPS VFPS VFPI

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Force Force -- displacement loops : Chidisplacement loops : Chi--Chi (1999)Chi (1999)

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Bearing displacement Time History: ChiBearing displacement Time History: Chi--Chi (1999) EarthquakeChi (1999) Earthquake

Comparison : Peak base shearComparison : Peak base shear

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Comparison: Peak Isolator displacementComparison: Peak Isolator displacement

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Benchmark Cable Stayed BridgeBenchmark Cable Stayed Bridge

Control of cable stayed bridges : Unique and

Challenging problem

2nd international workshop on Structural control

(Hong Kong, 1996) : Group formed to develop a

benchmark control problem for bridges

Benchmark control problem for seismically excited

cable stayed bridges (2000) : Dyke et al.

Benchmark cable stayed bridgeBenchmark cable stayed bridge

Bill Emerson Memorial bridgeBill Emerson Memorial bridge 5555

Three earthquake records and wind loads Three earthquake records and wind loads

Base shear and base moment in the longitudinal Base shear and base moment in the longitudinal

and transverse directionand transverse direction

Deck shear and deck moment in the longitudinal Deck shear and deck moment in the longitudinal

Benchmark Cable Stayed BridgeBenchmark Cable Stayed Bridge

Deck shear and deck moment in the longitudinal Deck shear and deck moment in the longitudinal

and transverse directionand transverse direction

Evaluation criteria : Cable tension, Deck Evaluation criteria : Cable tension, Deck

displacement, base shear in pylonsdisplacement, base shear in pylons

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Missouri Cable Stayed BridgeMissouri Cable Stayed Bridge

Benchmark Bridge ModelBenchmark Bridge Model

Benchmark Bridge ModelBenchmark Bridge Model

Earthquakes UsedEarthquakes UsedEl Centro

PGA = 0.36g

Gebze Turkey

PGA = 0.26g

Evaluation CriteriaEvaluation Criteria

�� Peak Responses (Peak Responses (JJ11

–– JJ66))

–– Base shear Base shear –– Shear at deck level Shear at deck level

–– Overturning moment Overturning moment –– Moment at deck levelMoment at deck level

–– Cable tensionCable tension

–– Deck displacement at abutmentDeck displacement at abutment

�� Normed Responses (Normed Responses (JJ77

–– JJ1111

))�� Normed Responses (Normed Responses (JJ77

–– JJ1111

))

–– Base shear Base shear –– Shear at deck level Shear at deck level

–– Overturning moment Overturning moment –– Moment at deck levelMoment at deck level

–– Cable tensionCable tension

�� Control Strategy (Control Strategy (JJ1212

–– JJ1818

))

–– Peak control force and device strokePeak control force and device stroke

–– Peak and total power requiredPeak and total power required

–– Number of control devices and sensorsNumber of control devices and sensors

Seismic Control System Seismic Control System

Using MR DampersUsing MR Dampers

� Sensors

– Five accelerometers

– Four displacement transducers– Four displacement transducers

– 24 force transducers for measuring control forces

� Control Devices

– 24 MR dampers (capacity: 1000 kN/each)

Dynamic Model Dynamic Model s of s of MR DampersMR Dampers

Models for small-scale

dampers

Bingham model (Stanway

et al. 1985, 1987)et al. 1985, 1987)

Simple Bouc-Wen model

(Spencer et al. 1997)

Model for large-scale damper

Modified Bouc-Wen model

(Spencer et al. 1997)24 MR Dampers:1000 kN Capacity

Optimized Parameters of Dynamic Model Optimized Parameters of Dynamic Model

for MR Dampersfor MR Dampers

Dynamic Degrees of FreedomDynamic Degrees of Freedom

Reduced Order Model

with 30 States

Control Strategy for Semiactive ControlControl Strategy for Semiactive Control

TimeTime--History History Response : Base Response : Base Shear Shear Force Force

• El Centro earthquake: 71% reduction in peak

kNkN

kNkN

• Gebze Turkey earthquake: 64% reduction in peak

• Mexico City earthquake: 54% reduction in peakkNkN

First generation structures First generation structures : without any code / systematic : without any code / systematic

proceduresprocedures

Design and analysis procedure for Design and analysis procedure for Second Generation Second Generation

StructuresStructures is available. Still catastrophic failures are is available. Still catastrophic failures are

ConclusionsConclusions

observed in severe earthquake attacks. observed in severe earthquake attacks.

Based on the performance of conventionally designed Based on the performance of conventionally designed

structures, there is a structures, there is a need forneed for Third Generation structuresThird Generation structures. .

Practically : use of isolators (LRB and FPS) and limited Practically : use of isolators (LRB and FPS) and limited

applications (Viscous and MR) of dampers in the world. applications (Viscous and MR) of dampers in the world.

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ConclusionsConclusions

Vibrations : Seismic and windVibrations : Seismic and wind

Experimental validation of devices is necessaryExperimental validation of devices is necessary

Inclusion of clauses in IS codesInclusion of clauses in IS codes

Newly developed control devices can be implemented in Newly developed control devices can be implemented in Newly developed control devices can be implemented in Newly developed control devices can be implemented in

constructions.constructions.

Devices can be used for retrofitting of existing structures. Devices can be used for retrofitting of existing structures.

Commonly used isolators : LRB, FPSCommonly used isolators : LRB, FPS

Commonly used dampers: Viscous dampers, Commonly used dampers: Viscous dampers, ViscoVisco--elastic elastic

dampers, Friction dampers.dampers, Friction dampers.6969

Thank you..Thank you..

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