Vol. 69 Núm. 286 (2018): Hormigón y Acero

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ASOCIACIÓN ESPAÑOLA DE INGENIERÍA ESTRUCTURAL

Revista cuatrimestral de

HORMIGÓN

y ACERO

HORMIGÓN Y ACERO

Septiembre-Diciembre 2018 | volumen 69 - número 286

Septiembre-Diciembre 2018

| volumen 69 - número 286

ISSN: 0439-5689

www.elsevierciencia.com/hya Seismic isolation of structures, Part II: A case study using the RNC isolator

Aislamiento sísmico de estructuras, parte II : un caso práctico con el aislador RNC

Mohammed Ismail . . . 177

Analysis of shear resisting actions by means of optimization of strut and tie models taking into account crack patterns

Análisis de mecanismos resistentes a cortante mediante optimización de modelos de bielas y tirantes considerando patrones de fi suración

Jesús Miguel Bairán, Antonio Marí, Antoni Cladera . . . 197

Análisis de un caso de inestabilidad lateral de un viga de hormigón pretensado de gran luz en fase de izado Case-study of lateral instability of a long-span prestressed concrete girder during lifting

Albert de la Fuente Antequera, Sergio Henrique Pialarissi Cavalaro, Jesús Miguel Bairán García . . . 207

Proportioning, fresh-state properties and rheology of self-compacting concrete with fi ne recycled aggregates Dosifi cación, propiedades en estado fresco y reología de hormigón autocompactante con áridos reciclados fi nos

Diego Carro-López, Belén González-Fonteboa, Fernando Martínez-Abella, Iris González-Taboada, Jorge de Brito,

Fernando Varela-Puga . . . 213

Mejora de la sostenibilidad y el comportamiento en servicio de estructuras de hormigón mediante el uso de fi bras metálicas recicladas

Improvement in sustainability and performance in service of concrete structures by using recycled metal fi bres

Giancarlo Groli, Alejandro Pérez Caldentey . . . 223

Estudio de las propiedades mecánicas residuales de hormigones expuestos a altas temperaturas Study of residual mechanical properties of concretes after exposure to high temperatures

Francisco B. Varona, Francisco J. Baeza, Salvador Ivorra . . . 235

Estudio de la sensibilidad a su propia deformación de escorias de alto horno activadas alcalinamente y reforzadas con fi bra de carbono

Sensitivity study of self-sensing strain capacity of alkali-activated blast furnace slag reinforced with carbon fi bres

F. Javier Baeza de los Santos, Josep Lluís Vilaplana Abad, Óscar Galao Malo, Pedro Garcés Terradillos . . . 243

Puentes mixtos continuos de ferrocarril en zona sísmica en el norte de Argelia Continuous railway composite bridges in a seismic zone in Northern Algeria

Diego Cobo del Arco, Ingrid Raventós Dudous, Steffen Mohr . . . 251

Revista cuatrimestral de la ASOCIACIÓN ESPAÑOLA DE INGENIERÍA ESTRUCTURAL (ACHE)

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Septiembre - Diciembre 2018 | volumen 69 – número 286

REVISTA CUATRIMESTRAL DE LA ASOCIACIÓN ESPAÑOLA DE INGENIERÍA ESTRUCTURAL (ACHE)

Etsi Caminos, Canales y Puertos

Avda. Profesor Aranguren, s/n. Ciudad Universitaria. 28040 Madrid

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Disponible en

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Disponible en

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Septiembre-Diciembre 2018 | volumen 69 - número 286

September-December 2018

|

volume 69 - number 286

Seismic isolation of structures, Part II: A case study using the RNC isolator

Aislamiento sísmico de estructuras, parte II : un caso práctico con el aislador RNC

Mohammed Ismail. . . 177 Analysis of shear resisting actions by means of optimization of strut and tie models taking into account

crack patterns

Análisis de mecanismos resistentes a cortante mediante optimización de modelos de bielas y tirantes considerando patrones de fi suración

Jesús Miguel Bairán, Antonio Marí, Antoni Cladera . . . 197 Análisis de un caso de inestabilidad lateral de un viga de hormigón pretensado de gran luz en fase de izado

Case-study of lateral instability of a long-span prestressed concrete girder during lifting

Albert de la Fuente Antequera, Sergio Henrique Pialarissi Cavalaro, Jesús Miguel Bairán García . . . 207 Proportioning, fresh-state properties and rheology of self-compacting concrete with fi ne recycled aggregates

Dosifi cación, propiedades en estado fresco y reología de hormigón autocompactante con áridos reciclados fi nos

Diego Carro-López, Belén González-Fonteboa, Fernando Martínez-Abella, Iris González-Taboada, Jorge de Brito,

Fernando Varela-Puga . . . 213 Mejora de la sostenibilidad y el comportamiento en servicio de estructuras de hormigón mediante el uso

de fi bras metálicas recicladas

Improvement in sustainability and performance in service of concrete structures by using recycled metal fi bres

Giancarlo Groli, Alejandro Pérez Caldentey . . . 223 Estudio de las propiedades mecánicas residuales de hormigones expuestos a altas temperaturas

Study of residual mechanical properties of concretes after exposure to high temperatures

Francisco B. Varona, Francisco J. Baeza, Salvador Ivorra . . . 235 Estudio de la sensibilidad a su propia deformación de escorias de alto horno activadas alcalinamente

y reforzadas con fi bra de carbono

Sensitivity study of self-sensing strain capacity of alkali-activated blast furnace slag reinforced with carbon fi bres

F. Javier Baeza de los Santos, Josep Lluís Vilaplana Abad, Óscar Galao Malo, Pedro Garcés Terradillos . . . 243 Puentes mixtos continuos de ferrocarril en zona sísmica en el norte de Argelia

Continuous railway composite bridges in a seismic zone in Northern Algeria

Diego Cobo del Arco, Ingrid Raventós Dudous, Steffen Mohr . . . 251

SUMARIO | CONTENTS

Revista cuatrimestral de la ASOCIACIÓN ESPAÑOLA DE INGENIERÍA ESTRUCTURAL (ACHE)

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Availableonlineat

ScienceDirect

www.e-ache.com HormigónyAcero2018;69(286):177–195 www.elsevierciencia.com/hya

Seismic

isolation

of

structures,

Part

II:

A

case

study

using

the

RNC

isolator

Aislamiento

sísmico

de

estructuras,

parte

ii

:

un

caso

práctico

con

el

aislador

RNC

Mohammed

Ismail

a,b,c

a_SENER_Ingeniería_y_Sistemas,₀₈₂₉₀_Barcelona,_Spain

b_Structural_Engineering_Department,_Zagazig_University,₄₄₅₁₉_Zagazig,_Egypt c_Universitat_Politécnica_de_Catalunya_–_{BarcelonaTECH}_(UPC),₀₈₀₃₄_Barcelona,_Spain

Received26March2017;accepted13December2017 Availableonline13February2018

Abstract

Thepresentpaperisthesecondoftwocompanionpapers.Theobjectiveofthispaperistominimizetwistofisolatedasymmetricstructures,together

withtheirtorsionalpoundingwithadjacentstructures,consideringinsufficientseismicgapsandstrongnear-faultgroundmotions.Concisely,the

presentstudyattemptstoprovideefficientseismicisolationundertheabovechallengingconditions.Theusedisolationsystemisreferredto

Roll-in-Cage(RNC)isolator.AmongthefeaturesoftheRNCisolatoraretwocharacteristicsthathelpachievingtheobjectivesofthepaper.The

firstistheindependencyofitsbearingandpre-yieldstiffnessmechanisms.Suchindependencyallowsforaccuratetuningoftheisolatorspre-yield

stiffnesstoshifttheircenterofrigidity,attheisolationlevel,tocoincidewiththeasymmetricsuperstructure’scenterofmassabovethatlevel.

Thisallowsforminimizingthestructuraltwistofanisolatedasymmetricstructure.Thesecondfeatureistheinherentbuffermechanismofthe

RNCisolator,whichdrawsdownanypossibleseismicpoundingoftheisolatedsuperstructure,withadjacentstructures,tooccuronlywithinthe

isolationbearingitself.Thisleadstoseismicpounding-freesuperstructureunderlimitedseismicgaps.Theobtainedresultsshowthatutilizing

theRNCisolatorthiswayisabletominimize,oreveneliminate,theout-of-plandisplacementresponsesofasymmetricisolatedstructuresunder

severenear-faultearthquakes,andconsequently,minimizesamajorcauseofstructuraldamageduetostructuraltorsionalpoundingwithclosely

spacedadjacentstructuresundersuchdestructivegroundmotions.

Keywords:SeismicIsolation;Asymmetricstructures;Pounding;FEM;RNCisolator

Resumen

Esteartículoeselsegundodedosartículoscomplementarios.Su objetivoesreducirlatorsióndeestructurasasimétricasaisladas,asícomo

elgolpeteotorsionalconestructurasadyacentes,considerandoloscasosdeespacioinsuficienteentrelasestructurasydefuertesmovimiemtos

sísmicosporproximidadaunafalla,pormediodelaisladorroll-in-cage(RNC).Deformaconcisa,esteestudiointentaproporcionarunaislamiento

sísmicoeficienteconlascondicionesdifícilesmencionadasanteriormente.ElsistemadeaislamientoutilizadohacereferenciaalaisladorRNC.

EntrelascaracterísticasdelaisladorRNChaydosqueayudanalograrlosobjetivosdelartículo.Laprimeraeslaindependenciadesusmecanismos

derigidezderodamientoydepredicciónderendimiento.Estaindependenciapermiteunajusteprecisodelarigidezdepredicciónderendimiento

delosaisladoresparadesplazarsucentroderigidez,respectoalniveldeaislamiento,paraquecoincidaconelcentrodemasadelasuperestructura

asimétricaporencimadeesenivel.Ellopermitereducirelgiroestructuraldeunaestructuraasimétricaaislada.Lasegundacaracterísticaes

elmecanismodeamortiguacióninherentedelaisladorRNC,queeliminacualquierposiblegolpeteosísmicodelasuperestructuraaislada,con

estructurasadyacentes,paraqueocurrasolodentrodelpropiorodamientodeaislamiento.Elloproduceunasuperestructurasingolpeteosísmicoen

condicionesdeinsuficienteespacioparamovimientodebidoalsismo.LosresultadosobtenidosmuestranquelautilizacióndelaisladorRNCdeesta

E-mailaddresses:[email protected],[email protected],[email protected]

https://doi.org/10.1016/j.hya.2017.12.001

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178 M.Ismail/HormigónyAcero2018;69(286):177–195

manerapuedereduciro,incluso,eliminarlasrespuestasdedesplazamientofueradelplanodelasestructurasasimétricasaisladasenterremotos

intensoscercadelafallay,enconsecuencia,reduceunacausaimportantededa˜noestructuraldebidoalgolpeteotorsionalestructuralconestructuras

adyacentesconpocoespacioentresíconmovimientosdetierratandestructivos.

Palabrasclave: Aislamientosísmico;Estructurasasimétricas;Golpeteo;FEM;AisladorRNC

1. Introduction

Thispaperisthesecondoftwocompanionpapers.It intro-ducestheseismicisolationconceptandaddressesthepossibility of nearly eliminating, or at least minimizing, the torsional responses of isolated asymmetric structures using the Roll-in-Cage (RNC) isolator considering near-fault (NF) ground motions.Then,theoutcomeofthisstudyisemployedinto fur-ther study onthe abilityof the RNCisolator topartiallyand entirelyeliminatetorsionalseismicpoundingofisolated asym-metricstructureswiththeirclosely-spacesurroundingadjacent structures under the same severe NF ground motions, which arerichofdisplacementandvelocitypulses.Tominimize tor-sionalresponses,theRNCisolatorhasaninherentlyindependent bearingandpre-yieldstiffnessmechanisms.Therefore,theRNC isolatorsarearrangedintofoursetswithunequalpre-yield elas-ticstiffnessunderneaththeasymmetricstructure.Suchdifferent elasticstiffnessareaccuratelytunedtoshifttheisolators’center ofrigidityattheisolationleveltocoincidewiththestructural centerofmassabovetheisolationlevel.Topreventdirectseismic poundingof theRNC-isolatedsuperstructurewithits closely-spacedadjacentstructures,theRNCisolatorisprovidedwith aninherentself-stopping(buffer)mechanismtolimitthepeak lateralbearingdisplacementandconsequentlythepeaklateral structuraldisplacementtoapresetdesignvaluebythedesigner, which is particularly usefulin case of having insufficient or limitedseismicseparationgapsbetweenadjacentstructures.

2. DynamicbehaviorimprovementofRNC-isolated asymmetricstructures

2.1. Torsionalresponseminimizationorelimination

Inthispaper,theRNCisolationisachievedintwodifferent ways.ThefirstisthroughusingonesetofRNCisolatorshaving thesamecharacteristics,especiallythelateralpre-yieldstiffness, oneisolatorundereachcolumn.Thisachievesseismicisolation butkeepsthe eccentricitiesbetweenthestructure’s centersof mass(CM)andrigidity(CR)unchangedduetotheadded uni-formhighflexibilityattheisolationlevel.Thereforeanddespite thefactthattheisolatedstructurewillbehavenearlyasarigid body,torsionalstructuralresponseswillstillexist.Alternatively, throughtheotherwayofachievingRNCisolationinthispaper, thetorsionalresponseoftheRNC-isolatedasymmetricstructure ismitigatedoreveneliminatedbyusingfoursetsoftheRNC isolators,whosehorizontalpre-yieldstiffnesscouldbeselected individually, i.e. an elastic stiffness value in X direction and

anothervalueinYdirectionforeachisolator’sset.Thisallows forshiftingthecenterofstiffnessoftheRNC-isolated asymmet-ricstructure,atitsisolationlevel,tocoincidewithitscenterof mass.Asaresult,torsionalstructuralresponsesaretheoretically eliminatedduetothelateraldominantbehavioroftheaddedhigh flexibilityattheisolation level,whichhasaCRcoincidentto theCMoftheasymmetricstructureabovetheisolationlevel.

Fig.1showsthein-planarrangementoftheRNCisolator’s foursets havingdifferentlateral pre-yieldstiffnesstoachieve coincidenceoftheRNCisolators’CRandtheasymmetric struc-tures’ CMinbothXandY directions.Theselected valuesof effectiveisolatorstiffnesskeff inXandYdirectionsarechosen

bytrialanderrormethodtoachieveafinaltoleranceof0.24% and0.21%inXandYdirections,respectively,betweentheCR attheisolationlevelandthestructure’sCMabovethatlevel.In thispaper, thewayofachievingseismicisolation usingRNC isolators ofdifferent lateral stiffness,toalmost eliminate tor-sionalresponses,is referredtoas “improved”RNCisolation. TheotherwayofseismicisolationusingoneRNCisolatorset with asinglevalue of lateralstiffness is referred toas “non-improved”RNCisolation.Thenon-improvedRNCisolatorsset hasthesamein-planarrangementasinFig.1butwithauniform lateraleffectivestiffnesskeffinXandYdirectionsthatprovides

nearlythesameisolationperiodasinthecaseofimprovedRNC isolation.

Performing modal analysisusing SAP2000,three casesof the asymmetric structure are considered; the fixed-base case, thenon-improvedRNCisolationcase,andtheimprovedRNC isolationcase.Thefundamentalmode’sdeformedshapeofeach caseisplottedin3D,withascalefactorof100,inFigs.2and3.

Fig. 2(a and b) shows that the fixed-base asymmetric struc-ture experiences severe torsional response, which is zero at the base massandmaximum atthe topmost floor. This indi-catesthatthewholestructureistwistedasaverticalcantilever aroundaverticalaxispassingthroughitsCRduetotheexisting eccentricitiesbetweenits CMandCRinXandYdirections.

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M.Ismail/HormigónyAcero2018;69(286):177–195 179

Mat foundation of asymmetric structure

Set 3

RNC Isolator

RNC Isolator of RNC isolators

Keff−x = 1110 kN/m

Keff−y = 1270 kN/m

Set 1

of RNC isolators

Set 4

Origin

X axis

Y axis

ex

of RNC isolators

Center of mass Center of rigidity

Set 2

of RNC isolators

Figure1. PlanviewoftheRNC-isolatedasymmetricstructure’sfoundationshowingthearrangementofRNCisolatorsandtheirgrouping.

Structure before deformation

(a) (b)

2

3

4

1

Fundamental mode of Fixed-base asymmetric structure,

Plan view

Fundamental mode of Fixed-base asymmetric structure,

Elevation view

Structure after deformation

Structure after

deformation

Figure2.Fundamentalmodeofvibrationofthefixed-baseasymmetricstructure:(a)elevationview;(b)planview.

demonstratedbyFig.4(aandb)usingtheimprovedRNC isola-tion,whichaimsatforcingtheasymmetricstructurestobehave as the symmetricones, whichexhibit no torsionalresponses,

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Structure before deformation Structuredeformation after Structure before deformation

(a) (b)

Fundamental mode of RNC-isolated asymmetric structure,elevation view

Before improvement (Equal lateral stiffness of RNC isolators)

Fundamental mode of RNC-isolated asymmetric structure,plan view

Before improvement (Equal lateral stiffness of RNC isolators)

2

3

4 1

Figure3.FundamentalmodeofvibrationoftheRNC-isolatedasymmetricstructurebeforeimprovement:(a)elevationview;(b)planview.

+

Fundamental mode of RNC-isolated asymmetric structure,elevation view

After improvement (Un3equal lateral stiffness of RNC isolators)

Fundamental mode of RNC-isolated asymmetric structure, plan view

After improvement (Un3equal lateral stiffness of RNC isolators)

(b)

2 3

4 1

(a)

Figure4.FundamentalmodeofvibrationoftheRNC-isolatedasymmetricstructureafterimprovement:(a)elevationview;(b)planview.

axes.Thisismainlyattributedtotheeliminationofeccentricities betweenbothCMandCRoftheisolatedasymmetricstructureby meansofintroducingfoursetsofflexibleRNCisolatorshaving aCRcoincidenttothestructure’sCM.

Moreassessmentof theimprovedRNCisolationiscarried out through performingnonlinear timehistory analysisusing SAP2000.Themainobjectiveistochecktheout-of-planpeak displacementresponsesofthetopmostfourcornerpointsshown in Figures 2(b), 3(b) and 4(b) under uni- and bidirectional NF groundmotions of Table3, companion paper PartI.The resultsareshowninFigs.5–7underunidirectionalX, unidirec-tionalYandbidirectionalXYseismiccomponents,respectively, consideringfixed-base,non-improvedandimprovedRNC iso-lationcases.UnderunidirectionalXgroundmotions,Fig.5(a–c) show both in-plan and out-of-plan peak displacement struc-turalresponses,atthetopmostfourcornerpoints,considering fixed-base,non-improved andimproved RNCisolationcases, respectively, at an isolation period of 3.0s. At each corner point, the in-plan peak displacement response is normalized to itself,while the out-of-plan response is normalized tothe

correspondingin-planone.AccordingtoFig.5(aandb),itseems obviousthatthepeakout-of-plandisplacementresponse repre-sentsaround30–50%ofthecorrespondingin-plandisplacement response atthe samecorner pointconsideringfixed-baseand non-improvedRNCisolationcases,respectively.Suchamount ofout-of-planresponsesunderunidirectionalXgroundmotion is attributed to the out-of-plan structural eccentricity ey of

0.9020m. Ontheotherhand,suchout-of-plan peak displace-mentresponsesinYdirectionarenearlynonexistentinthecase ofimprovedRNCisolationinFig.5(c)duetominimizingeyto

zerowithafinaltoleranceof0.21%.

InFig.6,thesamenormalizedresponsequantitiesofFig.5

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Fixed−base case

T1 m = 0.477 sec

Unidirectional kobe 0° (in X direction)

Unidirectional northridge 18° (in X direction) Topmost corner points 100

(a) (b) (c)

80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0

1 2 3 4 1 2 3 4 1 2 3 4

1 2 3 4

1 2 3 4 1 2 3 4 1 2 3 4

Topmost corner points

P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement

Topmost corner points Topmost corner points

Topmost corner points Topmost corner points Topmost corner points

Peak X displacement normalized to itself at a corner point

Peak Y displacement normalized to X displacement at a corner point Unidirectional northridge 18°

(in X direction)

Unidirectional northridge 18° (in X direction)

Unidirectional San−Fernando 164° (in X direction)

Isolated (Non−improved)

T1 m = 3.030 sec

Isolated (improved)

T1 m = 3.022 sec

Figure5.NormalizedpeakdisplacementsinXandYdirectionsatthetopmostcornerpointsoftheasymmetricstructureundertheunidirectionalcomponentsKobe 0◦,Northridge18◦andSanFernando164◦earthquakesinXdirection:(a)fixed-basecase;(b)non-improvedbase-isolatedcase;(c)improvedbase-isolatedcase.

Sucheccentricityisminimizedtozerowithafinalinaccuracy of0.24%bymeansoftheimprovedRNCisolationtooutput min-imalout-of-planpeakdisplacementresponsesinXdirection,as demonstratedbyFig.6(c).

Underbidirectionalground motions, thepeak relative dis-placementresponses,atthesamefourcornerpoints,arefound for the same three cases of fixed-base, non-improved and improvedRNCisolation.TheresultsareshowninFig.7(a–c). Although the ey isgreater thanex and theexcitation

compo-nentsinXdirectionarestrongerthanthoseinYdirection,most peakrelative displacementresponsesinY directionare lower

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Fixed−base case T1 = 0.477 sec Unidirectional kobe 90°

(in Y direction)

Isolated (Non−improved) T1 = 3.030 sec Unidirectional kobe 90°

(in Y direction)

Isolated (improved) T1 = 3.022 sec Unidirectional kobe 90°

(in Y direction)

P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement P eak nor maliz e d displacement 100 50 150 0 100 50 150 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0

1 2 3 4 1 2 3 4 1 2 3 4

Unidirectional northridge 288° (in Y direction)

Unidirectional San−Fernando 254° (in Y direction)

Peak X displacement normalized to Y displacement at the same corner point

Peak Y displacement normalized to itself at a corner point

(a) (b) (c)

Figure6.NormalizedpeakdisplacementsinXandYdirectionsatthetopmostcornerpointsoftheasymmetricstructureundertheunidirectionalcomponentsKobe 90◦,Northridge288◦andSanFernando254◦earthquakesinYdirection:(a)fixed-basecase;(b)non-improvedbase-isolatedcase;(c)improvedbase-isolatedcase.

non-improvedRNCisolation,whichisobviousunderKobeand Northridgeearthquakes.Thiscanbeparticularlyusefulunder relativelylimited seismicgapsbetweenadjacent structuresto mitigateoreventoavoiddirectstructuralpounding.Moreover, the peak structural displacementresponses atthe fourcorner points in Figure 7(c) are almost the same under each earth-quakeinXandYdirections,whichemphasizesthenearly-perfect translationalrigidbodybehavioroftheimprovedRNC-isolated structure,withoutexhibitingrotationaboutaverticalaxis, con-trarytothecasesofFig.7(aandb).

2.2. RNCisolationefﬁciency

ThissectioninvestigatestheinfluenceofimprovedRNC iso-lationontheisolationefficiencycomparedtothenon-improved RNCisolationandthefixed-basecases.Figs.8–10displaythe correspondingpeakabsolutestructuralaccelerations,atthesame topmost four corner points, tothe displacement responses of

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Fixed−base case T1 = 0.477 sec Bidirectional kobe (in XY directions)

Isolated (Non−improved) T1 = 3.030 sec Bidirectional kobe

(in XY directions)

Isolated (improved) T1 = 3.022 sec Bidirectional kobe

(in XY directions)

Bidirectional northridge (in XY directions)

Bidirectional San−Fernando (in XY directions)

Bidirectional San−Fernando (in XY directions) Bidirectional northridge

(in XY directions)

P

eak displacement (m)

P

0.25 0.5 0.4 0.3 0.2 0.1 0 0.5 0.4 0.3 0.2 0.1 0 0.2 0.15 0.1 0.05 0 0.25 0.2 0.15 0.1 0.05 0 0.2 0.15 0.1 0.05 0 0 0.2 0.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4

1 2 3 4 1 2 3 4 1 2 3 4

Peak displacement in X direction

Peak displacement in Y direction

(a) (b) (c)

Figure7.PeakdisplacementsinXandYdirectionsatthetopmostcornerpointsoftheasymmetricstructureundersimultaneousbidirectionalcomponentsofKobe, NorthridgeandSanFernandoearthquakesinXandYdirections,respectively:(a)fixed-basecase;(b)non-improvedbase-isolatedcase;(c)improvedbase-isolated case.

fixed-basecaseofFig.8(a),especiallytheout-of-plan acceler-ationsinFig.8(c),duetotheimprovedRNCisolation.

Similarly, Figs. 9(b and c) and 10(b and c) under unidirectional Y and bidirectional XY ground motions, respectively, demonstrate the RNC isolator’s ability for efficient protection against severe NF ground motions com-pared to Figs. 9(a) and 10(a). However, the variations between acceleration responses of improved and non-improved RNC isolation cases in Figs. 9 and 10 seem to be insignificant, if compared to the fixed-base case

in each figure, as they depend mainly on the excitation characteristics.

3. Torsionalpoundingeliminationwithadjacent structures

3.1. EfﬁciencyoftheRNCisolator’sbuffermechanism

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(in X direction)

Isolated (Improved) T1 = 3.022 sec Unidirectional kobe 0°

(in X direction)

Unidirectional northridge 18° (in X direction)

Unidirectional San−Fernando 164° (in X direction)

P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) 30 3 2 0 1 3 2 0 5 4 3 2 1 0 5 4 3 2 1 0 3 2 1 0 3 2 1 0 1 20 10 0 30 20 10 0 60 40 20 0

1 2 3 4 1 2 3 4 1 2 3 4

(a) (b) (c)

Peak absolute acceleration in X direction Peak absolute acceleration in Y direction

Figure8.PeakabsoluteaccelerationsinXandYdirectionsatthetopmostcornerpointsoftheasymmetricstructureundertheunidirectionalcomponentsKobe0◦, Northridge18◦andSanFernando164◦earthquakesinXdirection:(a)fixed-basecase;(b)non-improvedbase-isolatedcase;(c)improvedbase-isolatedcase.

structuresanditsmitigation,orevenelimination,undersevere NF earthquakes considering limited seismic gaps. Then, the influenceofsuchmitigationoreliminationofseismicpounding ontheRNC-isolatedstructuralresponsesisinvestigated, consid-eringthethreecasesoffixed-base,non-improvedRNCisolation andimprovedRNCisolation,whichaimsatsignificant reduc-tion of torsional effects. Particularly, theimpact of improved RNCisolationonseismicpoundingmitigationoreliminationis highlighted.

Figure 3 (companion paper, part I) shows the considered RNC-isolatedasymmetricstructuresurroundedfromtwosides byanL-shaperigid structure,ofthesameheight,toconsider poundinginXandYdirections.Thetopmostflooredgepoints

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(in Y direction)

Isolated (Improved) T1 = 3.022 sec Unidirectional kobe 90°

(in Y direction)

Unidirectional northridge 288° (in Y direction)

Unidirectional San−Fernando 254° (in Y direction)

P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) P eak absolute acceler ation (m/sec 2) 50 2.5 2 1.5 1 0.5 0 2.5 2 1.5 1 0.5 0 5 4 3 2 1 0 5 25 20 15 10 5 0 4 3 2 1 0 3 2 1 0 3 2 1 0 40 30 0 10 20 50 40 30 0 10 20

1 2 3 4 1 2 3 4 1 2 3 4

(a) (b) (c)

Figure9.PeakabsoluteaccelerationsinXandYdirectionsatthetopmostcornerpointsoftheasymmetricstructureundertheunidirectionalcomponentsKobe90◦, Northridge288◦andSanFernando254◦earthquakesinYdirection:(a)fixed-basecase;(b)non-improvedbase-isolatedcase;(c)improvedbase-isolatedcase.

earthquakes.Inaddition,theRNC-isolator’sbufferaimsat min-imizingorpreventingstructuralpoundingasitdrawsdownany possiblepounding ofthe superstructuretobe onlywithinthe solidboundaryoftheRNCisolator’smetallicbody.Thiscould beparticularlyusefulforseismicisolationunderinsufficientor limited seismic gaps that may result in severestructural and nonstructuraldamage duetostructuralpoundingunderstrong earthquakes.

Fig.11demonstratestheabilityoftheRNCisolatorto elimi-nate,oratleasttominimize,structuralpoundingunderninecases ofloadingregardingbothnon-improvedandimprovedRNC iso-lationataseismicgapof45.0cm,aRNCdesigndisplacement of40.0cmandan isolationperiod of3.0s.Eachloadcaseis

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Fixed−base case T1 = 0.477 sec Bidirectional kobe

(in XY directions)

Isolated (Non−improved) T1 = 3.030 sec Bidirectional kobe (in XY directions)

Isolated (Improved) T1 = 3.022 sec Bidirectional kobe

(in XY directions)

Bidirectional San−Fernando (in XY directions)

P eak accel. (m/sec2) P eak accel. (m/sec2) P eak accel. (m/sec2) P eak accel. (m/sec2) P eak accel. (m/sec2) P eak accel. (m/sec2) P eak accel. (m/sec2) P eak accel. (m/sec2) P eak accel. (m/sec2) 50 4 3 2 1 0 4 3 2 1 0 6 4 2 0 6 4 2 0 0 1 2 3 4 0 1 2 3 4 40 30 20 10 0 40 60 80 20 0 40 30 20 10 0

1 2 3 4 1 2 3 4 1 2 3 4

(a) (b) (c)

Figure10.PeakabsoluteaccelerationsinXandYdirectionsatthetopmostcornerpointsoftheasymmetricstructureundersimultaneousbidirectionalcomponents ofKobe,NorthridgeandSanFernandoearthquakesinXandYdirections,respectively:(a)fixed-basecase;(b)non-improvedbase-isolatedcase;(c)improved base-isolatedcase.

poundingisminimizedtoamaximumintensityof1.46×104kN inXdirectionunderunidirectionalXNorthridgegroundmotion component.

Approximately,thepeakstructuralpoundingratioafterand before the application of improved RNC isolation is 3.95%, which means significant structural pounding reduction under the same loading and structural conditions, disregarding the absolutestructuralpoundingeliminationundertwothirdsofthe sixcasesofpounding.Moreover,Fig.11(a)showssignificant

out-of-plan pounding under unidirectional ground motions, which isnot the caseunder improved RNCisolation casein

Fig.11(b).

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Peak structure pounding at the topmost floor levels

Isolated (Non-Improved), T1 = 3.0 sec

Seismic gap = 45 cm, RNC design displacement = 40 cm

Peak structure pounding at the topmost floor levels

Isolated (Improved), T1 = 3.0 sec

Seismic gap = 45 cm, RNC design displacement = 40 cm Exciting earthquakes (unideirectional and bidirectional) Pounding in X direction

(a)

(b) 4x 10

5

x 105

3

2

1

0

4

3

2

1

0

Pounding in Y direction

Str

ucture pounding (kN)

Str

ucture pounding (kN)

Kobe−X Kobe−Y Kobe−XY Northridge−X Northridge−Y Northridge−XY S.Fernando−X S.Fernando−Y S.Fernando−XY

Kobe−X Kobe−Y Kobe−XY Northridge−X Northridge−Y Northridge−XY SanFernando−X SanFernando−YSamFernando−XY Pounding in X direction

Exciting earthquakes (unideirectional and bidirectional)

Figure11.PeakstructurepoundingwithadjacentstructuresatthetopmostfloorsinXandYdirectionsunderuni-andbidirectionalnear-faultgroundmotions:(a) non-improvedRNC-isolatedcase;(b)improvedRNC-isolatedcase.

Peak RNC isolator inner pounding (for a single isolator)

Isolated (Non-Improved), T1 = 3.0 sec

Kobe−X Kobe−Y Kobe−XY Northridge−X Northridge−Y Northridge−XY SanFernando−X SanFernando−Y SamFernando−XY Pounding in X direction

(a)

(b)

Pounding in X direction Pounding in Y direction

RNC pounding (kN)

x 104

x 104 3

2.5

2

1.5

1

0.5

0

3

2.5

2

1.5

1

0.5

0

Figure12.PeakinnerpoundingofaRNCisolatorinXandYdirectionsunderuni-andbidirectionalnear-faultgroundmotions:(a)non-improvedRNC-isolated case;(b)improvedRNCisolatedcase.

isolatorpoundingunderthesameprevioussixloadcases hav-ingpounding.Suchpoundingisproportionaltotheamountof bearingdisplacementbeyondthechosenRNCisolator’sdesign displacementatthe sameconsideredvalueofbufferstiffness,

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Peak absolute structural acceleration

Fixed−base case, T1 = 0.477 sec

Isolated (Non−Improved), T1 = 3.0 sec

Seismic gap = 45 cm, RNC design displacement = 40 cm Exciting earthquakes (unideirectional and bidirectional) Exciting earthquakes (unideirectional and bidirectional)

Kobe−X Kobe−Y Kobe−XY Northridge−X Northridge−Y Northridge−XY SanFernando−X SanFernando−Y SamFernando−XY

P

eak accel.

(m/sec2)

P

eak accel.

(m/sec2)

P

eak accel.

(m/sec2)

Pounding acceleration in X direction Pounding acceleration in Y direction

Pounding acceleration in X direction Pounding acceleration in Y direction (a)

(b)

(c) 100

300

200

100

0

300

200

100

0 50

0

Figure13.PeakabsolutestructuralaccelerationinXandYdirectionsunderuni-andbidirectionalnear-faultgroundmotions:(a)fixed-basecase;(b)non-improved RNC-isolatedcase;(c)improvedRNC-isolatedcase.

compared tothe overallstructure pounding of somecasesin

Fig.11(a),theactivationoftheRNCisolator’sbufferoffersmore criticaladvantages.Forexample,itisnotonlyabletominimize orevenpreventstructuralpounding,andconsequentlyprevents thepossiblyresultingseverelocalorglobalstructuraland non-structural damages, but it also distributes pounding regularly on the isolated base floor’s in-plan area andkeeps pounding always within the solid metallic body of the RNC isolator. Therefore,the RNC isolator’s buffercould prevent structural pounding contact with no severe concentration of pounding forcesatalocalpointorzone anywhereintheRNC-isolated structure,whichisgenerallytranslatedintolessarisingnegative effects.According toFig.12(b), theimprovedRNCisolation hassignificantlyreducedtheRNCisolatorpoundingunderfive casesandeliminatedpoundingentirelyunderthesixthcaseof loading.Additionally,thereisnoout-of-planpounding gener-atedfromaunidirectionalgroundmotion.Suchimprovements couldbeattributedtothereducedin-planandout-of-planpeak structural displacementresponses, bymeans of the improved RNCisolation.

Thecorresponding influenceofRNCisolatorpounding on theisolationefficiencyisshowninFig.13regardingthepeak absolutestructural acceleration atthe topmost floor as a per-formance measure.Although the peak accelerationresponses ofthefixed-baseasymmetricstructureareactuallyhigh,asin

Fig.13(a),theyareevenamplifiedsignificantlyifstructuralor

RNC isolatorpoundingexists.The loadcasesthat exhibitno poundingshowminimalpeakstructuralaccelerationresponses. Theamplifiedstructuralaccelerationsduetopoundingareworse (moreamplified) inthecaseof non-improvedRNCisolation, as shownbyFig.13(b).In otherrespects,the improvedRNC isolation hasputanendtobidirectionalRNCisolator pound-ing for all load cases, except under bidirectionalNorthridge earthquake,asinFig.12.Therefore,ithasminimizedthe corre-spondingpeakstructuralaccelerationresponsesasdemonstrated byFig.13.Theremainingamplifiedaccelerations,exceptunder bidirectionalSanFernandoearthquake,arestillhigherthanthe fixed-basecasebutaresignificantlylowerthanthoseduetothe non-improved RNCisolation.In otherwords,instead of hav-ingelevenpeakaccelerationresponsesinFig.13(b)higherthan their corresponding values inthe fixed-base case, Fig. 13(a), onlyfouraccelerationresponsequantitiesremainunacceptable duetotheimprovedRNCisolation,Fig.13(c),withareduction percentageofaround64.0%.

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Peak absolute structural acceleration time history in X direction

Under bidirectional San−Fernando earthquake (SanFernando XY)

(at the topmost floor of the asymmetric structure)

Due to structural and RNC isolator pounding

Time (sec)

Due to RNC isolator pounding only

Due to structural and RNC isolator pounding

Peak absolute structural acceleration time history in Y direction

Under bidirectional San−Fernando earthquake (SanFernando XY)

(at the topmost floor of the asymmetric structure)

100 (a)

(b) 50

0

0 2 4 6 8 10 12 14 16 18 20

50

0 −50

−100

−50

Fixed−base Isolated(non−improved) Isolated(improved)

Absolute acceler

ation (m/sec

2)

Absolute acceler

ation (m/sec

2)

Figure14.PeakabsolutestructuralaccelerationtimehistoryinXandYdirectionsunderandbidirectionalSan-Fernandoearthquakeconsideringfixed-base, non-improvedisolatedandimprovedisolatedcases:(a)structurepoundingexists,consideringtheimprovedRNCisolation;(b)structurepoundingdoesnotexist, consideringtheimprovedRNCisolation.

displacementatthe pounding level resultsinlargeandquick accelerationpulsesintheoppositedirection,whichseems evi-dentasaresultofstructuralpoundingatthetopmostfloor,as indicatedinFig.14(aandb),wheretheaccelerationresponses are amplified and have significantly higher frequency in the case of non-improved RNC isolation. On the other side, the RNCisolatorpounding givesnosuch risetotheacceleration peakvalueandfrequency,asshowninFigure14(a)bythesolid blacklinerepresentingtheimprovedRNCisolation,which suf-fers only RNC isolator pounding in X direction. Thismight be seen as an advantage of inevitable RNC isolator pound-ing.BecauseofbothstructuralandRNCisolatorpounding in Xdirection, thecorresponding isolation efficiency isseverely deteriorated under non-improved RNC isolation as shown in

Fig.14(a),wheretheRNC-isolatedpeakstructuralacceleration ishigherthanthatofthefixed-basecase.Underthesame con-ditions,theimprovedRNCisolationshowsareasonablygood efficiencyexceptattheinstantofpounding,wherethe result-ingpeakaccelerationisstill evenlowerthanthatofthe fixed basecasewitharatioof74.40%.Fig.14(b)showsthe acceler-ationresponsesinYdirection,wherebothstructuralandRNC isolatorpoundingareconsiderably lessthanthoseinX direc-tion,asinFigs.11(a)and19(a),consideringthenon-improved RNCisolation case.Although,thepeakaccelerationresponse ofthat caseisremarkablyloweredbutisstill higherthanthe fixed-base case. On the other hand, both sources of pound-ing are nonexistent in the case of improved RNC isolation. Asaresult,thepeakabsolutestructuralaccelerationisgreatly reducedtorepresent aratioof 8.0% tothat ofthe fixed-base case.

3.2. MinimumSafeSeismicGap(MSSG)usingtheRNC isolator

Inthissection,thetermMinimumSafeSeismicGap(MSSG) isintroducedtoexpressthe smallestsufficientseparation dis-tance,betweentwoadjacentstructures,thatpermitsnostructural pounding.TheMSSGisusedhereinasaperformancemeasure fortheRNCisolator’sabilitytolimitthepeakdisplacementsof aRNC-isolatedstructuretomitigateoreventoentirelyavoidor eliminatestructuralpoundingconsequently.Alltheninecases ofloading,consideredinFigs.11–13,arereconsidered.Then, theworst,highest,singleresultunderthemallisrecordedfor eachcasestudy,regardlessoftheexcitation.Forty-five differ-entcasesarestudiedconsideringthevariationofbothisolation periodandtheRNCisolator’sdesigndisplacement.The peak responsequantitiesofinterestinthissectionarethestructural poundingatthetop-mostfloor,thecorrespondingRNCisolator poundingandthecorrespondingstructuralstorydriftinbothX andYdirectionsconsideringthetwomethodsofnon-improved andimprovedRNCisolation.Thebufferstiffnessisthesameas previous,whichis2.50×106kN/m.

Fig.15showstheMSSGinXdirectionandthecorresponding RNCisolatorpoundingundernon-improvedandimprovedRNC isolation.From Fig.15(aandb), itappearsthat theimproved RNCisolation produces moreregularvariation ofthe MSSG againsttheisolationperiodandtheRNCisolator’sdesign dis-placement. In addition, the MSSGsare remarkably lower in

Fig. 15(b), because of the improved RNC isolation, than in

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Minimum seismic gap in X direction, at which no structure pounding,

(Non−improved RNC isolation)

Corresponding peak inner pounding of a RNC isolator, in X direction,

(Improved RNC isolation)

RNC design displacement (m) RNC design displacement (m)

Isolation per iod (sec) Isolation per iod (sec) Isolation per iod (sec) Isolation per iod (sec) P

eak RNC pounding f

orce (kN)

P

eak RNC pounding f

orce (kN)

Min.

seismic gap (m)

0.8 (a) (b) (d) (c) 2 1.5 1 0.5 0 x 104

2

1.5

1

0.5

0 x 104 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 6.7 5.6 4 3 1.1 6.7 5.6 4 3

1.1 0.1 0.15

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 6.7 5.6 4 3 1.1 6.7 5.6 4 3 1.1 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Min.

seismic gap (m)

Minimum seismic gap in X direction, at which no structure pounding,

Figure15.MinimumsafeseismicgapinXdirection,atwhichnostructuralpoundingoccurs,andthecorrespondingpeakRNCisolatorpoundingconsidering theworstoftheninecasesofloading:(a)minimumsafeseismicgap,non-improvedRNCisolation;(b)minimumsafeseismicgap,improvedRNCisolation;(c) correspondingpeakRNCisolatorpounding,non-improvedRNCisolation;(d)correspondingpeakRNCisolatorpounding,improvedRNCisolation.

is lower than that of the non-improved RNC isolation case,

Fig.15(c).Additionally,Fig.15(aandb)showsthat the vari-ation of the RNC isolator’s design displacement affects the MSSG more than the isolation period. This is attributed to the activation of the buffer mechanism after a certain pre-determined bearing design displacement; regardless of how muchflexibleisthebearing.Suchbufferactivationcancelsthe effectof added isolatorflexibility toprovide higher isolation period.Therefore,the MSSGincreasessubstantiallywiththe increaseof RNCisolator’sdesigndisplacementandincreases slightlywiththeincreaseoftheisolationperiod,asillustrated by Fig. 15(a and b). Regarding the RNC isolator pounding of Fig.15(candd),it seemstobealmostinvariableatlower designdisplacementsandhigherisolationperiod,thenitstarts toremarkablydecreasesafteradesigndisplacementofaround 30.0cmastheRNCisolator’sdesigndisplacementgetsbigger. ThisdecreaseoftheRNCisolatorpoundingmaybeattributed totherelativelylowkineticenergyoftheisolatedstructurejust

before hitting the buffer atthose highRNCisolator’s design displacements.

Fig.16 showsthe sameresponse quantitiesof Fig.15but in Y directionunder the sameconditions. Similar toFig.15,

Fig.16showsasuperiorbehavioroftheimprovedRNCisolation to the non-improved oneregarding MSSGand RNCisolator pounding,whicharesignificantlylessundertheimprovedRNC isolation, asdemonstratedbyFig.16(bandd).Moreover,the variationoftheMSSGandthecorrespondingRNCisolatorin Ydirectionagainsttheisolationperiodandthebearingdesign displacementissimilartothatinXdirection.Theonlydifference isthattheimprovedRNCisolationhasloweredsignificantlythe peak structural displacements inY direction toa degree that hasnotonlypreventedstructural poundingatrelativelylower seismic gaps, butalso theRNC isolatorpounding is reduced considerablyandbecamenonexistentinmanycases.

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Minimum seismic gap in Y direction, at which no structure pounding,

Corresponding peak inner pounding of a RNC isolator, in Y direction,

Min.

seismic gap (m)

Min.

seismic gap (m)

P

eak RNC pounding (kN)

P

eak RNC pounding (kN)

2

1.5

1

0.5

0 x 104

6.7 5.6

4 3

1.1 0.1 0.15

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 6.7 5.6 4 3 1.1 2 1.5 1 0.5 0 x 104 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.8 (a) (b) (c) (d) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 6.7 5.6 4 3 1.1 6.7 5.6 4 3 1.1 Isolation per iod (sec) Isolation per iod (sec) Isolation per iod (sec) Isolation per iod (sec)

Figure16.MinimumsafeseismicgapinYdirection,atwhichnostructuralpoundingoccurs,andthecorrespondingpeakRNCisolatorpoundingconsidering theworstoftheninecasesofloading:(a)minimumsafeseismicgap,non-improvedRNCisolation;(b)minimumsafeseismicgap,improvedRNCisolation;(c) correspondingpeakRNCisolatorpounding,non-improvedRNCisolation;(d)correspondingpeakRNCisolatorpounding,improvedRNCisolation.

RNCisolator’sdesigndisplacementconsideringnon-improved andimprovedRNC isolation methods. Oncemore, Fig.17(b and d) show that the structural behavior is better using the improved RNC isolation, especially, the peak drift ratios in Y direction, Fig. 17(d), where the RNC-isolated asymmetric structurebehavesalmostas arigidbody,as aresult ofentire eliminationof bothstructural andRNC isolatorpounding, in manycasesathigherdesigndisplacementsoftheRNC isola-tor.However, theimportance ofpeak driftratiois tobeused asameasureofpossiblefuturestructuraldamageunder earth-quakes[1].Reference[1] specifiedfour seismicperformance levelsSP1(negligibledamage),SP2(minortomoderate dam-age),SP3(moderatetomajordamage)andSP4(majordamage). Thosefourseismicperformancelevelsareassociatedto maxi-mumdriftratiosof0.5%,1.5%,2.5%and3.8%,respectively. Accordingly,thehighesttwo,odd,peakdriftratiosofFig.17

are0.74%undernon-improvedRNCisolation,Fig.17(a),and 0.50%incaseofimprovedRNCisolation,Fig.17(b).The ear-lierislessthanhalfthelimitofSP2topredictminorstructural

damage,whilethelatterof0.50%meansnegligiblestructural damageoftheworst,highest,casestudyunderimprovedRNC isolation.Certainly,theremaininglowerpeakdriftratiosshould exhibitlessstructuraldamagetheoretically.Themainoutcome ofthissectionisthattheRNCisolatorcouldefficientlymitigate (or entirely)eliminatepossiblestructuralpoundingwith adja-cent structures,under severeNFground motions considering limited or insufficient seismicgaps, withminoror negligible negativeinfluenceonstructuraldamage.

3.3. AppropriateRNCisolatorcharacteristicsforno pounding

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Maximum corresponding story drift in X direction, (Non−improved RNC isolation)

Maximum corresponding story drift in Y direction, (Non−improved RNC isolation)

Maximum corresponding story drift in Y direction, (Improved RNC isolation)

Maximum corresponding story drift in X direction, (Improved RNC isolation)

Max. stor y dr ift(%) Max. stor y dr ift(%) Max. stor y dr ift(%) Max. stor y dr ift(%) Isolation per iod (sec) Isolation per iod (sec) Isolation per iod (sec) Isolation per iod (sec) 1.5 1 0.5 0 1.5 1 0.5 0 1.5 1 0.5 0 1.5 1 0.5 0 6.7 5.6 4 3 1.1 6.7 5.6 4 3 1.1 6.7 5.6 4 3 1.1 6.7 5.6 4 3

1.1 0.1 0.15

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (a) (b) (d) (c)

Figure17.Correspondingpeakstorydrift:(a)inXdirectionconsideringnon-improvedRNCisolation;(b)inXdirectionconsideringimprovedRNCisolation;(c) inYdirectionconsideringnon-improvedRNCisolation;(d)inYdirectionconsideringimprovedRNCisolation.

accelerationsandstructuralbaseshearreactionsareemployed as performance measures to assess the RNC isolation effi-ciency. The solution key under such conditions is through reducing the horizontal flexibility of the RNC isolator to a degree that allows for some reasonable structure-ground decoupling and prevents any pounding contact of the RNC-isolated structure withadjacentstructures within theselected limited gap. In addition, the resulting peak bearing displace-ment will be lower than a chosen relatively small design displacement of the RNC isolator. This could achieve rea-sonably efficientisolation withnopoundingatall.Moreover, the choice of a less flexible RNC isolator with a relatively small designdisplacementimposesconstraintsuponthepeak bearing displacement and velocity. Constraining the bearing displacementdecreasestheprobabilityofactivatingthebuffer mechanism, while constraining its velocity allowsthe RNC-isolatedstructuretohitthebufferwithsignificantlylowkinetic energy toproduce reasonablylow innerRNCisolator pound-ing withless arisingunwanted effects onthe otherstructural responses,comparedtothecaseofhighlyflexibleRNCisolator design.

In thissection, the seismicgapbetweenthe RNC-isolated asymmetricstructureandthesurroundingadjacentone,inboth XandYdirections,istakenlessthanorequalto:

SeismicgapofaRNC−isolatedstructure ≤ xdes+S AB

4 (1) where xdes is the RNC isolator’s design displacement,and S

is the horizontal separation distance,between two fixed-base structuresAandB,whichisobviouslyequaltothepeakrelative displacement response xrel betweenthoseadjacent fixed-base

structures.TheseparationdistanceSisgivenby[2,3]as:

SAB=xrel=

x2

A+x2B−2ρABxAxB (2)

wherexA,xB andxrel arethemean peakdisplacementvalues

of thetwoadjacentstructuresandtheirrelativedisplacement, respectively.Basedontheperiodratior=Tb/Ta,thecorrelation

coefficientxisgivenby[4,5]foratwoadjacentstructureswith equaldampingratioθas:

ρAB=

8ξ2(1+r)r3/2

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Peak absolute structural acceleration in X direction, Isolation period = 1.056 sec No structure pounding, No RNC inner pounding,

Peak absolute structural acceleration in Y direction, Isolation period = 1.056 sec No structure pounding, No RNC inner pounding,

Seismic gap = 41 cm, RNC design displacement = 35 cm Exciting earthquakes (unideirectional and bidirectional)

P

eak absolute acceler

ation (m/sec2)

P

eak absolute acceler

ation (m/sec2)

Kobe−X Kobe−Y Kobe−XY Northridge−X Northridge−YNorthridge−XY S.Fernando−X S.Fernando−Y S.Fernando−XY Kobe−X Kobe−Y Kobe−XY Northridge−X Northridge−Y Northridge−XY S.Fernando−X S.Fernando−YS.Fernando−XY 80

70

60

50

40

30

20

10

0

50

45

40

35

30

25

20

15

10

5

0 (a)

(b)

Fixed−base

RNC−isolated (non−improved)

RNC−isolated (improved)

Fixed−base

RNC−isolated (non−improved)

RNC−isolated (improved)

Figure18.Peakabsolutestructuralaccelerationconsideringlowisolationperiodandalimitedseismicgap,atwhichthereisnostructurepoundingnorinnerRNC pounding:(a)inXdirection;(b)inYdirection.

Inthissection, thedesign displacementofthe RNC isola-toristakenas35.0cm,whilethecalculatedseparationdistance accordingtoEqs.(2) and(3) isfoundtobe27.15cm. There-fore,andaccordingtoEq.(1),arelativelysmallseismicgapis consideredinthissectionas40.0cm.

Consideringasmall isolationperiod of 1.056s,chosenby trialanderror methodtofulfill theabove conditions,Fig.18

comparesthepeakabsolutestructuralaccelerationsofthe non-improved and improved RNC-isolated asymmetric structure with their corresponding values in the fixed-base case in X and Y directions. In addition to the nearly zero out-of- plan accelerationresponsesunderunidirectionalexcitationsusingthe improvedRNCisolation,theothermainobservationisthatthe RNC-isolatorisabletosignificantlyreducethepeakstructural accelerationsundermostofthesevereNFgroundmotioncases, atlowisolationperiodwithnopounding,regardlessbeing non-improvedor improvedRNCisolation. Although,itwasnoted thatthepeakstructuralandbearingdisplacementsarestilllower thantheirchosenlimitsundersomeexcitations.Therefore,atrial anderrormethodisusedtoobtainthemostappropriateisolation period of onlythe improvedRNCisolation under simultane-ousbidirectionalexcitationsofeachofthethreeconsideredNF

earthquakes, such that theresulting peak structural andRNC isolatordisplacementsarejustbelowtheir chosen limits.The resultingstructuralresponsesoftheRNC-isolatedasymmetric structureshouldbethelowestpossibleunderthebidirectional excitationswithinthoselimits.Therefore,theymayleadtoafair assessmentoftheRNCisolator’sefficiencyunderthespecified limitedconditions.

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direc-194 M.Ismail/HormigónyAcero2018;69(286):177–195

Peak X−X absolute structural acceleration due to kobe earthquake,

T1 = 1.393 sec, (no structural nor RNC isolator pounding)

Peak response quantities

RNC Xdes = 35cm, Seismic gap = 40 cm

Under kobe earthquake

Isolation period = 1.393 sec

Peak X−X absolute acceleration ratio% (RNC−isolated/Fixed−base) = 38% Peak Y−Y absolute acceleration ratio%

(RNC−isolated/Fixed−base) = 30%

Base X−X Shear ratio%

(RNC−isolated/Fixed−base) = 64% Base Y−Y Shear ratio%

Peak X−X Structure disp. = 35.98 cm Peak X−X RNC iso. disp. = 31.06 cm

Peak Y−Y RNC iso. disp. = 34.50 cm Peak Y−Y Structure disp. = 39.53 cm Peak Y−Y absolute structural acceleration due to kobe earthquake,

Fixed−base RNC−isolated Fixed−base RNC−isolated Abs . accel. (m/sec 2) Abs . accel. (m/sec 2) 20 10 0 −10 −20 20 0 −20

0 2 4 6 8 10 12 14 16 18 20

Time (sec)

(a) (b)

Figure19.LowestresponsequantitiesconsideringtheappropriateRNCisolatorcharacteristicstoachieveisolationwithoutanypoundingataseismicgapof40 cmandaRNCisolatordesigndisplacementof35cm:(a)peakabsolutestructuralaccelerationunderKobeearthquake;(b)peakresponsequantitiesunderKobe earthquake.

Peak X−X absolute structural acceleration due to northridge earthquake,

Peak Y−Y absolute structural acceleration due to northridge earthquake,

Fixed−base RNC−isolated Fixed−base RNC−isolated 20 10 0 0 5 10 −10 −20 −10 −5 Abs . accel. (m/sec 2) Abs . accel. (m/sec 2)

0 2 4 6 8 10 12 14 16 18 20

Time (sec)

Peak response quantities

RNC Xdes = 35cm, Seismic gap = 40 cm

Under northridge earthquake

Isolation period = 1.571 sec

Peak X−X absolute acceleration ratio% (RNC−isolated/Fixed−base) = 29% Peak Y−Y absolute acceleration ratio%

Base X−X Shear ratio%

(RNC−isolated/Fixed−base) = 54% Base Y−Y Shear ratio%

Peak X−X Structure disp. = 38.96 cm Peak X−X RNC iso. disp. = 34.96 cm

Peak Y−Y RNC iso. disp. = 31.49 cm Peak Y−Y Structure disp. = 34.76 cm

(a) (b)

Figure20.LowestresponsequantitiesconsideringtheappropriateRNCisolatorcharacteristicstoachieveisolationwithoutanypoundingataseismicgapof40 cmandaRNCisolatordesigndisplacementof35cm:(a)peakabsolutestructuralaccelerationunderNorthridgeearthquake;(b)peakresponsequantitiesunder Northridgeearthquake.

tion underbidirectionalNorthridgeearthquake, Fig.20(b), at anappropriateisolationperiodof1.571stojustavoid pound-ing.Thepeakaccelerationandbasesheararereducedto29.0% and54.0%inXdirection,respectively.UndersuchsevereNF excitation, the timehistory plots of peak structural accelera-tions,Fig.20(a),showafairlygoodbehavioroftheimproved RNCisolationinXdirection,whileinYdirectionthebehavior ismoderatelygood.InFig.20(a),therearenohighfrequency peakaccelerationpulses,whichindicatesnonexistentpounding. Undertheseverestgroundmotioninthispaper,regardingPGA, the RNC isolator has efficiently reduced the peak structural