Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska10NCEE SEISMIC RESPONSE OF TALL REINFORCED CONCRETE SPECIAL MOMENT RESISTING FRAMES DESIGNED WITH CURRENT CODE PROVISIONS T. Visnjic1, M. Panagiotou2, and J.P. Moehle3 ABSTRACT Seismicresponseoffour20-storytallreinforcedconcretespecialmomentframestoasetof near-field pulse-typeground motions is investigated to outline the nonlinear structural behavior inherenttotallermodernframesandcomparethecomputedresponsestothedesignforces predictedbytherepresentativestate-of-practicedesignprocedures.Theframedesignscomply withtheASCE7-10andACI318-11codes.Responsesareinvestigatedattwogroundmotion intensity levels: the DesignEarthquake(DE) and the Maximum Considered Earthquake (MCE) for a hypothetical site located in Los Angeles, CA. Keeping the uniform size and reinforcement ratiosincolumnsalongtheframeheightisshowntoreduceconcentrationofplasticityin columns above the base, while increasing the gross area of the exterior columns leads to smaller inter-storydriftratiosinthelowerportionofthebuildingandalsosmallerstraindemandon concrete. Axial elongation of the beams in the lower stories is found to increase the shear at the baseofthebuildingandshouldbeconsideredinthedesignandnonlineardynamicanalysisof RCframes.Commondesignproceduresgenerallyunderestimatecolumnshears.Preliminary investigationsshowthatalternativemethodsmaybesuitableforbetterestimationofcolumn shears. 1 Graduate Student Researcher, Dept. of Civil and Environmental Engineering, University of California, Berkeley, CA, USA 2 Assistant Professor, Dept. of Civil and Environmental Engineering, University of California, Berkeley, CA, USA 3 T.Y. and Margaret Lin Professor of Engineering, Dept. of Civil and Environmental Engineering, University of California, Berkeley, CA, USA Visnjic T, Panagiotou, M, and Moehle, JP. Seismic Response of Tall Reinforced Concrete Special Moment Resisting Frames Designed with Current Code Provisions. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014. SEISMIC RESPONSE OF TALL REINFORCED CONCRETE SPECIAL MOMENT RESISTING FRAMES DESIGNED WITH CURRENT CODE PROVISIONS T. Visnjic1, M. Panagiotou2, and J. P. Moehle3 ABSTRACT Seismic response of four 20-story tall reinforced concrete special moment frames to a set of near-fieldpulse-typegroundmotionsisinvestigatedtooutlinethenonlinearstructuralbehavior inherenttotallermodernframesandcomparethecomputedresponsestothedesignforces predictedbytherepresentativestate-of-practicedesignprocedures.Theframedesignscomply withtheASCE7-10andACI318-11codes.Responsesareinvestigatedattwogroundmotion intensitylevels:theDesignEarthquake(DE)andtheMaximumConsideredEarthquake(MCE) forahypotheticalsitelocatedinLosAngeles,CA.Keepingtheuniformsizeandreinforcement ratios in columns along the frame height is shown to reduce concentration of plasticity in columns above the base, while increasing the gross area of the exterior columns leads to smaller inter-story drift ratios in the lower portion of the building and also smaller strain demand on concrete. Axial elongationofthebeamsinthelowerstoriesisfoundtoincreasetheshearatthebaseofthe buildingandshouldbeconsideredinthedesignandnonlineardynamicanalysisofRCframes. Commondesignproceduresgenerallyunderestimatecolumnshears.Preliminaryinvestigations show that alternative methods may be suitable for better estimation of column shears. Introduction Overthelasttwodecades,urbandevelopmentacrosstheseismicallyactiveWestCoastofthe United States has lead to an increasing number of reinforced concrete residential and commercial buildingsexceeding50minheight.ManyofthesebuildingsutilizeperimeterSpecialMoment ResistingFrame(SMRF)construction.Thesearegenerallydesignedfollowingtheprescriptive guidelinesoftheASCE7[1]standardanddetailedpertheACI318Codeprovisions(various editions).Pastearthquakesexposedpotentialvulnerabilityoftallreinforcedconcreteframe buildingswithdamagereports[2]indicatingconsiderabledamagesustainedduringthe2011 M6.3Christchurch,NewZealand,earthquake.Theoccurrenceoflargedamagesuggests potentialvulnerabilityoftheframesystemsandwarrantsstudytobetterunderstandthecurrent U.S.designrequirements.Theaimofthepresentstudyistoinvestigatethebehavioroftall SMRFsunderstronggroundmotionandexplorehowseveralalterationsindesignaffectthe seismicresponse.Inaddition,code-basedmethodsforestimatingdesignshearincolumnsare investigated and alternative methods are proposed for better force estimation. 1 Graduate Student Researcher, Dept. of Civil and Environmental Engineering, University of California, Berkeley, CA, USA 2 Assistant Professor, Dept. of Civil and Environmental Engineering, University of California, Berkeley, CA, USA 3 T.Y. and Margaret Lin Professor of Engineering, Dept. of Civil and Environmental Engineering, University of California, Berkeley, CA, USA Visnjic T, Panagiotou, M, and Moehle, JP. Seismic Response of Tall Reinforced Concrete Special Moment Resisting Frames Designed with Current Code Provisions. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014. Frame Design and Numerical Model The four frames considered in this study correspond to a building configuration where the perimeterSMRFsframingintheprincipaldirectionsofthebuildingdonotinteract.Elevation and floor plan, identical in all four buildings, are shown in Figure 1.Each SMRF has four bays (each6.4m-long)and20stories(each3.7mtall).TotalbuildingheightisH=73.2m.Column lines A and E (1 and 5) are designated exterior columns, column lines B and D (2 and 4) are designated interior columns, and column line C (3) is designated the middle column. Figure 1.Archetype building elevation and plan. Thefourframescanbedividedintotwotypesaccordingtothecolumnconfigurations. TypeAhascolumnsizeandlongitudinalreinforcementratiothatdecreasealongheight,while TypeBhasuniformcolumnsizeandreinforcementratiooverbuildingheight.Thebeamsare identical in both frame types, with smaller beams in levels 11-20 than in levels 1-10. One Type A building is considered, designated A20-1. Three Type B buildings are considered, designated B20-1,B20-2,andB20-3.Table1listsbeamandcolumndimensionsandlongitudinaland transverse steel ratios. In building A20-1, column dimensions are constant from levels 1-10, with reduced dimensions in levels 11-20.Column longitudinal reinforcement is curtailed at levels 6, 11, and 16 (see Table 1). In building B20-1, column size and longitudinal reinforcement in every story are the same as those used in the first story of building A20-1. Buildings B20-2 and B20-3 are identical to B20-1 except the exterior column size and longitudinal steel ratio (Table 1). ThebuildingsweredesignedbasedonACI318-11[3]andASCE7-10provisions. Designforcesweredeterminedusingthecode-prescribedMRSAprocedureusingSRSSmodal combination rule with a response modification factor R = 8. The first five modes were included intheelasticanalysis,accouningformorethan90%ofthemodalmass. Thedesignbaseshear forceofeachSMRF(Vb)forallfourbuildingswascontrolledbyminimumbaseshear requirementsofASCE7,resultinginabaseshearcoefficientVb/W=5.36%.Concrete compressive strength, f'c, was 52MPa, and steel yield strength, fy, was 414MPa.4 bays @ 6.4 m = 25.6 m5.5 m36.6 m5.5 mPerimeter SMRFcolumn (typ.)Interior gravitycolumns (typ.)9.1 m 9.1 m9.1 m9.1 m203 mm slab36.6 mZone 1 A20Zone 2 A20Zone 3 A20Zone 4 A20Zone 1 B20Zone 2 B2020 stories @ 3.7 m = 73.2 mPerimeter SMRF4 bays @ 6.4 m = 25.6 m 5.5 m 5.5 m36.6 m4 bays @ 6.4 m = 25.6 m 5.5 m 5.5 mA B C D EA B C D E12345 Table 1. Frame element sizes and steel ratios (b = width, h = height, l, t = longitudinal and transverse reinforcement ratio, Note: * = t in first-story column only). A20-1B20-1B20-2B20-3 Zone1234121212 Stories1-56-1011-1516-201-1011-201-1011-201-1011-20 Beam b (mm)609609609609609609609609609609 h (mm)10671067914914106791410679141067914 l (%)2.22.21.81.82.21.82.21.82.21.8 t (%)1.01.00.90.91.00.91.00.91.00.9 Exterior Column b (mm)121912191067106712191219 1524152418291829 h (mm)121912191067106712191219 1524152418291829 l (%)2.81.11.11.02.82.8 2.02.01.71.7 t (%) 2.1* 1.2 1.21.21.2 2.1* 1.2 1.2 1.9* 1.2 1.2 1.9* 1.2 1.2 Interior & Middle Column b (mm)1219121910671067121912191219121912191219 h (mm)1219121910671067121912191219121912191219 l (%)1.51.01.11.01.51.51.51.51.51.5 t (%) 1.9* 1.6 1.61.61.6 1.9* 1.6 1.6 1.9* 1.6 1.6 1.9* 1.6 1.6 TheexteriorcolumnsofA20-1buildingwereinthetransitionregionbetween compression- and tension-controlled at the base. Base exterior columns of B20-1 and B20-2 were inthetransitionregionbetweentension-andcompression-controlledsections,whileforB20-3 building,theexteriorcolumnatthebasehadatension-controlledsection.InallthreeB20 buildings, interior and middle columns were in the tension controlled region and were identical. Furtherdetailsondesignofthebuildingsarepresentedin[4].Jointshearstrengthandstrong column-weakbeamrequirementsofACI318weresatisfiedinbothbuildings.Transverse reinforcementinbeamsandcolumnsofallframeswasdesignedtosatisfyshearstrengthand confinement requirements of ACI 318. The numericalanalysiswas performed on the Open System for Earthquake Engineering simulation(OpenSees)platform[5].ThecomputermodelconsistedofasingleSMRFwith lumped mass and vertical load applied at the joints.Force-based Euler-Bernoulli nonlinear fiber-sectionframeelementswithP-geometrictransformationwereusedtomodelallframe elements. The model accounted for the strain penetration of longitudinal reinforcement of beams in joints as well of the columns in the foundation.Rayleigh damping with 2% damping ratio was appliedinmodes1and3.Thegravityframingisassumedtoprovidesufficientstrengthand stiffnesstoresistsofteningP-effectsunderitsgravityloadonaccountofrigorousdetailing requirements in new buildings. The numerical models of buildings have similar modal characteristics with a first modal period T1 between 1.69 and 1.75 s and a ratio of first to second mode period T1 / T2 of about 2.9. Theforce-displacementrelationshipsaresimilarforthefourbuildingsintheeffectivelylinear range,withasystembaseshearofapproximately0.073Wat0.4%roofdriftratio,which correspondstosystemyield[4].Therelationsdivergebeyondthisduetodifferentcolumn flexural strengths.At 2% roof drift ratio, the base shear is between 1.7 and 1.9 times the design base shear of 0.054W, the increase due to design and section overstrength of the frame members. Seismic Hazard and Ground Motion Selection The studied buildings are considered to be at a site in Los Angeles, California, with soil type D [1]. The site seismic hazard and corresponding smooth design spectra were determined in accordancewithASCE7atbothDBEandMCElevels.Asetoffourteengroundmotionswas selectedandlinearlyscaledsuchthatthemeanspectrumapproximatelymatchesthesmooth design spectra over the period range of interest, which included the shortest third mode period of the uncracked buildings as the lower bound and 2.5 times the longest natural period for the four buildingsastheupperbound.Figures2(a)and(d)showthemeanpseudo-accelerationand displacement spectra, respectively, of the scaled ground motions together with the corresponding DBE and MCE design spectra.

Figure 2.Mean pseudo-acceleration and displacement spectra for ground motions used. Response Overview All four buildings showed similar mean roof drifts, base shears, and overturning moments for both DBE and MCE levels of shaking [4]. Response of A20-1 buildings is discussed in detail, and only the responses of Type B buildings that are significantly different are discussed here. For more details refer to [4]. Figure 4 presents mean envelopes of relative displacements, inter-story driftratios,storymoments,andstoryshearforcesforbuildingA20-1.Theenvelopesofall responsequantitieshavesimilarshapesfortheDBEandMCEresponselevels.Thecomputed mean roof drift ratios are 1.2% for the DBE and 1.8% for the MCE hazard levels. As shown in Figure 3(a), the mean displacement envelopes have a maximum value at the roof of the building. Figure 3.Mean response of building A20-1 for DBE and MCE levels [(a)-(c)] and (d) variation of inter-story drift ratio with increase of exterior column size (Type B buildings). Themeaninter-storydriftenvelopehassimilarvaluesbetween0.2Hand0.7Hatboth DBEandMCElevels,withlocalpeaksat0.3Hand0.6H.Thelargestvalueofthemeaninter-storydriftis2.2and3.1%,atDBEandMCElevels,respectively.Peakinter-storydriftratios 0.0 1.0 2.0 3.0 4.00.01.02.03.04.05.0Sa (g)(a)T (s)0 1 2 3 40100200300Sd (cm)(b)T (s)0.00 0.01 0.020.00.51.0Di / Hhi / HDisplacement(a)0.00 2.00 4.00 (%)Inter-Story Drift(b)A20-1 DBEA20-1 MCEASCE 7 MRSAPushover at D / H = 1.1%AdVMRSA DBEAdVMRSA MCE0.00 0.08 0.160.00.51.0Vi / WStory Shear(c)i0.00 0.04 0.08Mi / WHStory Moment(d) 0.00 1.50 3.000.00.51.0 (%)hi / HInter-Story Drift(e)B20-1 DBEB20-1 MCEB20-2 DBEB20-2 MCEB20-3 DBEB20-3 MCE computed for Type B buildings were almost identical to those in A20-1 building [4]. The inter-story drift envelopes, however, indicate that the increase in the exterior column size in buildings B20-2andB20-3leadtoprogressivelysmallerinter-storydriftsinthebottomhalfofthe building and increased inter-story drift in the top portion of the buildings. ThemeanbaseshearfortheDBEmotionsis0.12W,increasingto0.14WfortheMCE shakinglevel(Figure3[c]),whereasonly6%increaseisnotedinthemeancomputedstory momentsgoingfromDBEtoMCEhazardlevel(Figure3[d]).ThemeanbaseshearatDBEis 42% higher than the base shear computedfrom the nonlinear static pushover analysis using the first-modelateralforceprofileat1.2%roofdriftratio(themeanroofdriftratiofortheDBE motions),alsoplottedinFigure3(c),indicatinghigher-modecontributionstothesystembase shear response. The higher-mode contribution to story shear holds true for all four buildings. On the other hand, the story moment profile from the first-mode monotonic pushover analysis, also plottedforA20-1building,agreesverywellwiththemeanstorymomentenvelopesindicating negligible higher mode contribution to the system moment. Inelastic deformations occurred in columns above the bottom story in different locations alongtheheightofthebuildings[4].Thesearecomparedintermsoftheaveragestrain computedwithintheestimatedplastichingeregionthecolumnsandareincludedonlyfor qualitativecomparisonamongthefourbuildingconfigurations.Overthebuildingheight,the interiorandmiddlecolumnsdeveloproughly30%largerreinforcementtensilestrainsthanthe exterior column in building A20-1 [4]. The largest mean strain above thebottom two stories of thecolumnsoccursinthelocationsofcolumnsizereductionorlongitudinalcolumn reinforcement curtailment.ContrarytobehaviorofbuildingA20-1,thereinforcementtensilestrainvaluesatlevels 6,11,16ofB20-1forDBElevelwerebelowyielding.AttheMCElevels,themeantensile straininthesefloorsreachedupto0.7%forB20-1,whileforA20-1thestrainsatthesame locations reached 1.7%. Reinforcement tensile strains in the exterior column were less than 0.3% in all of these locations (Fig. 4) indicating that keepinga uniform columnsize and longitudinal reinforcementratiomayleadtolessplasticityconcentrationincolumnsincomparisontoa curtailedbuilding.TensilestrainlevelsreachedinbuildingsB20-2andB20-3weresimilarto those in B20-1. Figure 4.Mean tensile strains in column steel for buildings A20-1 and B20-1. The exterior columns of A20-1 at the base developed mean concrete compressive strains equalto1.0and2.3%atDBEandMCEhazardlevels,respectively[4].Meancompressive strainsinconcreteatthebaseoftheexteriorcolumnforB20-1,-2,and-3buildingswere1.0, 0.5, and 0.2% at the DBE level.At the MCE level, the mean compressive strains in concrete at this location were 2.2, 1.0, and 0.3%, for the three buildings. Increase of the exterior column size leadstosmallerstraindemandonconcrete,whichmayimprovetheperformanceofacolumn 0.00 0.01 0.020.00.51.0Exterior Column(a)A20-1hi / H0.00 0.01 0.02Interior Column(b)0.023 (DBE)0.053 (MCE)0.027 (DBE)0.059 (MCE)0.0210.00 0.01 0.020.00.51.0Exterior Column(c)B20-1hi / H0.00 0.01 0.02Interior Column(d)DBEMCE0.022 (DBE)0.052 (MCE)0.026 (DBE)0.059 (MCE) undersimultaneousshear,moment,andaxialforce.Thedifferenceinthereinforcementtensile strains along the building height above the base for the three B20 buildings was negligible. With the exception of the bottom story, mean tensile strains were either well below or slightly above the yielding levels for both ground motion intensities.Due to the increased exterior column size, the axial load ratio was reduced in the exterior columnsforbuildingsB20-2andB20-3comparedwiththatinB20-1,eventhoughtheactual exterior column axial force increased compared with that in B20-1 (by 9 and 19% for B20-2 and B20-3, respectively). For B20-2, the compressive axial load ratio at the base was 29% lower than thatofB20-1,whereasinbuildingB20-3,itwas45%lower.Reductionofaxialloadratios resultsindecreasedconcretecompressivestrainattheexteriorcolumnbase,whichwould correspond to smaller post-earthquake damage. Lastly,individualcolumnshearenvelopesforbuildingA20-1arenormalizedbyAg

areplottedinFigure5,alongwiththedesignforcescalculatedbydifferentmethodsforthe exterior,interior,andmiddlecolumns,respectively.ThecolumnshearcalculatedusingNRHA typicallyismorethantwicethevaluecomputedusingMRSA.Notethatwhilethemeanshear forceinthethird-storyinteriorcolumnis57%largerthanthecorrespondingexteriorcolumn shear, the relation switched in the first story, where the exterior column experiences 46% larger shearthantheinteriorcolumnattheDBEhazardlevel.Thelargerfirst-storyexteriorcolumn shears are a result of kinematic interaction between the beams and the columns due to axial beam elongation.Theincreasingaxialcompressioninexteriorbaybeamstowardthebottomofthe building[Figure6(c)]indicatesthatbeamelongationmostlyimpactsthecolumnsinthefirst storyand,toalesserextent,thesecondstoryforthebuildingstudied.Inexteriorcolumns,the meanshearis0.44Ag

fortheDBEand0.55Ag

fortheMCEgroundmotions.The magnitudeofthecalculatedforces,andtheshearstressesassociatedwiththem,suggeststhat beam growth can be an important component of the shear forces that develop in the columns in the first few stories, a factor that may should be considered in design. Exteriorcolumnshearstresswasalsoreducedbyusinglargerexteriorcolumns.Inthe first-storyexteriorcolumnofbuildingsB20-1,B20-2,andB20-3themeanshearforce normalizedwithAg

atDBE(MCE)levelswere0.46(0.55),0.36(0.44)and0.29(0.35), respectively. Figure 5.Mean column shear envelopes for A20-1 building. TheNRHA-computedcolumnshearsarecomparedwiththedesignshearscomputedby two methods specified in ACI 318. Method A considers the shear Vi developed in the column at the time when both of its ends reach the maximum probable moment strength,Mpr,c, associated with the range of factored axial loads, Pu, calculated from appropriate load combinations (ASCE 7).Thismethodisgenerallydeemedconservativeandseldomusedinpractice.Shearforces 0.0 0.3 0.60.00.51.0Vext,i / Ag (f 'c) hi / HExterior(a)0.0 0.3 0.6Vint,i / Ag (f 'c) Interior(b) 0.62A20-1 DBEA20-1 MCEACI 318 Method AACI 318 Method B1ACI 318 Method B2ASCE 7 MRSAPushover at D / H = 1.1%0.0 0.3 0.60.00.51.0Vmid,i / Ag (f 'c) hi / HMiddle(c) calculated by this method at the base of the columns were between 2.2-2.5 times the mean shear forcescomputedbytheNRHAfortheMCEhazardlevel.MethodBconsiderscolumnshear correspondingtodevelopmentofbeamprobablemomentstrengths,Mpr,b,atthejointsbutthe resistingmomentsincolumnaboveandbelowareindeterminateanditisuptoadesignerto decidethemomentdistributionpattern.Itisnotuncommoninpracticetoassumetheresisting momentMpr,batagivenjointtobedividedevenlybetweenthecolumnaboveandbelowthe joint,whichwouldroughlycorrespondtothepointofcontraflexurebeinglocatedatthestory mid-height.Thisapproach,termedhereB1,yieldsadesignshearatfloori>1equaltoVi= (Mpr,b,i+Mpr,b,i-1)/2lu,i.Inthefirststory,columndesignshearisobtainedbyreplacingthe Mpr,b,i-1 values by the column Mpr,c at level i-1, that is, at the base of the building. An alternative approach, B2, is essentially an upper-bound of Method B. It conservatively assumes that column at level i resists all the probable moments from beams framing into floors above and below the columnanditdoublesthevaluesofshearforcesfoundbyapproachB1,exceptatthebottom story. This is because both methods consider the development of Mpr,c at the base of the column, which is typically much larger than Mpr,b of the beams and thus controls the value of V1.Method B1 underestimated the shear forces in all columns along most of the bottom two-thirds of the building height. The exception was at the bottom story where Method B1 resulted in shear forces 1.2, 1.5, and 1.6 times the mean shears computed by the NRHA for the MCE level intheexterior,interior,andmiddlecolumns,respectively.MethodB2overestimatedtheshear forcesincolumnseverywhere,exceptatthesecondstoryexteriorcolumnwhereitslightly underestimates the mean MCE level response. The shears in theexterior columns near the base of the building are of particular interest because of the boost in shear resulting from beam axial growth.Inthefirststory,theshearbyMethodAis2.1timesthemeanvaluefromNRHAfor MCE motions.Methods B1 and B2 produce shears that are 1.2 and 1.3 times, respectively, mean shearsfromNRHAatthesamehazardlevel.Forthesecond-storyexteriorcolumnsofthe present study, which is also affected by the beam growth, the mean shear is 1.2 times the values estimated by Method B2 at MCE shaking level, respectively. Preliminary Estimation of Design Column Shears For system shear forces a modification of the elastic modal response spectrum analysis is proposedusingEquation1.Thisapproachisbasedonamplifyingtheshearforces,VMRSA, calculatedusingthecodeprocedure,bythesystemoverstrengthfactor,whichconsidersthe designandsectionhardeningoverstrength,andfactorAd,whichaccountsforhigher-mode effects. D u MRSA V V = (1) InEq.1,VMRSAistheshearcalculatedbytheelasticMRSAprocedureofASCE7.The factor is calculated using Equation 2 as the ratio of the system moment capacity at the base of thebuilding,Mb,, tothecorrespondingsystemmomentatthebase,Mb,u,computedfromthe MRSA.( ) , , , ,,, ,2pr c g T Cbb u b uBM P PMM M + + == (2) Mb,correspondstoalevelofresponseequalorlargerthanthatcorrespondingtothe DBE seismic hazard level.Mb, is calculated as the sum of the probable flexural strength of the columnsatthebaseofthebuildingandthemomentduetoaxialforcesinthecolumns.The Mpr,c,g is the sum of probable moment strengths of columns at the base when subjected to axial load equal to gravity load used for the NRHA, that is 1.0D + 0.25L. The latter term is calculated based on the axial forces PT, and PC, of the exterior columns at the base and is amplified with the factor to account for the relative contribution of the interior column axial forces to the base moment.Axial forces PT, and PC, are calculated using capacity method outlined in [4]. B is the distancebetweenthecenterlinesoftwoexteriorcolumns.Dynamicamplificationfactor Adwas calculatedforeachbuildingbydividingthebaseshearcomputedfromtheNRHAbythebase shear computed by MRSA multiplied by the system overstrength factor from Equation 1. Design factors Ad , , and computed for the individual buildings studied can be found in[4].ThecomputedmeanvalueofAdrangedfrom1.0-1.10forDBE,andfrom1.13-1.21for MCEshakinglevel.ValuesoffactorAdcomputedatthepeakvaluesoftheDBEandMCE levelsweresimilartothedynamicmagnificationfactor=1.3usedinNZS3101[6]for individual column shearforce estimation. An upper bound value isrecommended for use when estimating Vu during the design process, that is Ad = 1.2. Factor was calculated equal to 1.1 for the frames considered here [4]. Using the factors computed, design envelopes were generated for thesystemshearofthefourbuildings.ThesearepresentedinFigure3(c)andFigure6(a)-(c) alongwiththecorrespondingNRHA-computedresponseenvelopesatDBEandMCEshaking intensities.The system shear envelopes computed by the method presented bounded the NRHA-calculatedsystemshearforcesatalllevelsforbuildingA20-1andacrossallstories,exceptfor the top two stories of building B20-1 and in the second and third stories of B20-2 and B20-3. Figure 6.System shear for Type B buildings. While the estimated design system shear is not directly used as a design parameter, it can be an important tool in estimating the individual column shears.A correct distribution of story shearprovidestheestimateoftheindividualcolumnshears.Theapplicabilityoftheproposed methodtoestimatingindividualcolumnshearswasexploredbyapplyingtheamplification factorsandAdtoMRSA-estimatedcolumnshearenvelopesandcomparingtheobtained quantities to the NRHA shear demands. Findings are summarized in Figure 7.For all four buildings, the method provided conservative estimate of interior and middle column design shears in most of the stories.The NRHA-calculated shears slightly exceed those estimated by the proposed method in the upper and lower two stories of some buildings (Figure 10).In all cases, the method gave closer estimate to design shear than Method B2 of ACI 318. It is recommended that the column design shear estimated by the proposed method at a given story i not be taken less than the design shears in stories above, that is stories j > i. For the buildings consideredthisresultedinconservativeestimationofdesignshearforcesofallinteriorand middlecolumns.AlternativelyMethodB2providesamuchmoreconservativeestimatefor design shears in interior and middle columns. 0.00 0.08 0.150.00.51.0Vi / WB20-1 Story Shear(a)hi / H0.00 0.08 0.15Vi / WB20-2 Story Shear(b)0.00 0.08 0.15Vi / WB20-3 Story Shear(c) B20-1 DBEB20-1 MCEB20-2 DBEB20-2 MCEB20-3 DBEB20-3 MCE In the exterior column the method described in Eq. 1 provided a conservative estimate at theDBElevelinbuildingA20-1everywhereexceptthetopstoryandthebottomtwostories whichweresignificantlyaffectedbybeamelongationeffects.TheMCE-levelshearsslightly exceededthoseestimatedbythemethodproposedexceptthebasestorywherethe underestimationwassignificant.InTypeBbuildings,themethodincreasinglyunderestimated thecolumnshearasthesizeoftheexteriorcolumnincreased.Here,sheardemandswereon average1.1-1.5timesthedesignshearsestimatedbythemethodforDBEhazardlevel.The largestunderestimationwasobservedinthebottomtwostoriesandespeciallyinthefirstthat wasmostlyaffectedbybeamelongationeffects.Furtherrefinementofproposedshear calculationmethodisneededtofindamoresuitablewayforestimatingdesignshearforcesin exterior columns. Figure 7.Comparison of column mean shear force response envelopes with proposed design method and ACI 318 design shear force envelopes. 00.20.40.60.81A20-1hi / HExterior(a)Interior(b)Mi ddl e(c)00.20.40.60.81(d)B20-1hi / H(e) (f)00.20.40.60.81(g)B20-2hi / H(h) (i)0.00 0.25 0.5000.20.40.60.81V / Ag (f 'c) (j)B20-3hi / H0.00 0.25 0.50V / Ag (f 'c) (k)0.00 0.25 0.50V / Ag (f 'c) (l) NRHA DBENRHA MCEACI 318 Method AACI 318 Method B2AdVMRSAASCE 7 MRSA Conclusions Based on the results previously presented, the following conclusions are drawn: 1) All of the studied buildings developed significant inelastic deformations in the columns at the base of the building and in 70% of the beams along the building height for both DBE and MCE hazard levels. 2) Increasing the size of exterior columns significantly reduces compressive strains in confined concrete and, to a lesser extent, reinforcement tensile strains developed in the up-sized columns, possibly leading to less post-earthquake damage. Inter-story drift ratio of the base story decreased with increase of the size of the exterior columns. 3) Building A20-1, for which columns had progressively smaller cross-sections and amount of longitudinal reinforcement with height, developed moderate inelastic deformations in the columns around the levels where the size and reinforcement reduced with reinforcement tensile strains to range between 0.3-0.8% at the DBE and 0.7-1.7% at the MCE shaking level. The same locations of buildings B20-1, B20-2, and B20-3 developed negligible inelastic deformations. 4) Kinematic interaction between beams and columns at the bottom two stories due to beam elongation resulted in significant increase of the first-story exterior column shear.Mean values of first-story exterior column shears were between 1.4-2.0 times those in the first-story interior columns.This effect should be considered in the design of the columns. 7) ACI 318 procedures for determining column design shear resulted in widely different design values with the commonly used method (referred to as Method B2 herein, see section Response Overview for definition) significantly underestimating column shear across most of the stories. 8) Preliminary results indicate that alternative methods based on system overstrength may be suitable for better estimation of column shears. This is currently under development. Acknowledgments The study was partially supported from the Tall Buildings Initiative of the Pacific Earthquake Engineering Research Center, University of California, Berkeley. References 1.American Society of Civil Engineers (ASCE), 2010. Minimum design loads for buildings and other structures, ASCE 7-10, Reston, VA. 2.Elwood,K.J.,Pampanin,S.,andKam,W.Y.,2012.NZ22February2011ChristchurchEarthquakeand ImplicationsfortheDesignofConcreteStructures,inProceedings,InternationalSymposiumonEngineering Lessons Learned from the 2011 Great East Japan Earthquake, Tokyo, Japan, pp.1157-1158. 3.AmericanConcreteInstitute(ACI),2011.BuildingCodeRequirementsforStructuralConcrete,ACI318, Farmington Hills, MI. 4.Visnjic T, Panagiotou M, Moehle JP. Seismic Response of 20-story Tall Reinforced Concrete Special Moment Resisting Frames Designed with Current Code Provisions. Earthquake Spectra 2013; 29 (4): tbd-tbd. 5.McKenna,F.,Fenves,G.L.,andScott,M.H.,2007.OpenSystemforEarthquakeEngineeringSimulation (OpenSees). Pacific Earthquake Engineering Research Center. http://opensees.berkeley.edu/. 6.Standards New Zealand (SNZ), 2006. Concrete Structures Standard NZS3101, Wellington NZ.