Computational Modelling of a Four Storey Post-Tensioned Concrete Building Subjected to Shake Table Testing

Prior research into low-damage wall systems has predominately focu sed on the walls behaviour in isolation from other building components . Although the response of these isolated walls has been shown to perform well when subjected to both cyclic and dynamic loading, uncertainty exists when considering the effect of interactions between walls and other structural and non-structural components on the seismic response and performance of entire buildings . To help address this uncertainty a computational model was developed to simulate the response of a full -scale four-storey building with post-tensioned precast concrete walls that was subjected to tri-axial earthquake demands on the E-Defence shake table. The model accurately captured the buildings measured response by incorporating the in-plane and out-of-plane non-linear behaviour of both the wall and floor elements. The model was able to simulate the deformation demands imposed on the floor due to compatibility with the post-tensioned walls, closely matching the behaviour and damage observed during the test. Dynamic loading and wall-to-floor interaction were shown to significantly increase the over-strength actions that developed when compared to the wall system considered in isolation. Disciplines Civil Engineering | Geotechnical Engineering | Structural Engineering Comments This article is published as Watkins, J., Sritharan, S., Nagae, T., Henry, R.S. 2017. Computational Modelling of a Four Storey Post-Tensioned Concrete Building Subjected to Shake Table Testing, Bulletin of the New Zealand Society for Earthquake Engineering 50, no. 4, December 2017: 595-607. Posted with permission. Authors Beca Group, Ltd.; Sri Sritharan; Takuya Nagae; and Richard S. Henry This article is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/ccee_pubs/166 B11/le1i11 of !lie New Zealand Sociely for Ear1hq11ake E11gi11 eeri11g, Vol . 50, No . 4, Sep/ember 2017 COMPUTATIONAL MODELLING OF A FOUR STOREY POST-TENSIONED CONCRETE BUILDING SUBJECTED TO SHAKE TABLE TESTING Jonathan Watkins1, Sri Sritharan, Takuya Nagae and Richard S. Henry (S ubmitted April 2017; Reviewed J1111e 2017; Accepted Oclober 2017)


INTRODUCTION
Recent earthqu akes have confirmed that re inforced concrete (RC) buildings built to modern seisnlic design standards have generall y petformed as per the adopted design philosophy by protecting the li ves of their occupants.However, the structural damage suffered by convent ional RC buildings during maj or earthqua kes can result in the cost of repair being uneconomi cal, leading to their demolition.For exampl e , 60% of the multi-storey RC buildings in the C hristchurch city centre were demolished followin g the 2010-201 1 Canterb ury earthqu akes in New Zealand , despite many suffe rin g what was considered to be onl y moderate structural damage [l].These findings have increased the demand for development and implementation of low-damage building des igns that can be rapid ly re-occupied following a major earthquake, thereby limiting the econonli c conseq uences for the building ow ner.
the wa ll uplift.The effects of wall-to-floor interaction can be significant and coul d res ult in the building experienci ng residual drifts and not achieving its intended low-damage performance criteria due to the tim e req uired to repair fl oor dam age .Furthermore, the increased over-strength demands that occ ur due to wall -to-fl oor interaction may result in undesirable wa ll behaviour, such as shear fa ilure or base sliding.
Unbonded post-tensioned precast concrete wa lls are one alternati ve to achi eve a low-damage seismic resisting system.Since the late l 990's, the res ults of each ex perim enta l in vest igation into this wa ll system have repo rted that the wa lls ex hibit a dependable rocking behaviour with minimal structu ra l damage and residual drifts [2][3][4][5][6][7][8][9].However, th ere has been relatively little research condu cted on the seismi c response of buildings that utilise these wall systems.When subjected to a latera l-load , the behaviour of the wa ll is characterised by a single horizonta l crack opening up at the waLI base .This uplift , whi ch is comparable to that expected in cast-in -place wall buildings [5], introduces a relative vert ical displacement and rotation at each wa ll -to-floor interface, as shown in F igure l .Henry et al. [10] reported that wa ll-to-floor interaction increased the lateral-load capac ity of a prototype building th at utilised unbonded post-tensio ned precast concrete wa lls by as much as 50% at 2% latera l drift when compared to the prototype bui lding that isolated the floor from  To properly in vest iga te the effects of wall-to-floor interaction large-scale building tests are required.Notable tests of buildings th at utilised unbonded post-tensioned precast concrete walls include the PRESSS five storey building [2], the three-storey precast building tested on the UCSD shake tab le [11], and the four-storey precast post-tensioned building tested on the E-Defe nce shake table [12].The PRESSS and UCSD bu ilding used spec iall y designed wa ll-to-floor connectors that isolated the floor from the uplift of the waU to provide more dependable waU behaviour.The E-Defence building used a wall-to-floor detail that is typical of current practice , using precast floors and a cast-in-situ toppin g with continuity reinforcement.Prior numerical in vestigations into the response of the E-Defence building.did not full y consider the effect that the potential di splacement incompatibility between the wall and floor had on the response of the building [13 , 14].To address the effects of wall-to-floor interaction on the building response , an analytical investi gation was undertaken using a 3D numerical model representing the E-Defence test building.

TEST BUILDING
A brief description of the test building is provided to enable understanding of the computational model and full details of the building and test program were published by the joint Japanese and United States research team [1 2 , 15 , 16].The building was designed to a mixture of Japanese and United States standards and it should be noted that some details such ®- as the grouted post-tensioned columns are unlikely to be utilised in New Zealand.As show n in Figure 2, the plan dimensions of the building were 14.4 min the frame direction and 7 .2m in the wall direction , and included fo ur stories with an inter-storey heights of 3.0 m.Two-bay bonded postte nsioned moment frames were used in the frame direction alon g gridlines 3 and 4. Unbonded post tensioned precast concrete walls with additional energy di ss ipation provided by mild steel reinforcement were used at each end of the building in the wall direction alon g gridUnes A and C. The wall design was typical of precast wall s with hybrid connections involving unbonded post-tensioning and mild steel reinforcement and are referred to as Wall A and C. Unbonded post-tensioned beams spanned between the wall s and columns at the corners of the building on gridlines A and C. A sin gle bay moment frame was used along gridline B in the wall direction, as shown in Figure 2. Double-T precast floor units with a cast-insitu 100 mm toppin g were used for the floor system .At each storey the floor cantilevered out from the building perimeter between 0 .35m to 1.25 musing a cast-in-situ slab .

Walls
T he unbonded post-tensioned wa ll s were 2500 mm long and 250 mm thick , as shown in Figure 3.Each of the two ducts contained ten 15 .2mm (S WPR7B) prestressing strands that were post-tensioned to 60% of their 1600 MPa characteristi c yield strength.The tendons were anchored underneath the foundation and on top of the roof wall panel that gave the tendons an unbonded length of 13 ,450 nu11 .Eight 22 mm diameter (D22) mild steel reinforcing bars crossed the wall-tofound ation interface to provide additional energy di ssipation and strength to the wall .The 22 mm diameter reinforcin g bars were unbonded over a length of 1500 mm above the foundation interface to minimi se inelastic strains and were terminated at the top of the first storey wall panel.The first storey wall panel used confinement reinforcement with a characteri stic yield strength of 785 MPa and spaced at 75 mm to resist the hi gh compressive strains in the wall toe reg ion.The concrete mi x used in the first two storeys of wall A and the grout mix used between those pane ls and the wall-tofoundation joint contained steel fibres and all other concrete used conventional concrete mixes.The grout pad between the wall and foundation was 30 mm thick .

Frames
The beams in the wall direction were 300x300 nu11 and utilised two 17 .8nu11 prestressing strands (SWPRL19L), as shown in Figure 4 .The tendons were anchored on the external face of the exterior columns .The unbonded length for the tendons in both beams was 7650 mm as the tendons in PG2 I 597 beams passed through the hori zontal ducts in the wall panel.The columns were 450x450 mm with eight 21 mm diameter (SBPR1080/ 1230) prestressing bars.The beams in the frame direction were 500x300 mm with four prestressing tendons within each beam that was anchored on the outside face of the exterior columns.The tendons used fo r the first and second , third and roof beams in the frame direction were, three 15.2 mm (S WPR7BL) strands , one 19 .2mm (SWPR19L) strand , and one 17 .8mm (SWPRLl 9L) strand, respectively.After post-tensioning the prestressin g bar or tendon in the column and beams in the frame direction to 80% of the characteristic yield strength , the tendon ducts were filled with high strength grout.The characteristic yield stress of the prestressing strands was 1600 MPa and the prestressing bar was 1080 MPa.

Floors
The Double-T precast pre-stressed concrete floor unit was 2000 mm wide and 200 mm deep, as shown in Figure 5.The floor units were placed paralle l to the wall direction and were supported by the beams in the frame direction.The floor units bad a seating length of 30 nm1 and were tied into the supporting beams via the 100 rnrn cast-in-situ toppin g with continuity reinforcement .A two-way mesh of 10 mm diameter reinforcement at 200 mm centers was placed within the castin-situ topping.Mechanical couplers were cast within the wall at 200 llll11 centers that 13 mm dowe l bars screwed into and lapped with the floor reinforcement.The distance between the center of the first Double-T rib and the center of the wall was 600 mm.

Material Properties and Weights
T he average strength of the precast concrete elements and the topping concrete at the time of testing was 83.2 MPa and 40.9 MPa , respectively.The total weight of the building was measured as 5356 kN and the total effective we ight of each storey was reported as 822 kN (! st), 8 19 kN (2nd ), 822 (3 rd), and 996 kN (4th) .The fourth flo or was the hea viest due to approximately 200 kN of eq uipment such as air conditioning units .

Ground Motions
The test building was subjected to increasing intensities of the strong motion records from the IMA-Kobe and JR-Takatori stations during the 1995 Kobe earthquake (M w = 6.9).The

COMPUTATIONAL BUILDING MODEL
A three dimensional graphi ca l representation of the computational model developed for the building in SAP2000 v 18. I.I [19] is shown in Figure 7 .The layo ut of the elements in the model used the building centerline dimensions that were shown in Figure 2. Desc riptions of the main model features is provided with a more deta il ed account of the model development and validation publi shed separately [20].
The elastic beam column elements representing the wa lls were 2500 mm in length , 250 mm in thi ck ness and 3000 mm in height.A lumped plasticity fibre hinge section that behaved like a multi -spring macro model was used to capture the uplift and rocking at th e wall base.Thi s modelling technique has been pre viously validated against s ix isolated unbonclecl posttensionecl wall tests [20].The clisc retisation of the fibres in th e fibre hinge representin g the wa LI cross section is shown in Figure 8. Eac h fibre re prese nted an area of the wa ll cross secti on at its base and was ass igned the appropriate material mode l for that reg ion of the wall.The e nergy di ss ipating reinforcing steel that was unbonclecl over 1500 nm1 at the base of wall A and C was also included as fibres within the fibre hin ge.This approach has th e sa me outcome as modelling the re inforcement as extern al e le ments because the displacement 1500 mm abo ve the waLI base is almost identical to the uplift at the wall base .The unbondecl post-tensioned te ndons in Wall A and C were fixed I m below th e model's fo undat ion leve l and connected to the wa ll 0 .45m above the roof, representing the anchorage conditions of the tendon in the building.The post-tensioning stress in the wall and beam tendons were simulated by applying an initial di sp laceme nt to the non -linear tru ss ele ments an appropriate amount equal to the initial strain w ithin the tendons .To represent the width of th e wa ll at each floor level, ri gid e lements were attached to the wa ll ce ntreline e lement , as shown in red in Figure 7.These ri g id e lements had a stiffness ten times greater than the gross stiffness of the wa ll .The res ponse of the post-ten sio ned beams in the wall direction was domin ated by the rocking at the bea m end s; therefore , the mode llin g method discussed fo r the wall was also used to represe nt the behaviour of these beams .The res ponse of the frames in the wall directi on was dom in ated by rocking of the column bases and bea m end s, and hence, the modelling method used for the walls was used but with the prestress of the bonded tendons applied as an external ax ial load.During construction of the building the prestress in g tendons in the column and beams in the fram e directi on were post-tensioned and then the tendon end s were anchored , and after this the tendon ducts were grouted .To represent this construction sequence in the model , axial loads that represented the posttensioning force were applied at the location of the tendon anchors.The bonded prestressing te ndons were included in the fibre hin ge section• with the ir stress-strain back bone modified to account for the strain due to post-tensioning that was modelled by the external axial fo rce.This method accounted for the axial fo rce clue to post-tensioning and the increase in the tendon strain clue to rocking at the joint .' ' ' x Unconfined Concrete ' ' ' ' ' ' x Confined Concrele x Energy Dissipating Rcinforcment • In the frame direction , the moment demand in the column above and below the beam co lumn joints exceeded the column ' s cracking moment capacity.A detailed moment curvature analysis was performed in Response 2000 [21] for the column cross-section including the 19 mm diameter mild steel reinforcement and bonded prestressing tendons with an initial strain representing the post-tensioning .The model moment-curvature hinge used the average column axial demand as the effect of the variation in axial load was expli citl y accounted for by the fibre hinge at the base of the column.The plastic hinge len gth of the moment-curvature hinges was the same as the fibre hinge section at the column base and the hysteresis followed Takeda rules .The main purpose of these hinges was to capture the change in the columns flexural ri gidity and had negligible effect of the hysteretic energy dissipated in the model.The moment demand on the columns in the wall direction did not exceed the column's cracking moment, however, the column had already experienced cracking due to the demand from the frame moment.Hence , the moment of inertia (lg) of the e lastic beam column elements representing the columns flexural stiffness in the wall direction was reduced to 0 .6lg.The value of 0.6 was determined from the New Zealand Concrete Structures Standard , NZS 3101 :2006 Table C6.6 [22] for a col umn with a normalised axial demand (N*/Agfc) of approximately 0.17.
Research by Arteta [23] and Welt [24] suggest that material regularisation is not required if the fibre hinge section height was equal •to the damaged zone length where concrete spalling/cracking occur.Therefore , the fibre hinge lengths used for the model components was based on the observed damage to the test building , with the lengths/heights estimated from damage photographs [20].This resulted in fibre hinge lengths of 250 mm for the walls, 120 mm for the beams in the wall direction , 200 mm for the beams in the frame direction , and 180 mm for the columns.The material model for the concrete within the fibre hinge sections did not have any tensile capacity as the concrete in a rocking joint only res ists compression.Mander et al. [25] equations were used to define the backbone stress-strain curves for all the concrete material models.The ultimate confined concrete strain was calculated usi ng an equation provided by Moehle 's and Arteta [23,26].The hysteretic behaviour of all concrete elements in the model was governed by Takeda [27] rules .The Holzer et.al. [28] equation was used to define all the reinforcement stress-strain backbones used in the model and the hysteretic behaviour of the reinforcement st ress-strain models was governed by kinematic rules.The stress-strain backbone of all the prestressing tendons was defined by Devalapura and Tadros [29] .Further details about the material parameters used in the model reported in Watkins [20].
To investigate the wall -to-floor interaction , the non-linear behaviour of the floor in both the in-plane and out-of-plane directions needed to be included.The floor was represented by non-linear layered shell elements meshed at approx imately 500x500 mm; a detailed sensitivity study verified that further discretisation did not yield additional accuracy.The concrete shell layer was 130 mm thick and had five integration points through its thickness .The combined thickness of the in-situ topping and Double-T flange was used as no evidence of delamination between the two elements was observed during the test.The material model used for the concrete layer within the shell elements accounted for crack formation and rotation.
The concrete material model was a modified implementat ion of the two-dimensional Darwin-Pecknold [30] co-axially rotating smeared crack concrete material model.Darwin and Pecknold ' s original model was modified to include Vecchio and Collins [31] Modified Compression-Field Theory that accounts for compressive strength reduction based on perpendicular tensile strain .The in-plane behaviour of the floor 's t'wo way 10 mm diameter reinforcement mesh spaced at 200 mm was represented in the model by two smeared membrane layer.Bond slip and dowel behaviour of the floor reinforcement was not considered within the layered shell element as thi s was modelled separately for the wall-to-floor connection detail.The dowel bar connection between the floor and wall was modelled by zero length non-linear links using a bi-linear relationship proposed by He and Kwan [32].The stiffness of the Double-T ribs was considered important and thu s the ribs were represented by elasti c-beam column elements that were pinned at their connection to the beams in the frame direction to represent that they were only vertically supported by a short ledge on these beams in the building .
The damping a building experiences when subjected to earthquake excitation originates from many different sources that can be broadly categorised as either viscous or hysteretic damping.In the computational model hysteretic damping was explicitly captured throu gh the use of non-linear material behaviour assigned to the fibres within the fibre hinge sections .In iti al stiffness Rayleigh proport ional damping was used to capture the visco us damping.Viscous dampi11g was assumed to be 2.5% as per the procedure recommended by Pennucci et.al. [33].Shake table tests conducted by Twigden [7] and Nazari [34] both confirmed recommended damping of 2% for accurate non-linear time hi story analysis of isolated rock in g walls.Therefore , an increase in damping to 2 .5% was considered reasonable for a computational model that considered the entire building where additional sources of damping were present.Two additional modification s were made to the damping sc heme in order to avoid factitious damping forces when using initi al stiffness Rayleigh damping.First, any element in the model that had a high initi al stiffness and was expected to yield was assigned a stiffness proportion damping constant a1 scaled by 1/50 .This mimicked the updated tangential stiffness behaviour for yielding elements (a feature not available in SAP 2000) .Second , period elongation was considered so that damping is not over-estimated as inelastic behaviour and damage occurred.The initial period in the wa ll direction was 0.29s and the elongated period in the frame direction was 0.86s which resulted in ao and ai va lues of0.2732 and 0.0017 , respectively.Where ao and ai are the mass and stiffnessproportional damping coefficient used in determin in g the initial stiffness Rayleigh damping matrix.

MODEL RESULTS AND DISCUSSION
The building model was subjected to the Kobe 25 %, Kobe 50%, and Kobe 100% shake table accelerations consequently (as was done during testing).The resu lts presented focuses on the wa ll direction response as the design used for the frame direction , in particular the columns, are not considered representative of New Zealand practice.

Modal Properties
As discussed by Nagae et.al. [1 2], the test building exhibited a significant torsional response during all the imposed ea1thquake motions.The modal properties of the test building before being subjected to earthquake motions were investigated during this study to find a possible explanation for the observed torsional behaviour.Examination of the actuator di splacements showed there was negligible twisting of the shake table.Analys is of the accelerations meas ured at the accelerometer locations when the buil d ing was subjected to white noise at the beginn ing of the experimental test program found that in the waU d irect ion the ends of th e building were excited with differe nt mag nitudes , at the fo urth fl oor Wall C di splaced 24% fm1h er than Wa ll A. A detailed examination of the concrete strength at the time of testing fo r the wall pane ls reveal ed that three out of the fo ur wall panels in Wall Chad an average concrete strength of 72 MPa , 15.5 % less than the average concrete stre ngth of 83.2 MPa used fo r other precast elements .When the modulus of e lasticity of wall C was ad justed to represent the lower concrete strength , the model accurate ly captured the measured first mode shape in the wall directi on and fundamental period of 0 .29s, as shown in F igure 9a.
In the fra me directio n, the bui lding's accelerometers were all alig ned alo ng gri d li ne 3A.Analysis of the accelerations in the frame di rection can o nl y produce the normalised mode shape at the bui lding's center and not at each of the pe rimeter fra mes .The model accurate ly captured the experimental fra me directi on no rmali sed mode shape and fu ndamental period of 0.45s , as shown in F igure 9b .
T he acceleration hi story of the ea rthquake records coul d also acti vate a to rsional mode of the building.Analys is of the building response during the white noi se test did detect a pure ly torsio nal mode with a meas ured peri od of 0.2 l s.The building mode l accurately captured the torsio nal model peri od and norm alised mode shape , as shown in Figure 9c.However, it is diffic ult to determine if thi s e lasti c torsional mode was acti va ted during earthquake motio ns as th e building's inelasti c response changed its stiffness.accurately captu re the drift res ponse of the building .One reason for the reduced acc uracy was the mode l did not capture the resonance of the torsional mode after l 7s whi ch res ulted in a peak rotati on of 0.0082 radi ans.The model accurately captured the self-centerin g behaviour of the building at the end of the test with less than 2 mm (0 .02% drift) of residu al di splacement for both the model and ex periment.The model accurately captured the experimental base moment and base shear response from the start of the test to 16.5s.After 16 .5sthere was reasonable agreement between the amplitude of experimental and model base shear and moment capacity, even though the model response was out-of-phase with the experiment.The model accurately calculated the measured peak drift , base moment and base shear, which were 1.6%, 25,810 kNm , and 2860 kN, respectively.There was good agreement between the ex perimental and mode l base moment versus drift res ponse, with the envelope and shape of the hysteretic moment-drift response accuratel y captured by the model.There was also good agreement between the model and experiment for the inter-storey drift , storey shear and storey overturning moment e nvelope response, as shown in Figure 13.

Strength Components
Table 1 reports the contribution of various lateral-resisting systems at 1 % drift in the wall direction of the building when subjected to a uni-directional push-over and from Kobe 100% test between 18s to l 9s, full details of thi s analysis are reported in Watkins (20).Exterior and Interior framin g action refer to the outrigger effect of beam shears transferred into the ex terior and interior columns.Theoretically the global base moment from this framing act ion is the number of stories multiplied by the over-strength shear capacity of the rocking joint at the beam-column interface multiplied by the distance between the exterior or interior columns.Furthermore, the exterior boundary beams that frame into the edges of the wall provided additional moment capacity to the wall system through framing action.The increase in wall system moment capacity from the boundary beams increased the lateral force required to obtain the same uplift as an equivalent wall system without boundary beams framing into the wall ends.In the case of the building modelled thi s restraint was not sufficient to prevent the wall uplifting.The computational model incorporated the moment capacity of the framing beams and therefore captured the res traint on uplift of the wall .Table 1 shows the exterior columns had a 57 % reduction in their moment capacity primarily due to the large dynamic bidirectional rotational demands imposed upon them that resulted in significant spalling of concrete at the column base.While the interaction effects increased the axial demand at th e base of the columns, the large rotations caused the spal lin g of concrete and reduced moment capacity.The walls experienced some cyclic degradation; dynamic loadi ng and interaction effects resulted in a 25% increase in the base moment contribution from the exterior framing action in the wall direction.

Stiffness Degradation
The modal periods corresponding to the first mode in the wall direction before and after the Kobe 100% test for the experiment and model are reported in Table 2.The model did not capture the period elongation that occurred during the Kobe 50% test ; reasons for this include not capturing the peak excursion to 0.51 % drift and micro-cracking of the concrete elements and grout pad.However , it correctly estimated the magnitude of the period elongation during the Kobe 100%, which was equal to approximately 40% .The model captured approximately 45 % of the measured torsional rotation during all three earthquake tests except after l 7s during the Kobe 100% test.Investigation of the measured accelerations records suggested that after 17s the building torsional mode was resonating with the input excitation resulting in a peak torsional rotation of 0.0082 radians.Furthermore , the grout pad underneath wall C experienced significant damage at its ends clue to the lack of steel fibres (which wall A grout pad had) and it is probable that thi s damage contributed to the large torsional rotations observed .

Wall Response
The comparison between the moment-drift response of each wa ll during Kobe 100% in both the in-plane and out-of-plane directions are shown in Figure 14.There was good agreement with the base moment capacity, but each wall was subjected to different displacement demands due to the buildings torsional rotation.The out-of-plane moment capac ity of the wa lls was approximately 3.5 % of their in-plane capacity; a similar proportion to an isolated bi directional wall test that is di sc ussed by Watkins (20).
A comparison of the uplift at the ends of wall A and C for both the experiment and model are shown in Figure 15.The model accurately captured the uplift at the wall ends for both walls.The experimental peak rotation and uplift for wall C was under estimated by the model as the model only captured approximately 50% of the torsional rotation , as discussed previously.A comparison of the axial force in the prestressing tendons of wall C from the test and model are shown in Figure 16 .The model accurately captured the experimental response except for the peak rotation and ax_ial force , which the model under estimated clue to only capturing approximately 50% of the building ' s torsional rotation.The prestressing tendons were initiall y post-tensioned to 60 % of their characteristic yield strength , and at the peak wall rotation the stress of tendon 1 was 71.5 % of its measured yield strength (fy == 1760 MPa).Hence , the prestressing tendons in the wall remained in their elastic range which allowed the building to self-center in the wall direction after the ea1thquake motion ..9-The effect of dynamic load ing on the wa ll ax ia l force and base shea r was in ves tigated by comparing the response of th e mode l subj ected to a uni-directi onal pushover to the Kobe 100% earthquake record .As shown in Figure 17, there was good agreement between th e two model responses when considering wall ax ial fo rce, whi ch was expected as almost all of the axia l force imposed on the wall is du e to the prestress ing.However, there were significant differences between the base shear generated in wa ll A for the two load in g types, as shown in Figure 18 .T he peak base shear demand for wa ll A during Kobe 100% was 1262 kN at a wall A global drift of 1.3%, and at the same drift the base shear demand was 880 kN for the model pusho ver analysis.Therefore , dynamic load in g in creased the base shea r demand of wall A by 43 % when compared to the same model subj ec ted to a pseudo-static uni -directional pushove r ana lys is.In accorda nce with the New Zealand Co ncrete Structures Standard [22] (NZS 3 101 :2006) a dyn ami c shear magnification facto r of l .3 would apply to the test building (Appendix CD4.3) , wh ich sli ghtly underestimated the measured amplification.The building mode l peak wall base shea r durin g the Kobe l 00% earthquake was 110% greater than the sa me building model, which did not consider the wall-to-floor interaction or dynamic loading.Therefore, guidance is still req uired to assess the likel y overstrength res ultin g from wall-to-floor interacti on.It is important to note that the effect of wa ll -to-floor interaction in creasin g the wa ll base shear demand has the potenti al to be more severe for re in forced concrete wall s.The rei nforced concrete building with identical geometry tested adj acent to the post-tensioned building on the E-Defence shake table experienced shear sliding at the base of its wa lls [35], and it was noted the actu al base shea r demands were much higher than calculated , although th ese increased demands were less than the walls theo reti cal capacity to resist shea r sliding.The results of the post-tensioned building mode l wo uld stron gly suggest the increase in the reinforced conc rete wall base shear demands were du e to wall-to-floor interacti on.If the over-stren gth effect of wall-to-floor interaction is not accounted for in the capacity des ign process , undesirable fa ilure modes, such as shear sliding may occur .Perpendicul arly further out from wall A , there was no di scernible vertical di splacement.However, near gridline C, the edge of the upliftin g colunm subjected the length of the building in the wa ll direction to vertical displacements.Also the floor region to the left of the interio r colunms was uplifted along the length of the building in the wall direction , as highli ghted in the fi gure.A comparison between the experiment and model ve rtical displacement of the first storey floor at various locations during Kobe 100% 14.54s , is shown in Figure 2 1.The figure shows the model accurately captured the measured floor verti cal displacements, which provides further validati on that the bu il ding model developed can capture both the in-plane and out-of-plane floor behaviour and effects of wall-to -floor interaction.
! .. The componen ts of lateral-load resistance for the building model su bjected to a uni directi onal pushover in the wall direction at l % drift are reported in Table 3 .The model s floor behaviour was mod ified so that it used a rigid diaphragm type constraint (no floor), in-pl ane floor behaviour (membrane), and in-plane and out-of-plane behaviour (s hell ).Further information about these different techniques of modelling the floor is reported in Watkins [20].T he reported results show that in-plane and out-of-plane floor behaviour contributed to an increase in the buildings lateral load capacity of 2,482 kNm (14%) and 4,883 kNm , (28 %) res pecti vely .The vertical deformation of the floor contributed approx imately two-thirds of the addi tional lateral-load resistance and the elongation or sho rtening of the floor contributed the remain ing third .The in creased lateral strength highlighted the imp01tance of considering the wall -to-fl oor interaction and non-linear behaviour of the floor diaphragm.Column Response A comparison of the column base moment res ponse from the model during Kobe 100% and the model subjected to a unidirectional pushover analysis are shown in F igure 22 .In the fram e direction , the envelope of the time-hi story model response had some agree ment with the pushover response; however, in the wa ll direction the time-hi story model response enve lope was significantly less than the pushover response due to the bi-ax ial moment de mands.The effect that dynami c loading had on the column axi al fo rce was in vestigated by comparing the response of the model subj ected to a unidirectional pushover and to the Kobe 100% earthquake record .There were significant differences between the ax ial load in th e external column for the different model loading co nditi ons, as shown in Figure 23.The max imum and minimum axial force for the exterior columns durin g the Kobe 100% ea1thquake were 3741 kN and 1471 kN .The equi valent axial forces at 1. _ .
-------------------------;;; After the Kobe 100% test , signjficant damage was observed at the base of the corner columns , as shown for column 4C in Figure 24, and the damage shown was typical fo r the base of all the tes t building columns.Most of the cover concrete at the column base had spalled , exposing the tra nsverse reinforcement and some of the prestressing bar ducts.The local res ponse of the column bases was in vestigated to understand how thi s damage occurred.In both the experiment and model, the peak column base rotat ion in the frame direction was approx imately 4% .The large rotations in co njunction with the axia l forc e caused hi gh strains in the cover concrete zone, causing that region to spall excessively .After the concrete spalled , the fl ex ural ri g idity of these co lumns was greatly reduced , making their base con nection to be more like a pin support than a fix ed support .

Exposed prestressin g bar duct CONCLUSIONS
A computational model of a post-tensioned concrete bui ld ing tested on the E-Defence shake table was presented and subjected to three increasing intensities of the Kobe ea rthquake motion and compared to the meas ured respo nses .The model acc uratel y captured the building' s g lobal drift, base moment and base shear res ponse during the Kobe 25 % and 50 % test.These tests represented a serviceability level and design level earthquake in a moderate to hi gh seismicity region, respecti vely .From the acc uracy of these results , it is recommended that a viscous clamping ratio of 2.5% is appropriate for models of buildings th at utilise self-centering concrete wall s.
The mode l accurately captured the building response in the wa ll direction during the maximum credible earthquake test, Kobe 100% .Furthermore , the model acc urate ly captured th e local res ponse of the wall , including , wall uplift , neutral axis length , prestressing tendon axial fo rce , and longitudinal energy di ssipating reinforcement stra in.The effects of the floor interaction on the beams in the wall direction were also accurately captured.The fl oor pro vided aclclitional compress ive and tensile forces when the beams were subjected to positive and negati ve rotations.The model accurately calcul ated the response of the fl oo r due to verti cal deformations imposed by the wa ll and column uplift.The accuracy with which the model ca lcul ated the measured response of the building va lidates the modelling approach of unbonclecl post-tensioned concrete walls presented by Watkins [20].
Analysis of the building's fundamental mode shapes showed th at the first mode in the wall direction contained a torsional res ponse .This elastic torsional res ponse was captured when loca l va ri ations in the meas ured unconfined concrete compress ive strength and its effect on the wall st iffness were considered : During the Kobe 100% test, signifi cant torsional rotations were measured , des pite the building being sy mmetri ca l in plan and in elevation.On average , the model calculated approximately 50% of the measured torsional rotation for all the Kobe tests.Further research is required to understand the torsional rotations that occ ur during inelasti c response as this model was limited in its ability to capture thi s complex behaviour.However, it was clear that modelling of the tors ional response is important to accurately capture the response of the test building .
Furthermore, the dynamic load in g of the earthquake motion in creased the wall base shear and varied the column axial fo rce compared to that calculated by the mode l subjected to a uni -directional pusho ve r anal ys is .Dy nami c loading increased the wall base shear demand by 43 % and dec reased the column axial force by 25% compared to the same model subj ected to a pseudo-stat ic pushover anal ys is .The dynami c magnification estimates in the New Zealand Concrete Structures Standard (NZS 310 l :2006) are appropriate to account for the increase in wall base shear clue to dynamic loading.However, the design standard does not currently explicitly prescribe a dynamic magnifi cation factor for the column ax ial forces, and it is recomme nded that this should be considered as part of the capacity design process.
These results also show it is important to consider both the inplane and out-of-plane behav iour of the floor to accurate ly capture a seismic response of buildings and understand the over-strength actions that may develop and implication that thi s may have on the intended strength hi erarchy, in elastic mechani sms, and failure modes .Add itional g uidan ce on how to assess the likely over-strength from wall-to-floor interaction to prevent undesirable failure modes is req uired.

Figure 1 :
Figure 1: Lateral load behaviour of a rocking wall.
Internal fram e (grid B) tendon configuration

Figure 2 :
Figure 2: Plan and elevation overview of test building (dimensions in 111111).

Figure 3 :
Figure 3: Wall A and C first floor cross-section (dimensions in mm).

Figure 7 :
Figure 7: Computational model of th e E-Defence building (a) three-dimensional model (b) eleJ1ation of grid A and C.

Figure 8 :
Figure 8: Wall A and C fibre discretisation.

Figure 9 :
Figure 9: Comparison behveen test and model initial modal shapes.

22 Figure 11 :
Figure 11: Comparison between experimental and model global response in the wall direction for Kobe 50% (a) moment-drift response (b) drift response (c) moment response (d) shear response).

Figure 12 :
Figure 12: Comparison between experimental and model global response in the wall direction for Kobe 100% (a) moment-drift response (b) drift response (c) moment response (d) shear response).

2 Figure 17 :
Figure 17: Comparison behveen model subjected to pushover and Kobe 100%/or wall A axial force-drift response.

Figure 18 :
Figure 18: Comparison between model subjected to pushover and Kobe 100% for wall A base shear force -drift response.Beam ResponseA co mparison of the neutral axis length response for the beam on the first storey between wa ll C and grid 3 from both the test and model are shown in F igure 19.There was good agreement between the model and experimental response and the model accurately captured the effect that the floor slab had on the neutral ax is length of th e beams in the wall direction .The beam rotated further in the positive direction as thi s was the direction that the wall uplifted at the bea m end measured.A compressive force in the floor slab was developed when the beam rotated in the positi ve direction which reduced the neutral ax is length .When the beam was subjected to negative rotations , the floor was in tension and increased the compression forces and neutral axis length of the beam.Beam Rotatio n (rad) 300 -0.94 _ -0.02 o o.0_ 2 ---===o =" .0=4c: 250 -E 5 200•

Figure 19 :
Figure 19: Comparison behveen experimental and model for neutral axis length-drift response for first storey beam in wall direction during Kobe 100%.Floor Response A plan view of the building with contours representing the first storey vertical displacements from the model durin g Kobe 100% at 14.54s is shown in Figure 20.The vertical uplift of wall A and C subjected a localised floor region around the wall edge to significant vertical displacements.Approximately 50% of the verti cal displacement imposed on the floor by wall uplift was accommodated by local deformation fo r the floor slab between the wall and first Double-T rib (-600 mm).Perpendicul arly further out from wall A , there was no di scernible vertical di splacement.However, near gridline C, the edge of the upliftin g colunm subjected the length of the building in the wa ll direction to vertical displacements.Also the floor region to the left of the interio r colunms was uplifted along the length of the building in the wall direction , as highli ghted in the fi gure.A comparison between the experiment and model ve rtical displacement of the first storey floor at various locations during Kobe 100% 14.54s , is shown in Figure21.The figure shows the model accurately captured the measured floor verti cal displacements, which provides
Commence ment of wall uplift occurred at 14.4s , as defined by an in-plane wall rotation greater than 0.001 radians .The peak measured base moment of -19 ,380 kNm and base shear of 2250 kN were accurate ly captured by the model.There was generally good agreement between the ex periment and model for the global base moment versus drift response.The model's hysteretic moment-drift response accurately captured the experimental energy di ssipated durin g the Kobe 50% test and the model al so accurately captured the softening response of the building due to rocking at the wall base.
response from the start of the tes t up until 18s .Du ring thi s time range the model accurately captured the measured peak dri fts of 0 .095%and -0 .1 % .T he model a lso accurately captured the measured peak base shea r and moment capac ity of 8933 kNm and 11 26 kN , respecti ve ly .Between 18s and 20 .8s the model drifts shifted out of phase whe n co mpared to the experimental response, and the large exc urs ion to 0.1 6% drift was not accurate ly captured .After 20 .8s the model response returned to bein g in-ph ase with the experimenta l shown in F igure 11 .There was good agreeme nt between the ex periment al and model global drift , moment and shear response except fo r a couple of cycles .The model accurately calculated th e initial peak drift of 0 .2 1 % at 14.5s, and the peak drifts at 17 .5sand17 .7s of -0 .36%and0.28 %, respecti ve ly.The model was unab le to capture the large excursion to 0 .5 1 % dri ft at 18 .1 4s , instead it estimated a drift of 0 .33% .However, the model accurate ly captured the building self-ce ntering capability at the encl of the test with no sig nificant res idual di splacement.

Table 1 :
Wall direction global base moment contributions at 1% drift.

Table 2 :
First mode periods in wall direction.

Table 3 :
Wall direction global base moment contributions at 1% drift for the building model.
[22]wa ll drift estimated by the pushover model were 3267 kN and 196 1 kN, respectively.Therefore , the dynamic loadi ng increased and decreased the maximum and minimum ax ial force estimated by the pushover analysis by 15% and 25 %, respectively.Dynamic magnification for column axial fo rces is currentl y not ex plicitly prescribed in the New Zealand Concrete Structures Standard[22](NZS 3 101 :2006).Based on these res ults, it appears that the dynamic magnification of column ax ial forces should be included as part of the capacity des ign process . ______[__•