Engineering Structures 32 (2010) 1925–1936

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Engineering Structures

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Collapse modelling analysis of a precast soft storey building in AustraliaAri Wibowo a, John L. Wilson a,∗, Nelson T.K. Lam b, Emad F. Gad a,ba Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Victoria, 3122, Australiab Department of Civil & Environmental Engineering, University of Melbourne, Victoria, 3010, Australia

a r t i c l e i n f o

Article history:Available online 30 March 2010

Keywords:Precast concreteSoft storey structureForce–displacement relationshipEarthquake performance

a b s t r a c t

A unique experimental field test study that provides insight into the push-over load–deflection andcollapse behaviour of a soft storey building is reported in this paper. The five storey building hadbeen identified as being particularly vulnerable to earthquake excitation due to the particularlyweak connections at each end of the ground floor precast columns that constituted the soft storey.Consequently, four field testswere undertaken to investigate the actual lateral force–deflection behaviourof the soft storey columns. Interestingly, the tests indicated that the soft storey columns possessedsignificant displacement capacity despite significant strength degradation. An analyticalmodel developedto predict the overall force–displacement relationship that was influenced by the three componentmechanisms of (a) connection strength at column ends, (b) gravity rocking strength and (c) ground slabinteraction, was found to be in excellent agreement with the experimental test results. The presence ofthe ‘non-structural’ ground slab provided additional lateral strength to the system and greatly influencedthe ‘as-built’ performance. The displacement capacity of the precast soft storey systemwas much greaterthan an equivalent in situ system, due to the rigid body rocking behaviour of the columns. The precastsoft storey system was found to have sufficient displacement capacity for lower seismic regions, but theperformance was considered marginal for higher seismic regions.

Crown Copyright© 2010 Published by Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Background

A soft storey building (Fig. 1) is one that has a discontinuityin the stiffness of the building where one storey is significantlymore flexible than adjacent storeys. According to ASCE 7-05 [1],a soft storey has lateral stiffness less than 70% of that of the storeyimmediately above, or less than 80% of average stiffness of thethree storeys above. Under substantial ground shaking, soft storeybuildings behave like an inverted pendulum with the ductilitydemand concentrated at the soft storey elements.Soft storey buildings are considered to be particularly vulnera-

ble because the rigid block in the upper levels has limited energyabsorption capacity and displacement capacity, thus forcing thecolumns in the soft storey to deflect and absorb the seismic energywhilst also maintaining the axial gravity load carrying capacity.Collapse of the building is imminent when the energy absorptioncapacity or displacement capacity of the soft storey columns is ex-ceeded by the energy demand or the displacement demand. Thisconcept is best illustrated using the ‘Capacity Spectrum Method’

∗ Corresponding author. Tel.: +61 3 9214 4882; fax: +61 3 9214 8264.E-mail address: jwilson@swin.edu.au (J.L. Wilson).

0141-0296/$ – see front matter Crown Copyright© 2010 Published by Elsevier Ltd. Aldoi:10.1016/j.engstruct.2010.03.003

shown in Fig. 2 where the seismic demand is represented in theform of an acceleration–displacement response spectrum (ADRSdiagram) and the structural capacity is estimated fromanon-linearpush-over analysis expressed in an acceleration–displacement re-lationship [2].

1.2. Scope and objective

A unique research project has been conducted jointly bySwinburne University of Technology and the University ofMelbourne, which involved the experimental field testing of afive-storey soft storey building in Melbourne [3–7]. The buildinghad been identified as being particularly vulnerable to earthquakeexcitation due to the particularly weak connections at each endof the ground floor precast columns creating a weak soft storeywith an unknown displacement capacity. In contrast, in situcolumns with connections as strong as the members, would havecreated a more deterministic system in terms of lateral strengthand displacement capacity predictions using results from codesof practice and previous published test results. Consequently,four field tests were undertaken to investigate the actual lateralforce–deflection behaviour of the soft storey precast column softstorey system. The objective of the experimental investigationwasto study the actual load–deflection and collapse behaviour of softstorey buildings when subjected to lateral loading and to comparewith non-linear analytical predictions.

l rights reserved.

1926 A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936

Weak or soft storey Inverted pendulum

Earthquake Excitation

Fig. 1. Idealisation of soft storey structures [8].

Fig. 2. Capacity spectrum method.

This paper provides a unique insight into the collapse behaviourof a precast soft storey building, including details of the buildingconfiguration, experimental test set-up and instrumentation,force–deflection push-over curves, observed collapse behaviourand a comparison with detailed non-linear theoretical predictions.The results are then used to predict the likely seismic performanceof the building for regions of low and high seismicity using adisplacement based approach.

2. Building configuration and test set-up

2.1. Building configuration

The five storey test building shown in Fig. 3 consisted of fourlevels above the open plan ground storey. The upper levels of theresidential building consisted of precast walls and slabs creating arigid box whilst the ground floor was constructed from reinforcedconcrete columns and beams founded on individual pad footings.The building is significantly stronger in the short portal directioncompared with the long spandrel direction.Observations from the pre-trial test of adjacent buildings

indicated that the building to be used for the experimental testinghad a precast ground floor storey with connections significantlyweaker than the members they connected (Fig. 4). Consequently,the ground floor columns tended to rock when subject to ahorizontal load. Several material samples were also collected fromthe site to investigate the properties of the building elements, andwere tested to determine steel and concrete properties.

2.2. Test set-up

Four push-over field tests were undertaken on a ground floorbay consisting of four columns pre-loaded with kentledge. It wasdecided for safety reasons to demolish the upper levels of thebuilding to first floor level to create the test bay without damagingthe portal frames (Fig. 5). Four test bays were selected for testingand were separated from each other by saw cutting the floor slabbetween adjacent bays. A steel frame was constructed at first floorlevel and positively secured to the slab and beams to providesupport for the kentledge and to provide anchorage for the lateral

load to be applied to the soft storey bay. Horizontal loads wereapplied in both the strong andweak directions via steel tension tiesand hydraulic jacks secured to a piled reaction frame located somedistance from the test bay, as shown schematically in Fig. 6. Thefour columns in a typical bay would typically support around 200tonnes of dead load from the upper storeys. However, it was notdeemed practical to load the frame with the full gravity load andconsequently only 50 tonnes of kentledge in the form of precast‘jersey barriers’ was added to provide a reasonable loading. Overallthe self weight of the soft storey test frames including kentledgewas in the order of 600 kN.The slab on groundprovided significant restraint to the columns

at ground floor level and consequently two tests were conductedwith the ground slab intact and the other two tests with the slabcut away to prevent restraint. Overall, the following four field testswere undertaken:

a. Test 1: Strong direction with ground slab.b. Test 2: Weak direction with ground slab.c. Test 3: Strong direction without ground slab.d. Test 4: Weak direction without ground slab.

3. Instrumentation

Various measurement techniques were utilised to obtain theoverall load deflection behaviour of each test specimen as well ascurvature of the column and crack width. The applied horizontalloads were measured using load cells, whilst the displacementmeasurement techniques included global positioning system(GPS), total point station (TPS), laser scanner, photogrammetry,visual measurement using a theodolite and ruler, and LVDTtransducers. A degree of redundancy was built into the measuringsystems to ensure that if one system failed, results could beobtained from other sources. The theodolite was particularlyimportant for directly measuring the incremental displacementswhen the testing was in ‘displacement’ control. In addition, somesystems provided real time readings such as visual measurementand LVDT whilst other methods such as photogrammetry andthe laser scanner required some post processing. The overallmeasurement setup for Test 1 is shown in Fig. 7 showingpositions of the GPS antennas, total point station, laser scanner andtheodolite.

4. Test procedure and experimental results

4.1. Test procedure

A hydraulic jacking system with tension ties and a temporarypiled tie back anchorage system were used to apply the lateralloads to the frame. The test specimens were laterally loaded under‘force’ control in increments of 10 kN until the ultimate load wasreached. The loading was then applied in ‘displacement’ controlwith displacement increments of 25 mm up to around 250 mm inboth directions.

4.2. Experimental results

The experimental results are summarised in Table 1, whilstthe load–deflection curves for the four tests are shown in Fig. 8.The displacements shown correspond to the lateral displacementat the first floor slab level and the load is the total lateral forceimposed on the structure. In the strong direction, the majorityof the deformations were concentrated at the end connections,with gaps opening at the foundation and beam interfaces. Thiswas a clear indication that the columns were significantly strongerthan the connections. In the weaker direction, deformations were

A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936 1927

Fig. 3. Building configuration.

IIIIIIIVV

A A

GL GL

Foundation Cast in situ

Precast Column

Precast slab (130mm thick) Precast beam

75.00

8mm @ 3 00mm

4# 22 HIGH TENSILE STEEL BAR

380.00

10 .0 0

100 .00180.00100.00

94.8

512

0.30

85.94

Section A-A

1000

mm

780m

m24

00m

m

180.00Strong Direction Connection Weak Direction Connection

Fig. 4. Structural details of the test bay.

concentrated at the foundation interface and at the interface of theportal beams and the first floor slab. It can be shown analyticallythat the load–deflection behaviour of the strong direction ismostly affected by the connection strength at the top of thecolumn, whereas the gravity load rocking mechanism dominatesthe load–deflection behaviour in the weak direction.

Overall the lateral strength to self weight ratio in the strongdirection was around 40%–50% and in the weak direction 12%–20%as listed in Table 1. The soft storey column was found tohave significant displacement capacity irrespective of strengthdegradation. An important outcome of this work is that thecolumns maintained their gravity load carrying capacity at a

1928 A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936

Fig. 5. Demolition process of the buildings.

(a) Strong direction. (b) Weak direction.

Fig. 6. Test set-up.

MeasuringScale

GPS

W

Scan

ner

Posi

tion

BSP1

BSP2

GPS data Receiver

Base GPS antenna

TP3 Theodolite

Theodolite

TP4

TP2

TP1

Sout

h Fr

ame

SW

SE NE

NW

Bay 1

GPS

GPS NS

E GPS data Receiver

T

T

TPS

GPS data ReceiverN

orth Fram

e

Measuring Scale

Pulling Direction

Fig. 7. Measurement setup for Test 1.

(a) Results Test 1 and 3 (strong direction). (b) Results Test 2 and 4 (weak direction).

Fig. 8. Experimental test results.

lateral displacement of about 260 mm or a drift capacity ofabout 8% under these quasi-static conditions. Interestingly, theweak column/foundation and column/beam precast connectionsallowed the columns to rock about their ends, greatly enhancing

the displacement capacity of the soft storey system comparedwithrigid end column connections more typical of in situ construction.The ground slab, which is considered non-structural from a

design perspective, provides significant restraint to the frame,

A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936 1929

Table 1Summary of maximum load, displacement and drift of all tests.

Orientation Test Maximum load (kN) Maximum load (% self weight) Maximum displacement (mm) Maximum drift (%)

Strong direction Test 1 310 52 200 5.9Test 3 250 42 255 7.5

Weak direction Test 2 125 21 225 6.6Test 4 75 12 260 7.6

especially in the weak direction. The increase of load capacity dueto the existence of ground slab is about 25% in the strong directionand about 67% in the weak direction, which has a significant effecton the ‘as-built’ performance of the structure.

5. Theoretical prediction

This section develops a theoretical model to predict theload–deflection behaviour of the soft storey test bayswhich is thencompared with the experimental results. The ground floor framinghad been designed as a precast system with the connections sig-nificantly weaker than the members. Consequently, the horizontalcapacity could be calculated from both the connection capacity ofthe top and base of the column (FTC and FBC ) combined with thegravity load rocking mechanism (FR) and the additional restraintprovided by the slab on ground (FGS) as summarised in Table 2.The lateral capacity of bay was determined using Eqs. (1) and

(2):

• Strong direction test:

FH = FC + FR + FGS = FTC + FBC + FR + FGS . (1)

• Weak direction test:

FH = FC + FSF + FR + FGS= FTC + FBC + FSF + FR + FGS (2)

where:FC = horizontal capacity from connection strength at top andbase of columnFR = horizontal capacity from gravity load rocking mechanismFGS = horizontal restraint from the reaction of ground slabagainst the columnFSF = horizontal restraint from the steel frame connection on topof first floor slab.

5.1. Connection strength at the column ends (FC )

(a) Base connection strength (FBC )The moment strength of the base connection provides a

negligible contribution to the overall system capacity and canbe ignored. However, the shear strength of the base connectioninfluences the overall displacement behaviour for the tests thatinvolve column interaction with the ground slab. This will bediscussed further in Section 5.3.(b) Top connection strength (FTC )The strength of the top connection between the precast

concrete column and beam members is provided via the concretein compression and theunbonded steel tendon in tension (and fullybonded steel reinforcement, if present at the connection interface).The behaviour of precast concrete ductile connections has beenwidely investigated over the last two decades. Several approachesfor predicting the behaviour of this mechanism consist of trilinearidealisation of moment–rotation behaviour [9], calibration ofthe hysteresis parameter of hybrid connections [10] and finiteelement modelling [11]. Simple calculation for predicting theultimate strength of hybrid precast concrete has been illustrated

Fig. 9. Column lateral displacement–rotation relationship.

in NISTIR 5765 [12]. The top connection analysis in this paper wasdeveloped based on the moment–rotation principle proposed byPampanin [13].The presence of the unbonded tendon prevents the use of a

closed form solution to estimate the depth of the neutral axisbecause of strain incompatibility between the steel and concreteat the connection interface. Consequently, the neutral axis positionwas estimated from a trial and error procedure that solved theequilibrium equations at the connection interface by estimatingthe tendon tensile strains and forces from a global displacementand joint rotation consideration. In particular, the angle of the gapthat opens at the connection interface is assumed equal to thecolumn rotation as shown in Fig. 9.The algorithm used to solve the force–deflection relationship of

the top connection is outlined in the following steps:

Step 1. Fix increment of global displacement ∆ from 1 mm to250 mm, and calculate the related rotation for each ∆increment.Rotation of column:

θ = arctan(

∆

Lcolumn

)(3)

where:θ = angle of gap opening at beam–column interface∆= global displacement of structureLcolumn = height of column.

Step 2. Guess an initial value of both axis depth c and concretestrain εc (refer Fig. 10):• Evaluate the strain in unbonded high-strength (HS) steelbar∆pt.i = θ

(dpt.i − c

); εpt.i = ∆pt.i/Lubt (4)

where:∆pt.i = elongation at HS steelLubt = unbonded length of HS steeldpt.i = distance of HS bar from extreme fibre of

compression concrete.• Evaluate the strain in mild steel bar∆s.i = θ (ds.i − c) ; εs.i = ∆s.i/Lubs (5)where:∆s.i = elongation at mild steelLubs = unbonded length of mild steeldpt.i = distance of MS bar from extreme fibre of

compression concrete.

1930 A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936

Table 2General principles of lateral strength prediction analysis.

• Evaluate section equilibriumCc − Ts + Cs = Tpt + P (6)where:Cc = compression concrete forceTs = tension mild steel forceCs = compression mild steel force

Tpt = post-tensioning force acting as anexternal force

= Tin + f (εpt)Apt (7)Tin = initial prestress forceP = external load.The compression concrete force Cc is determined usingmoment-curvature analysis [14], whilst the forces in themild steel (Ts and Cs) and the force Tpt in HS steel bars arecalculated as a function of steel strain from MS and HS

stress–strain relationship respectively. In the case of thistest building, there were no bonded steel reinforcementbars at the connection interface and consequently Ts =Cs = 0 which simplifies the model as shown in Fig. 11.

Step 3. Iterate Step 2 until the equilibrium equation (6) is satisfiedand calculate the moment capacity (Eq. (8)) with theupdated values of c and εc .

M = Ccc2+

j∑i=1

Tids.i −j∑i=1

Tpt.idpt.i − Pc2. (8)

Step 4. Calculate the top connection horizontal load FTC .

FTC =MLcolumn

. (9)

Step 5. Repeat the whole process for the next increment ofdeflection∆ until∆ = ∆max.

A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936 1931

Fig. 10. Gap opening mechanism for general beam–column precast connection.

Fig. 11. Gap opening mechanism for beam–column connection field test.

5.2. Gravity rocking strength (FR)

The simple horizontal load prediction for the gravity rockingmechanism can be obtained by using an upper and lower boundestimate, based on the possible location range of the neutral axis

Fig. 12. Column gravity rocking mechanism.

(the neutral axiswas assumed at the centre and edge of the columnfor the lower and upper bounds respectively). In this section, theactual location of the neutral axis provided by top connectionanalysis has been used to calculate the horizontal capacity of therocking mechanism as expressed in the following equation andshown in Fig. 12:

FR =FV ∗ x1 +W ∗ x2

Lcolumn=FV(D−∆− c

2

)+W

(D−∆2

)Lcolumn

(10)

where:x1 = horizontal distance between the column axial load FV andthe neutral axisx2 = horizontal distance between column self weightW andthe neutral axis.

5.3. Ground slab restraint (FGS)

The ground slab provides a restraint to the lateral movement ofthe column. This additional restraintmodifies the global behaviourof the structure from a pure rocking mechanism into a partialcantilever column mechanism and as a result, a bending momentdevelops in the column at the level of the ground slab.An estimate of the lateral strength provided to the overall struc-

tural system by the ground slab can be obtained through simplestatics. The column is assumed as a cantilever beam supporting alateral force F at the free end. Froma simplemoment–areamethod,the angle of rotation θ and deflection ∆ at the free end relative tothe fixed end can be determined as:

θ =FL2

2EIand ∆ =

FL3

3EI. (11)

By substituting the curvature equation ϕ = M/EI into the dis-placement equation, the relationship between local curvature andglobal displacement can be expressed as:

ϕ =3∆L2. (12)

Based on this equation, for each increment of global structuredisplacement∆, the curvature andmoment capacity of the columncross-section at the ground slab location can be calculated and theequivalent force–displacement behaviour of the structural systemestimated.The base column connection does not affect the overall ultimate

lateral resistance of the soft storey system, but the shear behaviour

1932 A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936

Fig. 13. Effect of column base connection and ground slab restraint.

of the connection affects the post peak (declining) part of the push-over curve, by modifying the ground slab restraint mechanism inthree stages (refer Fig. 13):

Stage 1: Base connection prevents movement of the base columnresulting in cantilever column mechanism as previouslydescribed.

Stage 2: Localised horizontalmovement of the base column due todeformation and unzipping failure of the welded sectionof the U-bar base connection.

Stage 3: Pure rocking mechanism commences as the U-barconnection fractures.

The modelling approach used in the analysis is describedin Table 3 (together with Eqs. (13)–(22)) with the ground slabproviding a horizontal restraint and the column base connectionproviding a flexible spring restraint. Eqs. (13)–(14) describe theglobal displacement ∆T as a function of lateral force F for apinned base connection. The introduction of lateral flexibility intothe base connection increases the column top deflection due toa rigid body rotation of the column in addition to the columndeformation as described in Eqs. (15)–(18) for the weak directionand Eqs. (19)–(22) for the strong direction, by using unloadingstress–strain model for confined concrete illustrated by Sakai [15].The weakening of the column base connection results in thecolumn displacement increasing with a corresponding decreasein the lateral force capacity (i.e. the unloading section of theforce–displacement diagram).

5.4. Total horizontal capacity

The total horizontal load–deflection behaviour is the summa-tion of the three components (top and base connection strengths,gravity load rocking mechanism and the restraint of ground slab)as represented by Eqs. (1) and (2). The experimental results andanalytical predictions are in excellent agreement as summarisedin Tables 4 and 5 and Figs. 14–17.The load–deflection curve for the strong direction test with the

ground slab (Test 1) is shown in Fig. 14a, whilst the contributionsfrom the components are shown in Fig. 14b. Similarly, the resultswithout the ground slab (Test 3) are shown in Figs. 15a and 15b.The lateral resistance from the top connection (163 kN) ismarkedlyhigher than that from the rocking mechanism (92 kN), whilst thebase column connection provides negligible strength for both tests(i.e. around 0.1 kN). Significantly, the ground slab in Test 1 providesan additional 20% strength capacity, compared with the strengthachieved in Test 3 without the ground slab.The theoretical analysis results in the weak direction are also

in excellent agreement with the experimental field tests for Test 2

Fig. 14a. Comparison between experimental and analysis result for Test 1 (withground slab).

Fig. 14b. Components of lateral strength for Test 1.

(with ground slab, Figs. 16a and 16b) and Test 4 (without groundslab, Figs. 17a and 17b). In contrast to the strong direction test, thegravity rocking mechanism dominates overall load–displacementbehaviour of the structure in the weak direction. Moreover,the ground slab restraint increases the weak direction strengthcapacity by about 67% (i.e. Test 2 versus Test 4).The complete force–displacement relationship for the test bay

can be idealised into the following four stages as illustrated inFig. 18.(i) The resisting force increases steeply as a combination ofthe increase in both the connection and rocking mechanismstrength until the rocking mechanism reaches peak strengthat about 10 mm displacement (O–A).

(ii) The resisting force increases more gradually as the rockingstrength component decreases (A–B).

A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936 1933

Table 3Analysis of ground slab restraint.

s

where:kb = stiffness of column for hinge–hinge supporta= distance between column base and ground slabb= distance between ground slab and top of columnkBC = lateral stiffness of mild steel U-bar at column base∆T = global displacement of structure on top of columnAs = cross section area of mild steel U-bar at column baseIs = inertia moment of mild steel U-bar cross section at column baseLs = length of mild steel U-bar at column baseR= horizontal reaction at column base∆BC = lateral displacement of column base.

Fig. 15a. Comparison between experimental and analysis result for Test 3 (withoutground slab).

(iii) The resisting force plateaus as the unbonded high-strengthsteel bars yield and the concrete stress reaches ultimatestrength (B–C–D).

(iv) The resisting force then decreases significantly, as theconnection loses strength, high strength steel bars fracture,compression mild steel bars yield, concrete cover commencesto spall and the rocking mechanism dominates (D–E–F).

In summary, the lateral strength of the system in the strongdirection for Test 1was around 50% of the selfweight and consistedof 25% from the top beam–column connection, 15% from the

Fig. 15b. Components of lateral strength for Test 3.

rocking action and 10% from the ground slab restraint. Similarlyin the weak direction, the overall lateral strength of 20% consistedof approximately 5% from the top beam–slab connection, 7%from rocking and 8% from the ground slab restraint. Interestingly,a design calculation of lateral strength based on linear elasticprinciples would have excluded the strength components fromboth rocking and the ground slab restraint and hence significantlyunderestimated the actual strength of the soft storey system.The large drift capacity of the system in the order of 6%

was attributed to the rocking behaviour, with the maximumdisplacement controlled by the actual columndimensions together

1934 A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936

Fig. 16a. Comparison between experimental and analysis result for Test 2 (withground slab).

Fig. 16b. Components of lateral strength for Test 2.

Fig. 17a. Comparison between experimental and analysis result for Test 4 (withoutground slab).

Fig. 17b. Components of lateral strength for Test 4.

Table 4Horizontal capacity estimation for strong direction.

Predicted capacity Strong direction (kN) Weak direction (kN)(i) (ii) (i) (ii)

FC 164 160 0.04 0.04FSF 0 0 34 34FR 92 82 44 42FGS 69 65 50 48

FH (without ground slab) – 242 – 76FH (with ground slab) – 307 – 124

Note: (i) Maximum strength of each component. (ii) Strength of each component atmaximum lateral capacity.

B C DE

F

P

F

A

A = Peak of gravity Rocking MechanismB = High-Strength steel yield and strain

hardening C = Concrete reach the ultimate strength D = Concrete cover commence to spall E = Compression mild steel yield

Fig. 18. Typical lateral load–displacement relationship resulted from analysis.

with the P–delta effects. The rocking behaviour occurred becausethe precast column connectionswere significantlyweaker than themembers they connected. Interestingly, if the soft storey had beenconstructed in situ with connections as strong as the membersthey connected, then the lateral strength would have increased,but the drift capacity would have reduced substantially sincethe rocking mechanism would have been prevented, forcing thecolumns to deform inelastically in shear and flexure. Previousreinforced concrete column tests by the authors, indicate that thedrift capacity would have reduced to around 2% if the columns andconnections had been cast in situ [7] or a conservative 0.7% drift inaccordance with international guidelines [16,17].

6. Performance evaluation of soft storey buildings

The seismic performance of the building was assessed by usinga two tier displacement based seismic assessment of structurespresented in Wilson and Lam [2].

• First tier: The performance of the building can be simplyassessed using a ‘‘first tier’’ approach by comparing the seismicpeak displacement demand (PDD) with the displacementcapacity (∆c). If the PDD is less than ∆c , then the structure isdeemed satisfactory in terms of its ultimate performance.• Second tier: Alternatively, the capacity spectrum method(CSM) [16,17] can be used, where the seismic demand isrepresented in the form of an acceleration–displacementresponse spectrum (ADRS diagram) and the structural capacityis obtained from a push-over analysis (Refer Fig. 2). Theperformance of the structure to the design seismic event can beassessed from the point where the demand and capacity curvesintersect. The structure is considered to survive the design if thecapacity curve intersects the demand curve, and collapse if thecurves do not intersect.

The soft storey structure had considerable displacementcapacity beyond the traditional definition of failure used in highseismic regions, which is deemed to occur when the horizontalresistance capacity of the system is reduced to 80% of the nominalcapacity (for example, NZS1170.5:2004 [18]). Alternatively, amoredirect measure of failure could be considered, where failure isdefined at the point when the overall structure cannot supportthe gravitational loads resulting in catastrophic collapse. To allowfor some conservatism, it is suggested that this nominal failure

A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936 1935

Fig. 19. ADRS diagram for Z = 0.10g in accordance with AS1170.4 [19].

Table 5Comparison between predicted and experimental results.

Orientation Test Predicted capacity(kN)

Experimental maximumload (kN)

Strongdirection

Test 1 307 310Test 3 242 248

Weakdirection

Test 2 124 125Test 4 76 75

Table 6Displacement demand for Australia (for Z = 0.10g).

Site class A B C D E

Soil type Hard rock Rock Shallow soil Deep soil Very soft soilPDD (mm) 30 35 50 75 120

point be associated with a displacement limit set at 75% of themaximumdisplacement capacity. This preliminary and alternativedefinition which was supported by the experimental push-overtest, is considered more realistic, particularly for regions of lowerseismicity where the ground shaking is more modest in termsof displacement demand and duration and provides the basis forfurther study and investigation.

6.1. First tier assessment

In a soft storey building all the lateral displacement is concen-trated at one storey, hence the building can easily be representedas a single degree of freedom (SDOF) system, with the maximumdisplacement equal to PDD.The PDD is dependent on the seismicity of the region and the

soil type. For a lower seismic region such as Australia, an effectiveground acceleration for a 500-year return period is typically in theorder of Z = 0.10g , which is equivalent to a peak ground velocityof PGV = 75mm/s. The seismic demand in the form of an ADRS di-agram scaled to Z = 0.10g for the different soil types in accordancewith AS1170.4 (2007) [19], is illustrated in Fig. 19. The soil typesrange from A–E and represent hard rock (A), rock (B), shallow soil(C), deep soil (D) and very soft soil (E). Importantly, this responsespectra has a corner period between the regions of constant veloc-ity and constant displacement of T2 = 1.5 s, which is consideredrobust for earthquakes up to magnitude Mn = 7 [20,21]. The re-sulting PDD as a function of site class for Z = 0.10g is summarisedin Table 6.The displacement capacity ∆C of the soft storey for Tests 1

& 3 and Tests 2 & 4, was around 200 & 255 mm and 225 &260 mm as shown in Figs. 14–17 and summarised in Table 1.These displacement capacities reduce to 150 & 190 mm and 170& 195mm respectively for the test pairs using the modified failure

criteria associatedwith 75% of the displacement capacity. Since∆Cgreatly exceeds PDD for all soil types, the soft storey structures canbe deemed satisfactory in terms of their ultimate performance forZ = 0.1g .

6.2. Second tier assessment

The second tier method can be illustrated using the same softstorey building described in this paper and checking the per-formance for different seismic regions ranging from low to highseismicity (Z = 0.10g to Z = 0.40g), for a shallow soil site(Site Class C). It should be noted that this scaling is considered vi-able provided the earthquake magnitude does not exceedMn = 7(for larger magnitude events this scaling would be deemed un-conservative, since the corner period T2 would also increase andbe greater than 1.5 s, further explanation is provided in Refer-ence [21]).The soft storey capacity curves from Figs. 14–17 have been

superimposed on the ADRS diagram for both the strong andweak directions, creating the capacity spectrum diagram shownin Figs. 20(a) and (b). The intercept between the demand and ca-pacity curves provide an estimate of the likely performance point.For the strong direction Tests 1 and 3, the displacement demandsare found to be within elastic limit for Z = 0.10g , inelastic forZ = 0.20–0.30g , and insufficient for Z = 0.40g as shown inFig. 20(a). The results are similar for the weak direction Tests 2and 4, although the soft storey is considered marginal for Test 4at Z = 0.40g as indicated in Fig. 20(b). These results are based on ashallow soil site (site class C), whereas the performance would bedifferent for deep and softer soil sites, such as site classes D and E,where the displacement demands are significantly greater.

7. Conclusions

1. Four soft storey structures were tested in the strong andweak directions to obtain actual push-over force–displacementcurves. The preliminary results showed that the soft storeycolumns could sustain large drifts in the order of 6%–8% whilstmaintaining the gravity axial loads despite the reduced lateralstrength capacity due to P–delta effects. The horizontal strengthand drift capacity predicted by a non-linear rocking model was inexcellent agreement with the lateral capacity obtained from theexperimental tests. Significantly, the experimental tests confirmedthat the lateral displacement capacity of the soft storey systemwasdirectly controlled by the width of the rocking column, which is avery significant finding from a collapse failure perspective.2. The large drift capacity of the precast soft storey structurewas

attributed to the weak connections which allowed the columns toundergo non-linear rocking at each end. Interestingly, the lateralstrength capacity of the soft storey system would have increasedsignificantly if the column end connections were as strong as themembers, but the drift capacity would have reduced from around6%–8% to around 2% since the rockingmechanismwould have beenprevented forcing the columns to deform inelastically with bothshear and flexural deformations. Hence, the precast soft storeyconstruction resulted in a structure that was weaker than a moretraditional in situ reinforced concrete structure, but a structurewith a far greater drift capacity developed through a non-linearrocking mechanism.3. The ground floor slab, which from a design perspective is

considered ‘non-structural’ provided significant restraint to thebase of the columns and increased the system lateral capacity,particularly in the weaker spandrel direction. Significantly, thiscommonly found ‘non-structural’ component greatly influencedthe ‘as-built’ performance of the structure.4. The soft storey structure had considerable displacement

capacity beyond the traditional definition of failure used in highseismic regions, where failure is deemed to occur when the

1936 A. Wibowo et al. / Engineering Structures 32 (2010) 1925–1936

(a) Strong direction. (b) Weak direction.

Fig. 20. Capacity spectrum method performance evaluation of test structures.

horizontal resistance capacity of the system is reduced to 80%of the nominal capacity. A more direct definition of failure iswhen the overall structure cannot support the gravitational loadsresulting in catastrophic collapse. To allow for some conservatism,it is suggested that the nominal failure point could be reducedto a displacement limit set at 75% of the maximum displacementcapacity. This preliminary definition is considered more realistic,particularly for regions of lower seismicity where the groundshaking is more modest in terms of displacement demandand duration and P–delta effects are not as significant. Thisalternative failure definition provides the basis for further studyand investigation.5. A seismic performance evaluation using a displacement

based assessment showed that the precast soft storey structurewould perform satisfactorily in regions of lower to moderate seis-micity, whilst the performance would be compromised in regionsof high seismicity, where catastrophic collapse through P–deltaeffects could be expected due to the excessive displacement de-mands. In addition, an in situ reinforced concrete system wouldhave performed significantly worse due to the reduced drift capac-ity associated with column flexure deformations rather than rigidbody rocking of the precast system.

Acknowledgements

The authors acknowledge the financial support from the ARCDiscovery Grant #DPO772088. The active support in completingfield test fromDelta Demolitions, the Office of Housing, and FentonPartners, is gratefully appreciated. The authors are grateful to Dr.Phillip Collier and the postgraduate team from the University ofMelbourne including Rupali S. Bhamare, Elisa Lumantarna, BidurKafle, David Heath, Eldar Rubinov and Anna Donets.

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