Research ArticleCyclic Behaviour of Expanded Polystyrene (EPS) SandwichReinforced Concrete Walls

Ari Wibowo Indradi Wijatmiko and Christin R Nainggolan

Department of Civil Engineering Faculty of Engineering Brawijaya University Malang 65149 Indonesia

Correspondence should be addressed to Ari Wibowo ariwibowoubacid

Received 31 May 2018 Revised 12 October 2018 Accepted 8 November 2018 Published 26 December 2018

Academic Editor Pietro Russo

Copyright copy 2018 Ari Wibowo et al (is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Precast concrete walls become increasingly utilized due to the rapid needs of inexpensive fabricated house especially as traditionalconstruction cost continues to climb and also particularly at damaged area due to natural disasters when the requirement of a lotof fast-constructed and cost-efficient houses are paramount However the performance of precast walls under lateral load such asearthquake or strong wind is still not comprehensively understood due to various types of reinforcements and connectionsAdditionally the massive and solid wall elements also enlarge the building total weight and hence increase the impact ofearthquake significantly(erefore the precast polystyrene-reinforced concrete walls which offer light weight and easy installmentbecame the focus of this investigation (e laboratory test on two reinforced concrete wall specimens using EPS (expandedpolystyrene) panel and wire mesh reinforcement has been conducted Quasi-static load in the form of displacement controlledcyclic tests were undertaken until reaching peak load At each discrete loading step lateral load-deflection behaviour crackpropagation and collapse mechanism were measured which then were compared with theoretical analysis (e findings showedthat precast polystyrene-reinforced concrete walls gave considerable seismic performance for the low-to-moderate seismic regionreaching up to 1 drift at 20 drop of peak load However it might not be sufficient for high seismic regions at which double-panel wall type can be more suitable

1 Introduction

Tall buildings particularly with irregularities are prone tobehave poorly and collapse when subjected to lateral loadssuch as earthquake excitation or strong wind To overcomethis problem shear walls are commonly preferable to in-crease the lateral strength of structures significantly How-ever the added massive and solid shear walls result inincreasing the building weight and consequently the baseshear due to earthquake excitation which might reduce theeffectiveness of the shear wall use in the structures(e effortto reduce the weight of shear walls without losing lateralstrength capacity is necessary

(ere were many studies investigating lightweight con-crete shear walls with various techniques to reduce the ele-ment weight such as using lightweight aggregates applyingporous concrete system or inserting lightweight panel intothe wall Mousavi et al [1] studied the effectiveness of the JKsystem wall composed of EPS concrete (mortar with EPS

beads as fine aggregates) and galvanized steel reinforcementin sustaining lateral load It was observed that JK walls hadhigh ductility capacity but still need further observation forthe application in tall and medium buildings Yizhou [2]investigated that the use of gangue as an aggregate in concreteshear wall provided larger energy dissipation compared withnormal concrete shear wall Furthermore Hejin etal [3]focused on ash ceramsite as alternative for lightweight ag-gregate concrete shear wall which gave similar load-deflectionbehaviour and collapse mechanism to those on normalconcrete ones whereas Chai and Anderson [4] found that theperformance of concrete wall panels using perforated light-weight aggregate in low-rise buildings subjected to lateralforces was generally satisfactory Cavaleri et al [5] in-vestigated pumice stone in comparison with expanded clayand normal stone as aggregates in concrete shear wall whichshowed the benefit of the use pumice stones

On the other side reducing the weight of structuralelements can be achieved using the sandwich system by

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 7214236 9 pageshttpsdoiorg10115520187214236

inserting a lightweight panel inside the concrete element(is panel system is usually applied for insulation purpose aswell (e lightweight wall system investigated in this paperfocused on the use of the EPS panel as a filler and galvanizedwire mesh for reinforcing bar as shown in Figure 1

2 Research Methodology

(e specimens were designed as structural walls composinglow-rise building which were commonly found in house orschool precast buildings (e squat walls are generallydominated with shear behaviour which comparably differsto tall walls commonly found in high-rise building Concretetall walls have been considerably well-researched and well-understood [7ndash10] whereas concrete squat walls have beenincreasingly investigated [11ndash14] However innovationstudies on sandwich squat walls with the EPS panel were justinitially begun Previous experimental studies by Trombettiet al [15] and Ricci et al [16] showed that sandwich squatconcrete walls were comparable to those of regular RC wallsand able to sustain lateral load up to drift higher than 13whereas Palermo and Trombetti [17] comprehensively in-vestigated sandwich walls experimentally and analyticallywith the outcomes showed that properly designed walls canaccomplish high seismic performance requirement sug-gested by the code However the overall performance ofsandwich RC walls with lower steel reinforcement ratios(less than minimum requirements) still needs further in-vestigation and hence became the main focus of this study

(e laboratory tests on two specimens of sandwichreinforced concrete wall RCW4 and RCW8 have been un-dertaken Figure 2 shows the typical property of the walls Allspecimens had a height and width of 90 cm and 60 cm re-spectively (equivalent to aspect ratio of 15) (e RCW4 wallused a 4 cm thick EPS panel compared to the 8 cm EPS panelinstalled in the RCW8 wall (e specimens were reinforcedwith ϕ25ndash75mm wire mesh on each wall side and ϕ30mmsteel wires for connecting both mesh layers (e yield andultimate steel tensile strengths of the wire mesh were 600MPaand 680MPa respectively as shown in Figure 3 A 35mmthick shotcrete was applied on each outer side of walls with theconcrete strength of 15MPa (e walls and the foundationswere connected using ϕ10mm anchor bars spaced at 75mm

Quasi-static cyclic load procedure was applied at the tipof the wall specimens to obtain representative hystereticcurves of lateral load versus displacement (refer Figures 4and 5) as per ASTM E2126 code [18] (e drift-controlledorder was used for the loading test comprised drift in-crements of 0042 until attaining 0167 (representingcracking point) then drift increments of 016 untilreaching drift of 066 (representing yield point) andfollowed by inelastic stage at 066 drift increments (ehysteretic behaviours of walls were maintained using threeloading cycles at each drift ratio

During the testing process at each defined discretedisplacement stages the measurement of LVDTs dialgauges and crack propagation were recorded (e teststopped when the peak lateral strength of the specimenreduced by 20 (lateral load failure)

3 Experimental Test Results

Hysteretic curves of lateral load-drift relationship and thecrack pattern of all wall specimens are presented in Figure 6Both specimens RCW4 and RCW8 had similar peak lateralload of about 25 kN with different behaviour characteristicsRCW4 (EPS panel thickness of 40mm) developed moreclassical flexural mechanism whilst RCW8 (EPS panelthickness of 80mm) was more dominated with yield pen-etration behaviour due to the thinner concrete cover of wallfoundation As shown the specimen RCW4 managed tocomplete all three cycles of quasi-static cyclic load at 10drift and then failed at the first cycle of load at drift of 133whereas specimen RCW8 produced shorter maximum driftcapacity with failure at the first cycle of lateral load at 10drift A comparison of lateral strengths and drifts betweenthe experimental results and the theoretical predictions ispresented in Table 1

(e total lateral deformation consists of flexural shearand yield penetration components that were determinedusing dial gauge and LVDTand dial gauge measurements asshown in Figure 7

(e flexural displacement at the wall top at each i-segment of LVDTwas determined via the following equation(refer Figure 7(a))

Δfli 1113946L

0φ(x)xdx

Lminus Lvi

Lhδf2 minus δf1( 1113857 (1)

whereas the displacement of the elastic region at uppersegment was estimated analytically assuming uncrackedsection properties as follows

Δfl3 φL2

i

3

FL3i

3EcI (2)

where F lateral load Li segment length Ec concreteelastic modulus and I uncracked moment of inertia

(e shear deformation Δsh was predicted using diagonalLVDTs data (refer Figure 7(b)) as follows

Δsh δs1 minus δs2( 1113857

2sec ξ

δs1 minus δs2( 1113857

2

L2v + D2

1113969

Lv (3)

where D wall depth and δsi diagonal LVDTmeasurement

(e yield penetration component was measured using thevertical LVDTat the first level (refer Figure 7(c)) by assuminga rockingmechanismwithin the first section of wall An upperbound of the top displacement of the column can be cal-culated from the product of the slip rotation θslip and thecolumn height assuming rigid body rotation as follows

Δyp θslipLcolumn (4)

where θslip the slip rotation of tensile steel (δslip(dminus c)) asymp β β ((δf2 minus δf1)Lh) and c the neutral axisdepth at the column base interface (δf2(δf1 + δf2))Lh minusd2

(e deformation of walls comprising flexural shear andyield penetration components for RCW4 and RCW8specimens is shown in Figure 8 (e flexural deformationwas the most dominant component of about 75 and 55

2 Advances in Materials Science and Engineering

for RCW4 and RCW8 specimens respectively whilst theshear deformation was the least dominant deformationcomponent of below 5 for both specimens RCW4 andRCW8 Interestingly the yield penetration deformation ofRCW8 was about 27 compared to 21 of that of RCW4specimen which can be attributed to the smaller concretecover of sloof foundation on RCW8 and hence smaller bondslip strength between steel bar and concrete at foundation

4 Backbone Curve Models

Two simple models (backbone and simplified) were de-veloped for design purposes or basic assessment of lateralload-displacement capacity of such walls Both models forsandwich concrete walls are developed based on the modelpreviously developed by authors for lightly reinforcedconcrete walls [19]

41 Model 1 Detailed A detailed curve model is developedbased on displacement-based design methodology for pre-dicting the lateral load-drift behaviour (comprising fourstages cracking yield peak and lateral load failure) asshown conceptually in Figure 9

Smooth finish coat

Smooth finish coatElectrowelded

galvanised steel mesh

1 inch thick structural concrete(sprayed in 2 coats)

Expanded polystyreneinsulating core

Figure 1 Typical EPS sandwich concrete wall panel (refer [6])

Mortar

Wiremesh

EPS

5300350 350

350

350

400

110

0

(cm)

6000

Figure 2 Basic properties of wall specimens

0

100

200

300

400

500

600

700

800

0 00025 0005 00075 001

Stre

ss (M

Pa)

Strain (mmmm)

Figure 3 Stress-strain relationship of steel wire

Advances in Materials Science and Engineering 3

(a) Point A (cracking) the cracked lateral strength anddrift are calculated as follows

Fcr Mcr

L

ccr McrL

3EcIg

(5)

where the flexural tensile strength ft is taken as 06

fcprime1113969

(b) Point B (yield) the yield drift is calculated using the

effective second moment of area as follows

Fy My

L

cy MyL

3EcIe

(6)

(e Paulay and Priestley [8] model for effective momentof inertia is used as follows

(i) Flexure-dominated walls

Ie 100fy

+Pu

fcprimeAg

⎛⎝ ⎞⎠Ig (7)

(ii) Shear-dominated walls

Iw Ig

12 + C

C 30Ie

L2tD

(8)

where Pu nominal axial load Ag gross crosssection area of walls and t wall thickness

(c) Point C (peak strength) the model was developed byinvestigating the curvature within the plastic hinge regionusing the force equilibrium equation (N Cc + Cs minusT) withthe spalling strain (εcu 0003) used as a limit state forconcrete strain For low-rise buildings the presence ofgravity axial load is reasonably small and hence for sim-plicity the compression steel area is eliminated from theequilibrium equation (e peak flexural lateral load Fu andthe drift at concrete fracture cu can then be obtained asfollows

1415

500

500

123456789

101112131415161718192021222324

992

692

300

030

00

110

00

300

020

00

65001750 1750

10000

116

2

76

18

19 54

810

1213 20

11

2221

24

LVDT-∆controlLVDT-∆totalLVDT-∆totalLVDT-∆flexureLVDT-∆flexureDial gauge-∆flexureDial gauge-∆flexureDial gauge-∆ShearDial gauge-∆ShearDial gauge-∆up liftDial gauge-∆up liftDial gauge-∆base shearDial gauge-∆frame shearHydraulic jack 1Load cell 1ndash5tonLoad cell 2ndash10tonHydraulic jack 2ExtensometerRC wallSloofClampClampClampLoading frame

9

3

2317

Figure 4 Schematic of wall loading test setup

ndash15000ndash10000

ndash5000000

50001000015000

0 10 20 30 40 50

Def

lect

ion

(mm

)

Cycle no

Figure 5 Quasi-static lateral loading history

4 Advances in Materials Science and Engineering

Fu Mu

L

cpeak cy + cplmiddotp

(9)

where cplmiddotp (ϕpeak minus ϕy)Lp in which ϕpeak(εcukud)

(0003kud) and ϕy (3cyL) ku ((N + Astfy)085fcprimecdb) c 085minus 0007(fcprime minus 28) Ast tensile steelarea and εsm steel strain-hardening strain

(e plastic hinge length Lp can be estimated using thePaulay and Priestley model [8] as follows

Lp 0054L + 0022 dbfy (10)

(d) Point D (ultimate displacement) lateral load-displacement relationship of squat walls is dominated by

shear behaviour however for lightly reinforced squat walls theflexure behaviour still provides large influence on lateral load-drift behaviour (e failure mechanism which is influenced byshear strength degradation is needed hence the lateral loadfailure models developed for lightly reinforced concrete col-umns and walls [20 21] are modified for this model due to thesimilarity of lateral load-displacement behaviour betweenlightly reinforced concrete walls and columns

Shear strength (Vu) of RC walls consists of concretestrength (Vc) and steel strength (Vs) components as follows

Vu Vc + Vs (11)

In this model the concrete shear strength uses theformula developed based on principal tensile strength byauthors [22] whilst the steel strength proposed by Wesleyand Hashimoto [23] is used as follows

Vc 23Acr

ft( 11138572

+ftP

Acr

1113971

(12)

Vs chρh + cvρv( 1113857fydt (13)

whereAcr 085 ncρst( 1113857

036dt (14)

where d is the effective depth of RC walls which can beassumed as 08D and Ch 1minus cv in which

30

20

10

0

Late

ral l

oad

(kN

)

ndash10

ndash20

ndash30ndash150 ndash100 ndash050 000

Dri ()050 100 150

(a)

30

20

10

0

Late

ral l

oad

(kN

)

ndash10

ndash20

ndash30ndash150 ndash100 ndash050 000

Dri ()050 100 150

(b)

Figure 6 Crack patterns at 1 drift and hysteretic curves of all specimens (a) RCW4 (b) RCW8

Table 1 Strength and deformation properties of specimens RCW4and RCW8

Strength (kN) Drift ()Fcr Fy Fu δcr δy δu δlf

RCW4 Exp 28 18 235 017 047 100 133(eo 40 16 23 01 042 075 na

RCW8 Exp 23 20 245 017 055 067 100(eo 43 18 235 01 043 08 na

Note (e theoretical values were taken from moment-curvature analysis(flexural component only)

Advances in Materials Science and Engineering 5

cv 1 for alt 05

2(1minus a) for 05lt alt 1

0 for agt 1

(15)

with nc EsEc ρh the transverse reinforcement ratioρv the total longitudinal reinforcement ratio and ρst

the tension reinforcement ratio

As a note for moderate and slender walls (a gt 1 andhence cv 0) the steel strength component (equation (13))can be rewritten as a common shear strength formula

Vs ρhfy dt Avfyd

s (16)

(e ultimate drift can be obtained as follows

L

Lv3

Lv2

Lv1

Lh

Δf l

δf2

δf1β

(a)

D

L

Lv3

Lv2

Lv1

Δsh

δs1

ζ

δs2

Δsh1

(b)

DLH

d1 d2

c

Lv1

d

d

δf1

δslip

δf2

θslip

β

(c)

Figure 7 LVDT measurements for (a) flexure deformation (b) shear deformation and (c) yield penetration deformation

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7 8

FlexuralShearYield penetration

(a)

0

5

10

15

20

25

30

0 2 4 6 8 10

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7

FlexuralShearYield penetration

(b)

Figure 8 Variation of displacements due to flexure shear and yield penetration axial load-deformation relationship (left) and ratio of eachdisplacement to total displacement at each loading step (right) (a) RCW4 specimen (b) RCW8 specimen

6 Advances in Materials Science and Engineering

cu cy

k(1minus kα)minus 08

Fu

Vu1113890 1113891 (17)

where

k 03e57n

9minus a (18)

where α the drift ductility at the start of shear strengthdecrease

42 Model 2 Simplified (e simplified model is a simpleprocedure for estimating lateral load-drift behaviour oflightly reinforced concrete walls (is model consists oftrilinear stages with each state cracking yield and ultimateas shown in Figure 10

(a) Point A (cracking) the lateral strength at crackingpoint can be predicted by assuming cracking drift ccr

005(b) Point B (yield) the ultimate yield strength is cal-

culated using factored ultimate strength

Fy ϕFu (19)

whereas the corresponding yield drift (cy) is determinedusing the smallest values of the following alternatives

(i) Approximate value of cy 02ndash03(ii) Apply Ieff 05Ig (refer [24])

(c) Point C (ultimate) the ultimate drift (cm) can becalculated as a sum of the yield drift (cy) and the plastic drift(cpl) as follows (refer Figure 11)

cm cy + cpl (20)

(e plastic drift can be estimated by assuming amaximum acceptable strain in the steel bar at singlecrack at the wall base in the order of εs 50 and takinga more conservative approach to Priestley and Paulay[8] strain penetration length of lyp 4400 εy db asymp 15dbHence the following models can be obtained (referFigure 12)

Crack width

Wcr εs middot lyp 005 times 15db 075db (21)

Plastic drift

cpl θpl wcr

D 075

db

D1113888 1113889 (22)

(e lateral load-drift relationship between experimentaldata and proposed models are considerably in goodagreement as shown in Figures 13 and 14 More data arecertainly required to refine the models particularly for thedetailed model since it was developed using a semiempiricalapproach However interestingly the simplified model withthe pure analytical approach showed better prediction due tothe dominant combinations of flexural and yield penetrationbehaviour

Drift ()γy γpeak

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

D

γu

Fcr

γcr

B

θplp = (φpeak ndash φy)Lp

θplu = (φu ndash φy)Lp

Figure 9 (e backbone curve model of lateral load-drift capacity[20]

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Fcr

γcr

B

Figure 10 (e simplified model of lateral load-drift capacity

Wcr

D

γpl

Figure 12 Plastic rotation at wall base

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

Fcr

γcr

B

γpl = θpl = (φu ndash φy)Lp

Figure 11 Plastic drift of simplified model

Advances in Materials Science and Engineering 7

5 Conclusion

Two specimens of light-weight sandwich concrete walls havebeen tested in order to investigate the lateral load-driftbehaviour and collapse mechanism Specimen RCW4 witha thinner EPS panel developed more classic flexural be-haviour with drift capacity maxed at about 13 whilstspecimen RCW8 only managed to reached 10 withdominant yield penetration behaviour due to thinner con-crete cover of sloof foundation However the tests werestopped at 20 drop of peak load instead of further failure ataxial load collapse And hence the results can still beconsidered satisfactory for low-to-moderate seismic regionsbut might not be sufficient for high seismic regions

Two models comprising detailed and simplified ap-proach for predicting the load-displacement behaviour ofsandwich concrete wall subjected to lateral load have beendeveloped (e experimental data and the proposed modelsare in good agreement particularly the simplified model dueto the dominant behaviour of flexural and yield penetration

Data Availability

(e data that support the findings of this study are availablefrom the corresponding author upon reasonable request

Conflicts of Interest

(e authors declare that they have no conflicts of interest

References

[1] S A Mousavi S M Zahrai and A Bahrami-Rad ldquoQuasi-static cyclic tests on super-lightweight EPS concrete shearwallsrdquo Engineering Structures vol 65 pp 62ndash75 2014

[2] Z Yizhou ldquoMechanical properties of self-combusted ganguereinforced concrete shear walls under low-cyclic loadrdquoJournal of Zhejiang University Engineering Science vol 34no 3 pp 325ndash330 2000

[3] T Hejin Y Qingrong and S Xinya ldquoExperimental study onbBehaviours of reinforced ash ceramsite concrete shearwallsrdquo Journal of Building Structure vol 15 no 4 pp 20ndash301994

[4] Y H Chai and J D Anderson ldquoSeismic response of perfo-rated lightweight Aggregate concrete wall panels for low-risemodular classroomsrdquo Engineering Structures vol 27 no 4pp 593ndash604 2005

[5] L Cavaleri N Miraglia and M Papia ldquoPumice concrete forstructural wall panelsrdquo Engineering Structures vol 25 no 1pp 115ndash125 2003

[6] httpmpanelindonesiacomproductwall-panel[7] T Paulay ldquoEarthquake-resisting shear walls-New Zealand

design trendsrdquo ACI Journal vol 77 no 18 pp 144ndash152 1980[8] T Paulay and M J N Priestley Seismic Design of Reinforced

Concrete and Masonry Buildings Wiley Interscience Presspublication John Wiley amp Sons inc New York City NYUSA 1992

[9] O Esmaili S Epackachi M Samadzad et al ldquoStudy ofstructural RC shear wall system in a 56-story RC tall buildingrdquoin Proceedings the 14th World Conference on EarthquakeEngineering Beijing China October 2008

[10] A Carpinteri M Corrado G Lacidogna et al ldquoLateral loadeffects on tall shear wall structures of different heightrdquoStructural Engineering and Mechanics vol 41 no 3pp 313ndash337 2012

[11] P A Hidalgo C A Ledezma and R M Jordan ldquoSeismicbBehaviour of squat reinforced concrete shear wallsrdquoEarthquake Spectra vol 18 no 2 pp 287ndash308 2002

[12] T N Salonikios ldquoShear strength and deformation patterns ofRC walls with aspect ratio 10 and 15 designed to Eurocode8rdquo Engineering Structures vol 24 no 1 pp 39ndash49 2002

[13] T N Salonikios ldquoAnalytical prediction of the inelastic re-sponse of RC walls with low aspect ratiordquo ASCE Journal ofStructural Engineering vol 133 no 6 pp 844ndash854 2007

[14] J Carrillo and S M Alcocer ldquoShear strength of reinforcedconcrete walls for seismic design of low-rise housingldquordquo ACIStructural Journal vol 110 no 3 2013

[15] T Trombetti G Gasparini S Silvestri et al ldquoResults ofpseudo-static tests with cyclic horizontal load on cast in situsandwich squat concrete wallsrdquo in Proceedings of Ninth PacificConference on Earthquake Engineering Building anEarthquake-Resilient Society Auckland New Zealand April2011

[16] I Ricci M Palermo G Gasparini S Silvestri andT Trombetti ldquoResults of pseudo-static tests with cyclichorizontal load on cast in situ sandwich squat concrete wallsrdquoEngineering Structures vol 54 pp 131ndash149 2013

[17] M Palermo and T Trombetti ldquoExperimentally-validatedmodelling of thin RC sandwich walls subjected to seismicloadsrdquo Engineering Structures vol 119 pp 95ndash109 2016

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 13 Comparison between experimental data and theoreticalmodels for specimen RCW4

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 14 Comparison between experimental data and theoreticalmodels for specimen RCW8

8 Advances in Materials Science and Engineering

for RCW4 and RCW8 specimens respectively whilst theshear deformation was the least dominant deformationcomponent of below 5 for both specimens RCW4 andRCW8 Interestingly the yield penetration deformation ofRCW8 was about 27 compared to 21 of that of RCW4specimen which can be attributed to the smaller concretecover of sloof foundation on RCW8 and hence smaller bondslip strength between steel bar and concrete at foundation

4 Backbone Curve Models

Two simple models (backbone and simplified) were de-veloped for design purposes or basic assessment of lateralload-displacement capacity of such walls Both models forsandwich concrete walls are developed based on the modelpreviously developed by authors for lightly reinforcedconcrete walls [19]

41 Model 1 Detailed A detailed curve model is developedbased on displacement-based design methodology for pre-dicting the lateral load-drift behaviour (comprising fourstages cracking yield peak and lateral load failure) asshown conceptually in Figure 9

Smooth finish coat

Smooth finish coatElectrowelded

galvanised steel mesh

1 inch thick structural concrete(sprayed in 2 coats)

Expanded polystyreneinsulating core

Figure 1 Typical EPS sandwich concrete wall panel (refer [6])

Mortar

Wiremesh

EPS

5300350 350

350

350

400

110

0

(cm)

6000

Figure 2 Basic properties of wall specimens

0

100

200

300

400

500

600

700

800

0 00025 0005 00075 001

Stre

ss (M

Pa)

Strain (mmmm)

Figure 3 Stress-strain relationship of steel wire

Advances in Materials Science and Engineering 3

(a) Point A (cracking) the cracked lateral strength anddrift are calculated as follows

Fcr Mcr

L

ccr McrL

3EcIg

(5)

where the flexural tensile strength ft is taken as 06

fcprime1113969

(b) Point B (yield) the yield drift is calculated using the

effective second moment of area as follows

Fy My

L

cy MyL

3EcIe

(6)

(e Paulay and Priestley [8] model for effective momentof inertia is used as follows

(i) Flexure-dominated walls

Ie 100fy

+Pu

fcprimeAg

⎛⎝ ⎞⎠Ig (7)

(ii) Shear-dominated walls

Iw Ig

12 + C

C 30Ie

L2tD

(8)

where Pu nominal axial load Ag gross crosssection area of walls and t wall thickness

(c) Point C (peak strength) the model was developed byinvestigating the curvature within the plastic hinge regionusing the force equilibrium equation (N Cc + Cs minusT) withthe spalling strain (εcu 0003) used as a limit state forconcrete strain For low-rise buildings the presence ofgravity axial load is reasonably small and hence for sim-plicity the compression steel area is eliminated from theequilibrium equation (e peak flexural lateral load Fu andthe drift at concrete fracture cu can then be obtained asfollows

1415

500

500

123456789

101112131415161718192021222324

992

692

300

030

00

110

00

300

020

00

65001750 1750

10000

116

2

76

18

19 54

810

1213 20

11

2221

24

LVDT-∆controlLVDT-∆totalLVDT-∆totalLVDT-∆flexureLVDT-∆flexureDial gauge-∆flexureDial gauge-∆flexureDial gauge-∆ShearDial gauge-∆ShearDial gauge-∆up liftDial gauge-∆up liftDial gauge-∆base shearDial gauge-∆frame shearHydraulic jack 1Load cell 1ndash5tonLoad cell 2ndash10tonHydraulic jack 2ExtensometerRC wallSloofClampClampClampLoading frame

9

3

2317

Figure 4 Schematic of wall loading test setup

ndash15000ndash10000

ndash5000000

50001000015000

0 10 20 30 40 50

Def

lect

ion

(mm

)

Cycle no

Figure 5 Quasi-static lateral loading history

4 Advances in Materials Science and Engineering

Fu Mu

L

cpeak cy + cplmiddotp

(9)

where cplmiddotp (ϕpeak minus ϕy)Lp in which ϕpeak(εcukud)

(0003kud) and ϕy (3cyL) ku ((N + Astfy)085fcprimecdb) c 085minus 0007(fcprime minus 28) Ast tensile steelarea and εsm steel strain-hardening strain

(e plastic hinge length Lp can be estimated using thePaulay and Priestley model [8] as follows

Lp 0054L + 0022 dbfy (10)

(d) Point D (ultimate displacement) lateral load-displacement relationship of squat walls is dominated by

shear behaviour however for lightly reinforced squat walls theflexure behaviour still provides large influence on lateral load-drift behaviour (e failure mechanism which is influenced byshear strength degradation is needed hence the lateral loadfailure models developed for lightly reinforced concrete col-umns and walls [20 21] are modified for this model due to thesimilarity of lateral load-displacement behaviour betweenlightly reinforced concrete walls and columns

Shear strength (Vu) of RC walls consists of concretestrength (Vc) and steel strength (Vs) components as follows

Vu Vc + Vs (11)

In this model the concrete shear strength uses theformula developed based on principal tensile strength byauthors [22] whilst the steel strength proposed by Wesleyand Hashimoto [23] is used as follows

Vc 23Acr

ft( 11138572

+ftP

Acr

1113971

(12)

Vs chρh + cvρv( 1113857fydt (13)

whereAcr 085 ncρst( 1113857

036dt (14)

where d is the effective depth of RC walls which can beassumed as 08D and Ch 1minus cv in which

30

20

10

0

Late

ral l

oad

(kN

)

ndash10

ndash20

ndash30ndash150 ndash100 ndash050 000

Dri ()050 100 150

(a)

30

20

10

0

Late

ral l

oad

(kN

)

ndash10

ndash20

ndash30ndash150 ndash100 ndash050 000

Dri ()050 100 150

(b)

Figure 6 Crack patterns at 1 drift and hysteretic curves of all specimens (a) RCW4 (b) RCW8

Table 1 Strength and deformation properties of specimens RCW4and RCW8

Strength (kN) Drift ()Fcr Fy Fu δcr δy δu δlf

RCW4 Exp 28 18 235 017 047 100 133(eo 40 16 23 01 042 075 na

RCW8 Exp 23 20 245 017 055 067 100(eo 43 18 235 01 043 08 na

Note (e theoretical values were taken from moment-curvature analysis(flexural component only)

Advances in Materials Science and Engineering 5

cv 1 for alt 05

2(1minus a) for 05lt alt 1

0 for agt 1

(15)

with nc EsEc ρh the transverse reinforcement ratioρv the total longitudinal reinforcement ratio and ρst

the tension reinforcement ratio

As a note for moderate and slender walls (a gt 1 andhence cv 0) the steel strength component (equation (13))can be rewritten as a common shear strength formula

Vs ρhfy dt Avfyd

s (16)

(e ultimate drift can be obtained as follows

L

Lv3

Lv2

Lv1

Lh

Δf l

δf2

δf1β

(a)

D

L

Lv3

Lv2

Lv1

Δsh

δs1

ζ

δs2

Δsh1

(b)

DLH

d1 d2

c

Lv1

d

d

δf1

δslip

δf2

θslip

β

(c)

Figure 7 LVDT measurements for (a) flexure deformation (b) shear deformation and (c) yield penetration deformation

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7 8

FlexuralShearYield penetration

(a)

0

5

10

15

20

25

30

0 2 4 6 8 10

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7

FlexuralShearYield penetration

(b)

Figure 8 Variation of displacements due to flexure shear and yield penetration axial load-deformation relationship (left) and ratio of eachdisplacement to total displacement at each loading step (right) (a) RCW4 specimen (b) RCW8 specimen

6 Advances in Materials Science and Engineering

cu cy

k(1minus kα)minus 08

Fu

Vu1113890 1113891 (17)

where

k 03e57n

9minus a (18)

where α the drift ductility at the start of shear strengthdecrease

42 Model 2 Simplified (e simplified model is a simpleprocedure for estimating lateral load-drift behaviour oflightly reinforced concrete walls (is model consists oftrilinear stages with each state cracking yield and ultimateas shown in Figure 10

(a) Point A (cracking) the lateral strength at crackingpoint can be predicted by assuming cracking drift ccr

005(b) Point B (yield) the ultimate yield strength is cal-

culated using factored ultimate strength

Fy ϕFu (19)

whereas the corresponding yield drift (cy) is determinedusing the smallest values of the following alternatives

(i) Approximate value of cy 02ndash03(ii) Apply Ieff 05Ig (refer [24])

(c) Point C (ultimate) the ultimate drift (cm) can becalculated as a sum of the yield drift (cy) and the plastic drift(cpl) as follows (refer Figure 11)

cm cy + cpl (20)

(e plastic drift can be estimated by assuming amaximum acceptable strain in the steel bar at singlecrack at the wall base in the order of εs 50 and takinga more conservative approach to Priestley and Paulay[8] strain penetration length of lyp 4400 εy db asymp 15dbHence the following models can be obtained (referFigure 12)

Crack width

Wcr εs middot lyp 005 times 15db 075db (21)

Plastic drift

cpl θpl wcr

D 075

db

D1113888 1113889 (22)

(e lateral load-drift relationship between experimentaldata and proposed models are considerably in goodagreement as shown in Figures 13 and 14 More data arecertainly required to refine the models particularly for thedetailed model since it was developed using a semiempiricalapproach However interestingly the simplified model withthe pure analytical approach showed better prediction due tothe dominant combinations of flexural and yield penetrationbehaviour

Drift ()γy γpeak

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

D

γu

Fcr

γcr

B

θplp = (φpeak ndash φy)Lp

θplu = (φu ndash φy)Lp

Figure 9 (e backbone curve model of lateral load-drift capacity[20]

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Fcr

γcr

B

Figure 10 (e simplified model of lateral load-drift capacity

Wcr

D

γpl

Figure 12 Plastic rotation at wall base

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

Fcr

γcr

B

γpl = θpl = (φu ndash φy)Lp

Figure 11 Plastic drift of simplified model

Advances in Materials Science and Engineering 7

5 Conclusion

Two specimens of light-weight sandwich concrete walls havebeen tested in order to investigate the lateral load-driftbehaviour and collapse mechanism Specimen RCW4 witha thinner EPS panel developed more classic flexural be-haviour with drift capacity maxed at about 13 whilstspecimen RCW8 only managed to reached 10 withdominant yield penetration behaviour due to thinner con-crete cover of sloof foundation However the tests werestopped at 20 drop of peak load instead of further failure ataxial load collapse And hence the results can still beconsidered satisfactory for low-to-moderate seismic regionsbut might not be sufficient for high seismic regions

Two models comprising detailed and simplified ap-proach for predicting the load-displacement behaviour ofsandwich concrete wall subjected to lateral load have beendeveloped (e experimental data and the proposed modelsare in good agreement particularly the simplified model dueto the dominant behaviour of flexural and yield penetration

Data Availability

(e data that support the findings of this study are availablefrom the corresponding author upon reasonable request

Conflicts of Interest

(e authors declare that they have no conflicts of interest

References

[1] S A Mousavi S M Zahrai and A Bahrami-Rad ldquoQuasi-static cyclic tests on super-lightweight EPS concrete shearwallsrdquo Engineering Structures vol 65 pp 62ndash75 2014

[2] Z Yizhou ldquoMechanical properties of self-combusted ganguereinforced concrete shear walls under low-cyclic loadrdquoJournal of Zhejiang University Engineering Science vol 34no 3 pp 325ndash330 2000

[3] T Hejin Y Qingrong and S Xinya ldquoExperimental study onbBehaviours of reinforced ash ceramsite concrete shearwallsrdquo Journal of Building Structure vol 15 no 4 pp 20ndash301994

[4] Y H Chai and J D Anderson ldquoSeismic response of perfo-rated lightweight Aggregate concrete wall panels for low-risemodular classroomsrdquo Engineering Structures vol 27 no 4pp 593ndash604 2005

[5] L Cavaleri N Miraglia and M Papia ldquoPumice concrete forstructural wall panelsrdquo Engineering Structures vol 25 no 1pp 115ndash125 2003

[6] httpmpanelindonesiacomproductwall-panel[7] T Paulay ldquoEarthquake-resisting shear walls-New Zealand

design trendsrdquo ACI Journal vol 77 no 18 pp 144ndash152 1980[8] T Paulay and M J N Priestley Seismic Design of Reinforced

Concrete and Masonry Buildings Wiley Interscience Presspublication John Wiley amp Sons inc New York City NYUSA 1992

[9] O Esmaili S Epackachi M Samadzad et al ldquoStudy ofstructural RC shear wall system in a 56-story RC tall buildingrdquoin Proceedings the 14th World Conference on EarthquakeEngineering Beijing China October 2008

[10] A Carpinteri M Corrado G Lacidogna et al ldquoLateral loadeffects on tall shear wall structures of different heightrdquoStructural Engineering and Mechanics vol 41 no 3pp 313ndash337 2012

[11] P A Hidalgo C A Ledezma and R M Jordan ldquoSeismicbBehaviour of squat reinforced concrete shear wallsrdquoEarthquake Spectra vol 18 no 2 pp 287ndash308 2002

[12] T N Salonikios ldquoShear strength and deformation patterns ofRC walls with aspect ratio 10 and 15 designed to Eurocode8rdquo Engineering Structures vol 24 no 1 pp 39ndash49 2002

[13] T N Salonikios ldquoAnalytical prediction of the inelastic re-sponse of RC walls with low aspect ratiordquo ASCE Journal ofStructural Engineering vol 133 no 6 pp 844ndash854 2007

[14] J Carrillo and S M Alcocer ldquoShear strength of reinforcedconcrete walls for seismic design of low-rise housingldquordquo ACIStructural Journal vol 110 no 3 2013

[15] T Trombetti G Gasparini S Silvestri et al ldquoResults ofpseudo-static tests with cyclic horizontal load on cast in situsandwich squat concrete wallsrdquo in Proceedings of Ninth PacificConference on Earthquake Engineering Building anEarthquake-Resilient Society Auckland New Zealand April2011

[16] I Ricci M Palermo G Gasparini S Silvestri andT Trombetti ldquoResults of pseudo-static tests with cyclichorizontal load on cast in situ sandwich squat concrete wallsrdquoEngineering Structures vol 54 pp 131ndash149 2013

[17] M Palermo and T Trombetti ldquoExperimentally-validatedmodelling of thin RC sandwich walls subjected to seismicloadsrdquo Engineering Structures vol 119 pp 95ndash109 2016

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 13 Comparison between experimental data and theoreticalmodels for specimen RCW4

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 14 Comparison between experimental data and theoreticalmodels for specimen RCW8

8 Advances in Materials Science and Engineering

(a) Point A (cracking) the cracked lateral strength anddrift are calculated as follows

Fcr Mcr

L

ccr McrL

3EcIg

(5)

where the flexural tensile strength ft is taken as 06

fcprime1113969

(b) Point B (yield) the yield drift is calculated using the

effective second moment of area as follows

Fy My

L

cy MyL

3EcIe

(6)

(e Paulay and Priestley [8] model for effective momentof inertia is used as follows

(i) Flexure-dominated walls

Ie 100fy

+Pu

fcprimeAg

⎛⎝ ⎞⎠Ig (7)

(ii) Shear-dominated walls

Iw Ig

12 + C

C 30Ie

L2tD

(8)

where Pu nominal axial load Ag gross crosssection area of walls and t wall thickness

(c) Point C (peak strength) the model was developed byinvestigating the curvature within the plastic hinge regionusing the force equilibrium equation (N Cc + Cs minusT) withthe spalling strain (εcu 0003) used as a limit state forconcrete strain For low-rise buildings the presence ofgravity axial load is reasonably small and hence for sim-plicity the compression steel area is eliminated from theequilibrium equation (e peak flexural lateral load Fu andthe drift at concrete fracture cu can then be obtained asfollows

1415

500

500

123456789

101112131415161718192021222324

992

692

300

030

00

110

00

300

020

00

65001750 1750

10000

116

2

76

18

19 54

810

1213 20

11

2221

24

LVDT-∆controlLVDT-∆totalLVDT-∆totalLVDT-∆flexureLVDT-∆flexureDial gauge-∆flexureDial gauge-∆flexureDial gauge-∆ShearDial gauge-∆ShearDial gauge-∆up liftDial gauge-∆up liftDial gauge-∆base shearDial gauge-∆frame shearHydraulic jack 1Load cell 1ndash5tonLoad cell 2ndash10tonHydraulic jack 2ExtensometerRC wallSloofClampClampClampLoading frame

9

3

2317

Figure 4 Schematic of wall loading test setup

ndash15000ndash10000

ndash5000000

50001000015000

0 10 20 30 40 50

Def

lect

ion

(mm

)

Cycle no

Figure 5 Quasi-static lateral loading history

4 Advances in Materials Science and Engineering

Fu Mu

L

cpeak cy + cplmiddotp

(9)

where cplmiddotp (ϕpeak minus ϕy)Lp in which ϕpeak(εcukud)

(0003kud) and ϕy (3cyL) ku ((N + Astfy)085fcprimecdb) c 085minus 0007(fcprime minus 28) Ast tensile steelarea and εsm steel strain-hardening strain

(e plastic hinge length Lp can be estimated using thePaulay and Priestley model [8] as follows

Lp 0054L + 0022 dbfy (10)

(d) Point D (ultimate displacement) lateral load-displacement relationship of squat walls is dominated by

shear behaviour however for lightly reinforced squat walls theflexure behaviour still provides large influence on lateral load-drift behaviour (e failure mechanism which is influenced byshear strength degradation is needed hence the lateral loadfailure models developed for lightly reinforced concrete col-umns and walls [20 21] are modified for this model due to thesimilarity of lateral load-displacement behaviour betweenlightly reinforced concrete walls and columns

Shear strength (Vu) of RC walls consists of concretestrength (Vc) and steel strength (Vs) components as follows

Vu Vc + Vs (11)

In this model the concrete shear strength uses theformula developed based on principal tensile strength byauthors [22] whilst the steel strength proposed by Wesleyand Hashimoto [23] is used as follows

Vc 23Acr

ft( 11138572

+ftP

Acr

1113971

(12)

Vs chρh + cvρv( 1113857fydt (13)

whereAcr 085 ncρst( 1113857

036dt (14)

where d is the effective depth of RC walls which can beassumed as 08D and Ch 1minus cv in which

30

20

10

0

Late

ral l

oad

(kN

)

ndash10

ndash20

ndash30ndash150 ndash100 ndash050 000

Dri ()050 100 150

(a)

30

20

10

0

Late

ral l

oad

(kN

)

ndash10

ndash20

ndash30ndash150 ndash100 ndash050 000

Dri ()050 100 150

(b)

Figure 6 Crack patterns at 1 drift and hysteretic curves of all specimens (a) RCW4 (b) RCW8

Table 1 Strength and deformation properties of specimens RCW4and RCW8

Strength (kN) Drift ()Fcr Fy Fu δcr δy δu δlf

RCW4 Exp 28 18 235 017 047 100 133(eo 40 16 23 01 042 075 na

RCW8 Exp 23 20 245 017 055 067 100(eo 43 18 235 01 043 08 na

Note (e theoretical values were taken from moment-curvature analysis(flexural component only)

Advances in Materials Science and Engineering 5

cv 1 for alt 05

2(1minus a) for 05lt alt 1

0 for agt 1

(15)

with nc EsEc ρh the transverse reinforcement ratioρv the total longitudinal reinforcement ratio and ρst

the tension reinforcement ratio

As a note for moderate and slender walls (a gt 1 andhence cv 0) the steel strength component (equation (13))can be rewritten as a common shear strength formula

Vs ρhfy dt Avfyd

s (16)

(e ultimate drift can be obtained as follows

L

Lv3

Lv2

Lv1

Lh

Δf l

δf2

δf1β

(a)

D

L

Lv3

Lv2

Lv1

Δsh

δs1

ζ

δs2

Δsh1

(b)

DLH

d1 d2

c

Lv1

d

d

δf1

δslip

δf2

θslip

β

(c)

Figure 7 LVDT measurements for (a) flexure deformation (b) shear deformation and (c) yield penetration deformation

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7 8

FlexuralShearYield penetration

(a)

0

5

10

15

20

25

30

0 2 4 6 8 10

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7

FlexuralShearYield penetration

(b)

Figure 8 Variation of displacements due to flexure shear and yield penetration axial load-deformation relationship (left) and ratio of eachdisplacement to total displacement at each loading step (right) (a) RCW4 specimen (b) RCW8 specimen

6 Advances in Materials Science and Engineering

cu cy

k(1minus kα)minus 08

Fu

Vu1113890 1113891 (17)

where

k 03e57n

9minus a (18)

where α the drift ductility at the start of shear strengthdecrease

42 Model 2 Simplified (e simplified model is a simpleprocedure for estimating lateral load-drift behaviour oflightly reinforced concrete walls (is model consists oftrilinear stages with each state cracking yield and ultimateas shown in Figure 10

(a) Point A (cracking) the lateral strength at crackingpoint can be predicted by assuming cracking drift ccr

005(b) Point B (yield) the ultimate yield strength is cal-

culated using factored ultimate strength

Fy ϕFu (19)

whereas the corresponding yield drift (cy) is determinedusing the smallest values of the following alternatives

(i) Approximate value of cy 02ndash03(ii) Apply Ieff 05Ig (refer [24])

(c) Point C (ultimate) the ultimate drift (cm) can becalculated as a sum of the yield drift (cy) and the plastic drift(cpl) as follows (refer Figure 11)

cm cy + cpl (20)

(e plastic drift can be estimated by assuming amaximum acceptable strain in the steel bar at singlecrack at the wall base in the order of εs 50 and takinga more conservative approach to Priestley and Paulay[8] strain penetration length of lyp 4400 εy db asymp 15dbHence the following models can be obtained (referFigure 12)

Crack width

Wcr εs middot lyp 005 times 15db 075db (21)

Plastic drift

cpl θpl wcr

D 075

db

D1113888 1113889 (22)

(e lateral load-drift relationship between experimentaldata and proposed models are considerably in goodagreement as shown in Figures 13 and 14 More data arecertainly required to refine the models particularly for thedetailed model since it was developed using a semiempiricalapproach However interestingly the simplified model withthe pure analytical approach showed better prediction due tothe dominant combinations of flexural and yield penetrationbehaviour

Drift ()γy γpeak

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

D

γu

Fcr

γcr

B

θplp = (φpeak ndash φy)Lp

θplu = (φu ndash φy)Lp

Figure 9 (e backbone curve model of lateral load-drift capacity[20]

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Fcr

γcr

B

Figure 10 (e simplified model of lateral load-drift capacity

Wcr

D

γpl

Figure 12 Plastic rotation at wall base

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

Fcr

γcr

B

γpl = θpl = (φu ndash φy)Lp

Figure 11 Plastic drift of simplified model

Advances in Materials Science and Engineering 7

5 Conclusion

Two specimens of light-weight sandwich concrete walls havebeen tested in order to investigate the lateral load-driftbehaviour and collapse mechanism Specimen RCW4 witha thinner EPS panel developed more classic flexural be-haviour with drift capacity maxed at about 13 whilstspecimen RCW8 only managed to reached 10 withdominant yield penetration behaviour due to thinner con-crete cover of sloof foundation However the tests werestopped at 20 drop of peak load instead of further failure ataxial load collapse And hence the results can still beconsidered satisfactory for low-to-moderate seismic regionsbut might not be sufficient for high seismic regions

Two models comprising detailed and simplified ap-proach for predicting the load-displacement behaviour ofsandwich concrete wall subjected to lateral load have beendeveloped (e experimental data and the proposed modelsare in good agreement particularly the simplified model dueto the dominant behaviour of flexural and yield penetration

Data Availability

(e data that support the findings of this study are availablefrom the corresponding author upon reasonable request

Conflicts of Interest

(e authors declare that they have no conflicts of interest

References

[1] S A Mousavi S M Zahrai and A Bahrami-Rad ldquoQuasi-static cyclic tests on super-lightweight EPS concrete shearwallsrdquo Engineering Structures vol 65 pp 62ndash75 2014

[2] Z Yizhou ldquoMechanical properties of self-combusted ganguereinforced concrete shear walls under low-cyclic loadrdquoJournal of Zhejiang University Engineering Science vol 34no 3 pp 325ndash330 2000

[3] T Hejin Y Qingrong and S Xinya ldquoExperimental study onbBehaviours of reinforced ash ceramsite concrete shearwallsrdquo Journal of Building Structure vol 15 no 4 pp 20ndash301994

[4] Y H Chai and J D Anderson ldquoSeismic response of perfo-rated lightweight Aggregate concrete wall panels for low-risemodular classroomsrdquo Engineering Structures vol 27 no 4pp 593ndash604 2005

[5] L Cavaleri N Miraglia and M Papia ldquoPumice concrete forstructural wall panelsrdquo Engineering Structures vol 25 no 1pp 115ndash125 2003

[6] httpmpanelindonesiacomproductwall-panel[7] T Paulay ldquoEarthquake-resisting shear walls-New Zealand

design trendsrdquo ACI Journal vol 77 no 18 pp 144ndash152 1980[8] T Paulay and M J N Priestley Seismic Design of Reinforced

Concrete and Masonry Buildings Wiley Interscience Presspublication John Wiley amp Sons inc New York City NYUSA 1992

[9] O Esmaili S Epackachi M Samadzad et al ldquoStudy ofstructural RC shear wall system in a 56-story RC tall buildingrdquoin Proceedings the 14th World Conference on EarthquakeEngineering Beijing China October 2008

[10] A Carpinteri M Corrado G Lacidogna et al ldquoLateral loadeffects on tall shear wall structures of different heightrdquoStructural Engineering and Mechanics vol 41 no 3pp 313ndash337 2012

[11] P A Hidalgo C A Ledezma and R M Jordan ldquoSeismicbBehaviour of squat reinforced concrete shear wallsrdquoEarthquake Spectra vol 18 no 2 pp 287ndash308 2002

[12] T N Salonikios ldquoShear strength and deformation patterns ofRC walls with aspect ratio 10 and 15 designed to Eurocode8rdquo Engineering Structures vol 24 no 1 pp 39ndash49 2002

[13] T N Salonikios ldquoAnalytical prediction of the inelastic re-sponse of RC walls with low aspect ratiordquo ASCE Journal ofStructural Engineering vol 133 no 6 pp 844ndash854 2007

[14] J Carrillo and S M Alcocer ldquoShear strength of reinforcedconcrete walls for seismic design of low-rise housingldquordquo ACIStructural Journal vol 110 no 3 2013

[15] T Trombetti G Gasparini S Silvestri et al ldquoResults ofpseudo-static tests with cyclic horizontal load on cast in situsandwich squat concrete wallsrdquo in Proceedings of Ninth PacificConference on Earthquake Engineering Building anEarthquake-Resilient Society Auckland New Zealand April2011

[16] I Ricci M Palermo G Gasparini S Silvestri andT Trombetti ldquoResults of pseudo-static tests with cyclichorizontal load on cast in situ sandwich squat concrete wallsrdquoEngineering Structures vol 54 pp 131ndash149 2013

[17] M Palermo and T Trombetti ldquoExperimentally-validatedmodelling of thin RC sandwich walls subjected to seismicloadsrdquo Engineering Structures vol 119 pp 95ndash109 2016

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 13 Comparison between experimental data and theoreticalmodels for specimen RCW4

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 14 Comparison between experimental data and theoreticalmodels for specimen RCW8

8 Advances in Materials Science and Engineering

Fu Mu

L

cpeak cy + cplmiddotp

(9)

where cplmiddotp (ϕpeak minus ϕy)Lp in which ϕpeak(εcukud)

(0003kud) and ϕy (3cyL) ku ((N + Astfy)085fcprimecdb) c 085minus 0007(fcprime minus 28) Ast tensile steelarea and εsm steel strain-hardening strain

(e plastic hinge length Lp can be estimated using thePaulay and Priestley model [8] as follows

Lp 0054L + 0022 dbfy (10)

(d) Point D (ultimate displacement) lateral load-displacement relationship of squat walls is dominated by

shear behaviour however for lightly reinforced squat walls theflexure behaviour still provides large influence on lateral load-drift behaviour (e failure mechanism which is influenced byshear strength degradation is needed hence the lateral loadfailure models developed for lightly reinforced concrete col-umns and walls [20 21] are modified for this model due to thesimilarity of lateral load-displacement behaviour betweenlightly reinforced concrete walls and columns

Shear strength (Vu) of RC walls consists of concretestrength (Vc) and steel strength (Vs) components as follows

Vu Vc + Vs (11)

In this model the concrete shear strength uses theformula developed based on principal tensile strength byauthors [22] whilst the steel strength proposed by Wesleyand Hashimoto [23] is used as follows

Vc 23Acr

ft( 11138572

+ftP

Acr

1113971

(12)

Vs chρh + cvρv( 1113857fydt (13)

whereAcr 085 ncρst( 1113857

036dt (14)

where d is the effective depth of RC walls which can beassumed as 08D and Ch 1minus cv in which

30

20

10

0

Late

ral l

oad

(kN

)

ndash10

ndash20

ndash30ndash150 ndash100 ndash050 000

Dri ()050 100 150

(a)

30

20

10

0

Late

ral l

oad

(kN

)

ndash10

ndash20

ndash30ndash150 ndash100 ndash050 000

Dri ()050 100 150

(b)

Figure 6 Crack patterns at 1 drift and hysteretic curves of all specimens (a) RCW4 (b) RCW8

Table 1 Strength and deformation properties of specimens RCW4and RCW8

Strength (kN) Drift ()Fcr Fy Fu δcr δy δu δlf

RCW4 Exp 28 18 235 017 047 100 133(eo 40 16 23 01 042 075 na

RCW8 Exp 23 20 245 017 055 067 100(eo 43 18 235 01 043 08 na

Note (e theoretical values were taken from moment-curvature analysis(flexural component only)

Advances in Materials Science and Engineering 5

cv 1 for alt 05

2(1minus a) for 05lt alt 1

0 for agt 1

(15)

with nc EsEc ρh the transverse reinforcement ratioρv the total longitudinal reinforcement ratio and ρst

the tension reinforcement ratio

As a note for moderate and slender walls (a gt 1 andhence cv 0) the steel strength component (equation (13))can be rewritten as a common shear strength formula

Vs ρhfy dt Avfyd

s (16)

(e ultimate drift can be obtained as follows

L

Lv3

Lv2

Lv1

Lh

Δf l

δf2

δf1β

(a)

D

L

Lv3

Lv2

Lv1

Δsh

δs1

ζ

δs2

Δsh1

(b)

DLH

d1 d2

c

Lv1

d

d

δf1

δslip

δf2

θslip

β

(c)

Figure 7 LVDT measurements for (a) flexure deformation (b) shear deformation and (c) yield penetration deformation

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7 8

FlexuralShearYield penetration

(a)

0

5

10

15

20

25

30

0 2 4 6 8 10

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7

FlexuralShearYield penetration

(b)

Figure 8 Variation of displacements due to flexure shear and yield penetration axial load-deformation relationship (left) and ratio of eachdisplacement to total displacement at each loading step (right) (a) RCW4 specimen (b) RCW8 specimen

6 Advances in Materials Science and Engineering

cu cy

k(1minus kα)minus 08

Fu

Vu1113890 1113891 (17)

where

k 03e57n

9minus a (18)

where α the drift ductility at the start of shear strengthdecrease

42 Model 2 Simplified (e simplified model is a simpleprocedure for estimating lateral load-drift behaviour oflightly reinforced concrete walls (is model consists oftrilinear stages with each state cracking yield and ultimateas shown in Figure 10

(a) Point A (cracking) the lateral strength at crackingpoint can be predicted by assuming cracking drift ccr

005(b) Point B (yield) the ultimate yield strength is cal-

culated using factored ultimate strength

Fy ϕFu (19)

whereas the corresponding yield drift (cy) is determinedusing the smallest values of the following alternatives

(i) Approximate value of cy 02ndash03(ii) Apply Ieff 05Ig (refer [24])

(c) Point C (ultimate) the ultimate drift (cm) can becalculated as a sum of the yield drift (cy) and the plastic drift(cpl) as follows (refer Figure 11)

cm cy + cpl (20)

(e plastic drift can be estimated by assuming amaximum acceptable strain in the steel bar at singlecrack at the wall base in the order of εs 50 and takinga more conservative approach to Priestley and Paulay[8] strain penetration length of lyp 4400 εy db asymp 15dbHence the following models can be obtained (referFigure 12)

Crack width

Wcr εs middot lyp 005 times 15db 075db (21)

Plastic drift

cpl θpl wcr

D 075

db

D1113888 1113889 (22)

(e lateral load-drift relationship between experimentaldata and proposed models are considerably in goodagreement as shown in Figures 13 and 14 More data arecertainly required to refine the models particularly for thedetailed model since it was developed using a semiempiricalapproach However interestingly the simplified model withthe pure analytical approach showed better prediction due tothe dominant combinations of flexural and yield penetrationbehaviour

Drift ()γy γpeak

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

D

γu

Fcr

γcr

B

θplp = (φpeak ndash φy)Lp

θplu = (φu ndash φy)Lp

Figure 9 (e backbone curve model of lateral load-drift capacity[20]

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Fcr

γcr

B

Figure 10 (e simplified model of lateral load-drift capacity

Wcr

D

γpl

Figure 12 Plastic rotation at wall base

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

Fcr

γcr

B

γpl = θpl = (φu ndash φy)Lp

Figure 11 Plastic drift of simplified model

Advances in Materials Science and Engineering 7

5 Conclusion

Two specimens of light-weight sandwich concrete walls havebeen tested in order to investigate the lateral load-driftbehaviour and collapse mechanism Specimen RCW4 witha thinner EPS panel developed more classic flexural be-haviour with drift capacity maxed at about 13 whilstspecimen RCW8 only managed to reached 10 withdominant yield penetration behaviour due to thinner con-crete cover of sloof foundation However the tests werestopped at 20 drop of peak load instead of further failure ataxial load collapse And hence the results can still beconsidered satisfactory for low-to-moderate seismic regionsbut might not be sufficient for high seismic regions

Two models comprising detailed and simplified ap-proach for predicting the load-displacement behaviour ofsandwich concrete wall subjected to lateral load have beendeveloped (e experimental data and the proposed modelsare in good agreement particularly the simplified model dueto the dominant behaviour of flexural and yield penetration

Data Availability

(e data that support the findings of this study are availablefrom the corresponding author upon reasonable request

Conflicts of Interest

(e authors declare that they have no conflicts of interest

References

[1] S A Mousavi S M Zahrai and A Bahrami-Rad ldquoQuasi-static cyclic tests on super-lightweight EPS concrete shearwallsrdquo Engineering Structures vol 65 pp 62ndash75 2014

[2] Z Yizhou ldquoMechanical properties of self-combusted ganguereinforced concrete shear walls under low-cyclic loadrdquoJournal of Zhejiang University Engineering Science vol 34no 3 pp 325ndash330 2000

[3] T Hejin Y Qingrong and S Xinya ldquoExperimental study onbBehaviours of reinforced ash ceramsite concrete shearwallsrdquo Journal of Building Structure vol 15 no 4 pp 20ndash301994

[4] Y H Chai and J D Anderson ldquoSeismic response of perfo-rated lightweight Aggregate concrete wall panels for low-risemodular classroomsrdquo Engineering Structures vol 27 no 4pp 593ndash604 2005

[5] L Cavaleri N Miraglia and M Papia ldquoPumice concrete forstructural wall panelsrdquo Engineering Structures vol 25 no 1pp 115ndash125 2003

[6] httpmpanelindonesiacomproductwall-panel[7] T Paulay ldquoEarthquake-resisting shear walls-New Zealand

design trendsrdquo ACI Journal vol 77 no 18 pp 144ndash152 1980[8] T Paulay and M J N Priestley Seismic Design of Reinforced

Concrete and Masonry Buildings Wiley Interscience Presspublication John Wiley amp Sons inc New York City NYUSA 1992

[9] O Esmaili S Epackachi M Samadzad et al ldquoStudy ofstructural RC shear wall system in a 56-story RC tall buildingrdquoin Proceedings the 14th World Conference on EarthquakeEngineering Beijing China October 2008

[10] A Carpinteri M Corrado G Lacidogna et al ldquoLateral loadeffects on tall shear wall structures of different heightrdquoStructural Engineering and Mechanics vol 41 no 3pp 313ndash337 2012

[11] P A Hidalgo C A Ledezma and R M Jordan ldquoSeismicbBehaviour of squat reinforced concrete shear wallsrdquoEarthquake Spectra vol 18 no 2 pp 287ndash308 2002

[12] T N Salonikios ldquoShear strength and deformation patterns ofRC walls with aspect ratio 10 and 15 designed to Eurocode8rdquo Engineering Structures vol 24 no 1 pp 39ndash49 2002

[13] T N Salonikios ldquoAnalytical prediction of the inelastic re-sponse of RC walls with low aspect ratiordquo ASCE Journal ofStructural Engineering vol 133 no 6 pp 844ndash854 2007

[14] J Carrillo and S M Alcocer ldquoShear strength of reinforcedconcrete walls for seismic design of low-rise housingldquordquo ACIStructural Journal vol 110 no 3 2013

[15] T Trombetti G Gasparini S Silvestri et al ldquoResults ofpseudo-static tests with cyclic horizontal load on cast in situsandwich squat concrete wallsrdquo in Proceedings of Ninth PacificConference on Earthquake Engineering Building anEarthquake-Resilient Society Auckland New Zealand April2011

[16] I Ricci M Palermo G Gasparini S Silvestri andT Trombetti ldquoResults of pseudo-static tests with cyclichorizontal load on cast in situ sandwich squat concrete wallsrdquoEngineering Structures vol 54 pp 131ndash149 2013

[17] M Palermo and T Trombetti ldquoExperimentally-validatedmodelling of thin RC sandwich walls subjected to seismicloadsrdquo Engineering Structures vol 119 pp 95ndash109 2016

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 13 Comparison between experimental data and theoreticalmodels for specimen RCW4

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 14 Comparison between experimental data and theoreticalmodels for specimen RCW8

8 Advances in Materials Science and Engineering

cv 1 for alt 05

2(1minus a) for 05lt alt 1

0 for agt 1

(15)

with nc EsEc ρh the transverse reinforcement ratioρv the total longitudinal reinforcement ratio and ρst

the tension reinforcement ratio

As a note for moderate and slender walls (a gt 1 andhence cv 0) the steel strength component (equation (13))can be rewritten as a common shear strength formula

Vs ρhfy dt Avfyd

s (16)

(e ultimate drift can be obtained as follows

L

Lv3

Lv2

Lv1

Lh

Δf l

δf2

δf1β

(a)

D

L

Lv3

Lv2

Lv1

Δsh

δs1

ζ

δs2

Δsh1

(b)

DLH

d1 d2

c

Lv1

d

d

δf1

δslip

δf2

θslip

β

(c)

Figure 7 LVDT measurements for (a) flexure deformation (b) shear deformation and (c) yield penetration deformation

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7 8

FlexuralShearYield penetration

(a)

0

5

10

15

20

25

30

0 2 4 6 8 10

Late

ral l

oad

(kN

)

Displacement (mm)

ShearYield penetration

FlexuralTotal

0102030405060708090

100

1 2 3 4 5 6 7

FlexuralShearYield penetration

(b)

Figure 8 Variation of displacements due to flexure shear and yield penetration axial load-deformation relationship (left) and ratio of eachdisplacement to total displacement at each loading step (right) (a) RCW4 specimen (b) RCW8 specimen

6 Advances in Materials Science and Engineering

cu cy

k(1minus kα)minus 08

Fu

Vu1113890 1113891 (17)

where

k 03e57n

9minus a (18)

where α the drift ductility at the start of shear strengthdecrease

42 Model 2 Simplified (e simplified model is a simpleprocedure for estimating lateral load-drift behaviour oflightly reinforced concrete walls (is model consists oftrilinear stages with each state cracking yield and ultimateas shown in Figure 10

(a) Point A (cracking) the lateral strength at crackingpoint can be predicted by assuming cracking drift ccr

005(b) Point B (yield) the ultimate yield strength is cal-

culated using factored ultimate strength

Fy ϕFu (19)

whereas the corresponding yield drift (cy) is determinedusing the smallest values of the following alternatives

(i) Approximate value of cy 02ndash03(ii) Apply Ieff 05Ig (refer [24])

(c) Point C (ultimate) the ultimate drift (cm) can becalculated as a sum of the yield drift (cy) and the plastic drift(cpl) as follows (refer Figure 11)

cm cy + cpl (20)

(e plastic drift can be estimated by assuming amaximum acceptable strain in the steel bar at singlecrack at the wall base in the order of εs 50 and takinga more conservative approach to Priestley and Paulay[8] strain penetration length of lyp 4400 εy db asymp 15dbHence the following models can be obtained (referFigure 12)

Crack width

Wcr εs middot lyp 005 times 15db 075db (21)

Plastic drift

cpl θpl wcr

D 075

db

D1113888 1113889 (22)

(e lateral load-drift relationship between experimentaldata and proposed models are considerably in goodagreement as shown in Figures 13 and 14 More data arecertainly required to refine the models particularly for thedetailed model since it was developed using a semiempiricalapproach However interestingly the simplified model withthe pure analytical approach showed better prediction due tothe dominant combinations of flexural and yield penetrationbehaviour

Drift ()γy γpeak

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

D

γu

Fcr

γcr

B

θplp = (φpeak ndash φy)Lp

θplu = (φu ndash φy)Lp

Figure 9 (e backbone curve model of lateral load-drift capacity[20]

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Fcr

γcr

B

Figure 10 (e simplified model of lateral load-drift capacity

Wcr

D

γpl

Figure 12 Plastic rotation at wall base

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

Fcr

γcr

B

γpl = θpl = (φu ndash φy)Lp

Figure 11 Plastic drift of simplified model

Advances in Materials Science and Engineering 7

5 Conclusion

Two specimens of light-weight sandwich concrete walls havebeen tested in order to investigate the lateral load-driftbehaviour and collapse mechanism Specimen RCW4 witha thinner EPS panel developed more classic flexural be-haviour with drift capacity maxed at about 13 whilstspecimen RCW8 only managed to reached 10 withdominant yield penetration behaviour due to thinner con-crete cover of sloof foundation However the tests werestopped at 20 drop of peak load instead of further failure ataxial load collapse And hence the results can still beconsidered satisfactory for low-to-moderate seismic regionsbut might not be sufficient for high seismic regions

Two models comprising detailed and simplified ap-proach for predicting the load-displacement behaviour ofsandwich concrete wall subjected to lateral load have beendeveloped (e experimental data and the proposed modelsare in good agreement particularly the simplified model dueto the dominant behaviour of flexural and yield penetration

Data Availability

(e data that support the findings of this study are availablefrom the corresponding author upon reasonable request

Conflicts of Interest

(e authors declare that they have no conflicts of interest

References

[1] S A Mousavi S M Zahrai and A Bahrami-Rad ldquoQuasi-static cyclic tests on super-lightweight EPS concrete shearwallsrdquo Engineering Structures vol 65 pp 62ndash75 2014

[2] Z Yizhou ldquoMechanical properties of self-combusted ganguereinforced concrete shear walls under low-cyclic loadrdquoJournal of Zhejiang University Engineering Science vol 34no 3 pp 325ndash330 2000

[3] T Hejin Y Qingrong and S Xinya ldquoExperimental study onbBehaviours of reinforced ash ceramsite concrete shearwallsrdquo Journal of Building Structure vol 15 no 4 pp 20ndash301994

[4] Y H Chai and J D Anderson ldquoSeismic response of perfo-rated lightweight Aggregate concrete wall panels for low-risemodular classroomsrdquo Engineering Structures vol 27 no 4pp 593ndash604 2005

[5] L Cavaleri N Miraglia and M Papia ldquoPumice concrete forstructural wall panelsrdquo Engineering Structures vol 25 no 1pp 115ndash125 2003

[6] httpmpanelindonesiacomproductwall-panel[7] T Paulay ldquoEarthquake-resisting shear walls-New Zealand

design trendsrdquo ACI Journal vol 77 no 18 pp 144ndash152 1980[8] T Paulay and M J N Priestley Seismic Design of Reinforced

Concrete and Masonry Buildings Wiley Interscience Presspublication John Wiley amp Sons inc New York City NYUSA 1992

[9] O Esmaili S Epackachi M Samadzad et al ldquoStudy ofstructural RC shear wall system in a 56-story RC tall buildingrdquoin Proceedings the 14th World Conference on EarthquakeEngineering Beijing China October 2008

[10] A Carpinteri M Corrado G Lacidogna et al ldquoLateral loadeffects on tall shear wall structures of different heightrdquoStructural Engineering and Mechanics vol 41 no 3pp 313ndash337 2012

[11] P A Hidalgo C A Ledezma and R M Jordan ldquoSeismicbBehaviour of squat reinforced concrete shear wallsrdquoEarthquake Spectra vol 18 no 2 pp 287ndash308 2002

[12] T N Salonikios ldquoShear strength and deformation patterns ofRC walls with aspect ratio 10 and 15 designed to Eurocode8rdquo Engineering Structures vol 24 no 1 pp 39ndash49 2002

[13] T N Salonikios ldquoAnalytical prediction of the inelastic re-sponse of RC walls with low aspect ratiordquo ASCE Journal ofStructural Engineering vol 133 no 6 pp 844ndash854 2007

[14] J Carrillo and S M Alcocer ldquoShear strength of reinforcedconcrete walls for seismic design of low-rise housingldquordquo ACIStructural Journal vol 110 no 3 2013

[15] T Trombetti G Gasparini S Silvestri et al ldquoResults ofpseudo-static tests with cyclic horizontal load on cast in situsandwich squat concrete wallsrdquo in Proceedings of Ninth PacificConference on Earthquake Engineering Building anEarthquake-Resilient Society Auckland New Zealand April2011

[16] I Ricci M Palermo G Gasparini S Silvestri andT Trombetti ldquoResults of pseudo-static tests with cyclichorizontal load on cast in situ sandwich squat concrete wallsrdquoEngineering Structures vol 54 pp 131ndash149 2013

[17] M Palermo and T Trombetti ldquoExperimentally-validatedmodelling of thin RC sandwich walls subjected to seismicloadsrdquo Engineering Structures vol 119 pp 95ndash109 2016

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 13 Comparison between experimental data and theoreticalmodels for specimen RCW4

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 14 Comparison between experimental data and theoreticalmodels for specimen RCW8

8 Advances in Materials Science and Engineering

cu cy

k(1minus kα)minus 08

Fu

Vu1113890 1113891 (17)

where

k 03e57n

9minus a (18)

where α the drift ductility at the start of shear strengthdecrease

42 Model 2 Simplified (e simplified model is a simpleprocedure for estimating lateral load-drift behaviour oflightly reinforced concrete walls (is model consists oftrilinear stages with each state cracking yield and ultimateas shown in Figure 10

(a) Point A (cracking) the lateral strength at crackingpoint can be predicted by assuming cracking drift ccr

005(b) Point B (yield) the ultimate yield strength is cal-

culated using factored ultimate strength

Fy ϕFu (19)

whereas the corresponding yield drift (cy) is determinedusing the smallest values of the following alternatives

(i) Approximate value of cy 02ndash03(ii) Apply Ieff 05Ig (refer [24])

(c) Point C (ultimate) the ultimate drift (cm) can becalculated as a sum of the yield drift (cy) and the plastic drift(cpl) as follows (refer Figure 11)

cm cy + cpl (20)

(e plastic drift can be estimated by assuming amaximum acceptable strain in the steel bar at singlecrack at the wall base in the order of εs 50 and takinga more conservative approach to Priestley and Paulay[8] strain penetration length of lyp 4400 εy db asymp 15dbHence the following models can be obtained (referFigure 12)

Crack width

Wcr εs middot lyp 005 times 15db 075db (21)

Plastic drift

cpl θpl wcr

D 075

db

D1113888 1113889 (22)

(e lateral load-drift relationship between experimentaldata and proposed models are considerably in goodagreement as shown in Figures 13 and 14 More data arecertainly required to refine the models particularly for thedetailed model since it was developed using a semiempiricalapproach However interestingly the simplified model withthe pure analytical approach showed better prediction due tothe dominant combinations of flexural and yield penetrationbehaviour

Drift ()γy γpeak

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

D

γu

Fcr

γcr

B

θplp = (φpeak ndash φy)Lp

θplu = (φu ndash φy)Lp

Figure 9 (e backbone curve model of lateral load-drift capacity[20]

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Fcr

γcr

B

Figure 10 (e simplified model of lateral load-drift capacity

Wcr

D

γpl

Figure 12 Plastic rotation at wall base

Drift ()γy γm

Fy

Fu

Late

ral s

treng

th

A

C

Ieff

Fcr

γcr

B

γpl = θpl = (φu ndash φy)Lp

Figure 11 Plastic drift of simplified model

Advances in Materials Science and Engineering 7

5 Conclusion

Two specimens of light-weight sandwich concrete walls havebeen tested in order to investigate the lateral load-driftbehaviour and collapse mechanism Specimen RCW4 witha thinner EPS panel developed more classic flexural be-haviour with drift capacity maxed at about 13 whilstspecimen RCW8 only managed to reached 10 withdominant yield penetration behaviour due to thinner con-crete cover of sloof foundation However the tests werestopped at 20 drop of peak load instead of further failure ataxial load collapse And hence the results can still beconsidered satisfactory for low-to-moderate seismic regionsbut might not be sufficient for high seismic regions

Two models comprising detailed and simplified ap-proach for predicting the load-displacement behaviour ofsandwich concrete wall subjected to lateral load have beendeveloped (e experimental data and the proposed modelsare in good agreement particularly the simplified model dueto the dominant behaviour of flexural and yield penetration

Data Availability

(e data that support the findings of this study are availablefrom the corresponding author upon reasonable request

Conflicts of Interest

(e authors declare that they have no conflicts of interest

References

[1] S A Mousavi S M Zahrai and A Bahrami-Rad ldquoQuasi-static cyclic tests on super-lightweight EPS concrete shearwallsrdquo Engineering Structures vol 65 pp 62ndash75 2014

[2] Z Yizhou ldquoMechanical properties of self-combusted ganguereinforced concrete shear walls under low-cyclic loadrdquoJournal of Zhejiang University Engineering Science vol 34no 3 pp 325ndash330 2000

[3] T Hejin Y Qingrong and S Xinya ldquoExperimental study onbBehaviours of reinforced ash ceramsite concrete shearwallsrdquo Journal of Building Structure vol 15 no 4 pp 20ndash301994

[4] Y H Chai and J D Anderson ldquoSeismic response of perfo-rated lightweight Aggregate concrete wall panels for low-risemodular classroomsrdquo Engineering Structures vol 27 no 4pp 593ndash604 2005

[5] L Cavaleri N Miraglia and M Papia ldquoPumice concrete forstructural wall panelsrdquo Engineering Structures vol 25 no 1pp 115ndash125 2003

[6] httpmpanelindonesiacomproductwall-panel[7] T Paulay ldquoEarthquake-resisting shear walls-New Zealand

design trendsrdquo ACI Journal vol 77 no 18 pp 144ndash152 1980[8] T Paulay and M J N Priestley Seismic Design of Reinforced

Concrete and Masonry Buildings Wiley Interscience Presspublication John Wiley amp Sons inc New York City NYUSA 1992

[9] O Esmaili S Epackachi M Samadzad et al ldquoStudy ofstructural RC shear wall system in a 56-story RC tall buildingrdquoin Proceedings the 14th World Conference on EarthquakeEngineering Beijing China October 2008

[10] A Carpinteri M Corrado G Lacidogna et al ldquoLateral loadeffects on tall shear wall structures of different heightrdquoStructural Engineering and Mechanics vol 41 no 3pp 313ndash337 2012

[11] P A Hidalgo C A Ledezma and R M Jordan ldquoSeismicbBehaviour of squat reinforced concrete shear wallsrdquoEarthquake Spectra vol 18 no 2 pp 287ndash308 2002

[12] T N Salonikios ldquoShear strength and deformation patterns ofRC walls with aspect ratio 10 and 15 designed to Eurocode8rdquo Engineering Structures vol 24 no 1 pp 39ndash49 2002

[13] T N Salonikios ldquoAnalytical prediction of the inelastic re-sponse of RC walls with low aspect ratiordquo ASCE Journal ofStructural Engineering vol 133 no 6 pp 844ndash854 2007

[14] J Carrillo and S M Alcocer ldquoShear strength of reinforcedconcrete walls for seismic design of low-rise housingldquordquo ACIStructural Journal vol 110 no 3 2013

[15] T Trombetti G Gasparini S Silvestri et al ldquoResults ofpseudo-static tests with cyclic horizontal load on cast in situsandwich squat concrete wallsrdquo in Proceedings of Ninth PacificConference on Earthquake Engineering Building anEarthquake-Resilient Society Auckland New Zealand April2011

[16] I Ricci M Palermo G Gasparini S Silvestri andT Trombetti ldquoResults of pseudo-static tests with cyclichorizontal load on cast in situ sandwich squat concrete wallsrdquoEngineering Structures vol 54 pp 131ndash149 2013

[17] M Palermo and T Trombetti ldquoExperimentally-validatedmodelling of thin RC sandwich walls subjected to seismicloadsrdquo Engineering Structures vol 119 pp 95ndash109 2016

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 13 Comparison between experimental data and theoreticalmodels for specimen RCW4

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 14 Comparison between experimental data and theoreticalmodels for specimen RCW8

8 Advances in Materials Science and Engineering

5 Conclusion

Two specimens of light-weight sandwich concrete walls havebeen tested in order to investigate the lateral load-driftbehaviour and collapse mechanism Specimen RCW4 witha thinner EPS panel developed more classic flexural be-haviour with drift capacity maxed at about 13 whilstspecimen RCW8 only managed to reached 10 withdominant yield penetration behaviour due to thinner con-crete cover of sloof foundation However the tests werestopped at 20 drop of peak load instead of further failure ataxial load collapse And hence the results can still beconsidered satisfactory for low-to-moderate seismic regionsbut might not be sufficient for high seismic regions

Two models comprising detailed and simplified ap-proach for predicting the load-displacement behaviour ofsandwich concrete wall subjected to lateral load have beendeveloped (e experimental data and the proposed modelsare in good agreement particularly the simplified model dueto the dominant behaviour of flexural and yield penetration

Data Availability

(e data that support the findings of this study are availablefrom the corresponding author upon reasonable request

Conflicts of Interest

(e authors declare that they have no conflicts of interest

References

[1] S A Mousavi S M Zahrai and A Bahrami-Rad ldquoQuasi-static cyclic tests on super-lightweight EPS concrete shearwallsrdquo Engineering Structures vol 65 pp 62ndash75 2014

[2] Z Yizhou ldquoMechanical properties of self-combusted ganguereinforced concrete shear walls under low-cyclic loadrdquoJournal of Zhejiang University Engineering Science vol 34no 3 pp 325ndash330 2000

[3] T Hejin Y Qingrong and S Xinya ldquoExperimental study onbBehaviours of reinforced ash ceramsite concrete shearwallsrdquo Journal of Building Structure vol 15 no 4 pp 20ndash301994

[4] Y H Chai and J D Anderson ldquoSeismic response of perfo-rated lightweight Aggregate concrete wall panels for low-risemodular classroomsrdquo Engineering Structures vol 27 no 4pp 593ndash604 2005

[5] L Cavaleri N Miraglia and M Papia ldquoPumice concrete forstructural wall panelsrdquo Engineering Structures vol 25 no 1pp 115ndash125 2003

[6] httpmpanelindonesiacomproductwall-panel[7] T Paulay ldquoEarthquake-resisting shear walls-New Zealand

design trendsrdquo ACI Journal vol 77 no 18 pp 144ndash152 1980[8] T Paulay and M J N Priestley Seismic Design of Reinforced

Concrete and Masonry Buildings Wiley Interscience Presspublication John Wiley amp Sons inc New York City NYUSA 1992

[9] O Esmaili S Epackachi M Samadzad et al ldquoStudy ofstructural RC shear wall system in a 56-story RC tall buildingrdquoin Proceedings the 14th World Conference on EarthquakeEngineering Beijing China October 2008

[10] A Carpinteri M Corrado G Lacidogna et al ldquoLateral loadeffects on tall shear wall structures of different heightrdquoStructural Engineering and Mechanics vol 41 no 3pp 313ndash337 2012

[11] P A Hidalgo C A Ledezma and R M Jordan ldquoSeismicbBehaviour of squat reinforced concrete shear wallsrdquoEarthquake Spectra vol 18 no 2 pp 287ndash308 2002

[12] T N Salonikios ldquoShear strength and deformation patterns ofRC walls with aspect ratio 10 and 15 designed to Eurocode8rdquo Engineering Structures vol 24 no 1 pp 39ndash49 2002

[13] T N Salonikios ldquoAnalytical prediction of the inelastic re-sponse of RC walls with low aspect ratiordquo ASCE Journal ofStructural Engineering vol 133 no 6 pp 844ndash854 2007

[14] J Carrillo and S M Alcocer ldquoShear strength of reinforcedconcrete walls for seismic design of low-rise housingldquordquo ACIStructural Journal vol 110 no 3 2013

[15] T Trombetti G Gasparini S Silvestri et al ldquoResults ofpseudo-static tests with cyclic horizontal load on cast in situsandwich squat concrete wallsrdquo in Proceedings of Ninth PacificConference on Earthquake Engineering Building anEarthquake-Resilient Society Auckland New Zealand April2011

[16] I Ricci M Palermo G Gasparini S Silvestri andT Trombetti ldquoResults of pseudo-static tests with cyclichorizontal load on cast in situ sandwich squat concrete wallsrdquoEngineering Structures vol 54 pp 131ndash149 2013

[17] M Palermo and T Trombetti ldquoExperimentally-validatedmodelling of thin RC sandwich walls subjected to seismicloadsrdquo Engineering Structures vol 119 pp 95ndash109 2016

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 13 Comparison between experimental data and theoreticalmodels for specimen RCW4

ndash30

ndash20

ndash10

0

10

20

30

ndash350 ndash250 ndash150 ndash050 050 150 250 350

Late

ral l

oad

(kN

)

Drift ()

Figure 14 Comparison between experimental data and theoreticalmodels for specimen RCW8

8 Advances in Materials Science and Engineering

[18] ASTM E2126 Standard Test Methods for Cyclic (Reversed)Load Test for Shear Resistance of Walls for buildings ASTMInternational West Conshohocken PA USA 2005

[19] A Wibowo J L Wilson N T K Lam et al ldquoSeismic per-formance of lightly reinforced structural walls for designpurposesrdquo Magazine of Concrete Research vol 65 no 13pp 809ndash828 2013

[20] J L Wilson A Wibowo N T K Lam et al ldquoDrift behaviourof lightly reinforced concrete columns and structural walls forseismic design applicationsrdquo Australian Journal of StructuralEngineering vol 16 no 1 pp 62ndash74 2015

[21] A Wibowo J L Wilson N T K Lam et al ldquoDrift per-formance of lightly reinforced concrete columnsrdquo EngineeringStructures vol 59 pp 522ndash535 2014

[22] A Wibowo J L Wilson N T K Lam et al ldquoDrift capacity oflightly reinforced concrete columnsrdquo Australian Journal ofStructural Engineering vol 15 no 2 pp 131ndash150 2014

[23] D AWesley and P S Hashimoto ldquoSeismic structural fragilityinvestigation for the zion nuclear power plantrdquo ReportNUREGCR-2320 US Nuclear Regulatory CommissionBethesda MD USA 1981

[24] J W Wallace ldquoModelling issues for tall reinforced concretecore wall buildingsrdquo Ce Structural Design of Tall and SpecialBuildings vol 16 no 5 pp 615ndash632 2007

Advances in Materials Science and Engineering 9

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom