Simplified Calculation Model and Experimental Study of Latticed Concrete-Gypsum Composite ...

18 Pages·2015·8.1 MB·English

Article
Simplified Calculation Model and Experimental
Study of Latticed Concrete-Gypsum
Composite Panels
NanJiang1,2andShaochunMa1,*
Received:21August2015;Accepted:19October2015;Published:27October2015
AcademicEditor:JorgedeBrito
1 SchoolofCivilEngineering,TianjinUniversity,Tianjin300072,China;[email protected]
2 KeyLaboratoryofCoastalCivilEngineeringStructureandSafety(TianjinUniversity),
MinistryofEducation,Tianjin300072,China
* Correspondence:[email protected];Tel.:[phone]
Abstract: In order to address the performance complexity of the various constituent materials of
(dense-column)latticedconcrete-gypsumcompositepanelsandthedifficultyinthedetermination
of the various elastic constants, this paper presented a detailed structural analysis of the
(dense-column) latticed concrete-gypsum composite panel and proposed a feasible technical
solutiontosimplifiedcalculation. Inconformitywithmechanicalrules,atypicalpanelelementwas
selectedanddividedintotwohomogenouscompositesub-elementsandasecondaryhomogenous
element, respectively for solution, thus establishing an equivalence of the composite panel to a
simple homogenous panel and obtaining the effective formulas for calculating the various elastic
constants. Finally, the calculation results and the experimental results were compared, which
revealedthatthecalculationmethodwascorrectandreliableandcouldmeetthecalculationneeds
of practical engineering and provide a theoretical basis for simplified calculation for studies on
compositepanelelementsandstructuresaswellasareferenceforcalculationsofotherpanels.
Keywords: lattice;composite;equivalentconstants;simplifiedcalculation;experiment;method
1. Introduction
Gypsum is one of the three major cementing materials that are widely used in the fields of
building materials, food, precision casting, models and molds, medicine, paper, and paint fillers.
As early as 2000~3000 BC, humans attempted using gypsum as a cementing material to build the
famousEgyptianpyramids,ancientRomanarchitecture,MogaoCavesatDunhuang,etc. SinceLouis
XIV, known as France’s Sun King, issued a decree in 1667, calcined gypsum (building gypsum)
started to be widely used in the building industry. Building gypsum is primarily comprised of
beta-calcium sulfate hemihydrate (β-CaSO ‚1/2H O), whose content should be not lower than
4 2
60.0%[1]. Buildinggypsumexpandsby0.05%~0.15%afterhardening, withacompressivestrength
of5~10MPa,aflexuralstrengthof2.5MPa,andadensityof13.0~14.5kN/m3[2]. Intheconstruction
industry, gypsum is generally used for the cementing material, decorative gypsum boards, reliefs,
romancolumns, etc.; non-load-bearingpartitionssuchashollowgypsumboardsanddense-column
composite panels with low load-bearing capacity; and load-bearing, anti-seismic walls with high
load-bearingcapacitysuchasthe(dense-column)latticedconcrete-gypsumcompositepanelstudied
in this paper. The (dense-column) latticed concrete-gypsum composite panel is a composite of
environmentally-friendly gypsum, fiberglass, concrete, and steel bars that has excellent seismic
performance, is lighter than ordinary shear walls, and contains non-toxic, harmless, pollution-free
gypsum that can adjust indoor humidity automatically with good thermal and sound insulation
Materials2015,8,7199–7216;doi:10.3390/ma8105375 www.mdpi.com/journal/materials
Materials2015,8,7199–7216
and fire resistance [3]. The development and wide use of (dense-column) latticed concrete-gypsum
compositepanelshavepromotedtheinnovationinnewwallmaterialsandthedevelopmentofgreen,
energy-savingwalls. Thiskindofcompositepanelmakesfulluseoftheadvantagesofitsconstitute
materials. The tensile fiber increases the gypsum board’s ability to withstand forces. The gypsum
board performs the (dense-column) latticed concrete-gypsum composite panel’s maintenance and
thermal and sound insulation functions while serving as a stressed member [4]. The excellent
materialpropertiesofconcreteenableittobearheavyloads.Asindicatedabove,thecompositepanel
reflects an effective composite of the functional and mechanical aspects of the various constituent
materials. ScholarsinAustralia,China,India,theUnitedStates,andItalyhaveconductedextensive
experimental studies on composite panels [5–9]. However, few achievements have been made in
simplifying calculations that are difficult to operate and implement. A great number of gypsum
partitions that exist in the gypsum board of a (dense-column) latticed concrete-gypsum composite
panel partition the hollow gypsum board into several horizontal and vertical gypsum cavities.
After concrete pouring, a lattice of invisible beam-invisible column forms, making simplified
calculation difficult and challenging. The greatest difficulty confronting the simplified calculation
of composite panels lies in the determination of basic elastic constants due to the complexity of the
composite[10],directlyleadingtothedifficultyinengineeringsoftwaremodeling,agreatnumberof
computingelements,agreatamountofcalculationwork,andafailuretomakeeffectivecalculation.
The(dense-column)latticedconcretegypsumcompositepanelinthisstudyprimarilyconsisted
oftheporousgypsumboardwithcavitiesandtheinvisiblebeam-invisiblecolumnlatticeofconcrete.
The composite panel with this structure not only has a high bearing capacity, but also facilitates
the arrangement of steel bars and the processing of nodes. In order to find a feasible simplified
calculation model for the (dense-column) latticed concrete-gypsum composite panel, a technical
solution was established. A typical element of this composite panel was selected to establish an
effectivecalculationmodel.Throughaseriesoftheoreticaldeviations,afeasiblesimplifiedcalculation
model was obtained. Finally, the reliability of the simplified calculation model was validated by
comparingtheseismicexperimentalresultsandthecalculationresultsofthecompositepanel.
2. TechnicalSolutiontoSimplifiedCalculation
As shown in Figure 1, (1) is a gypsum partition; (2) is a cavity formed vertically by gypsum
partitions;(3)isacavityformedhorizontallybygypsumpartitions;(4)isaninvisibleconcretebeam
formedatthehorizontalcavityafterconcretepouring;and(5)isaninvisibleconcretecolumnformed
at the vertical cavity after concrete pouring. The invisible beams and invisible columns form an
entire beam-column lattice structure. The porous gypsum board primarily consists of two gypsum
side panels and n gypsum partitions (lengthˆwidthˆheight=94mmˆ20mmˆ160mm).
Gypsum partitions are reasonably arranged between the two gypsum side panels to form
many horizontal gypsum cavities (length ˆ width = 220 mm ˆ 94 mm) and vertical gypsum
cavities(lengthˆwidth=230mmˆ94mm)intheentiregypsumboard. Thesecavitiescanbeused
asthetemplatesforconcretepouring.
The above introduction revealed that a (dense-column) latticed concrete gypsum composite
panel has a complex structure, and the performance of its constituent materials differs greatly,
which determines the special complexity of its mechanical properties and makes it difficult to
calculate. Therefore,itishardtoobtaintheaccuratemechanicalresultsofcompositepanels. Simple
homogenizationhasbeenincompetent,andanewwayisrequired.Theaimofthisstudyistoenable
the calculation results to meet engineering requirements, simplify the calculation method as much
as possible and significantly reduce the amount of calculations and time required for calculations.
The specific technical solution is shown in Figure 2. From the perspective of the mechanics of
the composite, a typical homogenous composite element of the (dense-column) latticed concrete
gypsumcompositepanelwasselected,asshowninFigure2b. Thehomogenouscompositeelement
was then divided into two homogeneous composite sub-elements, as shown in Figure 2c,d. These
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two homogenous composite sub-elements were rendered homogenously equivalent, respectively.
Then the two equivalent homogenous composite sub-elements were used to constitute a secondary
homogenous element, as shown in Figure 2e. The secondary homogeneous element was used to
Materials 2015, 8, page–page 
substitute the original homogenous composite element, and the basic dimensions and mechanical
propMemrateteicreihaslason 2fi0c1ta5h,l  e8,p cproaogmpe–eppraotgiseei st eopf atnheel wcoemrepomsiatien tpaainneeld  wunerceh amnagiendtabineefdo reunacnhdanagfteedr ebqeufoivrea leanndt traefatetrm  ent,
equivalent treatment, thus realizing the transformation from a complex (dense‐column) latticed 
thusrealizingthetransformationfromacomplex(dense-column)latticedconcretegypsumcomposite
mcoencchraenteic gayl ppsruomp ecrotimesp oosfi tet hpea nceol mtop ao ssiimte pplea hnoeml owgeerneo umsa pinantaeiln, eadn du gnrcehaatlnyg reedd ubceinfogr teh ea dndif fiacuftletry  
paneltoasimplehomogenouspanel,andgreatlyreducingthedifficultyincalculation. Thevaluable
eiqnu ciavlacluelnatt iotrne.a Ttmhee nvta, luthaubsl er reeasluizlitns go bthtaei nterdan fsifnoarlmlya wtioilnl  bfero omf  gar ecaotm ppralecxti c(adl esnigsen‐icfoiclaunmcen )t ol atthtiec eind‐ 
resultsobtainedfinallywillbeofgreatpracticalsignificancetothein-depthstudiesonthemechanical
cdoenpctrhe tset ugydpiessu omn  ctohme pmoescithea pnaicnaell  ptoro ap seirmtipesle o hf o(mdeongseen‐cooulsu pmann)e ll,a attnicde dgr ceoantlcyr ereted ugcyipnsgu tmhe c doimffipcouslittye  
propiepnra tcniaeelslc ueollfeamt(idoeennn.t ssT eah-necd ov lsautlrumuacnbtu)lerl aerset.ts iucletds ocbotnacinreedte fginyapllsyu wmillc obme opfo gsrieteatp parnaectlicealel msigennitfsicaanndce sttor uthcetu irne‐s.
depth studies on the mechanical properties of (dense‐column) latticed concrete gypsum composite 
panel elements and structures. 

Figure 1. Perspective of the gypsum board. 
Figure1.Perspectiveofthegypsumboard. 
Figure 1. Perspective of the gypsum board. 

Figure 2. Technical solution to the calculation of elastic constants: (a) the (dense‐column) latticed 

concrete gypsum composite panel; (b) a typical homogenous composite element; (c) the homogenous 
FiguFrceiogmu2.rpeo Ts2ei.t ceTh enscuihcbna‐ielclaselom lseuonltuito tiIno; nt( odt)o t htthheee c cahalolccmuulolaagtteiioonnon uoosf f ceeolalmasstpitcoi csciotceno snstsautnbat‐nse:lt es(ma:)e (tanh)te  tIh(Id;e ean(ndsdee‐ nc(osele)u -mcao nlsu)e cmlaotnntdi)caelradyt  ticed
choonmcroegtee ngoyupss ucmom cpoomspitoe.s ite panel; (b) a typical homogenous composite element; (c) the homogenous 
concretegypsumcompositepanel;(b)atypicalhomogenouscompositeelement;(c)thehomogenous
composite sub‐element I; (d) the homogenous composite sub‐element II; and (e) a secondary 
composite sub-element I; (d) the homogenous composite sub-element II; and (e) a secondary
3. Thheoomroegtiecnaolu Ds ecorimvpatoisoitnes.  of Elastic Constants 
homogenouscomposite.
33.. 1T.h Beaosrice tAicsaslu mDpetriiovnast ions of Elastic Constants 
3. TheoreticalDerivationsofElasticConstants
(1) The gypsum board, fiberglass, and concrete were all isotropic materials and linearly elastic; 
3.1. Basic Assumptions 
(2) the fiberglass was evenly distributed in the gypsum board, and the various materials of the 
3.1. BasicAssumptions
comp(1o)s Tithe ep gaynpels ubmon bdoedar fdir, mfiblye;r galnads s(,3 a) nthde c eofnfcercetste o wf tehree  raelsl iidsoutarlo sptirce smseast earniadl ss tarnadin lsi nine atrhley  vealarsiotiuc;s  
((m21))a ttTehrhei eaflisgb yoerfp gtshluaesm sc owbmoapsao resdvit,eefin plbyae nrdegils lwatrseisbr,ue atiegndnd oicrneo dtnh c[e1r 1eg]ty.e pwsuemre baolalridso, tarnodp itchem vaateriroiualss manatderliianlse aorfl ytheel astic;
(2) thcoemfipbWoesirittghel  agpsraesnaetwl i nba‐ospnledavneeden  sfltiyrifmfndleyiss; star [ni1bd2u ](,t3 fe)l dothoriens e cftafhence ctsog noysfp ttrhsauein mr ethsbeid oouauartld‐ os,tfr‐aepsnlasdense t ahdneedfo vsrtamrraaiiontiuso snin om tfh aceot emvraipraoilossuitsoe  f the
mpaanteerlisa. lTsh oefr tehfoer ceo, omnplyo sthitee  ipna‐pnlealn we earceti iognn noereedds [ 1to1 ]b. e considered for a composite panel. In other words, 
With great in‐plane stiffness [12], floors can constrain the out‐of‐plane deformation of composite 
panels. Therefore, only the in‐plane action needs to b3e  considered for a composite panel. In other words, 
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Materials2015,8,7199–7216
compositepanelbondedfirmly; and(3)theeffectsoftheresidualstressesandstrainsinthevarious
materialsofthecompositepanelwereignored[11].
Withgreatin-planestiffness[12],floorscanconstraintheout-of-planedeformationofcomposite
panels. Therefore, only the in-plane action needs to be considered for a composite panel. In other
words, a composite panel can be treated as a plane. In the following, formula derivation was
Materials 2015, 8, page–page 
conductedforthesimplifiedcalculationofcompositepanels.
a composite panel can be treated as a plane. In the following, formula derivation was conducted for 
3.2. CalculationofElasticConstants
the simplified calculation of composite panels. 
E , E , G , and G represent the elastic modulus and shear modulus of the concrete and
c g c g
3.2. Calculation of Elastic Constants 
gypsum board, respectively (obtained through material tests). The equivalent elastic modulus of
the homoEgc,e Engo, uGsc, acondm Gpgo rseitperessuenbt- ethleem eleanstticI minodthuelusX anodr sYhedairr emcotidounluiss oEf Itxheo croEncIyre,tae nadndi tgsyepqsuumiv alent
shearbomarodd, urleusspeacntidvePlyo is(osobnta’isnerdat itohrionutghhe  mXYateprilaaln eteastrse). GThe aenqduivvalen,tr eeslpaestcitci vmeloyd.uSluims iolaf rltyh,et hose
Ixy Ixy
ofthheohmoomgoengoeunso cuosmcpoomsipteo ssiutbe‐esluebm-eenlet mI einn tthaer eX Eor Y, Edirec,tGion is, EaIxn odr vEIy, a,nrde sitpse ecqtiuvivelayl,enatn sdhetharo seof
IIx IIy IIxy IIxy
the smecoodnudluasr yanhdo mPooigsseonno’su rsaetiloe mine tnhte aXreY Epla,nEe ,arGe G,Ixya nanddv vIxy,, rreessppeeccttiivveellyy. .SDimuielatrolys, ythmomse eotfr yt,h1e /4 of
x y xy xy
thetwhoomhoogmenooguesn cooumspcoosmitep ossuibte‐esleumbe-enlte maree nEtsIIxw, EeIrIye, aGnIIaxyl,y zanedd ,vaInIxyd, trhesepeencttiivreelys,e caonndd athroyseh oomf othgee nous
secondary homogenous element are Ex, Ey, Gxy, and vxy, respectively. Due to symmetry, 1/4 of the two 
elementwasanalyzed,asdetailedbelow.
homogenous composite sub‐elements were analyzed, and the entire secondary homogenous element 
was analyzed, as detailed below. 
3.2.1. HomogenousCompositeSub-ElementI
3F.i2g.1u. rHeo3maosgheonwouss1 C/o4mopfothsietet hSurebe‐E-dleimmeennts Ii onalhomogenouscompositesub-elementI.Foreaseof
derivatioFni,gtuhree f3oar scheodwias g1r/4a mofs thoef tthhreehe‐odmimoegnesnioonuasl hcoommopgoesnioteuss ucobm-epleomsiteen stuibn‐etlheemXen–tZ I.a Fnodr eXa–seY opf lanes
weredgeriivveanti,onre, sthpee fcotrivcee ldyi.agFriagmurse of3 tbh,ec haormeotgheenocuaslc cuolmatpioosnitem soudb‐eelleamnednte iqnu thivea Xle–nZt amndo Xd–eYl pfolarnseos lving
EIx; wFiegrue rgeiv3edn,,e reasrpeectthiveelcya. lFciugluarteio 3nb,cm aored ethlea cnadlcuelqautioivna mleondteml aondde elqfuoirvasloenlvt imngodGelI xfoyr; sFoilgvuinrge E3Ifx;, g are
the cFailgcuurlea t3iodn,e maroed tehlea cnadlcueqlautiiovna lmenotdmel oadnedl efqourisvoallvenint gmEodIye,l afnodr sFoilgvuinrge G3hIxy;i sFtighuercea 3lcf,ugl aatrieo nthme odel
forsocalvlciunlgatvion m. odel and equivalent model for solving EIy, and Figure 3h is the calculation model for 
Ixy
solving vIxy. 

Figure 3. Models of Homogenous Composite Sub‐element I: (a) 1/4 of the three‐dimensional 
Figure 3. Models of Homogenous Composite Sub-element I: (a) 1/4 of the three-dimensional
homohgomenooguensocuosm cpomospiotesisteu bsu-ebl‐eemlemenetntI ;I;( b(b))t thhee ccaallccuullaattiioonn mmooddele flofro sroslvoilnvgin EgIx;E (c) ;e(qcu)ievqauleinvta mleondteml odel
Ix
for solving EIx; (d) the calculation model for solving GIxy; (e) equivalent model for solving GIxy;  
for solving E ; (d) the calculation model for solving G ; (e) equivalent model for solving G ;
Ix Ixy Ixy
(f) the calculation model for solving EIy; (g) equivalent model for solving EIy; and (h) the calculation 
(f)thecalculationmodelforsolvingE ;(g)equivalentmodelforsolvingE ;and(h)thecalculation
model for solving vIxy.  Iy Iy
modelforsolvingv .
Ixy
(1) Elastic modulus EIx: As shown in Figure 3b,c, the planar calculation model of the homogenous 
composite sub‐element I was divided into the three calculation domains, A1, B1, and C1. B1 and C1 are 
the gypsum boards, and A1 is concrete. In the7 X20 d2irection, the sum of the normal stresses of the 
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Materials2015,8,7199–7216
(1) Elastic modulus E : As shown in Figure 3b,c, the planar calculation model of the
Ix
homogenous composite sub-element I was divided into the three calculation domains, A , B , and
1 1
C . B andC arethegypsumboards,andA isconcrete. IntheXdirection,thesumofthenormal
1 1 1 1
stressesofthecalculationmodelofthecompositepanelandthatoftheequivalentmodelshouldbe
equalunderthesameloading[13].
σ “σ ,σ h B{2“σ h b{2`σ h pB{2´b{2q (1)
Ix C1x Ix 1 A1x 1 B1x 1
where σ , σ , σ , and σ arethe stresses ofconcrete, gypsum board (namely domain B and
A1x B1x C1x Ix 1
C ), and the equivalent model in the X direction, respectively. ε is the strain of the equivalent
1 Ix
elementIintheXdirection. Thestraininthehomogenouscompositesub-elementIintheXdirection
ε shouldbethesamebeforeandafterequivalenttreatment.
Ix
σ {E “σ {E “σ {E “ε (2)
Ix Ix A1x c B1x g Ix
Letb{B“λ. Equation(2)wassubstitutedintoEquation(1)toobtain
E “λE `p1´λqE (3)
Ix c g
(2) Elastic modulus E : As shown in Figure 3f,g, σ , σ , and σ are the stresses of concrete,
Iy cy gy Iy
thegypsumboard, andtheequivalentmodelintheYdirection, respectively, and ε isthestrainof
Iy
theequivalentelementIintheYdirection. Similarly,
σ BL{4“σ bl{4`σ pBL´blq{4 (4)
Iy c g
σ {E “σ {E “σ {E “ε (5)
Iy Iy c c g g Iy
Letl{L“β. Equation(5)andλweresubstitutedintoEquation(4)toobtain
E “λβE `p1´λβqE (6)
Iy c g
(3) Shear modulus G : τ , τ and τ are the shear stresses of concrete, the gypsum board
Ixy cx gx Ix
(namelydomainB andC ), andtheequivalentmodelintheX direction. AsshowninFigure3d,e,
1 1
thesimilarmethodwasusedtoobtain
G “λβG `p1´λβqG (7)
Ixy c g
(4)Poisson’sratiov :Theplanarcalculationmodelofthehomogenouscompositesub-element
Ixy
IwasdividedintothethreecalculationdomainsA , B , andC . B andC arethegypsumboards,
2 2 2 2 2
andA isconcrete.Whereσ ,σ ,andσ arethestressesofconcreteandgypsumboard(namely
2 A2x B2x C2x
domain B and C ) in the X direction. As shown in Figure 3h, the strain difference between the
2 2
combinationofA andB andC intheXdirectionis0.5lpν ´ν qε .
2 2 2 g c Iy
Accordingtotheconditionsforequilibriumofforces,
pB´bqσ “bσ (8)
C2x B2x
Since
ε “ν ε “ν ε ´σ {E (9)
Ix Ixy Iy g Iy C2x g
Thedisplacementsorstrainsontheleftandrightsideswererequiredtosatisfythecoordination:
σ L{2E `σ l{2E `σ pL´lq{2E “pν ´ν qε l{2 (10)
C2x g B2x c B2x g g c Iy
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LetE {E “α. λandβweresubstitutedtoobtain
g c
ν “ν ´βλpν ´ν q{rλ`p1´λqp1´β`αβqs (11)
Ixy g g c
3.2.2. HomogenousCompositeSub-ElementII
(1)ElasticmodulusE : AsshowninFigure4d,e,similarly,
IIx
Materials 2015, 8, page–page 
σ h B{2“σ h b{2`σ h pB´bq{2,σ {E “σ {E “σ {E “ε (12)
IIx 2 Dx 2 Ex 2 IIx IIx Dx c Ex g IIx
σ h B/2σ hb/2σ h (Bb)/2, σ /E σ /E σ /E ε   (12)
IIx 2 Dx 2 Ex 2 IIx IIx Dx c Ex g IIx

Figure 4. Models of Homogenous Composite Sub‐element II” (a) 1/4 of the three‐dimensional 
Figure 4. Models of Homogenous Composite Sub-element II: (a) 1/4 of the three-dimensional
homogenous composite sub‐element II; (b) the calculation model for solving EIIy; (c) equivalent model 
homogenous composite sub-element II; (b) the calculation model for solving E ; (c) equivalent
for solving EIIy; (d) the calculation model for solving EIIx; (e) equivalent model for solvIiInyg EIIx; (f) the 
model for solving E ; (d) the calculation model for solving E ; (e) equivalent model for solving
calculation modeIlI fyor solving GIIxy; and (g) equivalent model for soIIlxving GIIxy.  
E ; (f)thecalculationmodelforsolvingG ;and(g)equivalentmodelforsolvingG .
IIx IIxy IIxy
σIIy is the stress of the equivalent model in the Y direction. σDx, σEx, and σIIx are the stresses of 
σconcrisetteh, egysptrseusms obfoathrde, eaqnud itvhael eeqnutimvaolednetl minodthele inY tdheir Xec dtiiorenc.tiσon. ε,IIσx an,da εnIIdy aσre thea rsetrathines sotfr tehses esof
IIy Dx Ex IIx
equivalent model in the X and Y directions. 
concrete,gypsumboard,andtheequivalentmodelintheXdirection. ε andε arethestrainsof
IIx IIy
Therefore, 
theequivalentmodelintheXandYdirections.
Therefore, E λE (1λ)E   (13)
IIx c g
E “λE `p1´λqE (13)
IIx c g
(2) Elastic modulus EIIy: As shown in Figure 4b,c, similarly, 
(2)ElasticmσodBuLlu/s4EIIyσ: AbsL/sh4owσninBFigburLe4/b4,,c ,σsim/ilEarly, σ /E σ /E ε   (14)
IIy cy gy IIy IIy cy c gy g IIy
σ BL{4“σ bL{4`σ pB´bqL{4,σ {E “σ {E “σ {E “ε (14)
TherefIoIyre,  cy gy IIy IIy cy c gy g IIy
Therefore, EIIy λEc(1λ)Eg  (15)
E “λE `p1´λqE (15)
(3) Shear modulus GIIxy: τcx, τgx anIdIy τIIx are cthe shear strgesses of concrete (namely domain D),  
(t3h)e Sghyepasrumm obdouarldu s(nGamel:y τdo,mτain aEn),d aτnd thaer eeqthueivsahleenatr mstordeesls eins othfec oXn dcirreetceti(onna. mAes lsyhdowomn ainin   D),
IIxy cx gx IIx
Figure 4f,g, the same method was used to obtain 
the gypsum board (namely domain E), and the equivalent model in the X direction. As shown in
Figure4f,g,thesamemethodwasusedtoGobtainλG (1λ)G   (16)
IIxy c g
(4) Poisson’s ratio vIIxy: As showGn IinIx Fyi“guλreG 4cd`, wp1he´n λthqeG cgomposite panel is stretched evenly in (16)
the X direction, its contraction strain is equal to the sum of the contraction strains of gypsum and 
concrete in the Z direction, namely 
ε  ε B/2[b/2 (Bb)/2]ε   (17)
IIz IIxz IIx c g IIx
Similarly, λ was substituted to obtain 
   λ （1-λ）   (18)
IIxy IIxz IIyz c g
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Materials2015,8,7199–7216
(4) Poisson’s ratio v : As shown in Figure 4d, when the composite panel is stretched evenly
IIxy
intheXdirection,itscontractionstrainisequaltothesumofthecontractionstrainsofgypsumand
concreteintheZdirection,namely
ε “ν ε B{2“rν b{2`ν pB´bq{2sε (17)
IIz IIxz IIx c g IIx
Similarly,λwassubstitutedtoobtain
ν “ν “ν “λν `p1´λqν (18)
IIxy IIxz IIyz c g
Materials 2015, 8, page–page 
3.2.3. SecondaryHomogenousElement
3.2.3. Secondary Homogenous Element 
As shown in Figure 5a, the secondary homogenous element consisted of the homogenous
composite sAusb -sehloewmne nints FIigaunred 5IaI,. tσhe, sσeco,nτda,rya nhdomτogaennodusa reeletmheentn ocornmsiasltesdt roefs sthees ahnomdosgheenaoruss tresses
x y x y
oftheseccoomnpdoasirtye shuobm‐eloegmeennotsu Is aenlde ImI. eσnx,t σ,yr,e τsx,p aencdt iτvy ealnyd. are the normal stresses and shear stresses of the 
secondary homogenous element, respectively. 

Figure  5.  Models  of  Secondary  Homogenous  Element:  (a)  the  three‐dimensional  secondary 
Figure 5. Models of Secondary Homogenous Element: (a) the three-dimensional secondary
homogenous element; (b) the calculation model for solving Ey; (c) equivalent model for solving Ey;  
homoge(ndo) uthse ecalelcmuleantito;n( mb)odthele focra slcoulvliantgi oEnx; amnod d(ee)l efqourivsaolelvnit nmgodEeyl; fo(cr )soelqvuinigv aElxe. ntmodelforsolvingEy;
(d)thecalculationmodelforsolvingEx;and(e)equivalentmodelforsolvingEx.
(1) Elastic modulus Ey: As shown in Figure 5b,c, the sums of the normal strains of the two models 
under the same loading should be equal. 
(1)ElasticmodulusE :AsshowninFigure5b,c,thesumsofthenormalstrainsofthetwomodels
y
underthesameloadingshouldbeequal.εy(h1h2)h1εIyh2εIIy  (19)
The stresses in the Y direction are equal, namely 
ε ph `h q“h ε `h ε (19)
y 1 2 1 Iy 2 IIy
E ε E ε E ε σ   (20)
Iy Iy IIy IIy y y y
ThestressesintheYdirectionareequal,namely
Let h /h ζ, which was substituted into Equation (19) to obtain 
1 2
EIyEεIy“(1EIζI)yEεIIEy “/E(Eyεy“ζEσy)  (21) (20)
y Iy IIy Iy IIy
Leth1{h(22) “Elaζs,tiwc mhoicdhulwusa Esx:s Aubs ssthiotuwtne din iFnigtourEe q5ud,aet,i tohne m(1e9t)hotod ofobrt caailnculating EIIx was used. 
Therefore, 
E “p1`ζqE E {pE `ζE q (21)
y E =(ζEIy IIEy )/Iy(1ζ) IIy (22)
x Ix IIx
(2)Elas(t3i)c Smheoadr umloudsuEluxs: GAxsy: sThhoe wcanlcuinlaFtioignu mreod5edl ,aen,dth eequmiveatlhenotd mfoodrecl aalrceu slhaotiwnng iEn IFIixguwreass 5uf,sge. d.
TheTrheef omreet,hod for calculating GIIxy was used. 
Therefore,  E =pζE `E q{p1`ζq (22)
x Ix IIx
G =(ζG G )/(1ζ)  (23)
xy Ixy IIxy
(4) Poisson’s ratio vxy: The method for calculating vIIxy was used to obtain 
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 ( ζ )/(1ζ)  (24)
xy Ixy IIxy
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Materials2015,8,7199–7216
(3) Shear modulus G : The calculation model and equivalent model are shown in Figure 5f,g.
xy
ThemethodforcalculatingG wasused.
IIxy
Therefore,
G =pζG `G q{p1`ζq (23)
xy Ixy IIxy
(4)Poisson’sratiov : Themethodforcalculatingv wasusedtoobtain
xy IIxy
ν “pν ζ`ν q{p1`ζq (24)
xy Ixy IIxy
4. Experiment
Materials 2015, 8, page–page 
4.1. SampleDesignandLoadingSystem
4. Experiment 
Three samples (1520 mm ˆ 1520 mm ˆ 120 mm) were designed for the seismic experiment on
Materials 2015, 8, page–page 
the compo4s.1i.t eSampaplne eDlesiingnt ahnids Lsotaudidngy .SyTshteemy  were numbered Q-1, Q-2, and Q-3, respectively. The plan
and elevati4o. nExopferiemaecnht sample are shown in Figures 6 and 7 respectively. The steel bars arranged
Three samples (1520 mm × 1520 mm × 120 mm) were designed for the seismic experiment on the 
in the comcopmopsiotseitep paanneell iwn ethries sHtuRdyB.4 T0h0eyd wefeorer mnuemdbesrteede lQ‐b1a, rQs‐2w, ainthd Qa‐3d, iraemspeectteivreolyf. T1h4e mplman, aansd shown in
4.1. Sample Design and Loading System 
Figure 8. Telheveateioxnp oefr iemacehn staamlprlee saurel tsshoowfnth ine Fmigautreers i6a lasndo f7,t hreespceoctmiveploy.s Tithee pstaenele blaarsr earsrahnogwedn ins uthbes equently.
Three samples (1520 mm × 1520 mm × 120 mm) were designed for the seismic experiment on the 
composite panel were HRB400 deformed steel bars with a diameter of 14 mm, as shown in Figure 8. 
The compressive strength and elastic modulus of the gypsum board were 5.52 MPa and 4350 MPa,
composite panel in this study. They were numbered Q‐1, Q‐2, and Q‐3, respectively. The plan and 
The  experimental  results  of  the  materials  of  the  composite  panel  are  shown  subsequently.  
respectivelye.leTvahtieonc oofm eapchre ssasmivpele asrter eshnogwthn ina nFdiguerelas s6t iacndm 7,o rdesupleuctsiveolfy. tThhee sctoeenl cbraerst earrwanegreed 2in4 .t6he3  MPa and
The compressive strength and elastic modulus of the gypsum board were 5.52 MPa and 4350 MPa, 
2.72ˆ104rMecsopPmeacpt,oivsreietleys p.p aTenhceetli  vwcoeemlryep .HreRTssBhi4ve0e0 t sdetrenefonsrigmltehe dsa tnsrtdee enel lgbatashtrisc  womfitohtd haue dluiHas moRef Bteth4r e0o f0c 1o4sn tcmereemtle,  abwsa esrrhseo w2w4n.a 6is3n  FM6i5gP4ua.r 0ea 0n8.d M   Pa (D8),
The  experimental  results  of  the  materials  of  the  composite  panel  are  shown  subsequently.  
669.45MP2a.7(2D ×1 140)4, ManPda, 6re7s6p.e9c2tivMelPy.a T(hDe 2te0n)s,irlee ssptreencgtitvh eolfy th[1e 4H].RB400 steel bars was 654.00 MPa (D8),  
The compressive strength and elastic modulus of the gypsum board were 5.52 MPa and 4350 MPa, 
669.45 MPa (D14), and 676.92 MPa (D20), respectively [14]. 
respectively. The compressive strength and elastic modulus of the concrete were 24.63 MPa and  
2.72 × 104 MPa, respectively. The tensile strength of the HRB400 steel bars was 654.00 MPa (D8),  
669.45 MPa (D14), and 676.92 MPa (D20), respectively [14]. 

Figure 6. Plane of the composite panel. 
Figure6.Planeofthecompositepanel.

Figure 6. Plane of the composite panel. 

Figure 7. Elevation of the composite panel. 

Figure 7. Elevation of the composite panel. 
Figure7.Elevationofthecompositepanel.
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Materials2015,8,7199–7216
Materials 2015, 8, page–page 
Materials 2015, 8, page–page 

Figure 8. Reinforcement of the composite panel. 
Figure8.Reinforcementofthecompositepanel.
The loading devices at the experimental site are shown in Figure 9 and consisted of a horizontal 
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loading10d00e vkiNce haynddraualivc ejartcikc awlhlooFsaiegd ubirnaec g8k.  dRweeaivnsif coseercceu[m1r5eedn–t1  to7of]  tt.hheeT  chroeemacphtooiosrintiez  wpoaannltlea lo.l nc ythcel irciglhota dsidwe.a Tshiem vperotsiceadl by a
load was imposed by two 500 kN hydraulic jacks, which were secured to the sliding supports above. 
1000kN hydraulic jack whose back was secured to the reaction wall on the right side. The vertical
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loadwasimposedbytwo500kNhydraulicjacks,whichweresecuredtotheslidingsupportsabove.
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Theslidingsupportsweresecuredtothereactionsteelbeamabove. Inordertoaccuratelysimulate
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the action of vertical loading on the composite panel under earthquake events in the process of
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thedisplacementofthesamplewiththeload.Adialindicatorwasplacedattheendofthefixedbeam
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at the bottom of the sample to detect whether the sample in its entirety moved in the experimental
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on the sample could be used to measure the shear deformation of the panel. The data collected by the 
meter,dialindicator,andvariousresistancestraingauges,andthesensorsattachedtothejackswere
displacement meter, dial indicator, and various resistance strain gauges, and the sensors attached to 
storedinacomputerforreal-timecollection.
the jacks were stored in a computer for real‐time collection. 

Figure 9. Loading devices at the experimental site figure. 
9

Figure 9. Loading devices at the experimental site figure. 
Figure9.Loadingdevicesattheexperimentalsitefigure.
9
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Materials2015,8,7199–7216
Materials 2015, 8, page–page 
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aa loloaadd‐c-coonntrtorollleledd loloaaddiningg ssyysstetemm wwaass aaddoopptetedd. .WWhhenen ththe ecocommppoosistiete ppaanneel lwwaass inin ththee eelalasstitcic‐p-plalasstitcic 
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44.2.2. .MMaainin EExxppereirmimenentatal lRReseusultlst s
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inincclilnineedd crcarcakcsk sapappepaeraerde dbebloewlo wthet hineitiinali thiaolrihzoornitzaoln ctraalckcr aatc kthea tfotohte off otohte coofmthpeosciotem ppaonseilt.e Apsa tnheel .
loAasdt hwealso aindcwreaasseindc, rbeoatshe din,cblointhedin acnlidn ehdoarinzdonhtoarli zcoranctkasl cwraecrke sown etrheeo innctrheeaisnec. rWeahsee.nW thhee snatmhepslea mwpasle 
pwulalsedp uovlleerd ao dviesrtaancdei sotfa 3n.c2e8 omfm3.,2 a8 lomt mof, daelnoste o4f5°d ienncslein4e5d˝ cirnacclkins ewdhcicrahc dkisffwerheidc hind leifnfegrtehd aipnpeleanrgedth 
ina ptpheea mreidddinlet haenmd ildowdleera pnadrtlos wofe rthpea rctosmofptohseitceo pmapnoesl.i tSeopmaen eolf. Sthoem ceraocfkths einc rtahcek smiindtdhlee mpaidrtd olef pthaer t
coofmtphoesciotem ppaonseitl einptaenrseelcitnetde,r sceacutseidn,gc athues ignygptshuemg ybposaurdm tboo paeredl tsoligpheetllys. lAigsh ttlhye. lAosadth aeplpolaiedda tpop tlhieed 
ctoomtpheosciotem ppaonseilt ewpaasn inelcrweaasseidn,c trheea soeudt,stidhee sotuetesli dbaersst oeef lthbea rpsaonfelt hyeiepldaende,l ayniedl dtheed ,parnindcitphael pinrcinlicniepda l
cirnacclkin gerdadcuraacllky gtoroakd ushalalpyet.o Wokhesnh athpee .saWmphleen wtahse psualmlepdl eovwera sa dpiusltlaendceo ovfe r11a.5d0i mstamn,c iencolfin1e1d.5 c0ramckms ,
foinrcmliende da clraarcgkes pfoiercme eodf anelat rigne tphiee cmeiodfdnlee tpianrtt hoef mthied dcolemppaorstitoef pthaeneclo, mthpeo gsiytepspuamne bl,otahred gpyepesluedm 
sberoiaorudslpye, ealnedd stherei ocuosnlcyr,eatne datt htheec ofonoctr eotfe tahtet hcoemfopootsoitfet hpeanceolm wpaoss ictreapckaende lawndas ccrruaschkeedd, aans dshcoruwsnh eind ,
Faigsushreo w10na.i nThFeig euxrpee1r0ima.eTnht eweaxsp eenridmeden wthweans tehned ceodmwphoesniteth peacnoeml fpraocstiuterepda nseerliforuacstlyu.r edseriously.
(a) Q‐1  (b) Q‐2 (c) Q‐3 
Figure 10. Fracture of samples (a) Q‐1; (b) Q‐2; (c) Q‐3.  
Figure10.Fractureofsamples(a)Q-1;(b)Q-2;(c)Q-3.
The cyclic experimental process revealed that the three composite panel samples underwent four 
Thecyclicexperimentalprocessrevealedthatthethreecompositepanelsamplesunderwentfour
stages: the elastic stage when the load was initially applied to the panel, the elastic‐plastic stage when 
stages:theelasticstagewhentheloadwasinitiallyappliedtothepanel,theelastic-plasticstagewhen
the panel yielded, and the fracture stage when the displacement and deformation of the panel was 
the panel yielded, and the fracture stage when the displacement and deformation of the panel was
great while the load applied decreased gradually. The sample was approximately in a square shape 
greatwhiletheloadapplieddecreasedgradually. Thesamplewasapproximatelyinasquareshape
and exhibited shear fracture. The final fracture of the samples shown in Figure 10 were primarily 
and exhibited shear fracture. The final fracture of the samples shown in Figure 10 were primarily
reflected  by  the  cracking  and  crushing  of  the  concrete  at  the  foot  of  the  panel  samples  
reflectedbythecrackingandcrushingoftheconcreteatthefootofthepanelsamples(Q-1andQ-3)
(Q‐1 and Q‐3) or the occurring of the 45° principal inclined crack at the foot of the sample (Q‐2). 
ortheoccurringofthe45˝principalinclinedcrackatthefootofthesample(Q-2).
4.2.2. Hysteretic Characteristics 
4.2.2. HystereticCharacteristics
Hysteretic curves are the lateral load‐displacement curves for the composite panel under cyclic 
Hystereticcurvesarethelateralload-displacementcurvesforthecompositepanelundercyclic
loading. Figure 11 shows the hysteretic and skeleton curves for the panel samples Q‐1, Q‐2, and Q‐3 
loading. Figure 11 shows the hysteretic and skeleton curves for the panel samples Q-1, Q-2, and
obtained through experimental measurement. It can be seen that before the composite panel cracked, 
the load‐displacement curves generally showed a linear change. The hysteresis loops initially took a 
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