Different approaches in modeling of RC shear wall: A review

Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no.

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Different approache in !o"elin# of $C hear %all& % all& A revie% A. '. Mulla1, (atih $atho"2, ). $. (ur*a%anhi+ Dept. of Civil n#ineerin#, (PM( I!perial Colle#e of n#ineerin# an" reearch, /a#holi, Pune.

 Atract $C hear %all are ue" in ne% tructure a %ell a in the rehailitation of eitin# tructure. (hear %all 3(/ are vital to li!it "efor!ation "e!an" un"er earthua6e ecitation. (o correct !o"elin# of hear %all i !ot i!portant iue in linear an" nonlinear anal*e of uil"in# for Pre"ictin# the ehavior of $C hear %all un"er lateral loa" uch a %in" an" earthua6e. Thi paper preent variou !o"elin# techniue that have een ue" * reearcher in !o"elin# of $C hear %all. Thee ran#e fro! !acro-!o"el, !icro!o"el uch a finite ele!ent !o"el an" fire !o"el. 7or the purpoe of finite ele!ent !o"ellin#, "ifferent techniue utili8in# either hell ele!ent or co!ination of fra!e ele!ent %ith !i" pier fra!e can e ue". The paper "icue the efficienc* of each !o"ellin# approach in repreentin# oth the #loal an" local ehavior of $C hear %all. . The ai! of thi tu"* i to inveti#ate the uitailit*, i!plicit*, accurac*9 effectivene of "ifferent tructural !o"el In"e Ter!(hear Ter!(hear %all, Macro !o"ellin#, Micro !o"ellin#, 7ra!e ele!ent, (hell ele!ent.

I. I :T$;D
to evaluate the epecte" repone of an eitin# $C hear %all un"er certain lateral loa" ha8ar", an" to pre"ict it epecte" !o"e of failure in or"er to e ale to chooe the !ot uitale an" effective retrofittin# techniue for that %all that %oul" !eet a tar#et perfor!ance. The nu!erical !o"elin# of $C ele!ent tarte" * Clou#h et al. 31=>5 %hen the* propoe" the firt nonlinear !acro!o"el, an" * :#o an" (cor"eli 31=>? %ho propoe" the firt application of the finite ele!ent !etho" of anal*i in $C ele!ent. (ince then everal a"vance!ent %ere "one in the area of !o"elin# of $C ele!ent inclu"in# hear %all. The o@ective of thi paper i to preent the "ifferent nu!erical !o"el propoe" * reearcher for the anal*i of $C hear %all II. 'IT$AT<$ $I/ A. Anal*i of (hear /all %ith ;penin# <in# (oli">5 le!ent

B?

Previou reearche on the ehavior of hear %all %ith openin# au!e" elatic anal*i utili8in# hell an" ric6 ele!ent. The preent %or6 a"opt nonlinear finite ele!ent anal*i uin# oli">5 ele!ent. The anal*i co!prie oth !aterial an" #eo!etric nonlinearitie. nonlinearitie. (oli">5 ele!ent !o"el


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the nonlinear repone of concrete !aterial ae" on a contitutive !o"el for the triaial ehavior of concrete after /illia! an" /arn6e. 7ive hear %all !o"el %ith "ifferent openin# i8e are anal*8e". A ith !o"el of a oli" hear %all i alo preente" to co!pare the anal*i reult. The paper tu"ie the effect of the i8e of the openin# on the ehavior of the reinforce" concrete hear %all. Mo"elin# of (hear /all <in# (oli">5 le!ent The oli">5 ele!ent !o"el the nonlinear repone of reinforce" concrete. (oli">5 !o"el the concrete !aterial ae" on a contitutive !o"el for the triaial ehavior of concrete after /illia! an" /arn6e. It i capale of platic "efor!ation, crac6in# in three ortho#onal "irection at each inte#ration point. The crac6in# i !o"ele" throu#h an a"@ut!ent of the !aterial propertie that i carrie" out * chan#in# the ele!ent tiffne !atrice. If the concrete at an inte#ration point fail in uniaial, iaial or triaial co!preion, the concrete i au!e" cruhe" at that point. Cruhin# i "efine" a the co!plete "eterioration of the tructural inte#rit* of the concrete. A:()( allo% enterin# three reinforce!ent ar !aterial in the concrete, each !aterial correpon"in# to the , * an" 8

directionsthe of smeared element (ANSYS, release 5.5).

Figure 20: Solid65 element (ANSYS, release 5.5) . :u!erical tool for !o"elin# of $C hear %all B> Three "ifferent !o"elin# techniue of $C hear %all into the ;pen(( oft%are %ere "icue". Thee !o"el inclu"e fier ection !o"el, fleure-hear interaction !o"el an" c*clic oftene" !e!rane !o"el 3C(MM. :u!erical i!ulation of c*clic loa"in# tet of a len"er hear %all ae" on ;pen(( in thi paper ho% that C(MM an" fier ection !o"el are ale to i!ulate characteritic of the c*clic %all repone. (tren#th "eterioration, tiffne "e#ra"ation, h*teretic hape an" pinchin# ehavior are clearl* capture" in the anal*i reult, ho%ever ecaue of fe%er D;7 an" le co!putin# ti!e, the fier ection !o"el i applicale to tall hear %all too. Co!parion et%een anal*tical !o"el repone an" tet reult ho% that the fleure-hear interaction !o"el provi"e a reaonal* accurate repone pre"iction for a len"er hear %all. a. 7leure- hear interaction !o"el In or"er to capture the eperi!entall* oerve" hearfleure interaction in $C %all, ;ra6cal propoe" an anal*tical !o"el that incorporate $C panel ehavior "ecrie" * a rotation- an#le approach into the !ultiple-vertical-lineele!ent-!o"el 3M'M, 7i#ure 1E. The anal*tical !o"el %a ae" on the !etho"olo#* "evelope" * Petran#eli to the M'M ele!ent. 7leure-hear interaction !o"el involve !o"if*in# the M'M * ai#nin# a hear prin# for each uniaial ele!ent. ach uniaial ele!ent i then treate" a an $C panel ele!ent, %ith !e!rane action, %ith unifor! nor!al an" hear tree applie" in the in-plane "irection 37i#ure 1=. The interaction et%een fleure an" hear %a incorporate" at the uniaial ele!ent level. Thi !etho"olo#* involve the i!ple!entation of the finite ele!ent !etho" to#ether %ith a contitutive $C !e!rane !o"el. . 7ier ection !o"el In thi !o"el, there are a nu!er of control cro-ection alon# the ele!ent. ach cro-ection i u"ivi"e" into concrete an" teel fier %here uniaial tre-train la% are ue" to "ecrie the


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repone of the !aterial in the lon#itu"inal "irection 3parallel to the ele!ent ai. Thee ection are locate" at the control point of the nu!erical

integration

Figure !. "#$%" model

Figure &. Fle'ure s hear interaction model &*. C. :onlinear Anal*i Metho" for $einforce" Concrete uil"in# %ith (hear %all B5 $einforce" concrete 3$C hear %all are !o"ele" utili8in# "ifferent techniue either uin# hell ele!ent or co!ination of fra!e ele!ent. In the nonlinear anal*e, the nonlinear !aterial !o"el of !i"-pier fra!e i #enerall* ae" on platic hin#e concept locate" on the platic 8one at the en" of the tructural ele!ent or "itriute" alon# the !e!er pan len#th. The nonlinear ehavior of the hell ele!ent i #enerall* !o"ele" uin# !ulti-la*er hell ele!ent %ith la*ere" !aterial !o"el. In thi approach, the concrete an" the reinforce!ent ini"e the tructural ele!ent are !o"ele" repectivel* %ith "ifferent la*er. a.

'inear Mo"el for (hear%all

Application of the finite ele!ent !etho" for the anal*i of uil"in# tructure %ith hear %all reuire an un"ertan"in# of the approi!ation involve" in the !o"elin# au!ption to uil" thee ele!ent. The t%o !o"elin# proce"ure an" au!ption are eplaine" elo%& 7ra!e le!ent ae" Mo"el The hear %all are !o"ele" uin# a et of fra!e ele!ent. The !ot co!!on !o"elin# techniue i to ue a co!poition of !i"-pier fra!e to repreent the hear %all tiffne an" a hori8ontal fra!e 3ri#i" ar! to allo% proper connection %ith interectin# ea! an" la co!ponent. The !ot critical point for thi !o"el i the proper election of ri#i"it* an" tiffne propert* for the hori8ontal fra!e. Infinite ri#i"it* of the upper fra!e can hi#hl* overeti!ate the en"in# !o!ent epeciall* at the connectin# ea!. Thi !o"el i ue" %i"el* in practice to !o"el planar hear %all in uil"in# tructure for linear an" nonlinear anal*e. Thi !o"el !i#ht have no reliale reult for ver* lon#, interactin# or co!ple hear %all %ith openin#.


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(hell le!ent ae" Mo"el The hell ele!ent coni"ere" in !ot of the "ei#n oft%are ha i "e#ree of free"o! at each no"e an" an in-plane rotational "e#ree of free"o!, %hich !a6e it co!patile %ith three-"i!enional ea! t*pe finite ele!ent !o"el. It i %orth to 6no% that a ilinear hape function are ue" to "efine the "iplace!ent fiel" of the ua"rilateral ele!ent, /ilon 32002. Therefore, hear %all !o"elin# reuire a !eh "icreti8ation in or"er to #et realitic ehavior. The a"vanta#e of uin# hell ele!ent i the ailit* to !o"el ver* lon#, interactin# an" co!ple hear %all %ithin the three "i!enional !o"el. . :onlinear Material Mo"el (hear /all The nonlinear ele!ent !o"el of hear %all are ran#e" fro! three "i!enional nonlinear oli" ele!ent, t%o "i!enional nonlinear hell ele!ent to i!plifie" !o"el uin# fra!e ele!ent. Continuu! 7inite le!ent Mo"el The hear %all i !o"ele" %ith continuu! ele!ent uin# nonlinear oli" ele!ent eite" in !an* a"vance" finite ele!ent anal*e oft%are a A:()(, AAF<(, etc. The continuu! ele!ent offer uperiorit* in accuratel* !o"elin# the concrete an" reinforce!ent "etail 3:icolae an" $e*nouar", 2000. $einforce!ent can e "efine" in three "ifferent "irection. The platicit* !o"el for concrete i ae" on the flo% theor* of platicit*, on Mie *iel" criterion, iotropic har"enin# an" aociate" flo% rule. The continuu! ele!ent alo capture i!portant ehavioral repone uch a aial-fleure interaction, inelatic hear "efor!ation, teel confinin# effect on concrete ehavior, concrete co!preion oftenin#, an" concrete tenion tiffenin# 3(pacone an" lTa%il, 2004. Multi-'a*er (hell le!ent The hear %all i !o"ele" uin# a fine !eh of !eare" !ulti-la*er hell ele!ent. The !ulti-la*er hell ele!ent i ae" on the principle of co!poite !aterial !echanic an" it can i!ulate the couple" in-planeout-plane en"in# an" the couple" in-plane en"in#-hear nonlinear ehavior of $C hear %all 3Miao et al, 200>. The hell ele!ent i !a"e up of !an* la*er %ith "ifferent thic6ne. An" "ifferent !aterial propertie are ai#ne" to variou la*er 37i#ure 1?



+ear 2 / -oncrete lae +ear 

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7i#ure 1?. Multi-la*er hell ele!ent D. Co!parion of Practical Approache for Mo"ellin# (hear %all in (tructural Anal*e of uil"in# B4 (hell ele!ent for!ulation #enerall* conit of out-ofplane 3plate an" in-plane 3!e!rane "e#ree of free"o!. The !e!rane ele!ent %ith "rillin# "e#ree of free"o! %a a challen#e for the en#ineerin# co!!unit* for !an* "eca"e. The !e!rane ele!ent #enerall* co!ine" %ith plate ele!ent to for! a Hhell ele!ent that ha i "e#ree of free"o! at each no"e an" an in-plane rotational "e#ree of free"o!, %hich !a6e it co!patile %ith three-"i!enional ea!-t*pe finite ele!ent. Thi approach %a ucceful an" !an* anal*i oft%are have a"opte" variou for!ulation for the hell ele!ent. In practical en#ineerin#, althou#h the hell ele!ent appear to have full co!patiilit* %ith three"i!enional ea! ele!ent, o!e li!itation in the for!ulation %ere i"entifie". Althou#h "rillin# rotation allo% intro"ucin# eternal loa" in the for! of "rillin# !o!ent, anal*tical reult ho% inconitenc* an" enitivit* to !eh i8e an" loa"in# con"ition.


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a. (hell le!ent ae" Mo"el The hell ele!ent can e ue" efficientl* for the anal*i of uil"in# tructure %ith hear %all. The hell ele!ent coni"ere" in !ot of the "ei#n oft%are ha i "e#ree of free"o! at each no"e an" an in-plane rotational "e#ree of free"o!, %hich !a6e it co!patile %ith three-"i!enional ea!-t*pe finite ele!ent !o"el. It i %orth to 6no% that a ilinear hape function are ue" to "efine the "iplace!ent fiel" of the ua"rilateral ele!ent, /ilon 32002. Therefore, hear%all !o"elin# reuire a !eh "icreti8ation in or"er to #et realitic ehavior. The a"vanta#e of uin# hell ele!ent i the ailit* to !o"el ver* lon#, interactin# an" co!ple hear%all %ithin the three "i!enional !o"el. The opti!al i8e of the !eh an" the effect of !eh i8e on the reult are ho%n in the nu!erical ea!ple elo%. Althou#h the hell ele!ent for!ulation inclu"e the "rillin# "e#ree of free"o!, anal*tical reult ho% inconitenc* an" enitivit* of the "rillin# !o!ent to !eh i8e an" loa"in# con"ition. Thi hortco!in# ha i#nificant effect on the en"in# !o!ent of the in plane ea! connecte" to the hear%all. To reolve thi prole!, in en#ineerin# practice, the ea! connectin# to hear %all are #enerall* !o"ele" to o!e eten" ini"e the hear%all hell ele!ent.

+igid1 %lement

eam framing into 3all

7i#ure 14& $i#i" ele!ent "efine" alon# the top chor" of the %all

+igid1 %lement

eam framing

7i#ure 15& $i#i" ele!ent penetratin# alon# one !eh len#th a. 7ra!e le!ent ae" Mo"el The hear%all are !o"ele" uin# a et of fra!e ele!ent. The !ot co!!on !o"elin# techniue i to ue a co!poition of !i"-pier fra!e to repreent the hear%all tiffne an" a hori8ontal fra!e 3ri#i" ar! to allo% proper connection %ith interectin# ea! an" la co!ponent. The !ot critical point for thi !o"el i the proper election of ri#i"it* an" tiffne propert* for the hori8ontal fra!e. Infinite ri#i"it* of the upper fra!e can hi#hl* overeti!ate the en"in# !o!ent epeciall* at the connectin# ea!. Thi !o"el i ue" %i"el* in practice to !o"el planar hear%all in uil"in# tructure for linear an" nonlinear anal*e. Thi !o"el !i#ht have no reliale reult for ver* lon#, interactin# or co!ple hear%all %ith openin#.


+igid1 Arm

"id4ier %lement

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eam framing into 3all

all

Figure 6: "id4ier "odel ae" on nu!erical reult for "ifferent uil"in# !o"el an" hear%all confi#uration an" the "ifferent anal*e et reult of the ea!ple uil"in#, the follo%in# concluion can e !a"e In !o"elin# hear%all %ith Hhell ele!ent, the "rillin# !o!ent of the hear%all an" the en"in# !o!ent of the inplane connecte" ea! are chan#e" "ra!aticall* %ith !eh "enit*. 7or finer !ehe 10 ti!e re"uction of the "rillin# !o!ent can e eti!ate". Intro"uction of top chor" fra!e tailie the reult coni"eral*. Goo" eti!ation of the propertie of the top chor" fra!e i ver* i!portant not to affect the overall tiffne of the tructural *te!. et reult are otaine" uin# a top chor" fra!e ele!ent to enhance the fiit* of the ea! fra!in# into the hear%all. <in# one penetratin# ri#i" ele!ent alon# the top !eh #ive #oo" reult for coare !ehe. 7or finer !eh 32020 15J "ifference are eit in "rillin# !o!ent for hear%all an" en"in# !o!ent of the ea! alon# !a@or "irection. . A"vance!ent in !o"elin# of $C hear %all B+ Thi paper preent "ifferent !o"elin# techniue that have een ue" * reearcher in !o"elin# of $C hear %all. Thee ran#e fro! !acro-!o"el uch a lu!pe" platicit*, !ultiaial prin# !o"el, co!ine" !o"el, up to !icro!o"el uch a finite ele!ent !o"el an" fire !o"el. The paper "icue the efficienc* of each !o"el in repreentin# oth the #loal an" local ehaviour of $C hear %all. a. Micro-Mo"elin# veru Macro-Mo"elin# The t%o !ain approache for !o"elin# of $C !e!er are !icro-!o"elin# an" !acro !o"elin#. Micro-!o"elin# uch a the finite ele!ent anal*i or fier anal*i i ae" on repreentin# the ehaviour of "ifferent !aterial that co!poe the $C ele!ent an" the interaction et%een the!. The !e!er i "icreti8e" into !all ele!ent an" principle of euiliriu! are applie". Thi approach i co!ple an" nee" hi#h nu!erical procein# effort, an" hence it !i#ht not e practical for lar#e tructure an" it i li!ite" to !o"el in"ivi"ual tructural co!ponent uch a a colu!n, a ea! or a %all. ;n the other han", !acro-!o"elin# i ae" on repreentin# the overall ehaviour of the $C ele!ent, uch a the %all "efor!ation, tren#th, an" ener#* "iipation capacit*. The #loal ehaviour of the $C ele!ent uin# a !acro!o"el houl" e calirate" uin# an eperi!ental verification to a"@ut the para!eter nee"e" for the !o"el. Thi approach i i!ple an" "oe not reuire hi#h nu!erical effort, %hich !a6e it uitale to i!ulate the repone of lar#e tructure. . K*teretic Mo"el The c*clic ehaviour of $C hear %all houl" e "efine" uin# a h*teretic !o"el that i ale to i!ulate "ifferent inelatic pheno!ena of reinforce" concrete !aterial. The !o"elin# of the h*teretic ehaviour of the $C ele!ent can affect the ele!ent repone i#nificantl* 3An"eron an" To%nen" 1=??. Thee !o"el can e ue" to repreent the aial, fleure an" hear ehaviour of the ele!ent. The h*teretic !o"el conit of a pri!ar* curve 3ac6one curve that control the !onotonic loa"in# an" o!e h*terei rule that control the loa"in# an" unloa"in# ele!ent ehaviour un"er c*clic loa"in#. The control para!eter of the h*terei rule are a"@ute" to i!ulate the actual c*clic ehaviour of the tete" %all. c. Micro-Mo"elin# of $C (hear /all 7inite ele!ent !etho" of anal*i The nu!er of the finite ele!ent i choen accor"in# to the level of accurac* reuire" an" the availale anal*i tool. The 7M of anal*i i capale of trac6in# the !e!er #loal ehaviour 3e.#. !e!er force an" "iplace!ent in a""ition to it local ehaviour 3e.#. crac6 pattern, !aterial tree an" train. The firt 7 !o"el ue" for $C ele!ent %a propoe" * :#o an" (cor"eli


?

31=>?. The propoe" t%o-"i!enional linear !o"el ue" contant train trian#ular 3C(T finite ele!ent to !o"el the concrete an" teel ele!ent, lin6a#e ele!ent %ere ue" to repreent the on" et%een teel an" concrete ele!ent, an" the effect of crac6in# %a inclu"e" in the !o"el. 7ire 3la*er !o"el In thi !o"el, the !e!er i "ivi"e" lon#itu"inall* into everal e#!ent, an" each e#!ent conit of parallel la*er. (o!e la*er %oul" repreent the concrete !aterial an" other la*er %oul" repreent the teel !aterial. In other t*pe of !o"el, each in#le la*er %a "ivi"e" into a finite nu!er of fire a ho%n in 7i#ure 5 3a. The contitutive la% for concrete an" teel !aterial are "efine", an" hence the !o!ent-curvature relationhip of the !e!er can e calculate" at each loa" level. Thi !o"el account for the "itriution of fleiilit* alon# the !e!er len#th an" the

a'ial e'ure interaction.

Figure 5 (a) Fire eam element 7ro7osed

() "ulti laer 8nite element model

".

Macro-Mo"elin# of $C (hear /all T%o-co!ponent ea!-colu!n ele!ent The !o"el "evelope" * Clou#h et al. 31=>5 conite" !ainl* of t%o parallel co!ponent9 one %a full* elatic an" the other %a perfectl* elato-platic a ho%n in 7i#ure >. The t%o co!ponent %ere ale to repreent the !aterial *iel"in# 3elato-platic ehaviour an" the train har"enin# 3elatic ehaviour. The nonlinearit* of thi !o"el %a repreente" unifor!l* alon# the entire !e!er len#th. The !ain prole! of thi !o"el %a it inailit* to repreent the ele!ent tiffne

or strength degradation 3ith cclic loading.

Figure 6 93o com7onent  element model. ;ne-co!ponent ea!-colu!n ele!ent Thi ele!ent %hich %a "evelope" * Gieron 31=>? conite" of one linear elatic !e!er %ith t%o nonlinear rotational prin# at the t%o !e!er en" a ho%n in 7i#ure ?. The !e!er


E

nonlinear "efor!ation %ere au!e" to e lu!pe" at the 8ero-len#th en" prin# 3lu!pe" platicit*. 7or thi !o"el, the "efor!e" hape %a au!e" to have a "oule curvature %ith a fie" point of contrafleure at the !i""le of the !e!er, an" the plain ection %ere au!e" to re!ain plain. The one-co!ponent !o"el an" the #eneral t%oco!ponent !o"el nee" an appropriate h*teretic loa""efor!ation 3or !o!ent-curvature !o"el to e "efine". Thi reuire "efinition of "ifferent propertie of the !e!er platic hin#e uch a tiffne, tren#th, "uctilit*, c*clic ehaviour, etc., %hich !a* e "ifficult to e "efine" unle o!e au!ption %ere !a"e. Multiple prin# !o"el Multiple prin# !o"el Thi !o"el %a propoe" * Ta6a*ana#i an" (chnorich 31=?>. The !ultiple prin# !o"el conite" of a nu!er of inelatic prin# that are connecte" in erie uin# ri#i" !e!er a ho%n in 7i#ure ?. The inelatic propertie of each prin# %ere varie" accor"in# to the e#!ent propertie an" the level of aial loa" on that e#!ent, ho%ever the e#!ent propertie %ere au!e" to e contant alon# the e#!ent len#th. The !o"el %a ue" to repreent the ehaviour of couple" hear %all, %hile the couplin# ea! %ere !o"ele" uin# one-co!ponent ele!ent. Thi !o"el %a ue" * !ori an" (chnorich 31=E1 to !o"el the hear %all of a 10-tore* fra!e-%all uil"in#. 'inear hear "efor!ation %ere au!e" in the anal*i. The !o"el %ere foun" to atifactoril* repreent the nonlinear ehaviour of the tu"ie" tructure.

Figure  "ulti7le s7ring model Multi-aial prin# !o"el 3M( !o"el Thi !o"el %a propoe" * 'ai et al. 31=E4 to i!ulate the aial-fleure interaction of $C colu!n. The propoe" !o"el conite" of an elatic linear !e!er %ith t%o !ultiaial prin# ele!ent 3M( ele!ent of 8ero "i!enion locate" at the t%o !e!er en" a ho%n in 7i#ure E. The M( ele!ent conite" of 5 concrete an" 4 teel prin#, each prin# %a au!e" to e uniaiall* tree" an" it ehaviour %a #overne" * the h*teretic tre-train characteritic of the i!ulate" !aterial 3concrete or teel. The !ain input for thi !o"el %a the !aterial 3concreteteel contitutive la% rather than the loa"-"efor!ation relationhip of the %hole !e!er. Multi-linear curve %ere ue" to repreent the tretrain or 3force-"efor!ation relationhip for concrete an" teel prin#. The prin# "efor!ation %ere confor!e" to the


=

7lane section ssum7tion. a

Figure ! "ulti a  'ial s7ring model  $ai et al. (&!;): a) "emer model, )
c) %=ecti>e concrete and steel s7rings. 9russ models Thi !o"el au!e" that the %all %ill act a a taticall* "eter!inate tru. The !o"el conit of "ia#onal concrete co!preion trut, hori8ontal tenion tie 3repreentin# the hear reinforce!ent, an" t%o oun"ar* ele!ent at the %all en" to carr* the !o!ent actin#. 7i#ure =3a ho% the tru !o"el ue" * ;eterle at al. 31=E4 for anal*i of hear repone of $C hear %all. ;ther !o"el ae" on the a!e analo#* %ere ue" to calculate the capacit* of $C %all, uch a the (oftene"(trut-an"-Tie !o"el ho%n in 7i#ure E3. The !o"el %a ue" * )u an" K%an# 32005 to pre"ict the hear capacit* of $C uat %all. It i %orth notin# that, althou#h uch !o"el are ale to pre"ict the capacit* of $C ele!ent, the* cannot capture the c*clic or the h*teretic ehaviour of thee ele!ent.


10

Figure & (a) 9russ model used  ?esterle &!;) , et al. (

() Softened Strut and9ie model -omined models Three ertical 'ine le!ent 3T' !o"el The !o"el conite" of three vertical line ele!ent connecte" to each other * ri#i" ar at the top an" the otto! %all en", t%o e"#e lin6 %ith aial prin# repreentin# the oun"ar* ele!ent, an" the central one-co!ponent ele!ent %ith three prin# to control the vertical, hori8ontal, an" rotational "efor!ation of the %all a ho%n in 7i#ure 10. The !ain prole! aout thi !o"el %ere the lac6 of "efor!ation co!patiilit* et%een the %all an" the oun"ar* ele!ent, an" the "ifficult* in "efinin# the propertie of the prin#.


11

7i#ure 10 Three ertical 'ine le!ent !o"el

7i#ure 11 Aial-ele!ent-in-erie !o"el Multiple ertical 'ine le!ent 3M' !o"el The %all ele!ent %a repreente" * a nu!er of uniaial ele!ent connecte" in parallel uin# infinitel* ri#i" ar locate" at the top an" otto! %all en"9 t%o eternal ele!ent i!ulate the %all oun"ar* ele!ent, %hile the other ele!ent i!ulate the co!ine" aial-fleure ehaviour of the central panel. A hori8ontal prin# %a ue" to repreent the inelatic hear ehaviour of the %all. The author !o"ifie" the aialele!ent-in-erie !o"el 3A(M * havin# t%o-co!ponent !o"el for ele!ent 1, repreentin# the crac6e" concrete an" teel reinforce!ent ehaviour, intea" of the oneco!ponent ele!ent in the ori#inal !o"el a ho%n in 7i#ure 12. The contitutive la% for concrete 3crac6e" an" uncrac6e" an" teel ele!ent %ere "efine" to "ecrie the h*teretic repone

of the materials.

Figure 2"ulti7le >ertical line element model

Figure / "odi8edelement a'ial inseries


12

7. An anal*tical !o"el to pre"ict the inelatic ei!ic ehavior of hear-%all, reinforce" concrete tructure B2 2001 A hear failure !o"e !o"el ae" on eperi!ental reult ha een a""e" to the co!puter pro#ra! lar8. An" tu"ie" !ot relevant prole! an" olution "evie" "urin# the "evelop!ent of thi !o"el. ali"ation of the !o"el %a carrie" out * co!parin# it reult %ith the actual repone of t%o . Mo"el for fleural failure !o"e The (I:A h*terei !o"el i!ple!ente" in the lar8 co!puter pro#ra! 37i#. + %a a"opte" in thi tu"* to !o"el the non-linear fleural ehavior an" the !o!ent curvature h*teretic relation for %all ele!ent. A ho%n in 7i#. +, pinchin# effect an" tiffne an" tren#th re"uction "ue to repeate" c*cle at the a!e "efor!ation level %ere not i!ple!ente" in the !o"el for fleural ehaviorreal uil"in#. In pite of the fact that the !o"el i t%o-"i!enional an", hence, it i#nore the torional repone, the reult otaine"

are satisfactor

Fig. /. @steretic model for e'ural mode of failure (eams, colu!n, hear %all. Mo"el for hear failure !o"e (hear "o!inate" ehavior %a alo !o"ele" uin# the (I:A h*terei !o"el a ho%n in 7i#. 4. Pinchin# effect an" tren#th re"uction "ue to repeate" c*cle at the a!e "efor!ation level %ere no% i!ple!ente" in the h *terei !o"el. The !o"el for the hear failure !o"e au!e in"epen"ent of the hear tren#th of %all on oth the en"in#

moment and the a'ial force 7resent in the 3all.

7i#. 4. K*teretic !o"el for hear !o"e of failure 3hear %all. Thi tu"* ha propoe" an" i!ple!ente" a !o"el to inclu"e the hear failure !o"e for %all in availale co!puter pro#ra!. The !o"el "evelope" in thi tu"* i a !acro-!o"el vali"ate" %ith the eperi!ental reult of c*clic tet of hear %all G. Mo"elin# of reinforce" concrete hear %all for nonlinear anal*i co!inin# 7M panel !o"el an"


1+

oun"ar* ele!ent. B1 A !e!er !o"el of reinforce" concrete hear %all %ith oun"ar* colu!n an" ea! %a propoe" for nonlinear an" "*na!ic fra!e anal*i. The reinforce" concrete hear %all %a i"eali8e" a aial prin# for colu!n an" a panel un"er plane tre tate %ith ri#i" ea! at top an" otto! floor level. T%o !etho" %ere co!pare", in %hich iopara!etric ele!ent an" inco!patile rectan#ular ele!ent %ith four no"e for the panel ele!ent %ere ue". The !o"el %a verifie" throu#h the anal*i of T-hape" %all tet. The anal*tical reult otaine" * the propoe" !o"el ho%e" #enerall* #oo" correlation %ith the eperi!ental reult. (hear "efor!ation %a overeti!ate" * iopara!etric panel ele!ent, %herea inco!patile rectan#ular ele!ent, %hich incorporate" fleural "efor!ation * uin# internal "iplace!ent, #ave etter correlation %ith the eperi!ental reult of fleural *iel"in# %all. 7or the %all in hear failure, the anal*tical reult %ere aicall* a!e either * iopara!etric ele!ent or inco!patile ele!ent. a. Co!poition of $C /all Me!er Mo"el Three-ertical-'ine-le!ent-Mo"el 3T'M It %a for!ulate" BLae*aa%a, 1=E+ to i"eali8e a #eneric %all !e!er a three vertical line ele!ent %ith infinitel* ri#i" ea! at top an" otto! floor level. ;uti"e tru ele!ent %ere repreente" * the aial tiffne of oun"ar* colu!n, %hile the central ele!ent %a a uniaial !o"el %ith vertical 3aial, hori8ontal 3hear an" rotational prin#. Thi !o"el ha een verifie" * !an* tet "ata reultin# in a atifactor* correlation et%een calculate" an" !eaure" repone of tructure that ue hear %all. Ko%ever, it %a reporte" BColotti, 1==+ that the repone %a not a"euatel* "ecrie" for hi#h hear tree.

7i#ure 1& Macro-le!ent Mo"el for $C /all Me!er

7M Panel Mo"el In or"er to i!prove the pre"iction of the overall 3hear an" fleural ehavior of $C tructural %all, thi tu"* propoe a 4-no"e panel un"er iaial loa"in# to repreent the %all effect 37i#ure 13. The oun"ar* colu!n ue the a!e aial prin# propoe" in T'M. <in# @ut one panel to contitute the %all, hear train %ill e overeti!ate" * the iopara!etric ele!ent 37i#ure 23a, atifactor* reult cannot e otaine" for the fleural prole!. 7leural "efor!ation !ut e coni"ere" in the ele!ent. In thi tu"*, inco!patile rectan#ular ele!ent i ue", in %hich fleural "efor!ation can

e introduced (Figure 2()).

12

4+4 3a Iopara!etric le!ent 3 Inco!patile le!ent 7i#ure 2& Panel le!ent  Iopara!etric le!ent an"

1


14

Inco!patile le!ent A ne% !o"el for reinforce" concrete hear %all %a propoe", %hich co!ine" a 7M panel ele!ent an" oun"ar* line ele!ent. T%o !etho" uin# iopara!etric ele!ent an" inco!patile ele!ent for a panel %ere co!pare" %ith the tet reult. The !o"el %ith iopara!etric ele!ent li#htl* overeti!ate hear "efor!ation for fleural *iel" hear %all. The !o"el %ith inco!patile rectan#ular ele!ent i etter than the !o"el iopara!etric ele!ent for pre"iction of hear an" fleural "iplace!ent co!ponent. The !o"el #ave a #oo" correlation et%een anal*tical an" eperi!ental reult. III. C;:C'<(I;: A:D (
P.A. Ki"al#o1 , $.M. or"an2, M.P. Martine8 +, 32002, HAn anal*tical !o"el to pre"ict the inelatic ei!ic ehavior of hear%all, reinforce" concrete tructure, n#ineerin# (tructure 24 32002.pp E5=E

B+

L. Galal1 an" K. l-(o66ar*2, HA"vance!ent in !o"elin# of $C hear %all, 3The 14th/orl" Conference on arthua6e n#ineerin# ;ctoer 12-1?, 200E, ei@in#, China

B4

. Luin1, ). M. 7ah@an2 an" M. T. Tan +, 3200E, HCo!parion of Practical Approache 7or Mo"ellin#(hear%all in (tructural Anal*i of uil"in#, the 14 th/orl" Conference on arthua6e n#ineerin# ;ctoer 12-1?, 200E, ei@in#, China

B5

).M. . Luin 1 M.T. Tan 2, 32010, H:onlinear Anal*i Metho" for $einforce" Concrete uil"in# %ith (hear %all, 14th uropean Conference on arthua6e n#ineerin#

B> Ali (oltani1,.7arha" ehna!far2,.Liachehr ehfarnia+,.7arha" erah!an4, 32011H:u!erical tool for !o"elin# of $C hear %all,Eth International Conference on (tructural D*na!ic B?

Ma8en A. Mu!ar, 3201+, HAnal*i of (hear /all %ith ;penin# <in# (oli">5 le!ent, or"an ournal of Civil n#ineerin#, olu!e ?, :o. 2,

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Colle#e :a!e& - (PM( I!perial Colle#e of n#ineerin# an" $eearch, /a#holi, Pune


At. Prof. ).$.(ur*a%anhi PG-coor"inator Gui"e (tructural n#ineerin#

At. Prof. (atih $atho"

Prof. Dr. A. /. Dha%ale Kea" of Depart!ent Civil n#ineerin# -----------------------------------------------------------------------------------------------

15

Different approaches in modeling of RC shear wall: A review

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