69 PROPOSD MACRO-MODL FOR H ANALYSS OF NFLLD FRAM SRUCURS Fracco J. Crafll ad Athol J. Carr ABSRAC Reforced cocrete frae flled wth aor pael cottte a portat part of the hgh-r trctre dfferet rego of hgh ect. oe deelopg cotre, the are tll ed a a trctral te for low to ed re bldg. Coeqetl, relable ethod to aale flled frae are reqred order to redce the lo of lfe ad propert aocated wth a poble trctral falre. he eqalet trt odel, propoed the 96, a ple procedre to repreet the effect of the aor pael. Seeral proeet of the orgal odel hae bee propoed, a a relt of a better dertadg of the behaor of thee trctre ad the deelopet of copter oftware. h paper preet a ew acro-odel for the ealato of the global repoe of the trctre, whch baed o a lt-trt forlato,. he odel, pleeted a 4-ode pael eleet, accot eparatel for the copree ad hear behaor of aor g a doble tr echa ad a hear prg each drecto. he prcpal pree the deelopet of the odel are the ratoal coderato of the partclar charactertc of aor ad the adeqate repreetato of the hteretc repoe. Frtherore, the odel able to repreet dfferet ode of falre hear obered for aor fll. he coparo of aaltcal relt wth eperetal data howed that the propoed odel, wth a proper calbrato, able to repreet adeqatel the -plae repoe of flled frae.. NRODUCON flled frae are cople trctre whch ehbt a hghl olear elatc behaor. he ot portat factor cotrbtg to th behaor are fro ateral oleart, ael, () cracg ad crhg of the aor pael, () cracg of the cocrete, eldg of the reforcg bar ad local bod lp the rrodg frae, ad () degradato of the bod-frcto echa ad arato of the cotact legth alog the pael-frae terface. Geoetrc olear effect ca alo occr flled frae, epecall whe the trctre able to ret large horzotal dplaceet. Howeer, thee effect do ot preet a partclart ad ca be codered the aal g the ae ethodologe appled to reforced cocrete or teel trctre. he olear effect etoed aboe trodce aaltcal coplete whch reqred ophtcated coptatoal techqe to be properl codered the odellg. Frtherore, oe echacal properte are dffclt to defe accratel, epecall thoe of aor ad of the pael-frae terface. hee fact coplcate the aal of flled frae ad repreet oe of the prcpal reao to epla wh fll pael ha bee codered a "o-trctral eleet", depte ther trog flece o the global repoe. Dfferet odellg techqe hae bee ed for the aal of flled frae, whch ca be dded to two a grop: () local or cro-odel ad () plfed or acro-odel, Crafll, et al.,. he frt grop ole the odel whch the trctre dded to ero eleet (all of dfferet tpe) to tae accot of the local effect detal, wherea the ecod grop clde plfed odel baed o a phcal dertadg of the behaor of the fll pael. the later cae, a few eleet are ed to repreet the effect of the aor fll a a whole. Both tpe of odel preet adatage ad dadatage, ad the electo of the ore adeqate opto hold coder the charactertc of each cae ad the objecte of the aal. he tpcal eaple of the acro-odel for flled frae the dagoal trt odel, ee Fg. (a), deeloped eeral decade ago baed o the aaltcal wor codcted b Polao (a reported b Mallc ad Seer, 967). Later, Hole, 96, propoed that the eqalet dagoal trt hold hae a wdth eqal to oe thrd of the legth of the pael ad Stafford Sth, 96, proed the approach baed o eperetal data. h ta wa coted b a other reearcher, who refed the odel, al b coderg eeral trt to repreet the pael (a ore coplete decrpto ca be fod elewhere, Crafll, ). Facltad de geería, Uerdad Nacoal de Co. Medoza, Argeta (Meber). -al:jcra@c.ed.ar Departet of Cl geerg, Uert of Caterbr. Chrtchrch, New Zealad (Fellow). BULLN OF H NW ZALAND SOCY FOR ARHUA NGNRNG, Vol. 4, No., Je 7
7 order to aale large trctre or coplete bldg, t ee that a ple, bt phcall reaoable odel cottte the bet alterate. Coeqetl, th paper preet the deelopet ad pleetato of a acro-odel for the repreetato of the aor pael flled frae. h odel coder a lt-trt forlato, whch ca be efl whe the objecte of the aal foce o the global repoe of the trctre. (a) Model A A z/3 (b) Model B A / A /. PRLMNARY SUDY A prelar td wa codcted to etgate the ltato of the gle trt odel ad the flece of dfferet lt-trt odel o the trctral repoe of the flled frae. he td foced o the lateral tffe of the trctre ad o the acto dced the rrodg frae. Fgre lltrate the three trt odel codered the td, whch are referred a Model A, B ad C, repectel. he total area of the eqalet aor trt, A, wa the ae all the cae. t wa aed Model C that the ectoal area of the cetral trt wa the doble of that correpodg to the off-dagoal trt. he eparato betwee the trt Model B ad C wa adopted a a fracto of the cotact legth, z, defed b Stafford Sth, 966, t t be oted that the odel how Fgre are ald for tatc aal becae the trt are located order to repreet the dagoal copree feld that deelop the pael. Whe the trctre bjected to cclc or dac loadg, the dagoal trt hold chage accordg the drecto of the loadg. he e of ol oe dagoal trt retg copree ad tele force caot decrbe properl the teral force dced the eber of the frae. th cae, at leat two trt followg the dagoal drecto of the pael t be codered to repreet approatel the effect of the aor fll. t all aed that the dagoal trt are acte ol whe bjected to copree force. Howeer, copreo-ol eleet are ot aalable coo elatc copter progra. th cae, t recoed the e of teo-copreo tr eber both drecto wth half of the eqalet trt area each dagoal drecto. he e of th plfed odel relt gfcat chage the teral force the rrodg frae, epecall the aal force the col (tele force decreae, wherea copree force creae). he apto of a copreo-ol trt acceptable o the ba that the bod tregth at the pael-frae terface ad the tele tregth of the aor are er low. ele force, therefore, ca be traferred throgh the terface ol for all leel of ec ectato. h coderato a ot be ald whe ether hear coector are ed at the terface or the aor pael reforced wth horzotal or ertcal bar. Refed odel, howeer, ca coder the tele behaor, whch all doe ot affect gfcatl the relt. z/ (c) Model C A /4 A /4 A / Fgre. Strt odel codered the prelar td. Nercal relt obtaed fro the trt odel A, B ad C were copared wth thoe correpodg to a refed fte eleet odel (FM) pleeted wth the progra ABAUS. he geeral charactertc of th odel are decrbed b Crafll, 997. he lateral tffe of the trctre wa lar all the cae codered, wth aller ale for odel B ad C. t t be oted that, for the lttrt odel, the tffe a gfcatl chage depedg o the eparato betwee trt. Fgre copare the bedg oet dagra obtaed fro oe tpcal eaple accordg to the dfferet odel ed th td. Model A deretate the bedg oet becae the lateral force are prarl reted b a tr echa. O the other had, Model B lead to larger ale tha thoe correpodg to the fte eleet odel. A better approato obtaed fro Model C, althogh oe dfferece are at the ed of both col. Slar coclo ca be draw regardg the hear force. he a aal force the frae eber are approatel eqal all the odel, ee thogh the arato of the aal force alog the col how oe dcrepac at the top ed of the teo col ad at the botto ed of the copreo col. FM Model A Model B Model C Fgre. Bedg oet dagra obtaed fro dfferet odel. t ca be coclded that the gle trt odel, depte t plct, ca prode a adeqate etato of the tffe of the flled frae ad the aal force dced the frae
7 eber b lateral force. Howeer, a ore refed odel, Model C, reqred order to obta realtc ale of the bedg oet ad hear force the frae. 3. FALUR MODS OF H MASONRY PANL Accordg to the lteratre, the ot coo tpe of falre are, Crafll, 997: hear falre de to debodg of the ortar-brc terface (hear-frcto falre), whch ca occr followg a tepped cracg patter or b horzotal ldg alog a ortar jot, dagoal teo falre of the aor t, a a relt of a cobato of copree ad hear tree the aor, ad crhg of the aor at the corer de to hgh copree tree. Macro-odel, de to ther plct, caot repreet precel all the dfferet tpe of falre obered for aor pael. For th reao, a prelar td hold be codcted before odellg the trctre order to etate the epected ode of falre of the aor pael. h ca be acheed b applg the falre theor propoed b Ma ad Müller (98) or b Crafll et al. (995) ad (). After th prelar td, the falre of aor ca be adeqatel codered the odel g a proper cobato of trt ad hear prg. he falre de to crhg of the aor at the corer coo for flled reforced cocrete frae, althogh t ha bee obered flled teel frae. th cae, the rrodg frae ore fleble ad the cotact legth betwee the pael ad the frae aller. h tato ca be alo repreeted wth the trple trt odel lltrated Fg. 3, whch the cetral trt dded to two eleet wth dfferet area, order to coder approatel the creae of aal tree occrrg the corer of the pael. t worth otg that th dea preeted here a geeral ee. he practcal applcato of th odel reqre frther reearch order to etgate the ale of the area ad legth of the redced eleet of the cetral trt. 4. PROPOSD MACRO-MODL 4. Geeral decrpto of the odel A ew acro-odel propoed th paper order to repreet, a ratoal bt ple wa, the effect of aor fll pael. he odel pleeted a a 4-ode pael eleet whch coected to the frae at the bea-col jot. terall, the pael eleet accot eparatel for the copree ad hear behaor of the aor pael g two parallel trt ad a hear prg each drecto, ee Fg. 4. h cofgrato allow a adeqate coderato of the lateral tffe of the pael ad of the tregth of aor pael, partclarl whe a hear falre alog ortar jot or dagoal teo falre epected. Frtherore, the odel ea to appl the aal of large flled frae trctre. he a ltato of the odel relt fro t plct, ce the pael coected to the bea-col jot of the frae t ot able to predct properl the bedg oet ad hear force the rrodg frae. t aed the odel that the tffe of the hear prg,, eqal to a fracto, γ, of the total tffe of the aor trt A γ co θ () d where A the total area of the eqalet trt (defed b eeral reearcher baed o eperetal ad aaltcal data, ee Crafll, 997), the elatc odl of aor ad d the dagoal legth of the aor pael. he ter co θ trodced q. () to epre the tffe the horzotal drecto, beg θ the clato of the dagoal of the fll pael. he factor γ all are fro.5 to.75, accordg to the relt obtaed b the athor whe calbratg the odel. h z hear prg Redced eleet aor trt hz A /4 A /4 A / Fgre 3. Mlt-trt odel propoed to repreet the crhg of the aor at the corer of the pael. Fgre 4. Propoed lt-trt odel (ol the trt ad hear prg acte oe drecto are repreeted). he hteretc repoe of the hear prg odelled followg a elato-platc rle wth arable hear tregth (Crafll, 997). he hear tregth of the prg cotrolled b a hear-frcto echa whch ca be adeqatel repreeted b the Mohr-Colob crtero. herefore, the tregth ealated coderg two dfferet tage, ael, () elatc repoe before the bod-hear tregth reached,
7 ad () ldg, whch the tregth deped o the copree force of the trt. the latter cae, the hear tregth lted order to aod large ale de to hgh aal force the trt. he ealato of the tffe of the hear prg codered the odel, baed o q. (), doe ot reflect the actal hear behaor of the aor pael, bt repreet a practcal approach whch lead to adeqate ale of the lateral tffe of the flled frae. th wa, t poble to e the etg eprcal epreo propoed for the calclato of the eqalet wdth of the aor trt. Addtoal eperetal ad aaltcal reearch reqred order to deelop a ore ratoal procedre whch wll be able to tae to accot the hear repoe of the fll pael ot ol ter of tregth bt alo ter of tffe. he aal tffe of each trt, a, accot for the reag fracto (-γ ) of the total tffe whch aged to two trt wth eqal area, ee Fg. (b): ( γ ) A t a () d where t taget odl of the aor defed accordg to a adeqate hteretc odel for aor. h reqred order to codct olear dac aale of flled frae bjected to earthqae. the propoed odel, the repoe of the aal trt repreeted accordg to a hteretc tretra relatohp deeloped b Crafll, 997. he aal force ad the aal dplaceet the trt are related to the tre ad tra of the aor accordg to bac relatohp of the trctral aal. he area of the eqalet trt, A, ca decreae a the lateral dplaceet of the trctre, ad coeqetl the aal dplaceet of the trt, creae. h de to the redcto of the cotact legth betwee the pael ad the frae, ad de to the cracg of the aor fll. t aed the propoed odel that the area of the eqalet are a a fcto of the aal dplaceet a, followg the crtero lltrated Fg. 5. he arato of the trt area A trodced the odel to ga geeralt, ee thogh there ffcet forato to etate the practcal ale of th arato. Accordg to eperetal relt reported b Deca ad Fat (986) the eqalet wdth of the trt decreae b abot % to 5% de to cracg of the aor pael. Howeer, thee ale were dered der the apto that the odl t rea cotat, wherea the propoed odel coder a arable odl, whch decreae a the aal copree tra creae. he a adatage of th approach that the er ca cotrol the arato of the tffe ad the aal tregth of the aor trt. he repoe the tal tage prarl cotrolled b the hear prg ad the bedg oet ad hear force the frae are lar to thoe obtaed fro the trple-trt odel (Model C, Fg. ). After the hear tregth reached ad ldg tart, the echa chage reltg a gfcat creae of the acto dced the frae. a a Strt area A A Aal dplaceet Fgre 5. Varato of the trt area codered the odel. 4. Forlato of the odel he practcal pleetato of the propoed odel reqre the e of eeral prg eleet ad bea or bea-col eleet to repreet the aor pael ad the rrodg frae. order to plf the applcato of the propoed odel, fro the er pot of ew, a 4-ode pael eleet ha bee forlated ad pleeted the trctral progra RUAUMOO (Carr, ). th wa, the er ol eed to defe the charactertc of the aor fll a a whole eleet, wherea the progra ealate terall the properte of the trt ad the hear prg. Fg. 6 lltrate the a charactertc of the propoed pael eleet. he ertcal eparato of both trt, h z, are betwee z/3 ad z/, beg z the cotact legth betwee the pael ad the frae (Stafford Sth, 966): π z h (3) λ h where h the tore heght, t θ λ h h 4 (4) 4 c c h t the aor thce, c the elatc odl of the cocrete, c oet of erta of the col ad h the heght of the aor pael. hree dfferet et of ode are codered for the deelopet of the pael eleet, ael, eteral ode, teral ode ad d ode. he eteral ode are thoe coected to the prcpal trctre, wherea the teral ode are defed b a horzotal ad a ertcal offet, o ad o repectel, eared fro the eteral ode. h teded to repreet the redcto of the deo of the pael de to the depth of the frae eber.
73 h z 4 (a) r echa 3 4 f h z 3 teral d ode ( dof) 4.3 Aal behaor of the trt q. () ge the aal tffe of each trt local coordate (referred to the aal dplaceet). Coeqetl, a ere of traforato are reqred to obta the tffe atr global coordate ad related to the dplaceet of the eteral ode of the pael eleet. h proce deeloped accordg to the trctral cocept preeted Secto 4., ad copre three traforato, whch are decrbed the followg paragraph. ach traforato wll be referred g the b-de A, B ad C. o4 4 o4 4 θ teral ode (3 dof) θ (b) Shear behaor eteral ode (3 dof) f 3 3 he frt traforato reqred the aal relate the aal dplaceet of the trt, a, to the horzotal ad ertcal dplaceet, ad, at the ed j ad of the trt: a j j [ ] A (6) where the atr [] A defed a a fcto of the clato of the trt referred to the global te, θ, ee Fg. 6 (a): [ coθ θ coθ θ ] A (7) o o Fgre 6. Propoed 4-ode pael eleet. hree degree of freedo, the tralato ad ad the rotato θ, are codered each of the eteral ad teral ode. For d ode, wth tralatoal degree of freedo per ode, are reqred to defe the ed of the trt eber whch ot coected to the corer of the pael. he forlato of the tffe atr ad the odal force of the pael eleet codcted coderg the eqlbr ad copatblt eqato betwee the force ad dplaceet of the dfferet coordate te. hee relatohp, dered fro the prcple of Vrtal Dplaceet (Lel,975), dcate that f a traforato atr [] relate the dplaceet {} A ad {} B epreed two dfferet te of rectaglar coordate, the trapoe of th atr, [], alo trafor the odal force {F} B to {F} A. t ca be how that the tffe atr the coordate te B eqal to the doble prodct of the atr [] appled to the tffe atr the coordate te A : { } A { } B, { F} B { F} A (5a) [ ] B (5b) A hee relatohp are cceel appled to trafor the trctral paraeter of each trt ad prg of the odel to the global te of coordate, aocated wth the eteral ode of the pael eleet. he ecod traforato relate the dplaceet ad at both ed of the trt to the global dplaceet,, ad, at the teral ode of the pael eleet. t t be oted that each trt ha oe ed coected to a d ode ad the other ed coected drectl to a teral ode (ee Fg. 7). herefore the ecod traforato eed to be forlated two tep. he frt tep coder the relatohp betwee the dplaceet at the teral d ode j ad the adjacet teral ode ad : j j D D where the b-dee D ad refer to d ad teral ode, repectel. he atr [] D (6) ca be forlated g terpolato fcto whch relate the dplaceet ad correpodg to a pot located at a dtace fro the teral ode. t fod (Crafll, 997) that the ter of th atr are: (8) (,) D co θ + 5 e θ (,) D (,) D ( - 5 ) co θ e θ (,3) D co θ (,4) D 3 co θ + 6 e θ (,5) D (,4) D ( 3-6 ) co θ e θ (9) (,6) D 4 co θ (,) D θ + 5 co θ (,3) D θ (,5) D 3 θ + 6 co θ (,6) D 4 θ
where θ the clato of the edge (ee Fg. 7), 3 χ + χ 3 (χ χ + χ 3 ) L 3 3 χ - χ 3 () 4 ( χ + χ 3 ) L 5 χ 5 χ L the legth of the edge ad χ /L. teral ode teral d ode L j Fgre 7. Detal of oe edge of the pael eleet. At the other ed (ode ) the trt drectl coected to a teral ode ad o pecal calclato are reqred for the ecod tep th traforato. Baed o th coderato, ad tag to accot q. (8), the relatohp betwee the dplaceet at ad at the ed of the trt ad the global dplaceet at the three teral ode (repreeted b bde ) related to the trt : B j j () where the atr [] B clde the traforato defed b q. (): B () he fal traforato relate the dplaceet of the teral ode to the dplaceet of the eteral ode. h relatohp for oe ode ge b: (3) where the atr [] a fcto of the horzotal ad ertcal offet, o ad o, correpodg to ode, ee Fg. 6 (b): o o (4) he traforato dcated b q. (4) eed to be appled three te, ce each trt related to three eteral ode. For eaple, the trt Fg. 6(a) cotrbte to the eteral ode, ad 4. herefore, the coplete traforato : C (5) where the traforato atr : o o o o o o C (6) he coplete procedre for the forlato of the tffe atr ca be arzed the followg tep: a) Select the acte trt the odel ( ad 3, or ad 4) depedg o the drecto of the loadg. b) alate the aal tffe of the trt, a, g q. (). c) Calclate the tffe atr referred to the global dplaceet ad at both ed of the trt, accordg to q. (5b) ad (7): A a A A (7) (4 4) (4 ) ( 4) d) Calclate the tffe atr of the trt referred to the three teral ode (wth three degree of freedo at each θ D 74
ode,, ad ), coderg q. (5b) ad () B B A B (8) (9 9) (9 4) (4 4) (4 9) e) Calclate the tffe atr of the trt referred to the three eteral ode (wth three degree of freedo at each ode,, ad ), baed o q. (5b) ad (6) C C B C (8) (9 9) (9 9) (9 9) (9 9) f) Aeble the ter of the atr [ ] C to the atr of the pael eleet, [ p ], ( ), tag to accot the ode related to the trt. the cae of the trt, whch related to the eteral ode, ad 4, the cotrbto of th trt to the total tffe atr : p (9) where the bol dcate a ozero ter the atr, whch obtaed fro atr [ ] C. g) Repeat the ae proce for the ecod trt the odel order to coplete the tffe atr of the pael eleet. A lar proce of ccee traforato hold be appled order to aeble the ector of odal force ( ter), baed o q. (5a). 4.4 Shear behaor of the prg he coderato of the hear behaor of the pael eleet pler, ce ol oe prg eleet ed. h prg coected to two dagoall oppote teral ode depedg o the drecto of the hear force, ee Fg. 6(b). t worth otg that the pleetato of the propoed odel a pael eleet allow the calclato of the aal force the trt to be ed for ealatg the tregth of the hear prg. h ter-relatohp betwee dfferet eber ot poble to be codered ot of the etg progra for trctral aal. he tffe of the prg ad the hear force are aocated wth the horzotal dplaceet,, of the two dagoall oppote ode (ode ad 3 or ad 4, depedg o the loadg drecto). Coeqetl, the tffe atr of the hear prg related to the dplaceet of the teral ode ad : () where the ter defed b q. (). he ol traforato reqred th cae that ge b q. (3) ad (4), whch relate the teral ode to the eteral ode: D () where the traforato atr : o o o o D () Baed o q. (5b), the tffe atr of the hear prg related to the eteral to two eteral ode of the pael : D D D (3) (6 6) (6 6) (6 6) (6 6) Fall, the ter of the atr [ ] D eed to be added to the total tffe atr [ p ] coderg that the hear prg coected to ode ad 3 or ad 4, depedg o the loadg drecto. 5. CONSDRAONS FOR 3-D MODLS recet ear there ha bee a gfcat creae both the power of copter ad the capact of the oftware aalable for trctral aal. A a relt, toda t poble to perfor the olear aal of coplete trctre g 3D odel. he trt odel (gle or lt-trt) ha bee deeloped ad ed to ealate the -plae behaor of aor fll, howeer, the ot-of-plae repoe caot be adeqatel repreeted becae the fll behae a a reforced lab. Whe pleetg the propoed odel a 3-D copter progra the followg coderato hold be tae to accot. he aor pael the odel hold be a plae pael ( the defored tate). h ea tha the for ode of the pael hold be a plae. f the pael ot plae, other effect ca be portat (hell or ebrae behaor), whch are ot codered the odel preeted here. Whe the 75
76 drecto oral to the pael cocde wth oe of the global ae (e.g. the a Z), the olto ple. t t be codered that the tffe atr of the pael ( ) cotrbte ol to the global degree of freedo the plae of the pael (XY). th cae, the dplaceet alog Z ad the rotato abot X ad Y hold be gored, becae the odel ot able to repreet the ot-of-plae behaor. A ore prece repreetato of the patal behaor of the fll frae wll reqre the coderato of the ot of plae repoe. For eaple, the pael ca be codered a a lab, bt th behaor probabl degrade rapdl a the dplaceet creae. h cople repreetato of the fll pael eceed the cope of the trt odel, whch appled a a plfed repreetato. For ore refed odelg, the e of -D or 3-D olear fte eleet to repreet the etre pael cold be a proper olto. 6. NUMRCAL XAMPLS he propoed odel wa appled to repreet the repoe of a flled frae teted at the Uert of Caterbr der ertcal ad cclc lateral loadg, whch a hear falre occrred (Crafll, 997). Ug the copter progra RUAUMOO (Carr, ), the lateral ad ertcal force were appled ccee creet, whch the echacal properte of the trctre were pdated accordg to the tra ad dplaceet dced the dfferet copoet of the odel the preo tep. he eparato of the trt wa adopted a h z.3, whch eqalet to z/. he properte of the odel aocated wth the aal cclc behaor of aor were adopted fro tet of the ateral. Fgre 8 copare eperetal ad aaltcal relt the rage of all dplaceet order to obere clearl the repoe the tal tage. he force leel at whch hear cracg occr accordg to the aaltcal procedre, 59.8 N, agree er well wth the eared ale eqal to 65. N. he oerall theoretcal repoe copared Fg. 9 wth the tregth eelope eared drg the tet, dcatg that the propoed odel ca etate the lateral retace of the flled frae ad the tregth degradato obered for large dplaceet. addto, the falre echa properl repreeted, beg the aaltcal odel capable of decrbg the hear cracg of the aor pael ad the eldg of the teo col of the frae. he propoed odel ha bee alo pleeted the progra SeStrct (SeSoft, 6) ad ercal relt were copared to eperetal data b Sro et al. (6), howg the accrac of the odel to ealate the olear repoe of the trctre. Frtherore, the codcted a teretg ett aal to ealate the relate portace of the paraeter ed the odel to repreet the cclc repoe of aor. 7. CONCLUSONS h paper decrbe a refed acrocopc odel for flled frae, whch the prcpal pree are the ratoal coderato of the partclar charactertc of aor ad the adeqate repreetato of the hteretc repoe. Sce hear falre of the aor (hear frcto ad dagoal teo falre) the ot coo tpe of falre obered a aor pael, a lt-prg odel deeloped to repreet pecfcall th tato. he odel accot eparatel for the copree ad hear behaor of aor g a doble tr echa ad a hear prg each drecto. he propoed cofgrato allow the calclato of the aal force the trt to be ed for the ealato of the hear tregth of the aor pael. h cocept pleeted a 4-ode pael eleet whch beg corporated the copter progra RUAUMOO (Carr, ). he coparo betwee eperetal data obtaed b the athor ad other reearcher ad aaltcal relt dcate that the cclc repoe of flled frae ca be properl repreeted b the propoed odel. h, howeer, reqre a fe calbrato of the odel, whch all acheed after eeral adjtet, partclarl the paraeter defg the hteretc behaor of aor. he eed of thee adjtet dcate that the detal predcto of the real cclc repoe of flled frae tll a dffclt ta. Recoedato are alo ge for the aal of flled frae whe falre de to crhg of the corer epected the aor pael. Frther reearch reqred order to pleet th odel. Shear force (N) 8 6 4 - Shear cracg of the pael -4 -.4 -....4.6.8 Lateral dplaceet () et Nolear tatc aal Fgre 8. Coparo betwee eperetal ad aaltcal data the rage of all dplaceet. Lateral force (N) 8 4-4 -8 Yeldg of the teo col - - -5 - -5 5 5 Lateral dplaceet () et Nolear tatc aal Fgre 9. Coparo betwee eperetal ad aaltcal data the rage of all dplaceet.
77 8. ACNOWLDGMNS he athor epre ther deepet grattde to the late Profeor Robert Par for h alable gdace ad coto pport oer the drato of th project. ha are alo ge to Dr. Joé. Retrepo for h efl adce ad teret th reearch prograe. h etgato wa codcted a part of the PhD the of the frt athor. he cholarhp proded b the Mtr of teral Relato ad rade of New Zealad ad the facal atace ge b the Facltad de geería, Uerdad Nacoal de Co, Argeta, are gratefll acowledged. 9. RFRNCS ABAUS: heor Maal ad Uer' Maal, Hbbtt, arlo & Soree c. Stafford Sth, B. (966). Behaor of Sqare flled Frae, Proceedg of the Aerca Socet of Cl geerg, Joral of Strctral Do, Vol. 9, No. S, pp. 38-43. SeoSoft (6), SeoStrct A Copter Progra for the Statc ad Dac Aal of Fraed Strctre, http://www.eooft.co. Sro,., Blado-Urbe, C., Atoo, S., Pho, R. ad Crowle, H. (6). pleetato ad Verfcato of a Maor Pael Model for Nolear Pedo-Dac Aal of flled RC Frae, Proceedg of the Frt ropea Coferece o arthqae geerg ad Seolog. Geea, Swtzerlad. Carr, A. J. () RUAUMOO: elatc Dac Aal, Departet of Cl geerg, Uert of Caterbr. Crafll, F. J. (997). Sec Behaor of Reforced Cocrete Strctre wth Maor fll, PhD he, Departet of Cl geerg, Uert of Caterbr, 44 p. Crafll, F. J., Carr, A. J. ad Par, R. (). Aaltcal Modellg of flled Frae Strctre - A Geeral Reew. Bllet of the New Zealad Socet for arthqae geerg, Vol. 33, No., pp 3-47. Crafll, F., Carr, A. ad Par, R.(). Ratoal alato of the Lateral Stregth of flled Frae, 7th Natoal Coferece o arthqae geerg, Boto, USA. Deca, L. D. ad Fat, G.. (986). Modelo plfcado de la apotería clda e pórtco. Caracterítca de rgdez reteca lateral e etado líte ( Spah), Jorada Argeta de geería trctral, Beo Are, Argeta, Vol., pp. 87-836. Hole, M. (96). Steel Frae wth Brcwor ad Cocrete fllg, Proceedg of the ttto of Cl geer, Vol. 9, pp. 473-478. Lel, R.. (975) Matr Method of Strctral Aal, Secod dto, Pergao Pre, 77 p. Mallc, D. V. ad Seer, R.. (967) "he Behaor of flled Frae der Statc Loadg", Proceedg of the ttto of Cl geerg, Vol. 38, pp. 639-656. Ma, W. ad Müller, H. (98). Falre of Shear-Streed Maor - A larged heor, et ad Applcato to Shear Wall, Proceedg of the Brth Cerac Socet, Vol. 3, pp. 3-35. Stafford Sth, B. (96). Lateral Stffe of flled Frae, Proceedg of the Aerca Socet of Cl geerg, Joral of Strctral Do, Vol. 88, No. S6, pp. 83-99.