Biaxial seismic behaviour of reinforced concrete columns

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Baal sesmc behavor of reforced cocrete colms Hgo Rodrges, Varm Hmberto, rêde tóo To cte ths verso: Hgo Rodrges, Varm Hmberto,

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the are pblshed or ot. The docmets ma come from teachg ad research stttos race or abroad, or from pblc or prvate research ceters.

1 Baal sesmc behavor of reforced cocrete colms Hgo Rodrges, Varm Hmberto, rêde tóo To cte ths verso: Hgo Rodrges, Varm Hmberto, rêde tóo. Baal sesmc behavor of reforced cocrete colms. 2d EOMS Yog Ivestgators oferece (YI 23), Sep 23, Bordea, race. <hal-85592> HL Id: hal Sbmtted o 3 g 23 HL s a mlt-dscplar ope access archve for the depost ad dssemato of scetfc research docmets, whether the are pblshed or ot. The docmets ma come from teachg ad research stttos race or abroad, or from pblc or prvate research ceters. L archve overte plrdscplare HL, est destée a dépôt et à la dffso de docmets scetfqes de vea recherche, pblés o o, émaat des établssemets d esegemet et de recherche fraças o étragers, des laboratores pblcs o prvés.

The preset work focses o the assessmet of the strctral respose of R colms der bdrectoal horzotal loads three ma streamles.

2 YI23 Secod EOMS Yog Ivestgators oferece 2 6 September 23, Bordea, race Baal sesmc behavor of reforced cocrete colms H. Rodrges a,*, H. Varm a,. rêde b b vl Egeerg Departmet, Uverst of vero, vero, Portgal vero, Portgal b vl Egeerg Departmet, aclt of Egeerg, Uverst of Porto Porto, Portgal * hrodrges@a.pt bstract. The preset work focses o the assessmet of the strctral respose of R colms der bdrectoal horzotal loads three ma streamles. rst, a epermetal testg campag was performed o rectaglar colms, for dfferet tpes of loadg. Sbseqetl, the tested colms were smlated wth dfferet o-lear modellg strateges. all, a smplfed hsteretc model s proposed for the represetato of the o-lear respose of R members sbjected to baal bedg. ewords: R colms; cclc behavor; baal epermetal testg; refed o-lear modellg; smplfed o-lear modellg INTRODUTION The mportace of stdes addressg the 3D earthqake actos or to bldg rreglartes, whch dce a baal bedg demad combed wth aal load the colms. s well recogsed Dfferet modellg strateges have bee proposed for the smlato of the baal cclc behavor of R elemets wth aal force. However, t s beleved that the avalable baal models are ot matre eogh to be sed practce. The preset std, based o a etesve epermetal campag ad o the aalss of estet modellg strateges proposes a pgraded smplfed model for the represetato of the baal bedg respose of colms wth aal force, whch s based a estg aal model. 2 EXPERIMENTL MPIGN I the epermetal campag were tested 24 rectaglar R colms wth dfferet tpes of geometrc characterstc ad reforcemet detalg ad were cclcall tested for dfferet loadg hstores wth a costat aal force ad der dsplacemet cotrolled codtos. The cross-secto dmesos ad the reforcemet detalg are preseted gre. a) b) c) gre : Testg setp: a) R colm specme dmesos ad reforcemet detalg; b) Geeral vew; c) Global reslts of rectaglar colm PB2-N7 for rhombs load path The epermetal reslts show that the tal colm stffess was ot sgfcatl affected b the baal load path. The mamm stregth of the colms were lower for all baal tests compared wth those for the

3 2 H. Rodrges et al. Yog Ivestgators oferece 23 correspodg aal tests. The ltmate dctlt was sgfcatl redced colms sbjected to baal load paths. The stregth degradato creases after dsplacemet dctlt demads of abot 3 ad t the eqvalet global dampg for colms tested baall s clearl depedet o the load path [5]. 3 EIIENY O DIERENT NON-LINER MODELLING STRTEGIES The mercal aalses developed ad descrbed the preset paper wth dfferet o-lear modellg strateges were performed sg the compter program. I ths work three o-lear modellg strateges were appled to each colm specme ad the obtaed reslts were compared, based o: elemets wth lmped-plastct; elemets wth dstrbted elastct ad force-based formlato; ad elemets wth dstrbted elastct ad dsplacemet-based formlato. I order to evalate the accrac of the mercal models stded the represetato of the shear force evolto obtaed epermetall, the freqec doma error (DE) de was calclated. The DE de measres the devato betwee two waveforms (qatfes ampltde ad phase devatos betwee two sgals, gvg a error factor betwee ad ), ths case the shear force measred the test ad the correspodg calclated shear force for each modellg strateg. It s cosdered that a DE de larger tha.75 represets a poor correlato. The DE dces obtaed for all aalses are represeted Errer! Sorce d revo trovable.. a) Dstrbted Ielastct - DB Dstrbted Ielastct - B Lmped Plastct b) c) gre 2: DE de obtaed from the comparso betwee mercal ad epermetal shear force evoltos: a) aal tests; b) baal tests strog drecto (X); c) baal tests weak drecto (Y) rom the aalss of the obtaed reslts, smlar levels of adeqac were verfed sg the dstrbted elastct (force ad dsplacemet formlatos) ad the lmped plastct modellg strateges. However, based o the comparsos made the followg commets ca be draw: The tal stffess obtaed wth all the modellg strateges for the smlato of the baal tests presets dffereces, whe compared wth the epermetal vales, the rage of 25% to 5%. The secat stffess evolto of the colms was accratel represeted wth all modellg strateges. However, cosderable dffereces were observed, for all modellg strateges, betwee the mercal ad epermetal taget stffess evoltos, mal for the lower drft demads ad the last phase of the colms resposes. Ths aspect cofrms the dffcltes ormall fod represetg mercall the respose of colms wth models based o cremetal procedres, whch deped o the taget stffess. The cclc respose obtaed wth the three modellg strateges for all colms was fod to be satsfactor, bt dffcltes were fod captrg the stregth degradato for the hgher drft demads. lso, the majort of the models show lmtatos represetg the pchg effect the loadg-reloadg stage. ll modellg strateges ehbt dffcltes the represetato of the eerg dsspato evolto. The ma dffereces correspod to a derestmato of the dsspated eerg for lower drft demads assocated wth a qas-lear mercal respose ad to a overestmato for hgher demads assocated wth the lmtatos of the mercal models the represetato of the stregth degradato ad pchg effect. 4 SIMPLIIED HYSTERETI MODEL OR BIXIL BENDING RESPONSE 4. Uaal Model ad the baal Boc-We model or the developmet ad valdato of the smplfed baal model, the osta-osta aal hsteretc model [] was adopted. Ths model represets a geeralsato of the orgal Takeda model wth a trlear skeleto crve for mootoc loadg, defed b the crackg pot ad the eld pot, ad cldes pchg, stffess degradato ad stregth degradato effects.

4 H. Rodrges et al. Yog Ivestgators oferece 23 3 The baal costrcto of the Boc-We model the Wag ad We [2] form follows the same geeral dea as for the aal case. The restorg forces for both drectos are defed b:, wth sg sg sg sg (3.) whch the volved parameters have the same meag as for the aal case, bt are ow referred to the two orthogoal drectos X ad Y, b the sbscrpts ad respectvel. The hsteretc parameters ad are the defed b the followg copled dfferetal eqatos. osderg ow the defto of the cremetal orthogoal forces ad gve b, the frst part of ths sstem ca be wrtte, b a smple mathematcal trasformato, as: sg sg (3.2) whch matches to the aal cremetal restorg forces calclated for each drecto wthot baal teracto, ad the part of the sstem that correspods to the correcto factors f ad f accotg for the teracto betwee the two loadg drectos: f f sg sg (3.3) osderg that the cremetal forces ca be obtaed wth a aal hsteretc model, the preseted framework trodces a smple ad fleble form to represet baal bedg colms. Ths formlato reqres the same formato eeded for the correspodg aal PWL model, ol trodcg a addtoal correcto term whch coples the two loadg drectos (). f f (3.4) 4.2 Parameter detfcato for the scalg teracto factor mg at calbratg the parameters for the hsteretc baal model based o aal models wth a teracto fcto, a gradet based-method was adopted, seqetall assocated wth a evoltoar algorthm method. or the applcato of these models, the SDL/SDoLo optmsato lab compter program was sed [3]. The calbrato of the teracto fcto was performed two phases. I the frst phase, t was teded to select the aaltcal epresso-tpe most stable for the teracto scalg factor () fcto. fter the epresso tpe selecto, the secod phase, cossts the calbrato of the parameters of the teracto fcto as well as of the teracto scalg factor. fter a epresso of the scalg factor (), whch depeds o the colm propertes, the teracto fcto parameters were optmzed for all baal pshover crves, sg a cascade optmzato strateg. The covergece evolto of the cascade optmzato strateges the parameter detfcato are preseted Errer! Sorce d revo trovable.. Errer! Sorce d revo trovable. shows the plot of the Relatve Global Error for two statos, wth ad wthot cosderg the teracto fcto Qadratc error Iteratos/Geeratos LM+E+LM LM gre 3: overgece evolto of the cascade optmzato Wth teracto fcto optmzed -.25º Wth teracto fcto optmzed º Wth teracto fcto optmzed - 45.º Wth teracto fcto optmzed º Wth teracto fcto optmzed º Wthot teracto fcto -.25º Wthot teracto fcto º Wthot teracto fcto - 45.º Wthot teracto fcto º Wthot teracto fcto º Relatve Global Error drecto Y (%) Relatve Global Error drecto X (%) gre 4: Relatve Global of the smplfed model reslts, wth ad wthot teracto fcto Errer! Sorce d revo trovable. cldes selected eamples of pshover crves for dfferet colms ad dfferet pshover loadg agles. I each plot, for both drectos, the obtaed pshover crves are represeted: ) b the refed mercal fbre model; ) b the smplfed model wthot the baal bedg teracto fcto; ad ) b the smplfed model bt wth the teracto fcto. lso, the eamples Errer! Sorce d revo

5% c 25 25 =. Pshover - 45 o 2 s = % c 2 2 Pshover - 22.5 o 5 5 bre model (X drecto) bre model (Y drecto) Orgal (X) Orgal (Y) Optmzed solto (X) Optmzed solto (Y)...2.3.4.5 Horzotal Dsplacemet (m) 5 5 bre model (X drecto) bre model (Y drecto) Orgal (X) Orgal (Y) Optmzed solto (X) Optmzed solto (Y).

5 Base Shear (kn) Base Shear (kn) Base Shear (kn) 4 H. Rodrges et al. Yog Ivestgators oferece 23 trovable. cofrm the error redctos, both colm drectos, obtaed b adoptg the teracto fcto combed wth the optmzed scalg factor M22 M cm cm 2 =. 3 M6 =.2 s =.5% c Pshover - 45 o 25 35cm 2 s =.5% c =. Pshover - 45 o 2 s = % c 2 2 Pshover o 5 5 bre model (X drecto) bre model (Y drecto) Orgal (X) Orgal (Y) Optmzed solto (X) Optmzed solto (Y) Horzotal Dsplacemet (m) 5 5 bre model (X drecto) bre model (Y drecto) Orgal (X) Orgal (Y) Optmzed solto (X) Optmzed solto (Y) Horzotal Dsplacemet (m) 5 5 bre model (X drecto) bre model (Y drecto) Orgal (X) Orgal (Y) Optmzed solto (X) Optmzed solto (Y) Horzotal Dsplacemet (m) gre 5: Eamples of pshover crves for dfferet colms ad dfferet pshover loadg agles. or the valdato of the proposed smplfed model wth teracto fctos, the epermetal reslts of cclc tests were sed of the test campag [4, 5]. rst, the aal tests were modelled order to obta the prmar skeleto crves for each depedet drecto. The, sg the obtaed crves, the baal tests were smlated ad the reslts of the mercal model wth the teracto fcto are compared wth the test reslts. or colms der baal loadg the stregth degradato s dffclt to represet, partclarl for the last ccles of the epermetal respose. The eerg dsspato evolto s also well represeted. I geeral, a good agreemet betwee the predcted mercal reslts ad the epermetal hsteretc respose was observed, dcatg that the proposed strateg ma be stable to smlate the respose of colms to baal loadg based o aal behavor crves assocated wth properl calbrated coplg teracto fctos. gre 6: Base-shear verss drft of colm N5 Baal test, qadraglar dsplacemet patter 5 ONLUSIONS rom the epermetal reslts, t was clear the effects of the baal loadg ad ts mportace the colm respose, especall terms of the stregth degradato ad redcto of the dctlt capact. Wth the three refed mercal strateges stded, smlar level of accrac was verfed. The three modellg strateges revealed lmtatos the represetato of the stregth degradato, partclarl for larger drft demads, whch jstfes the poor estmato of the eerg dsspato evolto wth the mercal models. smplfed teracto model was proposed, based o a aal hsteretc model ad the teracto fcto developed from the Boc-We model. The valdt of the proposed smplfed model was demostrated throgh the aaltcal smlato of the respose of the R colms baall tested. The obtaed mercal reslts showed the model effcec, whch ecorages frther valdato to become a smple trdmesoal tool to smlate baall loaded R elemets. REERENES [].. osta ad. G. osta, "Hsteretc model of force-dsplacemet relatoshps for sesmc aalss of strctres," Natoal Laborator for vl Egeerg, Lsbo, 987. [2]. H. Wag ad Y.. We, "Evalato of pre-northrdge low-rse steel bldgs. I: Modellg " J. Strct. Eg., SE, V. 26(), 6-68., 2. [3]. drade-ampos, "Developmet of a Optmzato ramework for Parameter Idetfcato ad Shape Optmzato Problems Egeerg," Iteratoal Joral of Mafactrg, Materals, ad Mechacal Egeerg (IJMMME), vol., pp , 2.

6 H. Rodrges et al. Yog Ivestgators oferece 23 5 [4] H. Rodrges,. rêde, H. Varm, ad.g. osta, "Epermetal evalato of rectaglar reforced ocrete colm behavor der baal cclc Loadg," Earthqake Egeerg ad Strctral Damcs, Joh Wle & Sos, Ltd. 22. [5] H. Rodrges, "Baal sesmc behavor of reforced cocrete colms," PhD Thess PhD, vl Egeerg Departmet, Uverst of vero, vero, 22.

Simplified Model for the Non-Linear Behaviour Representation of Reinforced Concrete Columns Under Biaxial Bending

Simplified Model for the Non-Linear Behaviour Representation of Reinforced Concrete Columns Under Biaxial Bending Smplfed Model for the No-Lear Behavor Represetato of Reforced Cocrete Colms Uder Baal Bedg H. Rodrges Cvl Egeerg Departmet, Uverst of Avero, Portgal aclt of Natral Sceces, Egeerg ad Techolog - Oporto Lsophoe