Theoretical and Experimental studying on simply supported Steel shear wall

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1 Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China Thortical and xrimntal studing on siml suortd Stl shar wall A.Sazgari 1 and H.Vladi 2 1 Lcturr, Dt. of Civil nginring, Islamic Azad Univrsit Shabstar Branch,Shabstar,Iran ABSTRACT : 2 Lcturr, Dt. of Structural nginring, Tabriz Univrsit, Tabriz,Iran mail: arashcivil59@ahoo.com,hvladi@ahoo.com In this stud, th bhavior of siml suortd stl shar walls undr monotonic and also cclic loading has bn invstigatd. Initiall a small scimn was loadd with diagonal dirct tnsil loading and its bhavior comard with thortical rsults. Thn six scimns with various dimnsions wnt through cclic loading. Th ffcts of hight, width and thicknss hav bn studid and it is concludd that th drift nhancd with inasing hight whil a small rduction on th shar strngth was obsrvd. Comarison of tst and thortical rsults confirms th validit of th modls. KYWORDS: Stl Shar Wall, xrimntal, Thortical 1. INTRODUTIN In th ast two dcads, considrabl rsarch has bn conductd on stl shar walls. Du to th analog of th shar strngth in ths sstms and th lat girdrs, similar bhavior has bn usd in th stud of ths sstms. Advantags includ cost rduction, wight minimization and dsirabl absortion of th lastic nrg rvals th significanc of studis on this t of structurs. In comarison to th similar sstms, w lad to simlr fabrication and rction in th stl shar walls. Also du to strss concntration in thos structurs, it is not ncssar to contract th wld qualit. Post-buckling bhavior of th shar anls has bn initiall studid b Wagnr in H formulatd his tnsion fild thor aftr his through xrimnts on th thin shar aluminum anls [8]. Sinc thn, svral rsarchrs lik Kohn, Baslr, Racki, Portr studid tnsion fild of lat girdrs following Wagnr s studis and as a rsult, th ffct of flangs stiffnss wr considrd in th calculation of ultimat strngth of anls. ssntiall most studis in th rcnt 2 ars mlo th assumtion of diagonal tnsion fild dvlomnt aftr th stl lat buckling. According to th rsults of lat girdrs thor, Kulak t al wr th first rsarchrs who roosd th alication of thin stl shar walls in Univrsit of Albrta on Th concntratd thir rsarch on ths stl shar walls and aftr svral xrimntal invstigations, suggst rlacmnt of thin wb lat b sris of diagonal tnsil bars. lgaal has studid stl shar walls in gnral and bcaus of th xtrm strain at th nd of th corrsonding lat, h rlacd th lat with virtual stris accomanid a gusst lat at th nds. Thn h valuatd th strss and strain in th stri and gusst lat. His comutational modling indicats good agrmnt with xrimntal boltd and wldd scimns. [3] Brman and brunau dvlod an ffctiv ida on justifing th stri bars[2]. Th dividd th bhavior of stl shar walls into thr arts. Thn shar strngth of ach art was calculatd and surimosd togthr. In sit of thir innovation, th ultimat strngths of ths anls showd artial rror in comarison with Sabouri s thortical rlationshis. [2] 2. STUDYING OF THORTICAL BHAVIOR As mntiond arlir, th bhavior of a lat can b analzd in thr rgions whr shar strngth and

Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China strain can b studid saratl: 1.Pr-buckling bhavior 2.lasto lastic bhavior aftr buckling until anl ilds 3.

Panl bhavior is govrnd b linar lat quation. Margins of this ara ar slim comard to th othrs, and it can b ignord if th anl thicknss is vr small (.g. lss than 1/5) with rsct to its othr dimnsions.

2 Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China strain can b studid saratl: 1.Pr-buckling bhavior 2.lasto lastic bhavior aftr buckling until anl ilds 3.Post buckling bhavior aftr ilding until rutur strss attaind b adoting ror lastic constitut law 2.1. Pr-buckling bhavior In this rgion, th shar forc inass until buckling occurs. Panl bhavior is govrnd b linar lat quation. Margins of this ara ar slim comard to th othrs, and it can b ignord if th anl thicknss is vr small (.g. lss than 1/5) with rsct to its othr dimnsions. Critical strss obtaind basd on classic lat thor b: 2 kπ t 2 τ = ( ) (2.1) 2 12(1 υ ) b Whr k is dfind as: b 2 k = ( ) for b/d > 1 b k = 5.35( ) for b/d <1 d d Figur 1: stl shar wall anl In th abov rlations b, d, t ar width, hight and thicknss of th lat rsctivl (S figur1) 2.2. lasto-lastic bhavior aftr buckling until anl ilds In this has, which starts aftr buckling and continus to ild strss of th lat, w can rlac th lat b diagonal stris with angl of 45 [2] as shown in figur 2. Figur 2: Rlacing th lat with diagonal stris According to lgaal s tsts, th strain distribution on a stri lmnt is not constant and can b varid as shown in figur 3: [3] Figur 3: Th strain distribution on th stri lmnts = α (2.2)

3 Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China L L = L + ( ) = (2 + α) (2.3) α β = (2.4) 3 = (2.5) Dformation cofficint has bn rrsntd bα, which varis btwn 5 and 2. Whn th anl thicknss is small and boundar lmnts hav sufficint rigidit, α is about 2. On th othr hand, whn th anl is thick and boundar lmnts ar flxibl, th cofficint α will rduc to 5. Hnc: 5 α β Now, dfining X axis on th stri dirction, th strain distribution on comlt ilding of stri will b: (1 + υ) = τ + (2.6) x (1 + υ) = τ υ' (2.7) ' Whr υ. 5 is th lastic assion s ratio and σ is th ild strss of lat which can b obtaind b von-misss itria as: σ F 3 τ (2.8) Transforming ths strains to th rincil dirction, th shar strain whn th anl rachs to ild strss is: 2(1 + υ) γ = τ + (1 + υ')( ) (2.9) Substituting, w can calculat anl drift as: G = 2(1 + υ) τ U = + (1 + υ' )( ) d (2.1) G Whn th lat rachs to its ild strss, th total shar strngth can b obtaind using quilibrium mthod as: F = ( τ + 1/ 2σ k sin 2θ bt (2.11) ) Whr k is th modifid cofficint of shar strngth and varis as a function of asct ratio (b/h). It mans that for diffrnt hights, th formula calculats svral shar strngth. Figur 4 shows that b inasing th hight of anl, its strngth is rducd. This figur is also vrifid during this invstigation b/h ffct of b/h k Figur 4: ffct of b/h on th strngth of anl Th angl θ can b assumd b th cod of Canada (CAN/CSA-S ) as follows:

4 Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China tl Ac tan θ = 3 1 hs 1 + ths ( + ) A 36I L b c (2.12) Whr Ac is oss sction of th column and I c its momnt of inrtia. Also h s is th stor hight and A b is th oss sction of bam. It must b notd that th rror of θ in th calculation of ultimat strngth is ngligibl. (Lss than 2%) 2.3. Plastic bhavior aftr ilding until rutur strss W must not that th concts of lasticit ar not tru in this rgion but w can assum th lat as th stri lmnts. Th onl diffrnc in this formulation is rlacmnt of th lastic modul which will rduc. So, b assuming constant valu for stri sction during th formulation, w us t instad of. Bcaus of vr small valu of th thin lat, it can b justifid. Rrsnting σ for th strss valu in th bginning of th lastic rgion until its ultimat valu, th ultimat strss and strain on X and Y dirction ar: σ = σ + σ (2.13) u (1 + υ) x = τ + + (1 + υ) σ t σ (2.14) = τ υ' υ' (2.15) t In which, th ngativ sign indicats rduction of th strain. Whn th anl rachs its ultimat strss, th shar strain and drift ar as follow: 2 (1 + υ) σ γ = + + P τ (1 υ' ) + (2.16) t τ σ U = + (1 + υ' )( + ) d (2.17) G t In this cas th anl strngth is also: F = ( τ +1/ 2σ sin 2θ )bt (2.18) u 3.COMPARING OF THORITICALCONCPS AND TST RSULTS Svn scimns of siml suortd stl shar walls wr fabricatd and tstd undr monotonic and cclic loading. Th rsults wr broadl agrd with thortical concts and wr dsibd in saratd sctions A stl shar wall undr monotonic loads Dimnsion of this scimn wr (all in cntimtr). It was tstd undr diagonal tnsil tst until failur. Tabl 1 shows its charactristics: Tabl 3.1 Scimn charactrs Nam width lngth thicknss F kg/cm 2 Fu kg/cm 2 t Tst Using rlations (12) and (19), w hav: σ 229 γ = ( 1+ υ') β ( ) = (1.5)(7.33)( ) =.1156 τ σ P d U = + ( 1+ υ')( + ) = 12. G cos t mm U = = 3. 95mm cos F = ( τ bt + 1/ 2( σ 3τ ) bt) sin7 cos28.62

Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China = sin 7 ( 49.62 55.6 + 1/ 2(229 3 49.62) 55.6) = 3913.7kgf cos 28.62 From th tst rsults, k is about 1.76.

Figur7: comaring of tst and thortical rsults 3.2.

5 Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China = sin 7 ( / 2( ) 55.6) = kgf cos From th tst rsults, k is about Figur 5 shows tst mchanism and th scimn aftr failur has bn shown in figur6. Figur5: Schmatic of th tsts Figur 6: th scimn aftr loading Figur 7 shows comarison of th xrimntal and thortical rsults. Figur7: comaring of tst and thortical rsults 3.2. Six stl lat shar walls undr cclic loading In this tst, six stl shar walls wnt through cclic loading and thir sismic rsons wr invstigatd for various asct ratio and thicknss valus. Charactristics of ths scimns ar summarizd in tabl 2. Cclic loading wr alid using hdraulic jacks to a coul of stl wldd brackts on th to of stor bam. Figur 8 show schmatic of tst stu. Tabl3. 2: scifications of scimns Nam B(cm) H t(cm) F Y (kg/cm 2 ) τ (kg/cm 2 ) F kgf U(mm) rror (mm) /

Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China Figur8: tst lvation Figur9, shows coincidnc of th thortical rlationshis and xrimntal hstrsis loos for four scimns rfrrd as

6 Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China Figur8: tst lvation Figur9, shows coincidnc of th thortical rlationshis and xrimntal hstrsis loos for four scimns rfrrd as 39, 312, 38, 31. For th rst of scimns, good agrmnts hav also bn obsrvd. Using abov rlationshis, w can rdict th bhavior of stl shar walls undr monotonic or cclic loadings. Bcaus of th strain hardning, hstrsis loos graduall com aart of th thortical lin as a rsult of stl lat bhavior xrimntal thortical xrimntal thortical xrimntal -1 thortical Figur9: comarison of hstrsis loos and thortic rlation shis Figur 1 shows a scimn undr tst which illustrats th alication of latral loads on th stl brackts using hdraulic jacks. Buckling wavs ar clarl shown in th figur. In addition, out of lan bracing and fixing of th scimn ar also dmonstratd in th figur.

7 Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China Figur1: viw of th tst 3.3.ffct of hight on th shar strngth Gnrall, it sms that with hight rduction in constant width, th stiffnss inasd aftr ost-buckling. Th rason is ffctiv lngth rduction in th aralll bars. In such cas, th bam xrincs a littl dro and can orat as a stiffnr as shown in figur 11. Figur 11: Bam dro as a stiffnr for th anl As shown in figur 11, using th stri modl of stl shar wall, rduction of hight rducs th lngth of stris. Hnc it can function as a stiffnr on th anl. Clarl, introduction of a stiffnr on th anl nhancs its shar strngth. This conct is obsrvd in q. (2.11). In figur 12 w can s th shar strngth of two anls with qual width but diffrnt hight. As shown in th figur, hight rduction rsults in th nhancmnt of shar strngth and also rduction of drift which can b rsultd b q. (2.1).

8 Th 14 th World Confrnc on arthquak nginring Octobr 12-17, 28, Bijing, China Figur 12: Th ffct of hight on shar strngth 4.CONCLUSION 1. Our studis modifid dislacmnt- shar strngth rlationshis of siml suortd stl shar walls. 2. Comarison of thortical rlationshis and xrimntal rsults undr monotonic and cclic loadings shows a good rdiction of th bhavior of stl shar wall sstms. 3.All scimns rachd to th ultimat strngth on rlativ drift of 1.7%~2% and faild on 5% 4.Rduction of hight of shar anl rachs to rducing th drift and nhancmnt of shar strngth 5. Long hight of th anl rsults in th nhancmnt of anl drift and absorbs a significant lastic nrg and it lads to small rduction on shar strngth. 6.nhancmnt of width rachs to significant inasing on shar strngth of anl and drift rduction RFRNC 1- Astanh-Asl, A. (2) Stl lat shar walls.us. -Jaan worksho on sismic fractur issus in stl structur Fbruar. San Francisco., 2- Brman.J, M.ASC, and Brunau.M, M.ASC(23) Plastic Analsis and Dsign of Stl Plat Shar Walls. Journal of Structural nginring, 129(11), Novmbr 1 3- lgaal.m (1998) Thin stl lat shar walls bhavior and analsis Thin-Walld Structurs Sabouri-Ghomi, S., and Robrts, T. M. (1991)"Nonlinar dnamic analss of thin stl lat shar walls." Como and Struct., 39(112), , 5- Sabouri-Ghomi.S; Vntura.C, M.ASC; and Mhdi H. K. Kharrazi, (25) Shar Analsis and Dsign of Ductil Stl Plat Walls Journal of structural nginring ASC / JUN 6-Takahashi, Y.. Takmoto, " Takda, T., and Takagi, M.. "xrimntal stud on thin stl shar walls and articular bracings undr altrnativ horizontal load." Prliminar R., ABS Sm. on Rsistanc and Ultimat Dformabilit of Struct. Actd on b Wll-Dfind Ratd Loads, Intrnational Association 7- Tan Chn.S, Jng.V, (21) Sismic Assssmnt and Strngthning Mthod of xisting RC Buildings in Rsons to Cod Rvision arthquak nginring and nginring Sismolog 67, 3(1), 67 77, March 8-Wagnr.H and Ballrstdt.W (1935) Tnsion filds in originall curvd thin shts during Sharing strsss NACA

EXPERIMENTAL AND THEORETICAL POST-BUCKLING STUDY OF STEEL SHEAR WALLS

EXPERIMENTAL AND THEORETICAL POST-BUCKLING STUDY OF STEEL SHEAR WALLS 4th Intrnational Confrnc on arthquak nginring Taipi, Taiwan Octobr 12-13, 2006 Papr No. 114 XPRIMNTAL AND THORTICAL POST-BUCKLING STUDY OF STL SHAR WALLS Abdolrahim. Jalali 1 and Arash.Sazgari 2 ABSTRACT