A DESIGN FORMULA FOR PREDICTING THE SHEAR STRENGTH OF EXTERIOR BEAM COLUMN JOINTS UNDER SEISMIC LOADING

Transcription

1 13 t World Conferene on Eartquake Enineerin Vanouer, B.C., Canada Auust 1-6, 2004 Paper No A DESIGN FORMULA FOR PREDICTING THE SHEAR STRENGTH OF EXTERIOR BEAM COLUMN JOINTS UNDER SEISMIC LOADING Gaetano RUSSO 1 and Giuliana SOMMA 2 SUMMARY Te beaior at failure of 50 exterior beam-olumn joints tested by arious autors as been examined to identify a model for omputin te sear strent of exterior beam-olumn joints under seere seismi ations. Tis exam as pointed out tat, durin te yli loadin, a lare diaonal rakin omes toeter wit a joint olumetri expansion. Tree resistin ontributions aainst te aboe mentioned expansion ae been identified: te onrete one, te beam lonitudinal reinforement one, and te stirrup one. Te oerall sear strent as been taken as te sum of tese tree ontributions, ea dependent on a multiplyin fator wi as been unioally determined from te aailable experimental data. Te so obtained expression predits te sear strent in a mu more aurate and uniform way tan te Euroode, New Zealand and ACI Codes expressions. INTRODUCTION Beam-olumn joints are ritial reions in reinfored onrete frames subjeted to seere seismi attak beause beam moment reersals an produe i sear fores and bond breakdown into te joint, and ene its rakin. Te onsequent joint stiffness dereasin an lead to lare oerall story drift and damae of te struture. Altou te first experimental study on beam-olumn joints was done by Hanson and Conner [1] in te first sixties, only in te last years te researes on joints ae been intensified. A lot of desin ode reommendations and analytial expressions for omputin te exterior beam-olumn joints sear strent under seismi loadin exist [2-7], but are not able to supply an aurate predition, mainly beause of te seeral parameters tat take part and statially indetermination of te problem. Tere are different approaes followed by arious odes and autors, tryin to predit te real sear strent beaior of an exterior beam-olumn joint under eartquake loads. 1 Full Professor, Department of Ciil Enineerin, Uniersity of Udine, Italy 2 PD Enineer, Department of Ciil Enineerin, Uniersity of Udine, Italy

2 On te basis of strent meanisms wi resist to joint expansion always obsered in tests, an analytial expression is ere proposed. JOINT BEHAVIOR AT FAILURE Experimental results of 50 exterior beam-olumn joints tested by arious autors from 1967 to 2000 ae been olleted [1, 8-15]. Tese tests ae been arried out by applyin an orizontal alternate load at te top of te beam element, and often a ertial onstant load on te olumn (Fi.1). Fi.1: Usual test set-up for beam-olumn joint [10] Beause of te ylially alternatin fores, applied durin te test, joints ollapsed sowin an appreiable diaonal rak openin. A poto of a joint tested by Milburn and Park [16] is sown in Fi.2: wen failure ours, a joint expansion is marosopially apparent (Fi.2). Diaonal rakin eidenes relatie motion between rak sides oriinally in ontat. Due to rak widt inreasin, te distane of opposite orners of te joint panel inreases wit orizontal load or wit te number of yles in te inelasti rane. So it may be stated tat, under te load ations wi simulate te seismi ation, witin te joint tere is te deelopment of a diaonal rakin field wit lare rak widt, leadin to relatie motions wit omponents in bot ertial and orizontal diretions. Fi.2: Joint rakin at failure [16]

3 Te onfinement ation aainst te ertial omponent of te expansion is proided by te axial load and te olumn ertial reinforement. Tis onfinement ation may reasonably be approximated by ertial ompressie stresses σ a and σ V, respetiely due to te axial load (atie onfinement) and to te ertial reinforement (passie onfinement), wi is assumed to be distributed oer all te setion. Te orizontal omponent of te joint expansion is opposed by te passie onfinement ations proided by beam lonitudinal reinforement bars and by te transerse (orizontal) reinforement into te joint, respetiely indiated wit j,l and j,. SHEAR STRENGTH COMPUTING MODEL On te basis of preious onsiderations, an expression is proposed, wi takes into aount te followin resistin meanisms to joint expansion: (1) ertial stresses transmitted by olumn, (2) lonitudinal beam reinforement, and (3) passie onfinement due to stirrups into te joint, if present. Te proposed expression for sear strent of an exterior reinfored onrete joint is j j, + j, l + j, = (1) were j, is te sear strent ontribution proided by onrete and ertial stresses σ a and σ V, j,l is te strent ontribution proided by beam lonitudinal reinforement, and j, is te strent ontribution proided by stirrups. Conrete ontribution Tis ontribution depends on te onrete tensile strent, on σ a and on te onfinement ation proided by te olumn lonitudinal reinforement. By onsiderin on an orizontal plane between te upper and lower beam lonitudinal reinforements te ation of a mean sear stress, τ,, a mean axial ompressie stress σ a, and a mean ertial onfinement stress, σ V, from Mor's irle te prinipal tensile stress is expressed as wi ies pt τ 2 σ a σ σ a + σ 2 = + + τ, (2) 2 2 σ + σ a, = pt 1+ (3) pt As te onrete tensile strent in a biaxial state of tension-ompression is lower tan tat in a uniaxial stress state, f t, it follows tat p t < f t. Moreoer te maximum ertial ation is obtained wen te bars are yielded, so tat σ V = f V, were A f y f V = kv (4) A were f y and A are respetiely te yieldin strent and ross setion area of te ertial olumn reinforement, A is te area of te joint transerse setion, and k V is a numerial oeffiient to be determined. By puttin p t = f t and σ = f V, Eq. (3) proides te limitin onrete sear strent ontribution σ + f a V j, lim = ft 1 + (5) ft Te real onrete sear strent ontribution is lower tan te limitin one, and ene it is expressed by j, = k0 j, lim (6) were k 0 < 1 is a numerial oeffiient to be determined.

4 Beam lonitudinal reinforement ontribution Bein beam reinforement subjeted to lare alternate yli ations makin non linear steel beaior, it is diffiult to ealuate te maximum stress atin on te two reinforement leels (at top and bottom), as far as te maximum onfinement effet due to tese bars. It is assumed tat te joint sear resistane due to te onfinement ation proided by beam lonitudinal reinforement, sould be proportional to te yieldin strent and to te aerae area of te beam lonitudinal reinforement, f y and A s. Consequently te sear strent due to beam reinforement is f y As, (7) A j l = k 1 were k 1 is a numerial oeffiient to be determined. Stirrups ontribution Te joint sear strent ontribution due to te passie onfinement ation aainst expansion proided by stirrups present in te joint, is expressed as follows j, f y, As, = k2 (8) A were k 2 is a numerial oeffiient to be determined, and f y, and A s, are respetiely te yieldin strent and ross setion area of te stirrups in te joint. On te basis of Eqs.(1), (5) and (6-8), te expression for omputin te sear strent of an exterior beamolumn joint is a + f f y As f V y, As, j = k0 f t 1+ σ (9) f t A A wit i = k i / k 0, f V proided by Eq.(4), and f t expressed by te Oluokun [17] followin formula 0.69 f t = f ' (10) were f is te ompressie onrete strent. To ealuate te unknown parameters 50 speimens of exterior reinfored onrete joints tested by arious autors ae been onsidered. Te alues of te tree unknown oeffiients, k V, 1 and 2 appearin in Eqs.(4) and (9) ae been iteratiely aned wit te purpose to minimize te oeffiient of ariation, COV, alulated as te ratio between te standard deiation, STD, and te aerae alue, AVG, of te experimental and omputed sear strent ratio. Te alue of te unknown oeffiient k 0 ae been alibrated to obtainin te exat mean equality between experimental and omputed sear strent, i.e. AVG = 1. So proeedin tere ae been found te alues k 0 =1/3, k V =1/2, 1 =3/2 and 2 =1/2, wi proided a COV = So te sear strent of an exterior reinfored onrete beam olumn joint is proided from Eq.(9) by a + fv = 1 1 j f t 1+ σ + ( 3 f y As + f y, As, ) (11) 3 f t 2A f = A f 2A. wit f t proided by Eq.(10), and ( ) V y PROPOSED MODEL RELIABILITY Te reliability of te proposed model in preditin te sear strent of exterior reinfored onrete joints, is ompared wit te followin sear strent Code expressions

5 New Zealand Standard 3101:1995 [2] f ' f y, A s, j = * 6 α f A j y s were A * s is te reater of te area of top or bottom beam reinforement, and σ 1 f ' A a α j = (13) * f ' 15 f A Te sear strent j must be su as 0.14 f ' 0.20 f '. Euroode 8 (1998) [3] j 2/ f ' y s j = for joints witout stirrups (14) j = 2/ 3 ( 0.48 f ' + f f ) 2/ 3 As, f yd 0.04 f ' a d + for joints wit stirrups (15) A were f d and f yd are respetiely te desin onrete ompressie strent and te desin yieldin strent of stirrups, expressed as fd = f' γ and fyd = f y, γ s, were γ =1.5 and?γ s =1.15. ACI Code [4] j = f ' (16) (12) Teoretial joint sear strent as been omputed for all te 50 tested speimens by means of Eqs.(11), (12), (14) or (15), and (16). Te ratios between measured to alulated joint sear strent are sown in Fi.3 ersus te onrete ompressie strent f. Te oeffiients of ariation and aerae alues, relatie to ea expression, are also indiated. Te measure of te predition uniformity is ien by te oeffiient of ariation, COV: te lower tis alue is, te reater te uniformity. From diarams and COV alues it is eident tat te proposed expression leads to te most uniform predition of te sear strent of exterior reinfored onrete beam olumn joints: a COV alue at least 50% lower tan tose proided by te onsidered Codes is obtained. Tis result onfirms te reliability of te meanial model based on te onfinement ations. Te omparison wit te Paulay and Priestley [6] expression leads to AVG = 1.02 and COV = DESIGN FORMULA Te aboe mentioned reliability of te meanial model leads to dedue from Eq.(11) a desin formula, wi meanly predits sear strent alues on te safe side. In fat, by multiplyin Eq.(11) by a fator, only AVG anes, wile COV doesn t. A arateristi expression, leain on te safe side 95% of te predited alues, is proposed for desin. On te basis of te 50 ere onsidered speimens, te multiplyin fator, leadin to 95% of safety, results 3/4. Consequently te desin formula is a + fv = 1 1 j, d f t 1+ σ + ( 3 f y As + f y, As, ) (17) 4 f t 2A For te 50 onsidered speimens te mean measured to alulated sear strent ratio results 1.33.

6 CONCLUSIONS By analyzin te reports of experimental tests arried out on 50 exterior beam olumn subjeted to lare seismi ation, it as been notied tat a olumetri joint ore expansion ours at failure. A meanial model, based on te resistin meanisms to tis expansion, eiter in ertial and orizontal diretion, as been sown to be ery reliable. From tis model an expression is deried, wi takes into aount te onfinement ation proided by te upper and lower olumn portions, by beam lonitudinal reinforements, and stirrup reinforement. Te proposed expression for omputin te joint sear strent exibits a mu more uniform predition of experimental results tan New Zealand Standards, Euroode and ACI Code. Tis demonstrates te alidity of te meanial model, already proposed for interior joints [18 and 19], also for exterior ones. Te proposed desin formula is affeted by a mean safety fator of 33%. AVG = 1.05 COV = 0.36 AVG = 0.82 COV = 0.56 AVG = 0.90 COV = 0.26 AVG = 1.00 COV = 0.12 Fi.3: Measured to alulated sear strent ratio ersus f, for te 50 exterior joints

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