Experimental study on the effective width of flat slab structures under dynamic seismic loading

Transcription

1 Exprimntal study on th ffctiv width of flat slab structurs undr dynamic sismic loading Amado Bnavnt-Climnt, Digo Zamora-Sánchz, José Francisco Gil-Villavrd ABSTRACT This papr invstigats th ffctiv width of rinforcd concrt flat slab structurs subjctd to sismic loading on th basis of dynamic shaking tabl tsts. Th study is focussd on th bhavior of cornr slabcolumn connctions with structural stl I- or channl-shapd sctions (sharhads) as shar punching rinforcmnt. To this nd, a 1/2 scal tst modl consisting of aflatslab supportd on four box-typ stl columns was subjctd to svral sismic simulations of incrasing intnsity. It is found from th tst rsults that th ffctiv width tnds to incras with th intnsity of th sismic simulation, and this incras is limitd by th dgradation of adhrnc btwn rinforcing stl and concrt inducd by th strain rvrsals causd by th arthquak. Also, significant diffrncs ar found btwn th ffctiv width obtaind from th tsts and th valus prdictd by formula proposd in th litratur. Ths diffrncs ar attributd to th stiffning ffct providd by th stl profils that constitut th punching shar rinforcmnt. 1. Introduction Flat slabs ar xtnsivly usd to rsist wind and sismic forcs in low-to-modrat sismicity rgions such as th Mditrranan ara. Th bhavior of this typ of structural systm undr gravitational loads is wll stablishd. In contrast, its bhavior undr latral loads is not wll undrstood, particularly undr dynamic sismic loadings. In common practic, flat slab structurs with a rgular distribution of columns ar analyzd as two-dimnsional frams in th lastic domain, applying two approachs: torsional mmbr mthods and ffctiv slab mthods. Th most common procdur prtaining to th first approach is th so-calld Equivalnt Column Mthod [1]. It dfins a transvrs torsional spring to modl th torsional stiffnss of th slab adjacnt to th slabcolumn connction. This torsional stiffnss is combind with column stiffnss to dfin th proprtis of an quivalnt column. In th ffctiv slab width mthod [2-12], th slab is modld as a bam and its quivalnt width is adjustd to simulat th actual bhavior of th thr-dimnsional systm, whil dpth rmains th actual dpth of th slab. Th calculatd ffctiv width taks into account that th slab is not fully ffctiv across its transvrs width. Th study prsntd in this papr focuss on th ffctiv slab width mthod, which, in contrast to th torsional mmbr mthod, can b asily usd with convntional fram analysis softwar. Th ffctiv width of th slab is calculatd using normalizd or convntional approximations, gnrally basd on Finit Elmnt Mthod calculations [10], and static or quasi-static xprimnts [11,12]. Hnc, thr is a nd for documntd xprimnts surrounding th quivalnt width of flat slabs in th prsnc of ralistic dynamic sismic loads. Th bhavior of structurs undr dynamic loads is not th sam as undr static loads, bcaus of th influnc of strain rat ffcts. Th rsistanc of rinforcd concrt (RC) mmbrs can incras anywhr from 7% to 20% with dynamic xcitations [13]. Dspit xtnsiv work conductd in th past by numrous authors, th dynamic bhavior of flat slab structurs undr latral displacmnts is not wll undrstood, maning thr is room for improving latral dsign mthods. Also scarc is rsarch on th sismic bhavior of cornr slab-column connctions that rly on structural stl I- or channl-shapd sctions (sharhads) as shar rinforcmnt. Indd, sharhads in cornr connctions ar not spcifically contmplatd undr th usual norms, for instanc ACI Building Cod [14-18] or Eurocod 2 [19]. Morovr, th contribution of this typ of punching shar rinforcmnt (i.. sharhads) cannot b compltly includd in wll-known formulas for prdicting ffctiv width, such th on proposd by Grossman [9] or Luo and Durrani [7,8]. Grossmañs quation [9] cannot account for th ffct of sharhads, whil th quations proposd by Luo and Durrani [7,8] only partially includ th ffct of sharhads by mans of th critical shar ara considrd in th stiffnss rduction factor.

2 On formula proposd by Luo and Durrani is basd on prvious rsarch conductd by Pcknold [2], who in 1975 dvlopd a modl of quivalnt slab width in which th ffctiv width cofficint (ratio btwn ffctiv and original width) was dducd via lastic plat thory and a Lvy typ solution. Latr, in 1977, Alln and Darvall [3] mployd a Fourir sris tchniqu and publishd rsults that ar concordant with Pcknold's. Dspit postrior dbat, Pcknold's quation was nvr widly accptd by nginrs bcaus it provd hardly practical. In this contxt, this papr dscribs xprimntal invstigation to study th ffctiv width of RC cornr flat slab-column connctions with sharhads as punching rinforcmnt, subjctd to dynamic shaking tabl tsts. Th papr discusss th prdictions providd by diffrnt formula proposd in th litratur. It is obsrvd that th ffctiv width tnds to incras with incrasing valus of th pak acclration applid to th structur, and that this incras is limitd by th loss of adhrnc btwn th rinforcing stl and th surrounding concrt. Also, a simpl procdur is suggstd for stimating th ffctiv width on th basis of th xprimntal rsults. 2. Exprimnts A prototyp on-bay and on-story structur was dsignd, from which a tst modl was constructd and tstd using th shaking tabl of th Laboratory of Structural Dynamics at th Univrsity of Granada, as xplaind blow. (a) (b) Stl C-sction 600 dpth (sharhad) RC slab^ 2700 gags in top rbars gags in bottom rbars Loading dirction Box-typ stl ^L \ sction 80x80x4- (dimnsions in muimtrs) 2400 SHAKING TABLE - Stl C-sction 600 dpth (sharhad) Top: 6mm bars spacing 100mm in ach way 435 Bottom: 6mm bars spacing 75mm in ach way 2.1. Dscription of prototyp structur Th prototyp structur consistd of a 0.25 m dp RC flat slab supportd by four box-typ stl columns. Th hight of th structur was 2.8 m and its dimnsions in plan 4.8 x 4.8 m 2. In th slabcolumn connctions, punching shar rinforcmnt (sharhads) wr includd. Th prototyp was hypothsizd to b locatd in th most arthquak pron rgion of Spain (th ara of Granada), whr th dsign pak ground acclration (PGA) according to th currnt Spanish sismic cod [20] is 0.23g (g bing th acclration of gravity). Th prototyp was dsignd according to Spanish cods NCSE-02 [20], CTE [21], and EHE [22] Dscription of th tst spcimn A rducd-scal modl satisfying th similitud laws was dsignd from th prototyp structur. Th tst modl was drivd applying as scaling factors for gomtry, acclration and strss, rspctivly: 1 = 1/2, l a = 1 and X a = 1. Th tst modl was built in th Structural Enginring Laboratory at th Univrsity of Granada. Th slab, 125 mm dp, was rinforcd with two stl mshs, th on at th top consisting of 6 mm diamtr bars at 100 mm, and th on at th bottom of 6 mm diamtr bars at 75 mm. Th punching shar rinforcmnt at th cornrs of th slab consistd of 60 mm dp stl C-shaps. Th C-sctions wr with stirrups of 6 mm diamtr spacd 75 mm. Fig. 1 shows th gomtry and rinforcing dtails. Th avrag yild strss,/ s, of th rinforcing stl was 467 MPa, whil th avrag concrt strngth was f c = 23.5 MPa. Th columns wr built with an 80 x 80 x 4 mm hollow-stl sction. Th avrag yild strss, f y, of th stl usd for th columns was 216 MPa. Th channls and th stl columns wr joind by mans of arc wlding. Fillt wlds wr usd. Th confining rinforcmnt on th C-sctions consistd of 6 mm diamtr stirrups spacd 75 mm (=0.7d). Thr ar no significant diffrncs in shar rinforcmnt rquirmnts btwn th Spanish concrt cod EHE and th ACI cod, but it is worth noting that in th ACI th maximum 2700 Fig. 1. Tst modl: (a) lvation and (b) plan (bottom viw). spacing of shar rinforcmnt is 0.5d, whil in th Spanish cod it rangs from 0.30d to 0.75d dpnding on th ratio btwn th factord shar strngth dmand and th nominal shar strngth providd by concrt Stup, sismic loading and instrumntation Fig. 2 dscribs th xprimntal st-up and instrumntation. Fig. 3 shows th tst modl just bfor starting th sismic simulations. Th tst modl was boltd to th shaking tabl. In ordr to satisfy th similitud laws btwn prototyp and tst modl, additional mass in form of stl blocks was addd to th top of th RC slab. Th total mass of th tst modl including th stl blocks was m = 7.39 N s 2 /mm. Th stl blocks that form th additional mass wr fixd to th slab by mans of short sgmnts of L- shapd stl profils. During ach sismic simulation, displacmnts, strains and acclrations wr acquird simultanously. Vrtical auxiliary mmbrs consisting of L-shapd aluminum profils wr attachd to th shaking tabl to fix th displacmnt transducrs (LVDTs) that masurd th rlativ horizontal displacmnts btwn th slab and th shaking tabl, as shown in Fig. 2. Th displacmnt transducrs labld as LVDT 1 and LVDT 2 masurd th rlativ displacmnt btwn th slab and th shaking tabl in th dirction of th sismic xcitations. Th displacmnt transducr labld as LVDT 3 masurd th rlativ displacmnt btwn

3 (a) Pair 1 of acclromtrs Additional mass (stl blocks) Bolt x Pair 2 of acclromtrs I Pair 3 of acclromtrs JL I U LVDT 3 f-f ^ n IUII.'.^T-. I..ATI7TT' Strain gags at nd-sction of columns Rbars of 6mm diamtr ((j)6) Stirrups ( )6 confining th C-sctions C-sction strain gags C-sction Fig. 4. Instrumntation of a sction prpndicular to th dirction of shaking (mm). (b) Pali 3 $ liclllígrtíitiri Additional mass (stl blocks) Pair 1 of acclromtrs Fig. 2. St-up: (a) lvation prpndicular to th dirction of shaking and (b) lvation paralll to th dirction of shaking. Fig. 5. Crack pattrns. Fig. 3. Photograph of th tst st-up and instrumntation. th slab and th shaking tabl in th dirction prpndicular to th sismic xcitation. Thr pairs of acclromtrs wr fixd at thr diffrnt points of th slab as shown in Fig. 2. Th acclromtrs labld "Pair 2 of acclromtrs" and "Pair 3 of acclromtrs" masurd th horizontal acclration in th dirction of th sismic xcitation. Th acclromtrs labld "Pair 1 of acclromtrs" masurd th horizontal acclration in th dirction prpndicular to th dirction of th sismic xcitation. An additional acclromtr pr-installd in th shaking tabl masurd its horizontal acclration. Elctrical rsistanc strain gaugs wr attachd to th top and bottom longitudinal rinforcing bars nar th cornr of th slab prior to casting th concrt, as indicatd in Fig. 4. Strain gaugs wr also attachd at th uppr and lowr nds of th columns as shown in Fig. 2. Data collction was continuous, with a sampling rat of 200 Hz. Th tst modl was tstd by applying th signal of th Calitri 1980 NS arthquak (Campano-Lucano, Italy). Th shaking tabl was subjctd to a sris of svn conscutiv sismic simulations with incrasing pak acclrations (PA), namly 0.16g, 0.31g, 0.47g, 0.62g, 0.78g, 0.94g, and 1.10g. Th original (unsald) Calitri arthquak has a pak ground acclration (0.16g) clos to typical dsign valus prscribd by cods in th Mditrranan ara. Th main charactristic that maks it dsirabl to us for xprimntal work is that it has a wid window of priods (btwn 0.5 and 1.5 s approximatly) whr th acclration amplification factor is about 2.5.

4 3. Exprimntal rsults 3.1. Ovrall rspons Th columns startd to plastify at th top and at th bottom nds in th sismic simulation corrsponding to 0.47g, which limitd th maximum bnding momnt transfrrd from th column to th slab. Th rinforcing stl of th slab did not rach its nominal yild strss in any of th sismic simulations, though it did gt vry clos (up to approximatly 90% of th yild strss). Fig. 5 shows th cracks on th concrt slab at th column locations. Th cracks followd an approximatly concntric pattrn cntrd on th column, and th outrmost crack was locatd about 570 mm from th cornr of th slab. This slab cracking pattrn is consistnt with th dcras of th strains of th stl bars aftr about 600 mm, as discussd in th nxt subsction Strains in longitudinal bars Fig. 6a-n shows th distribution of strains for all sismic simulations, in th top and bottom rinforcmnt of th slab. Each row corrsponds to a diffrnt sismic simulation charactrizd by PA. Th lft column of figurs shows th strain distribution at th instant whn th maximum latral displacmnt of th slab rlativ to th tabl was rachd in th positiv dirction. Th right column of figurs shows th strain distribution at th instant of maximum latral displacmnt of th slab in th ngativ dirction. As can b obsrvd in Fig. 6, th strains of th stl bars dcras significantly aftr about 600 mm masurd from th cornr of th slab. Th maximum strains byond 600 mm in Fig. 61-n ar lss than 25% of th maximum strain masurd within th 600 mm width. This indicats that th collaboration of th longitudinal rbars locatd byond 600 mm from th cornr of th slab in rsisting th latral actions was rlativly small. This pattrn on th strain distribution can b obsrvd whil th stl columns ar on th lastic rang (i.. for th sismic simulations with PA = 0.16gand PA = 0.32g), and also aftr th onst of plastification of th stl columns (i.. th sismic simulations with PA qual or gratr than 0.47g). Dsrving mntion in viw of Fig. 6 is that in th sismic simulations with PA gratr than 0.47g, svral bars supposdly in comprssion according to th sign of th bnding momnt applid at (a) PA=0.16g (b) PA=0.16g (C) PA=0.31g (d) F PA= 0.31g ~~~-^ () PA=0.47g ^ (f) PA=0.47g (g) S* PA=0.62g (h) \ PA=0.62g " ^ ^ \ / - Fig. 6. Strain distribution at th instant of maximum latral drift of th slab rlativ to th tabl, in th positiv dirction (lft) and in th ngativ dirction (right).

5 (i) PA=0.78g Ü) PA=0.78g / (k) PA= =0.94g (O PA= =0.94g _y\ N / (m) PA=1.1g * I PA= =1.1g ^" ~--/ \ ""v/ Fig. 6 {continud) that instant, wr in fact in tnsion. This phnomnon is attributd mainly to th loss of adhrnc btwn stl and th surrounding concrt du to bond dtrioration undr rpatd cycls of loading. To furthr clarify this point, Fig. 7 plots th strains masurd in th top rinforcing bar locatd 45 cm from th cornr of th slab against th latral rstoring forc Q_ xrtd by th structur. Whn Q_ is positiv th bnding momnt on th slab is also positiv and th bar is in th comprssion zon. Th load vrsus strain plot indicats that th bar xprincd cyclic tnsion and comprssion dur Latral forc Q (kn) M a Slippag /"* m gjftf^... Hw^ 'Ja :?., Ü>-»S>-.. «lipép DA_ft A-I Strain in top bar locatd at 45 cmfromslab comr (xlo") Fig. 7. Rlation btwn strains in th top bar locatd 45 cm from th cornr of th slab and th latral rstoring forc xrtd by th structur. ing th sismic simulations PA = 0.42g, PA = 0.62g and PA = 0.78g, but comprssiv strains wr smallr and smallr as th numbr of sismic simulations and th numbr of cycls of loading applid to th slab incrasd. Thraftr, th bginning of slippag was obvious, as indicatd by th apparanc of tnsil strains of incrasing magnitud, whn th bar was on th comprssion sid of th slab (i.. whn Q_ was positiv). This bhavior of th strain vrsus load curvs is typical whn thr is loss of adhrnc btwn stl bars and surrounding concrt, and it has bn obsrvd in past xprimntal studis [23]. Othr ffcts such as rsidual cracks causd by th crack opning and closing procss and th axial forcs in th concrt slab may hav also affctd th strain bhavior of rinforcmnt to som xtnt. Ths ffcts, howvr, ar blivd to b of minor importanc, bcaus th rinforcing stl rmaind within th lastic rang, and th width of th cracks and lvl of th axial forcs acting on th slab wr small. Th ffct is mor xacrbatd in th top rbars than in th bottom ons, probably owing to th concrt casting procss that rsults in wors adhrnc conditions for th uppr bars than for lowr bars, and to th lowr amount of rinforcmnt at th top slab msh. As a rsult, th contribution of th comprssd rinforcing stl for sustaining th maximum bnding momnt transfrrd by th column is smallr undr positiv bnding than undr ngativ bnding momnts. Consquntly, for similar absolut valus of th maximum momnts undr positiv and ngativ bnding, and for similar ratios of th top and bottom rinforcmnt, th strains that nd to b dvlopd by th tnsion rinforcmnt bcom largr undr positiv bnding momnts (bottom rinforcmnt in tnsion) than undr ngativ momnts (top rinforcmnt in tnsion). This fact

6 (i.. th strains on bottom rinforcmnt undr positiv bnding bing largr than th strains in top rinforcmnt undr ngativ bnding) can b actually obsrvd in 6, although th bottom rinforcmnt ratio is 1.33 tims highr than th top rinforcmnt ratio. Howvr, th main rason of this bhavior in th tsts conductd for this study is that th maximum bnding momnt transfrrd by th column to th slab was largr undr maximum positiv displacmnt (i.. maximum positiv momnt on th slab) than undr maximum ngativ displacmnt (i.. maximum ngativ momnt on th slab). Th bnding momnt on th columns was calculatd from th strains masurd by th gags attachd to th stl column (s Fig. 2). Th strain diffrnc btwn stl and surrounding concrt du to th aformntiond loss of adhrnc can b roughly stimatd assuming that: (i) th distanc btwn th cntroid of th tnsion rinforcmnt and th rsultant of th comprssiv strss in th concrt is approximatly 0.9d, and (ii) that th strss distribution in th concrt is triangular. On th basis of ths assumptions, it was found that th strain diffrnc btwn top rinforcmnt and surrounding concrt was about for th sismic simulation with PA = 0.94g, and about for th sismic simulation with PA= l.lg Effctiv width prdiction with formula proposd in past rsarch Givn th RC slab shown in Fig. 8, whos dimnsion prpndicular to th dirction of th horizontal loading is / 2, th ffctiv width undr this loading is dfind as th fictitious width which, supporting a uniform rotation along its whol xtnsion, givs th sam displacmnt in columns than th original slab. Th ratio btwn ffctiv and original widths is usually notd as a. On of th formula for calculating th ffctiv width od 2 is th on proposd by Grossman [9], which is applicabl to th spcimn tsts for this study bcaus it is totally symmtric. Th xprssion is: al 2 = K c 0.3Í! c h c 2-ci 0.9h Kn (1) whr K D is a factor considring dgradation of stiffnss of slabs at various latral load lvls (1.1 for th xisting latral drift), ^ is th lngth of span of supports in dirction paralll to latral load, Oi is th siz of support in dirction paralll to latral load, c 2 is th siz of support in dirction transvrs to latral load, d is th ffctiv dpth of slab, h is th slab thicknss and K FP is a factor that must b takn 1.0 for intrior supports, 0.8 for xtrior and dg supports, and 0.6 for cornr supports). Furthrmor, in th cas of xtrior columns, corrctions ar mad using a factor qual to [/ 3 + (/ 2 /2)]/ l 2} whr l 3 is th distanc btwn th cntr lin of th column and th paralll dg of th slab. Ths valus for K D, K FP and th xtrior column corrction factor wr suggstd by Grossman [9]. Finally, particularizing Eq. (1) for th spcimn tstd in this study givs: ai 2 = l.l mm 2400 It can b obsrvd that this width (270 mm) is vry small in comparison with th width of th slab whr significant strains wr masurd in th rinforcmnt during th tsts (about 600 mm, as can b sn in Fig. 6). On xplanation for this disagrmnt is that Grossman's formula cannot tak into account th ffct of th sharhads that form th punching shar rinforcmnt. Likwis, applying th formula obtaind from xprimntal calibration of th Pcknold solution by Luo and Durrani [7], which is valid for intrior connctions with a dtrmind rang of variabls (0.5 sc d/c 2 si 2.0; 0.5 s k l 2 % 2.0), th ffctiv width ratio can b prdictd as follows: Eq. (2) must b multiplid by a corrction factor x that accounts for th concrt cracking, which is givn by: X= AcVñ (3) whr V g is th gravity load shar, f. is th spcific concrt strngth and A c is th ara of concrt sction rsisting shar transfr. As for A c, two possibl valus can b adoptd in rfrnc to Fig. 9 according to ACI On possibility is to ignor th sharhads and to tak th primtr as dfind by plans paralll and distancd from th column facs half th ffctiv dpth of th slab,/l cl. Th scond option, mor appropriat for th tst modl undr study, is to incorporat th contribution of th punching shar rinforcmnt basd on C-shap mtallic profils of 60 mm dpth by adopting as primtr for th critical sction that indicatd as A c2 in Fig c/2 : /4{Lv-/2) l/4{i.,-c/2) (2) Load C W ^ -J + / * vx X A i XX* A & J ^ P Fig. 8. Paramtrs of th Grossman's formula. Fig. 9. Primtr of th critical ara for shar transfr.

7 Thrfor, introducing A c2 and th data of th tstd modl into Exprssions (2) and (3), th following valus ar obtaind: ( : i AT / 80 mm ' "^«400 mm 4047 lb in. 4.1 in.,/3408 psi í í.í( Th quivalnt width ratio givn by Eq. (2) is for intrior connctions. For xtrior connctions, such as thos tstd in our study, th authors bliv that an additional rduction factor of at last 0.5 should b introducd. Adopting th rduction factor 0.5, th quivalnt width providd by Luo and Durrani's approximation is 430 mm. (4) (5) Luo and Durrani [8] proposd a furthr xprssion for stimat ing th ffctiv width of xtrior connctions: Oil h (6) K t + K s whr K t is th torsional stiffnss of th torsional mmbrs, and K s is th flxural stiffnss of th slab considrd in th connction. Th main difficulty in applying Eq. (6) is how to includ th ffct of th sharhads usd as punching shar rinforcmnt. An attmpt was mad to calculat th torsional stiffnss K t with th formula providd by ACI, that is, K t = E9 c S C/[/ 2 (l - c 2 // 2 ) 3 ], whr E cs is th lastic modulus of th concrt slab and C is a gomtric paramtr. Sinc in th typ of connction tstd in this study thr is no dg bam, but two C-shap stl profils, th formula for stimating C providd by ACI, i.. C= 2(1-0.63x/y)x 3 y/3 cannot b usd. Thus, it was dcidd to stimat K t and K s from finit lmnt modls (FEMs) that includ composit sctions as shown in Fig. 10. Fig. 10a shows th FEM that rprsnts th torsional mmbr that providd K t. Fig. 10b shows th FEM that rprsnts (a) Modl for calculating Kt SECTION B-B 355 p* 1c lam )d( nd ^ A1 Fr nd F SECTION A-A O ID Stl lmnts (3D brick) -n Concrt lmnts (3D brick) Ti lmnts (2D linar) (mm) L-> B' ci=80 lilllililllt F (b) Modl for calculating Ks ELEVATION 2400 Clampd nd I 1 SECTION A-A' O 10 Ü Stl lmnts (3D brick) ^ Concrt lmnts (3D brick) h=187.5 (mm) Fig. 10. Finit lmnt modl usd to calculat: (a) K t and (b) K s.

8 th flxural mmbr that providd K s. For th calculation of K t, on nd of th mmbr (th lft nd in Fig. 10a) was clampd whil th othr nd was fr. For th calculation of K s, on nd of th mmbr (th right nd in Fig. 10b) was clampd, whil th othr nd was fr to displac horizontally and rotat, but rstraind against vrtical displacmnts. Th matrials wr assumd to rmain within th lastic rang. Th Young modulus assumd for concrt was 2.36 x 10 4 N/mm 2 and for stl 2.1 x 10 5 N/mm 2. Uppr bound valus wr usd in th modl assumptions; th concrt was assumd to b uncrackd, and thus th initial lastic (uppr bound valu) Young modulus was usd. Th channls providd a rasonabl incras in stiffnss. Th stiffnss valus K t and K s calculatd with th stl channls wr about 60% and 50%, rspctivly, gratr than th corrsponding valus without th stl channls. K t and K s wr calculatd with a convntional softwar program, giving K t = 2 x 10 8 N mm and K s = 5 x 10 8 N mm. Substituting ths valus in Eq. (6) and multiplying by th corrction factor that taks into account th concrt cracking givs th following: 2 x 10 8 N mm <*hx = 2xl0 8 Nmm- 5x lo'nmm 2400 mm 0.9 = 617 mm (7) This rsult is vry clos to th width of th slab whr significant strains wr masurd in th rinforcmnt during th tsts (about 600 mm as can b sn in Fig. 6). It is worth noting that th ffctiv width formula by Grossman [9] and Luo and Durrani [7] wr dvlopd for concrt columns. In gnral, stl columns rquir smallr sctions and hav diffrnt stiffnss in comparison to concrt columns. From th point of viw of th siz of th sction, th authors bliv that th formula by Grossman [9] and by Luo and Durrani [7] ar applicabl to stl columns as long as th dimnsions C\ and c 2 ar within th rquird rang of valus, i.. (0.5 < Oi/c 2 < 2.0; 0.5 < li/l 2 < 2.0) for Luo and Durrani's formula. Howvr, th diffrnt stiffnss providd by th stl columns in comparison to th concrt columns could b a contributing factor to th diffrnc masurd and ffctiv widths calculatd Proposal for calculation of th ffctiv width of th slab from th tst rsults In this sction, th ffctiv width of th cornr slab-column connction with punching shar rinforcmnt (sharhads) tstd in this study is calculatd from th strains masurd in th slab rinforcmnt during th xprimnts. Fig. 11 shows a sction of on half of th slab, togthr with th strain distribution of th top and bottom rbars at a givn instant of th loading procss. Th maximum strains in th top and bottom rinforcmnt ar namd si and s^, rspctivly, in th figur. Th ffctiv width b j is dfind hr as th fictitious width of th slab (masurd from th cornr in th dirction transvrs to th latral load) which, bing rinforcd with th actual rbars locatd within b ff and assuming that all ths rbars hav th sam strain s^x or s^, would hav th sam flxural capacity as that of th half slab calculatd with th actual strain distribution in th rbars. By applying th abov dfinition, th ffctiv width of th slab can b calculatd in a gnral cas as follows. First, th sction of on half of th slab is dividd into sgmnts of lngth b' as shown in Fig. 12. Each sgmnt i starts at a distanc x masurd along th slab prpndicularly to th dirction of loading. Th ara of th uppr and lowr rbars within ach sgmnt, Af p and A bot, is takn qual to Af p = Q +tí af p (x)dx anda bot = Q +tí a bot (x)dx rspctivly, whr a t p {x),a bot {x) dnot th aras (pr unit lngth) of th uppr and lowr rinforcmnt. Th strain of th uppr and lowr rbars of ach sgmnt ar stimatd from th strain distributions masurd during th tsts, and thy ar dnotd by f p and s bm as shown in Fig. 11. Hr, f p and s bm dnot th avrag strains within x and (x, + b'). Assuming a linar strain distribution btwn f p and bot along th hight of th sgmnt, th bnding momnt M, sustaind by ach sgmnt is simply obtaind from a convntional fibr analysis and th strss-strain rlationships obtaind from th matrial tsts. In th sgmnts of th slab whr bond dgradation occurs and M cannot b calculatd using this procdur, th following altrnativ formula is usd: M t =AJ s d[\-(aj s /\.7b'fc<T)] (8) whr A s is th rinforcmnt ara in tnsion within >' and/ s is th avrag strss of th rbars in tnsion within >'. Eq. (8) disrgards th prsnc of comprssion rinforcmnt and assums that th distribution of comprssiv strss on th concrt can b approximatd by an quivalnt rctangular strss block of 0.85/ c ' whos dpth is ftc. Hr, c is th distanc from th xtrm comprssion surfac to th nutral axis and ft is a constant. Following ACI [18], ft is takn qual to 0.85, sinc th concrt usd for th tsts was/ c ' < 27.5 MPa. Th valu of c is obtaind by quating <-«M sgmnt of slab Fig. 11. Assssmnt of th strain distribution in ach sgmnt. b' i 4 sgmnt of slab sction /.' *. x,+by ~J / M distribution of strains * > f Fig. 12. Explicativ schm of th artificial divisions considrd in th slab.

9 th comprssion, 0.85/ c ' >''ftc, and tnsion, A f s. Onc c is dtrmind, Eq. (8) is obtaind by taking momnts at th cntroid of th rctangular concrt strss block. Thn, adding up th bnding momnts M, along all th sgmnts of th half slab, th total bnding momnt M is obtaind, i..: M = ^M. Th total bnding momnt M calculatd in this way was compard with th corrsponding momnt sustaind by th columns (which was calculatd from th strains masurd with gaugs fixd at th nd-sction of th column), and similar valus wr obtaind (diffrncs lss than 11%). Nxt, a portion of slab of trial width b // is considrd, whos aras of uppr and lowr rinforcmnt ar A l ^ = 0 s a t p {x)dx and A b g = j Q ' s a h s ot {x)dx, rspctivly. Th uppr and lowr rbars of this portion of slab ar assumd to hav a uniform strain distribution dfind by é^ax and s b^x rspctivly (s Fig. 11). Th bnding momnt sustaind by this portion of slab, M //, is calculatd through a fibr analysis basd on th assumption that th strain varis linarly along th hight btwn é^ax and jj^, just as it did for th portions of width b'. Through a trial and rror itration procdur, th valu of b j that maks M = M j is dtrmind, and it is takn as th ffctiv width of th cornr slab-column connction. By applying th procdur xplaind abov, th ffctiv width b ffvjas computd for ach sismic simulation, using th strain distributions at th instant of maximum latral displacmnt. Th rsults ar shown in Fig. 13. As sn in th figur, b tnds to incras with th intnsity of th sismic simulation. Th rat of this incras with PA is largr whil th stl column rmains lastic (i.. for PA lss or qual to 0.47g), than aftr th plastification of th column (i.. for PA gratr than 0.47g). Th most important incras in th ffctiv width occurs whn PA changs from 0.47g to 0.62g. In this incras of th lvl of sismic xcitation from 0.47g to 0.62g th loss of adhrnc phnomna is not yt prsnt. Th ffctiv width obtaind with th proposd procdur is btwn th valu providd by Grossman (i mm) and th uppr bound valu (617 mm) providd by Luo and Durrani's xprssion with K t and K s stimatd using Finit Elmnt Modling. It is worth noting that btwn th onst of yilding at th outrmost fibrs of th sction of th stl column (which occurrd in th sismic simulation corrsponding to 0.47g), and th full plastification of th sction, th bnding momnt on th column incrass. Also, aftr plastification, th bnding momnt on th column can still incras du to strain hardning ffcts of th matrial. Ths two aspcts xplain why th maximum strains and th calculatd ffctiv widths incras with incrasing valus of applid acclration Effctiv width b _ (mm) ff O' PA=0.62gO OpA=0.31g PA=0.16g O PA=0.47g Q O'""' PA=0.78g Oi -^PA=1.1g PA=0-949 Pak acclration of th sismic simulation (g) Fig. 13. Effctiv width calculatd from th tst rsults by applying th proposd mthod Conclusions This papr dscribs xprimntal invstigation of th ffctiv width of RC cornr flat slab-column connctions with sharhads (stl C-shaps) as punching rinforcmnt, subjctd to ralistic sismic loadings through dynamic shaking tabl tsts. It is found that th prdiction of th ffctiv width has to tak into account th diffrncs of rigidity insid th slab du to th prsnc of stl profils that constitut th punching shar rinforcmnt. Owing to this fact, important diffrncs ar obsrvd btwn th rsults of th tsts conductd in this study and th prdictions providd by th formula proposd in th litratur. In particular, it is found that if th xprssion proposd by Luo and Durrani for xtrior connctions is usd in combination with a prcis valuation of th torsional stiffnss of th sharhads, th ffctiv width prdictd using Luo and Durrani's formula is vry clos to th width of th slab whr significant strains wr masurd in th rinforcmnt during th tsts. Th papr also puts forth a mthod for stimating th ffctiv width from th strains in th rbars masurd during th tsts, basd on th quivalnc of flxural capacity. By analyzing th volution through conscutiv sismic simulations of incrasing intnsity, it is found that th ffctiv width tnds to incras with incrasing valus of th pak acclration applid to th structur. This incras is limitd (or vn slowd down) by th loss of adhrnc btwn th rinforcing stl and th surrounding concrt inducd by th strain rvrsals causd by cyclic loading. Furthr xprimntal work must b undrtakn to fully clarify th influnc of th mbddd stl profils on th ffctiv width of flat slabs subjctd to arthquak-typ dynamic loading. Acknowldgmnts This rsarch was fundd by th local govrnmnt of Spain, Consjría d innovación, Cincia y Tcnología (Projct P07-TEP ) and by th Europan Union (Fonds Europén d Dvlopmnt Rgional). W also xprss spcial thanks to th Spanish Ministry of Education for Grant Numbr FPU-AP Rfrncs [1] Corly WG, Jirsa JO. Equivalnt fram analysis for slab dsign. ACI Struct J 1970;67: [2] Pcknold DA. Slab ffctiv width for quivalnt fram analysis. ACI Struct J 1975;4: [3] Alln F, Darvall P. Latral load quivalnt fram. ACI Struct J 1977;74(7): [4] Vandrbilt DM. Equivalnt fram analysis of unbracd rinforcd concrt buildings for static latral loads. Civil Enginring Dpartmnt, Colorado Stat Univrsity, Structural rsarch rport; p. 36. [5] Hwan SJ, Mohl JP. An xprimntal study of flat-plat structurs undr vrtical and latral loads. Rport no. UCB/SEMM-90/11. Dpartmnt of Civil Enginring, Univrsity of California, Brkly; p [6] Farhy DN, Adin MA, Yanklvsky DZ. RC flat slab-column subassmblags undr latral loading. J Struct Eng, ASCE 1993;119(6): [7] Luo YH, Durrani AJ. Equivalnt bam modl for flat-slab buildings - part I: intrior connctions. ACI Struct J 1995;92(l): [8] Luo YH, Durrani AJ. Equivalnt bam modl for flat-slab buildings - part II: xtrior connctions. ACI Struct J 1995;92(2): [9] Grossman JS. Vrification of proposd dsign mthodologis for ffctiv width of slabs in slab-column frams. ACI Struct J 1997;94(2): [10] Kim HS, L DG. Efficint analysis of flat slab structurs subjctd to latral loads. Eng Struct 2005;27(2): [11] Shin M, Lafav JM. Rinforcd concrt dg bam-column-slab connctions subjctd to arthquak loading. Mag Concr Rs 2004;56(5): [12] Dovich LM, Wight JK. Effctiv slab width modl for sismic analysis of flat slab frams. ACI Struct J 2005;102(6): [13] Otani S. Effct of strain rat on stl and concrt. In: Procdings of th Japan Concrt Institut, vol. 21; p [14] Building cod rquirmnts for structural concrt (ACI318-95) and commntary (ACI318R-95). Amrican Concrt Institut Committ 318, Farmington Hills, MI.

10 [15] Building cod rquirmnts for structural concrt (ACI318-99) and commntary (ACI318R-99). Amrican Concrt Institut Committ 318, Farmington Hills, MI. [16] Building cod rquirmnts for structural concrt (ACI318-02) and commntary (ACI318R-02). Amrican Concrt Institut Committ 318, Farmington Hills, MI. [17] Building cod rquirmnts for structural concrt (ACI318-05) and commntary (ACI318R-05). Amrican Concrt Institut Committ 318, Farmington Hills, MI. [18] Building cod rquirmnts for structural concrt (ACI318-08) and commntary (ACI318R-08). Amrican Concrt Institut Committ 318, Farmington Hills, MI. [19] Eurocod 2: dsign of concrt structurs - part I: gnral ruls and ruls for buildings. Europan Committ for Standardisation (CEN), Brussls, ENV [20] NCSE-02 Norma d Construcción Sismorrsistnt Part gnral y dificación. Spanish Ministry of Construction, Madrid; [21] CTE Código Técnico d la Edificación. Spanish Ministry of Housing, Madrid; [22] EHE-08 Instrucción d Hormigón Estructural, Comisión Prmannt dl Hormigón. Spanish Ministry of Construction, Madrid; [23] Quintro-Fbrs CG, Wight JK. Exprimntal study of rinforcd concrt intrior wid bam-column connctions subjctd to latral loading. ACI Struct J 2001;98(4):