Shake-table tests of a reinforced concrete frame designed following modern codes: seismic performance and damage evaluation

Transcription

1 Shake-table tests f a reinfred nrete frame designed fllwing mdern des: seismi perfrmane and damage evaluatin Amade Benavent-Climent David Eslan-Margarit Leandr Mrillas SUMMARY This paper presents shake-table tests nduted n a tw-fifths-sale reinfred nrete frame representing a nventinal nstrutin design under urrent building de prvisins in the Mediterranean area. The struture was subjeted t a sequene f dynami tests inluding free vibratins and fur seismi simulatins in whih a histrial grund mtin rerd was saled t levels f inreasing intensity until llapse. Eah seismi simulatin was assiated with a different level f seismi hazard, representing very frequent, frequent, rare and very rare earthquakes. The struture remained basially undamaged and within the inter-stry drift limits f the 'immediate upany' perfrmane level fr the very frequent and frequent earthquakes. Fr the rare earthquake, the speimen sustained signifiant damage with hrd rtatins f up t 28% f its ultimate apaity and apprahed the upper bund limit f inter-stry drift assiated with 'life safety'. The speimen llapsed at the beginning f the 'very rare' seismi simulatin. Besides summarizing the experimental prgram, this paper evaluates the damage quantitatively at the glbal and lal levels in terms f hrd rtatin and ther damage indexes, tgether with the energy dissipatin demands fr eah level f seismi hazard. Further, the ratis f lumn-t-beam mment apaity remmended by Eurde 8 and ACI-318 t guarantee the frmatin f a strng lumn-weak beam mehanism are examined. 1. INTRODUCTION AND RESEARCH SIGNIFICANCE One f the mst mmn seismi fre-resisting systems fr building strutures is the reinfred nrete (RC) frame. Fllwing the paradigm f perfrmane-based design, mdern seismi des establish seismi perfrmane levels (SPL) that the struture must satisfy under different seismi hazard levels (SHLs). Fr SHLs assiated with rare r very rare earthquakes (i.e., with return perids P r f the rder f abut 475 and 2000 years, respetively), the RC frame is allwed t dissipate energy thrugh plasti defrmatins (i.e., underging strutural damage) at speial regins alled plasti hinges by develping a stable plasti 'strng lumn-weak beam' mehanism. T this end, brittle failures must be prevented at the latins where plasti hinges are expeted, by applying apaity design riteria. Althugh the frame is allwed t enter int the nnlinear range in the ase f severe grund mtins, mmn seismi design predures are aimed at nverting the mpliated nnlinear dynami behavir f the struture int an equivalent linear prblem. This simplifiatin is amplished by the use f fre redutin fatrs that depend n the inelasti

2 respnse harateristis f the strutural system and that rely strngly n the frmatin f the afrementined strng lumn-weak beam mehanism. There is a need t assess the inelasti respnse harateristis and perfrmane f typial strutures designed in view f prvisins established by urrent seismi des and t verify the adequay f these prvisins t meet the design perfrmane bjetives [1] under presribed SHLs. Of paramunt imprtane amng these prvisins is the rati f the mment apaity f lumns t beams framing int a jint, t assure the frmatin f a strng lumn-weak beam mehanism. It is als imprtant t quantify the level f damage expeted in a struture in eah senari f seismi hazard, nt nly in terms f maximum defrmatins (i.e., maximum hrd rtatin r inter-stry drift) but als in terms f umulative damage (i.e., dissipated energy). Prgress in all these aspets alls fr labratry data and experimental evidene, and the best sure fr suh infrmatin is the dynami shake-table test. Shaking table tests reprdue in a mst realisti way the seismi demands n strutures subjeted t grund mtins, partiularly within the nnlinear range and inlude umulative damage effets. The behavir f real strutures an be sensitive t rate f lading effets hardly aptured with numerial mdels. Strain rate effets an mdify the nminal resistane f the strutural members and alter the intended hierarhy f strengths that guarantee the frmatin f a strng lumn-weak beam mehanism. Furthermre, a mputatinally effetive mdeling f the hystereti behavir f RC elements requires intrduing many simplifiatins (regarding the pinhing effets, the strength and stiffness degradatin, et.) that may nditin the atual respnse f the struture. The use f suh analytial mdels entails alibratin and verifiatin thrugh experimental data. The general bjetive f this study is t assess experimentally, thrugh shake-table tests, the seismi perfrmane f RC frames with dutile reinfrement details designed arding t mdern des. The study fuses n the quantitative evaluatin f damage (in terms f maximum defrmatin, dissipated energy, hrd rtatins and damage indexes) imparted t the struture under eah SHL, examining the rati f mment apaity f lumns t beams framing int a jint t guarantee the frmatin f a strng lumn-weak beam mehanism. T this end, shake-table tests f a partial strutural mdel were nduted in the Labratry f Dynamis f Strutures f the University f Granada. The speimen was a tw-fifths-sale mdel that represents a prtin f a prttype building typial f nventinal RC frame strutures with regular and symmetri nfiguratin, designed in view f urrent seismi des in the Mediterranean area. The speimen was subjeted t fur seismi simulatins f inreasing intensity until llapse. The test results prvide a quantitative evaluatin f the glbal and lal damage and energy dissipatin demands fr eah SHL Design f the prttype struture 2. PROTOTYPE STRUCTURE AND TEST SPECIMEN The three-stry and three-bay RC mment-resisting frame shwn in Figure 1 is nsidered as the prttype struture in this study. The struture is representative f existing mdern buildings in the Mediterranean area. It is designed with the limit state design methd nsidering gravity lads (dead lads f 3.22kN/m 2 fr flrs and 2.95 kn/m 2 fr the rf; and live lads f 2kN/m 2 fr flrs and 1 kn/m 2 fr the rf) and lateral seismi lading fllwing the prvisins f the urrent Spanish seismi de NCSE-02 [2]. The prttype building is assumed t be lated in Granada (Spain), where the design grund aeleratin (assiated with a design earthquake f P r = 500 years), a b, is a b = 0.23g (g is the gravity aeleratin). The nrete mpressive strength f assumed in the alulatins was f = 25 MPa, and the yield strength fr the steel was f y = 500 MPa. The flr system nsisted f ne-way jists spaed 80 m supprted by the main beams (jist-band flr system). In turn, the ne-way jists supprted a thin nrete slab 6 m thik. The rss setin f the RC lumns measured 40x40 m 2. The setin f the main beams that supprted the jist was 30 x 40 m 2 ; the rss setin f the beams perpendiular t the main beams was 25 x 35 m 2. Dutile reinfrement details and apaity design riteria were used s that the frame wuld develp a dutile strng lumn-weak beam plasti mehanism under lateral lads. The behavir fatr q

3 I Test substruture Figure 1. Prttype struture. adpted fr the seismi design was q = 3.0, and the resulting base shear fre effiient f the prttype struture was Arding t the Spanish de, the behavir fatr f q = 3 rrespnds t a full dutile struture that frms a strng lumn-weak beam mehanism under lateral lading and satisfies several requirements suh as minimum amunt f lngitudinal reinfrement, maximum spaing f stirrups, and s n. The required strength f lumns s that the struture develped the weak beam-strng lumn plasti mehanism shwn in Figure 2 was based n the fllwing nsideratins: (i) an inverted triangle distributin f lateral lads was adpted; (ii) the plasti hinges at beam ends (with symbl in Figure 2) are nentrated at a distane d r =0.5h + h b, where h and h b are the depth f the lumn and f the beam, respetively; and (iii) the ultimate bending apaity f beams at plasti hinge regins, M ub, was determined assuming that the atual yield stress was 1.25/j,. Capaity design was als applied at the plasti hinge level t prevent shear failure befre the members reahed their ultimate fiexural apaity Design and fabriatin f the test speimen Frm the prttype, a partial strutural mdel was separated frm the riginal prttype by utting thrugh pints f nminal zer bending mment under lateral lads. These lines are pltted with dts in Figure 1. The partial strutural mdel has the height f ne stry and a half, and the width f ne bay and a half in the diretin f the main beams (i.e., thse supprting the gravity lading). The test speimen was defined by applying sale fatrs f X L = 2/5 fr length, X a = 1 fr aeleratin and X 0 = 1 fr stress. Sale fatrs fr the rest f the physial quantities were set t satisfy similitude L-2dR affi Figure 2. Plasti mehanism at glbal level.

4 requirement [3]. Figures 3 and 4 shw the gemetry and reinfring details f the tw idential main frames that frmed the test speimen. The tw frames were nneted by the fllwing: (i) the jists and the thin slab reinfred with a steel mesh; and (ii) the perpendiular beams (sendary beams). Cupn tensin tests were nduted n samples f reinfring bars frm eah bath and size, giving a yield stress f 551 MPa fr the lngitudinal reinfrement and 636 MPa fr the stirrups. Cmpressin tests were nduted n nrmalized nrete ylinders n the 28 th day and the day f the tests, giving 35 and 41 MPa, respetively. The nrete strength f the test speimen was smewhat higher than assumed in the design f the prttype, prbably due t the hemial admixtures used t make the nrete mre fluid and failitate the asting. This nrete verstrength was nt nsidered in the design f the prttype, althugh it was taken int aunt when pressing the experimental data. The rati sldb f the transversal reinfrement spaing s t the diameter f the lngitudinal bar db, at the beam ritial setins was 5.7 (fr the average value f the tw diameters used as beam lngitudinal reinfrement <i f = 8mm and 4 = 6mm). The rati sldb at lumn ritial setins was sldb = 5. The area f lngitudinal reinfrement A st t the grss setin A g f the lumns was AJA g = 0.016, and AJA g = in the regins were lumn bars where lap splied. 3. TEST SETUP, INSTRUMENTATION AND SEISMIC SIMULATIONS 3.1. Test setup and instrumentatin The speimen was plaed n the uniaxial MTS 3 x 3 m 2 shake-table f the University f Granada (Spain) as shwn in Figures 5 and 6. The struture was riented s that the diretin f the uniaxial mvement f the shake-table inided with that f the main beams. T represent the gravity lads ating n the flrs and t satisfy similitude requirements between prttype and test mdel, steel blks were attahed at the tp the RC slab and at the tp f half lumns f the send stry, as shwn in Figure 5 (added weight). T reprdue the bundary nditins (i.e., zer bending Figure 3. Test speimen. Dimensins in mm

5 f " 1 k * SECTION A-A' 136 \ H06 SECTION B-B' - Strain gage Dimensins in mm Figure 4. Reinfring details f the reinfred nrete setins and latin f strain gages. \04 ACCELEROMETER ADDED WEIGHT AUXILIARY FRAME LVDT-6 H B 8 S PL, jh{ PIN JOINT ADDED WEIGHT PIN JOINT LVDT-4-5 ACCELEROMETER n I I n n I I ^ n I I Pi ~u u u u LVDT-1-2 LVDT-3! -_ff LVDT-7- H 5 -» 3 3 ACCELEROMETER ACTUATOR 3000X3000 mm 2 SHAKING TABLE XXX XXX Figure 5. Test setup and instrumentatin. mment) f the substruture when the verall prttype building is subjeted t lateral fres, pin jint nnetins were used at the tp f the half-lumns in the send stry and at the ends f the halfbeams f the first flr. The restritin against vertial mvements f the ends f the half-beams f the first flr was amplished by means f pin-ended steel bars that nneted the end f the beams with the steel plates (added weight) lated n the tp f the speimen, whih have very large flexural stiffness in mparisn with that f the RC frame. When the shake-table was aelerated, the inertial fre generated in these steel blks dynamially laded the test mdel. The ttal mass f the test speimen (inluding the additinal masses) was 10,070 kg. It is wrth nting that the purpse f the experiments was t investigate the behavir f the test speimen under earthquake-type dynami lading, nt t reprdue the partiular respnse that the partial strutural mdel wuld experiene inside the verall frame under a partiular grund mtin, whih is influened by dynami interatins with the upper part f the struture. The speimen was instrumented with 192 strain gages, 10 uniaxial aelermeters and 9 displaement transduers (linear variable differential transfrmers). Strain gages were attahed t the surfae f lngitudinal

6 Figure 6. General verview f the tests. reinfrement when nstrutin was in prgress; they were lated, as shwn in Figures 3 and 4, at lumn and beam ends. The displaement transduers measured the in-plane translatins and the inter-stry drifts in the diretin (Figure 5) f the seismi lading. Data were aquired ntinuusly with a san frequeny f 200 Hz. Five vide ameras rerded the experiments, fur f them fusing n lumn bases, beam ends and beam-lumn jints Seismi simulatins The speimen was subjeted t dynami tests that nsisted f fur seismi simulatins referred t as C50, CI00, C200 and C300 herein, in whih the shake-table reprdued the grund mtin rerded at Calitri during the Campania-Luania (1980) earthquake, respetively saled in time by the saling fatr l t = \fhjk = 0.63 and in amplitude t 50%, 100%, 200% and 300%. Their rrespnding peak grund aeleratins, PGAs, were 0.08, 0.16, 0.31 and 0.47 g, respetively. Eah PGA represents a different SHL at the site (Granada) that will be referred t hereafter as SHL-1, SHL-2, SHL-3 and SHL-4 respetively. SHL-1 represents a 'very frequent' earthquake, SHL-2 a 'frequent' earthquake, SHL-3 a 'rare' earthquake, and SHL-4 a 'very rare' r the 'maximum nsidered' earthquake. The SHLs an respetively be assiated with P r f 17, 97, 500 and 1435 years. The relatin between P r and PGA was btained frm the Spanish seismi de NCSE-02 [2] n the basis that: (i) the basi aeleratin a bpr fr a given P r is a bpr = a b (P r /500) OA ; and (ii) the building is f rdinary imprtane, and it is lated n sft sil (type IV). Arding t NCSE-02, fr this type f sil, PGA = 134a bpr. Free vibratin tests were perfrmed befre and after eah simulatin Dynami haraterizatin 4. TEST RESULTS AND INTERPRETATION The third and furth lumns f Table I shw the fundamental perid Tj and the damping rati btained frm the free vibratin tests nduted befre and after eah seismi simulatin. Tj was alulated by averaging the time between respnse peaks fr several yles and dividing by the number f yles; f was determined using the lgarithmi derement methd. As antiipated, Tj and f inrease with the intensity f the table mtin, refleting inreasing levels f damage. Until

7 Seismi simulatin Prir test C50 (end) CI00 (end) C200 (end) C300 a C300 (end) SHL SHL-1 SHL-2 SHL-3 SHL-4 SHL-4 Table I. Overall respnse parameters f the speimen. Stry 1 Stry 2 Tp r, (s) f (%) u' max (g) ID (%) ID r (%) wj^ (g) ID (%) ID r (%) ID (%) ID r (%) SPL SEAOC ID (%) ATC ID (%) FEMA ID (%) SHL, seismi hazard level; ID, identifiatin; SPL, seismi perfrmane level; IO, immediate upany; LS, life safety; C, llapse. a At the instant f llapse; V t, ttal lateral shear fre in stry i; P t, ttal gravity lad in stry i IO LS LS C C >2.5 >2.5 < >033Vi/P, >033Vi/P, < >4 >4

8 seismi simulatin C200, Tj and i; remained basially unhanged, indiating an undamaged struture that kept its initial lateral stiffness. After seismi simulatin C200, the perid Tj enlarged by abut 70% and abut 40%, whih reflets the urrene f plasti defrmatins n the struture (damage) and a drp in the lateral stiffness f up t abut 35% (= / ) f the initial value, as disussed later Overall respnse Fr nveniene in the frthming disussins, the speimen is mdeled as fllws. Beams and lumns f eah f the tw frames that nstitute the speimen are idealized with mar mdels nsisting f a linear elasti member nneting tw plasti hinges at the ends that nentrate the inelasti flexural defrmatins, as shwn in Figure 7. Eah plasti hinge is labeled with an identifiatin number k. The flr diaphragm with the added weight and the added weight put n the tp f the lumns an be assumed t behave as tw rigid blks, and they are idealized as tw nentrated masses m t f 5910 and 4160 kg, respetively. A degree f freedm nsisting f the hrizntal translatin in the diretin f shaking is assigned t eah nentrated mass. With this mdel, the equatin f dynami equilibrium f the speimen is as fllws: mii + ii+f s 0 (1) where m is the diagnal mass matrix, ii' is the vetr f abslute aeleratins, is the damping matrix, li is the vetr f relative velities, and F s is the vetr f restring fres exerted by the struture. Beause m is knwn and ii' was measured with the aelermeters, the ttal shear fre F IB exerted by the inertial fres Fi = mii' = (u+fg) at the base f the struture an be readily alulated as FIB = F^l, where 1 is the unit vetr. F IB is pltted in Figure 8 against the displaement f the tp f the struture 8 T, fr eah seismi simulatin. The results f simulatin C300 are drawn until the instant f llapse; after this instant, many hannels f the data aquisitin system verflw. The F IB -8 T urve shwn in Figure 8 indiates that up t llapse, the verall respnse f the speimen was haraterized by a stable energy dissipatin behavir with minr pinhing in the lps. In the instants f maximum lateral displaement, the velity is zer, and therefre, the damping fres ii are null. At these instants, F IB inides with the base shear fre arried by the struture Q B. Values f F IB when the velity is zer and thus, F IB = Q B were alulated fr eah seismi simulatin, and they are pltted in Figure 8 with pen irles. These pints define a plygnal urve that is drawn with bld lines, whih an be interpreted as the 'apaity urve' f the struture. Frm this apaity urve, a yield base shear fre, Q By and a yield tp displaement 8 T are defined fr eah dmain f lading, giving Q + By = 36A kn, >J=11.7mm, <2 _ B;v = 43.7kN, and 8T = 13 mm. This apaity urve allws us t alulate the average base shear fre effiient, a B = 0.5( )/100.7 = 0.4 and initial stiffness e = ( )/(l ) = 3.24kN/mm. Cmparing a B with the base shear fre effiient used in the design (0.22), it is nluded that the struture has an verstrength f 0.4/0.22= 1.8. This value is abut 40% larger than the verstrength speified by Eurde 8 [4]. The initial fundamental perid estimated with K e and the ttal mass f the speimen ( = kg) is 0.35 s, whih is lse t that btained frm vibratin tests (Table I). iiiniii MINIMI iiiiniii MINIUM Figure 7. Idealizatin f the reinfred nrete frames in the diretin f the seismi lading.

9 Figure 8. Base shear fre due t inertial fres versus tp displaement. A mre detailed examinatin f the verall respnse f the speimen after eah seismi simulatin is summarized in Tables I and II. Fr eah seismi simulatin, Table I shws in lumns 5 t 10 the maximum respnse aeleratin ii'max, the maximum inter-stry drift ID and the residual inter-stry drift ID r f eah stry. Clumns 11 and 12 shw the maximum drift ID and the residual drift ID r relative t the base at the tp f the speimen. In the ase f simulatin C300, there are tw rws in Table I; the first ne rrespnds t the instant f llapse, as disussed later, and the send ne t the end f the seismi simulatin. Table II summarizes the maximum strains measured in the lngitudinal bars lated at the member end setins f the tw RC frames. Eah member end setin is a ptential plasti hinge under lateral ladings, and it is identified with the number shwn in Figure 7. In Table II, the member end setins are gruped arding t their psitin in the frames (base, interir beam-lumn nnetin and exterir beam-lumn nnetin). Several lngitudinal reinfring bars were instrumented at eah member end setin (Figures 3 and 4); Table II shws the maximum max, the average e and the standard deviatin er f the strains measured at eah setin. The strains rrespnding t seismi simulatin C300 are nt inluded, beause during this simulatin mst gages reahed their maximum measurable strain and stpped funtining. The yield strain f the steel y was 2625 (j.m/m. The verall respnse f the tested struture is haraterized by the frmatin f the expeted strng lumn-weak beam mehanism, as indiated by the measurements f the strain gages, and by the fat that, fr all seismi simulatins, the inter-stry drift ID reahed very similar values in bth stries. Plasti hinges develped basially at lumn bases and at beam ends, althugh sme unexpeted plasti strains (up t lazy) were measured in ne f the lumns (setins 41 and 42 in Figure 7) when the struture was n the verge f llapse. The members exhibited dutile flexural failures; shear r axial failures were nt bserved. A detailed desriptin f the perfrmane under eah SHL is presented in the sueeding disussin. The seismi simulatin C50 represented a lw SHL fr the building site, that is, a frequent earthquake expeted t take plae during the nventinal wrking life f the building, therefre having a P r shrter than 50 years. After this level f seismi atin, referred t as SHL-1, the speimen shwed n visible damage. The strains in the reinfring bars at the base f the lumns remained belw 0.7 y and thse at beams ends belw 0.5 y. The minr inrease f 0.01 s in T 1 shwn in Table I an be attributed t the nrete mirraking. There was n residual inter-stry drift r ther permanent strutural defrmatin. The verall damage in qualitative terms was therefre very light. The maximum inter-stry drift ID reahed 0.24% f stry height. This ID is

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11 within the range 0.2 < ID < 0.5 that Strutural Engineers Assiatin f Califrnia (SEAOC) [5] assiates with the SPL f 'immediate upany' (IO). The SPL f IO rrespnds t the SPL f 'damage limitatin' (DL) in Eurde 8 [4], whih als limits the ID t 0.5% if the stry has brittle nnstrutural elements attahed t the struture. Fr strutures f rdinary imprtane, Eurde 8 remmends pursuing the SPL f DL fr a seismi atin f P r = 95 years. The seismi simulatin CI00 rrespnds t a mderate level earthquake, that is, an 'asinal' earthquake with a P r between 75 and 200 years. During this level f seismi atin, referred t as SHL-2, the lngitudinal reinfrement at the base f the lumns yielded, reahing strains up t abut 2Zy. The setins at the ends f the beams were n the brim f yielding, exhibiting strains n the lngitudinal reinfrement very lse r slightly abve Zy. The lngitudinal reinfrement f the lumns at setins ther than the base apprahed the yield strain (up t 0.75 y). This was ampanied by sme raking. The permanent defrmatins were negligible. The struture was basially undamaged and retained its integrity, full vertial lad-bearing apaity, and suffiient residual lateral strength and stiffness t sustain additinal shakings. The maximum ID was 0.5% f stry height. Arding t SEAOC [5], this ID is the bundary between the SPL f IO (0.2 < ID < 0.5) and 'life safety' (LS) (0.5 < ID < 1.5). The value f P r fr the seismi simulatin CI00 (97years) is very lse t the mean return perid f seismi atin (95 years) under whih Eurde 8 remmends that the struture shuld respnd in the SPL f DL, whih is haraterized by ID 0.5%. Frm this pint f view, it an be said that the speimen behaved n the limit f what Eurde 8 remmends. The seismi simulatin C200 represents a strng grund mtin (the design earthquake) at the building site, that is, a rare earthquake with a P r f abut 500 years, and is referred t as SHL-3. A visual inspetin f the speimen after this test revealed signifiant damage (SD; extensive fiexural raks at the base f the lumns and at beam ends), althugh the gravity-lad bearing system kept funtining. Plasti hinges with dutile fiexural yielding develped at the base f the lumns and at beam ends. The maximum strains f the lngitudinal reinfrement at the base f the lumns ranged between 5E,, and lzy, and thse lated at beam ends sillated between l.lzy and 6.3e r Cnrete rushing was bserved at the base f the lumns. The frame develped a mplete strng lumn-weak beam mehanism. Exepting in the setins at the base, lumns remained basially elasti, althugh sme slight inelasti exursin was measured in ne lumn at hinges number 41 and 42 (Figure 7), where e exeeded the yield strain up t l.4 y. Permanent defrmatin was very small (0.04% f stry height). The maximum ID was 1.19% f stry height. Arding t SEAOC [5], this ID is lse t the bundary between the SPLs f LS (0.5 < ID < 1.5) and 'llapse preventin' (CP) (1.5 < ID < 2.5). The SPL f LS and CP is the unterpart f the SPLs denminated 'SD' and 'near llapse' by Eurde 8. The seismi simulatin C300 represents a very rare r the maximum nsidered earthquake, with quted values f the mean return perid in the rder f years. Under this seismi atin, referred t as SHL-4, the struture was very heavily damaged. The rerds f a vide amera that fused n ne f the beam ends shwed that abut 8 s after the nset f the mvement f the shake-table, a fiexural rak pened abruptly at the beam end, reahing a maximum width f abut 3 mm, whih was ampanied by a sudden vertial slide f apprximately 10 mm between the tw sides f the fiexural rak, as shwn in Figure 9(a). Simultaneusly, the inter-stry drifts reahed abut fur times the maximum values attained in previus simulatins. This vertial slide, and the fat that the gages attahed t the lngitudinal reinfrement f this beam experiened a sudden inrease in strain and stpped measuring, pint t the exhaustin f the beam's 'ultimate' apaity. At this instant, the lateral drift at the tp f the speimen (i.e., at the enter f the pinned ends f the lumns f the send stry) was 4.06% f the ttal height (2020 mm). This is taken hereafter as the instant f llapse. At this same instant, severe nrete rashing was als bserved at the lumn bases as shwn in Figure 9(b). The test ntinued after this instant, and lateral drift reahed abut 8% f stry height, whereas residual defrmatins amunted t abut 4%. This SPL learly rrespnds t a situatin f llapse (C) arding t SEAOC [5] (ID > 2.5%). Fr the sake f mpleteness, Table I indiates the limiting values f the ID fr eah SPL arding t ATC-40 [6] and FEMA-356 [7]. It is wrth nting that Eurde 8 [4] speifies in lause (3) the requirement t prvide inlined reinfrement in tw diretins t prevent shear sliding failure.

12 Figure 9. Damage at: (a) beam ends and (b) the base f lumns during simulatin C300. Appling this lause t the prttype struture under investigatin gives an area f required inlined reinfrement in eah diretin rssing the ptential sliding plane f 11.1 mm 2. Figure 10 represents, in absissa, the IDs and rrespnding SPLs disussed earlier, and in rdinates the SHLs. The SPL dented by O means 'peratinal' and desribes a nditin in whih the faility has suffered pratially n strutural r nnstrutural damage and an ntinue serving the riginal intentin f its design. The 'perfrmane bjetive' fr strutures f rdinary imprtane is t fulfill the relatinship between SPL and SHL indiated by the area shaded with lines inlined 45. The atual respnse f the tested frame is represented by the area shaded with lines inlined 45. It fllws frm Figure 10 that the perfrmane f the tested struture in terms f ID is basially within aeptable limits fr SHL-1, SHL-2 and SHL-3, yet just barely; but fr SHL-4, the perfrmane is utside the aeptable limits Damage evaluatin at glbal level The energy balane f the struture at any instant t when it is subjeted t a hrizntal translatinal mpnent f the grund mtin is given by Eq. (2). Here, Ej is the (relative) [8] energy input by the earthquake; W% is the energy dissipated by the inherent damping mehanism; W p is the hystereti (plasti strain) energy; W es is the elasti strain energy; and W* is the kineti energy. The sum f the kineti and the elasti strain energies nstitutes the elasti vibratinal energy W e (=W es + Wk). The energy input Ej and the kineti energy W* an be easily alulated by Eqs (3) and (4) frm the masses m t, their relative displaements u t and the aeleratin n the shake-table u g measured during the tests. The hystereti (plasti strain) energy W p and the elasti strain energy W es an be estimated as explained in Setin 4.4 later. Further, arding t Eq. (2), the differene between the input energy and the elasti vibratinal energy W e, that is, Ej W e = Ej {W^+ W es ), is equal t the ttal absrbed energy, that is, the sum f hystereti and visus energies, W p + W%. Figure 11(a) shws the histries SHL1 SHL2 SHL3 SHL4 zzzz Objetive ^ Atual perfrmane btained frm the tests OU.il U.O 1.0 Z.O 4 <"\">) 0 10 LS CP Perfmane levels Figure 10. Cmparisn between perfrmane bjetives and tested behavir.

13 Ef ttal input energy - W\- W: ttal absrbed energy We : damping energy fr \ frm the test We_ : damping energy fr \=VA (Nmm) a) C50 C100 C200 C300 Figure 11. Histries f aumulated energy: (a) up t llapse; (b) fr C50; and () fr ClOO. f input energy E T and the ttal absrbed energy W p + W& aumulated in the suessive seismi simulatins frm the beginning f simulatin C50 until llapse. The amunts f energy input during seismi simulatins C50 and ClOO are muh smaller than that f simulatin C200; the energies fr C50 are abut ne-fifth f thse f ClOO and the latter abut ne-fifth f C200. T better view the histry f energies fr simulatin C50 and ClOO, a zm f Figure 11(a) in the tempral range f these simulatins is shwn in Figure 11(b) and (). In the ase f simulatin C300, it was nt pssible t alulate the energies beynd llapse due t the large displaements and defrmatins experiened by the struture, whih aused verflw in the measurements f many hannels f the data aquisitin system. E, = Wf + W p + W es + W k (2) 2 ' Ei = 2 I niiiiguidt i=l 0 (3) W t 1 2 (4) Wtl' 0 u T Cudt (5) A prtin f the ttal absrbed energy W p + W^ is dissipated by visus damping, Wg. Yet, it is nt pssible t alulate W% with auray, beause in a shake-table test, whih ges deeply int the nnlinear range, it is hard t distinguish hystereti frm visus damping. An attempt was nnetheless made t btain a rugh estimatin f W% as fllws. First, the tested struture was idealized as a tw-dimensinal mdel with tw lumped masses. Send, the visus damping f the struture was represented by the traditinal Rayleigh damping matrix using the frequenies btained fr the first and send vibratin mdes frm an eigenvalue analysis, and adpting the same

14 damping rati i; fr bth mdes. Third, the histry f velities f eah mass was alulated by deriving the histry f displaements measured with the transduers during the tests, t arrive at the vetr f relative velity li. Finally, W% was estimated with Eq. (5). In this alulatin, a key pint is the value assumed fr f. One apprximatin t estimate W% fr a given seismi simulatin is t use the damping ratis f btained frm the free vibratin test nduted at the end f previus seismi simulatins, whih are shwn in Table I. These values f f are larger than thse used in studies that applied a similar apprah fr representing damping [9]. Martinelli and Filippu [9] predited the nnlinear respnse f a full-sale seven-stry RC struture tested n a shaking table under fur suessively input mtins using a mmn damping rati f = 1 % fr all seismi simulatins and fund that analytial results led t a gd agreement between the measured and predited respnse. Fr illustrative purpses, the histry f W% estimated with the f btained frm the free vibratin test at the end f a previus seismi simulatin is shwn in Figure 11 with thin dash lines, whereas W% alulated with if = 1 in all seismi simulatins is shwn in Figure 11 with thin dtted lines. Finally, fr nveniene Ej an be nrmalized with respet t the ttal mass {mi + m i) an d expressed by equivalent velity V E defined by V E =j2e,/'zm i (6) Table III summarizes the (aumulated) input energy V E frm the nset f the tests up t the end f a given seismi simulatin r t llapse. It is wrth nting that the values V E are alulated fr the speimen frm the test results and that the speimen was saled by the fatrs indiated in Setin 2.2. T btain the rrespnding energies in the prttype (real) struture, V ErP, the values must be divided by the saling fatr fr velity l v = l L /l t = Damage evaluatin at lal level The elasti and plasti strain energy absrbed/dissipated by a given plasti hinge k f the struture during the yli lading, W es # + W p j is the sum f the energy dissipated by the nrete, W,k, an d the energy dissipated by the lngitudinal reinfrement, Ws,k [10]. Ws,k was estimated frm the data measured during the seismi simulatins as fllws. The histry f strain in a given lngitudinal rebar r, Zs r (f), was measured diretly by the strain gages, whereas the rrespnding stress Gsrif) an be apprximated frm Zsrif) using an energy nservative steel mdel that inrprates strainhardening and Baushinger effets. Calling A Sr the area f rebar r and assuming a length l p fr the plasti hinge, Ws,k is R W s,k = 2 \l p A sr u sr ds sr (7) r=\ where the summatin is extended t the R steel lngitudinal rebars f the rss setin f the plasti hinge k. On the ther hand, the energy dissipated by the nrete W,k in a given plasti hinge k is mputed by applying the fllwing predure: (i) the depth h f the rss setin f the RC member is divided in N parts (referred t as fibers), eah fiber j having a width b and an area b{hln)\ (ii) the plane-remaining plane assumptin is made and the strain y(0 at a given fiber j is estimated frm the urvature measured with the strain gages n the steel rebars; (iii) the rrespnding stress Table III. Energies in terms f equivalent velities. Cumulative values up t seismi simulatin Speimen V E (m/s) Prttype V E, P (m/s) C C C C300 (up t llapse)

15 C j(f) is apprximated frm /f) using a mdified Kent and Park material mdel [11, 12] with linear lading and relading paths and n tensile strength; and (iv) the energy W,k is alulated by N h w,k = Lttpb aqdsj 7=1 N (8) Amng the several frmulatins prpsed in the literature t determine l p, in the frmer Eqs (7) and (8), the plasti hinge length was made equal t the element depth. The elasti and plasti strain energy absrbed/dissipated by a given plasti hinge k is thus W,. W, p,k w. st W, C,k (9) Further, W p k an be estimated frm (W p k + W es> k) by remving frm the latter the reversible elasti part. The ttal elasti and plasti strain energy absrbed/dissipated by the struture W es + W p is the sum f the ntributins f the p plasti hinges, that is, W. W {w es, k w, p,k) (10) The energy absrbed/dissipated by the plasti hinges during eah seismi simulatin, as alulated with Eqs (7) and (8), was gruped and summed up as fllws: energy absrbed/dissipated at the base f the lumns (i.e., hinges number 10, 20, 30 and 40 in Figure 7), energy absrbed/dissipated at beam ends (i.e., hinges number 50, 51, 52, 60, 61, 62 in Figure 7), energy absrbed/dissipated at the upper ends f the lumns f the first stry (hinges number 11, 21, 31, 41 in Figure 7) and energy absrbed/dissipated at lwer ends f the lumns f the send stry (hinges number 12, 22, 32, 42 in Figure 7). The ttal energy absrbed/dissipated by the hinges f eah grup is pltted in Figure 12(a). These energies aumulated in the suessive seismi simulatins, frm the nset f a) Wp + Wes (Nm) Base lumnsfiijststry (hinges n. 10j, 20,30,40) Upper end lumnsfirststry (hinges n. 1131,21,41) Lwer end lumns send stry (hinges n. 12,32,22,42) Beam ends (hinges n. 50,51,52,60,61;62) i'r C \'i'r -1 i'r C100 -«C200 C W +W es (Nm) b) 0 ) Figure 12. Energy absrbed/dissipated by hinges: (a) up t llapse; (b) C50; and () C100.

16 simulatin C50 until llapse during simulatin C300. Beause the amunts f energy input during seismi simulatins C50 and CI00 are muh smaller than that f simulatin C200, a zm f Figure 12(a) in the tempral range f simulatins C50 and CI00 is shwn in Figure 12(b) and (), respetively. Given that the speimen develped a strng lumn-weak beam mehanism, the energy absrbed/dissipated by the upper ends f the lumns f the first stry and by the lwer ends f the lumns f the send stry is small in mparisn with that dissipated at the base f the lumns and at beam ends. Until the end f seismi simulatin C200, the energy absrbed/ dissipated at the base f the lumns is frm 1.5 t 2 times larger than that dissipated by the beams. Hwever, when the speimen is n the brim f llapse (at the beginning f simulatin C300), there is an abrupt inrease f the energy dissipated at beam ends, whereas that dissipated at lumn bases inreases nly 1.6 times. The urves d nt inrease mntnially due t the presene f elasti strain energy; this effet is negligible in seismi simulatin C200, beause the amunt f elasti strain energy is very small in mparisn with the energy dissipated thrugh plasti defrmatins. During seismi simulatin C50, the main sure f energy dissipatin was the plasti defrmatin f nrete, beause the lngitudinal reinfrement did nt yield. During seismi simulatin CI00, bth nrete and lngitudinal reinfrement dissipated energy by means f inelasti strains. Cnversely, during seismi simulatin C200, energy dissipated by nrete is negligible in mparisn with that by steel. The damage at the level f eah individual hinge k was estimated in terms f maximum hrd rtatin demand Q m in relatin t hrd rtatin at ultimate apaity 9 U, that is,0 m /0 u = max{ \0 m + /0 u + \,\0 m ~/0 u ~\} the energy-based damage index D t prpsed by Darwin and Nmai [13] and the well-knwn index f damage DI PA develped by Park and Ang [14]. The results are shwn in Table IV. The hrd rtatin demand Q m was estimated frm the measurements prvided by displaement transduers during the tests. The hrd rtatin apaities at ultimate 9 U were predited using the equatin remmended by Eurde 8 - Part 3 (Annex A) [15] based n the wrk by Fardis [16] and thers. The damage index D t, and the Park and Ang index f damage D PA at a given hinge k were alulated by means f the fllwing equatins: Dt = W, p,k 0.5 (MX M: (11) D F 0.5 W, p,k.5 \M;e + u M: (12) The hrd rtatin at yielding 0 y was als predited with the equatin remmended by Eurde 8 - Part 3 (Annex A) [15]. The parameter /? was taken /? = 0.1. The yielding mments under psitive and negative bending, M+ and M~ were estimated with the fllwing expressins fr beams: and fr lumns: M y = 0.9M/, (13) ifn max >N>(0Abhf ) : M y = (O.Mfyh M2 / C ) (N max - N) JVmax - (0.4M/J (14) if(0.4m/ ) > N > 0 : M y = (0.8A/ y /i) + 0.5A%{1 - [N/(bhf )}} (15) if 0 > N > N min : My = O.SAf h + OANh (16)

17 3 4^ UJ t 4^ UJ t t IO t t M ^ M OvOvO\UUlUl-^UtO tt H a Oq ft P C I ft O O O O O O O O O O O O O O O O O O *5 aiuiuiuiuiui\a\a\a\ ^ bbbbbbbbbbbbbbb t O M t O M U t O t O t O M ^ W ^ U W a W M ^ f < bbbbbbbb4^bbbbbwbub t O M M H - J ^ U U U O \ 0 \ 0 \ 0 \ 0 \ H O \ H - J O P a - s 3^ b b b b b b b b b b b b b b b b b b bbbbbbbbtttiitttii O O O O O O O O O N O N O N O N O N O N O O O O O O O C I a a 1 ft 3' a ^001000^104^-1^ b b b b b b b b b v 4 ^ 4 ^ w t O ^ J O C n t bbbbbbbbbbbbbbbbbb s bbbbbbbhhthrhirmi ^ 0 4 ^ t 0 4 ^ 4 ^ 4 ^ a \ a \ t O js ' ' ' ' ' ' ' ' ^ ^ ^ ^ ^ ^ ' ' ' : ^i^i^i^i^i^iaiaiaiai f ppppppppuilui^wtuikjoui -^Qb^tbbbUb^i^^wwbU: upo\010'0000\-t'u--jomoio--j^toh b b b b b b b b b b b b b t t b H C ai^aitw4^m;

18 where N is the axial fre in the lumn (psitive in mpressin); N max = bhf + Agf y ; N min = Agf y,; A, is the area f lngitudinal reinfrement in tensin; A g is the ttal area f lngitudinal reinfrement in the setin; and b, h are the base and depth f the setin. The damage in the plasti hinges was basially null fr the seismi simulatins C50 and CI00. At the end f this simulatin C200, the speimen experiened SD, attaining hrd rtatins f abut ne-furth f the apaity at ultimate; the damage index D t reahed 7.38 and the index f damage by Park and Ang DI PA reahed In general, damage was larger in the plasti hinges at the base f the lumns than at beam ends. At the instant f llapse, during seismi simulatin C300, the hrd rtatin demand reahed the ultimate apaity with ratis 9J9 U very lse t 9 m l9 u = 1; the damage index D t reahed 22.32, and the damage index DI PA was abut 1. The pattern f larger damage at lumn bases than at beam end bserved during simulatin C200 remained at llapse. The fllwing nsideratins must be made t interpret these results. First, the fat that the llapse f the hinges at lumn bases and at beam ends urred fr values f 9J9 U very lse t 1 indiates that the frmula remmended by Eurde 8 - Part 3 fr assessing hrd rtatin apaities at ultimate f RC beams, and lumns subjeted t yli lading prdues very gd estimates. Send, n the basis f extensive experimental studies, Darwin and Nmai [13] nluded that the range f D t fr well-behaving RC beams was between 17 and 142; further, these authrs remmended D t = 35 t prvide adequate perfrmane under yli lading. The RC beams tested in the shake-table sustained values f D t larger than 17 (i.e., 22.32) and an thus be lassified as 'well-behaving beams', but the values are lwer than the ne remmended by these authrs (35). Third, the results f the shake-table test indiate that the use f ultimate hrd rtatin apaities 9 U estimated with Eurde 8 - Part 3, using the fatr/? = 0.1 (as suggested by Park et al. fr nminal strength deteriratin) t alulate the index D PA with Eq. (11), prvides a very gd estimate f the level f damage in the range D PA = 0 (n damage) t D PA = 1 (llapse) Beam-t-lumn strength rati In rder t assure the frmatin f a strng lumn-weak beam mehanism and redue the likelihd f yielding in lumns, seismi des typially require that the sum f flexural strengths f lumns framing int a jint be larger than the sum f flexural strengths f the beams framing t the same jint. The amunt by whih the strength f the lumns must exeed that f the beam varies depending n the de. ACT [17] requires 2 M n > M n b and Eurde 8 [4] ^M R > 1.3' l M Rb. Here, M n and M nb are the nminal flexural strengths f lumns and beams, whereas M R and M Rb are the rrespnding design values. In bth ases, the bending mments M n, M n b, M R, M R b must be evaluated at the faes f the jint. The last lumn f Table II shws the beam-t-lumn nminal mment strength ratis evaluated at the faes f the jints fr the speimen tested. M U and Mub were mputed frm nminal dimensins and the material strengths desribed in Setin 2.2, in ardane with de definitins, prvisins and assumptins f the strength design methds f ACT318-08, the rrespnding steel reinfrement fr beams, and the rrespnding steel reinfrement and axial lad fr lumns. The ratis TMufZMui, btained are high due t the verstrength prvided in lumns at the design stage. In the ase f interir jints, the rati ^im u J^M ub = 2.QB is learly abve the minimum required by ACI and Eurde 8, but this fat did nt prevent sme plasti defrmatin frm taking plae in the lngitudinal reinfrement f ne f the lumns (up t 1.4 times the yield strain). 5. CONCLUSIONS Shake-table tests resulting in llapse were nduted n a tw-fifths-sale RC frame struture designed arding t urrent building seismi des that fllw the strng lumn-weak beam philsphy and apaity design riteria. The speimen was subjeted t fur seismi simulatins representative f very frequent, frequent, rare and very rare earthquakes assiated with return perids f 17, 97, 500 and 1435 years, respetively, in the Mediterranean area. The results f the tests lead us t put frth the fllwing nlusins that are transferable t similar strutures:

19 Fr the 'frequent earthquake', the speimen remained basially undamaged, with maximum interstry drifts f 0.5%, Park and Ang's index f damage in the plasti hinges belw 0.01 and maximum hrd rtatins belw 11 % f their ultimate apaity. The speimen perfrmed n the bundary f the IO and LS seismi levels, that is, n the limit f what Eurde 8 remmends. Fr the 'rare earthquake' (design earthquake), the speimen develped a strng lumn-weak beam mehanism and experiened SD. Maximum strains f lngitudinal reinfrement in lumn bases and at beam ends reahed abut seven times the yield strain, the maximum inter-stry drift was 1.19%, and the maximum hrd rtatins reahed 28% f their ultimate apaity. The seismi perfrmane apprahed the upper bund f the LS level. The speimen llapsed at the beginning f the seismi simulatin that represented the very rare event (maximum nsidered earthquake). Cllapse was haraterized by the pening f large flexural raks f abut 3 mm and simultaneus severe vertial sliding (f abut 10 mm) between the tw sides f the rak. At this instant, the lateral drift exeeded 4%, Park and Ang's index f damage in the plasti hinges was abve 1 in all hinges (reahing 1.28 in ne f them), and maximum hrd rtatins reahed the ultimate rtatin apaity. In general, the struture designed arding t mdern des perfrmed adequately (yet n the limit) fr the SHLs rrespnding t a frequent earthquake and t a 'design earthquake', but the perfrmane was nt satisfatry fr the very rare r maximum nsidered earthquake. The test data when the speimen reahed the pint f llapse were mpared with the frmula remmended by Eurde 8 (Part 3, infrmative Annex A). Cmparisn suggests that Eurde 8 prdues very gd estimates n ultimate hrd rtatin apaities f RC beams and lumns under yli lading. Park and Ang's damage index with /? = 0.1 was alulated at the instant f llapse fr eah plasti hinge, giving values very lse t 1. This rrbrates that the Park and Ang index with /? = 0.1 is a gd indiatr f the level f damage n RC elements subjeted t bending, in a range between 0 (n damage) and 1 (llapse). ACKNOWLEDGEMENTS This paper is funded by the Spanish Ministry f Siene and Innvatin with funding numbers BIA and BIA , and the Eurpean Unin (Fnds Eurpeen de Develpment Reginal). REFERENCES 1. Applied Tehnlgy Cunil (ATC). FEMA P695 Quantifiatin f Building Seismi Perfrmane Fatrs. Federal Emergeny Management Ageny (FEMA): Redwd City, Ministeri de Fment. Nrma de Cnstruin Sismrresistente: Parte General y Edifiain (NSCE-02). Bletin Ofiial de Estad: Madrid, (in Spanish) 3. Harris HG, Sabnis GM. Strutural Mdeling and Experimental Tehniques. CRC Press: Ba Ratn, Eurpean Cmmittee fr Standardizatin (CEN). Eurde 8: Design f Strutures fr Earthquake Resistane. Part 1: General Rules, Seismi Atins and Rules fr Buildings. Eurpean Standard EN :2004. Eurpean Cmmittee fr Standardizatin: Brussels, Strutural Engineers Assiatin f Califrnia & Visin 2000 Cmmittee. Perfrmane Based Seismi Engineering f Buildings. Califrnia Offie f Emergeny Servies: Sarament, Applied Tehnlgy Cunil (ATC). ATC-40 Seismi Evaluatin and Retrfit f Cnrete Buildings. ATC: Redwd City, Federal Emergeny Management Ageny (FEMA). FEMA 356: Prestandard and Cmmentary fr the Seismi Rehabilitatin f Buildings. FEMA: Washingtn DC, Uang CM, Berter VV. Evaluatin f seismi energy in strutures. Earthquake Engineering & Strutural Dynamis 1990; 19(l): Martinelli P, Filippu F. Simulatin f the shaking table test f a seven-stry shear wall building. Earthquake Engineering & Strutural Dynamis 2009; 38(5): DOI: /eqe Park H, Em T. A simplified methd fr estimating the amunt f energy dissipated by flexure-dminated reinfred nrete members fr mderate yli defrmatins. Earthquake Spetra 2006; 22(2):459^-90. DOI: / Kent DC, Park R. Flexural members with nfined nrete. ASCE Jurnal f the Strutural Divisin 1971; 97(7):