13 t World Conferene on Eartquake Engineering Vanouver, B.C., Canada August 1-6, 24 Paper No. 2581 VALIDATION OF SEISMIC DESIGN CRITERIA FOR CONCRETE FRAMES BASED ON MONTE CARLO SIMULATION AND FULL SCALE PSEUDODYNAMIC TESTS Fabio BIONDINI 1, Giandomenio TONIOLO 1 SUMMARY Te paper presents an aurate metod to quantify te beavior fator of strutural systems, by means of a full probabilisti evaluation of te involved quantities. Te riteria of te probabilisti evaluation of seismi apaity are based on Monte Carlo metod for wi undreds of dynami analyses are performed wit different material properties and seismi ations. Te ground motions are desribed by artifiial aelerograms ompatible wit te response spetrum assumed in Euroode 8. Te assessment of te design rules of te Euroode is made wit referene to two reinfored onrete frames, one representing a ast-in-situ struture, te oter representing a preast struture, bot analyzed in four levels of sway stiffness. Te results are expressed in terms of frequeny distribution urves of te overstrengt ratio between atual and design seismi apaity. Te results sow tat ast-in-situ and preast frames ave te same seismi beavior wit respet to dutility resoures and ultimate apaity. Te experimental verifiation of tese teoretial results is also found by means of pseudodynami tests on full-sale astin-situ and preast prototypes. Te results of te tests are presented and ompared wit te results of a numerial simulation. Te good agreement between numerial and experimental results onfirms te reliability of te teoretial model and, wit it, te results of te statistial analysis too. INTRODUCTION Euroode 8 (EC8), like many oter odes for te seismi design of strutures, defines te design seismi ations for an elasti analysis of te struture. Tese ations represent te fores orresponding to te peak aeleration of te struture subjeted to te ground motion. Tey are properly redued by a oeffiient q alled beavior fator in order to take into aount te atual beavior of te struture, wi as some resoures able to attenuate te effets of te ground motion (dutility, overstrengt, damping, redundany). EC8 gives a sale of q-fators related to te different types of strutures, wit teir potential apaity of energy dissipation onventionally evaluated on te base of te ultimate failure meanism. At present su q-values are defined more or less on te base of empirial oies, not supported by a rigorous investigation of suffiient reliability. Terefore, even if te experiene of different seismi ountries ontributed to tis definition troug ompromises reaed during te works of te ompetent 1 Dept. of Strutural Engineering, Tenial University of Milan. P.za L. da Vini, 32 2133 Milan (Italy). biondini@stru.polimi.it, toniolo@stru.polimi.it
European ommittee, su empirial proedure may lead to unjustified inequalities between different materials and strutures. Te paper is dediated to te validation of te seismi design riteria proposed by EC8 for a speifi type of reinfored onrete struture, onsisting of te one-storey frames largely employed for industrial buildings. In partiular, in order to try a more reliable definition of te beavior fator for su kind of strutures, an aurate metod based on a full probabilisti analysis of te seismi strutural response is presented. Te riteria of te probabilisti proedure are based on Monte Carlo simulation, for wi undreds of dynami analyses are performed wit different material properties and seismi ations. Te ground motions are desribed by artifiial aelerograms, generated so to be ompatible wit te response spetrum assumed in EC8. Based on su riteria, te assessment of EC8 design rules is made wit referene to two reinfored onrete frames, one representing a ast-in-situ struture, te oter representing a preast struture, bot analyzed in four levels of sway stiffness. Te overstrengt ratio between te atual seismi apaity obtained by te simulation proess and te design seismi apaity dedued by te riteria of EC8 is assumed as representative quantity of te seismi strutural performane. Te results of te probabilisti analysis are expressed in terms of frequeny distribution urves of te overstrengt, wi sow tat ast-in-situ and preast frames ave te same seismi beavior wit respet to dutility resoures and ultimate apaity. Finally, te experimental verifiation of tese teoretial results is seared for by means of pseudodynami tests on full-sale ast-in-situ and preast strutures. Te results of te tests are presented and ompared wit te results of a numerial simulation in order to onfirms te reliability of te teoretial model and, wit it, te results of te statistial analysis too. EVALUATION OF SEISMIC CAPACITY Model of yli degrading stiffness Te model of te degrading elastoplasti stiffness as been derived from Takeda model [8], ompleted wit a final dereasing bran as suggested by Priestley, Verma and Xiao for wall elements [5] and applied by Biondini and Toniolo [1] to olumns in flexure. Fig. 1 sows te envelope urve of te alternate loading yles wit te limit points of its profile. Te symbol F indiates te first order ontribution of te sear fore V at te olumn base: Nad V = F d (1) ontribution evaluated on te basis of te bending moment M of te ritial setions. In partiular F = 2M/ for te monoliti arrangement of Fig. 2.a, and F = M/ for te inged arrangement of Fig. 2.b. Te negative term represents te seond order effet of te ating vertial load N ad. F 1 2 3 4 1' d 4' 3' 2' Fig. 1. Degrading stiffness model.
d N ad d N ad V M V M V (a) M V Fig. 2. Traslatory stiffness of (a) ast-in-situ and preast olumns. Te limit points of te envelope urve orrespond respetively (1) to te first raking limit of te ritial setion, (2) to te full yielding of te reinforement, (3) to te spalling of onrete over and (4) to te failure limit of te onrete onfined ore. Te slope of te desending end bran between points 4 and 5 as been empirially defined on te base of te available experimentation ( k u F 2 d 2 ). Tis bran represents te failure proess wi leads to te ollapse of te struture, due to te fall of flexural stiffness of te ritial setions, togeter wit te inreasing seond order effets of te vertial load. For te definition of te alternate loading and unloading branes of te subsequent yles, like te one dased in Fig. 1, referene sall be made to Biondini and Toniolo [1]. For wat onerns te onsisteny of te Takeda model wit te results of yli and pseudo dynami tests, see Saisi and Toniolo [6]. Inremental non-linear dynami analysis For te types of one-storey frames onsidered in te present study, te non-linear dynami analysis refers to single degree of freedom systems and is elaborated on te base of te following motion equation m d & ( t) + d & ( t) + k( d) d( t) = m a( t) (2) were m = W g is te vibrating mass, is te visous damping oeffiient (assumed equal to te 5% of te ritial one), k (d) is te degrading elastoplasti stiffness and a (t) is te ground aeleration. Te stati term is diretly given as: N ad k( d) d( t) = V ( d) = F( d) d( t) (3) wit F = F(d) given by te model already disussed, on te base of te preeding loading istory. Te dynami variations of te vertial loads during te eartquake are negleted. In tis way te axial ompression fores on te olumns are onsidered onstant and equal to teir stati value. Moreover, te analytial model onsiders only te flexural mode of failure of te ritial zones of te olumns. Tis assumes tat a proper apaity design ad exluded sear failures and oter types of failures, su as tose of joint onnetions. Te inremental proedure, assumed for te definition of te ultimate apaity of te struture, onsists of te repetition, for any single aelerogram, of te integration of te motion equation, wit intensities inreasing up to failure. Te intensity α g =a g /g orresponds to te peak ground aeleration a g =PGA normalised wit te gravity onstant g. Starting from a basi value α g, orresponding to about te servieability level of te struture, te intensity α g is inreased wit small inrements α g so to at, wit suffiient auray, te ultimate apaity α gmax of te struture, tat is te ultimate response of stable vibratory equilibrium before ollapse. In te numerial analysis te ollapse itself is pointed out by te loss of vibratory equilibrium, wit unlimited amplifiation of te displaement due to te ombined effets of te seond order moments on te falling stiffness of te struture.
ASSESSMENT OF EC8 DESIGN RULES Comparison between tested and alulated apaity In order to find a reliable definition of te beavior fator q assumed by EC8 for te seismi design of onrete frames, a omparison sall be made between te ultimate apaity alulated wit te design rules and te ultimate apaity tested on te struture under te same seismi ation. Te tested apaity is assumed to be te arateristi value orresponding to te 5% fratile of te ultimate aeleration α gmax omputed following te full probabilisti approa and wit te inremental dynami analysis desribed before. Te input aelerograms of tis analysis sall be ompatible wit te response spetrum of EC8. Te alulated apaity is dedued from te EC8 rules as a funtion of te natural vibration period T = 2π m k δ (4) were m=w/g is te vibration mass orresponding to te gravity load W. Te traslatory stiffness κ δ of te single degree of freedom systems sown in Fig. 2, inlusive of te seond order effets, is given by: 12k ϕ N 3k ad ϕ N ad kδ = k 3 δ = 3 (5) for te ast-in-situ solution of Fig. 2a and for te preast solution of Fig. 2b, respetively, were k ϕ is te flexural stiffness of te raked ross-setion subjeted to te ombined ation of te bending moment M=.75M rd and te axial fore N=N ad. Wit te redution funtion η=η(t) of te design response spetrum of EC8, te alulated apaity beomes agd qfrd M α gd = = F g 2.5η ( T ) W = rd rd (6) wit =2 for te ast-in-situ frame, =1 for te preast frame, and were: η( T ) = S for T B T T C TC η( T ) = S 8q for TC T TD (7) T TCTD η( T ) = S 8q for TD < T 2 T In te present appliation a subsoil type 1B is assumed (very dense sand or gravel), wit S=1.2, T B =.15 se, T C =.5 se and T D =2. se. Te omparison between te tested and te alulated apaity an be made wit referene to teir ratio α g max κ = (8) α gd were κ =1 indiates te perfet orrespondene and κ >1 indiates an overstrengt of te struture wit respet to te previsions of EC8 design rules. Misoneptions about te seismi beavior of preast strutures Te strutures onsidered in te following refer to te strutural semes of Fig. 3, wi represent te typial ast-in-situ monoliti solution and preast inged solution, respetively. As known, some proposals would penalize te preast solution by a lower q-fator, sine te ritial zones were te energy dissipation develops are four in te monoliti ase and only two in te inged ase. Contrarily to tis assumption, te tesis assumed in tis paper is tat, under te same seismi fore, te monoliti arrangement of Fig. 3.a, wit four ritial setions dimensioned for a bending moment m F/2, may dissipate te same amount of energy wi te inged arrangement of Fig. 3.b dissipates in its two ritial setions, dimensioned as tey are for a doubled bending moment M=F 2m (4u 2U).
m m F u u F F F u u U U m m M M (a) Fig. 3. Energy dissipated by one-storey r.. frames: (a) monoliti and inged arrangements. Proportioning of te sample strutures As mentioned, te strutures onsidered in te present appliation refer to one-storey industrial buildings. Tey are sown in Fig. 4, were (a) represents te typial arrangement of a ast-in-situ frame and represents te typial arrangement of a preast frame. A span lengt of te beam l=12. m is osen for bot te arrangements, wile two different ases are onsidered for te eigts of te olumns. For te ast-in-situ arrangement a taller solution wit =6. m and a lower solution wit =5. m are firstly seleted. Te eigts for te preast arrangement are ten orrespondingly osen in order to aieve te same vibration periods T of te ast-in-situ solutions. Finally, te size and te reinforement of te olumns vary for two levels of strengts as indiated in Fig. 5, were te details of te ross-setions are sown. Su ross-setions are proportioned in su a way tat te two type of frames ave approximately te same design seismi apaity. Combined wit te two eigts, te four types of frames listed in Tab. 1 are derived for ea arrangement, wi orresponds to as many levels of stiffness. A total load of 6. kn/m 2 is applied on te roof, of wi 1.2 kn/m 2 of snow. Wit a spaing between te frames equal to 6. m, an axial fore N ad =216. kn omes down on ea olumn, wit a total effetive load (wit 1/3 of snow) 2W=2 187.2 kn ating on te frame. In Tab. 1 te prinipal strutural parameters are summarized, were: M rd =M rd (N ad ) is te resistant moment of te setion orresponding to te design values f d =f k /γ and f sd =f yk /γ s of te material strengts; F rd =M rd / is te first order ontribution of te sear fore at te olumn base; ν d =N ad /N rd is te speifi value of te axial ation wit respet to te ultimate strengt N rd =A f d +A s f sd ; ν E =N ad /N E is te speifi value of te axial ation wit respet to te ritial load N E 1k ϕ (/2) 2 ; d y is te first yield displaement, omputed as d y =χ y 2 /3; wit =2 for te ast-in-situ frame and =1 for te preast frame. Table 1. Design data of te prototype. Type [m] M rd [knm] ν d ν E d y [mm] F rd [kn] 1a/tall 6. 91.1 74.164 79.4 3.37 1a/low 5. 91.1 74.114 55.1 36.44 2a/tall 6. 178.5 5 5 48.1 59.5 2a/low 5. 178.5 5 35 33.4 71.4 1b/tall 5.6 178.5 5.174 83.8 31.88 1b/low 4.672 178.5 5.121 58.3 38.21 2b/tall 5.245 348.5 37 57 53.7 66.44 2b/low 4.374 348.5 37 4 37.3 79.68
l l (a) Fig. 4. One-storey frames. (a) Monoliti and ast-in-situ. Hinged and preast. TYPE 1a TYPE 1b TYPE 2a TYPE 2b 8φ14 1st.φ6/5 8φ16 1st.φ6/55 8φ16 1st.φ6/55 8φ2 1st.φ mm 45 mm 45 mm 6 mm Fig. 5. Cross setion details of te olumns. Te beams are proportioned for te non-seismi onditions. In te ast-in-situ arrangement te beams ave flexural stiffness mu larger tan te olumns and teir resistant moments at te ends remains larger tan at te onneted olumns. In tis way, te strutural systems are redued to te single degree of freedom represented by te storey drift d, ontrolled by te ritial setions of te olumns. Te prinipal vibratory parameters of te strutures are summarized in Tab. 2, were: k ϕ is te flexural stiffness of te raked ross-setion; k δ is te traslatory stiffness of te olumn, inlusive of te seond order effets of N ad ; T is te first natural vibration period of te struture; η=η(t) is te redution funtion of te design response spetrum of EC8; α gd is te seismi ultimate apaity omputed wit q=4.5. It is wort noting te very ig intrinsi seismi ultimate apaity of te strutures ere examined. It is due to te very redued response of te more flexible proportioning and to te large overstrengt of te stiffened proportioning. Te sizes and reinforement dedued for te olumns from te non-seismi onditions (wind pressure or rane ations) are normally suffiient also for te no-ollapse verifiation under seismi onditions. Te limits given for te servieability states to te storey drift, under te redued ation of te more frequent eartquake, beome determining. Table 2. Vibratory parameters of te prototypes. Type k ϕ [knm 2 ] k δ [kn/m] T [se] η α gd 1a/tall 4729 226.7 1.82.36.811 1a/low 4729 41.8 1.35.444.789 2a/tall 15531 826.8.95.632.95 2a/low 15531 1447.7.72.833.824 1b/tall 15531 226.7 1.82.36.851 1b/low 15531 41.8 1.35.444.827 2b/tall 41752 826.8.95.632 11 2b/low 41752 1447.7.72.833.92
MODELLING OF UNCERTAINTY Probabilisti approa As already mentioned, for te evaluation of te seismi apaity a full probabilisti proedure is applied to take into aount mainly te large random variability of te seismi ation. For tis probabilisti evaluation, te Monte Carlo metod is applied, wi implies some undreds of repetitions of te inremental dynami analysis in order to rea a stable statistial representation of te response. Te randomness of bot te seismi ation and te material properties are onsidered. Tey are te quantities wi lead to te larger variability of te response. Smaller effets ome from te variability of te geometri dimensions of te struture wi are ere taken as deterministi and equal to te design values used in alulation. Also te mass involved in te vibration is taken as deterministi. Atually, te random variability of te mass ould lead to large effets on te response, but in te present work it as not been investigated. Statistial independene of te random variables is also assumed. Coie of te aelerograms Te oie of te input ation for te dynami analysis may be oriented eiter on real aelerograms reorded during te eartquakes, or to artifiial analytial simulations of te ground motion. Te use of tese aelerograms refers to te quoted statistial investigation from wi some representative values of te atual strutural response sould be obtained so to be ompared to te orresponding value alulated following EC8 rules. To make tis omparison possible, te features of te input ation sould be onsistent wit te orresponding design models assumed in te ode. Based on su onsiderations, te use of artifiial aelerograms appears to be more appropriate for te purpose of te present investigation. Tey an be generated wit proper numerial proedures wi introdue some random parameters (SIMQKE [7]). Te amplitude of te generated ground motions follows an envelope sape urve wit random duration of its pases (initial, stationary and desending), as sown in Fig. 6. Te present appliation assumes a duration of te strong stationary pase variable from 1 to 2 se following a uniform distribution law. Te signal is a omposition of many sinusoidal armonis were any single amplitude is osen so to mat te given response spetrum all witin its range of frequenies, wile te pase is a random variable. Fig. 7 sows two of tese aelerograms togeter wit te orresponding elasti response spetra. Te good ompliane wit EC8 spetrum is learly verified. I(t) t1 t2 t t t 3 1 2 = 2 to 1 se = 1 to 2 se = 5 to 3 se t t t 1 2 3 Fig. 6. Envelope sape urve of ground motion. 5 t Materials variability For onrete, te random variation of ompression strengt is represented by a lognormal distribution defined by te mean value f m =f k +ks and by te standard deviation s. For te present appliation te following values are taken: f k = 4 MPa s = 5 MPa k = 1. 551 (9) were f k is te arateristi strengt assumed in design alulations.
Aeleration a (t )/PGA Aeleration a (t )/PGA Time [se].8.6.4.2 -.2 -.4 -.6 -.8-5 1 15 2 25 3 35 4 45 5 Time [se].8.6.4.2 -.2 -.4 -.6 -.8-5 1 15 2 25 3 35 4 45 5 Time [se] Aeleration a max/pga Aeleration a max/pga 3.5 Period [se] 3. 2.5 2. 1.5.5.5 1.5 2. 2.5 3. 3.5 4. 4.5 5. Period [se] 3.5 3. 2.5 2. 1.5.5.5 1.5 2. 2.5 3. 3.5 4. 4.5 5. Period [se] Fig. 7. Sample of two artifiial aelerograms and teir elasti response spetra. For any random value f, te limit strains, te tensile strengts and te elasti modulus are omputed wit 2 3 f t =.25 f ε 1 =.2% ε tu = f tf E (1).3 f tf = 1.3 f t ε u =.35% E = 22( f 1) For setional analysis te onrete onstitutive laws desribed in Fig. 8.a are assumed, respetively at te full yielding limit and te ultimate ollapse limit, wit f = f γ γ = 1. 5 ε u= ε u+. 5ω w (11) were γ simulates te yli strengt deay of te onrete ore and ω w is te meanial ratio of te onfining reinforement. Also for te reinforing steel te random variation of yield strengt is represented by a lognormal distribution defined by te mean value f ym =f yk +ks and by te standard deviation s. For te present appliation te following values are taken: f yk = 5 MPa s = 3 MPa k = 1. 597 (12) were f yk is te arateristi strengt assumed in design alulations. For any random value f y, te setional analysis is made wit te onstitutive laws desribed in Fig. 8.b, respetively at te full yielding limit and te ultimate ollapse limit. Te yli strengt deay of te setion is simulated by te redued stress f y = f y γ s γ s = 1. 15 (13) Te orresponding random variation of te degrading stiffness model of Fig. 1 is sown in Fig. 9, were a sample of 1 envelope urves is drawn (frame type 1a/tall).
f f ' ε =ε ε /ε 1 1 u u s fy f ' y E =26 MPa s ε ε u ε ε 1 1 u ε ε y = f y / E s (a) Fig. 8. Constitutive laws of te materials. (a) Conrete. Steel. ε s Fore F [kn] 5 4 3 2 1-1 -2-3 -4-5 - -.75 -.5 -.25.25.5.75 Displaement d [m] Fig. 9. Random models of degrading stiffness (1 envelope urves). PROBABILISTIC ANALYSIS Te appliation of te proposed probabilisti approa assumes 1 artifiial aelerograms generated as previously speified. So many random inputs of te dynami analysis ave been neessary to rea a stable statistial representation of te response, oming out from a pretty large set of random quantities (te sape parameters of te ground motion and te strengt parameters of te materials). Te results are summarized in Fig. 1, wi sows te frequeny distribution istograms of te overstrengt ratio κ for te eigt types of strutures ere examined. Te diagrams of Fig. 1 sow a low sattering of te results and a regular ourse wi an be well represented by fitting urves drawn aording to a lognormal model starting from κ = κ min. Based on tis model, te 5% and 1% fratile values, listed in Tab. 3 togeter wit te orresponding minimum and mean values, are dedued. Tese values of te overstrengt ratio remain around te tresold value κ =1, wi represents te limit of full reliability of te design rules, wit sensible deviations wi sow tat, in some ases, te value q=4.5 of te beavior fator ould be inadequate. In addition, a diret omparison of te diagrams of Fig. 1 lead us Table 3. Carateristi, mean and orrelation values for te overstrengt ratio κ (lognormal model). Levels of Cast-in-situ arrangement Preast arrangement Correlation Stiffness κ min κ. 5 κ. 1 κ m κ min κ. 5 κ. 1 κ m Coeffiient ρ 1/tall.73.8.83 7.69.78.81 4.969 1/low.76.86.9 1.14.73.83.86 1.1.954 2/tall.85.96 1.27.76.88.92 1.18.915 2/low.93 1.14 1.2 1.57.85 6 1.11 1.46.916
also to appreiate te equivalene in average of te seismi apaities of te two type of frames. Tis is also onfirmed by te regression diagrams of Fig. 11, wi sows te lose orrelation between te responses of te two types of strutures for te sample sets of 1 aelerograms. Te orresponding orrelation oeffiients are listed in Tab. 3. 3. 3. 2.4 1.8 1.2.6 1a/tall 2.4 1.8 1.2.6 1b/tall.5 1.5 2. 2.5 3. 2.5 Overstrengt κ.5 1.5 2. 2.5 3. 2.5 Overstrengt κ 2. 1.5.5 1a/low 2. 1.5.5 1b/low.5 1.5 2. 2.5 3. 2.5 Overstrengt κ.5 1.5 2. 2.5 3. 2.5 Overstrengt κ 2. 1.5.5 2a/tall 2. 1.5.5 2b/tall.5 1.5 2. 2.5 3. 1.75 Overstrengt κ.5 1.5 2. 2.5 3. 1.8 Overstrengt κ 1.4 5.7.35 2a/low 1.5 1.2.9.6.3 2b/low.5 1.5 2. 2.5 3. Overstrengt κ.5 1.5 2. 2.5 3. Overstrengt κ Fig. 1. Density distribution diagrams of te seismi ultimate apaity in term of overstrengt κ.
3. 3. Overstrengt κ - Type 1b/tall 2.5 2. 1.5.5 Overstrengt κ - Type 2b/tall 2.5 2. 1.5.5.5 1.5 2. 2.5 3..5 1.5 2. 2.5 3. Overstrengt κ - Type 1a/tall Overstrengt κ - Type 2a/tall 3. 3. Overstrengt κ - Type 1b/low 2.5 2. 1.5.5 Overstrengt κ - Type 2b/low 2.5 2. 1.5.5.5 1.5 2. 2.5 3..5 1.5 2. 2.5 3. Overstrengt κ - Type 1a/low Overstrengt κ - Type 2a/low Fig. 11. Regression diagrams of te seismi ultimate apaity in term of overstrengt κ. EXPERIMENTAL INVESTIGATION Pseudodynami tests Te pseudodynami tests desribed in te following ave been performed at ELSA European Laboratory for Strutural Assessment of te Joint Resear Centre of te European Commission at Ispra (Italy). Two strutural prototypes ave been designed, bot onsisting of six olumns wit eigt = 5. m, onneted by two lines of beams wit span l = 4. m, and an interposed slab wit span b = 3. m. Te onnetions between olumns and beams are made wit monoliti joints for te ast-in-situ arrangement and wit inged joints for te preast one. Figs. 12a and 12b- sow te seme of te testing plant and te detail of te instrumentation at te base of te olumns, respetively. Te ross-setions of te olumns are sown in Figs. 12.d-e. Wit regards to te materials, te strengt lass for onrete is C4/5 and te steel type is B5. Te total weigt of te dek is W = 72 kn. Su weigt is applied by means of proper vertial jaks. Te orresponding vibration periods of te frames are T=2 se for te ast-insitu arrangement and T=1.15 se for te preast arrangement. Te inertia fores are numerially simulated
in te model governing te pseudodynami proedure, togeter wit te related seond order effets. For more detailed information about te testing set up see Biondini et al. [3]. Te seismi ation for te pseudodynami test as been simulated by te artifiial aelerogram sown in Fig. 13, generated so to be ompatible wit te EC8 response spetrum for a subsoil type 1B (very dense sand or gravel). Taking into aount te expeted ollapse limits α gu =.9 for te ast-in-situ frame and α gu =8 for te preast frame, as omputed by using te EC8 design rules, te following tree load steps ave been seduled: α g =.32 (.33α gu ), α g =.64 (.67α gu ), and α g =.8 (.83α gu ) for te astin-situ frame; α g =.36 (.33α gu ), α g =.72 (.67α gu ), and α g = 8 (α gu ) for te preast frame. RIGHT JACK PRECAST PROTOTYPE LEFT JACK HORIZONTAL JACKS () VERTICAL JACK VERTICAL JACK 8φ14 8φ16 mm 45 mm (a) (d) (e) Fig. 12. (a) Testing plant and loation of te atuators. Details of te instrumentation at te base of te olumns for te ast-in-situ and () te preast prototypes, respetively. Crosssetions of te olums for (d) te ast-in-situ and (e) te preast prototypes, respetively. 4..75 3.5 Aeleration a(t)/pga.5.25 -.25 -.5 Aeleration a(t)/pga 3. 2.5 2. 1.5 -.75.5-5. 1 15. 2 25. 3 Time[se] (a).5 1.5 2. 2.5 3. Period [se] Fig. 13. (a) Time istory and elasti response spetrum of te artifiial aelerogram used in te pseudodynami tests.
From te large set of data reorded during te tests, tis paper reprodue te fore-displaement diagrams only. A diret omparison of su diagrams, sown in Fig. 14 for te tree levels of seismi ation, igligt te good yli performane of te two types of frames and lead us to appreiate te substantial equivalene of te seismi beavior of te ast-in-situ and te preast prototypes. Wit regards to te atual seismi apaity of te frames, it is wort noting tat at te tird level for te preast prototype (α g = 8) te amplitude of te motion took te jaks to te end of stroke and te test ad to be stopped. However, te maximum displaement of 4 mm was reaed witout any inipient deay of te reation fore and te over of te ritial zones of te olumns was still intat. Te ultimate ollapse limit was still far. Fig. 15 sows a view of te prototypes during te pseudodynami tests. 4 4 Sear Fore [kn] 2 1-1 -2 Sear Fore [kn] 2 1-1 -2 - α g =.32 - α g =.36-4 -4 - -2-1 1 2 4 4-4 -4 - -2-1 1 2 4 4 Sear Fore [kn] 2 1-1 -2 Sear Fore [kn] 2 1-1 -2 - α g =.64 - α g =.72-4 -4 - -2-1 1 2 4 4-4 -4 - -2-1 1 2 4 4 Sear Fore [kn] 2 1-1 -2 Sear Fore [kn] 2 1-1 -2 - α g =.8 - α g =8-4 -4 - -2-1 1 2 4 Drift [mm] (a) -4-4 - -2-1 1 2 4 Drift [mm] Fig. 14. Load-displaement urves: (a) ast-in situ and preast frames.
(a) Fig. 15. View of te prototypes during te pseudodynami tests: (a) ast-in-situ and preast frame. Displaement [mm] 4 2 1-1 -2 - Cast-in-situ (α g =.64) Displaement [mm] -4 5 1 15 2 25 3 35 4 Time [se] 4 2 1-1 -2 Preast (α g =.72) - -4 5 1 15 2 25 3 35 4 Time [se] Fig. 16. Displaement time-istories for te seond level of te pseudodynami tests: numerial (tik lines) versus experimental results (tin lines). Calibration of te numerial model Te results of te pseudodynami test allowed to assess te yli model used in te dynami analyses of te probabilisti simulation. Te model as been alibrated taking into aount te atual values of te strengt parameters as tested in samples of te materials. For te two iger levels of seismi ation, te point 1 of te model of Fig. 1 as been omitted, sine te strutures ad already overome te first raking limit. A value = of te visous damping as been assumed, onsistently to te pysial beavior of te prototypes under te pseudodynami tests and to te ontrol algoritm. Te good agreement between numerial and test results an be appreiated from Fig. 16, wi reprodues te omputed vibration urves superimposed to te experimental urves at te seond level of peak ground aeleration for bot
te prototypes. Te same agreement as been found also for te oter levels, as sown in Biondini and Toniolo [2]. Te very good orrespondene of te omputed and experimental responses onfirms te reliability of te analytial model and, wit it, te results of te preeding statistial analysis. CONCLUSIONS In tis paper it as been sown by a teoretial probabilisti approa tat ast-in-situ and preast onrete frames ave te same seismi apaity, even if te value q = 4.5 given by Euroode 8 to te beavior fator for tese frames seems to be not always appropriate. It is to be noted tat te apaity of te frames for q = 4.5 is very ig, more tan double of wat required in Italy for seismi zones of first ategory. Tis is due to te ig values of teir natural vibration periods, wi lead to a redued response to te ground motion. Terefore, tese type of frames ave a large margin of safety wit respet to seismi ollapse. Tey find teir dimensioning from te non-seismi onditions (su as te wind pressure and te rane ations) and te seismi servieability limit state referred to te storey drift. In order to find an experimental onfirmation of te teoretial results disussed above, real full sale pseudo-dynami tests on ast-in-situ and preast reinfored onrete frames ave been programmed at ELSA European Laboratory for Strutural Assessment of te Joint Resear Centre of te European Commission at Ispra (Italy). Te results of te tests igligt te good yli performane of te two types of frames and te substantial equivalene of te seismi beavior of te ast-in-situ and te preast prototypes. In addition, su results are ompared wit tose obtained from a numerial simulation of te tests. Te good agreement between numerial and experimental results onfirms te reliability of te teoretial model and, wit it, te results of te statistial analysis too. ACKNOWLEDGEMENTS Te experimental tests ave been performed witin te Eoleader Programme, wi is reserved to te European Consortium of Laboratories for Eartquake and Dynami Experimental Resear (JRC Contrat n HPRI-CT- 1999-59). Partiular tanks are given to Mr. Georges Magonette and Mr. Javier Molina wo managed te setting up of te instrumentation plant and te exeution of te loading tests, ensuring wit teir ig professional ability te perfet aomplisment of te experimentation. Tanks also to Mr. Carlo Bonfanti, wo managed te design and te exeution of te prototype, for te important ontribution of is experiene. Te resear as been led jointly wit Prof. Matej Fisinger and is assistants of te Ljubliana University. REFERENCES 1. Biondini F. and Toniolo G., Comparative Analysis of te Seismi Response of Preast and Cast-in-situ Frames. Studies and Researes, Graduate Sool for Conrete Strutures, Politenio di Milano, 21, 1-17, 2. 2. Biondini F. and Toniolo G., Teoretial and Experimental Investigation on te Seismi Beavior of Conrete Frames. Pro. of te 2 nd Int. Conf. on Strutural Engi. and Constrution, Rome, Italy, September 23-26, 23. 3. Biondini F., Ferrara L., Negro P., and Toniolo G., Results of Pseudodynami Test on a Prototype of Preast R.C. Frame. Pro. of te International Conferene on Advanes in Conrete and Strutures (ICACS), Beijing- Xuzou-Sangai, Cina, May 25-27, 24. 4. CEN-prENV 2, Euroode 8: Design of Strutures for Eartquake Resistane, European Committee for Standardization, Brussels. 5. Priestley M.J.N., Verma R. and Xiao Y., Seismi Sear Strengt of R.C. Columns, ASCE Journal of Strutural Engineering, 12(8), 231-2329, 1994. 6. Saisi, A., Toniolo, G., Preast r.. olumns under yli loading: an experimental program oriented to EC8. Studi e Riere, Graduate Sool for Conrete Strutures, Politenio di Milano, 19, 373-414, 1998. 7. SIMQKE, A Program for Artifiial Ground Motion Generation. User s Manual and Doumentation, NISEE, Department of Civil Eng., Massausetts Institute of Tenology, 1976. 8. Takeda T., Sozen M.A. and Nielsen N.N., Reinfored Conrete Response to Simulated Eartquakes, ASCE Journal of te Strutural Division, 96(12), 2557-2573, 197.