NUMERICAL ANALYSIS OF REINFORCED CONCRETE FRAME BUILDINGS WITH DECOUPLED INFILL WALLS

Značajan deo konstrukcija na svetu predstavljaju AB okvirne zgrade sa zidanom ispunom. Jednostavan razlog za to je potreba da se razdvoje prostorije unutar zgrade kao i da se razdvoji unutrašnjost zgrade od spoljašnje sredine. Pored toga, zidana ispuna je pokazala dobre performanse i trajnost u pogledu zvučne izolacije, vlage i požara kao i dobre termičke karakteristike. Zbog svega navedenog, upotreba zidane ispune u AB okvirnim zgradama česta je u mnogim zemljama, kao i u seizmički aktivnim oblastima. Međutim, kada su izložene dejstvu zemljotresa, AB okvirne zgrade sa zidanom ispunom pokazale su loše ponašanje, često praćeno značajnim oštećenjima zidane ispune. Ovo je potvrđeno u brojnim izveštajima koji prikazuju oštećenja AB okvirnih zgrada sa ispunom usled skorašnjih zemljotresa u: L’Aquila (Italija) 2009. godine [1], Lorca (Španija) 2011. godine [2], Van (Turska) 2011. godine [3] i Centralna Italija 2016. godine [4]. Velika i rasprostranjena oštećenja zidane ispune praćena kolapsima celih zidanih panela na nižim spratovima zgrada (slika 1a) prikazana su u izveštaju [5]


INTRODUCTION
Significant portion of structures in the world goes to RC frame buildings with the masonry infill walls. The simple reason for that is need for separating space inside the building and between internal space of buildings and external environment. Furthermore, masonry infills demonstrated reasonable performance and durability with respect to noise, moisture and fire as well as good heat and sound insulation properties. Due to this, the use of masonry infill walls in RC frame buildings is common in many countries, as well as in the seismic active regions too. However, when subjected to an earthquake excitation, masonry infilled RC frame buildings behave rather poor experiencing very often severe damage of infill walls. This is confirmed with several reports presenting damage to RC frame buildings with masonry infill walls during the recent earthquake events in L'Aquila (Italy) in 2009 [1], in Lorca (Spain) in 2011 [2], in Van (Turkey) in 2011 [3] and Central Italy in 2016 [4]. Heavy and widespread damage of masonry infills with the collapse of infill panels at the lower stories of the buildings o poslednjem zemljotresu koji se dogodio u Albaniji u novembru 2019. godine. Brojne studije su pokazale da oštećenja zidane ispune predstavljaju značajan deo ukupnih troškova i gubitaka AB zgrada usled zemljotresa [6,7].
Za vreme zemljotresa, zidovi ispune su izloženi dejstvu opterećenja u ravni, koje se javlja usled deformacije okvira. Visoko deformabilni AB okviri dovode do krtog odgovora krute ispune, što uzrokuje značajna oštećenja. Ponašanje zidane ispune pri takvom opterećenju istraživali su mnogi [13][14][15][16][17]. Pored opterećenja u ravni, ispuna je izložena i opterećenju upravno na ravan zida forces, koje se javlja usled ubrzanja i same mase zida. Optrećenje van ravni zida deluje upravno ne njegovu ravan i ponašanje ispune pri ovakvim uslovima, između ostalih, ispitivali su autori [18][19][20]. Sveobuhvatni pregled literature u vezi sa One of the reasons for such a poor behaviour is that infill walls significantly increase the stiffness of RC frame buildings and thus change their dynamic characteristics. However, in everyday design this is not taken into account. Instead, infills are considered as non-structural elements. Field observation after the April 25th earthquake in Nepal showed that infills produced significant increase of stiffness that influenced the natural frequencies of the structure [8]. In addition, dynamic response of a damaged two-story infilled RC building confirming contribution of the infills to the lateral resistance of this structure was investigated in [9] adding that the potential damage in the infills should be accounted with the use of sophisticated numerical models. Several researchers [10][11][12] investigated change of period of structure due to the infill presence. Depending on the predominant periods of the earthquake, decrease in the natural period due to infill may produce increase or decrease of the expected seismic response.
Uobičajeni problem dispozicije jeste fleksibilni sprat uzrokovan odsustvom zidova ispune ili postojanjem značajno manje zidova ispune na spratu iznad ili ispod. Ovakva konfiguracija javlja se usled funkcionalnih zahteva kao što su radnje i potreba za parking mestima. U [34] pokazano je da čak i kada se koriste zahtevi dati u propisima za ojačanje nosećih elemenata okvira, projektanti moraju modelirati zidanu ispunu i treba da verifikuju da se fleksibilni sprat neće javiti. Uticaji fleksibilnog sprata numerički su ispitivani u [35] primenom 3D modela, dok je u [36] pokazano da čak ni seizmička izolacija ponekad ne može da pomogne u slučaju nejednakog rasporeda ispune i formiranja fleksibilnog sprata, uz zaključak da se značajna oštećenja mogu workmanship could significantly affect the panel OOP behaviour by disturbing their boundary conditions. The influence of in-plane/out-of-plane interaction was studied in [22] saying that in-plane loading can disable development of out-of-plane arching effect due to the detachment of infill walls from the surrounding RC frames. In this paper authors also show that the frame structure with infill has much lower IP drifts when compared to the bare frame structure, but when IP/OOP interaction is taken into account the drifts with infill walls are even higher than in the case of bare frame structure. Other researchers [23][24][25][26] also pointed out the necessity to take into account IP/OOP interaction. Just a few researchers [26][27][28] studied in-plane and out-of-plane loading acting simultaneously on the infill walls, although it is expected that during the earthquake infills are loaded in both directions. Experimental tests performed and presented in [26]showed high decrease of both in-plane and out-ofplane capacity, explaining that deformation of the frame causes loss of connection between frame and infill, thus making infill walls vulnerable to out-of-plane loads.
If infills are not considered during the design as load carrying elements, problems such as additional demands to the RC frame components can be missed. Most common damage configurations caused by irregular distribution of infill walls are torsion, weak and/or soft stories and short columns. Buildings located on the street corners usually have infill panels on the non-street sides, which can result in a torsional response during an earthquake that might be detrimental to the global performance of the building. As described in [29] the unbalanced distribution of infill walls can introduce global torsion in buildings, which can induce larger demands in columns that were not considered in the original design. Effects of the irregular placement of the infills on the seismic damage of RC buildings was investigated in [30], concluding that these effects are less pronounced for the buildings with strong RC shear walls. Structural failure due to torsion and soft-storey effects may occur even in cases where Eurocode 8 [31] does not require the amplification of the action effects [32]. In [33] it was concluded that torsional effects due to the irregular infill distribution would probably result in failure of the infill wall through out-of-plane collapse.
Very common configuration problem is a weak and/or soft story caused by the absence of infill walls or the presence of many fewer infill walls than the story above and/or below. This configuration appears due to the functional demands such as parking and shops. In [34] it was shown that even when using code provisions for strengthening open-story frame members, designers must model the infill walls and should verify that a weak story will not form. Soft story effect using numerical model on a 3D building was investigated in [35], whereas [36] showed that even base isolation sometimes cannot help with the irregular infill distribution and creation of soft storey effect, concluding that heavy damage is to be expected in the base isolated structures subjected to near-fault earthquakes.
Short column can appear in a case of non-structural partial-height masonry infills that are in a rigid contact with the columns causing high demand that even strong columns cannot take. In [37] it was reported that the presence of the partial height wall decreases the ultimate lateral load capacity of the system by 47%. As solution for očekivati u slučaju seizmički izolovanih konstrukcija koje se nalaze blizu epicentra.
short column, [38] proposed an application of separation gap between infill and frame. In [39] it was suggested that the short column effect should be avoided during the architectural design stage itself adding that the infills in the short column region should be isolated from adjoining columns.
One option to improve the behaviour of masonry infilled RC frame buildings is to model the infills during the design phase. For this purpose the macro-modelling approach is the most convenient. This approach is used to describe the effect of the masonry infill walls to the global seismic behaviour of RC buildings. During the long period of studying the behaviour of infilled frames, there have been different proposals for macro-modelling approach. Using the strut to model the infill is undoubtedly the mostly accepted and the mostly studied approach. However, its application is also a difficult task and so far there is no overall consensus about the unique approach.
As it is the case for the width of the strut, many proposals for the strength are given in order to determine the capacities for the various failure modes that infill walls can experience. The equations for some of the in-plane failure modes are given by [41,49,56], considering the omitted ones as negligible. One of the important advantages of the approach proposed by [51,52] for the calculation of strut strength is its ability to account for all failure mechanisms. This was also done by [57]. Definition of constitutive relations for the strut is necessary in order to implement a strut model in software for structural calculations. The types of constitutive models required to set the strut models depend on the type of analysis (linear elastic or nonlinear) and the type of loading (monotonic, cyclic or dynamic).One of the first to propose forcedisplacement relationship for the equivalent strut defining initial stiffness, hardening and softening branch followed with the residual strength was [52]. Similarly, [58] proposed a nonlinear force-displacement relationship to describe the response of equivalent strut. Similar relation with the tri-linear response for the strut was proposed in [59,60]. In order to run dynamic nonlinear analysis the hysteretic behaviour of the material must be established. In literature just a few hysteretic models for diagonal strut can be found, because most researchers studied the behaviour of infill masonry under monotonic loading, but also due to the fact that the modelling of hysteretic behaviour increases not only the computational complexity but also the uncertainties of the problem. One of the early attempts was conducted by [61]. One of the most commonly used models was proposed by [43,62]. More recently, [63] improved the hysteresis law proposed in [64] by introducing a detailed force-displacement law accounting for cyclic or monotonic behaviour of an equivalent strut, calibrated against experimental results. Although, experimental studies show necessity for taking into account in-plane/out-of-plane interaction, incorporating it in the numerical models is highly complex task being at the starting phase of development and verification.
Second option for improvement of the behaviour of masonry infilled RC frame buildings is to apply some construction measures to the infills itself. This can be done by increasing the infill strength with addition of reinforcement to the infill wall [65,66] or by applying textile reinforced mortars for plastering [67][68][69]. Improving the behaviour of the infills by subdividing the wall in horizontal sections with special sliding surfaces between them was proposed by several authors [70][71][72][73]. In this way deformability of the infill panel is increased.
The third approach considers the complete in-plane isolation of non-structural elements from the surrounding frame, so to allow frame deformation and thus delayed infill activation. The simplest way to separate infill from the frame is by creating the gaps between them. This can be done by filling the gap with soft material [29,74,75]. Additional benefit of infill/frame decoupling is reduction of stresses induced to the frame because of the soft contact. Important aspect which should be covered in this approach is adequate out-of-plane restrain to prevent the infill wall to collapse due to the perpendicular loads. okvira preko čeličnih ankera ispitivana je u [76,77]. Izolacija ispune takođe je data kao jedno od rešenja u međunarodnim preporukama i propisima [78][79][80].
The problem that can be found is that there are many approaches and the process has not been standardized in order to be used by the practical engineering community. Furthermore, many solutions bring the benefit to the infills, but so far no complete solution is proposed that solves the problems of the behaviour of the masonry infill walls under earthquake excitations. Shortcomings are different, from complicated to practically inapplicable solutions and solutions not effective for simultaneous inplane and out-of-plane load. For some of them the application is problematic with respect to flexible room use and they are inapplicable to all types of bricks. One solution that has shown promising results is the decoupling system described in [81]. This system called INODIS (Innovative Decoupled Infill System) is able to effectively decouple and delay the activation of the infill walls, thus reducing the infill/frame interaction and the undesirable effects of it. Due to its features and the shape providing sufficient out-of-plane connection for infill walls, this system is chosen for detailed numerical study presented in this paper.
In order to determine whether the decoupling system is a better solution compared to traditional unreinforced masonry walls, a series of numerical linear and non-linear analyses were performed. The novelty of the paper is study of the behaviour of the RC frame buildings with decoupled infill walls at the structural level. Similar studies were done for traditional infills but none is performed on decoupled infills. Since the INODIS system provides inplane decoupling it removes in-plane/out-of-plane interaction, as shown experimentally [81]. Therefore, in the numerical analyses just in-plane behaviour of the infill walls was considered.

DECOUPLING SYSTEM
In this section the decoupling system INODIS is briefly described. Its details and features are thoroughly given in [81,82]. The basic idea of the INODIS system ( Figure 3) is decoupling of infill masonry and RC frame in in-plane direction combined with the out-of-plane connection measures along the edges of the infill panel. It aims to raise the in-and out-of-plane resistance by means of dissipative and sliding connections along the contact areas of the infill to the RC frame. INODIS decouples the infill wall and RC frame with the U-shaped elastomers placed at the top and along the vertical edges of an infill, together with the elastomer divided in three strips at the bottom of the infill. The U-shaped elastomers are designed to allow the design drift of the reinforced concrete frame without inducing damages to the infill wall. Furthermore, the viscoelastic bearings enhance the overall damping capacity of the building. Plastic profiles are attached by metal nails or screws to the surrounding frame while U-shaped elastomers are glued to the masonry infill on one side and placed around plastic profiles on the other side ( Figure 3), thus preventing the out-of plane failure. Flanges of the U-shaped elastomers shown on Figure 3 are made of soft elastomer while stiffer elastomers are used for the webs. The stiffest elastomer is applied at the bottom in a form of three strips. Figure 3. Layout of the INODIS system [81] 3 NUMERIČKI MODELI U ovom poglavlju, predstavljeni su pristupi modeliranja svih komponenti AB okvira sa izolovanom ispunom. Budući da su tema istraživanja AB okviri sa zidanom ispunom, modeliranje se može podeliti na tri dela, jedan vezan za AB okvir, drugi se odnosi na zidanu ispunu i treći na elemente izolacije ispune. Tri različita modela su razvijena: prazan okvir, okvir sa ispunom i okvir sa izolovanom ispunom. Softverski paket SAP2000 [83] izabran je zbog široke upotrebe u projektantskoj praksi.

NUMERICAL MODELS
In this section, modelling approaches for all parts of the RC frames with decoupled infills are presented. Since the topic of the investigation are masonry infilled RC frames, the modelling approaches can be divided into three sections, one related to the RC frame, second to the infill wall and third to the decoupling elements. Three different models have been developed: the bare frame model, the infilled model and model of the frame with the decoupled infills. The software SAP2000 [83] was chosen because it is a widely used commercial program in design practices.

Modelling of the concrete frame
Beams and columns are modelled as onedimensional frame elements, assuming fixed end restraints at the base of the columns (Figure 4a). In order to perform nonlinear analysis, models include nonlinearity properties of materials and section, through a distributed plasticity approach. In particular, at the end section of the elements plastic hinges are placed ( Figure  4a). For concrete elements, the hinge properties are taken from Tables 6-7 for beams and 6-8 for columns from FEMA-356 [84]. The force or moment-deformation curve is based, on the curve shown in Figure 5, where five different points (A to E) must be defined. The points represent the place of origin, yielding, ultimate capacity, residual strength and failure, respectively [83]. Za definisanje poprečnog preseka betonskih elemenata upotrebljena je posebna opcija dostupna u programu SAP2000 koja se zove "Section Designer". Uz pomoć nje je moguće definisati proizvoljnu geometriju preseka i kreirati kombinaciju materijala. U opciji "Section Designer" moguće je definisati presek betona s različitim karakteristikama materijala kao i tačan raspored armature. Za zaštitni sloj betona definisan je neutegnuti beton dok je za ostali deo preseka zadat utegnuti beton. Glavna razlika je da pri niskom nivou napona, poprečna armatura je slabo opterećena i beton se ponaša kao neutegnut. Dok pri naponima bliskim jednoaksijalnoj nosivosti betona, pojava pukotina u betonu dovodi do značajne aktivacije uzengija koje onda pružaju utezanje betonskom elementu. Na ovaj način se obezbeđuje značajno povećanje nosivosti i duktilnosti betonskog elementa [85]. Kriva napon-dilatacija za utegnuti i neutegnuti beton (slika 6) zasniva se na modelu predloženom u [86]. Prema njoj, nosivost na pritisak i granična dilatacija određuje se u funkciji poprečne armature. Bitne karakteristike Manderove krive su da se može koristiti i za statička i dinamička opterećenja, kada su ona zadata monotono ili ciklično [86,87]. Upotrebnom For creating specific frame section properties separate utility built into SAP2000 called "Section Designer" is used. It allows sections of arbitrary geometry and combinations of materials to be created. In Section Designer it is possible to create a section with different concrete material properties and precise disposition of reinforcement. For the concrete cover unconfined concrete was assigned and confined for the rest of the section. The main difference is that under the low levels of stress, transverse reinforcement is barely stressed and the concrete behaves like unconfined concrete. At stresses close to the uniaxial strength of concrete, fracturing causes the concrete to stress the stirrups which then provide confining action in concrete element. In this way, a significant increase of strength and ductility of concrete is present [85]. The stress-strain curve used for the confined and unconfined concrete( Figure 6) is based on the concrete model proposed [86]. It derives the compressive strength and ultimate strain values as a function of the transverse reinforcement. Important characteristic is that Mander's curve can be used for both static and dynamic loadings, when they are applied monotonically or cyclically [86,87]. With the use of automatskog definisanja karakteristika plastičnih zglobova, program određuje krivu moment-rotacija i ostale karakteristike plastičnog zgloba prema FEMA 356 [84] kriterijumu koristeći preciznu geometriju i definiciju materijala datu u "Section Designer" [85]. automatic hinge properties, program calculates the moment-rotation curve and other hinge properties according to FEMA 356 [84] criteria using precise geometry and material defined in Section Designer [85]. Figure 6. Stress-strain curves for unconfined and confined concrete [86] Kako bi se modelirala plastifikacija duž elementa i po širini poprečnog preseka korišćen je takozvani "fiber" presek. Upotrebom "fiber" zglobova moguće je definisati uvezano ponašanje aksijalne sile i momenta savijanja. Poprečni presek diskretizuje se u niz aksijalnih vlakana koja se protežu podužno kroz celu dužinu plastičnog zgloba. Ovi plastični zglobovi su elastoplastični i sastoje se od seta materijalnih tačaka, gde svaka predstavlja deo poprečnog preseka i ima njegove materijalne karakteristike. Krive sila-deformacija i moment-rotacija nisu definisane, već se određuju u toku analize na osnovu krive napon-dilatacija za svaku materijalnu tačku [83].
Definisane su samo karakteristike u pravcu U1 nelinearnom krivom sila pomeranja. Za definisanje ove To model distributed plasticity along the member length and across the section so-called fibre section models are used. With the employment of fibre hinges it is possible to define coupled axial force and bending behaviour. The cross section is discretized into a series of representative axial fibres which extend longitudinally along the hinge length. These hinges are elastic-plastic and consist of a set of material points, each representing a portion of the cross-section having the same material. Force-deflection and moment-rotation curves are unspecified, but computed during the analysis from the stress-strain curves of the material points [83].

Modelling of the infill wall
In order to model the in-plane behaviour of the infill walls, a macro modelling approach was employed, using link element to model equivalent strut. Link elements can be used to connect two joints together and they are able to capture a nonlinear behaviour. Therefore, they are a suitable choice for modelling in-plane behaviour of infill panel. A link element is assumed that is made of six springs for each of the six degrees of freedom. For each spring it is possible to assign different types of linear or nonlinear properties. Between several types of link elements available in SAP 2000 the multi-linear plastic link element was chosen due to its ability to present nonlinear behaviour of infill wall. Two link elements are placed inside the frame connecting diagonal opposite corners (Figure 4b).
where K1 and K2 take the values from Table 1 and where Em is the masonry panel's modulus of elasticity; EcIc is the column's flexural rigidity, tm is panel thickness of the infill panel; h is the column's height between beams' centre lines; hm is the height of the infill; Θ is the angle between the horizontal and the diagonal of the wall as seen in Figure 2. Nosivost dijagonalog elementa na pritisak definisana je uzimajući u obzir četiri tipa loma ispune: (i) zatezanje po dijagonali σbr(1); (ii) klizanje po horizontalnim malterskim spojnicama σbr(2); (iii) lom u uglu zida σbr(3); i (iv) lom po dijagonali usled pritiska σbr(4), definisanog prema sledećim jednačinama: The compression failure stress of the strut is defined so that it takes into account four different failure modes: (i) diagonal tension σbr(1); (ii) bed joint sliding shear σbr(2); (iii) corner crushing σbr (3); and (iv) diagonal compression failure σbr (4), defined according to the following equations: where σm0 is the compression strength, τm0 is the shear strength measured taken from the diagonal compression test, fsr is the joint slide resistance, and σ0 is the vertical stress of the applied loads.

Modelling of the decoupling elastomer
Since elastomers are used for decoupling of frame and infill wall, an element that can present hyperelastic behaviour of elastomer should be chosen. For that purpose also multi linear plastic link element was employed. Link elements presenting elastomers are placed in the corners connecting infill's link element and frame ( Figure 8). U ovom poglavlju prikazana je kalibracija i validacija numeričkih modela s ciljem da se razvije numerički model koji može da predstavi eksperimentalne testove na praznim AB okvirima, AB okvirima s tradicionalnom ispunom i AB okvirima sa izolovanom ispunom. Cilj je da se nakon toga validirani modeli iskoriste za parametarsku analizu na 2D ramovima konstrukcije i na 3D modelu zgrade.

VALIDATION WITH THE EXPERIMENTAL RESULTS
In this section the calibration and validation of the different models will be presented, the goal is to develop a numerical model to simulate tests on RC bare frame, traditionally infilled RC frame and RC frame with decoupled infills. The purpose is to later use this calibrated frame models to simulate the behaviour of the 2D structural frames and 3D building.
For the validation of the numerical model, test results for in-plane loading conditions from [81] will be used. Test campaign consisted of in-plane cyclic loading on full scale bare frame, traditionally infilled frame and frame with decoupled infills. Experimental campaign and all the details are given in [81]. Here, the calibration of the numerical models is first performed using pushover analysis and comparing the results with the envelope of the hysteretic curve and then the time history analysis is employed for calibrating the model to match the hysteretic curve from the cyclic loading. a) b) c)

Bare frame
To validate the numerical approach used for the concrete frame modelling, the test onfull-scale RC frame is used. The frame was designed according to [90,91] considering the German national annexes for ductility class L. Columns have a square cross section of 25x25cm with a 1.48% longitudinal reinforcement, 0.63% transverse reinforcement at the start and end of the column, as well as 0.42% middle section stirrups. On the other hand, the beam was designed with a size of 25x45cm (height x width) with a 1.05% of longitudinal reinforcement and 0.35% and 0.23% of transverse reinforcement at beam start/end and in middle section, respectively.
A relative distance of 0.05 and 0.95 was considered for the location of fibre hinges in the model (Figure 4a). Exact dimensions and reinforcement distribution was defined in the cross sections. With the use of Section Designer reinforced concrete elements can be modelled quite precise (Figure9). As it can be seen, the exact location of the rebars is obtained as well as two different material properties of concrete (confined -yellow colour; unconfined -blue colour). Two different cross sections were generated for beams and also for columns, as there is a change in longitudinal reinforcement and spacing of stirrups. Beam and columns cross section A is the ones used near the edges while cross section B is used in the mid-section (Figure 9). Figure 9 also shows mesh distribution and fibre position. Each section was divided into three types of fibres for different kind of materials. For concrete material, the Mander model [86] was used for the definition of the stress-strain curves, which are auto defined by the program (Figure 10). For the rebars, a user defined stress-strain curve was defined, with the material characteristics described in [82]. Numerički rezultati statičke nelinearne analize (pushover) upoređeni su sa anvelopom histerezisne krive iz eksperimentalnih rezultata (slika 11). Iz rezultata se može primetiti da je kriva dobijena iz numeričkog modela prilično blizu eksperimentalne krive. I degradacija krutosti i kapacitet nosivosti praznog okvira dobro se poklapaju. Numerički rezultati pokazuju skoro isti kapacitet do trenutka dostizanja maksimalne nosivosti i treba istaći da i numerički model i eksperimentalni rezultati pokazuju da je maksimalna nosivost dostignuta pri 2% relativnog međuspratnog pomeranja. Nakon toga postoji blago razilaženje ove dve krive, ali u granicama zadovoljavajućeg.
The results from the numerical pushover analysis were compared to the envelope curve of the hysteresis experimental results (Figure 11). From the results obtained it is possible to notice that, in general, the pushover curves from the numerical model are pretty close to one obtained in experimental test. Both stiffness degradation and strength capacity of the bare frame are matched very well. The numerical results follow almost the same capacity curve until it reaches a peak load capacity; it should be pointed out that both numerical and experimental results reach the peak at 2% of inter storey drift. After the peak there is a small and tolerable diversion between both curves. Slika 11. Poređenje između numerički dobijene pushover krive i anvelope eksperimentalne histerezisne krive Figure 11. Comparison between pushover curve from numerical model and the envelope of experimental hysteresis Kako bi se uhvatilo histerezisno ponašanje materijala, histerezisni model je definisan za beton i za čelik definisan za armaturu. Za model betona, uzet je faktor degradacije energije s = 0. Za model armature, parametri korišćeni za kalibraciju dati su u Tabeli 2.
In order to capture the hysteretic behaviour of the materials, the concrete hysteresis model was defined for concrete and for steel material of rebars degrading hysteresis model. For the concrete model, an energy degradation factor s = 0, was assigned. For the rebar model, the parameters used after calibration can be found in the Table 2.
From the results of the time history analysis shown in Figure 12, it can be seen a very good matching of the stiffness and maximum load capacity. In addition, hysteresis loops are very similar, confirming the validity of the bare frame model.

RC frame with traditional infills
The traditional infilled frame, used in the experimental tests performed by [81], was composed of the same frame that was infilled with masonry wall made of hollow clay bricks with thin-layer mortar connection. Detailed material characteristics of the bricks and masonry are given in [81,82]. For the force-displacement curve defined for the link element, a four branch model based on [51,52] was used. In order to define it, the calculation of the dimensionless parameter λh was performed using Equation 2. The following Table 3 shows the values used: For the calculation of the strut width, Equation 1 was used. As seen in Table 3, for λh values in between 3.14 and 7.85, K1 and K2 are equal to 0.707 and 0.010 respectively, which gives the strut width equal 514.93 mm.

Tabela 3. Određivanje parametra λh
Since the diagonal compression test was not performed in the experiments, the masonry shear strength was calculated using Equation 12 with a compressive strength, f'm, equal to 3.1 N/mm 2 . The bed joint shear strength was also calculated, using Equation 13 as shown below: For calculating the compression failure stress of the strut Equations 3-6 were used and results are shown in the Table 4. ), and the infill wall stiffness when it is completely cracked, Kmfc (Equation 11), were used obtaining K0 = 299.8 kN/mm. Also a modification is proposed for the elastic stiffness and the infill stiffness taking only 15% of the infill stiffness, giving a value of Kmfc = 13.04 kN/mm, and 60% of the elastic stiffness, giving a value of K0 = 63.34 kN/mm. The final branch defined with Kmr is considered to have negative slope equal to 35% of the infill stiffness. Figure 13 shows the results obtained with the numerical model and experimental test. A good matching of stiffness and maximal load capacity can be seen. This demonstrates a good calibration and validates the infill frame model. For the definition of the hysteresis model for the infill wall a pivot model was chosen. This model is defined by adjusting the loading and unloading branches, with the parameters α1, α2, β1 and β2. The α parameters adjust the unloading zone while the β parameters adjust the loading zone. Since the tension strength of the infill panel is unconsidered, parameters α1 and β1 are set to 0, while α2 is set to 5 [83]. Results of the time history analysis in Figure 14 show a good resemblance between the numerical results (red) and the experimental results (blue), confirming the validity of using the model for nonlinear time history analysis.

RC frame with decoupled infills
In order to take into account decoupling with the elastomers that are applied in the INODIS system, nonlinear link elements are added to the corners of the infill panel connecting the diagonal links with the frame (Figure 8). Using the strut width of the infill (ω) and its angle Θ, contact length between the diagonal strut and the column, Lc, and beam, Lb, are determined: cos 380.89 c mm L  = = (14) sin 346.51 c mm L  == (15) Uzimajući širinu elastomera od 250 mm, kotaktna površina je određena kao Ac = 95222.52 mm 2 i Ab = 86628.43 mm 2 .
Using the width of the elastomers of 250 mm, the contact area is calculated giving a value of Ac = 95222.52 mm 2 and Ab = 86628.43 mm 2 .
Thickness of the column elastomers is of 37.5mm and for the beams 25 mm. Using this data, the forcedisplacement curves were defined ( Figure 15) and assigned to the links presenting the elastomers. The Takeda model was used for the definition of the hysteretic model for the elastomers. This is the simplest model as it does not require definition of any parameter. Figure 15.
In-plane test on the decoupled infilled frame was used for validation of the numerical model and results ( Figure  16) show a good resemblance between the numerical model (red) and the experimental results (blue). The time history results for the pure in-plane test ( Figure 17) and for the combined in-plane and out-of-plane loading phase ( Figure 18) show a good matching as well, with slightly narrower loops compared with the experimental ones. This also confirms that in-plane behaviour is independent on the out-of-plane load when decoupling is applied.
After validating all three models with the experimental results, it is possible to study and analyse the influence of decoupling on the behaviour of multi storey buildings in two and three dimensions with different configurations of infill walls

ANALYSIS OF 2D STRUCTURAL FRAMES
After validating numerical models using experimental results further analysis of the behaviour of RC frame structures with decoupled infills can be done. Two dimensional structural frames were analysed using pushover and dynamic time-history analysis. In order to model structural frames with several floors and bays, the previously validated models of one-bay and one-storey frame were multiplied in height and width. All crosssection and properties of beams, columns, infills and elastomers were kept the same.
For this purpose a medium (M) rise six story building was analysed. Following the approach by [93], different infill configurations were studied including: bare frame, fully infilled frame, open ground storey frame and partially open ground storey frame. For all these configurations, both traditional and decoupling approaches were studied. That means seven different configurations were analysed ( Figure 19 Figure 19. Disposition of infill walls for medium rise building [93]

Types of analysis
First, a modal analysis was performed to compare the dynamic characteristics of different configurations and check the influence of the infill walls on the structural frame. Then static nonlinear (pushover) analysis is used to check force-displacement capacity and base shear forces. At last, nonlinear time history analysis is employed to compare the displacements and inter storey drifts. Accelerogram used in time history analysis is generated artificially based on a Eurocode 8 [31] linear elastic response spectrum Type 1, with soil condition B, for two different PGA values, PGA=0.1g and PGA=0.3g, and damping ratio of 5 %. Generation of accelerogram is done using software SeismoArtif [94] with the sampling rate of 256 Hz and total duration of 25s with the base line correction. Figure 20 shows response spectrum for PGA=0.3g and corresponding accelerogram.
When locating the periods on the response spectrum curve (Figure 22), it can be seen a clear difference between the bare frame (blue) and the traditionally infilled frames (red), showing significant underestimation of the seismic load if infill walls are not taken into account during the design. Traditional infills fall into the plateau with the spectral acceleration almost three times higher than for bare frame. For the frames with decoupled infills instead (green), not only the periods remain close in between each other, but also are much closer to the ones of the bare frame. The difference in the seismic load level is less than 12%, showing that bare frame model can be used for the design of RC frames with decoupled infill walls.
The inter storey drifts of the fully open ground storey for frame with traditional infills, show that a soft storey behaviour occurred (Figure 24). Looking at the results of the nonlinear time history analysis for PGA=0.1g the maximum inter story drift at the first level is 0.93%. It can be observed that for the first floor and second floor, there was a significant and abrupt reduction in the drift, 0.07% and 0.04%. For PGA=0.3g fully open ground storey frame with traditional infills had inter storey drift of 0.15% and 0.11% at first and second floor, remaining small and almost constant for the rest of the floors; whereas 3.85% of drift occurred at the ground floor. This drift is three times higher than for the case of partially open ground floor and four times higher than fully infilled frame.
As it was expected due to the increase in stiffness caused by the infill walls, the top floor displacement of the frames with traditional infills are significantly lower than for the other frames. Also for both systems, it can be noticed an increase in absolute displacements as the amount of infilled frames in the ground floor is reduced. For the traditional infill, for the partial and fully open ground floor the absolute displacements were 0.307m and 0.351m, respectively; while with the decoupling system, they were 0.616m and 0.635m respectively. The same behaviour can be seen for both PGA levels. It can be observed that for the traditional infilled systems, the absolute displacements are several times smaller than the bare frame and the decoupled system. This is true for the structural frame fully infilled with traditional infills and also for the partially open ground floor configuration.
traditional infills experienced highest displacement in the ground floor. The displacements of the decoupled frame fall in between the displacements of the bare frame and the traditional one, but they resemble more and are closer to the values of the bare frames.
On the contrary, for the decoupling system, there is a smooth reduction of inter storey drift from its maximum along the first floors up to its minimum at the top floor. What is more important is that all infill configurations for nonlinear time history analysis, frames with decoupled infills had drifts in a range of bare frame model distributed in the same manner along the frame height. Furthermore, soft storey effect is absent in the case of decoupled infills and there is no sudden increase of drift between the floors.

ANALYSIS OF A 3D BUILDING
For the three-dimensional building, three infill configurations were studied, besides a bare frame ( Figure  25a). A five-storey high building consisting of 3 bays in the transversal direction and 5 bays in the longitudinal direction was analysed. In the first configuration infills are located in the most outer frames creating an infill core (Figure 25b). Second configuration represents the buildings located in a corner where two adjacent sides are without infill walls, whereas the other two are infilled (Figure 25c). This configuration is common in practice and important to be studied because if the walls are not symmetrically placed along the whole plan of the building, the position of the centre of stiffness and mass could be mismatch creating a torsional effect on the building. As discussed in introduction, the study of the soft storey mechanism is important due to the common practice to remove infill walls in the ground storey because of the functional requirement for shops or garages. Therefore, this configuration is also investigated (Figure 25d

Types of analysis
For the 3D building model, the same analyses (modal, pushover and nonlinear time history) as for 2D structural frames were used. Artificial accelerograms created for 2D structural frames are also used for the nonlinear time history calculations.

Results for 3D building
Starting from the modal analysis, it can be observed that the building which uses a traditional infills, presents a much stiffer behaviour in comparison with the one with decoupled infills. From the results (Figure 27), the completely infilled building with traditional infills has a two times smaller first period with respect to the bare frame building. Instead, for the building fully infilled with the decoupled walls, the reduction was of only 6% for the first period. For this building with decoupling system, the other two periods also presented a lower decrease in the period, with 10% and 14% representing the second and third mode period, respectively. In contrast, the traditional infilled system had a reduction of 62% and 69% of the second and third mode period. This difference is slightly smaller in the case of corner and open ground building for traditional infill, whereas it is almost the same for the decoupled infills in all three configurations. What is even more important that the buildings with the mass presenting decoupled infills have almost the same periods as the one with struts used for decoupled infills. Kada se periodi postave na spektar odgovora (slika 28), može se videti da zgrada sa izolovanom ispunom ima nivo opterećenja koji je blizak za sve konfiguracije, i on je blizak i s vrednošću za zgradu s praznim okvirima. S druge strane, zgrade s tradicionalnom ispunom nalaze se na platou spektra odgovora, daleko od vrednosti koja odgovara zgradi s praznim okvirima. Ukoliko se zgrade s tradicionalnom ispunom projektuju prema modelima praznih okvira, slično kao i za 2D okvire, potcenjuje se nivo spektralnog ubrzanja za više od 50%, dok je za zgrade sa izolovanom ispunom ta razlika zanemarljiva (manja od 10%). Rezultati pokazuju da se AB okvirne zgrade sa izolovanom ispunom, kada je ona predstavljena samo preko mase prikazane linijskim opterećenjem, poklapaju s nivoom seizmičkog opterećenja sa zgradama u kojima je ispuna modelirana pritisnutim dijagonalama. Stoga, jednostavan model s praznim okvirima s masom umesto pritisnutih dijagonala može biti iskorišćen za projektovanje AB ramovskih konstrukcija sa izolovanom ispunom.
When the periods are located on the response spectrum curve (Figure 28), it can be seen that the buildings with the decoupling system are close together for all configurations, and also very close to the position of the bare frame period. On the other hand, it can be seen that the periods of the traditional infilled building are all located at the plateau of the response spectrum, far away from the bare frame. If buildings with traditional infills are designed with the bare frame model, similar to 2D structural frames, underestimation of the spectral acceleration would be more than 50%, whereas for the decoupled infills it is negligible (less than 10%). The results show that RC frame buildings where decoupled infills are taken into account as a line load presenting their mass match the seismic load level of the building with the struts presenting decoupled infills and bare frame building. Therefore, simple bare frame model with the mass instead of struts can be used for the design of RC frame buildings with decoupled infills.
Similar to the results from the 2D frames, the traditionally infilled frame buildings activate higher maximum base shear force in both X and Y direction than the building with decoupled infills and bare frame building ( Figure 30). The traditional system also experiences a fast or sudden drop in load when the maximum was reached followed by a curve that follows the capacity curve of the bare frame. It can also be noticed that removing traditional infill walls in the ground floor reduces by 50% the maximum base shear attained by the structure. Building with open ground floor with traditional infills has reached its deformation capacity much sooner than all other configurations. In contrast, buildings with decoupled infills behave almost the same for all configurations, not experiencing sudden drop in the base shear force and providing higher deformation capacity. Što se tiče konfiguracija sa izolovanom ispunom, apsolutna pomeranja za sasvim pune okvire, zgradu na uglu i zgradu sa otvorenim prizemljem u granicama su vrednosti zgrade s praznim okvirima. Pojava fleksibilnog sprata nije prisutna ni u jednoj od konfiguracija sa izolovanom ispunom. Ovo je značajno unapređivanje koje dolazi kao rezultat toga da izolacija ispune uklanja efekat povećanja krutosti usled zidova ispune i usled toga nema skokova u nivou krutosti između različitih spratova.
Results of nonlinear time history analyses (Figure 31 and 32) show that buildings with traditional infills have in overall a lower absolute displacements and a much smaller inter storey drift, except for the case of the open ground configuration. For this situation huge difference in the inter storey drift between ground floor and first floor can be seen. This is more pronounced in Y direction and even higher for the case of PGA = 0.3g, whereas in X direction the change in inter storey drift is much smoother but with a noticeable higher change in the values compared with the rest of the models. For the corner building with traditional infills, a similar behaviour can be seen but with a smaller inter storey drifts in the ground floor.
For the decoupled infills, the absolute displacements for the fully infilled building, the corner building and the open ground floor building are in the range of the values of the bare frame model. The soft story effect cannot be observed in any of the configurations having decoupled infills. This is significant improvement coming from the decoupling measure that diminishes increase of stiffness coming from the infill walls and thus there are no jumps in stiffness between the floors.
Due to the irregular distribution of the infill walls in the corner building configuration, it is interesting to analyse the results in the perpendicular direction of the applied load. For the traditional infill, a prominent and uneven distribution of absolute displacements and inter storey drift can be observed in this case. These effects coming from the activation of the torsional displacements are absent in the case of buildings with decoupled infill walls, showing that decoupling can be used as measure to solve torsional problems in the case of irregular distribution of infill walls, specifically corner building.
First, calibration and validation of the numerical model was done on one-bay frames with one storey, previously tested experimentally. Then, 2D structural frames with different infill distribution were analysed. Three different infill configurations were studied including: fully infilled frame, open ground storey frame and partially open ground storey frame and its behaviour was compared with the bare frame. For all these configurations, both traditional and decoupling approaches were studied. Results show that traditional infill walls significantly reduce natural period of the frame, thus considerably change the level of seismic loading acting on the structure. This is not the case with decoupled infills, where the change of period is insignificant. Force-displacement curves obtained in pushover analysis confirm low deformation capability of traditionally infilled frames in comparison with the bare frames and frames with decoupled infills. Nonlinear time history analysis showed in the best way negative effects of traditional infills on the behaviour of structural frames. In the case of open ground floor configuration huge jump in the inter storey drift can be noticed on the ground floor in comparison with the other storeys. In contrast, RC frames with decoupled infill walls behaved similarly as the bare frame configuration Za 3D zgradu analizirana je petospratnica s pet spratova i tri polja u poprečnom pravcu i pet polja u podužnom pravcu. Konfiguracija sa ispunom u spoljašnjim okvirima ispitivana je zajedno sa zgradom na uglu i zgradom sa otvorenim prizemljem. Pored zgrade sa praznim okvirima, ove tri konfiguracije su istražene za slučaj tradicionalne i izolovane ispune. Pored toga, dodatna tri modela su napravljena koji su imali masu zadatu kao linijsko opterećenje na mestima izolovane ispune. Rezultati jasno pokazuju veliku razliku u periodima oscilovanja između zgrade s praznim okvirima i zgrade s tradicionalnom ispunom. Ovo nije slučaj sa zgradama sa izolovanom ispunom kod kojih se periodi oscilovanja razlikuju za 10% u odnosu na zgradu s praznim okvirima. To značajno utiče na nivo sizmičkog opterećenja koje deluje na zgradu, koji je u slučaju s tradicionalnom ispunom 50% veći u odnosu na zgradu s praznim okvirima koja se uobičajeno koristi danas u praksi u toku proračuna. Međutim, razlika u slučaju izolovane ispune je zanemarljiva. Ovo jasno pokazuje prednosti pristupa izolacije, koji pruža jasan i jednostavan postupak proračuna, s obzirom na to što eventualna primena izolacije ispune beznačajno menja trenutnu građevinsku praksu. Pored toga, rezultati oblika odgovora zgrade na uglu pokazuju značajne torzione efekte u slučaju tradicionalne ispune, što nije slučaj kada se primeni izolovana ispuna. Razlog za to je činjenica da izolovanje ispune uklanja efekat povećanja krutosti koja dolazi od zidane ispune.
For the three-dimensional building a five-storey building was analysed, consisting of 3 bays in the transversal direction and 5 bays in the longitudinal direction. Configuration with outer frames completely filled with masonry walls was studied, together with the case of corner and open ground floor building. Besides bare frame building, these three configurations were studied in the case of traditional infills as well as decoupled infills. Furthermore, additional three models were investigated with only mass as line load presenting decoupled infill walls. The results clearly show huge difference in natural period between bare frame configuration and building with traditional infill walls. This is not the case with buildings having decoupled infills, where natural periods defer from the bare frame ones less than 10%. This affects a lot the level of seismic load actually acting on the building, which in the case of traditional infill can be even 50% higher than in the case of bare frame configuration that is usually used in the design today. However, the difference in the case of decoupled infills is negligible. This shows the advantage of decoupling approach having clear and simple design process, since the eventual implementation of decoupling system alter only marginally the current design practice. Furthermore, results for the mode shapes of corner building configuration show significant torsional effects in the case of traditional infills, which is not the case for the decoupled infill walls. This is due to the fact that decoupling diminishes increase of stiffness coming from the infill walls.
Similar to the results from the 2D frames, the traditionally infilled frames presented a higher maximum base shear in both X and Y direction than the decoupled and bare frame structures. In addition, building with open ground floor and traditional infills has reached its deformation capacity much sooner than all other configurations.
Nonlinear time history analysis show disastrous effects of traditional infill walls on the overall building behaviour. Rigid connection between infills and frame produce significant change in the stiffness of the overall building, resulting in reduction of displacements but producing torsional behaviour in the case of corner building and soft storey effect in the case of open ground floor. Results show that buildings with traditional infills have lower absolute displacements and inter storey drifts than other configurations, except in the case of open ground floor configuration where a huge inter storey drifts are present at the ground floor. The absolute displacements along the building height confirm appearance of soft storey in the case of traditional infills, resulting in the highest displacements of all configuration even the inter storey drifts at higher floors are low. This is due to the very high displacement in the ground floor producing whole building to move significantly. These negative effects are removed with the application of decoupling resulting in smooth change of displacement and inter storey drift. The soft storey effect is absent in the case of decoupled infill because the decoupling diminishes change of stiffness between the floors that comes from the infill walls. Both absolute displacements and inter storey drifts of the buildings with decoupled infills are in the range of the bare frame configuration. This praznim okvirima u proračunu AB okvirnih konstrukcija sa 8 LITERATURA