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SDEE Hatzigeorgiou Liolios

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  Nonlinear behaviour of RC frames under repeated strong ground motions George D. Hatzigeorgiou a,  , Asterios A. Liolios b a Department of Environmental Engineering, Democritus University of Thrace, GR-67100 Xanthi, Greece b Department of Civil Engineering, Democritus University of Thrace, GR-67100 Xanthi, Greece a r t i c l e i n f o  Article history: Received 19 December 2009Received in revised form6 April 2010Accepted 12 April 2010 a b s t r a c t This paper presents an extensive parametric study on the inelastic response of eight reinforced concrete(RC) planar frames which are subjected to forty five sequential ground motions. Two families of regularand vertically irregular (with setbacks) frames are examined. The first family has been designed forseismic and vertical loads according to European codes while the second one only for vertical loads, tostudy structures which have been constructed before the introduction of adequate seismic design codeprovisions. The whole range of frames is subjected to five real seismic sequences which are recorded bythe same station, in the same direction and in a short period of time, up to three days. In such cases,there is a significant damage accumulation as a result of multiplicity of earthquakes, and due to lack of time, any rehabilitation action is impractical. Furthermore, the examined frames are also subjected toforty artificial seismic sequences. Comprehensive analysis of the created response databank isemployed in order to derive important conclusions. It is found that the sequences of ground motionshave a significant effect on the response and, hence, on the design of reinforced concrete frames.Furthermore, it is concluded that the ductility demands of the sequential ground motions can beaccurately estimated using appropriate combinations of the corresponding demands of single groundmotions. &  2010 Published by Elsevier Ltd. 1. Introduction The past four decades have seen a rapid development of knowledge in seismic analysis and design of reinforced concrete(RC) framed structures. Various rational approaches have beenproposed, which are mainly based on the inelastic materialsbehaviour. The majority of modern seismic design codes, as forexample the European code EC8 [1], permit the structuralnonlinearity. However, even these codes have their drawbackswhere two of them are important. The first is that the structuralbehaviour is usually estimated by a rather irrational manner.More specifically, the design procedure is divided into two stages[1,2]: evaluation of member internal forces by linear analysis of the whole structure followed by the ultimate limit state design of individual cross-sections assuming the ideal nonlinear propertiesof the materials. This design procedure provides no verification of the compatibility between the isolated member and the memberas part of the whole structure. Nowadays, where the capabilitiesof the structural modelling are much larger, an engineer canperform analyses which give considerably better predictionsof stresses, displacements, limit loads and mechanisms of thedamage. The second limitation of these codes is the exclusiveadoption of the isolated and rare ‘design earthquake’ while theinfluence of repeated earthquake phenomena is ignored. Despitethe fact that the problem has been qualitatively acknowledged [3],very few studies have been reported in the literature regardingthe multiple earthquake phenomena. To be sure, Amadio et al. [4]examined the effect of repeated earthquake ground motions onthe nonlinear response of single degree of freedom (SDOF)systems. However, as the authors themselves recognized, theirwork cannot be considered exhaustive since they examined onlyone natural and two artificial ground motions. Recently, Hatzi-georgiou and Beskos [5] and Hatzigeorgiou [6,7] examined the influence of multiple earthquakes in numerous SDOF systems andfound that seismic sequences lead to increased displacementdemands in comparison with the ‘design earthquake’. However,these works are concerned with SDOF and not with RC framedstructures. To the best of the authors’ knowledge, there is onlyone work that has evaluated the effect of repeated earthquakes onconcrete structures where an RC bridge is examined under onereal and one artificial seismic sequence [8]. Thus, the need for thedevelopment of an efficient methodology for the inelastic ana-lysis of RC framed structures, as multi-storey buildings, undersequential ground motions is apparent.This paper presents an extensive parametric study on theinelastic response of eight reinforced concrete planar frames ARTICLE IN PRESS Contents lists available at ScienceDirectjournal homepage: www.elsevier.com/locate/soildyn Soil Dynamics and Earthquake Engineering 0267-7261/$-see front matter  &  2010 Published by Elsevier Ltd.doi:10.1016/j.soildyn.2010.04.013  Corresponding author. Tel./fax: +302541079373. E-mail address:  gchatzig@env.duth.gr (G.D. Hatzigeorgiou). Please cite this article as: Hatzigeorgiou GD, Liolios AA. Nonlinear behaviour of RC frames under repeated strong ground motions. SoilDyn Earthquake Eng (2010), doi:10.1016/j.soildyn.2010.04.013 Soil Dynamics and Earthquake Engineering  ]  ( ]]]] )  ]]] – ]]]  ARTICLE IN PRESS under forty five seismic sequences. This study employs, for thefirst time, as-recorded seismic sequences to determine thenonlinear behaviour of RC framed structures. More specifically,the first five multiple earthquakes have been recorded by thesame station, in the same direction and in a short period of time,up to three days. In such cases, there is a significant damageaccumulation as a result of multiplicity of earthquakes, and due tolack of time, any rehabilitation action is impractical. Furthermore,the examined RC frames are also subjected to forty artificialseismic sequences. Two families of regular and vertically irregular(with setbacks) frames are examined. The first family of frameshas been designed for seismic and vertical loads according toEuropean codes while the second one for vertical loads only, tostudy structures which have been constructed before theintroduction of adequate seismic design code provisions. Thetime-history responses of these concrete frames are evaluated bymeans of the structural analysis software RUAUMOKO [9].Comprehensive analysis of the created response databank isemployed in order to derive significant conclusions. Morespecifically, this study focuses on the results which are relatedto the following critical parameters: local or global structuraldamage, maximum displacements, interstorey drift ratios, devel-opment of plastic hinges and response using the incrementaldynamic analysis ( IDA ) method [10]. The last one is also known as dynamic pushover analysis  [10] and can be characterized as one of the most accepted methods for determining seismic response.It has been used in many applications as for evaluation of the seismic performance of structures [11], for studies related todamage measure [12] and for the validation of simplified proce-dures for the prediction of approximate  IDA  curves [13,14].However, to the best of the authors’ knowledge, the  IDA  techniquehas not yet been applied to examine the structural behaviour of  Fig. 1.  Frames A1 and B1 properties. G.D. Hatzigeorgiou, A.A. Liolios / Soil Dynamics and Earthquake Engineering   ]  ( ]]]] )  ]]] – ]]] 2 Please cite this article as: Hatzigeorgiou GD, Liolios AA. Nonlinear behaviour of RC frames under repeated strong ground motions. SoilDyn Earthquake Eng (2010), doi:10.1016/j.soildyn.2010.04.013  ARTICLE IN PRESS RC structures under multiple or sequential ground motions.Examining the results of this study, it is found that the sequencesof ground motions have a significant effect on the response and,hence, on the design of reinforced concrete frames. Additionally,the accumulation of permanent displacements due to multipleearthquakes is also examined. Finally, a simple and effectivecombination of ductility demands of single events is proposed toestimate the corresponding demand of the sequential groundmotions. 2. Description of structures and modelling  Four structures (Family A — Frames: A1, A2, A3 and A4) areconsidered to represent low-rise (three-storey) and medium-rise(eight-storey) RC buildings for study. They consist of four typicalbeam–column RC frame buildings without shear walls, located ina high-seismicity region of Europe considering both gravity andseismic loads where a design/peak ground acceleration ( PGA ) of 0.2g and soil class B according to EC8 [1] are assumed. Thesestructures have been designed for the following loading combina-tions [1,15]:a) 1.35 G +1.50 Q  b) 1.00 G + c Q  +1.00 E  c) 1.00 G + c Q   1.00 E  where  G ,  Q   and  E   correspond to dead, live and earthquakeloads, respectively, and c is the combination coefficient for liveload, assumed to be  c ¼ 1.00 in this study.Most of the existing reinforced concrete buildings weredesigned according to early seismic provisions or, sometimes,without applying any seismic provision. In order to examine suchbuildings designed for gravity only, another family of structures Fig. 2.  Frames A2 and B2 properties. G.D. Hatzigeorgiou, A.A. Liolios / Soil Dynamics and Earthquake Engineering   ]  ( ]]]] )  ]]] – ]]]  3 Please cite this article as: Hatzigeorgiou GD, Liolios AA. Nonlinear behaviour of RC frames under repeated strong ground motions. SoilDyn Earthquake Eng (2010), doi:10.1016/j.soildyn.2010.04.013  ARTICLE IN PRESS (Family B — Frames: B1, B2, B3 and B4) is also considered. Thus,this group has been designed only for the aforementioned firstloading combination.Families A and B have the same geometry and loads but theyhave different reinforcement. This paper, examining thesefamilies of structures, does not focus into a rigorous comparisonbetween them but mainly into the effect of multiple earthquakeson both of them. The case of shear failure is not examined hereassuming adequate transverse reinforcement. However, thetransverse reinforcement of older RC frames appears to bevery light for columns and for this reason the confinement of concrete is not taken into account for Family B. It is well-knownthat the cross-sectional dimensions of frames designed forseismic loading tend to be larger than those that are not designedto resist seismic forces. However, the identical geometryand loads allow the comparison of structural responses betweenthem since their elastic dynamic properties (periods of vibration,etc.) are also identical. The dead loads (excluding self-weight) andlive loads are equal to 20 and 10kN/m, respectively, and aredirectly applied on the beams. All floors are assumed to be rigid inplan to account for the diaphragm action of concrete slabs.Material properties are assumed to be 20MPa for the concretecompressive strength (concrete grade C20) and 500MPa for theyield strength of both longitudinal and transverse reinforcements(steel grade S500s). Both the examined 3- and 8-storey buildingshave 3 equal bays with total length equal to 15m. Typicalfloor-to-floor height is equal to 3.0m, while for the first floor of the 8-storey buildings the height is equal to 4.0m. Thecharacteristic interior frames of these structures, as shown inFigs. 1–6, represent 2-D models of these buildings. Modalproperties of the first three modes are given in Table 1. Thecolumn and beam dimensions used in this study are typicalframe element proportions in the existing buildings. The3-storey buildings are 9.0m in elevation. All their beams are30cm  40cm, all their columns are square with side 30cm andthe selected longitudinal reinforcement amount (number of barsand diameters in mm) and arrangement, is shown in Figs. 1 and 2.The 8-storey buildings are 25.0m in elevation. All beams havewidth equal to 30cm and height equal to 40–60cm, all columnsare square with side 30–40cm and the selected longitudinalreinforcement, i.e., amount (number of bars and diameters inmm) and arrangement, is shown in Figs. 3–6. It is evident that thereinforcement amount for columns of Family A buildings is higherthan that of Family B buildings. This difference has to do with theconcept of capacity design, i.e., strong columns–weak beams.More specifically, the design of columns of Family A structures Fig. 3.  Frame A3 properties. G.D. Hatzigeorgiou, A.A. Liolios / Soil Dynamics and Earthquake Engineering   ]  ( ]]]] )  ]]] – ]]] 4 Please cite this article as: Hatzigeorgiou GD, Liolios AA. Nonlinear behaviour of RC frames under repeated strong ground motions. SoilDyn Earthquake Eng (2010), doi:10.1016/j.soildyn.2010.04.013
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