Estimating torsional demands in plan irregular buildings using pushover procedures coupled with linear dynamic response spectrum analysis

Transcription

1 Estimating torsional demands in plan irreglar bildings sing pshover procedres copled with linear dynamic response spectrm analysis C. Bhatt 1 and R. Bento 2 1,2 Institto Sperior Técnico, Technical University of Lisbon Av. Rovisco Pais, , Lisbon, Portgal 1 cbhatt@civil.ist.tl.pt, 2 rbento@civil.ist.tl.pt Abstract The limitation of the commonly sed Nonlinear Static Procedres (NSPs), inclding the ones recommended by the seismic codes (Erocode 8 - N2 method, ATC40 and FEMA440 Capacity Spectrm Method, CSM) is their inability to captre the torsional behavior of plan-asymmetric bildings. Fajfar and his team have extended the N2 method to this kind of strctres throgh the application of correction factors which depend on both, linear dynamic response spectrm analysis and pshover analysis. In this paper, the proposed correction factors are applied to the N2 method and to the CSM with the featres recommended in FEMA440 in order to assess the seismic response of three existing plan irreglar bildings. The torsional demands estimated by the aforementioned NSPs are dly compared with the ones defined by means of the most precise nonlinear dynamic analyses for several levels of seismic intensity. The torsional correction factors sed seem to improve the performance of existing code pshover methodologies in estimating the seismic response of plan irreglar strctres. 1 Introdction The se of NSPs on the seismic assessment or design of strctres has gained considerable poplarity in recent years, backed by a large nmber of extensive verification stdies that have demonstrated their relatively good accracy in estimating the seismic response of reglar strctres (planar frames and bridges). However, the extension of sch se to the case of 3D irreglar strctres has been the object of a limited nmber of scientific stdies, which effectively ends p by limiting significantly the se of NSPs to assess actal existing strctres, the majority of which do tend to be non-reglar [1, 2, 3, 4]. The major limitations of the existing NSPs, inclding the ones recommended by the seismic codes (e.g. the N2 method [5, 6] proposed in Erocode 8 [7] and the CSM [8, 9] with the featres presented in ATC40 [10] and in FEMA440 [11]), is their inability to captre the torsional behavior of plan irreglar bildings.

2 2 Generally they cannot captre the torsional effects distorting the real strctral response. Fajfar and his team have developed the Extended N2 method [1, 12] which is able to captre the torsional behavior of plan-asymmetric bildings. This procedre is based on the application of correction factors to the pshover reslts obtained with the N2 method. The correction factors depend on the reslts of a dynamic elastic analysis and of a pshover analysis. Bhatt and Bento have also extended the CSM-FEMA440 to plan asymmetric bildings [13] sing the same correction factors definition proposed by Fajfar. In this paper the reslts obtained in three existing plan irreglar bildings, sing the extended N2 method and the extended CSM-FEMA440 to plan asymmetric strctres, are compared with the nonlinear dynamic median reslts and with the linear response spectrm analysis. The application of torsional correction factors to improve the performance of existing code pshover methodologies in estimating the seismic response of sch strctres is therefore evalated. In the first part of the work, the extension of both code procedres to the 3D case is described. Afterwards, the three case stdies analysed, their modelling options as well as the seismic action considered are depicted. The reslts obtained with the evalated procedres are presented in terms of normalized top displacements in order to better nderstand the torsional response of the bildings. Final conclsions are pointed ot in the end. 2 Torsional correction factors to se in pshover methods Extensive parametric stdies have been performed by Fajfar and his coworkers [1] in order to investigate the parameters that inflence the inelastic torsional response of bilding strctres. Several conclsions were drawn and are herein presented: 1) The inelastic torsional response is qalitatively similar to the elastic torsional response. Qantitatively, the torsional effects depend on the dctility demand, therefore on the grond motion intensity; 2) An pper bond of the torsional amplifications can be estimated with a linear dynamic response spectrm analysis; 3) The torsional effects decrease with the increase of plastic deformations. This trend is clear with the smaller amplification of displacements on the flexible side. However, if the strctre is sbjected to small plastic deformations, characterized by dctility less than 2.0, the amplification on the flexible edge may be slightly higher than in the elastic strctre; 4) The response on the stiff edge depends on the inflence of different modes of vibration and on the grond motion in the transverse direction. This response depends on the strctral and grond motion characteristics in both directions. It is difficlt to make general conclsions abot the response on the stiff side. De-amplification of displacements de to

3 torsion on the stiff side decreases with increasing plastic deformations in elastic torsionally stiff strctres. Sometimes, it cold happen a transition from de-amplification to amplification. In elastic torsionally flexible strctres the amplification de to torsion decreases with increasing plastic deformations; 5) For large plastic deformations, the smaller torsional effects in the inelastic range when compared with the elastic range are sally illstrated by a flattening of the displacement envelopes in the horizontal plane; 6) The dispersion of reslts is larger in the inelastic range than in the elastic regime. 3 Based on the reslts obtained, the following conclsions were taken [1]. They are important for the development of simplified analysis methods and code gidelines: 1) A conservative estimation of the amplification of displacements de to torsion in the inelastic range can be determined by a dynamic elastic analysis; 2) Any redction of displacements on the stiff side compared to the conterpart symmetric bilding, obtained from elastic analysis, will decrease or even disappear in the inelastic range. These conclsions were sed by Fajfar and his team [1, 12] to develop an extension of the N2 method to plan asymmetric bilding strctres. The entire procedre can be smmarized in the following steps: 1) Perform pshover analyses with positive and negative sign for each X and Y direction of a 3D nmerical model. Compte the target displacement displacement demand at the CM at roof level for each direction as the larger vale of the + and sign pshover, sing the original N2 method proposed in Erocode 8; 2) Perform a linear modal response spectrm analysis in two X and Y direction combining the reslts according to the SRSS rle; 3) Determine the torsional correction factors. This factor is compted by the ratio between the normalized roof displacements obtained by the elastic response spectrm analysis and by the pshover analysis. The normalized roof displacement is obtained by normalizing the displacement vale at a specific location with respect to those of the centre of mass (CM). If the normalized roof displacement obtained from the elastic response spectrm analysis is smaller than 1.0, one shold consider 1.0 to avoid any favorable torsional effect (redction of displacements) given by the elastic analysis; 4) Mltiply the qantity nder stdy at a certain location by the correction factor calclated for that location.

4 4 As one can conclde from the previos steps, the extended N2 method ses both nonlinear static pshover and elastic dynamic analysis. The displacement demand and its distribtion along the height at the centre of mass of each storey are determined sing the original N2 method. The amplification of displacements de to torsion is calclated by elastic dynamic analysis. The redction of displacements de to torsion is not taken into accont. The reslts obtained by Fajfar and his team show that this extended procedre leads to conservative estimations of the torsional response of plan asymmetric bildings. In [13] Bhatt and Bento have extended the CSM-FEMA440 to plan asymmetric bildings following the aforementioned procedre sggested by Fajfar. The difference lies in step 1), where the target displacement is calclated sing the CSM with the featres proposed in FEMA Case stdies Three real plan-asymmetric RC bildings were analysed in this endeavor. The first case stdy is the three storey SPEAR bilding. It represents typical existing three-storey bildings in the Mediterranean region following Greece s concrete design code in force between 1954 and This strctre was designed only for gravity loads based on the constrction practice applied in the early 1970s that inclded the se of smooth rebars. A prototype was tested in fll scale at Ispra within the Eropean framework project SPEAR. Frther details on the strctre and its psedo-dynamic testing can be fond in [14] and [15]. The SPEAR bilding is plan-asymmetric in both X and Y directions bt it is reglar in elevation (Figre 1). Fig. 1: Three storey bilding configration: a) in plan; b) at the soth west facade (nits in meters).

5 The second case stdy is a five storey bilding. It is a real Trkish reinforced concrete strctre which experienced the 1999 Golck earthqake withot any damage. The bilding is asymmetric along the X axis, Figre 2a), and all the floors keep the same height, Figre 2b). There are potential weak connections de to the existence of beams framing into beams. There are also walls and elongated colmns (wall-like colmn), as presented in Figre 2a). For more details on the bilding s characteristics see [16]. 5 Fig. 2: Five storey bilding configration (a) Plan View (cm), (b) Lateral View (m). The last case stdy is a real 8 storey Trkish reinforced concrete bilding [17]. It is a plan-asymmetric strctre in both X and Y axis, see Figre 3a). The first storey is 5.0m height and the pper floors are 2.7m height, Figre 3b). There are beams framing into beams leading to possible weak connections in the strctre. There are also walls and elongated colmns (wall-like colmn), as presented in Figre 3a), with the higher dimension always along the Y direction. For this reason, the strctre will be more stiff and resistant along the Y direction. The Trkish five and eight storey bildings were designed according to the 1975 Seismic Code of Trkey. Fig. 3: Eight storey bilding configration (a) Plan View (cm), (b) Lateral View (m).

6 6 4 Modelling options The 3D models representing the bildings nder analysis were developed with the fibre element based finite element program SeismoStrct [18]. They were bilt sing space frames assming the centrelines dimensions. The inelastic behavior of the strctral elements was modelled sing a fibre element model, with each fibre being characterised by the material relationships described below. The concrete was represented by a niaxial model that follows the constittive relationship proposed by Mander et al. [19] and the cyclic rles proposed by Martinez-Reda and Elnashai [20]. The confinement effects provided by the lateral transverse reinforcement are taken into accont throgh the rles proposed by Mander et al. [19] whereby constant confining pressre is assmed throghot the entire stress-strain range. A compressive strength of 25MPa was considered for the SPEAR bilding and 16.7MPa for the Trkish bildings. The constittive model sed for the steel was the one proposed by Menegotto and Pinto [21] copled with the isotropic hardening rles proposed by Filippo et al. [22]. The average yield strength of 360 MPa was assmed for the SPEAR bilding and 371 MPa for the Trkish bildings. The rigid diaphragm modelling calibration of the SPEAR bilding can be fond in [23]. The comparisons between the analytical reslts and the experimental tests for this strctre are described in Bento et al. [24]. 5 Seismic assessment In this section the parametric stdy is described, as well as the seismic action definition and the nmerical model sed in the performed strctral analyses. 5.1 Seismic action Seven bi-directional semi-artificial grond motion records from the SPEAR project fitted to the EC8 [7] elastic design spectrm (Type 1 soil C) were sed in the three storey bilding case. For the five and eight storey bildings, combinations of three bi-directional semi-artificial grond motion records were applied. The three considered grond motions are real records from the PEER s database website [25]. They were fitted to the Erocode 8 elastic design spectrm (with the Trkish code featres Type 1 soil A) sing the software RSPMatch2005 [26]. The grond motions were scaled and applied for a wide range of peak grond intensities in order to assess the performance of the NSPs throghot different levels of strctral inelasticity. The accelerograms were scaled for peak grond accelerations of 0.05, 0.1, 0.2 and 0.3g for the three storey bilding and to 0.1, 0.2, 0.4, 0.6 and 0.8g for the Trkish bildings. The median displacement response spectra of each set of grond motions were sed to compte the nonlinear static procedres response. They are represented in Figre 4a) and b) as defined for the

7 three storey bilding and for the Trkish bildings respectively. In these figres are also plotted the EC8 s response spectra with which the real accelerograms were matched. 7 disp. (mm) disp. (mm) EC8 Median Compatible X Median Compatible Y EC8 Median Compatible T (sec.) Fig. 4 Displacement response spectra a) three storey, b) five and eight storey bildings. 5.2 Strctral analyses performed In the pshover analyses, lateral forces were applied to the strctre in the form of modal load pattern (for the N2 method, a niform distribtion was also applied). The loads were applied independently in the two horizontal positivenegative directions, reslting in for analyses. For each one, the target displacement was compted with the larger vale in each direction being chosen. The reslts were combined in the two directions sing the SRSS combination. For the nonlinear dynamic analysis of the 3 storey SPEAR bilding the aforementioned seven bidirectional semi-artificial grond motion records were applied in 4 different configrations: X+Y+, X+Y-, X-Y-, X-Y+. For the nonlinear dynamic analysis of the Trkish bildings, the abovementioned three bidirectional semi-artificial grond motion records were sed. Each record was applied twice in the strctre changing the direction of the components, reslting in 6 models, each one with five intensity levels for the 5 storey bilding and three intensity levels for the 8 storey bilding. The reslts in terms of normalized top displacements in the two directions were calclated and compared for all seismic intensity levels, and for all nonlinear static and dynamic analyses. T (sec.) 6 Dynamic properties of the case stdies The modal properties of the three analysed bildings are herein presented. The three storey bilding has a fndamental mode of 0.617sec characterized by translation along the X direction, a second mode of 0.527sec with torsional motion and a third mode of 0.441sec with translation along the Y direction. It is mentioning

8 8 that, in this case stdy, both translational modes are copled with torsion. The five storey bilding presents a first mode of 0.617sec with translation along the X direction, a second mode of 0.593sec with translation along the Y direction and a third mode of 0.509sec with torsional motion. Finally the eight storey bilding has a first mode of 1.445sec with translation along the X direction, a second mode of 0.636sec with torsional motion and a third mode of 0.482sec with translation along the Y direction. Frther details on the modal reslts can be fond in [27]. The analysed bildings present torsional featres de to their irreglarities inplan. According to Fajfar [1] the period ratios of a strctre have an important inflence on its torsional behavior. The period ratios Ωx and Ωy are defined as the ncopled translational period divided by the ncopled torsional period in the X and Y directions. The inflence of the predominantly torsional mode of vibration on the response in the direction considered when compared with the predominantly translational mode increases if the period ratio decreases. Strctres with period ratios larger than 1 are sally classified as torsionally stiff and strctres with period ratios smaller than 1 as torsionally flexible. A strctre can be torsionally stiff in one direction and torsionally flexible in the other. In Table 1 are represented the period ratios in the X and Y direction for the three analysed bildings. One can conclde that the three storey bilding is classified as torsionally stiff in the X direction and torsionally flexible in the Y direction. The five storey bilding is torsionally stiff in both X and Y direction. The eight storey bilding is torsionally stiff in the X direction and torsionally flexible in the Y direction. Table 1 Period ratios. Ωx Ωy 3 storey bilding storey bilding storey bilding Reslts of the parametric stdies The reslts obtained with the extension of the N2 method and of the CSM- FEMA440 for plan asymmetric bildings are plotted against the median timehistory nonlinear dynamic reslts (TH), the response spectrm analysis (RSA) and the original procedres, in terms of normalized top displacements. When dealing with plan-asymmetric bildings the normalized top displacements is the measre one shold analyse in order to nderstand the torsional behavior of the strctre [1]. This measre is obtained by normalizing the edge displacement vales with respect to those of the centre of mass. Several plots are presented showing the performance of the analysed procedres in estimating the torsional motion of the evalated bildings.

9 In Figres 5 and 6 and 7 are depicted the reslts of the extended N2 method and in Figres 8, 9 and 10 are presented the reslts of the extended CSM- FEMA440, for the three analysed bildings, for different seismic intensities. More reslts on the performance of the extended N2 method and of the extended CSM- FEMA440 can be fond in [27] and in [13] respectively. From the obtained reslts, one can observe that the two original N2 and CSM- FEMA440 methods lead to similar normalized top displacements in the three analysed bildings. The same happens with both extended procedres. One can conclde that torsional effects are generally higher for lower grond motion intensities. For increasing seismic intensities, one can nderstand a flattening on the normalized top displacements. This can be observed in all the analysed bildings. This conclsion confirms the idea that torsional effects are generally smaller in the inelastic range compared to what happens in the elastic one C8 CM C2 C8 CM C2 Extended N2 N2 TH RSA Fig. 5 Normalized top displacements, three storey bilding a) X direction, 0.1g, b) Y direction, 0.2g S1 CM S23 S1 CM S23 Extended N2 N2 TH RSA Fig. 6 Normalized top displacements, five storey bilding a) X direction, 0.2g, b) X direction, 0.6g.

10 S9 CM S69 S9 CM S69 Extended N2 N2 TH RSA Fig. 7 Normalized top displacements, eight storey bilding a) X direction, 0.2g, b) X direction, 0.4g C8 CM C2 S1 CM S23 RSA CSM FEMA440 Extended CSM FEMA440 TH Fig. 8 Normalized top displacements a) three storey bilding, X direction, 0.1g, b) five storey bilding, X direction, 0.1g. The plots clearly show that the RSA estimates an pper bond of the torsional amplification on the flexible side of the bildings, in both elastic and inelastic range. The extended procedres reprodce in a very good fashion the nonlinear dynamic reslts for all the bildings analysed and throgh all the seismic intensities tested. These methods show, for these case stdies, a mch better performance in estimating the torsional behavior of the bildings than the original methods. Generally the last ones are not capable to reprodce the torsional response of the bildings. The abovementioned plots show that the extended methods reprodce in a very accrate way the torsional amplification on the flexible edge in all the bildings analysed throgh all the increasing intensities. This good performance is jstified becase these extended procedres se a correction factor based on a RSA which also leads to very good estimations of the torsional amplifications, as shown in the

11 plots. The original methods generally nderestimate the torsional amplification of the displacements on the flexible side S1 CM S23 S1 CM S23 RSA CSM FEMA440 Extended CSM FEMA440 TH Fig. 9 Normalized top displacements, five storey bilding a) X direction, 0.2g, b) X direction, 0.6g S9 CM S69 S9 CM S69 RSA CSM FEMA440 Extended CSM FEMA440 TH Fig. 10 Normalized top displacements, eight storey bilding a) X direction, 0.2g, b) X direction, 0.4g. From the plots it is evident that both RSA and the original methods consider the torsional de-amplification on the stiff side of the bildings, leading in some cases to nderestimated reslts. For example, Figre 5b) (colmn C8), Figre 6b) (colmn S23) and Figre 7a) (colmn S69) illstrate the cases where the RSA leads to normalized top displacements smaller than one on the stiff edge, being these reslts non-conservative when compared with the timehistory. Therefore, whenever the RSA leads to normalized top displacements smaller than one, the extended methods consider this vale to be eqal to one. This recommendation avoids the extended methods to prodce non-conservative reslts on this stiff edge. One can say that this is a safe criterion for designing and assessment of strctres. In fact it mst not be forgotten that this simplified procedres are de-

12 12 veloped to be applied in design offices where the reslts shold rather be conservative than almost close to timehistory bt slightly nderestimated. The original methods always provide a linear estimation of the torsional motion from one side of the bilding to the other, throgh all the seismic intensities. The extended methods do not consider any de-amplification of displacements de to torsion, leading in some cases to very accrate reslts and in others to conservative responses on the stiff edge of the bildings. The reslts obtained in this paper seem qite optimistic regarding the implementation of the extended N2 procedre in Erocode 8 and of the extended CSM- FEMA440 in the next version of ATC gidelines. However, one shold be aware that the interplay among grond motion, inelastic amplification or de-amplification of displacements and strctral system is complex. Therefore, more stdies in different bildings shold be developed in order to consolidate these nonlinear static approaches. 8 Conclsions In this work, the torsional seismic response of plan irreglar bildings was assessed sing pshover code procedres N2 method (Erocode 8) and CSM (FEMA440) and their extensions to the 3D case. These improvements are based on torsional correction factors, which depend on a pshover analysis and on a linear dynamic response spectrm analysis. The reslts obtained with the evalated NSPs were compared with the nonlinear dynamic analysis and with the linear response spectrm analysis. The case stdies evalated were three existing plan irreglar bildings with three, five and eight storeys. The procedres were evalated by comparing the reslts in terms of normalized top displacements of the three case stdies for different grond motion intensities. This measre gives an idea abot the torsional behavior of the strctres. The reslts obtained from this stdy showed that torsional effects are in general higher for lower grond motion intensities. In fact, for increasing seismic intensities, one can notice a flattening on the normalized top displacements of each bilding. This confirms the idea that torsional effects are generally smaller in the inelastic range than in the elastic stage. The extended methods performed in a mch more accrate way than their original conterparts in estimating the torsional behavior of all bildings analysed throgh all the seismic intensities tested. They generally captred in a very precise way the torsional amplification in terms of displacements on the flexible side of the bildings. The extended procedres do not take into accont any de-amplification of displacements de to torsion. Therefore, the response on the stiff side of the bildings was in some cases estimated in a very precise way by the methods, and overestimated in others.

13 The original methods are not capable in general to reprodce the torsional motion of the bildings, sally leading to a linear estimation of the torsional motion from one side of the bilding to the other. The original procedres considered the de-amplification on the stiff side of the bildings, nderestimating in some cases the response. On the flexible side, the normalized top displacements were generally non-conservative in respect to the timehistory reslts. Recently, several procedres have been proposed taking into accont torsion in simplified nonlinear static procedres, however definitive answers have not yet been reached. The reslts obtained herein added to the ones already pblished [1, 12, 3, 27, 28], confirm the idea that the extended N2 method has potential to be implemented in the next version of Erocode 8 in order to correctly estimate the torsional response in real plan-asymmetric RC bildings throgh the se of pshover analysis. The extension of the CSM-FEMA440 also presents potential to be incorporated in ftre codes, namely the ATC gideline. However, this procedre shold be frther tested in order to consolidate definitive conclsions. 13 Acknowledgments The athors wold like to thank Dr. Ihsan Bal for providing valable data related to research work on the topic of this article. A special acknowledgment to Dr. Ri Pinho for the valable discssions that certainly enriched the work herein presented. The athors wold like to acknowledge the financial spport of the Portgese Fondation for Science and Technology (Ministry of Science and Technology of the Repblic of Portgal) throgh the research project PTDCECM and throgh the PhD scholarship SFRHBD granted to Carlos Bhatt. References [1] Fajfar P., Marsic D., Pers I. (2005) Torsional effects in the pshover-based seismic analysis of bildings. Jornal of Earthqake Engineering 9(6): [2] Chopra A.K., Goel R.K. (2004) A modal pshover analysis procedre to estimate seismic demands for nsymmetric-plan bildings. Earthqake Engineering and Strctral Dynamics 33: [3] D'Ambrisi A., Stefano M., Tanganelli M. (2009) Use of Pshover Analysis for Predicting Seismic Response of Irreglar Bildings: a Case Stdy. Jornal of Earthqake Engineering 13: [4] Erdran E., Ryan K. (2011) Effects of torsion on the behavior of peripheral steel-braced frame systems. Earthqake Engineering and Strctral Dynamics 40(5): [5] Fajfar P., Fischinger M. (1988) N2 - A method for non-linear seismic analysis of reglar bildings. Proceedings of the Ninth World Conference in Earthqake Engineering, pp Tokyo-Kyoto, Japan. [6] Fajfar P. (2000) A nonlinear analysis method for performance-based seismic design. Earthqake Spectra 16(3): [7] CEN, Comité Eropéen de Normalisation (2004) Erocode 8: Design of strctres for earthqake resistance. Part 1: general rles, seismic actions and rles for bildings. EN :2004. Brssels, Belgim.

14 14 [8] Freeman S.A., Nicoletti J.P., Tyrell J.V. (1975) Evalation of existing bildings for seismic risk - A case stdy of Pget Sond Naval Shipyard, Bremerton, Washington. Proceedings of U.S. National Conference on Earthqake Engineering, pp Berkeley, USA. [9] Freeman S.A. (1998) Development and se of capacity spectrm method. Proceedings of the Sixth U.S. National Conf. Earthqake Engineering. Seattle, Oakland, USA. [10] ATC, Applied Technology Concil (1996) Seismic Evalation and Retrofit of Concrete Bildings, vol. 1 and 2, Report No. ATC-40. Redwood City, CA. [11] ATC (2005) Improvement of Nonlinear Static Seismic Analysis Procedres, FEMA440 Report. Redwood City, CA. [12] Fajfar P., Maršic D., Pers I. (2005) The extension of the N2 method to asymmetric bildings. Proceedings of the 4th Eropean workshop on the seismic behavior of irreglar and complex strctres. Thessaloniki. [13] Bhatt C., Bento R. (2011) Extension of the CSM-FEMA440 to Plan-Asymmetric Real Bilding Strctres. Earthqake Engineering and Strctral Dynamics 40(11): [14] Fardis, M.N. (2002) Design of an Irreglar Bilding for the SPEAR Project -Description of the 3-Storey Strctre. Research Report. University of Patras, Greece. [15] Fardis M.N., Negro P. (2006) SPEAR - Seismic performance assessment and rehabilitation of existing bildings. Proceedings of the International Workshop on the SPEAR Project. Ispra, Italy. [16] Vran E., Bal Y.E., Crowley H., Pinho R. (2008) Determination of eqivalent SDOF characteristics of 3D dal strctres. Proceedings of the 14th World Conference on Earthqake Engineering, pp. S Beijing, China. [17] Bhatt C., Bento R., Pinho R. (2010) Verification of nonlinear static procedres for a 3D plan-irreglar bilding in Trkey. Proceedings of the 14th Eropean Conference on Earthqake Engineering. Ohrid, Macedonia. [18] Seismosoft (2006) Seismostrct - A compter program for static and dynamic nonlinear analysis of framed strctres. Available online from URL: [19] Mander J.B., Priestley M.J.N., Park R. (1988) Theoretical stress-strain model for confined concrete. ASCE Jornal of Strctral Engineering 114(8): [20] Martinez-Reda, J.E., Elnashai, A.S. (1997) Confined concrete model nder cyclic load. Materials and Strctres 30(197): [21] Menegotto M., Pinto P.E. (1973) Method of analysis for cyclically loaded RC plane frames inclding changes in geometry and non-elastic behavior of elements nder combined normal force and bending. Symposim on the Resistance and Ultimate Deformability of Strctres anted on by well defined loads, International Association for Bridges and Strctral Engineering, pp Zrich, Switzerland. [22] Filippo F.C., Popov E.P., Bertero V.V. (1983) Modelling of RC joints nder cyclic excitations. Jornal of Strctral Engineering 109(11): [23] Pinho R., Bhatt C., Antonio S., Bento R. (2008) Modelling of the horizontal slab of a 3D irreglar bilding for nonlinear static assessment. Proceedings of the 14th World Conference on Earthqake Engineering, pp Beijing, China. [24] Bento R., Bhatt C., Pinho R. (2010) Using Nonlinear Static Procedres for Seismic Assessment of the 3D Irreglar SPEAR Bilding. Earthqakes and Strctres 1(2): [25] PEER (2009) Strong Grond Motion Database, Available from: [26] Hancock J., Watson-Lamprey J., Abrahamson N.A., Bommer J.J., Markatis A., McCoy E., Mendis R. (2006) An improved method of matching response spectra of recorded earthqake grond motion sing wavelets. Jornal of Earthqake Engineering 10(S1): [27] Bhatt C, Bento R. (2011) Assessing the Seismic Response of Existing RC Bildings Using the Extended N2 Method. Blletin of Earthqake Engineering 9(4): [28] Koren D., Kilar V. (2011) The applicability of the N2 method to the estimation of torsional effects in asymmetric base-isolated bildings. Earthqake Engineering and Strctral Dynamics 40(8):