A Target Displacement For Pushover Analysis To Estimate .

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Journal of Rehabilitation in Civil Engineering 7-3 (2019) 103-116journal homepage: http://civiljournal.semnan.ac.ir/A Target Displacement for Pushover Analysis toEstimate Seismic Demand of Eccentrically BracedFramesA. Fakhraddini 1 , M. J. Fadaee 2* and H. Saffari 21. Shahid Bahonar University of Kerman, Kerman, Iran2. Department of Civil Engineering, Shahid Bahonar University of Kerman, Kerman, IranCorresponding author: mjfadaee@uk.ac.irARTICLE INFOArticle history:Received: 17 December 2017Accepted: 14 July 2018Keywords:Pushover Analysis,Seismic Assessment,Target Displacement,Eccentrically Braced Frames.ABSTRACTA main challenge for performance-based seismic engineeringis to develop simple, practical and precise methods eperformance objectives. Pushover analysis is a simplifiednonlinear analysis technique that can be implemented forestimating the dynamic demands imposed on a structureunder earthquake excitations. In this method, structure issubjected to specified load pattern to reach a isplacement for estimating the seismic demand ofeccentrically braced frames (EBFs). A parametric study isconducted on a group of 30 EBFs under a set of 15accelerograms. The results of nonlinear dynamic analyses ofEBFs have been post-processed by nonlinear regressionanalysis and a relation is proposed for target displacement. Inorder to verify the capability of the proposed procedure,three EBFs are assessed by the present method in which theresults show that the proposed method is capable ofreproducing the peak dynamic responses with relatively goodaccuracy. Additionally, the comparison of obtained resultswith those of other conventional target displacementmethods such as N2 method, and displacement coefficientmethod confirms the efficiency of the suggested one.1. IntroductionFormerly, elastic analysis was the major toolin seismic design of structures. However,DOI: 10.22075/JRCE.2018.13427.1245behavior of structures during severeearthquakes indicates that relying on justelastic analysis is not adequate. Alternatively,nonlinear dynamic analysis, while providesaccurate results, is time consuming and such

104A. Fakhraddini et al./ Journal of Rehabilitation in Civil Engineering 7-3 (2019) 103-116analysis must be repeated for a group ofacceleration time histories and needsextensiveinterpretationofresults.Researchers have long been interested indeveloping prompt and practical methods tosimulate nonlinear behavior of structuresunder earthquake loads. During the lastdecade, the nonlinear static pushover analysishas been gaining ground among the structuralengineering society as an alternative mean ofanalysis. The purpose of the pushoveranalysis is to assess the structuralperformance by estimating the strength anddeformation capacities using static nonlinearanalysis and comparing these capacities withthe demands at the correspondingperformance levels. The assessment is basedon the estimation of important structuralparameters, such as global and inter-storydrift, element deformations and internalforces. The analysis accounts for thegeometrical nonlinearity and materialinelasticity, as well as the redistribution ofthe internal forces.In static pushover analysis, the starting pointis to calculate a target displacement and apredefined lateral load pattern. Subsequently,a static analysis of the structural model iscarried out to reach the target displacement.The load pattern is applied step by step untilstructure reaches a predetermined targetdisplacement. Various target displacementsare recommended in valid codes to perform apushover analysis. One of the first stepstaken in this approximate solution is to assessthe maximum roof displacement, known astarget displacement.Typically, the traditional procedure is to pushthe structure with a target displacement suchas capacity spectrum, and coefficient methodby means of a lateral load distribution. Thecapacity spectrum method (CSM) [1] isknown as a seismic evaluation method insome guidelines [2, 3]. This method is able topredict the demands of forces anddeformations of low to medium buildings.Some researchers in earthquake engineeringhave made lots of efforts to develop therelated theory and application for pushoveranalysis.Fajfar[4]proposedacomprehensive, relatively simple, N2 methodfor seismic damage analysis of reinforcedconcrete buildings. The N2 method as aspecial form of the CSM has beenimplemented in the Eurocode-8 [5], in whichthe demand is represented by an inelasticspectrum. Chopra and Goel [6, 7] establishedthe demand diagram of an inelastic systemaccording to the constant-ductility inelasticresponse spectra, and calculated the ductilityfactor of the system based on the intersectionpoint of capacity and demand diagrams.Gencturk and Elnashai [8] developed anadvanced CSM, incorporating the inelasticresponse history analysis of SDOF system, inwhich the updating bilinear idealization ofstructural system according to the selectedtrial performance point on the capacitydiagram improves the accuracy of CSM.Displacement Coefficient Method (DCM)defined in ASCE41-13 [9] is based on thecapacity diagram derived from staticpushover analysis. However, these methodsfor estimating seismic demands have somedrawbacks [10-11].The principal objective of this study is toprovide a pushover analysis procedure basedon a new target displacement for estimatingseismic demands of steel eccentrically bracedframes. For this purpose, a parametric studyis conducted on a group of 30 EBFs under aset of 15 far-field and near-fieldaccelerograms scaled to different amplitudesto adapt various performance levels. Theresults of nonlinear dynamic analyses of

A. Fakhraddini et al./ Journal of Rehabilitation in Civil Engineering 7-3 (2019) 103-116EBFs have been post-processed by nonlinearregression analysis in order to extract relationfor target displacement. The capability andvalidity of proposed method is evaluatedthrough nonlinear dynamic analysis asbenchmark solutions. The results indicatethat the proposed method has goodestimation of inter-story drifts rather thanthose of N2, and DCM.2. Review of Some Existing Methodsof Target Displacement2.1 Displacement Coefficient MethodDisplacement Coefficient Method (DCM)expressed in ASCE41-13 [9] is based on thecapacity diagram derived from staticpushover analysis. In this technique, thegreatest displacement demand is obtainedusing some coefficients. Target displacementis shown by δt. Computation of performancepoint is depicted in Fig. 1 [9]. The target roofdisplacement can be determined as follows: T 2 t C 0C 1C 2 S a e 2 4 g (1)where C0 is a modification factor that relatesspectral displacement of an equivalent singledegree-of-freedom (SDOF) system to theroof displacement of the multi-degree-offreedom (MDOF) system, C1 is amodification factor to relate expectedmaximum inelastic displacements todisplacements calculated from a linear elasticanalysis, C2 is a modification factor torepresent the effect of hysteretic behavior onthe maximum displacement response, Sa isthe response spectrum acceleration at theeffective fundamental vibration period anddamping ratio of the building underconsideration, and Te is the effectivefundamental period of the structures.105Fig. 1. Determination of performance point by DCM[9].2.2. N2 MethodOne of simplified nonlinear methods is theN2 method [4, 5]. The N2 method combinespushover analysis of a MDOF system withthe response spectrum analysis of anequivalent SDOF model. According to theN2 method, the following procedure isemployed in order to compute the peak floordisplacements of the EBFs.In this method, in order to obtain the capacitydiagram, the frame is pushed with a targetdisplacement equal to 10 percent of thestructure's height at the first step. The 15selected ground motions are scaled for threeperformance levels and response spectraresulting from each of records are drawn.Inelastic demand spectra are determined fromthe elastic design spectra [12] and convertedinto acceleration displacement responsespectra (ADRS) format that provides thedemand spectrum. The intersection of thecapacity spectrum and demand spectrumprovides an estimate of the inelasticacceleration and displacement demand.Capacity diagrams are idealized with elastic–perfectly plastic curves. (Fig. 2).

106A. Fakhraddini et al./ Journal of Rehabilitation in Civil Engineering 7-3 (2019) 103-116three stories possess columns with W14x311section sizes, while the three higher storiespossess columns with W14x132 sectionsizes.Fig. 2. Idealization of capacity curve by N2method [5].3. Parametric StudyFig. 3. Typical configuration of EBFs.3.1. Description of the Case StudyStructures3.2. Earthquke Ground MotionsIn order to obtain relation for the targetdisplacement, a group of thirty eccentricallybraced frames has been used. Typicalconfiguration of 2-D frames is shown in Fig.3. The uniform story height and bay lengthare 360 and 900 cm, respectively. Thenumber of stories of the frames, ns, takes thevalues 3, 6, 9, 12 and 15. Taking the linklength, e, equal to aL (see Fig. 3), six values,0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 are assigned forparameter a, in the design phase.Fifteen different ground motions areconsidered for the nonlinear time historyanalysis of this study. This category includesboth far-field and near-field records [17]. Thenear-field ground motion selected from SAC[18] database and far-field records selectedfrom FEMA P695 [19]. The records areavailable in the Pacific r.berkeley.edu/smcat. The basicparameters of the records are summarized inTable 2 as well as their elastic responsespectra shown in Fig. 4.43.5Pseudo-acceleration (g)All frames have three bays with simplebeam-to-column connections. The uniformdead and live loads of all beams are 2.1 and1.05 ton/m, respectively. The EBFs havebeen designed based on AISC 360-10 [13],AISC 341-10 [14] and ASCE7-10 [15] usingETABS [16] software. All frames areassumed to be founded on firm soil, class Cof NEHRP, and located in the region ofhighest seismicity. The yield strength of steelis assumed as 3515 kg/cm2 for all structuralmembers. Final section sizes of all frames aresummarized in Table 1. In this table, phraseslike 3(14x311) 3(14x132) show that the first32.521.510.5000.511.522.533.5Period (Sec)Fig. 4. Acceleration spectra of the 15 selectedrecords.4

A. Fakhraddini et al./ Journal of Rehabilitation in Civil Engineering 7-3 (2019) 103-116Table 1. Section sizes of the EBFs.3-StoryEBFsnLinklengtha e/ 30)3(14x30)3(14x30)3(14x30)3(14x38) 3(14x38)3(14x38) 3(14x30)3(14x38) 3(14x30)3(14x38) 3(14x30)3(14x38) 3(14x30)3(14x38) 3(14x30)3(14x48) 3(14x38) 3(14x30)3(14x48) 3(14x38) 3(14x30)3(14x48) 3(14x38) 3(14x30)3(14x48) 3(14x38) 3(14x30)3(14x48) 3(14x38) 3(14x30)3(14x48) 3(14x38) 3(14x30)3(14x61) 3(14x48) 3(14x38) 3(14x30)3(14x61) 3(14x48) 3(14x38) 3(14x30)3(14x61) 3(14x48) 3(14x38) 3(14x30)3(14x61) 3(14x48) 3(14x38) 3(14x30)3(14x61) 3(14x48) 3(14x38) 3(14x30)3(14x61) 3(14x48) 3(14x38) 3(14x30)3(14x68) 3(14x61) 3(14x48) 76)3(14x176)3(14x311) 3(14x132)3(14x311) 3(14x132)3(14x311) 3(14x132)3(14x311) 3(14x132)3(14x426) 3(14x176)3(14x426) 3(14x176)3(14x500) 3(14x311) 3(14x132)3(14x500) 3(14x311) 3(14x132)3(14x500) 3(14x311) 3(14x132)3(14x500) 3(14x311) 3(14x132)3(14x665) 3(14x426) 3(14x176)3(14x665) 3(14x426) 3(14x176)3(14x665) 3(14x500) 3(14x311) 3(14x132)3(14x665) 3(14x500) 3(14x311) 3(14x132)3(14x665) 3(14x500) 3(14x311) 3(14x132)3(14x665) 3(14x500) 3(14x311) 3(14x132)3(14x730) 3(14x665) 3(14x426) 3(14x176)3(14x730) 3(14x665) 3(14x426) 3(14x176)3(14x730) 3(14x665) 3(14x500) Link beam*3(14x48)14x53 2(14x48)2(14x53) 14x482(14x68) 14x532(14x68) 14x532(14x132) 14x822(14x53) 3(14x48)2(14x68) 4(14x48)4(14x68) 2(14x48)14x82 2(14x74) 2(14x68) 14x482(14x132) 4(14x68)4(14x132) 2(14x68)4(14x53) 5(14x48)Gravitybeam*(all 14x10914x10914x10914x10914x10914x109brace **Periods (Sec.)T1, T2, T32(6x1/2) 6x1/46x1/2 2(6x1/4)6x1/2 2(6x1/4)8x1/2 6x1/2 6x1/48x1/2 6x1/2 6x1/42(6x1/2) 6x1/45(6x1/2) 6x1/43(6x1/2) 3(6x1/4)3(6x1/2) 3(6x1/4)4(6x1/2) 2(6x1/4)4(6x1/2) 2(6x1/4)4(6x1/2) 2(6x1/4)7(6x1/2) 29,0.58,0.331.60,0.61,0.331.23,0.44,0.253(14x68) 2(14x53) 4(14x48)6(14x68) 14x53 2(14x48)3(14x82) 2(14x74) 3(14x68) 14x485(14x132) 14x82 3(14x68)14x1097(6x1/2) 2(6x1/4)1.42,0.58,0.3314x1096(6x1/2) 3(6x1/4)1.54,0.58,0.3514x1097(6x1/2) 2(6x1/4)1.59,0.62,0.3614x1096(6x1/2) 3(6x1/4)1.61,0.72,0.407(14x132) 2(14x68)14x1097(6x1/2) 2(6x1/4)1.63,0.78,0.444(14x68) 2(14x53) 6(14x48)14x1099(6x1/2) 3(6x1/4)1.62,0.56,0.338(14x68) 4(14x48)14x1099(6x1/2) 3(6x1/4)1.71,0.74,0.413(14x132) 4(14x82) 3(14x74) 2(14x68)3(14x132) 4(14x82) 3(14x74) 2(14x68)9(14x132) 14x82 14x74 14x686(14x132) 6(14x132)14x1099(6x1/2) 3(6x1/4)1.87,0.80,0.4214x1098x1/2 8(6x1/2) 3(6x1/4)1.99,0.88,0.4414x1096(8x1/2) 3(6x1/2) 3(6x1/4)2.08,0.90,0.4514x1097(8x1/2) 3(6x1/2) 2(6x1/4)2.14,0.98,0.518(14x68) 2(14x53) 5(14x48)14x1095(8x1/2) 8(6x1/2) 2(6x1/4)1.93,0.67,0.38107

108A. Fakhraddini et al./ Journal of Rehabilitation in Civil Engineering 7-3 (2019) 103-1163(14x38) 3(14x311) 3(14x30)3(14x132)0.23(14x68) 3(14x730) 14x132 14x1093(14x61) 3(14x665) 2(14x82) 3(14x48) 3(14x500) 3(14x74) 3(14x38) 3(14x311) 9(14x68)3(14x30)3(14x132)0.33(14x68) 3(14x730) 7(14x132) 14x1093(14x61) 3(14x665) 3(14x82) 3(14x48) 3(14x500) 2(14x74) 3(14x38) 3(14x311) 2(14x68)3(14x30)3(14x132)0.43(14x68) 6(14x730) 10(14x132) 14x1093(14x61) 3(14x500) 14x82 3(14x48) 3(14x370) 14x74 3(14x38) 3(14x145)3(14x68)3(14x30)0.53(14x68) 6(14x730) 2(14x159) 14x1093(14x61) 3(14x665) 3(14x145) 3(14x48) 3(14x426) 7(14x132) 3(14x38) 3(14x176)14x82 3(14x30)14x74 14x680.63(14x68) 6(14x730) 5(14x176) 14x1093(14x61) 3(14x665) 2(14x159) 3(14x48) 3(14x426) 2(14x145) 3(14x38) 3(14x176)5(14x132) 3(14x30)14x68* These elements, are W-type pattern. ** These elements, are HSS-type pattern.5(8x1/2) 8(6x1/2) 2(6x1/4)2.02,0.75,415(8x1/2) 8(6x1/2) 2(6x1/4)2.13,0.75,0.417(8x1/2) 6(6x1/2) 2(6x1/4)2.30,0.81,0.439(8x1/2) 5(6x1/2) 6x1/42.42,0.85,0.4611(8x1/2) 3(6x1/2) 6x1/42.56,0.88,0.51Table 2. Characteristics of earthquake ground motions.EventRSN821 ERZINCAN ERZ-EWRSN1106 KOBE KJM000RSN1120 KOBE TAK000RSN879 LANDERS LCN260RSN3548 LOMAP LEX000RSN828 CAPEMEND PET000RSN1063 NORTHR RRS228RSN143 TABAS TAB-L1RSN125 FRIULI.A A-TMZ000RSN169 IMPVALL.H H-DLT262RSN1116 KOBE SHI000RSN848 LANDERS CLW-LNRSN900 LANDERS YER270RSN752 LOMAP CAP000RSN953 NORTHR 536.97.287.286.936.69MechanismStrike slipStrike slipStrike slipStrike SlipReverse ObliqueReverseReverseReverseReverseStrike SlipStrike SlipStrike SlipStrike SlipReverse ObliqueReverseRjb 6215.239.44PGA 80.240.510.443.3. Computational Methodology andFramewrk of the Present Studybehavior of the link beams with short,intermediate and long length.The 30 EBFs of Table 1 are analyzed todetermine their response to each of the 15seismic excitations of Table 2. TheOPENSEES [20] software has beenemployed for the nonlinear time historyanalyses. In EBFs, the inelastic response oflink beam has been modeled by means of theapproach that proposed by Bosco et. al [21].The model simulates the effect of the shearforce and flexural bending on the inelasticThe link model includes five elementsconnected in series as shown in Fig. 5. Themiddle element (EL0) has the identicallength and moment of inertia of the link andtakes the flexural elastic response of the linkinto account. There are two zero lengthelements (EL1 and EL2) in this simulation.Whereas (EL1) considers the elastic andinelastic shear response of half a link, (EL2)considers the inelastic flexural response of

A. Fakhraddini et al./ Journal of Rehabilitation in Civil Engineering 7-3 (2019) 103-116the ending part of the link. The nodes of EL1and EL2 are permitted to have independentlyrelative vertical displacements and relativerotations, respectively [21].MEL2MEL2VVEL0EL1eEL1Fig. 5. Modelling of the link [21].Beams, columns, braces and beam segmentsoutside of the links are modelled with the aidof elastic elements to remain essentiallyelastic. Based on Bosco model [21], thematerials of shear and flexural springs aredefined as uniaxial material BrbDallAsta[20]. Elastic beam-column element is used tomodel beams and columns. Braces have beenmodeled by means of truss element. TheRayleigh damping is considered in theanalyses. Stiffness and mass coefficients arespecified in order that the first and the thirdmodes of the frame are determined by anequivalent viscous damping factor equal to0.05.For each pair of frame and ground motion,the scale factors (SF) of the ground motionwhich correlate to a specific performancelevel are determined by IncrementalDynamic Analysis (IDA). The peak interstory drifts have been recorded at thefollowing performance levels based onacceptance criteria of ASCE 41-13 [9]: Immediate Occupancy (IO) of theframe (target drift 0.005 oracceptance criteria of link rotationangle).Life Safety (LS) of the frame (targetdrift 0.02 or acceptance criteria oflink rotation angle).109 Collapse Prevention (CP) of theframe ( target drift 0.03 oracceptance criteria of link rotationangle)The peak inter-story drifts at the time that theframe reaches to a desired performance levelare recorded to generate the databank forEBFs. This procedure includes finding ascale factor (SFi, i 1, 2, 3) of the groundmotion for each pair of EBF and groundmotion, such that the response of the frame tobe in the performance level [22-28].Subsequently, the ground motion ismultiplied by SFi and through running threenonlinear time history analyses. Finally, thecorresponding three peak inter-story driftpatterns of each frame are derived.3.4. Proposed Target Displacement inPushover AnalysisIn the following section, simple formula isproposed to estimate an approximate targetdisplacement in regular EBFs. The targetdisplacement of each pair of frame andground motion is obtained by the summationof the peak inter-story drift at each floor.n t i(2)i 1where t is the target displacement of theroof and i is the peak inter-story drift at ithfloor. The Levenberg-Marquardt algorithm ofSPSS software [29] is employed fornonlinear regression analysis. By analyzingthe response databank, it is specified that, themain parameters affecting the targetdisplacement are the number of stories (n),performance level and the ratio of link length(e) to span length (L). Therefore, a proposedformula is developed for estimating of thetarget displacement of EBFs based ondisplacement coefficient method [9].

110A. Fakhraddini et al./ Journal of Rehabilitation in Civil Engineering 7-3 (2019) 103-116 e t C 0C 1IDR . L 0.2 T2 20n 0.45 S a 2 g 4 (3)where IDR (Inter-story Drift Ratio) relatesthe performance level to the targetdisplacement, g is acceleration of gravity, Sais pseudo acceleration spectrum and T is thefundamental period.It is worth noting that nonlinear regressionfor matching nonlinear random functions isbased on the data derived from independentvariables to reach the maximum value of thecoefficient of determination (R2). R2 is theproportion of the variance in the dependentvariable that is predictable from theindependent variables. In this study, thecoefficient R2 for Eq. (3) is taken equal to92.2.4. ValidationMethodoftheProposedIn order to assess the accuracy of theproposed target displacement, the resultsobtained with the approx

decade, the nonlinear static pushover analysis has been gaining ground among the structural engineering society as an alternative mean of analysis. The purpose of the pushover analysis is to assess the structural performance by estimating the strength and deformation capacities using static nonlinear analysis and comparing these capacities with the demands at the corresponding performance .

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