selection of seismic excitations for nonlinear analysis of reinforced concrete frame buildings ...

Selection of seismic excitations for nonlinearanalysis of reinforced concrete frame buildings1

Lan Lin, Nove Naumoski, Murat Saatcioglu, Simon Foo, Edmund Booth,and Yuling Gao

Abstract: The selection of seismic motions is one of the most important issues for the time-history analysis of buildings.This paper discusses four different methods for obtaining spectrum-compatible acceleration time histories (i.e.,accelerograms) of seismic motions. Based on these methods, four sets of accelerograms compatible with the designspectrum for Vancouver were selected for this study. These included (i) scaled real accelerograms, (ii) modified realaccelerograms, (iii) simulated accelerograms, and (iv) artificial accelerograms. The selected sets were used as excitationmotions in the nonlinear analysis of three reinforced concrete frame buildings designed for Vancouver. The buildingsincluded a 4-storey, a 10-storey, and a 16-storey building, which can be considered representative of low-rise, medium-rise,and high-rise buildings, respectively. The storey shears, interstorey drifts, and curvature ductilities for beams and columnsobtained from the analysis were used for the evaluation of the effects of the selected sets on the responses of the buildings.Based on the results from the analysis, scaled real accelerograms are recommended for use in time-history analysis ofreinforced concrete frame buildings.

Key words: seismic response, accelerogram, spectrum, reinforced concrete, building, analysis, drift, curvature ductility.

Résumé : Le choix des mouvements sismiques est l’une des questions les plus importantes de l’analyse de l’historiquetemporel des bâtiments. Cet article aborde quatre méthodes différentes pour obtenir des historiques temporels d’accélérationdes mouvements sismiques (c.-a-d. accélérogrammes) selon le spectre. En se basant sur ces méthodes, quatre ensemblesd’accélérogrammes compatibles avec le spectre de réponse pour Vancouver ont été choisis pour cette étude. Ilscomprenaient (i) des accélérogrammes réels proportionnés, (ii) des accélérogrammes réels modifiés, (iii) desaccélérogrammes simulés et (iv) des accélérogrammes artificiels. Ces ensembles sélectionnés ont été utilisés commemouvements d’excitation dans l’analyse non linéaire de trois immeubles a ossature de béton armé conçus pour Vancouver.Les immeubles comprenaient un immeuble de quatre étages, un de 10 étages et un de 16 étages, ce qui peut être considérécomme respectivement représentatif d’immeubles de faible hauteur, de moyenne hauteur et de grande hauteur. Les effortstranchants aux étages, les mouvements inter-étages et la réponse ductile de la courbure pour les poutres et les colonnestirés de l’analyse ont été utilisés pour évaluer les effets des ensembles choisis sur les réponses des immeubles. En se basantsur les résultats de l’analyse, il est recommandé d’utiliser les accélérogrammes réels proportionnés lors de l’analyse del’historique temporel des immeubles a ossature de béton armé.

Mots-clés : réponse sismique, accélérogramme, spectre, béton armé, immeuble, analyse, mouvement, réponse ductile de lacourbure.

[Traduit par la Rédaction]

Introduction

The nonlinear time-history analysis is the most reliablemethod for the assessment of the behaviour of buildings sub-jected to seismic loads. It has been widely used in research onthe performance of buildings with the purpose of the valida-tion and the improvement of the code provisions for seismicdesign. In recent years, the nonlinear time-history analysis has

been extensively used for research related to performance-based earthquake engineering (Moehle and Deierlein 2004). Indesign practice, the application of nonlinear analysis is verylimited, and has been used only for the seismic evaluation ofimportant buildings.

Given the progress in earthquake engineering in the last fewdecades and the availability of new-developed advanced meth-ods and software for nonlinear modelling and analysis of

Received 16 April 2011. Revision accepted 6 September 2012. Published at www.nrcresearchpress.com/cjce on XX October 2012.

L. Lin and Y.L. Gao. Department of Building, Civil and Environmental Engineering, Concordia University, 1455 boul. de Maisonneuveouest, Montreal, QC H3G 1M8, Canada.N. Naumoski and M. Saatcioglu. Department of Civil Engineering, University of Ottawa, 161 Louis Pasteur St. Ottawa, ON K1N 6N5,Canada.S. Foo. Public Works and Government Services Canada, Place du Portage, Phase III - 8A1, Gatineau, QC K1A 0S5, Canada.E. Booth. Edmund Booth, Consulting Engineer, 2 Miswell Cottages, Icknield Way, Tring HP23 4JU, United Kingdom.

Corresponding author: Lan Lin (e-mail: [email protected]).1This paper is one of a selection of papers in this Special Issue on Innovations and IT.

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Can. J. Civ. Eng. 39: 1–16 (2012) Published by NRC Research Pressdoi:10.1139/l2012-103

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http://dx.doi.org/10.1139/l2012-103

buildings, recent editions of modern building codes allow theuse of nonlinear dynamic analysis in the design of buildingslocated in seismic regions (e.g., Standards New Zealand 2004;NRCC 2010; ASCE 2010). To perform nonlinear dynamicanalysis, acceleration time histories (i.e., accelerograms) of theseismic excitations are needed. The codes require that theseaccelerograms be compatible with the design spectrum. Themain issues related to the use of spectrum-compatible accel-erograms are: the types of accelerograms (recorded or artifi-cial) for use in the analysis, the method for the selection andscaling of the spectrum-compatible accelerograms, and thenumber of the accelerograms needed for the analysis. TheNational Building Code of Canada (NBCC) (NRCC 2010),which also requires the use of spectrum-compatible accelero-grams, does not provide guidance for the foregoing issues.Given this, the specifications for spectrum-compatible accel-erograms prescribed in the US Standard ASCE/SEI 7–10(ASCE 2010) are used in this study. The use of this Standardis considered appropriate since the Canadian and the USseismic design requirements are quite similar.

According to the ASCE Standard, a minimum of threeaccelerograms are required for two-dimensional analyses ofbuildings. Real (i.e., recorded) accelerograms are preferred foruse in the analysis. Artificial accelerograms can be used ifappropriate real accelerograms are not available. Regardingthe spectrum compatibility, ASCE requires that the selectedaccelerograms are properly scaled such that the 5% dampedmean spectrum of the set is above the design spectrum for allperiods between 0.2T and 1.5T, where T is the fundamentalperiod of the building for the direction of the response beinganalysed. The ASCE Standard also requires that if less thanseven accelerograms are used, then the maximum values of theresponses should be considered for the design. If seven ormore excitations are used, then the average values of theresponse parameters should be used in the design.

In the past, different approaches have been used for the selectionand scaling of spectrum-compatible accelerograms for use in non-linear analyses. In Canada, several studies have been conductedusing eight accelerograms for eastern and eight accelerograms forwestern Canada simulated by Atkinson and Beresnev (1998) (e.g.,Tremblay and Atkinson 2001; Dincer 2003; Amiri-Hormozaki2003). Also, different scaling methods have been used (e.g.,scaling to the spectral ordinate at the fundamental buildingperiod, and scaling to the spectral area) as discussed in Amiri-Hormozaki (2003). Very recently, Atkinson (2009) generateda comprehensive library of simulated accelerograms for east-ern and western Canada. Because of the lack of recordedmotions from Canadian earthquakes, it is expected that theseaccelerograms will be extensively used in the future.

While different methods for the selection and scaling ofaccelerograms are in use, very few investigations on the ef-fects of different types of accelerograms on the nonlinearresponse have been conducted so far. Naeim and Lew (1995)reported that accelerograms scaled in the frequency domainare not appropriate for use in the seismic design since theymight have unrealistic velocities, displacements, and energycontent. Lew et al. (2008) suggested that to cover all theresponse effects, tall buildings need to be analysed using muchmore ground motion accelerograms than the sets of three orseven accelerograms that are normally used in the current

design practice. Naumoski et al. (2006) investigated the non-linear responses of two 6-storey and one 5-storey buildings,and reported significant differences in the responses from theaccelerograms simulated by Atkinson and Beresnev (1998)and those from scaled accelerograms.

This paper discusses four different methods for the selectionof spectrum-compatible seismic excitations for use in nonlin-ear analysis. Based on these methods, four sets of accelero-grams were selected for this study. Nonlinear time-historyanalyses were conducted on three reinforced concrete framebuildings designed for Vancouver (i.e., a 4-storey, a 10-storey,and a 16-storey building) by subjecting the building models tothe selected sets of accelerograms. The nonlinear responses arepresented in terms of maximum interstorey drifts, curvatureductilities for beams and columns, and storey shears.

Description of buildings and designparameters

The buildings considered in this study are shown in Fig. 1.They are for office use and are located in Vancouver, which isin a high seismic hazard zone (NRCC 2010). The buildings areidentical in plan but have different heights. As seen in Fig. 1,the buildings include a 4-storey, a 10-storey, and a 16-storeybuilding, which can be considered representative of low-rise,medium-rise, and high-rise buildings, respectively.

The plan of each building is 27.0 m � 63.0 m. The storeyheights are 3.65 m. The lateral load resisting system consistsof moment-resisting reinforced concrete frames in both thelongitudinal and transverse directions. There are four frames inthe longitudinal direction (designated Le and Li in Fig. 1;Le — exterior frames, and Li — interior frames) and eightframes in the transverse direction (Te and Ti). The distancebetween both the longitudinal and transverse frames is 9.0 m.Secondary beams between the longitudinal frames are used atthe floor levels to reduce the depth of the floor slabs. Thesecondary beams are supported by the beams of the transverseframes. The floor system consists of one-way slab spanning inthe transverse direction, supported by the beams of the longi-tudinal frames and the secondary beams. The slab is castintegrally with the beams.

In this study, the interior transverse frames (Ti) of thebuildings were considered. For ease of discussion, the4-storey, the 10-storey, and the 16-storey frames are referredto as the 4S, the 10S, and the 16S frames, respectively. Theframes were designed as ductile reinforced concrete frames inaccordance with the National Building Code of Canada(NBCC) (NRCC 2005). Note that the design would be thesame if it were done according to the latest edition, i.e., 2010edition of NBCC (NRCC 2010). The design base shears werecalculated using the seismic design spectrum for Vancouver.The foundations were assumed to be on stiff soil representedby site class C in NBCC (shear wave velocity between 360 m/sand 750 m/s). The fundamental periods of the frames, fordetermining the base shears, were calculated according to thecode formula, Ta � 0.075hn

3/4, where hn is the height of theframe above the base in metres. The other parameters used inthe calculation of the base shears were the ductility-relatedforce modification factor Rd � 4, the overstrength-relatedforce modification factor Ro � 1.7, the higher mode factorMv � 1, and the importance factor IE � 1. The resulting baseshear coefficients (V/W, where V is the base shear and W is the


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total dead load) for the 4S, the 10S, and the 16S frames were0.089, 0.046, and 0.035, respectively.

Compressive strength of concrete fc= � 30 MPa, and yieldstrength of reinforcement fy � 400 MPa were used in thedesign. The dimensions of the beams and columns, and thereinforcement obtained from the design are given in Lin(2008).

Modelling of frames for dynamic analysisInelastic models of the frames were developed for use in the

two-dimensional (2D) inelastic dynamic analysis programRUAUMOKO (Carr 2004). The beams and the columns weremodelled by a beam–column element, which is represented bya single component flexural spring. Inelastic deformations areassumed to occur at the ends of the element where plastichinges can be formed. The effects of axial deformations inbeams are neglected. Axial deformations are considered forcolumns, but no interaction between bending moment andaxial load is taken into account.

For the purpose of the frame models, moment–curvaturerelationships for the end sections of each beam and columnwere computed using the stress–strain model for confinedconcrete proposed by Mander et al. (1988) (Lin 2008). Nom-inal values for material strengths (i.e., concrete and reinforce-ment resisting factors Φc � Φs � 1) were used in the com-putation of the moment–curvature relationships. Based on the

shapes of the moment–curvature relationships, a trilinear hys-teretic model was selected for the columns, and a bilinear(modified Takeda) model was selected for the beams (Fig. 2).Both models take into account the degradation of the stiffnessduring nonlinear response. The parameters of the trilinearmodel for each column were based on the computed moment–curvature relationships. For the bilinear model (Fig. 2b), val-ues for the coefficients � and � of 0.5 and 0.6, respectively,were used as suggested by Carr (2004).

For the purpose of the analysis, Rayleigh damping of 5% ofcritical was assigned to the first and second vibration modes ofthe models. The damping was specified to be proportional to theinitial stiffness of the models. The first mode periods of the 4S,the 10S, and the 16S frame models, obtained by RUAUMOKO, are0.94 s, 1.96 s, and 2.75 s, respectively.

Spectrum-compatible seismic excitationsFour sets of seismic excitations were used in this study,

which include

Set 1: scaled real accelerograms,Set 2: modified real accelerograms,Set 3: simulated accelerograms, andSet 4: artificial accelerograms.

While Set 1 consists of actual accelerograms recorded dur-ing earthquakes, Sets 2 to 4 can all be considered as synthetic.

Fig. 1. Plan of floors and elevations of transverse frames of the buildings.


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The names “modified real,” “simulated” and “artificial” referto the method for deriving the accelerograms of these sets, asdiscussed below.

To conduct time-history analysis, the number of accerlero-grams used in the analysis should be decided first. As mentionedin the Introduction, three accelerograms (as a minimum) or morethan seven accelerograms can be used for the nonlinear time-history analysis according to ASCE/SEI-7 (2010). If less thanseven accelerograms are used, the maximum values of theresponse parameters from the analyses should be consideredfor the design. If seven or more accelerograms are used, thenthe average values of the response parameters should be usedin the design. However, these limits on the number of groundmotion excitations are based on engineering practice. Veryrecently, Reyes and Kalkan (2012) conducted a comprehen-sive study on the investigation of the number of records usedin the ASCE/SEI-7 ground motion scaling procedure. In theirstudy, structural responses were estimated based on the resultsfrom time-history analyses using 30 records, less than 7 re-cords, and between 7 and 10 records, separately. They con-cluded that the use of 7 records is sufficient to determine thedesign values of the response parameters.

Given the limitations of their study, e.g., only the single-degree-of-freedom systems and the maximum displacementwere considered in the analysis, 20 accelerograms were se-lected for each set of ground motion excitations used in thisstudy. The accelerograms of each set are scaled such that themean acceleration spectrum of the set is above the designspectrum for Vancouver within the period range between 0.2 sand 4.0 s. The value of 0.2 s corresponds approximately to0.2T1–4S (where T1–4S � 0.94 s is the first mode period of the

4S frame), and the value of 4.0 s is close to 1.5T1–16S (whereT1–16S � 2.75 s is the first mode period of the 16S frame). Thisperiod range was selected to use the same intensity of therecords in the analysis of all three frames. It satisfies the ASCE(2010) requirement for the spectral compatibility range (i.e.,between 0.2T1 and 1.5T1) for each frame individually and forall three frames together. More discussion of the compatibilityand other characteristics of the sets are given in the followingsubsections.

In addition to the use of 20 accelerograms, analyses werealso conducted by using 10 accelerograms for each set ofexcitations. It was found that the design values (i.e., the meanvalues) of the response parameters considered resulting from10 accelerograms and 20 accelerogrmas were very close. Forthe purpose of the statistic analysis, i.e., to get a reliableestimation on the standard deviation (see the discussion inSection “Analysis and response parameters”), the results fromthe time-history analyses using 20 accelerograms for each setof excitations were used to evaluate the seismic responses ofthe three frames considered in this study.

Set 1: scaled real accelerogramsIn the past decades a number of records have been obtained

from earthquakes in southwestern British Columbia includingVancouver, however most of the records represent weak mo-tion (Atkinson 2005; Cassidy et al. 2008). In addition, themagnitudes and distances of the recorded ground motions donot cover the magnitudes and the distances of the earthquakesthat have the largest contributions to the seismic hazard forVancouver (see the discussion below). To date the strongestshaking recorded in Vancouver was from the Mw 5.3 Penderearthquake that occurred in 1976 (J.F. Cassidy. 2012. Personalcommunication). Given these, recorded ground motions fromearthquakes in California were selected. It is commonly ac-cepted that the characteristics of earthquakes that might occurin the Vancouver region are similar to those of Californiaearthquakes (G.M. Atkinson. 2009. Personal communication).

A set of 20 earthquake records was selected from the strongmotion database of the Pacific Earthquake Engineering Re-search (PEER) Center (Table 1), the records correspond to thehorizontal components of the earthquake ground motions. Asseen in Table 1, pairs of horizontal components were selectedfor records No. 1 to No. 12, this is because the responsespectra of the pair of components were very close. Howeverfor records No. 13 to No. 20, it was found that the responsespectra of the pair of the horizontal components recorded atthe given station were far apart. Therefore, only the horizontalcomponent of which the response spectrum close to the designspectrum was selected (Table 1). It should be noted that onlythe horizontal components were used in the time-history anal-ysis (i.e., vertical components were not used in the analysis)following the requirements given in 2010 NBCC and ASCE/SEI-7. The records are obtained at sites with shear wavevelocities between 360 m/s and 750 m/s (i.e., NBCC site classC, which was assumed in the design of the buildings). Therecords are obtained from five earthquakes with magnitudesbetween 6.9 and 7.4, at distances from 36 km to 127 km. Boththe magnitude and the distance ranges cover the magnitudesand the distances of the earthquakes that have the largestcontributions to the seismic hazard for Vancouver, as reportedin Halchuk et al. (2007).

Fig. 2. Hysteretic models used in this study: (a) for columns and(b) for beams. (Adopted from Carr 2004).


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To achieve spectral compatibility with the design spec-trum, the records were scaled in two steps. In the first step,the method known as “scaling to partial spectral area” wasused (Amiri-Hormozaki 2003). In this method, each recordwas scaled such that the area of the 5% damped accelerationspectrum of the record within the period range between 0.2 sand 4.0 s is equal to the area under the design spectrum withinthe same period range. The mean spectrum of the scaledaccelerograms, resulting from this method, was close to thedesign spectrum, with some parts being above and some partsbelow the design spectrum. To have a mean spectrum abovethe design spectrum for the periods between 0.2 s and 4.0 s,additional scaling was conducted by multiplying the accelero-grams (already scaled in the first step) by a factor of 1.18. Thisvalue was determined by trials using different factors. Thespectra of the scaled accelerograms, the mean spectrum of theset, and the design spectrum for Vancouver are shown inFig. 3a. It is seen in the figure that the mean spectrum of theset is above the design spectrum, as required by ASCE (2010).

Set 2: modified real accelerogramsA method described by Naumoski (2001) was used for the

generation of spectrum compatible accelerograms by modify-ing real accelerograms. In this method, a selected (i.e., initial)accelerogram is modified iteratively until its spectrum matches

the prescribed design spectrum. The initial accelerogram canbe any ground motion record (i.e., real or synthetic). In thisstudy, the originally selected earthquake records for Set 1(listed in Table 1) were used as initial accelerograms. Thespectrum to be matched was the design spectrum for Vancou-ver for soil class C.

The modifications of the initial accelerogram are conducted inthe frequency domain. In the first iteration, the ratios of thespectral ordinates of the design spectrum to those of the acceler-ation spectrum of the initial accelerogram are computed for all theperiods considered. Based on these ratios, the frequency contentand the amplitudes of the initial accelerograms are modified suchthat the spectrum of the modified accelerogram becomes closer tothe design spectrum. The modified accelerogram is used in thenext iteration, and the iterative process continues until the spec-trum of the accelerogram matches the design spectrum through-out the period range of interest. An important feature of themethod is that it preserves the phases of the Fourier components(sinusoids) of the initial accelerogram, i.e., the phases in thegenerated accelerogram are the same as those in the initial accel-erogram. Detailed explanations for the method can be found inNaumoski (2001).

Figure 3b shows the spectra of the accelerograms generatedfor use in this study. To raise the mean spectrum to be abovethe design spectrum, the accelerograms generated as describedabove were scaled by multiplying by 1.08.

Table 1. Selected earthquake records from the PEER database.

Rec. No. Earthquake and date Magn. Dist. (km) Station Component. ID*

1 Landers, 1992/06/28 7.3 88.5 32075 Baker Fire station BAK0502 BAK1403 Landers, 1992/06/28 7.3 36.1 23559 Barstow BRS0004 BRS0905 Landers, 1992/06/28 7.3 69.2 21081 Amboy ABY0006 ABY0907 Landers, 1992/06/28 7.3 51.7 12206 Silent Valley – Poppet Flat SIL0008 SIL0909 Kern County, 1952/07/21 7.4 41.0 1095 Taft Lincoln School TAF021

10 TAF11111 Landers, 1992/06/28 7.3 95.9 12168 Puerta La Cruz PLC00012 PLC09013 Landers, 1992/06/28 7.3 64.2 24577 Fort Irwin FTI090

FTI000 (not selected)14 Loma Prieta, 1989/10/18 6.9 57.1 58219 APEEL 3E Hayward CSUH A3E090

A3E000 (not selected)15 Loma Prieta, 1989/10/18 6.9 77.0 58130 SF – Diamond Heights DMH090

DMH000 (not selected)16 Trinidad, 1980/11/08 7.2 71.9 1498 Rio Dell Overpass, FF B-RDL270

B-RDL000 (not selected)17 Loma Prieta, 1989/10/18 6.9 47.8 58373 APEEL 10 – Skyline A10000

A10090 (not selected)18 Loma Prieta, 1989/10/18 6.9 46.5 58378 APEEL 7 – Pulgas A07090

A07000 (not selected)19 Loma Prieta, 1989/10/18 6.9 46.4 1161 APEEL 9 – Crystal Springs Res A09227

A09137 (not selected)20 Kern County, 1952/07/21 7.4 127.0 80053 Pasadena – CIT Athenaeum PAS270

PAS180 (not selected)

*Record designation in the PEER database.


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Fig. 3. Response spectra (5% damping) of the sets of accelerograms used in this study: (a) Set 1, scaled real accelerograms; (b) Set 2, modified real accelerograms; (c) Set 3,simulated accelerograms; and (d) Set 4, artificial accelerograms.

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Set 3: simulated accelerogramsA comprehensive library of simulated accelerograms com-

patible with the 2005 NBCC uniform hazard spectra wasestablished by Atkinson (2009). Of importance for this studyare the simulated accelerograms for western Canada fromcrustal and in-slab earthquakes. A stochastic finite-faultmethod is used for the simulation of the accelerograms. Themethod is described in detail in Atkinson (2009) and onlyits main features are summarized here. In this method, a largefault is divided into a number of subfaults and each subfault isconsidered as a point source. Ground motions of the pointsources are simulated using the stochastic point-source ap-proach. The simulation is based on a specified Fourier spec-trum of ground motion as a function of magnitude and dis-tance. The simulation model also includes the sourceparameters characteristic for the geographic region consid-ered, and takes into account the effects of the magnitude anddistance on the duration of the ground motion. The accelero-grams simulated for the point (i.e., subfault) sources along thefault are summed (with a proper time delay) in the timedomain to obtain the ground motion from the entire fault.

Using this method, Atkinson (2009) simulated accelero-grams for western Canada for earthquake magnitudes of 6.5and 7.5, and for a wide range of source-to-site distances. Theseaccelerograms are available on the web site of EngineeringSeismology Toolbox (www.seismotoolbox.ca). Among theseaccelerograms, a set of 20 accelerograms was selected for thisstudy. The selected accelerograms correspond to a magnitudeof 7.5, distances ranging from 47 km to 100 km, and soil classC. The accelerograms were scaled such that the mean spec-trum of the set is above the design spectrum (Fig. 3c).

It is necessary to point out that the seismic hazard modelsemployed by Geological Survey of Canada to produce hazardvalues for 2010 NBCC only affect the hazard results for low-seismicity regions in eastern Canada compared with those used in2005 NBCC (Humar et al. 2010; Mitchell et al. 2010; Adams2011). Therefore, the simulated accelerograms generated forwestern Canada by Atkinson (2009) compatible with 2005NBCC as discussed above can still be used in the time-historyanalysis for the three frames considered in this study.

Set 4: artificial accelerogramsArtificial accelerograms compatible with the design spec-

trum for Vancouver were generated using the method pro-posed by Gasparini and Vanmarcke (1976), incorporated inthe computer program SIMQKE. The method is based on thewell-known principle that each accelerogram can be repre-sented as a sum of sinusoids. In the first step, sinusoids aregenerated at a specified number of frequencies within thefrequency range of the design spectrum. The phase angles ofthe sinusoids are produced using random number generationsoftware. The amplitudes of the sinusoids are determined fromthe spectrum density function, which is derived based on thedesign spectrum. Then, an accelerogram is obtained by sum-mation of the sinusoids. The accelerogram is multiplied by aspecified shape function (i.e., intensity envelope function) tosimulate the shape of a real earthquake motion. The responsespectrum of the resulting accelerogram is computed and com-pared with the design spectrum. Based on the ratios of the

ordinates of the computed spectrum and those of the designspectrum, the spectrum density function is modified for use inthe calculation of the amplitudes of the sinusoids for the nextiteration. The iterative process continues until the spectrum ofthe accelerogram is close to the design spectrum.

The matching of the spectra of the artificial accelero-grams and the design spectrum is shown in Fig. 3d. Theshape function used in the generation of the accelerograms isillustrated in Fig. 4. It was selected by considering the shapesof real records obtained from earthquakes in California withmagnitudes and distances within the ranges of those used inthe selection of Set 1. As seen in Fig. 4, the maximum intensityof the shape function is 0.47g which corresponds to the peakground acceleration for Vancouver for the probability of ex-ceedance of 2% in 50 years (NRCC 2010).

Analysis and response parametersNonlinear time-history analyses were conducted by subject-

ing the 4S, the 10S, and the 16S frames to the selected sets ofaccelerograms. Among a number of response parameters re-sulting from the analyses, storey shears, interstorey drifts, andcurvature ductilities at the end sections of beams and columnswere used in this study.

The storey shear represents a global force demand on abuilding structure subjected to seismic motions. It is also anindicator for the seismic moments in the columns of thestorey considered, and in the beams at the floors above andbelow the storey (i.e., larger seismic storey shear indicateslarger seismic moments in columns and beams of the sto-rey). The interstorey drift is a global deformation parame-ter. Seismic design codes normally specify the maximuminterstorey drift for use in design. In 2010 NBCC, themaximum allowed interstorey drift for buildings of normalimportance is 2.5% of storey height. The curvature ductil-ity, on the other hand, is a local deformation parameter andrepresents the extent of inelastic deformations at a specifiedsection of a structural member. The curvature ductility fora given section of a member represents the ratio of themaximum curvature experienced during the response to theyield curvature of the section.

For each excitation motion, maximum values for theshear and drift at each storey, and maximum curvatureductility for each end section of the beams and columnswere computed. These maximum values are the peak valuesfor the response parameters considered from a single time-history analysis. Given the large number of time-historyanalyses, and the large number of structural members in the

Fig. 4. Shape function of the artificial accelerograms.


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frames, the consideration of the results from each time-history analysis was impractical. Therefore, the shearforces, drifts, and ductility demands resulting from the setsof excitations were statistically analysed to compute themean (M) and the mean plus one standard deviation (M �SD) values. For each set of excitations, mean and M � SDvalues for shear forces and drifts were computed for eachstorey. The computation of the mean and M � SD curvatureductilities for the columns of each storey was done byconsidering only the largest ductility from all bottom andtop sections of the columns of the storey, resulting fromeach excitation in the set. Similarly, the mean and M � SDcurvature ductilities for the beams at each floor were com-puted by using the largest ductility from all end sections ofthe beams of the floor, obtained from each excitation in theset. Note that the mean values for the shear, drift, andcurvature ductility at each storey from a given set of exci-tations were calculated by using the sum of the maximumresponses (i.e., peak values of the response parameter) ofthe storey due to each time-history analysis divided by thetotal number of excitations in the set, which is 20 in thisstudy.

Discussion of results

4S frameThe results from the dynamic analysis of the 4S frame are

presented in Figs. 5 to 8. While it is normal practice to presentforces first and then deformations, in this paper the deforma-tions (interstorey drifts and curvature ductilities) are discussedfirst followed by a discussion of the shear forces. This is forbetter understanding of the results, i.e., some characteristics ofthe shear forces can be explained based on the curvatureductilities. Figure 5 shows the results for interstorey drifts, andFigs. 6 and 7 show the curvature ductilities for beams andcolumns, respectively. The horizontal bars in these figuresrepresent the mean response values for each storey, and the lineextensions to the bars show the M � SD response values. Figure 8shows the mean (M) shear forces at each storey (referred to asstorey shears in the further discussion). The M � SD shearsare not included in the figure since these are relatively close tothe mean values, as discussed below in this section.

The variations of the responses from the sets are quanti-fied by considering the differences between the largest andthe smallest mean response values from the sets obtained at

Fig. 5. Interstorey drifts for the 4S frame.

Fig. 6. Beam curvature ductilities for the 4S frame.


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each storey. For simplicity, these differences are expressedin percentages relative to the smallest mean responses. Theuse of the mean values is considered appropriate becausethese values are more “stable” (i.e., they have smallervariations) than the M � SD values, and the use of meanresponses is recommended by ASCE (2010) when each setcontains seven or more excitations. Figures 5 to 7 show thatthe excitations of Set 1 (scaled real accelerograms) producethe largest deformation responses. Note that the deformationresponses from Set 3 (simulated accelerograms) are very closeto those from Set 1. The ranges of the differences betweenthe largest and the smallest mean response values from thefour sets (expressed in terms of the smallest values) are 12%to 27% for interstorey drifts, 10% to 26% for beam ductilities,and 6% to 25% for column ductilities (Table 2).

While the focus of this section is to discuss the effects ofdifferent types of spectrum-compatible excitations on the re-sponses of the 4S frame, as described above, it is useful todiscuss briefly the behaviour of the frame in view of itsexpected performance for the ductility level used in the design(i.e., for ductile frame). For the purpose of this discussion,Table 3 shows the maximum mean and M � SD drifts and

ductilities obtained from the four sets of excitations. Note thatthese (maximum) values can be at any storey of the frames,and they can be from any set of the accelerograms. It can beseen in Table 3 and Fig. 5 that the drifts are well below the codelimit of 2.5%, which is due to the conservatism in the design.The maximum M � SD interstorey drift is 1.5% at the secondstorey. The ductilities of the beams show that yielding occursat the end sections of the beams of all floors (i.e., the beamductilities are all larger than 1.0) (Fig. 6), as expectedfor ductile frames. The maximum mean and M � SD beam

Fig. 7. Column curvature ductilities for the 4S frame.

Fig. 8. Shear forces for the 4S frame.

Table 2. Ranges of the differences (in %) between the largest and thesmallest mean response values from the selected sets of excitations.

FrameInterstoreydrift (%)

Beamductility

Columnductility

Storeyshear

4S 12–27 10–26 6–25 2–610S 11–27 9–23 4–27 3–616S 14–31 13–34 6–24 1–10

Note: Percentages are expressed relative to the smallest response values.


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ductilities are 3.1 and 3.8, respectively, both occurring at thesecond storey. The ductilities of the columns indicate thatcertain inelastic deformations occur at the columns of the topstorey and at the bottom sections of the first storey columns(Fig. 7). Inelastic deformations at these locations are allowedaccording to the capacity design method (Paulay and Priestley1992). The columns of the second and the third storey behavealmost elastically (i.e., they have ductilities of about 1.0). Themaximum mean and M � SD column ductilities are 1.6 and2.0 (Table 3), respectively, which occurred at the bottomsections of the first storey columns (Fig. 3). In general, thebeam and column curvature ductilities observed for the frameare not significant because members of well-designedmoment-resisting frames can sustain curvature ductilitiesof 10 to 20 (Heidebrecht and Naumoski 2002). Based on theanalysis results of the 4S frame, it was found that the maxi-mum mean values of the deformation responses correspondto Set 1 (scaled real accelerograms) while the maximumM � SD values correspond to Set 3 (simulated accelerograms)(Table 3).

The results for the shear forces (Fig. 8) show that all four setsof excitations produce storey shears that are very close to oneanother. The differences between the largest and the smallest

values for the mean storey shears from the ensembles arebetween 2% and 6%. Also, the M � SD storey shears fromeach set are close to the corresponding mean values (i.e., thestandard deviations, SD, of the storey shears are very small).Such results are not surprising considering the observations forthe ductilities discussed above. Namely, since the beams at thefloor levels experience yielding from the majority of the ex-citations (Fig. 6), the variations of the maximum forces in thebeams (and consequently in the columns) during the nonlinearresponse are very small because of the small post-yield stiff-ness of the beams (Fig. 2).

10S frameThe results for the 10S frame are presented in Figs. 9 to

12. The deformation response results (Figs. 9 to 11) fromthe four excitation sets show that the largest responses atdifferent storeys correspond to the excitations of Set 1 (scaledreal accelerograms). The ranges of the differences between thelargest and the smallest mean responses obtained from thefour sets are 11% to 27% for interstorey drifts, 9% to 23% forbeam ductilites, and 4% to 27% for column ductilities (Ta-ble 2). These values are comparable with those for the 4Sframe.

Table 3. Maximum mean and mean � standard deviation (M � SD) response values from the selected sets of excitations.

Frame

Interstorey drift (%) Beam ductility Column ductility

Mean M � SD Mean M � SD Mean M � SD

4S 1.2 (Set 1*) 1.5 (Set 3) 3.1 (Set 1) 3.8 (Set 3) 1.6 (Set 1) 2.0 (Set 3)10S 1.2 (Set 1) 1.4 (Set 1) 3.5 (Set 1) 4.1 (Set 1) 1.4 (Set 1) 1.7 (Set 3)16S 1.0 (Set 1) 1.2 (Set 1) 3.2 (Set 1) 3.8 (Set 1) 1.2 (Set 1) 1.5 (Set 1)

*Set of the accelerograms governs the value of the parameter.



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As for the 4S frame, the maximum mean and M � SDvalues for the interstorey drifts for the 10S frame (Table 3),which are 1.2% and 1.4%, respectively, are also below thecode limit of 2.5%. The maximum mean and M � SD ductility

values for the beams are 3.5 and 4.1 (Table 3), respectively,and both are for the beams at the eighth storey. The ductilitiesfor the beams are all larger than about 1.7 (Fig. 10). Thisindicates that all four sets of excitations produce nonlinear




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deformations (i.e., yielding) in all beams of the frame. Re-garding the columns, the maximum mean ductility value of 1.4and M � SD value of 1.7 are observed for the columns of thetop storey. The column ductilities for all other storeys aresmaller than 1.0 indicating elastic behaviour of the columnsfrom all four sets of excitations. In summary, the curvatureductilities for the beams and columns show that the seismicbehaviour of the 10S frame is as expected for a ductile framedesigned according to the capacity method, i.e., all inelasticdeformations to be in the beams, and the columns to remain inthe elastic range. Certain inelastic deformations in the topstorey columns (as indicated by the observed column ductili-ties in Fig. 11) are allowed according to the capacity method(Paulay and Priestley 1992). It can be seen in Table 3 that bothmaximum mean and maximum M � SD values of the defor-mation responses for the 10S frame are governed by theexcitations of Set 1 (scaled real accelerograms) except theM � SD value of the column ductility which is governed bythe excitations of Set 3 (simulated accelerograms).

The observations for the storey shears (Fig. 12) are similarto those for the 4S frame. The mean storey shears from thefour excitation sets are very close. Also, the dispersions of theshears around the mean values (i.e., the standard deviations,SD) are very small. The differences between the largest andthe smallest shear values from the sets are 3% to 6% for boththe mean and the M � SD storey shears. As discussed for the4S frame, these features of the storey shears are due to the

nonlinear behaviour (i.e., the yelding) of the beams, in whichthe storey shears are limited to a level that is associated withthe yield strengths of the beams.

16S FrameThe response quantities obtained for the 16S frame are

presented in Figs. 13 to 16. It is observed that the distributionsof the deformation responses along the height of the frame(Figs. 13 to 15), and the values of the maximum deformations(Table 3) are comparable with those for the 10S frame. Thedeformation responses from the four sets show somewhatlarger variations compared to those for the 4S and the 10Sframes. The differences between the largest and the smallestmean response values from the sets are 14% to 31% forinterstorey drifts, 13% to 34% for beam ductilities, and 6% to24% for column ductilities (Table 2). As seen in Figs. 13 to 15,the largest responses are from the excitations of Set 3, with theexception of the top three storeys for which the responses fromSet 1 are somewhat larger than those from Set 3. It is alsoobserved that in the majority of cases the smallest deformationresponses are from Sets 2 and 4. The results in Table 3 showthat the excitations of Set 1 produce the maximum deforma-tion responses along the height of the frame among the foursets of excitations used in this study.

The deformation responses of the 16S frame are as expectedfor a ductile frame. The curvature ductilities for the beams,which range between about 1.5 and 3.8 (Fig. 14), indicate that



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the beams at all storeys undergo inelastic deformations. Thecolumn ductilities (Fig. 15) show that certain inelastic defor-mations occur at the top storey columns (which have ductili-ties of about 1.6), and all other columns remain in the elasticrange (i.e., they have ductilities of less than 1.0).

The storey shears for the 16S frame (Fig. 16) have verysimilar features to those of the 4S and the 10S frames. All thesets of excitations produce similar storey shears, and conse-quently small dispersions (i.e., small differences between themean and the M � SD values). The differences between thelargest and the smallest mean storey shears from the four setsare between 1% and 10% as given in Table 2.

Discussion and conclusionsThe National Building Code of Canada, as well as other

modern building codes around the world, prefer the use ofdynamic time-history analysis in the design of buildings lo-cated in regions of high seismicity and for buildings that arehigher than specified height levels. The codes require theseismic excitations (i.e., the accelerograms) used in the anal-ysis to be compatible with the design spectrum for the buildinglocation. The selection of spectrum-compatible accelerogramsis one of the major issues for the time-history analysis ofbuildings. The objective of this study is to determine theimplications of the use of different methods for the selection ofaccelerograms in the estimation of the structural responses of

buildings. Four sets of accelerograms compatible with thedesign spectrum for Vancouver were selected for use inthe analysis. These include: (i) scaled real accelerograms,(ii) modified real accelerograms, (iii) simulated accelero-grams, and (iv) artificial accelerograms. Each set consists of20 accelerograms. Nonlinear time-history analyses wereconducted on three moment-resisting reinforced concreteframe buildings with heights of 4 storeys, 10 storeys, and 16storeys, designed for Vancouver. Each building was sub-jected to the selected sets of accelerograms. Interstoreydrifts, curvature ductilities for beams and columns, andstorey shear forces were used in the evaluation of the effectsof the selected excitations.

The main observations and conclusions from this study areas follows:

1. Among the four sets of accelerograms, the spectra of theset with scaled real accelerograms and that with simulatedaccelerograms (i.e., sets designated (i) and (iii) above)show the largest dispersion around the mean spectra of thesets. Very small (unrealistic) dispersion of the spectra isobserved for the set with modified real accelerograms andthat with artificial accelerograms (i.e., sets designated (ii)and (iv) above).

2. The variability of the deformation responses (i.e., intersto-rey drifts and curvature ductilities) from the four sets ofaccelerograms is comparable for all three buildings. The



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maximum differences between the largest and the smallestmean values of the deformation responses (expressed aspercentages of the smallest mean values) are about 30%.

3. The variability of the storey shear forces from the four setsof excitations is quite small for all three buildings. Themaximum differences between the largest and the smallestmean storey shears from the sets are about 10%.

4. The largest response values for interstorey drifts and cur-vature ductilities at different storeys are either from thescaled real accelerograms or from the simulated accelero-grams for the 4-storey building, from the scaled real ac-celerograms for the 10-storey building, and from the sim-ulated accelerograms for the 16-storey building.

5. The maximum mean response values for interstorey driftsand curvature ductilities along the height of the buildingare from the scaled real accelerograms. This is the case forall three buildings considered in this study.

6. Based on the considerations of both the spectral character-istics of the selected sets and the response results from theanalysis, scaled real accelerograms are preferred for use intime-history analyses of buildings. The accelerogramsshould be selected from earthquakes occurred in regionswith similar seismological characteristics to those of thelocation considered, and properly scaled such that theirspectra are close to the design spectrum. If such accelero-grams are not available, then simulated accelerogramsshould be used. The methods for the generation of such

accelerograms take into account certain seismologicalcharacteristics of the region considered.

AcknowledgementsWe would like to acknowledge the two anonymous re-

viewers for their constructive comments that helped toimprove the manuscript, some of their comments are veryuseful for the further study on the seismic evaluation ofbuilding structures.

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selection of seismic excitations for nonlinear analysis of reinforced concrete frame buildings ...

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