Effect of Earthquake Ground Motion Duration on the Seismic ...

Research ArticleEffect of Earthquake Ground Motion Duration on the SeismicResponse of a Low-Rise RC Building

Martin O Martineau Alvaro F Lopez and Juan C Vielma

Escuela de Ingenierıa Civil Pontificia Universidad Catolica de Valparaıso Valparaıso 2362804 Chile

Correspondence should be addressed to Alvaro F Lopez alvarolopezpucvcl

Received 25 June 2020 Revised 14 September 2020 Accepted 18 September 2020 Published 5 October 2020

Academic Editor Haiyun Shi

Copyright copy 2020 Martin O Martineau et al +is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

+is paper investigates the effect of earthquake ground motion duration on the seismic response of a low-rise reinforced concreteshear wall building Two sets of spectrally equivalent ground motion sets were determined to isolate the effect of duration fromother earthquake record characteristics A numerical model that accounts for P-delta effects and degradation of strength andstiffness of the structural elements was used Detailed nonlinear dynamic analysis for both the design and collapse levels of shakingwas performed considering the spectral acceleration at the fundamental period of vibration with intensity measure and materialstrains as engineering demand parameters +e results showed that at the design level of shaking slightly larger interstory driftswere obtained under the short-duration events However the maximum values for interstory drifts were small and minor damageis expected in the structure When both seismic record sets were incrementally scaled until collapse a slight increase in thematerial strains was found under the short-duration seismic events Overall it is indicated that ground motion duration does notinfluence the seismic response of low-rise buildings with low deformation capacity

1 Introduction

In recent years there has been a resurgence interest instudying the effect of ground motion duration on the seismicperformance and collapse assessment of structures +istopicrsquos interest has been primarily due to the field observationafter large-magnitude long-duration earthquakes such as the2010 Maule Chile (Mw88) and the 2011 Tohoku Japan(Mw90) megathrust earthquakes which caused significantstructural damage to critical infrastructures like bridges andbuildings [1ndash4] Moreover such events and others fromsubduction regions have made available new long-durationstrong motion records allowing a better study of the effects ofearthquake duration on structural performance For instancethe lack of available long-duration ground motion records inthe past required the generation of artificial records to addressthis topic adequately [5ndash7] +e previous events have shownthat ground motion duration should be duly considered instructural design However the effect of ground motionduration is not yet explicitly considered as a parameter in

current seismic design codes [8ndash10] and performance as-sessment throughout the world [11 12]

A vast number of research studies on the effects ofground motion duration on structural performance havebeen reported in the literature in the past decades often withinconclusive results due to the parameters used On the onehand investigations using cumulative response measuressuch as the number of inelastic cycles or energy dissipationshowed a good correlation between duration and damage[13ndash16] On the other hand research studies using only peakresponse measures such as peak deformation or peakinterstory drift did not show a significant influence ofduration on structural response [15 17 18] However theinadequacy of structural models in capturing the effect ofenergy capacity degradation cyclic and in-cycle strengthdegradation and scarcity of long-duration ground motionrecords made it difficult to address duration effects inprevious research adequately [19] Likewise the problem ofisolating duration from other key explanatory variables ofthe ground motion such as frequency content spectral

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8891282 12 pageshttpsdoiorg10115520208891282

amplitude and spectral shape added another challengesince the spectral content of the earthquake record can bemodified [20] In this regard using spectrally equivalentground motion pairs for isolating the effect of duration hasmade available a more robust way of analyzing groundmotions for nonlinear dynamic analyses since the spectralcontent is almost not altered [21 22]

More recent investigations employing numerical modelsthat captured structural componentsrsquo degradation have shownthat long-duration ground motions can induce higher defor-mations and affect the structural collapse capacity [22ndash25]Chandramohan et al [22] presented results showing that long-duration records induce higher deformations for large shakingintensities By analyzing 2D models of a modern 5-story steelspecial moment frame and a single reinforced concrete (RC)bridge pier they concluded that the median collapse capacity ofthe structural systems could experience a reduction of 29 and17 respectively when the structures are subjected to long-duration motions Raghunandan and Liel [23] studied theinfluence of duration on the collapse capacity of eight non-ductile RC frames and nine modern ductile RC frames using2D nonlinear models +e authors concluded that earthquakeduration plays a significant role in the collapse resistance of thestructural systems +ey reported reductions in the collapseresistance ranging from 26 to 56 due to duration effectsimpacting the buildingsrsquo vulnerability Barbosa et al [24]quantified the influence of duration on the damage (ie notonly at collapse stage) of 3- 9- and 20-story steel buildingsdesigned according to pre-Northridge codes Spectrallyequivalent records from subduction and crustal earthquakeswere used as input in the 2D nonlinear models It was con-cluded that the increase in energy dissipation demands in thestructures subjected to long-duration motions significantlyincreased the expected levels of structural damage at the higherintensities of shaking Belejo et al [26] studied the seismicbehavior of a substandard plan-asymmetric RC framedbuilding through 3D nonlinear modeling and found thatgroundmotion duration influence is evident only for intensitiesleading to the collapse of the structure +is result agrees withthe conclusions reported by Raghunandan and Liel [23] sincestructural systems with low ductile capacity are not influencedby earthquake duration due to the inability to reach largedeformations and dissipate energy before failure Bravo-Haroand Elghazouli [25] analyzed 50 steel moment frames throughdetailed nonlinear dynamic analysis using a suite of 77 spec-trally equivalent pairs of short and long earthquake recordsSimilar to previous studies they reported that the effects ofduration are significant for structures showing high rate ofcyclic degradation levels Reductions of about 20 on thecollapse capacity were observed due to duration reaching up toa 40 reduction in buildingswith a high cyclic degradation rateSamanta and Pandey [27] studied the effect of duration on a 15-story RC building and they found that earthquake duration canbecome a determining factor in the levels of maximum peakstory drift ratio under low hazard levels Bhanu et al [19] founda reduction in ductile RC framed structuresrsquo dynamic defor-mation capacity under the increased cyclic demands imposedby long-duration ground motions Vega and Montejo [28]found that long-duration records impose larger inelastic

demands and that the effect of duration is more detrimental inrelatively rigid structures and poorly detailed flexible structuresLiapopoulou et al [29] investigated the effect of duration on aseries of ductile SDOF models and reported up to 60 re-duction in the collapse capacity due to duration effects in thecase of flexible bilinear systems under low levels of P-Δ effect

On the other hand the structural response to long-du-ration events is directly related to ductility a property necessaryto study under earthquake-induced deformations on buildingsNonetheless traditional analysis methods do not consider theeffects of earthquake duration and the use of deterioratingstructural models that directly affect the structurersquos demand[19 30] +erefore the assessment of the effects of earthquakegroundmotion duration on these structures is not feasible As amatter of fact current seismic design practice for reinforcedconcrete structures in Chile is based on the conventional code-prescribed force method However after the recent occurrenceof significant seismic events such as the 2010 Maule earth-quake changes to the regulation were introduced afterwards toimprove the structural response of walls by ensuring theductility of these and including recommendations for esti-mating structural deformations It is well known that Chile islocated in one of the most seismically active regions of theworld where the geological conditions (from a tectonic pointof view) near the Chilean coast mostly consist of interplateareas where subduction events occur frequently and aregenerally of large magnitude and also of long duration [31]+is last feature has not been considered in the seismic-re-sistant design despite the local conditions therefore it isnecessary to promote research works that include durationeffects on structural behavior

In this paper the effect of ground motion duration on theseismic performance of RC building structures is investigated Asample four-story RC shear wall building is used as a case study+is building represents a typical low-rise residential buildinglocated in Central Chile designed according to current Chileanseismic provisions A 3D nonlinear finite element model of thesample structure is developed in SeismoStruct [32] which allowsincorporating the in-cycle and cyclic deterioration of stiffnessand strength as well as the fiber modeling approach withmaterial inelasticity for structuralmembers A set of 20 spectrallyequivalent pairs of long and short earthquake records is used toevaluate the effects of ground motion duration on the structuralresponse Particular attention is given to effects of duration onmaterial strains and interstory drift ratios +e results in thisinvestigation indicate that ground motion duration does notplay a key role in the damage state of the low-rise building

2 Sample Building and Model Description

21 General Description +e sample structure correspondsto an existing low-rise RC shear wall building of whichstructural configuration is typical of residential housing builtin Chile +e prototype building is a 4-story structure with astory height of 244m+e buildingrsquos lateral load and gravity-resisting systems comprise interior and outer RC shear wallsin both longitudinal and transverse directions and 12 cm RCslabs at each floor +e typical floor plan and elevations areillustrated in Figure 1+e compressive strength of concrete is

2 Advances in Civil Engineering

W1 e = 20cm

W12 e = 20cm

W8

e = 2

0cm

W5

e = 2

0 cm

W9

e = 2

0cm

W6

e = 2

0cm

W4

e = 2

0cm

W11e = 20cm

e = 20cm

W10e = 20cm

W2e = 20cm

W3e = 20cm

1 2 43 5

G

F

E

D

C

B

A

54321

A

B

C

D

E

F

G

223 2233645 3645

Slab thicknesse = 12cm




B9 B10

B11

B12

e = 20cmW7

B3

B1B7

B5

B8B6

B2

B4

MHA

142

142

324

324

(a)

Figure 1 Continued

Advances in Civil Engineering 3

assumed to be 20MPa and the tensile strength of rein-forcement is 420MPa +e floor area is about 120m2 perstory and the dead and live loads were calculated approxi-mately as 279 kNm2 and 67 kNm2 respectively +ebuilding was analyzed as per current Chilean seismic pro-visions [9] and the ACI318-14 [33] requirements +ebuilding is assumed to be located in seismic zone 3 on soilclass D according to the Chilean seismic code NCh433 [9]classification +e seismic force reduction factor (R) pre-scribed for this system is 4

22 Modeling Approach Linear and nonlinear numericalmodels were considered in this study Given that the buildingalready exists onsite the structural elementrsquos design was notcarried out since dimensions of the elements and the rein-forcement layout for each of the elements were available

Instead a design check was performed confirming that theirbehavior was flexural dominated+e structural drawings weretherefore used for modeling the building +e 3D linear elasticmodel used for this study was first generated using the softwarepackage ETABS [34] to determine the structurersquos main dy-namic properties using the response spectrum analysis as percurrent Chilean seismic regulations [9] As a result the crackedfundamental periods of vibrations obtained for the structurewere 0095 and 0088 seconds in the x- and y-directions re-spectively for the second and third main vibration modes (themodes that accumulate 90 of the mass participation)

Despite the softwarersquos capabilities for the linear staticanalysis it is not possible to conduct robust nonlinear dy-namic analyses +is aspect is relevant for this study as itspurpose is to evaluate the effects of ground duration on theseismic behavior of the structure +erefore numericalmodels that accurately characterize structural performance at

W5 e = 20cm

W5 e = 20cm

W5 e = 20cm

W5 e = 20cm

A D G

1037

732

488

000

213

521

35

213

521

35

110

587 587

ϕ820

ϕ8201 + 1ϕ16

ϕ820

ϕ820

2ϕ12

4ϕ10

1 + 1ϕ16244

E + LATϕ820E + LATϕ820

MLML

25

(b)

Figure 1 Sample residential housing (a) typical floor plan of the building and (b) elevations of outer longitudinal and inner transverse shearwalls


large nonlinear demands should be duly used To this endstructural models that can capture the in-cycle and cyclicdegradation of strength and stiffness of elements are needed[35] since it is the main factor affected by the duration ofearthquake records+erefore the SeismoStruct software [32]was used to develop a continuous 3D nonlinear numericalmodel of the building +is software allows to performamong several other options nonlinear dynamic analysis byusing accelerograms so that the corresponding loads areapplied to the structure A rigid diaphragm is assumed foreach floor Soil-structure interaction was not considered inthis study +e 3D view floor plan and elevation of thenumerical model of the structure are illustrated in Figure 2

23Material andElementModels As previously mentionedthe nonlinear finite element model for the building wasdeveloped in SeismoStruct [32] To this end the rein-forcement details specified in the structural drawings wereincluded in the model +e shear walls were modeled usingfiber elements with force-based (FB) formulation [36ndash38]and using a distributed inelasticity approach along the el-ement length GaussndashLobatto numerical integration quad-rature rule is used for the FB elements +e fiber-basedelement model used for the shear walls is presented inFigure 3 A linear elastic hinge at midheight of the walls ateach story was provided to capture the elastic shear de-formations It is worth mentioning that the shear hingesrsquostiffness was equal to the cracked shear area of the wallsmultiplied by the shear modulus and divided by the storyheight A factor of 01 was applied to the wall gross area toaccount for the loss of the area due to cracking [39]

+e concrete material was defined using the uniaxialconstant confinement model that follows the constitutive re-lationship proposed by Mander et al [40] and the cyclic re-sponse theory proposed by Martinez-Rueda and Elnashai [41]+e confinement effects provided by the lateral transversereinforcement were modeled with a confinement factor de-fined as the ratio between the confined and unconfinedcompressive strengths of concrete In SeismoStruct [32] theconfinement factor is calculated using the confinement modelproposed byMander et al [40] Table 1 presents the fivemodel-calibrating parameters defined to fully describe the mechanicalfeatures of the concrete Regarding the reinforcing steel it wasmodeled using a uniaxial steel model based on the stress-strainrelationship proposed by Menegotto and Pinto [42] coupledwith the isotropic hardening rules developed by Filippou et al[43] Nine model-calibrating parameters fully describe themechanical characteristics of the reinforcing steel which arepresented in Table 2 +ese material models were generatedusing data calibrated in the laboratory and captured the effectof cycles on sections of reinforced concrete with transversereinforcement and reinforcement steel elements +e reasonthesemodels were used is related to the fact that they are widelyaccepted by the research community in structural engineeringand that they are also well adapted to the events recorded overthe past several years in terms of structural performance +ehysteresis rules used for each material model are shown inFigure 4

3 Ground Motion Sets

Two paired sets of spectrally equivalent long- and short-duration records were selected to investigate the effect ofground motion duration on the sample building modelLarge-magnitude earthquakes occurred in subduction zoneswere chosen for the long-duration set and obtained from the1985 Valparaiso and 2010 Maule Chile [44] and the 2003Hokkaido and 2011 Tohoku Japan [45] earthquakesSimilarly ground motions from shallow crustal events werechosen from the PEER NGA-West [46] database Althoughthere is still no consensus in the earthquake engineeringcommunity on a standard ground motion duration defi-nition in this study the 5 to 95 significant duration(Ds5minus95

) metric was used +is duration metric is defined asthe time required to develop the Arias intensity [47] in therange between 5 and 95 of the total energy of the record[48] as presented in equation (1) Here a(t) corresponds tothe ground motion acceleration record T is the total du-ration of the recording tR is the desired time over whichpercentage of the total energy is reached (eg 90) t is thetime integration parameter and R is the calculated fractionof the Arias intensity index

IA(R) 1001113946tR

0(a(t))

2dt 1113946T

0(a(t))

2dt (1)

+e criterion used to categorize a ground motion as along or short duration was based on the threshold proposedby Chandramohan et al [22] upon which a significantduration Ds5minus95

is higher than 25 s for long duration andlower than 25 s for a short duration +e selected long-duration ground motions are summarized in Table 3 Forbrevity only the component with higher PGA is listed in thetable

To isolate the effect of duration from other groundmotion characteristics such as intensity and spectral shapethe methodology proposed by Al Atik and Abrahamson [49]was used to match each ground motion set spectrally +ismethodology allows us to obtain spectral equivalence be-tween the long- and short-duration records without havingto correct their baseline which is advantageous since thismethod ensures the stability and convergence in the cal-culations Table 4 summarizes the selected short-durationevents and records +ese short-duration records wereobtained exclusively from worldwide shallow crustalearthquakes Figures 5(a) and 5(b) depict the geometricmean and standard deviation spectra for the long- and short-duration records Moreover Figure 5(c) compares bothgeometric mean spectrums indicating a good agreementbetween both ground motion sets

4 Nonlinear Time-History Analysis

A dynamic time-history analysis was performed in thisstudy Accordingly the two sets of groundmotions were firstscaled to match the NCh 433 design response spectrum forseismic zone 3 and soil class D [9] and then uniformlyapplied at the base of the building model +e resulting


maximum interstory drifts for the sample building areshown in Figure 6 and were obtained by gathering theavailable information on the nodes of the structure asso-ciated with the center of gravity of the four floors +eNCh433 [9] uses interstory drifts as a damage control pa-rameter and limits the building to a maximum interstorydrift of 0002 of the story height for linear elastic analysis Forthe immediate occupancy (IO) evaluation used in the per-formance-based procedure indicated in the ASCESEI 41-17[11] the maximum interstory drift is limited to 0004 As

seen in Figure 6 none of the sets surpasses these limitswhich might be attributed to the great lateral stiffness of thesample building due to the significant presence of shearwalls When comparing the values obtained for both groundmotion sets there is a slight increase in the interstory driftsfor the short-duration ground motion set compared to thosefor long-duration earthquakes However it should bementioned that the values obtained in both cases are notsignificantly far from each other with an increase of 2005for short-duration events It is therefore not possible to

(a)

1

G

F

E

D

C

B

A X

y

2 3 4 5

(b)

Story 4

Story 3

Story 2

Story 1

Base

A A A A A

1

Z

X

2 3 4 5

(c)

Figure 2 Low-rise RC building model for numerical analysis (a) 3D view (b) typical floor layout and (c) elevation A1-5

Figure 3 Discretized FB element model for RC shear walls


conclude that the short-duration events generate a signifi-cant increase in drifts compared to the long-duration eventsthus an incremental dynamic analysis (IDA) was thenperformed to have a deeper understanding of thisphenomenon

As stated previously to better estimate the influence ofground motion duration a series of IDAs were performedto the sample structure obtaining results for eachstructural element IDA is a parametric dynamic analysistechnique used in earthquake engineering to conduct acomprehensive assessment of the seismic performance ofstructures under seismic loads [50] +e procedure in-volves multiple nonlinear dynamic analysis of a structuralmodel under scaled ground motions until collapse thusproducing curves of engineering demand parameter(EDP) as a damage measure (DM) versus an intensitymeasure (IM) +e ground motions are characterized bythe IMs which should be related to the structural responseof interest to reduce the number of time-history analyses[51] Among the existing IMs the peak ground acceler-ation (PGA) peak ground velocity (PGV) spectral ac-celeration and Arias intensity are the most widely used+e DM can be any structural parameter related to per-formance limit states of the structure corresponding toseveral damage levels Typical options are the global andlocal maximum interstory drift global and local maxi-mum ductility and material strain limit among others Inthis study the spectral acceleration at the fundamentalperiod of vibration of the structure with 5 damping Sa(T0 5) while different EDPs was analyzed Finally theselected EDPs were the concrete and steel rebar strains forthe IDA It is worth to mention that the collapse stage wasdefined as the instant at which the main structural walls ofthe structure failed

Given that the results for the maximum interstory driftobtained from the nonlinear time-history analysis at thedesign level of shaking as per Chilean seismic regulations [9]were rather low and not conclusive the results of the IDA are

presented in Figures 7 and 8 for the outer wall of thestructure identified as ldquoA 1ndash4rdquo according to the floor planshown in Figure 2 Figure 7 shows slightly higher steel rebarpeak strains for the short-duration ground motions com-pared to the long-duration set In particular there is anincrease of 8 in the peak strain of the steel rebar for short-duration events However when observing the yield pointfor the reinforcement steel 8 cases exceed this point forlong-duration events while 7 cases exceed this point forshort-duration events

Similarly when considering concrete strains as EDP theresults showed a slight tendency to obtain higher defor-mations under the short-duration ground motion set Forexample Figure 8 shows 2 cases in which the cracking ofconcrete occurs at a deformation value exceeding the de-termined value of 2 per thousand Meanwhile for the long-duration events there is only one case for which this limit isexceeded as can be seen in Figure 8 +e obtained peaks ofconcrete strain show an increase of 17 for the short-du-ration suite compared to the long-duration suite for a PGAof 38 (g)

Overall it is generally possible to observe a slightincrease in the demand on the structure under the short-duration ground motion set In this regard for this casestudy and to a slightly greater extent the demand on thestructure in terms of the chosen EDPs was higher underthe short-duration earthquakes records than the long-duration earthquakes records although minimal damageis expected under both sets of records +is phenomenonshould be highlighted since the previous results[22ndash24 30] have shown that there are higher levels ofdeformations therefore more damage induced by long-duration seismic records However the unalike resultsobtained in this research are mainly attributed to the lowlevel of deformation exhibited by the sample structurewhich can be supported by the obtained interstory driftvalues It should be noted that the structure underconsideration was a rather rigid building with a large

Table 1 Data required to generate the concrete stress-strain curve

Value Descriptionfc 25MPa Mean compressive strengthEc 23500MPa Modulus of elasticityft 25MPa Maximum tension strengthεc minus00022 Strain at peak strength in compressionεt minus00020 Strain at peak strength in tension

Table 2 Data required to generate the stress-strain curve of reinforcing steel

Value DescriptionEs 25MPa Modulus of elasticityfy 2times105MPa Yield strengthμ 0005 Strain hardening parameterR0 20 Transition curve initial shape parameterA1 1850 Transition curve shape calibrating coefficientA2 015 Transition curve shape calibrating coefficientA3 000 Isotropic hardening calibrating coefficientA4 100 Isotropic hardening calibrating coefficientb 01 Fracturebuckling strain


presence of walls and a low height which restricted thedeformation capacity and energy dissipation capacitybefore failure considering how the building was struc-tured +e obtained results confirmed that for structuralsystems with low ductility capacity the demand wouldnot be influenced by ground motion duration [23]

5 Conclusions

+is paper examined the influence of earthquake groundmotion duration on the seismic performance of a low-riseRC shear wall building typical of Chilean residential con-struction A 3D nonlinear finite element model was

3

0

ndash3

ndash6

ndash9

ndash12

ndash15

ndash18

ndash21

ndash24

ndash27

ndash31

Stre

ss (M

Pa)

ndash0008 ndash0006 ndash0004 ndash0002 0 0002Strain (mm)

(a)St

ress

(MPa

)

ndash0008 0008ndash0004 00040Strain (mm)

450

300

150

0

ndash150

ndash300

ndash450

(b)

Figure 4 Constitutive models used in the nonlinear numerical model (a) concrete and (b) reinforcing steel

Table 3 Long-duration set summary

Earthquake Magnitude Year Station PGA (g) Significant duration (s)

Valparaiso Chile 78 1985CauquenesEndesaLa Ligua

011013018

511044952835

Hokkaido Japan 83 2003 ShibetsuHonbetsukai

050048

32002696

Maule Chile 88 2010Vintildea CentroValparaısoMatanzas

033030034

256527154215

Tohoku Japan 90 2011 TohwaOkhuma

081070

58202810

Table 4 Short-duration set summary

Earthquake Magnitude Year Station PGA (g) Significant duration (s)Cape Mendocino USA 70 1985 Rio Dell Pass 055 1534Friuli Italy 65 1976 Tolmezzo 035 1696Hector Mine 71 1999 Hector 034 1165Imperial Valley 65 1979 El Centro Array1 038 1705Loma Prieta 69 1989 Gilroy Array3 056 637Northridge 67 1994 Canyon Country 048 556Northridge 67 1994 Beverly Hills 052 921San Fernando 66 1971 LA-Hollywood 021 1049Superstition Hill 65 1987 El Centro Imp Co 036 1605Superstition Hill 65 1987 Poe Road (temp) 045 1381


2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)

MeanMean + stddevMean ndash stddev

(a)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(b)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)

Long durationShort duration

(c)

Figure 5 Geometric meanplusmn one standard deviation for spectra of (a) the long-duration set and (b) the spectrally equivalent short-durationset (c) Comparison between geometric means for both ground motion sets

10

8

6

4

2

0

Floo

r hei

ght (

m)

0 0001 0002 0003 0004 0005Interstory dri (mm)

ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(a)

10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(b)

Figure 6 Interstory drift results for the 4-story model as per the Chilean code shaking level for (a) the long-duration set and (b) the short-duration set


developed in SeismoStruct which explicitly accounted for P-delta effects and inherent nonlinearities of the materials Onthe other hand two ground motion sets with equivalentspectral shapes but different durations were obtained toisolate the effects of ground motion duration from otherground motion characteristics +e sample building modelwas then subjected to time-history analysis at the design levelof shaking and to extensive IDA using the long- and short-duration record sets Overall the influence of duration wasshown to be not significant in the sample structure presentedherein

Based on the results obtained in this study it is expectedthat groundmotion duration does not influence significantlythe peak values of EDPs in low-rise RC shear wall buildingswhen considering long-duration ground motion recordsWhen comparing the maximum interstory drifts at thedesign level of shaking to the limits imposed by the NCh433for linear elastic analysis and the ASCESEI 41-17 for per-formance-based evaluation the values were found to besmall and slight which resulted in minimum damage to thesample building Moreover the structurersquos behavior re-garding the drifts is generally quite similar in both situations

and slightly higher for the short-duration set than for thelong-duration set It should be mentioned that the structurewas designed as per the current seismic Chilean seismiccode which resulted in a rather rigid structure+e behaviorof the structure in terms of deformations was consequentlyrestricted to its linear range which led to low levels ofdeformation capacity

To better understand the effect of the duration ofearthquakes on the structure thoroughly the samplebuilding was subjected to incrementally scaled groundmotion records to higher levels of shaking using IDAConcrete and steel rebar strains were used as EDPs +eresults showed a slight difference between the curves ob-tained for short-duration records and those obtained forlong-duration records Regarding the material peak strainshigher peaks by approximately 8 for reinforced steel andby approximately 17 for concrete were obtained for short-duration events Furthermore it should be noted that anincrease in material strains for the short-duration events wasgenerally obtained although this increase was not significant+e results obtained in this study confirmed that forstructural systems with low ductility capacity the influence

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)

Figure 7 IDA curves considering steel rebar strains as EDP for (a) the long-duration set and (b) the short-duration set

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)

Figure 8 IDA curves considering concrete strains as EDP for (a) the long-duration set and (b) the short-duration set


of duration is not significant due to the incapacity to reachlarge deformation and dissipate energy before failure

Further research is recommended to study structuresthat can reach higher levels of deformation to obtain arelevant structural demand regarding seismic loading andresults related to the performance of the materials consid-ering their nonlinear behavior +ereby it would be possibleto have a deeper and a more conclusive understanding of theeffect of the duration of a seismic event since the increasednumber of cycles imposed by long-duration groundmotionsare one of the main concerns when conducting such studies

Data Availability

Some or all data models or code generated or used duringthe study are available from the corresponding author uponrequest

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors wish to acknowledge the support from theSchool of Civil Engineering of the Pontificia UniversidadCatolica de Valparaıso for providing the funds for thepublication of this article +is research has been possiblethanks to the support of the School of Civil Engineeringfrom the Pontificia Universidad Catolica de Valparaıso

References

[1] C Alarcon M A Hube R Junemann and J C de la LleraldquoCharacteristics and displacement capacity of reinforcedconcrete walls in damaged buildings during 2010 Chileearthquakerdquo Bulletin of Earthquake Engineering vol 13 no 4pp 1119ndash1139 2015

[2] K Kawashima and I Buckle ldquoStructural performance ofbridges in the Tohoku-oki earthquakerdquo Earthquake Spectravol 29 no 1 2013

[3] I Buckle M Hube G Chen W H Yen and J AriasldquoStructural performance of bridges in the offshore mauleearthquake of 27 February 2010rdquo Earthquake Spectra vol 28no 1 pp 533ndash552 2012

[4] F Rojas F Naeim M Lew et al ldquoPerformance of tallbuildings in concepcion during the 27 February 2010 momentmagnitude 88 offshore Maule Chile earthquakerdquo 4eStructural Design of Tall and Special Buildings vol 20 no 1pp 37ndash64 2011

[5] R Saragoni and G Hart ldquoSimulation of artificial earth-quakesrdquo Earthquake Engineering amp Structural Dynamicsvol 2 no 3 pp 249ndash267 1973

[6] R Tremblay ldquoDevelopment of design spectra for long-du-ration ground motions from Cascadia subduction earth-quakesrdquo Canadian Journal of Civil Engineering vol 25 no 6pp 1078ndash1090 1998

[7] M Sarieddine and L Lin ldquoInvestigation correlations betweenstrong-motion duration and structural damagerdquo in Pro-ceedings of the 2013 Structures Congress pp 2926ndash2936Pittsburgh PA USA May 2013

[8] ASCE Minimum Design Loads for Buildings and OtherStructures ASCESEI 7-16 Press Reston VA USA 2016

[9] Instituto Nacional de Normalizacion Diseno Sismico deEdificios Instituto Nacional de Normalizacion SantiagoChile in Spanish 2012

[10] CEN Eurocode 8 Design of Structures for EarthquakeResistancemdashPart 1 General Rules Seismic Actions and Rulesfor Buildings No English +e European Union Per Regu-lation 3052011 Directive 9834EC Directive 200418EC2004

[11] ASCE Seismic Evaluation and Retrofit of Existing StructuresASCESEI 41-17 ASCESEI 7-16 Press Reston VA USA2014

[12] FEMA P695 Quantification of Building Seismic PerformanceFactors FEMA Washington DC USA 2009

[13] C Oyarzo-Vera and C Nawawi ldquoEffect of earthquake du-ration and sequences of ground motions on structural re-sponsesrdquo in Proceedings of the 10th International Symposiumon Structural Engineering for Young Experts ISSEYEpp 1881ndash1886 Changsha China January 2008

[14] J Hancock and J J Bommer ldquoA state-of-knowledge review ofthe influence of strong-motion duration on structural dam-agerdquo Earthquake Spectra vol 22 no 3 pp 827ndash845 2006

[15] I Iervolino G Manfredi and E Cosenza ldquoGround motionduration effects on nonlinear seismic responserdquo EarthquakeEngineering amp Structural Dynamics vol 35 no 1 pp 21ndash382006

[16] A Dutta and J B Mander ldquoEnergy based methodology forductile design of concrete columnsrdquo Journal of StructuralEngineering vol 127 no 12 pp 1374ndash1381 2001

[17] E Bojorquez I Iervolino G Manfredi and E CosenzaldquoInfluence of ground motion duration on degrading SDOFsystemsrdquo in Proceedings of the 16 th European Conference onEarthquake Engineering and Seismology pp 3ndash8 GenevaSwitzerland September 2006

[18] C A Cornell ldquoDoes duration really matterrdquo in Proceedingsof the FHWANCEER Workshop on the National Represen-tation of Seismic Ground Motion for New and ExistingHighway Facilities pp 125ndash133 Burlingame CA USA May1997

[19] V Bhanu R Chandramohan and T J Sullivan ldquoInvesti-gating the influence of ground motion duration on the dy-namic deformation capacity of reinforced concrete framedstructuresrdquo in Proceedings of the 11th Pacific Conference onEarthquake Engineering Auckland New Zealand April 2019

[20] J Hancock and J J Bommer ldquoUsing spectral matched recordsto explore the influence of strong-motion duration on in-elastic structural responserdquo Soil Dynamics and EarthquakeEngineering vol 27 no 4 pp 291ndash299 2007

[21] M Mashayekhi M Harati M Ashoori Barmchi andH E Estekanchi ldquoIntroducing a response-based durationmetric and its correlation with structural damagesrdquo Bulletin ofEarthquake Engineering vol 17 no 11 pp 5987ndash6008 2019

[22] R Chandramohan J W Baker and G G DeierleinldquoQuantifying the influence of ground motion duration onstructural collapse capacity using spectrally equivalent rec-ordsrdquo Earthquake Spectra vol 32 no 2 pp 927ndash950 2016

[23] M Raghunandan and A B Liel ldquoEffect of ground motionduration on earthquake-induced structural collapserdquo Struc-tural Safety vol 41 pp 119ndash133 2013

[24] A R Barbosa F L A Ribeiro and L A C Neves ldquoInfluenceof earthquake ground-motion duration on damage estima-tion application to steel moment resisting framesrdquo


Earthquake Engineering amp Structural Dynamics vol 46 no 1pp 27ndash49 2017

[25] M A Bravo-Haro and A Y Elghazouli ldquoInfluence ofearthquake duration on the response of steel moment framesrdquoSoil Dynamics and Earthquake Engineering vol 115pp 634ndash651 2018

[26] A Belejo A R Barbosa and R Bento ldquoInfluence of groundmotion duration on damage index-based fragility assessmentof a plan-asymmetric non-ductile reinforced concretebuildingrdquo Engineering Structures vol 151 pp 682ndash703 2017

[27] A Samanta and P Pandey ldquoEffects of ground motionmodification methods and ground motion duration onseismic performance of a 15-storied buildingrdquo Journal ofBuilding Engineering vol 15 pp 14ndash25 2018

[28] E Vega and L A Montejo ldquoInfluence of ground motionduration on ductility demands of reinforced concrete struc-turesrdquo International Journal of Advanced Structural Engi-neering vol 11 no 4 pp 503ndash517 2019

[29] M Liapopoulou M A Bravo-Haro and A Y Elghazoulildquo+e role of ground motion duration and pulse effects in thecollapse of ductile systemsrdquo Earthquake Engineering ampStructural Dynamics vol 49 no 11 pp 1051ndash1071 2020

[30] A Mantawy and J C Anderson ldquoEffect of long-durationearthquakes on the low-cycle fatigue damage in RC framebuildingsrdquo Soil Dynamics and Earthquake Engineeringvol 109 pp 46ndash57 2018

[31] R Dobry I M Idriss and E Ng ldquoDuration characteristics ofhorizontal components of strong-motion earthquake rec-ordsrdquo Bulletin of the Seismological Society of America vol 68no 5 pp 1487ndash1520 1978

[32] SeismoSoft 2019 SeismoStruct 2019mdashA Computer Programfor Static and Dynamic Nonlinear Analysis of FramedStructures httpswwwseismosoftcom

[33] ACI Committee 318 Building Code Requirements for Struc-tural Concrete ACI Committee 318 Farmington Hills MIUSA 2014

[34] CSI CSI ETABS Analysis Reference Manual Comput StructInc Berkeley CA USA 2013

[35] L F Ibarra R A Medina and H Krawinkler ldquoHystereticmodels that incorporate strength and stiffness deteriorationrdquoEarthquake Engineering amp Structural Dynamics vol 34no 12 pp 1489ndash1511 2005

[36] E Spacone F C Filippou and F F Taucer ldquoFibre beam-column model for non-linear analysis of RC frames partI Formulationrdquo Earthquake Engineering amp Structural Dy-namics vol 25 no 7 pp 727ndash742 1996

[37] E Spacone F C Filippou and F F Taucer ldquoFibre beam-column model for non-linear analysis of RC frames part IIApplicationsrdquo Earthquake Engineering amp Structural Dy-namics vol 25 no 7 1996

[38] A Neuenhofer and F C Filippou ldquoEvaluation of nonlinearframe finite-element modelsrdquo Journal of Structural Engi-neering vol 123 no 7 pp 958ndash966 1997

[39] J S Pugh L N Lowes and D E Lehman ldquoSeismic design ofslender concrete wallsrdquo in Proceedings of the 10th US Na-tional Conference on Earthquake Engineering Frontiers ofEarthquake Engineering Anchorage AK USA July 2014

[40] J B Mander M J N Priestley and R Park ldquo+eoreticalstress-strain model for confined concreterdquo Journal of Struc-tural Engineering vol 114 no 8 pp 1804ndash1826 1988

[41] J Martınez-Rueda and A S Elnashai ldquoConfined concretemodel under cyclic loadrdquo Materials and Structures vol 30no 3 pp 139ndash147 1997

[42] M Menegotto and P E Pinto ldquoMethod of analysis for cy-clically loaded R C plane frames including changes in ge-ometry and non-elastic behavior of elements under combinednormal force and bendingrdquo Proceedings of IABSE Symposiumon Resistance and Ultimate Deformability of Structures Actedon by Well Defined Repeated Loads pp 15ndash22 1973

[43] F C Filippou E P Popov and V V Bertero ldquoEffects of bonddeterioration on hysteretic behaviour of reinforced concretejointsrdquo Report National Science Foundation Berkeley CAUSA 1983

[44] University of Chile Earthquakes of Chile University of ChileSantiago Chile 2010

[45] K-NET Kyoshin Network Database National Research In-stitute for Earth Science and Disaster Resilience 2019

[46] Pacific Earthquake Engineering Research Center PEERGround Motion Database Shallow Crustal Earthquakes inActive Tectonic Regimes NGA-West2 2017

[47] A Arias A Measure of Earthquake Intensity Seismic Designfor Nuclear Power Plants MIT Press Cambridge MA USA1970

[48] M D Trifunac and A G Brady ldquoA study on the duration ofstrong earthquake ground motionrdquo Bulletin of the Seismo-logical Society of America vol 65 no 3 pp 581ndash626 1975

[49] L Al Atik and N Abrahamson ldquoAn improved method fornonstationary spectral matchingrdquo Earthquake Spectra vol 26no 3 pp 601ndash617 2010

[50] D Vamvatsikos and C Allin Cornell ldquoIncremental dynamicanalysisrdquo Earthquake Engineering amp Structural Dynamicsvol 31 no 3 pp 491ndash514 2002

[51] J Kiani and S Pezeshk ldquoSensitivity analysis of the seismicdemands of RC moment resisting frames to different aspectsof ground motionsrdquo Earthquake Engineering amp StructuralDynamics vol 46 no 15 pp 2739ndash2755 2017


amplitude and spectral shape added another challengesince the spectral content of the earthquake record can bemodified [20] In this regard using spectrally equivalentground motion pairs for isolating the effect of duration hasmade available a more robust way of analyzing groundmotions for nonlinear dynamic analyses since the spectralcontent is almost not altered [21 22]

More recent investigations employing numerical modelsthat captured structural componentsrsquo degradation have shownthat long-duration ground motions can induce higher defor-mations and affect the structural collapse capacity [22ndash25]Chandramohan et al [22] presented results showing that long-duration records induce higher deformations for large shakingintensities By analyzing 2D models of a modern 5-story steelspecial moment frame and a single reinforced concrete (RC)bridge pier they concluded that the median collapse capacity ofthe structural systems could experience a reduction of 29 and17 respectively when the structures are subjected to long-duration motions Raghunandan and Liel [23] studied theinfluence of duration on the collapse capacity of eight non-ductile RC frames and nine modern ductile RC frames using2D nonlinear models +e authors concluded that earthquakeduration plays a significant role in the collapse resistance of thestructural systems +ey reported reductions in the collapseresistance ranging from 26 to 56 due to duration effectsimpacting the buildingsrsquo vulnerability Barbosa et al [24]quantified the influence of duration on the damage (ie notonly at collapse stage) of 3- 9- and 20-story steel buildingsdesigned according to pre-Northridge codes Spectrallyequivalent records from subduction and crustal earthquakeswere used as input in the 2D nonlinear models It was con-cluded that the increase in energy dissipation demands in thestructures subjected to long-duration motions significantlyincreased the expected levels of structural damage at the higherintensities of shaking Belejo et al [26] studied the seismicbehavior of a substandard plan-asymmetric RC framedbuilding through 3D nonlinear modeling and found thatgroundmotion duration influence is evident only for intensitiesleading to the collapse of the structure +is result agrees withthe conclusions reported by Raghunandan and Liel [23] sincestructural systems with low ductile capacity are not influencedby earthquake duration due to the inability to reach largedeformations and dissipate energy before failure Bravo-Haroand Elghazouli [25] analyzed 50 steel moment frames throughdetailed nonlinear dynamic analysis using a suite of 77 spec-trally equivalent pairs of short and long earthquake recordsSimilar to previous studies they reported that the effects ofduration are significant for structures showing high rate ofcyclic degradation levels Reductions of about 20 on thecollapse capacity were observed due to duration reaching up toa 40 reduction in buildingswith a high cyclic degradation rateSamanta and Pandey [27] studied the effect of duration on a 15-story RC building and they found that earthquake duration canbecome a determining factor in the levels of maximum peakstory drift ratio under low hazard levels Bhanu et al [19] founda reduction in ductile RC framed structuresrsquo dynamic defor-mation capacity under the increased cyclic demands imposedby long-duration ground motions Vega and Montejo [28]found that long-duration records impose larger inelastic

demands and that the effect of duration is more detrimental inrelatively rigid structures and poorly detailed flexible structuresLiapopoulou et al [29] investigated the effect of duration on aseries of ductile SDOF models and reported up to 60 re-duction in the collapse capacity due to duration effects in thecase of flexible bilinear systems under low levels of P-Δ effect

On the other hand the structural response to long-du-ration events is directly related to ductility a property necessaryto study under earthquake-induced deformations on buildingsNonetheless traditional analysis methods do not consider theeffects of earthquake duration and the use of deterioratingstructural models that directly affect the structurersquos demand[19 30] +erefore the assessment of the effects of earthquakegroundmotion duration on these structures is not feasible As amatter of fact current seismic design practice for reinforcedconcrete structures in Chile is based on the conventional code-prescribed force method However after the recent occurrenceof significant seismic events such as the 2010 Maule earth-quake changes to the regulation were introduced afterwards toimprove the structural response of walls by ensuring theductility of these and including recommendations for esti-mating structural deformations It is well known that Chile islocated in one of the most seismically active regions of theworld where the geological conditions (from a tectonic pointof view) near the Chilean coast mostly consist of interplateareas where subduction events occur frequently and aregenerally of large magnitude and also of long duration [31]+is last feature has not been considered in the seismic-re-sistant design despite the local conditions therefore it isnecessary to promote research works that include durationeffects on structural behavior

In this paper the effect of ground motion duration on theseismic performance of RC building structures is investigated Asample four-story RC shear wall building is used as a case study+is building represents a typical low-rise residential buildinglocated in Central Chile designed according to current Chileanseismic provisions A 3D nonlinear finite element model of thesample structure is developed in SeismoStruct [32] which allowsincorporating the in-cycle and cyclic deterioration of stiffnessand strength as well as the fiber modeling approach withmaterial inelasticity for structuralmembers A set of 20 spectrallyequivalent pairs of long and short earthquake records is used toevaluate the effects of ground motion duration on the structuralresponse Particular attention is given to effects of duration onmaterial strains and interstory drift ratios +e results in thisinvestigation indicate that ground motion duration does notplay a key role in the damage state of the low-rise building

2 Sample Building and Model Description

21 General Description +e sample structure correspondsto an existing low-rise RC shear wall building of whichstructural configuration is typical of residential housing builtin Chile +e prototype building is a 4-story structure with astory height of 244m+e buildingrsquos lateral load and gravity-resisting systems comprise interior and outer RC shear wallsin both longitudinal and transverse directions and 12 cm RCslabs at each floor +e typical floor plan and elevations areillustrated in Figure 1+e compressive strength of concrete is


W1 e = 20cm

W12 e = 20cm

W8

e = 2

0cm

W5

e = 2

0 cm

W9

e = 2

0cm

W6

e = 2

0cm

W4

e = 2

0cm

W11e = 20cm

e = 20cm

W10e = 20cm

W2e = 20cm

W3e = 20cm

1 2 43 5

G

F

E

D

C

B

A

54321

A

B

C

D

E

F

G

223 2233645 3645





B9 B10

B11

B12

e = 20cmW7

B3

B1B7

B5

B8B6

B2

B4

MHA

142

142

324

324

(a)

Figure 1 Continued






W5 e = 20cm

W5 e = 20cm

W5 e = 20cm

W5 e = 20cm

A D G

1037

732

488

000

213

521

35

213

521

35

110

587 587

ϕ820

ϕ8201 + 1ϕ16

ϕ820

ϕ820

2ϕ12

4ϕ10

1 + 1ϕ16244


MLML

25

(b)









IA(R) 1001113946tR

0(a(t))

2dt 1113946T

0(a(t))

2dt (1)









(a)

1

G

F

E

D

C

B

A X

y

2 3 4 5

(b)

Story 4

Story 3

Story 2

Story 1

Base

A A A A A

1

Z

X

2 3 4 5

(c)
















5 Conclusions


3

0

ndash3

ndash6

ndash9

ndash12

ndash15

ndash18

ndash21

ndash24

ndash27

ndash31

Stre

ss (M

Pa)


(a)St

ress

(MPa

)


450

300

150

0

ndash150

ndash300

ndash450

(b)





011013018

511044952835


050048

32002696


033030034

256527154215


081070

58202810




2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(a)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(b)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(c)


10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(a)

10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(b)







5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)


5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)





Data Availability




Acknowledgments


References























































W1 e = 20cm

W12 e = 20cm

W8

e = 2

0cm

W5

e = 2

0 cm

W9

e = 2

0cm

W6

e = 2

0cm

W4

e = 2

0cm

W11e = 20cm

e = 20cm

W10e = 20cm

W2e = 20cm

W3e = 20cm

1 2 43 5

G

F

E

D

C

B

A

54321

A

B

C

D

E

F

G

223 2233645 3645





B9 B10

B11

B12

e = 20cmW7

B3

B1B7

B5

B8B6

B2

B4

MHA

142

142

324

324

(a)

Figure 1 Continued






W5 e = 20cm

W5 e = 20cm

W5 e = 20cm

W5 e = 20cm

A D G

1037

732

488

000

213

521

35

213

521

35

110

587 587

ϕ820

ϕ8201 + 1ϕ16

ϕ820

ϕ820

2ϕ12

4ϕ10

1 + 1ϕ16244


MLML

25

(b)









IA(R) 1001113946tR

0(a(t))

2dt 1113946T

0(a(t))

2dt (1)









(a)

1

G

F

E

D

C

B

A X

y

2 3 4 5

(b)

Story 4

Story 3

Story 2

Story 1

Base

A A A A A

1

Z

X

2 3 4 5

(c)
















5 Conclusions


3

0

ndash3

ndash6

ndash9

ndash12

ndash15

ndash18

ndash21

ndash24

ndash27

ndash31

Stre

ss (M

Pa)


(a)St

ress

(MPa

)


450

300

150

0

ndash150

ndash300

ndash450

(b)





011013018

511044952835


050048

32002696


033030034

256527154215


081070

58202810




2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(a)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(b)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(c)


10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(a)

10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(b)







5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)


5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)





Data Availability




Acknowledgments


References



























































W5 e = 20cm

W5 e = 20cm

W5 e = 20cm

W5 e = 20cm

A D G

1037

732

488

000

213

521

35

213

521

35

110

587 587

ϕ820

ϕ8201 + 1ϕ16

ϕ820

ϕ820

2ϕ12

4ϕ10

1 + 1ϕ16244


MLML

25

(b)









IA(R) 1001113946tR

0(a(t))

2dt 1113946T

0(a(t))

2dt (1)









(a)

1

G

F

E

D

C

B

A X

y

2 3 4 5

(b)

Story 4

Story 3

Story 2

Story 1

Base

A A A A A

1

Z

X

2 3 4 5

(c)
















5 Conclusions


3

0

ndash3

ndash6

ndash9

ndash12

ndash15

ndash18

ndash21

ndash24

ndash27

ndash31

Stre

ss (M

Pa)


(a)St

ress

(MPa

)


450

300

150

0

ndash150

ndash300

ndash450

(b)





011013018

511044952835


050048

32002696


033030034

256527154215


081070

58202810




2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(a)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(b)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(c)


10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(a)

10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(b)







5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)


5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)





Data Availability




Acknowledgments


References





























































IA(R) 1001113946tR

0(a(t))

2dt 1113946T

0(a(t))

2dt (1)









(a)

1

G

F

E

D

C

B

A X

y

2 3 4 5

(b)

Story 4

Story 3

Story 2

Story 1

Base

A A A A A

1

Z

X

2 3 4 5

(c)
















5 Conclusions


3

0

ndash3

ndash6

ndash9

ndash12

ndash15

ndash18

ndash21

ndash24

ndash27

ndash31

Stre

ss (M

Pa)


(a)St

ress

(MPa

)


450

300

150

0

ndash150

ndash300

ndash450

(b)





011013018

511044952835


050048

32002696


033030034

256527154215


081070

58202810




2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(a)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(b)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(c)


10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(a)

10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(b)







5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)


5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)





Data Availability




Acknowledgments


References

























































(a)

1

G

F

E

D

C

B

A X

y

2 3 4 5

(b)

Story 4

Story 3

Story 2

Story 1

Base

A A A A A

1

Z

X

2 3 4 5

(c)
















5 Conclusions


3

0

ndash3

ndash6

ndash9

ndash12

ndash15

ndash18

ndash21

ndash24

ndash27

ndash31

Stre

ss (M

Pa)


(a)St

ress

(MPa

)


450

300

150

0

ndash150

ndash300

ndash450

(b)





011013018

511044952835


050048

32002696


033030034

256527154215


081070

58202810




2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(a)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(b)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(c)


10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(a)

10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(b)







5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)


5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)





Data Availability




Acknowledgments


References



































































5 Conclusions


3

0

ndash3

ndash6

ndash9

ndash12

ndash15

ndash18

ndash21

ndash24

ndash27

ndash31

Stre

ss (M

Pa)


(a)St

ress

(MPa

)


450

300

150

0

ndash150

ndash300

ndash450

(b)





011013018

511044952835


050048

32002696


033030034

256527154215


081070

58202810




2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(a)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(b)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(c)


10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(a)

10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(b)







5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)


5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)





Data Availability




Acknowledgments


References
























































5 Conclusions


3

0

ndash3

ndash6

ndash9

ndash12

ndash15

ndash18

ndash21

ndash24

ndash27

ndash31

Stre

ss (M

Pa)


(a)St

ress

(MPa

)


450

300

150

0

ndash150

ndash300

ndash450

(b)





011013018

511044952835


050048

32002696


033030034

256527154215


081070

58202810




2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(a)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(b)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(c)


10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(a)

10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(b)







5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)


5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)





Data Availability




Acknowledgments


References























































2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(a)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(b)

2

15

1

05

0

S a (g

)

0 1 2 3 4T (sec)


(c)


10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(a)

10

8

6

4

2

0

Floo

r hei

ght (

m)


ID fo

r ela

stic a

naly

sis (N

Ch43

3)

ID fo

r inm

edia

te o

ccup

ancy

(ASC

ESE

I 41-

13)

(b)







5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)


5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)





Data Availability




Acknowledgments


References



























































5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)


5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(a)

5

4

3

2

1

0

S a (g

)

0 0002 0004 0006 0008 001Strain (mm)

(b)





Data Availability




Acknowledgments


References

























































Data Availability




Acknowledgments


References




















































































Date post:	14-Mar-2022
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