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In many seismic analyses, ground motion time series are required inaddition to the design response spectrum.

Linear DynamicAnalysis

Non- Linear DynamicAnalysis

Procedures for selecting and scaling ground-motion records for a site-specic hazard are descried in uilding codes and ha!e een thesu"ect of much research in recent years.

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What does the building coderecommends?

CBC (2003) 1659A !2 "ime #istories

Pairs of appropriate horizontal ground motion time history components shall eselected and scaled from no less than 3 recorded e$ents.Appropriate time histories shall ha!e magnitudes, fault distances and sourcemechanisms that are consistent #ith those that control the design asisearthqua$e.%here three appropriate recorded ground motion time histories are nota!aliale, appropriate simulatedground motion time history pairs may e used.

&imply the codes in 'nited &tatesrequires(

%se at least 3 ground

motion &airs and ta'e themaimum

*+ ,ou ha$e more than -&airs o+ ground motion.

,ou can use thea$era e

%BC 199- And *BC 2000Increase the numer of selected ground motion pairs and calculate thea!erage response)or each scaled pair pair calculate the &*&& spectrum +square-root-sum ofthe squares+&*&& f he #o /orizontal 0omponents 1 &hould Not 2e Less han 3.4

he Design &pectrum rdinates In he *ange )rom 5.6 o 3.7

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It is common practice to select emprical recordings of ground motionand scale these ground motions to the le!el of design spectrum.

/%8

he selection of the

records and theamount of scalingthat can e appliedremain contro!ersial9

ypically, the time series isselected from recorded groundmotions #ith similarmagnitudes and similardistances.

Deaggregation of the hazardidenties the main contriutorsto the hazard

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:'*0D:

he set of accelerograms, regardless if they are natural, articial, or simulated,should match the follo#ing criteria(

a! a minimum of 3 accelerograms should be used;

b! the mean of the zero period spectral response acceleration values (calculatedfrom

the individual time histories) should not be smaller than the value of ag S for the

site in question;c! in the range of periods between 0,2! and 2!, where ! is the fundamental

period of the structure in the direction where the accelerogram will be applied;no value of the mean "# damping elastic spectrum, calculated from all timehistories, should be less than $0# of the corresponding value of the "#damping elastic response spectrum.

:0< specify that a minimum of = records should e selected and that, if lessthan > records are used, the ma?imum structural response +in asolute termsmust e used as the asis for design and assessment.

Alternati!ely, if > or more time-histories are employed, then the a!eragestructural response can e considered

.

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:'*0D:&teps to dene seismic action according to the hazard at the site; from left to right( target spectrumfor the limit-state of interest; disaggregation of seismic hazard for &a+3; selection of a set ofrecords compatile to disaggregation and matching the target spectrum in a range of periods

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:0 /election and /caling o+ round otion ecords

he ground motion time histories used to represent an intensity measure corresponding to a

particular hazard le!el +or return period should re@ect the magnitude, distance, site

condition, and other parameters that control the ground motion characteristics.

&election of records ha!ing appropriate magnitudes is important ecause magnitude strongly in@uences frequency content and duration of ground motion.

It is desirale to use earthqua$e magnitudes #ithin 5.67 magnitude units of the target magnitude . &election of records ha!ing appropriate fault-site distances is important especially for near-fault sites, ecause the characteristics of near-fault groundmotions diBer from those of other ground motions.

&ite conditions ha!e a ma"or eBect on the characteristics and frequency content of the strong ground motion records. :!en though the ground motions are amplied in soft soils, the high frequency motions are attenuated.

Cenerally, the ground motions amplication eBects can e oser!ed in spectral acceleration of the records at intermediate to long period.

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:0 ethod o+ round otion /caling

ur$ish seismic code +D22/, 655> allo# the use of articially generated, pre!iously

recorded or simulated accelerograms as input ground motions for linear and nonlinear

seismic analyses. he follo#ing criteria and specications should e considered(

E he duration of the strong motion part shall neither e shorter than 7 times the

fundamental period of the uilding nor 37 seconds.

E Fean spectral acceleration of generated ground motions for zero periods shall not e

less than Ao g and the mean spectral accelerations of articially generated acceleration

records for 7G damping ratio shall not e less than H5G of the elastic spectral

accelerations, &ae+, in the period range et#een 5.63 and 63 #ith respect to

dominant natural period, 3 , of the uilding in the earthqua$e direction considered.

E he local site conditions should e considered in recorded earthqua$es or physically

simulated ground motions.

E At least three ground motions shall e used #here the ma?imum of the results, and if

at least se!en ground motions are used the mean !alues of the results shall e

considered for design.

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:0 ethod o+ round otion /caling

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"here are to main a&&roaches used to de$elo& designground motions4

(a) scaling the ground motions(b) adusting the ground motions to match a design s&ectrum!

/caling re+ers to multi&l,ing the record b, a constant +actorat all time &oints and called time domain a&&roach!

&caled to match the PCA

&caled to match thespectral acceleration ata specic period

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"he selection o+ the starting time histories +or use in eitherscaling or s&ectral matching is im&ortant due to nonlinearres&onse o+ the soil and structure!

It is commonpractice to select

the initial groundmotion timehistories ased onthe seismological

properties such asmagnitude anddistance to thefault.

&imilar site

conditions, styleof faulting anddirecti!ity eBectsmay also econsidered in theselection process.

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Additionally, the scale factor required to scale the time series to thedesign spectrum may also e considered. In general, scale factorscloser to unity are preferred and many ground motion e?pertsrecommend a limit on the amount of scaling applied.

ecommendations41!/elect the records based on seismological&ro&erties4

5.7 magnitude units +can e e?tended to 5.7%ide distance range +e?(5-=5 $mAll styles of faulting earthqua$es + ut same tectonicsetting0onsider directi!ity conditions +for#ard, a!erage,ac$#ard

0onsider site classes +for hard roc$ sites it is est to selectthe hard roc$ recordingsNo limits in the amount of scaling92! rom the suite o+ candidate recordings4'se a simple non-linear system as a pro?y for morecomplicated full model of the structure

&elect records that gi!e closest to the a!erage response ofthe sim le non-linear s stem.

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7am&le stud, +or bridgeres&onse4

arget response

spectrum forscaling

A& 3HH>,Fagnitude >and Distance 7$m

334 recordingsare selected

2 di8erent scaling a&&roaches4-same scale factor to all components +code approach

-diBerent scale factors to diBerent components

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&ame scale factor to all components +code approach(

lease notethat4

here is a large!ariaility in theresponse for therecords that ha!ethe similar scalefactor.

&o, e!en if thescale factor for arecord is nearunity, that recordmay not gi!e agood estimate of

the a!erageresponse.

ariaility of theresponse is notsensiti!e to thescaling of the

record.

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DiBerent scale factor to diBerent components(

lease notethat4

&ome of therecords #ithlarge scalefactors produceresponse close toa!erage,#hereas, some ofthe records #ithscale factorsclose to unityproduct response!alues greaterthan or less than

the a!erage.

It is possile toget uniasedresults e!en forlarge scale

factors

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/&ectrum Com&atible ethods (s&ectralmatching)

*eal strong motion records ha!e response spectral pea$s and troughsthat impact the non-linear response of a structure.

&pectrum compatile time histories are modied in terms of theirfrequency content to match the entire spectrum.

Ideally, #e should use unmodied time histories to sample this eha!ior,ut sampling requires numerious time histories.

If the spectrum compatile methods are used, then a small numer ofsets of time histories can e used and still pro!ide a reliale estimate ofthe a!erage response of the structure.

he do#nside of the spectrum compatile method is the elimination of

the !ariaility of response y matching the time history to the targetspectrum.

It is a money sa!ing method and depends on the personal feelings of thestructural engineers.

/atch so+tare ma, be used +or s&ectral mathching

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he goal is to modifya+t such that the

spectrum computedfrom the time historymatches the targetspectrum across the#hole frequencyrange #hile

maintaining realistic!elocity anddisplacement timehistories.

It is an iterati!e

procedure andselecting a recordcloser to the targetspectrum is !eryimportant.

/&ectrum Com&atible ethods (s&ectralmatching)

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)irst, you #ill need to createyour target spectrum

compatile #ith theprogram format9

o do this #e #ill usesetarget.e?e

Input le format is(

setarget!dat (%our &'Sfrom '")1!0 (scale factor)0!0 0!0 +constants, do

not touch0!01 5!0 250 +period andand numer of points forinterpolationsetarget1!tgt +your targetspectrum

/&ectrum Com&atible ethods (s&ectralmatching)

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Input le format is(

35 Jma?imum no. ofiterations5.57 Jtolerance for ma?imummismatch +in fraction oftarget3.5 Jcon!ergence dampingK Jmodel3.67 5.67 3.5 4.5 Jalpha model, a3, a6,f3, f66 5. Jscale flag, scale period toPCA +5 no, 3 yes, 6 yes ut once

3 Jinterpolate to 3Mdt)lag3.5e-54 Jminimum eigen!alue=5 Jgroup size0! ma +re:5.5 5.5 4 f2and, nPole5 Fod PCA +3yes5 5.5 randomize target8 +i&eed,ran)actor1!0 100! +re:atch5 aseline cor @ag +3yes3.5 scale factorsetarget!tgttest!accrun1!accrun1!rs&

run1!unm

hen, you #ill use*&PFatch.e?e

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"he ;rst iteration is matched onl, u& to a &eriod o+ 1!0s! "hereason +or matching onl, the lo &eriod range on the ;rstiteration (0!1 s to 1!0s) is to maintain the non

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*n the second iteration. thes&ectrum is no matched

out to a &eriod o+ 2!0s!

"his iterati$e &rocess

is carried out until thes&ectrum has beenmatched out to thedesired &eriod. in thiscase 10!0s!

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2efore spectralmatching

After spectralmatching

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he scatter inoth of the

responseparametersreduces ase?pected.

he decrease in

the !ariaility ofthe response isdue to thereduced!ariaility in theground motion

records that aremodied tomatch the targetspectrum.

7am&le stud, +or bridgeres&onse4