fragility analysis of mid-rise rc frame buildings

Engineering Structures 28 (2006) 1335–1345www.elsevier.com/locate/engstruct

.ng to thes. Sampled for those

d on thoselumber off stories ofnstructed

Fragility analysis of mid-rise R/C frame buildings

Murat Serdar Kirc¸il ∗, Zekeriya Polat

Department of Civil Engineering, Yıldız Technical University, 34349 Istanbul, Turkey

Received 26 April 2005; received in revised form 12 December 2005; accepted 9 January 2006Available online 20 March 2006

Abstract

Fragility curves are useful tools for showing the probability of structural damage due to earthquakes as a function of ground motion indicesThe aim of this study is to develop the fragility curves for mid-rise R/C frame buildings in Istanbul, which have been designed accordi1975 version of the Turkish seismic design code, based on numerical simulation with respect to the number of stories of the building3, 5 and 7 story buildings were designed according to the Turkish seismic design code. Incremental dynamic analyses were performesample buildings using twelve artificial ground motions to determine the yielding and collapse capacity of each sample building. Basecapacities, fragility curves were developed in terms of elastic pseudo spectral acceleration, peak ground acceleration (PGA) and elastic spectradisplacement for yielding and collapse damage levels with lognormal distribution assumption. To investigate the effect due to the nstories of the building on fragility parameters, regression analysis has been carried out between fragility parameters and the number othe building. It was observed that fragility parameters change significantly due to the number of stories of the building. Finally, using cofragility curves and statistical methods, the maximum allowable inter-story drift ratio and spectral displacement values that satisfy the “immediateoccupancy” and “collapse prevention” performance level requirements were estimated.c© 2006 Published by Elsevier Ltd

Keywords: Fragility curves; Damage; Yielding; Collapse; Performance levels; R/C frames

tho

thsiz

tsmeo

lityth

erct

tio

23

ofsed

signngsntncyvethe[ageage

red,blens,

minengsdo-

rveies,

1. Introduction

The behavior of reinforced concrete structures undereffect of ground motions has always been a subjectinvestigation, especially in seismic regions. Meanwhile,damage to buildings from recent earthquakes has emphathe need for risk assessment of existing building stockestimate the potential damage from future earthquakes. Seirisk analysis of a building is important for identifying thseismic vulnerability of a structural system under the effectpotential seismic ground motions. For this purpose, fragicurves are useful tools, since they allow estimation ofprobability of structural damage due to earthquakes asfunction of ground motion indices or various design paramete.g, peak ground acceleration (PGA), elastic pseudo speacceleration(Sa), and elastic spectral displacement(Sd). Thisapproach is useful for retrofitting decisions, damage estima

∗ Corresponding author. Tel.: +90 212 259 70 70x2679; fax: +90 21241 77.

E-mail address: [email protected] (M.S. Kircil).

0141-0296/$ - see front matterc© 2006 Published by Elsevier Ltddoi:10.1016/j.engstruct.2006.01.004

ef

eedoic

f

eas,ral

n,

6

loss estimation and disaster response planning. The aimthis study is to develop the fragility curves for mid-riR/C frame buildings in Istanbul which have been designeaccording to the 1975 version of the Turkish seismic decode with respect to different numbers of stories of buildiand the estimation of limit values of spectral displacemeand inter-story drift ratio that satisfy the immediate occupaand collapse prevention performance levels. Representati3, 5 and 7 story buildings were designed according toformer version (1975) of the Turkish seismic design code1].Although previous studies have employed different damlevels and corresponding quantities to specify those damlevels, in this study only yielding and collapse are considesince they can be determined analytically with reasonaaccuracy. Under the effect of twelve artificial ground motioincremental dynamic analyses were performed to deterthe yielding and collapse capacity of the sample buildiin terms of Sa, PGA andSd. Those capacities are evaluateby statistical methods to develop the fragility curves. A twparameter lognormal distribution is assumed for fragility cuconstruction, as was done traditionally in previous stud

http://www.elsevier.com/locate/engstruct

mailto:[email protected]

http://dx.doi.org/10.1016/j.engstruct.2006.01.004

1336 M.S. Kircil, Z. Polat / Engineering Structures 28 (2006) 1335–1345

isc

ct

em

cuoeag

thot

eiout

eetlri.in

dn

uc

ge

tioa

t

ret

ultsndrialndand

and a set of fragility curves was developed in terms ofSa,PGA andSd. In addition to the fragility curves, limit valuesof inter-story drift ratio and spectral displacement that satthe immediate occupancy and collapse prevention performanlevel requirements were estimated by using the construfragility curves and statistical methods.

2. Sample buildings

Sample 3, 5 and 7 story R/C residential buildings wdesigned according to the 1975 version of the Turkish seisdesign code. Although it was revised in 1998, the formversion was used for the design of sample buildings, sinmost of buildings were constructed before 1998. The structsystem of the sample buildings consists of R/C frames in twdirections.Fig. 1 shows the typical ground floor plan of thsample buildings. A building that is symmetrical in plan mbe chosen for simplicity. However, this type of sample buildinwould not be representative, since most of the buildingsIstanbul are not symmetrical. InFig. 2, a typical upper floorplan is shown. As is seen from the figures, almost allperimeter beams of the building are removed at the upper floThis is a widely practiced structural system in Istanbul andsurrounding area. The typical floor area is 275.4 m2 (16.2 m×17 m) and the story height is 2.90 m. Concrete slabs arstory levels with 12 cm thickness. Soil–structure interactwas not considered and the base of the columns at the grofloor are assumed to be fixed. Following common practice,characteristic compressive strength of concrete is assumbe 16 MPa for the design of the sample buildings. This valua realistic one, taking structural design practice in Turkey inconsideration. Also, two different types of reinforcement steeGrade 220 and 420, were considered, which have characteyield strengths of 220 MPa and 420 MPa, respectivelycombination of 12 sample buildings is considered by varythenumber of stories and the type of reinforcement (Table 1).The uncertainty due to the scatter of material properties wasconsidered. Only mean values ofmaterial strength determineby experiment were taken into consideration. Two dimensiononlinear dynamic analyses were performed separatelyeach direction of each sample building, since the structconfigurations in the X and Y directions are different to eaother.

3. Material properties

For the nonlinear dynamic analysis of the sample buildinas-built material strengths determined by experiment wtaken into consideration. For concrete, a normal distribuwith a mean strength of 13.6 MPa and a standard deviatiof 6.6 MPa was used. This distribution is the result ofexperimental study conducted by Akcay et al. [2] basedon concrete samples of 511 buildings in Istanbul andsurrounding area. The modified Kent & Park [3] model wasused to describe the stress–strain relationship of the concThe confinement effect was neglected, since transvreinforcement of the columns and beam ends of the exis

fyeed

reic

ereral

y

in

ers.

he

atnnd

hed tois

o,sticAg

not

alforralh

s,re

onnn

he

ete.rseing

Fig. 1. Typical ground story plan of the sample buildings.

Fig. 2. Typical upper story plan of the sample buildings.

Table 1Sample buildings

Samplenumber

Direction Initial period(s)

Reinforcementgrade

Number ofstories

1 X 0.46 220 32 Y 0.57 2203 X 0.46 4204 Y 0.57 420

5 X 0.62 220 56 Y 0.71 2207 X 0.62 4208 Y 0.71 420

9 X 0.76 220 710 Y 0.83 22011 X 0.76 42012 Y 0.83 420

buildingsdoes not have a significant confinement effect. Resof another experimental study, carried out by Akyuz aUyan [4] based on reinforcing bar samples tested in the matelaboratory of Istanbul Technical University between 1979 a1988, show that the mean yield strengths of the Grade 220

M.S. Kircil, Z. Polat / Engineering Structures 28 (2006) 1335–1345 1337

tio

veaa

a

ont

one

tdiI)unna[

fow

nohte

abthrtltd

are

f

ive;asel has[e

tor.

ayator.

tosure.ageareent,sentcan

Fig. 3. 5% damped elastic acceleration spectra of generated ground mo

420 reinforcements are 330 MPa and 440 MPa, respectiTri-linear and bilinear stress–strain relationships with strhardening were used for the reinforcement of Grade 220420 respectively.

4. Ground motions

The random nature of earthquakes makes the damestimation problem probabilistic. Shome and Cornell [5] haveshown that, for mid-rise buildings, ten to twenty ground motirecords are usually enough to provide sufficient accuracy inestimation of seismic demand. Twelve artificial ground motihave been used in this study to take the random naturearthquakes into consideration.Fig. 3 shows the accelerationspectra of the generated ground motions. For the generaof ground motions, a computer program developed in KanObservatory and Earthquake Research Institute (KOERBogazici University was used that generates artificial gromotions randomly for the specified magnitude, fault distaand duration, considering the given local spectra. Earthqurisk assessment study for the Istanbul metropolitan area6],carried out in KOERI, considered a magnitude of 7–7.5earthquake scenarios of Istanbul. Thus, a magnitude of 7.5specified for the generation of artificial ground motions usedthis study. The specified duration is 40 s for all ground motioFault distance was considered tobe 20, 30, 40 and 50 km tobtain ground motions with different characteristics. For eacfault distance, three different ground motions were generaThe local spectrum was randomly selected from the availlocal spectra of the Zeytinburnu region, which is one ofmost densely populated regions in the south-western paIstanbul.Figs. 4(a)and4(b)show the third and eighth artificiaground motions. Generated ground motion characteristicshave a10%probability of being exceeded in a 50-year perioare tabulated inTable 2.

5. Damage levels

Yielding and collapse are considered as basic damlevels for this study. Similar recent studies considered diffedamage levels and corresponding limit values in termsdifferent damage measures. Forinstance, for building types ostructure, Kircher et al. [7] and Smyth et al. [8] specified four

ns.

ly.innd

ge

hesof

ionlliatd

ceke

ras

ins.

d.leeof

hat

gentof

Fig. 4(a). Ground motion 3.

Fig. 4(b). Ground motion 8.

Table 2Properties of generated ground motions

Number ofground motion

Magnitude Faultdistance (km)

Duration(s)

Peak groundacceleration(g)

1 7.5 20 40 0.5062 7.5 20 40 0.5363 7.5 20 40 0.5994 7.5 30 40 0.5165 7.5 30 40 0.4786 7.5 30 40 0.5307 7.5 40 40 0.5258 7.5 40 40 0.5429 7.5 40 40 0.408

10 7.5 50 40 0.55211 7.5 50 40 0.57912 7.5 50 40 0.455

different damage levels: slight; moderate; major or extensand complete or collapse. Maximum inter-story drift ratio waccepted as the damage measure and each damage levan assumed limit value of inter-story drift ratio. Javanoska9]used similar damage levels. However, the Park–Ang damagindex [10] was employed by them as a damage indicaFor bridges, the Park–Ang damage index [10] was preferredby Karim and Yamazaki [11–13]. Furthermore, Shinozuket al. [14,15] and Saxena et al. [16] used the section ductilitdemand and corresponding limit values as a damage indicAlmost all damage levels used in previous studies are relatedthe assumed limit values of the considered damage meaDetermining those limit values of the considered dammeasure using an analytical method is very difficult. Theybased on the results of few experiments, engineering judgmand experience from previous earthquakes. For the prestudy, only yielding and collapse are considered, since theybe determined analytically with reasonable accuracy.


n 2

siese

suunseedece.t tgAnerwit

tethendityttuyre.unyst o

ioere

theeldthIn

e,edthurIDAthle

n 4
Fig. 5. IDA curve generated for 7 story sample building with ground motioin the X–X direction.
6. Incremental dynamic analysis

Incremental dynamic analysis (IDA) is a parametric analymethod that is usefulfor estimating structural performancunder several ground motions. The method is discuscomprehensively by Vamvatsikos and Cornell [17]. It mainlyinvolves producing one or more curves of damage meaversus intensity measure under the effect of scaled gromotions as a result of several non-linear dynamic analyFor this study, the maximum inter-story drift ratio is assumas a best damage indicator and a 5% damped elastic spacceleration is selected as the ground motion intensity measurEach ground motion is scaled monotonically with respecthe individual spectral acceleration based on the correspondinelastic fundamental period of each sample building.increment of 0.05 g in spectralacceleration is selected in ordto capture the yield and collapse capacity of the structurea reasonable sensitivity. The IDARC computer package [3] isused for non-linear dynamic analysis, and the maximum instory drift ratio is recorded at the end of each run. Up toyield point, the relationship between spectral acceleration athe maximum inter-story drift ratio is linear. The yield capacof the structure is defined as the spectral acceleration poinat which the curve leaves the linear path. When the strucreaches its collapse capacity, practically, an increase in intensitmeasure produces an infiniteincrease in damage measuTo determine the collapse capacity of the structure, gromotion is scaled up and several non-linear dynamic analare carried out until dynamic instability occurs as a resula non-converging run. Unless dynamic instability occurs at aninter-story drift ratio lower than 3%, an inter-story drift ratof 3% and the corresponding intensity measure is considas the collapse capacity of the structure.Fig. 5 shows theIDA curve generated for the sample 7 story building, withsecond generated ground motion in the X–X direction. Yiand collapse points are indicated in the figure. Generally,shape of the IDA curve is different for each ground motion.Fig. 6, a wavy IDA curve is shown. As is clear from the figursometimes lower damage measure values may be obtainfor an increasing value of intensity measure compared toobtained at the previous step for a lower intensity measUsing the generated ground motions, for each building, 24curves were generated: 12 for the X–X direction and 12 forother direction. All of the IDA curves obtained for the sampbuildings are shown inFigs. 7–9.

s

d

reds.

tral

o

h

r-

re

desf

d

e

ate.

e

Fig. 6. IDA curve generated for 5 story sample building with ground motioin the Y–Y direction

(a) Reinforcement grade 220.

(b) Reinforcement grade 420.

Fig. 7. IDA curves generated for 3 story sample building.





heagtutifytio

eg

g.o

bionilita

ac

a

cath

an

7

20

s

ortion.ral

o

n-nt-ple

od

ni--

e-




The definition of the load–deformation relationships of tcross-sections has particular importance in defining damdue to the effect of earthquakes. The moment–curvarelationships generated by IDARC-2D were used to idencross-sectional load–deformation characteristics. In addito a skeleton curve, the IDARC-2D needs threeparametersto identify the hysteretic behavior. The nominal values ofthe parametersα, β and γ suggested by authors werused to consider the effect of stiffness degradation, strendegradation and pinching.

7. Fragility curves

Fragility curves express the probability of structural damadue to earthquakes as a function of ground motion indicesthe present study, fragility curves are constructed in termsSa, Sd and PGA. It is assumed that the fragility curves canexpressed in the form of two-parameter lognormal distributfunctions. Based on this assumption, the cumulative probabof the occurrence of damage, equal to or higher than damlevel D, is expressed as

P(≤D) = Φ(

ln X − λ

ζ

)(1)

whereΦ is the standard normal distribution,X is the lognormaldistributed ground motion index (e.g.,Sa, Sd, PGA), and λ

and ζ are the mean and standard deviation of lnX . Themean and standard deviation of ground motion indices for edamage level are obtained, as shown inFig. 10, which is alognormal plot of lnX and the corresponding standard normvariable. This method is based on plotting lnX versus thecorresponding standard normal variable on a lognormal sand performing a linear regression analysis to determinemean and standard deviation of lnX for each damage level [18].The relationship between the standard normal variable

ere

n

th

eInf

e

yge

h

l

lee

d

Fig. 10. Lognormal probability plot for collapse probability curve of samplestory building with reinforcement grade 420.

Fig. 11. Fragility curve of sample 5 story building for reinforcement grade 2and 420.

the mean and standarddeviation of lnX can be expressed afollows:

s = ln X − λ

ζ(2)

where s is the standard normal variable.Fig. 10 showsthe typical lognormal probability plot for the collapse of asample 7 story building.Table 3shows themean and standarddeviation of lognormal distributed ground motion indices feach sample building and damage level under consideraFragility curves of a sample 5 story building in terms of spectdisplacement are shown inFig. 11. Note that two differentfragility curves were constructed for each building, since twdifferent reinforcement types have been considered.

8. Combined fragility curves

Since twodifferent types of reinforcement steel were cosidered for each sample building, two different reinforcemetype-dependent fragility curves were obtained for each sambuilding in terms of each ground motion index. The methproposed by Shinozuka et al. [15] was used for combiningreinforcement-type-dependent fragility curves to obtain a ufied fragility curve for a mixed set of populations of buildings, in which there areN1 and N2 buildings with Grade 220and Grade 420, respectively.N1 and N2 define the ratio ofbuildings with Grade 220 and buildings with Grade 420 in thpopulation of building stock, respectively. It is highly recommended that one should see Ref. [15] for details of this method.


Table 3Reinforcement-type-dependent fragility curve parameters

Story number Reinforcement grade Indices ParametersYielding Collapseλ ζ λ ζ

3 220 Sa −1.85 0.273 0.412 0.276PGA −2.59 0.225 −0.334 0.197Sd −4.56 0.186 −2.3 0.279

3 420 Sa −1.52 0.296 0.593 0.258PGA −2.26 0.283 −0.151 0.185Sd −4.22 0.169 −2.11 0.253

5 220 Sa −2.06 0.177 0.25 0.302PGA −2.714 0.164 −0.431 0.244Sd −4.25 0.113 −1.94 0.26

5 420 Sa −1.87 0.181 0.359 0.276PGA −2.57 0.169 −0.344 0.222Sd −4.07 0.143 −1.83 0.224

7 220 Sa −2.39 0.313 0.152 0.346PGA −3.01 0.205 −0.474 0.225Sd −4.21 0.235 −1.68 0.287

7 420 Sa −2.12 0.257 0.211 0.371PGA −2.74 0.17 −0.415 0.244Sd −3.94 0.192 −1.62 0.308

,

edalle

on.

esof

ondethat,isrmal

n,

theangeus,ory

Fig. 12. Combined fragility curve of 5 story sample building.

The combined fragility curve can be expressed as follows:

Fc(X) = P1F1(X) + P2F2 (X) (3)

whereFc(X) is the combined fragility curve, andF1(X) andF2(X) are fragility curves of building with Grades 220 and 420respectively.P1 andP2 can be expressed as follows:

P1 = N1

N1 + N2(4)

P2 = N2

N1 + N2(5)

whereN1 and N2 are the populations of buildings constructwith reinforcement Grades 220 and 420, respectively. Finbased on(2), the mean and standard deviation of the combinfragility curves can be expressed as follows:

λc = P1λ1 + P2λ2 (6)

ζ 2c = P1ζ

21 + P2ζ

22 + P1(1 − P1)λ

21

+P2(1 − P2)λ22 − 2P1P2λ1λ2 (7)

y,d

Fig. 13(a). Fragility curves for yielding with respect to spectral accelerati

where λ1 and λ2 are the means of buildings with Grad220 and 420, andζ1 and ζ2 are the standard deviationsbuildings with Grades 220 and 420, respectively.Fig. 12showsthe fragility curves presented inFig. 11 with the combinedfragility curve. Since there is not enough informationthe populations of buildings constructed with either Gra220 or Grade 420, in the present study it is assumedP1 = P2 = 0.5. Note that, for the combined fragility curvethe lognormal distribution is no longer valid. However, itstill reasonable to assume that the combined curve is lognowith the mean and standard deviation estimated by(6) and(7), respectively [15]. All the combined fragility curves foryielding and collapse are shown inFigs. 13and14 in terms ofelastic pseudo spectral acceleration, peak ground acceleratioand elastic spectral displacement, respectively.

9. Extended fragility curves

It is observed from the fragility curves given so far thatfragility curve parameters, mean and standard deviation, chwith respect to the number of stories of the buildings. Thto extend the fragility curves constructed for 3, 5 and 7 st


nt

ion

nd

s,nt

ve

ent.

redsults,

uresond-y

Fig. 13(b). Fragility curves for yielding with respect to peak groundacceleration.

Fig. 13(c). Fragility curves for yielding with respect to spectral displaceme

Fig. 14(a). Fragility curves for collapse with respect to spectral accelerat

Fig. 14(b). Fragility curves for collapse with respect to peak grouacceleration.

buildings to the fragility curves for 4 and 6 story buildinglinear regression analyses havebeen performed. The regressiomodels that are used to obtain the relationship betweenfragility curve parameters and the number of stories are gi

.

.

hen

Fig. 14(c). Fragility curves for collapse with respect to spectral displacem

(a) Regression analysis for mean.

(b) Regression analysis for standard deviation.

Fig. 15. Regression analysis results.

below:

λ = an + b (8)

ζ = cn2 + dn + e (9)

wheren is the number of stories of the building, anda, b, c, andd are coefficients obtained from regression analyses.Fig. 15shows the regression analysis results ofλ and ζ for collapsewith respect toSa. Table 4shows the regression coefficientsobtained for yield and collapse capacities in terms ofSa, Sdand PGA. It is worth noting thatR2 valuesare very high, sincethe number of data is the minimum number of data requifor a regression analysis. Using the regression analyses reextended fragility curves are shown inFigs. 16and17.

10. Performance limits

Recently developed performance based design procedconsider the inelastic displacement demand and corresping deformations as the main performance indicator. Recentl


Table 4List of the regression coefficients

Indices Yielding Collapse

λ = an + b ζ = cn2 + dn + e λ = an + b ζ = cn2 + dn + e

a b R2 c d e R2 a b R2 c d e R2

Sa 0.1425 −1.2558 0.999 0.03 −0.303 0.968 1 −0.0803 0.7308 0.982 0.0068 −0.048 0.3653 1PGA −0.1125 −2.0848 0.999 0.0218 −0.2355 0.8148 1 −0.0506 −0.1052 0.941 −0.0031 0.0375 0.1276 1Sd 0.0787 −4.6021 0.934 0.0233 −0.2305 0.7283 1 0.139 2.607 0.992 0.0105−0.101 0.4915 1

on.

d

ent

laclsc

loc-aliowba

ion.

nd

ent.

r-edse-di-

h theni-

Fig. 16(a). Fragility curves for yielding with respect to spectral accelerati

Fig. 16(b). Fragility curves for yielding with respect to peak grounacceleration.

Fig. 16(c). Fragility curves for yielding with respect to spectral displacem

published documents ATC 40 [19] and FEMA 356 [20] rec-ommend several methods to estimate the inelastic dispment of the structures under the effect of earthquakes. Asome performance levels and corresponding performanceteria are specified by the same documents based on theinelastic deformation demand and capacity of structural members. Performance based design procedures are more recompared to the widely used linear design philosophy. Hever, theseprocedures are also time-consuming. Thus, glo

.

e-o,ri-al

stic-l

Fig. 17(a). Fragility curves for collapse with respect to spectral accelerat

Fig. 17(b). Fragility curves for collapse with respect to peak grouacceleration.

Fig. 17(c). Fragility curves for collapse with respect to spectral displacem

structural performance criteria in terms of the maximum intestory drift ratio or spectral displacement, which can be usfor fast but approximate evaluation of structures, may be uful. In the present study, two main performance levels, immeate occupancy and collapse prevention, are associated wityielding and collapse probability curves considering the defitions of performance levels given by ATC 40 [19] and FEMA356 [20] to estimate the global performance criteria.


e

foae

ceere

e,l-

n-byn14o

rmha-ftiohi

edeve

n

ygs

nsethe

dtioning

these

lityhch

lr at

f

se

ses.nd7s

eof

mitthece

rale

edntral

heit

d

Fig. 18(a). Inter-story drift ratio limit for immediate occupancy performanclevel.

Fig. 18(b). Inter-story drift ratio limit for collapse prevention performancelevel.

The immediate occupancy performance level is the permance level at which the structure has almost pre-earthqustiffness. Considering this expression, it is assumed that thmaximum allowable inter-story drift ratio for this performanlevel can be defined as the inter-story drift ratio at which this a high confidence of a low probability of yielding on thyield probability curve.Figs.18(a)and18(b) show three dif-ferent fragility curves constructed for yielding and collapsrespectively. InFig. 18(a), each curve provides the probabiity of yielding at varying levels of inter-story drift ratio for agiven level of confidence. The fragility curve which has a cofidence level of 50% is a typical fragility curve constructedthe methodology used in the present study. It is worth notithat each of those fragility curves was constructed usingmaximum inter-story drift ratios, regardless of the numberstories of the sample buildings. As mentioned earlier, the immdiate occupancy performance level limit can be defined in teof the maximum inter-story drift ratio at which there is a higconfidence of a low probability of yielding on the yield probbility curve in Fig. 18(a). For this study, a confidence level o95%and collapse probability of 5% are selected and a drift raof 0.0013 was specified as the maximum allowable inter-stdrift ratio for the immediate occupancy performance level. Tpoint is indicated inFig. 18(a). This shows the inter-story driftratio that causes yielding of 5% of the sample buildings. Bason the same assumptions, a drift ratio of 0.0216 was specifiethe maximum allowable inter-story drift ratio for a collapse prvention performance level using the collapse probability cur

r-ke

e

g4fe-s

orys

das-.

Table 5Spectral displacement limits of performance levels

Story number Sd (cm)Immediate occupancy Collapse preventio

3 0.7 6.24 1 7.65 1.1 9.16 1.1 107 1 10.4

This point is indicated inFig. 18(b)and shows the inter-stordrift ratio that causes collapse of 5% of the sample buildinwith a confidence level of 95%.

Since spectral displacement is a very common respoparameter that shows the demand of ground motions onstructures, limit values of spectral displacement were estimatefor both immediate occupancy and collapse prevenperformance levels. The procedure followed for estimatlimit spectral displacement values is summarized below.

• Following the same procedure used for the estimation oflimit inter-story drift ratio, limit spectral displacement valueare estimated for the immediate occupancy performanclevel at which there is a high confidence of a low probabiof yielding on the yield probability curve using eaccombined yielding probability curve constructed for eanumber of stories.Fig. 19(a) shows the estimated spectradisplacement and combined yielding probability curve fosample 7 story building. All thelimit spectral displacemenvaluesestimated for the immediate occupancy performancelevel are tabulated inTable 5with respect to the number ostories of the sample buildings.

• Limit spectral displacement values for the collapprevention performance level are estimated following thesame procedure, but this time using the combined collapprobability curve constructed for each number of storieFig. 19(b) shows the estimated spectral displacement acombined collapse probability curve for a samplestory building. All the limit spectral displacement valueestimated for the collapse prevention performance level artabulated inTable 5with respect to the number of storiesthe sample buildings.

• Regression analyses are carried out between the lispectral displacement values and the story number ofsample buildings to obtain simple equations that produthe story-number-dependent maximum allowable spectdisplacement for immediate occupancy and the collapsprevention performancelevels, respectively.

For the regression analysis, linear equations are assumto be sufficient for representing the relationship betweethe number of stories and the maximum allowable specdisplacement.Fig. 20 shows the regression analysis resultsand confidence intervals for a confidence level of 90%. Tfollowing equations were obtained, which produce the limspectral displacement in “cm” for immediate occupancy an


for

pse

f

t ace

totiofo

tur,e

/C

tos aal

ilitydu

iate

pse

lysiseenandof

mnteth

plen thes

pse

id-rdingFortionriesfor

ncees a

hork.to

Fig. 19(a). Spectral displacement limit of 7 story sample buildingimmediate occupancy performance level.

Fig. 19(b). Spectral displacement limit of 7 story sample building for collaprevention performance level.

collapse prevention performance levels, respectively:

Sd = 0.07n + 0.63 (cm) (10)

Sd = 1.04n + 3.38 (cm) (11)

whereSd is the maximum allowable spectral displacement othe corresponding performance level andn is the number ofstories of the building. Note that the correlation betweenn andSd for the immediate occupancy performance level is nohigh as the correlation for the collapse prevention performanlevel. All the regression coefficients are given inTables 6and7for each confidence levels.

11. Conclusions

The uncertain nature of future ground motions is leadingthe development of probabilistic structural damage estimaprocedures. The fragility curve approach is a useful methodestimating the structural damage for certain types of strucunder the effect of potential earthquakes. In this studymethod for obtaining the fragility curves for mid-rise R/C frambuildings is defined and the fragility curves of a mid-rise Rframe building, typical of the inventory of existing buildings inIstanbul, were constructed in terms ofSa, PGA andSd underthe effect of twelve artificial ground motions with respectdifferent numbers of stories. The considered damage levelyielding and collapse, since they can be determined analyticwith reasonable accuracy. It is observed from the fragcurves that there is an effect on fragility curve parameters

s

nrea

rely

e

Fig. 20(a). Relationship between spectral displacement limit of immedoccupancy performance level and story number of building.

Fig. 20(b). Relationship between spectral displacement limit of collaprevention performance level and story number of building.

to the number of stories in the buildings. Regression anahas been carried out to determine the relationship betwthe fragility curve parameters and the number of stories,extended fragility curves were constructed with the helpthe results of regression analysis. Furthermore, the maximuallowable inter-story drift ratio and spectral displacemevalues that satisfy the immediate occupancy and collapsprevention performance level requirements are estimated wirespect to the number of stories of the buildings usingconstructed fragility curves and statistical methods. Simequations were obtained that show the relationship betweelimit values of spectral displacement and the number of storieof the building for the immediate occupancy and collaprevention performance levels, respectively. Those simpleequations may be used for the preliminary evaluation of mrise R/C frame structures that have been designed accoto the 1975 version of the Turkish seismic design code.the collapse prevention performance level, a good correlabetween spectral displacement limit and the number of stois observed. However, the same observation is not validthe immediate occupancy level. Thus, for this performalevel, the maximum allowable spectral displacement may bcalculated using the curve of a confidence level of 90% alower bound.

Acknowledgements

The authors are grateful to Professor M.N. Aydinoglu, wprovided useful comments that helped to improve this woThe authors would also like to express their gratitude


Table 6Regression analysis results for immediate occupancy performance level

Confidence level10% 50% 90%

Sd = an2 + bn + c Sd = an + b Sd = an2 + bn + ca b c a b a b c

0.0038 0.0325 0.8858 0.07 0.63 −0.0038 0.108 0.3728

Table 7Regression analysis results for collapse prevention performance level

Confidence level10% 50% 90%

Sd = an2 + bn + c Sd = an + b Sd = an2 + bn + ca b c a b a b c

0.0148 0.8925 4.3798 1.04 3.38 −0.0148 1.1875 2.3802

io

n

oo

Cy

a

bq

g;

i.

ge-al

itylityII;

ityEng

y.

f

ilitynal00.

g

g.

tioncy;

Research Assistant B.H. Akman, who conducted the generatof the artificial ground motions. Both are from KOERI.

References

[1] Turkish Seismic Design Code. Ministry of Public Works and SettlemeAnkara; 1975 [in Turkish].

[2] Akcay B, Onen YH, Oztekin E. Experimental concrete quality inspectifor building in Istanbul. In: Technical notes, 16th technical Congresscivil eng.;2001 [in Turkish].

[3] IDARC-2D V5.0 computer program. Inelastic damage analysis of Rbuilding structures, State University of New York; 1996. Developed bPark YJ, Reinhorn AM, Kunnath SK.

[4] Akyuz S, Uyan M. A review on the reinforcement bars used in Turkey.CCE Tech J 1992; April:497–508 [in Turkish].

[5] Shome N, Cornell CA. Probabilistic seismic demand analysis of nonlinestructures. Ph.D. dissertation. Stanford: Stanford University; 1999.

[6] Executive summary of earthquake risk assessment for Istanmetropolitan area. Bogazici University Kandilli Observatory and EarthResearch Institute. Istanbul; 2002.

[7] Kircher CA, Nassar AA, Kustu O, Holmes WT. Development of buildindamage functions for earthquake loss estimation. Earthq Spectra 199713(4):663–80.

[8] Smyth A, Altay G, Deodatis G, Erdik M, Franco G, G¨ulkan P et al.Benefit-cost analysis for earthquakemitigation: Evaluating measures forapartment houses in Turkey. Earthq Spectra 2004;20(1):171–203.

[9] Jovanoska ED. Fragility curves for reinforced concrete structuresSkopje (Macedonia) region. Soil Dyn and Earthq Eng 2000;19(6):455–66

n

t,

nn

r

ul

n

[10] Park YJ, Ang AH-S, Wen YK. Seismic damage analysis and damalimiting design of R/C buildings. Civil Engineering Studies-Technicreport no. SRS 516. University of Illinois. Urbana. 1984.

[11] Karim KR, Yamazaki F. Comparison of emprical and analytical fragilcurves for RC bridge piers in Japan. In: Proc., 8th ASCE Speciaconference on probabilistic mechanics and structural reliability, vol.2000. p. 205–12.

[12] Karim KR, Yamazaki F. Effect of earthquake ground motions on fragilcurves of highway bridge piers based on numerical simulation. EarthqStruct Dyn 2001;30(12):1839–56.

[13] Karim KR, Yamazaki F. A simplified method of constructing fragilitcurves for highway bridges. Earthq Eng Struct Dyn 2003;32(10):1603–26

[14] Shinozuka M, Feng MQ, Kim HK, Kim SH.Nonlinear static procedurefor fragility curve development. J Eng Mech 2000;126(12):1287–95.

[15] Shinozuka M, Feng MQ, Lee J, Naganuma T. Statistical analysis ofragility curves. J Eng Mech 2000;126(12):1224–31.

[16] Saxena V, Deodatis G, Shinozuka M, Feng MQ. Development of fragcurves for multispan reinforced concrete bridges. In: Proc. internatioconference on Monte Carlo simulation. Balkema Publishers; 20p. 499–504.

[17] Vamvatsikos D, Cornell AC. Incremental dynamic analysis. Earthq EnStruct Dyn 2002;31(3):491–514.

[18] Gunduz A. Probability, statistics, risk and reliability in engineerinIstanbul: Kure publications; 1996 [in Turkish].

[19] ATC-40. Seismic evaluation and retrofit of existing concrete buildings.Redwood City (CA): Applied Technology Council; 1996.

[20] FEMA 356. Prestandard and commentary for the seismic rehabilitaof buildings. Washington DC: Federal Emergency Management Agen2000.

fragility analysis of mid-rise rc frame buildings

Documents