displacement based fragility functions

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Displacement-Based Fragility Functionsfor Low- and Mid-rise OrdinaryConcrete Buildings

Sinan Akkar,a

Haluk Sucuoglu,a

M.EERI,and Ahmet Yakuta

Fragility functions are determined for low- and mid-rise ordinary concretebuildings, which constitute the most vulnerable construction type in Turkey aswell as several other countries prone to earthquakes. A hybrid approach isemployed where building capacities are obtained from field data and theirdynamic responses are calculated by response history analyses. Field dataconsists of 32 sample buildings representing the general characteristics of two-

to five-story substandard reinforced concrete buildings in Turkey. Lateralstiffness, strength, and deformation capacities of the sample buildings are

determined by pushover analyses conducted in two principal directions.Uncertainties in lateral stiffness, strength, and damage limit states areexpressed by using statistical distributions. The inelastic dynamic structural

characteristics of the buildings investigated are represented by a family ofequivalent single-degree-of-freedom systems and their seismic deformationdemands are calculated under 82 ground-motion records. Peak ground velocityPGVis selected as the measure of seismic intensity since maximum inelasticdisplacements are better correlated with PGV than peak ground accelerationPGA. Fragility functions are derived separately for different number ofstories, which is a prominent parameter influencing the vulnerability ofexisting substandard concrete buildings. DOI: 10.1193/1.2084232

INTRODUCTIONFragility functions are the essential tools for seismic loss estimation in built environ-

ments. They represent the probability of exceeding a damage limit state for a givenstructure type subjected to a seismic excitation Shinozuka et al. 1999. The damagelimit states in fragilities may be defined as global drift ratio maximum roof drift nor-malized by the building height, interstory drift ratiomaximum lateral displacement be-tween two consecutive stories normalized by the story height, story shear force, etc. Inthis study, the global drift is chosen to identify the damage limit states, as the selected

buildings do not possess soft stories that may invoke excessive local drift demands. Theground motion intensities in the fragility functions can be spectral quantities, peakground motion values, modified Mercalli scale, etc. In this respect, fragility curves in-volve uncertainties associated with structural capacity, damage limit-state definition, and

record-to-record variability of ground motion intensity.

a Earthquake Engineering Research Center, Department of Civil Engineering, Middle East Technical University,

06531 Ankara, Turkey

901

Earthquake Spectra, Volume 21, No. 4, pages 901927, November 2005; 2005, Earthquake Engineering Research Institute


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A particular structure type is considered in this study, namely, two- to five-story ex-

isting reinforced concrete buildings, which generally do not comply with modern seis-mic resistant design and construction practice. These buildings constitute the majority ofthe vulnerable building stock in Turkey, which is revealed by the recent strong earth-quakes in the last decade. Fast urban growth after the 1970s, substantiating uncontrolleddevelopment of the physical environment, is the primary source of such existing risks.The buildings investigated are categorized into subgroups with respect to their number

of stories. Field observations after recent damaging earthquakes have clearly indicated asignificantly increasing damage trend with the number of stories. Although this may not

be expected in buildings conforming to seismic design regulations, it is very likely oth-

erwise. Figure 1 shows the damage distribution in 6,478 two- to five-story buildings inDzce after the 12 November 1999 M7.1 Dzce earthquake Sucuoglu and Yilmaz2001. Buildings with none/light damage were allowed to be in continuous use after theearthquake, but retrofitting was required for moderately damaged buildings, and severelydamaged buildings had to be demolished, with no permission for further occupation. In-crease in damage with the number of stories is notable.

The objective of this study is to determine the fragility functions for two- to five-

story substandard concrete buildings in Turkey. A realistic description of the fragilitiesfor such buildings is important because almost 75 percent of approximately one million

buildings in Istanbul are in this category, and Istanbul is under a significant seismic riskParsons et al. 2000. The uncertainties in structural characteristics are taken into ac-count by considering the variability in fundamental period of vibration, lateral strength,

and damage limit state that are obtained from field data. Using a set of 82 strong groundmotions spanning a broad range of intensities, on the other hand, incorporates random-ness of seismic excitations. The fragility functions are determined separately for two- tofive-story concrete buildings as the probabilities of exceeding the specifieddisplacement-based damage limit states under ground excitations, where seismic inten-sities are expressed in PGV terms.

Figure 1. Damage distribution in Dzce after the 12 November 1999 M7.1 Dzce earthquake,

with respect to the number of stories.

902 S. AKKAR, H. SUCUOGLU, AND A.YAKUT


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FIELD DATABASE

Lateral-load deformation characteristics of typical reinforced concrete buildings in

Turkey have been determined by investigating 32 sample buildings. These buildingswere selected to represent a typical subset of a comprehensive database consisting ofnearly 500 buildings that were compiled in the city of Dzce after the 1999 earthquakes,

based on post-earthquake damage assessmentsAydogan 2003, Yakut et al. 2003. Thepopulation of 500 buildings approximately represented the story and damage distribu-tion in Dzce after the 1999 earthquake, shown in Figure 1. All buildings were rein-

forced concrete frame structures with masonry infill walls, the most common and domi-nant construction type in Turkey. They were further classified into four height groups

based on the number of stories. The average heights for two, three, four, and five stories

were 6.0, 8.9, 11.7, and 14.4 meters, respectively. Design drawings were available for

the selected 32 sample buildings.

SEISMIC PERFORMANCE EVALUATION BY NONLINEAR STATIC PROCEDURE

Three-dimensional models of each sample building were prepared in the SAP2000environment Computers and Structures 2000. Nonlinear static analysis was conductedto determine the base shear versus roof displacement relationshipcapacity curve. Thenmodal properties were determined consistently that conform to the initial linear part ofthe bilinear representation of the capacity curves. Flexural elements for beams, beam-

column elements for columns, strut elements for infill walls, and rigid diaphragms forfloors were employed for modeling the structural components of the buildings.

Nonlinear flexural characteristics of the individual frame members were defined bymoment-rotation relationships of plastic hinges assigned at the member ends. Flexuralmoment capacities were based on the section and material properties of members. Col-umn capacities were calculated from the three-dimensional axial force-bending momentinteraction diagrams. A typical moment-rotation relationship for frame members is

shown in Figure 2. The segment AB, representing initial linear behavior, is followed bythe post-yield behavior BC. Point C corresponds to the ultimate strength, where a sud-den loss of strength occurs when the associated plastic rotation level is exceeded. The

Figure 2. Idealized moment-rotation relationship of a frame member-end.

DISPLACEMENT-BASED FRAGILITY FUNCTIONS FOR LOW- AND MID-RISE CONCRETE BUILDINGS 903


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drop from C to D represents the initiation of failure in the member. It has to be notedthat certain inferior characteristics of reinforced concrete members such as bond slip orlap splice failure cannot be incorporated directly in the model shown in Figure 2.

The infill walls were modeled by equivalent diagonal struts whose properties depend

on the infill material and wall dimensions, as given in Equation 1 ASCE 2000.

k=Gbt

h

Tc=fmft

1.5fm+ft

Ny= cAvh

b. 1

In the above equations, c denotes the shear strength of the rectangular panel corre-

sponding to diagonal cracking, andfmandftare the compressive and tensile strengths ofthe masonry, respectively. The variable Av is the shear area, h is the height, b is thewidth, and tis the thickness of the infill wall panel.

A displacement controlled nonlinear static procedure was employed with an invertedtriangular lateral-load distribution for obtaining the capacity curves of each building.The resulting capacity curves for typical buildings, representing two-, three-, four-, andfive-story buildings, are shown in Figure 3.

All four buildings in Figure 3 have more or less similar ultimate global drift capaci-ties, around 1.5 percent. However, their lateral strength and stiffness decrease with thenumber of stories. The strength difference between the two- and three-story buildings

Figure 3. Selected capacity curves for 2-, 3-, 4-, and 5-story buildings.



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appears to be higher than the difference between three- and four-story buildings and be-tween four- and five-story buildings. This is most likely due to the significant contribu-

tion of infill walls to the lateral load-resisting capacity of the two-story building for thisparticular case. However, when the entire building inventory is considered, the mean andmedian strength values for the story-based building groups do not show such abruptchanges while passing from one group to the other. These statistics are listed in Table 1and discussed in detail in the paper. Since higher seismic displacement demands are

placed on systems with lower stiffness and yield strength, damage vulnerability in-creases inevitably with the number of stories.

Figures 4 and 5 present the structural plan layout of the two- and four-story buildingsfor which the capacity curves are plotted in Figure 3. Despite some variations that areusually experienced, these layouts and plan dimensions represent the general features ofmost of the low- and mid-rise reinforced concrete buildings in Turkey. The correspond-ing plastic hinge patterns at significant yielding and ultimate capacity states are shown

in Figures 6 and 7, respectively. The symbols used for hinges indicate whether the yield-ing is at an initial level in the vicinity of point B in Figure 2, majoron portion BC inFigure 2, or exceeds the failure initiation state on portion DE in Figure 2. The two-story building was pushed in the longitudinal direction, and the four-story building was

pushed in the transverse direction that is indicated in Figures 4 and 5, respectively. It is

noteworthy to state that the capacity curves for the buildings in the two principal direc-tions may be significantly different, especially for buildings having rectangular floor

plans.

It may be observed from Figures 6 and 7 that the damage sequence in both framesstarts with the cracking of infill walls, then the yielding of beam ends at the lower sto-

Table 1. Statistics of the capacity curve parameters

Parameter Story Number Mean Median Standard Deviation

All 0.14338 0.12500 0.06620

2 0.21990 0.19300 0.08082

3 0.16233 0.14100 0.05478

4 0.11667 0.10600 0.03438

5 0.09339 0.09000 0.02927

y All 0.001150 0.00110 0.00037

2 0.001175 0.00100 0.00054

3 0.001117 0.00110 0.00035

4 0.001291 0.00120 0.00040

5 0.001084 0.00110 0.00026

u All 0.01335 0.01400 0.00432

2 0.01460 0.01600 0.00334

3 0.01410 0.01500 0.00463

4 0.01390 0.01500 0.00380

5 0.01130 0.01200 0.00430



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ries, which further propagates to upper stories, and finally with the yielding of columnbases. This is an expected sequence in achieving a ductile beam mechanism, yet the ul-timate global drifts are less than 2 percent. The main reason for such low deformation

Figure 4. Plan layout of the 2-story building.

Figure 5. Plan layout of the 4-story building.



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capacity of frames is insufficient rotation capacities of unconfined yielding regions. Glo-

bal failure occurs quite suddenly when no other reserve members are left that can beactivated for maintaining the inelastic capacity.

IDEALIZATION OF BUILDING RESPONSE BY A SDOF SYSTEM RESPONSE

The capacity curve of each building was approximated with a bilinear curve usingthe guidelines given in FEMA-356ASCE, 2000. A typical idealization of a capacitycurve is shown in Figure 8. It is required to specify the yield and ultimate strength ca-

pacities and their associated global drift values for constructing the approximate bilinearcapacity curve. The global drifts are used here to represent the damage limit states of the

buildings because none of the buildings in the data set showed a soft-story mechanism.

The yield global drift ratio y represents significant yielding of the system when the

yield base shear capacity Vy of the building is attained, whereas the ultimate global

drift ratio u corresponds to the state at which the building reaches its deformation ca-pacity. The base shear coefficient= Vy / W in Figure 8 is the ratio of yield base shearcapacity to the building weight.

It should be noted that there is no universal consensus on how to approximate a ca-

pacity curve with a bilinear force-deformation representation. An initial stiffness target-

ing at the state of significant global yielding may lead to considerable variations in Vy

Figure 6. Plastic hinge patterns for the selected 2-story building: a status at global yield, andb status at the global ultimate capacity.



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and y because there is no specific point on the capacity curve exactly describing sig-nificant yielding Sullivan et al. 2004. These variations affect the effective periodap-

proximate fundamental period and global ductility as well. The approach employed

Figure 7. Plastic hinge patterns for the selected 4-story building: a status at global yield ca-pacity, andb status at global ultimate capacity.

Figure 8. A typical bilinear capacity curve.



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herein is consistent with the assumptions made in the modeling and analysis phases. Thebilinear idealizations of the calculated capacity curves presented in Figure 3 are shownin the same figure for comparison.

CAPACITY STATISTICS OF THE SAMPLE BUILDINGS

Relationships between the fundamental period, building height and story number ob-

tained from the investigated building stock are presented in Figure 9. The fundamentalperiods of the buildings in two principal directions range approximately from0.15 s to 0.90 s. Apparent scatter for each story group reflects the natural characteristics

of the representative building stock employed. The boxes shown in Figure 9a representeffective period intervals selected for each story group mean plus/minus one standarddeviation where the effective period ranges for two-, three-, four-, and five-story build-ings are 0.150.30, 0.250.45, 0.300.55, and0.400.65 seconds, respectively. Figure9b shows the period versus height scatters for the building stock with simple fits to de-scribe the mean and plus/minus one standard deviation trends in fundamental period asa function of building height. If the sample buildings in this study are assumed to re-

semble the typical Turkish construction practice, the regressed values suggest stifferbuildings in Turkey with respect to those in the United States that can be classified in thesame structural system category.

The variation of yield base shear coefficient with effective period for the buildings inthe database is shown in Figure 10. The spectral variations of the Turkish code yield base

shear coefficient that was promulgated in 1975 and updated in 1998 Turkish Ministry1975, 1998 are also displayed in Figure 10, and compared with the field data. There isrelevant information to support that all buildings in the database were dated from the

post-1975 era; accordingly, their seismic designs were expected to conform to the pro-visions of the 1975 edition of the Turkish Seismic Code 1975. The inherent over-strength in the two- and three-story buildings compared to the 1975 code can be attrib-

Figure 9. Variation of fundamental period with a the number of stories, and b building

height.



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uted to different sources such as structural behavior as well as the detailing and material

properties. However, for the low-rise buildings considered in this study, the major con-tribution is most likely the initial lateral strength of the infill walls. Figure 10 also re-veals that the minimum base shear capacity requirement of the Turkish code is not sat-isfied for most of the four- and five-story sample buildings. In addition to the yield base

shear coefficient, two displacement parameters indicated on the capacity curve in Fig-

ure 8, namely, the yield drift ratio y and the ultimate drift ratio u, are of essential im-

portance in the displacement-based performance evaluation of buildings. The statisticalproperties of these three parameters are given in Table 1, both for all buildings in theinventory, and separately for each number of stories. The approach used in these statis-tics is denoted as counted statistics and measure the central tendency and the dispersion

around the central tendency for each building group. There is a clear trend that andudecrease with an increase in the number of stories. The statistics are based on the model

pushover results that lack detailed modeling of bond slip and lap splice failure, whichare important in determining the ultimate drift capacity. The information provided inTable 1 can be considered as an upper bound for the quantitative description of general

capacity trend for the building inventory presented in this study.

Representative probability density functions of y and u are shown in Figure 11.

When global ductility capacities u /y are calculated, artificially high values around

1015 are obtained. This is misleading as the buildings investigated possess high initialstiffness hence low ydue to presence of stiff infill walls and short spans Figures 4 and5. It is more appropriate to employ u in assessing the deformation capacities of such

buildings, which are fairly low as revealed in Table 1.

The peculiarities of existing Turkish buildings, which are reflected quite well in the

data set, are taken into consideration in assigning performance limit states in terms of

Figure 10. Comparison of the base shear capacities of sample buildings with code

requirements.



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global drift ratios. Three performance limits immediate occupancy, life safety, and col-lapse prevention that are specified in several other international guidelines are adoptedhere. The performance limits are computed under the guidance of story-specific median

y and u. Considering the uncertainty in modeling the structural deficiencies as de-scribed in the preceding paragraphs and the left-skewed tendency in the ultimate drift

probability density function computed from the overall building data, the collapse pre-

vention performance limit CPis taken as the 75 percent of the median ucomputed foreach story-based building group. The proposed values are slightly higher than the cor-responding mean minus one standard deviation of the ultimate drift ratios listed in Table1. The life safety performance is assigned as the third quartile of the suggested collapse

prevention limit. The median y computed for each story-based building group is ac-

cepted to be the limiting value for the immediate occupancy performance level. It is as-sumed that light, moderate, and severe damage states are experienced when the imme-diate occupancy, life safety, and collapse prevention drift limits are exceeded,respectively. The selected performance limits that are described qualitatively in Table 2

Table 2. Assumed drift ratio limits for performance

levels

Performance Level Limit

Collapse Prevention CPLife Safety

3

4CP

Immediate Occupancy y

Figure 11. Representative sketch of the probability density functions for drift ratios.



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are conjectural and could be argued as subjective. However, they agree well with the

statistical comparisons made by using the actual building damage data in Turkey that isdiscussed in detail in the succeeding sections of the paper.

COMPARISON WITH OTHER STUDIES

A number of attempts have been made recently to recommend idealized capacitycurves for the common building types in Turkey. A study conducted by the Japan Inter-

national Cooperation Agency JICA 2002 and the Istanbul Metropolitan Municipality2002 focused on estimating losses from future earthquakes that are likely to impactIstanbul. The study by this joint venture idealized the capacity curves using the elasto-

plastic approximation that were obtained from the simplified analyses. A further en-deavor by Bogazii University BU dealt with the earthquake risk assessment for theIstanbul region Bogazii 2002. The capacity curves were represented by elastoplastic

behavior similar to the JICA study.

In order to investigate the differences between the capacity curves of the buildingsemployed herein and those proposed in other studies, the mean capacity curves obtainedfor each height category are compared in Figures 12a and 12b. Included in these figuresare the capacity curves for similar buildings recommended by HAZUS NIBS 1997.The HAZUS recommendations are valid for the U.S. buildings that are designed accord-

ing to the requirements of the moderate code buildings designed and constructed in theperiod 19401973. The significant difference between HAZUS and Turkey is quite ex-pected due to the differences in construction practices as well as the code enforcement

and compliance efforts. Another source for the differences between this study and JICAand BU is the simplifications implemented in modeling. However, none of these expla-

nations justify the gross overestimation of capacities in the JICA study, which is re-

garded as the basic document for loss estimation in Istanbul based on an expectedM7.5earthquake in the Western Marmara Sea. The curves in this study were obtained from theanalyses that were based on 3-D modeling, whereas the JICA and BU studies are theresults of simpler analyses using certain approximations and assumptions.

Figure 12. Comparisons of capacity curves foralow-rise1- to 3-story, andbfor mid-rise4- to 7-story buildings with other studies.



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GROUND MOTION DATA

A set of 82 strong ground-motion records were used to compute the empirical build-ing fragility curves based on the building information given in the previous sections.

Important features of the ground-motion data are listed in Table A1 in the Appendix. Thestrong ground-motion data consists of dense-to-firm soil records with surface magni-

tudes Ms ranging from 5.2 to 7.6. The soil profiles correspond to NEHRP C and Dsites with average shear-wave velocities of360 m/svs750 m/s and180 m/svs360 m/s, respectivelyASCE 2000. These soil conditions are consistent with the as-sociated local site geology of the building data set. The magnitude range represents

ground motions of moderate to large earthquakes. The site-to-source distance d is

bounded by 20 kmsince the urban areas located in the near-source region of active seis-mic zones are more vulnerable to damage and the seismic loss estimation is a more se-rious concern for such locations Peterson et al. 2000. In this study, near-source recordswith dominant pulse signals due to forward directivity effects were excluded from thedatabase as much as possible. Such records have distinct frequency and duration char-

acteristics and dominate the structural behavior depending on the pulse durationKrawinkler et al. 2003, Iwan et al. 2000. A lack of consensus in the simplified proce-dures to account for such effects in estimating the seismic performance of existing

buildings led to such a compilation for the ground-motion data set. Figures 13 and 14present the variation of PGA and PGV with respect to magnitude and distance in log

scale for the ground motions used here. Although the magnitude scatter plots in Figure13 display a dispersive behavior, both PGA and PGV values tend to increase with in-creasing magnitude. The distance scatters presented in Figure 14 show an exponential

decay for PGA and PGV as the closest site-to-source distance values increase. This trendis observed more clearly for PGV.

Among various ground motion intensity measures, PGA and PGV can be consideredas fairly robust and easy to compute. These two intensity parameters are comparativelyevaluated herein for obtaining the most consistent representation of structural damage

Figure 13. Variation of PGA and PGV with respect to magnitude.



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variation in the empirical fragility curves. The elastic e and inelastic ie spectraldisplacement scatter diagrams are drawn in Figures 15 and 16, respectively, as functionsof PGA and PGV for comparison purposes. The inelastic spectral displacements in Fig-ure 16 are presented for elastoplastic behavior with lateral capacities described by the

strength reduction factorR. This factor is defined as the elastic strength demand nor-malized by the yield strength of an SDOF system under a given earthquake ground mo-

tion. Equation 2 gives the definition ofR

R=mSa

Fy2

wherem is the mass, Sa is the elastic pseudo-spectral acceleration, andFy is the lateralyield strength of the system. The product ofSaandm is the elastic strength for that par-ticular SDOF system. Therefore, given a specific R value, the inelastic spectral displace-ment i.e., maximum absolute lateral deformation of the SDOF system describes themaximum inelastic deformation demand for the corresponding yield strength level. Thisspectrum type is denoted as constant R-spectrum Ruiz-Garca and Miranda 2003.

The left and right columns in Figures 15 and 16 show the scatter diagrams as a func-tion of PGA and PGV, respectively, whereas the rows correspond to the vibration periods

of0.2 s, 0.5 s, and1.0 s simulating relatively short, medium, and long structural peri-ods. It can be observed from Figure 15 that the relation between the elastic i.e.,R = 1structural deformation demand and ground motion intensity is described fairly well byPGA for short and medium period structural systems. As the structural period shifts to

longer values i.e., 1.0 s, PGV correlates well with the elastic structural deformationdemand. Inelastic deformation scatters, that are generically drawn for an elastic strength

to yield strength ratio of 4 i.e., R = 4, in Figure 16 suggest that PGV is a superior in-dicator of deformationdamageto PGA over the period range considered. In Figure 16,weaker correlation of PGA with the increasing deformation demand is noteworthy. Con-fined to the ground motions presented in this study, the above remarks are also observed

Figure 14. Variation of PGA and PGV with respect to distance.



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Figure 15. Scatter diagrams for 5 percent damped elastic spectral displacements as functions of

PGA and PGV for all 82 earthquake records.



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Figure 16. Scatter diagrams for 5 percent damped elastoplastic spectral displacements as func-

tions of PGA and PGV for all 82 earthquake records.



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for otherR and period values. Thus PGV appears to be a more suitable ground motionintensity parameter for describing deformation demands in structures that deform be-yond the elastic range.

The observations highlighted in the preceding paragraph confirm the conclusions de-rived by Wald et al. 1999; in their study, Wald et al. indicated that low levels of struc-tural damage identified by the modified Mercalli scale less than VII correlate well withPGA. As structural damage increases i.e., modified Mercalli scale greater than VII,PGA values level off and PGV is more indicative for defining the correlation betweenstructural damage and ground motion intensity. Under the guidance of these observa-

tions, PGV is selected as the ground motion intensity measure in the derivation of em-pirical fragility curves. A detailed description of the analytical method for obtaining thefragility functions is presented in the next section.

ANALYTICAL METHOD

Generically, fragility curves are conditional cumulative distribution functions thatdefine the exceedance probability of a damage state for a given ground motion intensitylevel. The probability distribution function is the standard lognormal distribution in mostcases and the curves represent median fragility values. The lognormal distribution fit isassured by certain optimization algorithms and goodness-of-fit tests Shinozuka et al.2000, Kircher et al. 1997. The following sections summarize the methodology used inderiving the fragility curves.

DISPLACEMENT-BASED DAMAGE LIMIT STATES

Table 3 lists the damage threshold levels used for defining the performance levels ofbuilding groups with different number of stories. The details of the pertinent statisticsand the computation of these thresholds were given in the previous sections.

The values of the median life safety and collapse prevention drift thresholds have adecreasing trend with increase in the number of stories. On the other hand, the threshold

for immediate occupancy that can be considered as a transition boundary between globalelastic to inelastic behavior practically attains the same level regardless of the number ofstories. It is noteworthy that all of the above drift-based performance levels are smallerthan the ones proposed in the building rehabilitation standards of the United States orJapanASCE 2000, JICA 2002, NIBS 1997. This has to be recognized as a serious con-

Table 3. Assumed thresholds for performance levels and the associated damage limit states in termsof global drift

Story

Number

Immediate Occupancy, ICLight Damage

Life Safety, LSModerate Damage

Collapse Prevention, CPSevere Damage

2 0.0011 0.0090 0.012

3 0.0011 0.0080 0.011

4 0.0012 0.0080 0.011

5 0.0011 0.0068 0.009



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cern for addressing the country specific vulnerabilities and, accordingly, loss estimationpolicies. The damage levels presented in Table 3 are consistent with other individualstudies that investigate the drift capacity of reinforced concrete frame buildings in Tur-

keySucuoglu et al. 2004.

STORY-BASED PERIOD AND STRENGTH RANGES

The relationship between the fundamental period of vibration, base shear capacity,and the number of stories was established by using the field data presented previously.

For each building group identified with different number of stories, the relevant meanand standard deviation statistics were computed for the associated base shear capacityand fundamental period of vibration distribution. These statistics were then employed tofind the effective base shear and period ranges that represent the group of buildings in-vestigated. The corresponding ranges cover the intervals of mean plus/minus one stan-dard deviation for the parameters of interest to account for their central dispersion. Fig-ure 17 illustrates these intervals with respect to the number of stories with the

superimposed actual trend of the building data. Each block in Figure 17 represents theoverall distribution of period and base shear for a building group with a particular storynumber. It can be observed that the variation in base shear capacity decreases whereasthe dispersion in period increases with the increasing number of stories.

NONLINEAR DYNAMIC RESPONSE HISTORY ANALYSES

The set of 82 records comprising the ground motion data was used to compute theinelastic displacement response histories of equivalent SDOF systems representing the

base shear capacities and fundamental vibration periods of building groups discussedabove. The variations in building periods and base-shear coefficients were describedmore accurately by dividing the rectangular blocks in Figure 17 into finer meshes. For

Figure 17. Effective period and base shear capacity ranges for different building groups.



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the sake of uniformity, the period range of each rectangular block was divided into

equally spaced intervals of0.05 seconds. Similarly, the corresponding base shear coef-

ficient ranges were divided into four equal intervals. The global drift values for eachyield base shear coefficient versus periodT pair was computed by using the ap-

proximate procedure described in Equations 3a and 3b.

R=Sa

Cm 3a

=top

H =

1

HC0ieT,R . 3b

This approximate procedure is similar to the displacement coefficient method de-

scribed in the FEMA-356ASCE 2000 document except for the C1 coefficient that re-lates the elastic spectral displacement to inelastic spectral displacement for an idealized

bilinear hysteretic model. Instead, the inelastic spectral displacements were computed di-rectly from response history analyses. The base shear coefficient was converted tostrength reduction factorR using Equation 3a, where Sa designates the elastic pseudo-spectral acceleration at periodT for a specific ground motion. The coefficient Cm is theeffective mass modification term to account for the effective modal mass computed forthe fundamental mode. This parameter was taken as 1.0 and 0.9 for the two- and three-,

four-, and five-story building groups, respectively. These values are consistent with theFEMA-356 document. The two modification coefficients C2 and C3 in FEMA-356,which account for the hysteretic model and dynamic P-delta effects, respectively, are not

included in Equation 3b since they were taken as 1.0. The modification factorC0relatesthe spectral displacement of the equivalent SDOF system to the approximate roof dis-

placementtop and values between 1.0 and 1.1 were assigned depending on the story

number that approximately represents the first-mode participation factors of the buildingstock described. The global drift values were calculated by normalizing the approximate

top-story displacements with the average building heights Hdefined for the building in-ventory.

A total of 9,020 equivalent SDOF inelastic response history analyses were carriedout for the associated period and base shear combinations. The capacity curves com-

puted from the building data were represented by a bilinear hysteretic model with 3percent strain hardening, which corresponds to the median post yielding stiffness ratioof the building data set. The global drift ratios were computed via Equations 3a and 3b

as described in detail in the above paragraph. This process assumes a fundamental modedominant structural behavior, which can be considered as a reasonable assumption forthe existing low- to mid-rise buildings in the data set.

The proposed procedure only offers an approximation to the global drift values andclearly has limitations confined to the certain simplifications described in the previous

paragraphs. These limitations might be surmounted by using exact nonlinear responsehistory analyses of the building data at the expense of significant computational time

that requires a considerable effort, which is not efficient for the loss estimation of largebuilding stocks in big metropolitan areas like Istanbul in Turkey.



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COMPUTATION OF FRAGILITY CURVES

The maximum global drift values computed by the approximate procedure were as-

sumed to represent the seismic performance of the investigated concrete frames. Usingthe damage threshold levels defined in Table 3, the exceedance probabilities of that par-ticular fragility curve were computed from the PGV versus maximum global drift scat-ters specific to each building group i.e., two-, three-, four-, and five-story buildings.The scatter diagrams were clustered for different PGV intervals and the global drift per-

centiles greater than a given damage threshold level were computed by using the log-normal distribution to estimate the exceedance probabilities of the fragility curves. Ex-

ponential functions were fit over the jaggedly varying exceedance probability points to

achieve smooth fragility curves for that specific damage state and building group. A rep-resentative sketch for the above procedure is shown in Figure 18.

RESULTS AND DISCUSSIONS

The fragility curves produced by the presented methodology are shown in Figures19ad for two-, three-, four-, and five-story concrete buildings, respectively. The threecurves in each figure represent the probability of exceeding the immediate occupancylight damage, life safetymoderate damage, and collapse prevention severe damagelimit states, respectively, from left to right. They are also grouped separately in Figures20ac for the three limit states, respectively, to compare the effect of the number of sto-ries on fragility. It can be observed from Figure 20 that the number of stories has a sig-nificant effect on the probability of exceeding the moderate and the severe damage limit

states. Furthermore, the moderate and severe damage fragility patterns of the two- andthree-story building groups and the four- and five-story building groups follow a closertrend to each other. These two distinct groups can be designated as low- and mid-riseconcrete frame buildings for the construction practice in Turkey.

The fragilities presented in Figure 19 can be compared and verified with the damagedistribution observed in Dzce, which is shown in Figure 1. Before this comparison, the

Figure 18. The scatter diagram and the corresponding fragility curves for the 3-story buildings.



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Figure 19. Fragility curves fora 2-, b 3-, c 4-, andd 5-story buildings.

Figure 20. Fragility curves fora light, b moderate, andc severe damage limit states.



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difference in damage definitions in Figures 1 and 19 is assessed. The global drift de-mands were calculated for the two- to five-story buildings by assuming bilinear hyster-etic model with 3 percent post-yielding stiffness and with strength and period ranges de-fined in Figure 17 under the horizontal components of the Dzce record. The results aregiven in Table 4, where the calculated damages based on average global drift demands

DD are in good agreement with the observed damages in the 32 sample buildings.

A comparison of the calculated probabilities of exceeding moderate and severe dam-age limit states, and the corresponding observed damage ratios for the Dzce case givenin Figure 1 are listed in Table 5 for two- to five-story buildings. It is appropriate to ex-

clude undamaged and lightly damaged buildings since they are not separated in Figure 1.The PGV values recorded along the two horizontal components in Dzce are listed in

Table A1 in the Appendix, and their geometric mean is 70.8 cm/ s. Accordingly, the fra-gilities associated with this PGV value can be read from the related curves in Figure 19.Fragilities exceed the observed damages by 10 and 23 percent in the two-story buildings

Table 4. Comparison of calculated and observed damages in 32 samplebuildings

Story

Number LS CP DD

Damage

Decision

Observed

Damage

2 0.0090 0.0120 0.0061 Light 5 Light

3 0.0084 0.0113 0.0075 Light 5 Light

4 Moderate

4 0.0084 0.0113 0.0081 Light 3 Light

4 Moderate

5 0.0068 0.0090 0.0080 Moderate 4 Light

3 Moderate

3 Severe

Table 5. Comparison of predicted and observed damagedistributions

Story

Number

Damage Limit

Statea

Prediction

MedianObserved

Damage Ratio

2 M 37.7 34.1

S 15.1 12.3

3 M 47.8 51.9

S 20.5 19

4 M 81.4 86.4

S 43.1 39.4

5 M 93.6 97.4

S 69.8 67.1

a M and S denote moderate and severe damage, respectively



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at moderate and severe damage limit states, respectively. The differences between pre-dicted and observed fragilities are less than 10 percent at both damage limit states in the

three-, four-, and five-story buildings. Considering the uncertainties inherent in the fra-gilities and randomness of ground intensities, these results can be accepted as satisfac-tory, suggesting that the proposed procedure can be implemented to large building

stocks in Turkey for loss estimation.

CONCLUSIONS

Fragility functions are derived for groups of existing concrete buildings in Turkey, as

a function of number of stories. These curves can be used for regional loss estimationstudies in different seismic prone zones of Turkey. The parameters that were consideredas uncertain in the analysis are the ground motion intensity, fundamental period of vi-

bration, yield strength, and global drift that is used to identify the damage limit states.

There are two basic conclusions that can be derived from this study. First, fragility

functions taking into consideration the basic regional characteristics of an investigatedbuilding stock, based on field data, serve for reliable estimates of expected loses in simi-lar buildings from strong ground shaking. Here, the field data is collected from a groupof representative existing concrete buildings in Turkey that sustained various degrees ofdamage during the 1999 Dzce earthquake. The number of stories in buildings was em-

ployed as a dominant structural parameter influencing their seismic performance. The

results have revealed that the fragility curves for different number of stories are wellseparated, hence they are informative on the distribution of expected damages. Further-more, they were successful in reproducing the damage distribution in 6,478 two- to five-story buildings in Dzce observed after the 1999 Dzce earthquake.

These results are readily applicable to Istanbul where an earthquake with a M7.5 is

considered as the scenario event Note: a smaller magnitude event is more probable thantheM7.5event. There are approximately 120,000 concrete buildings housing 2 millionresidents in nine subprovinces of Istanbul that are located along the western Marmara

coast, at a distance of10 to 15 km from the major Marmara Sea segment of the NorthAnatolian Fault. This fault was last broken with a M7.6 earthquake in 1766. Microzo-nation studies conducted recently JICA 2000 indicated that the expected PGV valuesin this region during the scenario earthquake varies between 50 and60 cm/ s, excludingisolated pockets of high site amplification. When the results of this study are applied

conservatively, for a PGV of50 cm/s, the probabilities of exceeding severe damage intwo-, three-, four-, and five-story buildings are obtained as 3, 5, 7, and 20 percent, re-spectively. It has to be noted that almost 25 percent of all buildings in this region arefive-story, and 60 percent range in height between two- and five-story concrete construc-tion according to the latest building census data. There are no calibrated tools other than

the one proposed herein for a reliable damage estimation of large urban building stocksin Turkey.

The second major conclusion relates to the use of PGV as a measure of strong mo-tion intensity in fragility functions developed for large building stocks. It is commonly

accepted that PGV has a good correlation with MMI for large magnitude earthquakes.



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The results of this study have confirmed this observation and revealed that the inelasticdynamic response displacements are significantly better correlated with PGV than PGA

across the structural period range from 0.2 s to 1.0 s.

ACKNOWLEDGMENTS

The research work presented in this study is supported in part by the Scientific andResearch Council of Turkey TUBITAK under Grant YMAU-ICTAG-1574, and by

NATO Scientific Affairs Division under Grant NATO SfP977231. The authors would liketo express their gratitude to Dr. Altug Erberik for discussing some specific issues in the

computation of fragility curves presented in this study. The careful and constructivecomments of two anonymous reviewers are acknowledged that led to significant im-

provements in the text.

APPENDIX

Table A1.List of ground motions used in the study

Earthquake Record and Component M d km Site1

Fault2

PGAcm/s2

PGVcm/s

Cape Mendocino 04/25/92 Petrolia, 000 7.1 9.5 D RN 578 48.4

Cape Mendocino 04/25/92 Rio Dell Over pass, 360 7.1 18.5 C RN 539 42.1

Chi-Chi 09/20/99 WNT, E 7.6 1.2 D RN 940 68.8

Chi-Chi 09/20/99 TCU076, N 7.6 2.0 D RN 408 64.2

Chi-Chi 09/20/99 TCU049, W 7.6 4.5 D RN 287 47.9

Chi-Chi 09/20/99 TCU049, N 7.6 4.5 D RN 246 61.2

Chi-Chi 09/20/99 TCU082, W 7.6 5.7 D RN 219 58.4

Chi-Chi 09/20/99 CHY028, W 7.6 7.3 D RN 641 72.8

Chi-Chi 09/20/99 TCU051, W 7.6 8.3 D RN 183 49.3

Chi-Chi 09/20/99 TCU074, W 7.6 13.7 D RN 586 73.3Chi-Chi 09/20/99 CHY006, E 7.6 14.9 D RN 357 55.4

Chi-Chi 09/20/99 TCU070, N 7.6 19.1 C RN 166 62.3

Coalinga 05/02/83 Pleasant Valley P.P.Yard, 045 6.5 8.5 D RO 581 60.2

Coyote Lake 08/06/79 Gilroy Array #3, 050 5.7 6.0 D SS 267 18.7



Coyote Lake 08/06/79 San Juan Bautista, 213 5.7 15.6 C SS 106 7.6

Coyote Lake 08/06/79 SJB Overpass Bent 3 G.L., 067 5.7 17.2 C SS 95 5.9

Duzce 11/12/99 Duzce Meteorology Sta, 180 7.3 8.2 D SS 341 60.0

Duzce 11/12/99 Duzce Meteorology Sta, 270 7.3 8.2 D SS 525 83.5

Gazli 05/17/76 Karakyr, 000 7.3 3.0 D RN 596 65.4

Gazli 05/17/76 Karakyr, 090 7.3 3.0 D RN 704 71.6

Imperial Valley 10/15/79 El Centro Array 6, 230 5.2 13.1 D SS 359 20.8

Imperial Valley 10/15/79 Calexico Fire Sta, 315 6.5 10.6 D SS 198 16.0

Imperial Valley 10/15/79 Parachute Test Site, 315 6.5 14.2 C SS 200 16.1

Imperial Valley 10/15/79 El Centro Array #1, 230 6.5 15.5 D SS 132 10.7



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Table A1. cont.


Fault2 PGAcm/s2 PGVcm/s

Imperial Valley 10/15/79 EC Meloland Overp FF, 000 6.9 0.5 D SS 308 71.8

Imperial Valley 10/15/79 El Centro Ar ray #7, 140 6.9 0.6 D SS 331 47.6

Imperial Valley 10/15/79 El Centro A rray #5, 140 6.9 1.0 D SS 509 46.9

Imperial Valley 10/15/79 Bonds Corner, 140 6.9 2.5 D SS 577 45.2

Imperial Valley 10/15/79 Bonds Corner, 230 6.9 2.5 D SS 760 45.9



Imperial Valley 10/15/79 El Centro Diff Ar ray, 230 6.9 5.3 D SS 471 40.8

Imperial Valley 10/15/79 EC Co Center FF, 002 6.9 7.6 D SS 209 37.5

Imperial Valley 10/15/79 Aeropuerto Mexicali, 315 6.9 8.5 D SS 255 24.9

Imperial Valley 10/15/79 Aeropuerto Mexicali, 045 6.9 8.5 D SS 321 42.8


Imperial Valley 10/15/79 Sahop Casa Flores, 270 6.9 11.1 D SS 496 31.0



Kocaeli 08/17/99 Arcelik, 000 7.4 17.0 C SS 215 17.7

Landers 06/28/92 Morango Valley, 000 7.3 19.3 C SS 184 16.6

Landers 06/28/92 22170 Joshua Tree 7.4 11.6 C SS 279 43.2

Livermore 01/24/80 San Ramon Kodak Bldg, 270 5.8 17.6 D SS 75 6.1

Livermore 01/27/80 Livermore Morgan Terr Park,

265

5.4 8.0 C SS 194 11.7

Loma Prieta 10/18/89 Gilroy Array #6, 090 6.9 19.9 C RO 167 14.2

Loma Prieta 10/18/89 Corralitos, 000 7.1 5.1 C RO 632 55.2

Loma Prieta 10/18/89 LGPC, 000 7.1 6.1 D RO 553 94.8

Loma Prieta 10/18/89 Gilroy Array #2, 000 7.1 12.7 D RO 360 32.9


Loma Prieta 10/18/89 Saratoga W Valley Coll, 270 7.1 13.7 C RO 326 61.5


Loma Prieta 1989/10/18 47006 GilroyGavilan Coll.,

067

7.1 11.6 C RO 350 28.6

Loma Prieta 1989/10/18 47006 GilroyGavilan Coll.,

337

7.1 11.6 C RO 319 22.3

Morgan Hill 04/24/84 Halls Valley, 240 6.1 3.4 D SS 306 39.4

Morgan Hill 04/24/84 Gilroy Array #6, 000 6.2 11.8 C SS 218 11.4

Morgan Hill 04/24/84 Gilroy Array #7, 090 6.2 14.0 D SS 111 6.0

Morgan Hill 04/24/84 Gilroy Array #3, 090 6.2 14.6 D SS 197 12.7

Morgan Hill 04/24/84 Gilroy Array #2, 000 6.2 15.1 D SS 159 5.1Morgan Hill 04/24/84 Gilroy Gavilan Coll, 067 6.2 16.2 C SS 112 3.6

N. Palm Springs 07/08/86 Fun Valley, 045 6.0 15.8 C RO 126 6.4

N. Palm Springs 07/08/86 Palm Springs Airport, 000 6.0 16.6 D RO 155 12.4

Northridge 01/17/94 Sylmar-Converter Sta-East, 2886.7 6.1 D RN 484 74.6

Northridge 01/17/94 SylmarHospital, 090 6.7 6.4 D RN 593 78.2



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REFERENCES

American Society of Civil EngineersASCE, 2000.Prestandard and Commentary for the Seis-mic Rehabilitation of Buildings, prepared for the SAC Joint Venture, published by the Fed-

eral Emergency Management Agency, Report No. FEMA-356, Washington, D.C.

Aydogan, V., 2003. Seismic Vulnerability Assessment of Existing Reinforced Concrete Build-

ings in Turkey, masters thesis, Department of Civil Engineering, Middle East Technical Uni-

versity, Ankara.

Bogazii University, 2002. Earthquake Risk Assessment for Istanbul Metropolitan Area, FinalReport, Kandilli Observatory and Earthquake Research Center, Istanbul.

Computers and Structures, Inc., 2000. SAP 2000 Nonlinear, Version 7.21, Structural Analysis

Program, Berkeley, CA.

Table A1. cont.


Fault2 PGAcm/s2 PGVcm/s

Northridge 01/17/94 Newhall, 090 6.7 7.1 D RN 572 75.5

Northridge 01/17/94 Newhall, 360 6.7 7.1 D RN 579 97.3

Northridge 01/17/94 Pacoima Kagel Canyon, 360 6.7 8.2 C RN 424 51.5

Northridge 01/17/94 Sepulveda VA, 360 6.7 8.9 D RN 921 76.6

Northridge 01/17/94 NorthridgeSaticoy, 180 6.7 13.3 D RN 468 61.5

Northridge 01/17/94 90009N. HollywoodCWC,

180

6.7 14.6 C RO 292 25.0

Northridge 01/17/94 24688 LAUCLA Grounds,

090

6.7 14.9 C RN 273 22.0

Northridge 01/17/94 24688 LAUCLA Grounds,

360

6.7 14.9 C RN 465 22.2

Northridge 01/17/94 Canoga Park-Topanga Canyon,196

6.7 15.8 D RN 412 60.8

Northridge 01/17/94 TarzanaCedar Hill Nursery

A, 360

6.7 17.5 B RN 971 77.6

Northridge 01/17/94 638 Brentwood V.A. Hospital,

195

6.9 16.3 C RO 183 23.7

Parkfield 06/28/66 Cholame #5, 085 6.1 5.3 D SS 433 24.7

Superstition Hills

11/24/87

El Centro Imp Co Center, 090 6 .6 13.9 D SS 253 40.9

Superstition Hills

11/24/87

El Centro Imp Co Center, 000 6 .6 13.9 D SS 351 46.4

Westmoreland 04/26/81 Fire Station, 090 5.8 1 3.3 D SS 361 48.7

Whittier 10/01/87 Bell Gardens-Jaboneria, 207 6.0 9.8 D RN 214 18.9

Whittier 10/01/87 Brea-S. Flower Av, 020 6.0 1 7.9 D RN 113 7.1

1 NEHRP site classification ASCE 20002

SS, RN, and RO designate strike normal, reverse normal, and reverse oblique, respectively.



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Iwan, W. D., Huang, C.-T., and Guyader, A. C., 2000. Important features of the response of

inelastic structures to near-field ground motion, 12th World Conference on Earthquake En-

gineering, Auckland, New Zealand, Paper No. 1740.Japan International Cooperation Agency JICA and Istanbul Metropolitan Municipality, 2002.

The Study on a Disaster Prevention/Mitigation Basic Plan in Istanbul Including Seismic Mi-

crozonation in the Republic of Turkey, Final Report, Istanbul.

Kircher, C. A., Nassar, A. A., Kustu, O., and Holmes, W. T., 1997. Development of building

damage functions for earthquake loss estimation, Earthquake Spectra 12 4, 663682.

Krawinkler, H., Medina, R., and Alavi, B., 2003. Seismic drift and ductility demands and their

dependence on ground motions,Eng. Struct. 25, 637653.

National Institute of Building Sciences NIBS, 1997. Earthquake Loss Estimation Methodol-ogy HAZUS97 Users Manual, prepared for the Federal Emergency Management Agency,

Washington, D.C.

Parsons, T., Toda, S., Stein, R. S., Barka, A., and Dieterich, J. H., 2000. Heightened odds of

large earthquakes near Istanbul: An interaction-based probability calculation, Science 288,

661665.

Peterson, M. D., Toppozada, T. R., Cao, T., Cramer, C. H., Reichle, M., and Bryant, W. A.,

2000. Active fault near-source zones within and bordering the state of California for the

1997 Uniform Building Code, Earthquake Spectra 16 1, 6984.

Ruiz-Garca, J., and Miranda, E., 2003. Inelastic displacement ratios for evaluation of existing

structures, Earthquake Eng. Struct. Dyn. 32, 12371258.

Shinozuka, M., Feng, M. Q., Lee, J., and Naganuma, T., 2000. Statistical analysis of fragility

curves, J. Struct. Eng. 126, 12241231.

Shinozuka, M., Grigoriu, M., Ingraffea, A. R., Billington, S. L., Feenstra, P., Soong, T. T., Re-

inhorn, A. M., and Maragakis, E., 1999. Research Progress and Accomplishment 1999

2000: Selected Papers, MCEER, SUNY at Buffalo, NY.

Sucuoglu, H., Gr, T., and Gnay, M. S., 2004. Performance-based seismic rehabilitation of

damaged buildings, J. Struct. Eng. 130, 14751486.Sucuoglu, H., and Yilmaz, T., 2001. Dzce, Turkey: A city hit by two major earthquakes in

1999 within three months, Seismol. Res. Lett. 72, 679689.

Sullivan, T. J., Calvi, G. M., and Priestley, M. J. N., 2004. Initial stiffness versus secant stiffness

in displacement based design, 13th World Conference on Earthquake Engineering, Vancou-

ver, B. C., Canada, Paper No. 2888.

Turkish Ministry of Public Works and Settlement, 1975. Specifications for Buildings Con-

structed in Disaster Areas, Ankara.

Turkish Ministry of Public Works and Settlement, 1998. Specifications for Buildings Con-

structed in Disaster Areas, Ankara.

Wald, D. J., Quitariano, V., and Heaton, T. H., 1999. Relationships between peak g round accel-

eration, peak ground velocity, and Modified Mercalli intensity in California, Earthquake

Spectra 15 3, 557564.Yakut, A., Yilmaz, N., and Bayili, S., 2003. Analytical assessment of the seismic capacity of

RC frame buildings,International Conference in Earthquake Engineering to Mark 40 Years

from Catastrophic 1963 Skopje Earthquake, Skopje-Ohrid, Paper No. 50.

Received 28 February 2004; accepted 25 January 2005


displacement based fragility functions

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