hod

les, Lity, L

Revised 30 September 2014Accepted 15 December 2014Available online 30 December 2014

Keywords:Seismic retrotSteel plate shear wallsLow yield point steel

design of new and retrot of existing buildings. Employment of low yield point (LYP) steel inll plateswith considerably low yield strength and high ductility, on the other hand, has been shown in a number

design to performance-based design. The performance-based

[2] denition, such seismic design methodology can provide acost-effective means to (i) reduce earthquake nancial loss dueto structural and nonstructural damage, (ii) design a structure fora range of performance levels when subjected to differentlevels of ground motion, (iii) obtain minimum structural and

selected yield mechanism, and showed the advantages of thisAnother perfor-nted for inyield mechss of this m

in design of SPSW systems was demonstrated as well.Development of fragility functions for structural system

key component of the performance-based seismic design. Fragilityfunctions are performance-prediction models that relate the prob-ability of reaching, or exceeding, structural and nonstructural dam-age/repair states with an intensity measure of the earthquakeinput motions. So, development of such statistical models, i.e. fra-gility functions, is essential to enable the performance-based seis-mic design of SPSWs as efcient lateral force-resisting systems.

Corresponding author.E-mail addresses: zhangj@ucla.edu (J. Zhang), Tadeh.Zirakian@lmu.edu

(T. Zirakian).

Engineering Structures 85 (2015) 195205

Contents lists availab

Engineering

lseseismic design methodology permits design of new and upgradeof existing buildings with a realistic understanding of the risk ofcasualties, occupancy interruption, and economic loss that mayoccur as a result of future earthquakes [1]. According to Goulds

inelastic displacement-based design method.mance-based plastic design procedure that accoubehavior by using pre-selected target drift andwas also developed by Bayat [4]. The effectivenehttp://dx.doi.org/10.1016/j.engstruct.2014.12.0270141-0296/ 2014 Elsevier Ltd. All rights reserved.elasticanismethod

s is aBased on the lessons learned from the past and recent cata-strophic seismic events with considerable casualties, structuraldamages, and economic losses along with the major advancementsin the elds of structural and earthquake engineering, designmethodology for structures is gradually moving from prescriptive

for continued operations in a structure following a design levelseismic event.

Recently, performance-based design procedures for steel plateshear wall (SPSW) systems have been developed by researchers.Ghosh et al. [3] proposed a performance-based seismic design pro-cedure for SPSW systems based on a target inelastic drift and pre-Probabilistic seismic demand analysisFragility function

1. Introductionof studies to improve the structural performance of SPSW systems. By considering the various sources ofrandomness and uncertainties involved in the design and retrot process, adoption of a probabilisticmethodology can result in a robust seismic performance assessment of such structural systems. Thispaper presents the results of a study on the seismic performance and vulnerability of retrotted struc-tures employing SPSW systems and LYP steel material through probabilistic seismic demand analysis(PSDA). Three 9-story code-designed and retrotted structural models including a moment-resistingand two SPSW frames are considered. Appropriate seismic response and ground motion intensity param-eters, and damage as well as repair states are selected. Structural and nonstructural drift and accelerationfragility functions are subsequently developed based on nonlinear time-history analysis results. Theeffectiveness of SPSW systems in improving the seismic performance and reducing the vulnerability ofbuildings is demonstrated through seismic response assessment and fragility analysis. Also, it is shownthat employment of relatively thicker LYP steel inll plates in seismic design and retrot of SPSWs resultsin smaller damage potential and better seismic performance of such systems.

2014 Elsevier Ltd. All rights reserved.

nonstructural damage in a moderate seismic event, and (iv) allowArticle history:Received 4 April 2014

Steel plate shear walls (SPSWs) have been used as primary lateral force-resisting systems in seismicProbabilistic assessment of structures witinll plates using fragility function meth

Jian Zhang a, Tadeh Zirakian b,aDepartment of Civil and Environmental Engineering, University of California, Los AngebDepartment of Civil Engineering & Environmental Science, Loyola Marymount Univers

a r t i c l e i n f o a b s t r a c t

journal homepage: www.eSPSW systems and LYP steel

os Angeles, CA 90095-1593, USAos Angeles, CA 90045-2659, USA

le at ScienceDirect

Structures

vier .com/ locate /engstruct

addition, the effectiveness of use of low yield point (LYP) steel withconsiderably low yield stress and high ductility and elongation

Z LS 1 lnEDPlnaIMb 2

ng Sproperties in improving the seismic performance of SPSW systemsis evaluated.

In order to achieve the objectives of this study, nonlinear time-history analyses are performed in order to evaluate the seismicperformances of 9-story moment-resisting and code-designed aswell as retrotted SPSW frames employing conventional and LYPsteel inll plates. To this end, the drift and acceleration structuralresponses are considered as two effective seismic demand param-eters. By considering different damage and repair states speciedfor the structural and nonstructural systems and components,proper analytical fragility functions are subsequently developedbased on the numerical analysis results. Ultimately, the effective-ness of seismic design of new and retrot of existing structuresusing SPSW systems and LYP steel material is evaluated probabilis-tically using the fragility function method.

2. Fragility function methodology

A major step in performance-based earthquake engineeringassessments is to estimate the probabilistic structural responseas a function of ground motion intensity. The objective of this stepis to estimate the probability distribution of a structural responseparameter, herein termed as the engineering demand parameter(EDP), as a function of earthquake ground motion intensity, hereintermed as the intensity measure (IM). There are several methodsavailable for obtaining such an estimate, which have been dis-cussed by Baker and Cornell [7].

The ground motions are characterized by the intensity measurewhich can be selected from the peak ground velocity (PGV), peakground acceleration (PGA), and other characteristics of the earth-quake recordings. The structural responses of buildings, on theother hand, may be represented by various parameters such asinterstory drift and/or oor acceleration. The choice of the inten-sity measure (IM) and the structural response parameter (EDP)plays an important role in running the fragility analysis.

In this study, the probabilistic seismic demand model (PSDM)was employed to derive analytical fragility functions using nonlin-ear time-history responses of the structural models. The PSDMwasThese can be generated either empirically using experimental dataor analytically through seismic response assessment using numer-ical simulations.

In studies reported by Berman et al. [5] and Baldvins et al. [6],experimental results and observations from previous publishedstudies were reviewed, and twelve damage states were conse-quently proposed based on the extent of the possible damage tothe web-plate and boundary frame elements of an SPSW systemand the associated drift levels. By considering the extent of therequired repair for each damage, the twelve damage states werenally consolidated into ve repair states, and fragility curves werethen developed for the resulting repair states.

In the aforementioned studies initial and major steps weretaken towards performance-based design of SPSW systems bydeveloping design procedures and fragility curves. In this study,one further step is taken in this regard and the seismic vulnerabil-ity of code-designed and retrotted SPSW systems subjected toearthquake ground motions is assessed probabilistically throughfragility function method. The adopted probabilistic methodologyis considered as a robust approach for seismic performance assess-ment of structures, which accounts for the uncertainties and vari-ability in input ground motions in a systematic manner. In

196 J. Zhang, T. Zirakian / Engineerideveloped using a cloud approach for relating EDPs to IMs, whichuses a set of un-scaled ground motions [7] and is termed here asthe probabilistic seismic demand analysis (PSDA). The PSDM canPEDP LSjIM10

12p

p fEDPjIM EDP

e 2 fEDPjIM dEDP:

3If it is assumed that the EDP variable has a lognormal distribu-

tion, then ln(EDP) can be considered to be normally distributed.Accordingly, the probability that EDP attains or exceeds LS for agiven IM can be alternatively calculated using the standard normalcumulative distribution function, denoted by U(), as

PEDP LSjIM 1U lnLS lnaIMb

fEDPjIM

!: 4

3. Specications and modeling of structural systems

3.1. Selected structural models

Three structural models were considered for the purpose of thisstudy; these include: (i) a 9-story moment-resisting frame (MRFmodel) selected from the SAC building in FEMA 355C [9] with somemodications, designed for seismic and wind conditions in LosAngeles (per-Northridge design), (ii) a retrotted gravity framefrom the SAC building using code-designed and conventional steelSPSW system (GF-CSPSW model), and (iii) a retrotted GF-CSPSWmodel using LYP steel inll plates of double thickness (GF-LYPSPSW2 model). Fig. 1 shows the oor plan and elevation forthe considered and modied Los Angeles 9-story SAC buildingmodel. It is noted that GF-LYPSPSW2 model is considered as a viableretrot option for the GF-CSPSW model, which employs LYP steelinll plates with relatively larger thickness and lower yield strength.

In design of the GF-CSPSW model, the equivalent lateral forceprocedure, per ASCE 7-10 [10], was used to determine the designseismic loads for the web plates, assumed to resist the entire storyshear demand. The horizontal and vertical boundary elements inthe GF-CSPSW model were designed using capacity design princi-ples per AISC 341-10 [11] seismic provisions. In addition, ASTMA36 and ASTM A572 Gr. 50 steel material were considered inbe also developed using a scaling approach, termed as the incre-mental dynamic analysis (IDA). In the IDA approach, all motionsare scaled to selective intensity levels corresponding to a pre-scribed seismic hazard level and incremental dynamic analysis isperformed at different hazard levels [8]. The PSDA method usesregression analysis in order to estimate the conditional mean andstandard deviation of EDP given IM. The mean EDP can be relatedto the IM using

EDP aIMb or lnEDP b lnIM lna; 1where a and b are constant regression coefcients to be estimatedfrom linear (or nonlinear) regression of the response data from non-linear time-history analyses. If the remaining variability in ln(EDP)for a given IM is assumed to have a constant variance for all IM, thenits standard deviation can be estimated using [7]

fEDPjIM

PNi1lnEDPi lnaIMib

2

N 2

s; 2

in which N is the number of EDPIM data pairs, and EDPi and IMi arethe values of the i-th data pair. Ultimately, by assuming a lognormaldistribution of EDP for a given IM, the fragility functions deningthe probability of EDP reaching or exceeding a specied limit state(LS) for a given IM can be represented using

tructures 85 (2015) 195205design of the inll plates and the boundary frame elements,respectively. The GF-LYPSPSW2 model was developed by onlyreplacing the inll plates of the GF-CSPSW model with LYP steel

J. Zhang, T. Zirakian / Engineering Structures 85 (2015) 195205 197inll plates of double thickness. Sections of the beam and columnelements in the moment-resisting and gravity frames, per FEMA355C [9], are summarized in Table 1. Included in the table are also

Fig. 1. Floor plan and elevation for the modied LA 9-story SAC building model.the boundary element sections and web-plate thicknessesdesigned for the GF-CSPSW model.

3.2. Finite element modeling and analysis

ANSYS 14.0 [12] nite element software was used for numericalsimulation of the structures in this research. A typical wall-framestructural model with the considered nite element mesh schemeis shown in Fig. 2. The frame beam and column components wereassumed to be laterally braced against out-of-plane deformations.Constraints were also used at story level column nodes to simulatethe effect of a rigid diaphragm.

BEAM188 element was used to model the frame beam and col-umn components. This element is based on Timoshenko beam the-ory. It is suitable for analyzing slender to moderately stubby/thickbeam structures and is well-suited for linear, large rotation, and/orlarge strain nonlinear applications. As shown in Fig. 2, strip model

Table 1Properties of the moment-resisting and gravity frames (pre-Northridge design) from the L

Story/oor Moment-resisting frame

Girders Columns

Exterior Interior

9/Roof W24 68 W14 233 W14 2578/9 W27 84 W14 233, W14 257 W14 257, W14 2837/8 W30 99 W14 257 W14 2836/7 W36 135 W14 257, W14 283 W14 283, W14 3705/6 W36 135 W14 283 W14 3704/5 W36 135 W14 283, W14 370 W14 370, W14 4553/4 W36 135 W14 370 W14 4552/3 W36 160 W14 370, W14 370 W14 455, W14 5001/2 W36 160 W14 370 W14 500approach was used to represent the SPSW behavior. Accordingly,the web plates were represented by 15 equally-spaced discretepin-ended and tension-only strips in each direction oriented at45 relative to the vertical. The strips were modeled using LINK180truss element with three degrees of freedom at each node and plas-ticity, creep, rotation, large deection, and large strain capabilities.Further, seismic and lumped masses consistent with the FEMA355C [9] values were placed at each story level on the beam-col-umn intersection nodes. These were modeled using MASS21 pointelement with up to six degrees of freedom.

The material properties of the ASTM A36 and LYP100 steelselected for the inll plates and ASTM A572 Gr. 50 steel selectedfor the frame members are shown in Fig. 3. The von Mises yield cri-terion was adopted for material yielding, and kinematic hardeningrule was incorporated in the nonlinear time-history analyses.

Rayleigh proportional damping was used for the seismic analy-sis. Consistent with the studies reported by Gupta and Krawinkler[13] and Berman [14] on the performance of moment-resisting andSPSW frames, respectively, a damping ratio of 2% was selected forthe analysis of the structural models. The Rayleigh damping coef-cients were determined by considering the 1st and 5th modal fre-quencies in order to set the damping ratio at 2%.

Nonlinear time-history analyses with geometrical and materialnonlinearities were performed for seismic response and perfor-mance assessment of the structural models. P-delta effects werealso considered in the analyses by applying the gravity load priorto the time-history analysis. Ground accelerations were subse-quently applied to the base of the structural model with the gravityload kept constant.

Fig. 2. Typical wall-frame structural model.The adequacy of the adopted nite element strip modelingapproach was veried by comparing the numerical predictionswith experimental results. To achieve this, experimental resultsfrom the testing of a single-story SPSW specimen with stocky

A 9-story SAC building model and SPSW structure.

Gravity frame SPSW

Beams Columns HBEs VBEs tp (mm)

W16 26 W14 48 W30 391 W14 605 1.59W18 35 W14 48, W14 82 W30 391 W14 605 3.18W18 35 W14 82 W30 391 W14 665 4.76W18 35 W14 82, W14 109 W30 391 W14 665 6.35W18 35 W14 109 W30 391 W14 730 7.94W18 35 W14 109, W14 145 W27 146 W14 730 7.94W18 35 W14 145 W30 391 W14 730 9.53W18 35 W14 145, W14 193 W27 146 W14 730 9.53W18 35 W14 193 W27 146 W14 730 9.53

and LYP100 steel inll plate [15] and a three-story SPSW specimenwith thin and conventional steel inll plates [16] were considered.The modeling details and comparison results for the two test spec-imens are provided in Figs. 4 and 5, respectively. It is clearlyobserved that predictions of the strip model agree well with the

experimental results. This is indicative of the adequacy and capa-bility of the adopted strip model in predicting the responses of sin-gle- and multi-story SPSWs with various geometrical and materialproperties.

3.3. Ground motion suite

In the PSDA method, it is important to select a sufcient num-ber of earthquake records. This can result in development of reli-able fragility functions and accurate prediction of the seismicresponse. On this basis, a suite of thirty Los Angeles ground motionrecords considered in the SAC steel research project [9] was used inthis study. The suite consists of ground motions with probabilitiesof exceedance of 50% in 50 years, 10% in 50 years, 2% in 50 yearsand includes uncertainties in the seismic characteristics. Detailsof the selected earthquake records are provided in Table 2.

Fig. 6 shows the distributions of the peak ground velocity andacceleration of the selected ground motion records. With referenceto Table 2 and Fig. 6(a) and (b), the selected earthquake recordshave PGV values ranging between 0.22 m/s and 1.94 m/s and

050

100150200250300350400450500

0 0.1 0.2 0.3 0.4 0.5Strain

Stre

ss (M

Pa)

E = 200000 MPav = 0.3

ASTM A572 Gr. 50 (y = 345 MPa)

ASTM A36 (y = 250 MPa)

LYP100 (y = 100 MPa)

Fig. 3. Material properties of the adopted steel.

-1300

-650

0

650

1300

-50 -30 -10 10 30 50

In-plane lateral displacement (mm)

Load

(kN

)

ExperimentalStrip Model

Fig. 4. Modeling details and analysis results for Chen and Jhangs [15] specimen No. 1.

1800

198 J. Zhang, T. Zirakian / Engineering Structures 85 (2015) 195205(a) Strip model

-1800

-900

0

900

1800

-90 -45 0 45 90

In-plane lateral displacement (mm)

Load

(kN

)

ExperimentalStrip Model

-40 -20 0 20 40Lo

(c) Cyclic analysis results (2F)

Fig. 5. Modeling details and analysis result-1800

-900

In-plane lateral displacement (mm)

ExperimentalStrip Model-1800

-900

0

900

-130 -65 0 65 130

In-plane lateral displacement (mm)

Load

(kN

)

ExperimentalStrip Model

(b) Cyclic analysis results (3F)

0

900

1800

ad (k

N)(d) Cyclic analysis results (1F)

s for Park et al.s [16] SC2T specimen.

nce

ing STable 2Details of selected LA ground motions for probabilistic seismic demand analysis.

SAC name Record Earthquake magnitude Dista

LA02 Imperial Valley, El Centro, 1940 6.9 10LA04 Imperial Valley, Array #05, 1979 6.5 4.1LA06 Imperial Valley, Array #06, 1979 6.5 1.2LA08 Landers, Barstow, 1992 7.3 36LA10 Landers, Yermo, 1992 7.3 25LA11 Loma Prieta, Gilroy, 1989 7 12LA13 Northridge, Newhall, 1994 6.7 6.7LA16 Northridge, Rinaldi RS, 1994 6.7 7.5LA18 Northridge, Sylmar, 1994 6.7 6.4LA19 North Palm Springs, 1986 6 6.7

LA21 Kobe, 1995 6.9 3.4LA22 Kobe, 1995 6.9 3.4LA23 Loma Prieta, 1989 7 3.5LA24 Loma Prieta, 1989 7 3.5LA25 Northridge, Rinaldi, 1994 6.7 7.5

J. Zhang, T. Zirakian / EngineerPGA values ranging between 0.11 g and 1.33 g. The ground motionsare selected in a manner to cover wide ranges of PGV and PGAintensity measures.

3.4. Seismic responses of structural models

The process of selecting effective demand measures forcharacterizing the seismic performance and probabilisticallyevaluating the seismic vulnerability of structures is a challengingtask. In fact, the choice of an appropriate seismic demandparameter is a function of the structural system and the desiredperformance objectives [17]. A search of the literature reveals thatalthough various demand parameters have been proposed andapplied in the probabilistic seismic demand analysis of structures,interstory drift and oor acceleration have been deemed signicantdemand measures. For instance, in the Federal EmergencyManagement Agency (FEMA)/National Institute of BuildingSciences (NIBS) earthquake loss estimation methodology,commonly known as HAZUS, building damage is estimated based

LA26 Northridge, Rinaldi, 1994 6.7 7.5LA27 Northridge, Sylmar, 1994 6.7 6.4LA28 Northridge, Sylmar, 1994 6.7 6.4LA29 Tabas, 1974 7.4 1.2LA30 Tabas, 1974 7.4 1.2

LA41 Coyote Lake, 1979 5.7 8.8LA43 Imperial Valley, 1979 6.5 1.2LA44 Imperial Valley, 1979 6.5 1.2LA45 Kern, 1952 7.7 107LA46 Kern, 1952 7.7 107LA49 Morgan Hill, 1984 6.2 15LA54 Parkeld, Cholame 8 W, 1966 6.1 8LA56 North Palm Springs, 1986 6 9.6LA57 San Fernando, 1971 6.5 1LA58 San Fernando, 1971 6.5 1

012345678

0.2-0.

4

0.4-0.

6

0.6-0.

8

0.8-1.

0

1.0-1.

2

1.2-1.

4

1.4-1.

6

1.6-1.

8

1.8-2.

0

PGV (m/s)

Num

ber o

f rec

ords

(a) PGV

Fig. 6. Characteristics of selected earthquake reco(km) Scale factor PGV (mm/s) PGA (mm/s2) Probability of exceedance

2.01 599.0 6628.8 10% in 50 years1.01 771.0 4786.5 10% in 50 years0.84 474.4 2300.8 10% in 50 years3.2 656.8 4174.9 10% in 50 years2.17 603.5 3533.5 10% in 50 years1.79 791.4 6524.9 10% in 50 years1.03 955.5 6649.3 10% in 50 years0.79 1007.6 5685.8 10% in 50 years0.99 1189.3 8014.4 10% in 50 years2.97 682.7 9994.3 10% in 50 years

1.15 1427.0 12580.0 2% in 50 years1.15 1231.6 9027.5 2% in 50 years0.82 737.6 4099.5 2% in 50 years0.82 1369.1 4637.6 2% in 50 years1.29 1603.1 8516.2 2% in 50 years

tructures 85 (2015) 195205 199on interstory drift and oor acceleration [18]. Accordingly, thepeak interstory drift ratio (PIDR) and peak oor acceleration(PFA) seismic response parameters were considered as the poten-tial EDPs.

The effectiveness of various ground motion intensity parame-ters considered for the seismic performance assessment of struc-tures has also been investigated by researchers. Among variousgroundmotion intensity measures, PGV and PGA can be consideredas fairly robust and easy to compute [19]. These have beenemployed by many researchers in the development of fragilitycurves [20]. Accordingly, PGV and PGA were taken as the potentialIMs for the purpose of this study.

In order to evaluate the peak drift and acceleration responses ofthe structural models under the considered suite of earthquakerecords, the average PIDR (%) and PFA (g) values were computedfrom the corresponding peak values and shown in Fig. 7. In the caseof the peak drift response, the GF-LYPSPSW2 model with the low-est average PIDR (%) value shows the best performance in limitingthe seismic-induced interstory drift. In the case of the peak

1.29 1639.8 9252.9 2% in 50 years1.61 1304.9 9087.0 2% in 50 years1.61 1935.3 13041.0 2% in 50 years1.08 710.5 7934.5 2% in 50 years1.08 1388.3 9725.8 2% in 50 years

2.28 1390.4 5783.4 50% in 50 years0.4 848.6 1406.7 50% in 50 years0.4 451.3 1094.5 50% in 50 years2.92 247.0 1414.9 50% in 50 years2.92 243.0 1560.2 50% in 50 years2.35 269.4 3124.1 50% in 50 years2.92 320.8 7750.5 50% in 50 years2.75 254.2 3716.6 50% in 50 years1.3 216.7 2481.4 50% in 50 years1.3 270.8 2265.4 50% in 50 years

0.0-0.

2

0.2-0.

4

0.4-0.

6

0.6-0.

8

0.8-1.

0

1.0-1.

2

1.2-1.

4

PGA (g)

Num

ber o

f rec

ords

(b) PGA

012345678

rds for probabilistic seismic demand analysis.

acceleration response, it is found that the GF-CSPSW modelpossesses a larger average PFA (g) value relative to the MRF modeldue to its considerably higher stiffness. Retrotting of theGF-CSPSW model with LYP steel inll plates of double thicknessfavorably results in comparatively higher stiffness and lower aver-age PFA (g) value. These results demonstrate the desirable drift andacceleration performances of the GF-LYPSPSW2 model.

The behaviors of the frame beam and column members in the

Overall, these results and ndings demonstrate the superiorseismic performance of the GF-LYPSPSW2 model with LYP steelinll plates of double thickness as a desirable retrot option forthe code-designed and conventional steel GF-CSPSW model.

4. Fragility analysis of structural systems

4.1. Selection of appropriate EDPIM data pairs

A PSDM relates IMs to EDPs, hence the choice of EDPIM pair inthe demand model is critical for a successful PSDA. An optimalPSDM is required to be practical, effective, sufcient, and efcient,and selection of an appropriate EDPIM pair for such a PSDM isnot easy [21]. Detailed explanations in this regard are providedby Mackie and Stojadinovic [21] and Jankovic and Stojadinovic[22].

In this study, it was tried to search for appropriate EDPIM pairsfrom the four potential PIDRPGV, PIDRPGA, PFAPGV, and PFAPGA data pairs for optimal PSDMs with lower degrees of scatter.To this end, ln[EDP] and ln[IM] were plotted against each otherfor the three structural models. Typical plots developed for thePFAPGA data pairs are shown in Fig. 8. As seen in this gure, a lin-ear regression analysis of the ln[EDP] and ln[IM] data in each caseproduces a line through the cloud of the EDPIM data points. Thecorresponding linear equation and R2 value are also provided in

MRF GF-CSPSW GF-LYPSPSW2

Ave. PFA (g)Ave. PIDR (%)

2.73

1.80

1.33

0.907

1.617

1.086

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Fig. 7. Average PIDR (%) and PFA (g) values for the MRF, GF-CSPSW, and GF-LYPSPSW2 models.

200 J. Zhang, T. Zirakian / Engineering Structures 85 (2015) 195205three models were also investigated for any possible local failures.The analysis results showed the occurrence of local yielding at theends of beam members and all 1st story column bases in the MRFmodel. In the GF-CSPSW model, on the other hand, local yieldingwas found to occur at the ends of HBEs and all 1st story VBE andcolumn bases, while the localized yielding zones were desirablyconned to HBE ends and 1st story VBE bases in the GF-LYPSPSW2model. These ndings are indicative of desirable performances ofthe SPSW frames, especially in the case of the GF-LYPSPSW2model, in absorbing the input energy and reducing the overallsystem demand on the frame members outside the SPSW.

ln[EDP ] = 0.5876ln[IM] + 0.2352R2 = 0.8846

0

1

2

DP

= PFA

(g)]-2

-1

-2.5 -2 -1.5 -1ln[ IM = PGA (g)]

ln[E

-0.5 0 0.5

(a) MRF

ln[EDP ] = 0.6748ln[IMR2 = 0.8551

-2

-1

0

1

2

-2.5 -2 -1.5ln[ IM

ln[EDP

= PFA

(g)]

(c) GF-L

Fig. 8. Relationship between ln[EDP-1 -0.5 0 0.5= PGA (g)]each individual case.The coefcient of determination, i.e. R2 value, is a statistic which

was considered as a measure of variation in here. The R2 valuesobtained from the linear regression analyses of the data pairs aregiven in Table 3. From the table, PGA appears to have a strongercorrelation with the two considered EDPs compared to PGV. Fur-ther, PGA is found to be better correlated with PFA relative to PIDR.As a result, fragility curves developed based on PFAPGA and PIDR-PGA data pairs were believed to be more reliable in providing a bet-ter representation of probability of the structural damage and/orrepair.

ln[EDP ] = 0.6869ln[IM] + 0.8501R2 = 0.8028

-2

-1

0

1

2

-2.5 -2 -1.5 -1 -0.5 0 0.5ln[IM = PGA (g)]

ln[EDP

= PFA

(g)]

(b) GF-CSPSW

] + 0.4458YPSPSW2

= PFA (g)] and ln[IM = PGA (g)].

4.2. Determination of lognormal distribution parameters

Based on the satisfactory correlation between PFA and PGA aswell as PIDR and PGA data pairs, as demonstrated in the previoussection, these EDP and IM parameters were consequently selectedin this process. The values of the a and b constant coefcientsdetermined from the linear regression analysis and the standarddeviations calculated using Eq. (2) for the selected EDPIM pairsas well as the structural models are given in Table 4. Included inthe table are also the functional relations between the EDP andIM parameters, which were determined using the regression coef-cients and the power model given in Eq. (1). These tabulated

PSDM parameters were utilized in development of fragility curvesfor the considered structural models.

Lastly, as an example, the PFAPGA data plots together with thecorresponding power trendlines developed for the three structuralmodels are illustrated in Fig. 9. It should be noted that the corre-sponding power functions as well as the R2 values can be alsoobtained directly from nonlinear regression analysis of data.

4.3. Considered damage and repair states

One of the important issues in performance-based earthquakeengineering methodology is the denition of meaningful damagestates in relation to repair actions. Damage and the associatedrepair models are often developed based on experimental observa-tions and engineering judgment. Building damage is estimatedbased on threshold values of structural response parameters, e.g.interstory drift and oor acceleration, that initiate different statesof damage [18]. These threshold values are referred to as the limitstates, which are denoted by LS in Eqs. (3) and (4).

According to the HAZUS-MH MR5 [18], fragility curves describethe probability of damage to the buildings structural system, drift-sensitive nonstructural components, and acceleration-sensitivenonstructural components and contents. In addition, damage isdescribed by one of the four Slight, Moderate, Extensive, andComplete discrete damage states. On this basis, separate fragility

Table 3R2 values obtained from linear regression of ln[EDP] and ln[IM] variables.

ln[EDP] Model ln[IM]

ln[PGV (m/s)] ln[PGA (g)]

ln[PIDR] MRF 0.6725 0.6245GF-CSPSW 0.5506 0.7450GF-LYPSPSW2 0.6239 0.7315

ln[PFA (g)] MRF 0.5369 0.8846GF-CSPSW 0.4714 0.8028GF-LYPSPSW2 0.5844 0.8551

Table 4Regression coefcients, standard deviation, and functional relation for selected EDPIM data sets.

Model Selected Regression coefcients fEDP|IM Functional relation

EDP IM a b

MRF PIDR PGA (g) 0.0375 0.6913 0.3792 PIDR = 0.0375(PGA)0.6913

GF-CSPSW PIDR PGA (g) 0.0271 0.8409 0.3481 PIDR = 0.0271(PGA)0.8409

GF-LYPSPSW2 PIDR PGA (g) 0.0197 0.8363 0.3585 PIDR = 0.0197(PGA)0.8363

MRF PFA (g) PGA (g) 1.2651 0.5876 0.1501 PFA = 1.2651(PGA)0.5876

GF-CSPSW PFA (g) PGA (g) 2.3400 0.6869 0.2409 PFA = 2.3400(PGA)0.6869

GF-LYPSPSW2 PFA (g) PGA (g) 1.5618 0.6748 0.1965 PFA = 1.5618(PGA)0.6748

J. Zhang, T. Zirakian / Engineering Structures 85 (2015) 195205 201EDP = 1.2651IM 0.5876

R2 = 0.8846

0.0000.2000.4000.6000.8001.0001.2001.4001.6001.800

IM = PGA (g)

EDP

= PF

A (g

)

0 0.25 0.5 0.75 1 1.25 1.5(a) MRF

0.0000.3000.6000.9001.2001.5001.8002.1002.4002.700

0 0.25 0.5 0IM =

EDP

= PF

A (g

)

(c) GF-LY

Fig. 9. Relationship between PFAPGA data seEDP = 2.3400IM 0.6869

R2 = 0.8028

0.0000.4000.8001.2001.6002.0002.4002.8003.2003.600

IM = PGA (g)

EDP

= PF

A (g

)

(b) GF-CSPSW

EDP = 1.5618IM 0.6748

R2 = 0.8551

0 0.25 0.5 0.75 1 1.25 1.5

.75 1 1.25 1.5PGA (g)PSPSW2

ts for the considered structural models.

different seismic design levels. Table 5 lists the interstory drift

GF-CSPSW, and GF-LYPSPSW2 models using the PSDA method.These fragility curves are presented respectively in Figs. 1012.

Table 5HAZUS-MH MR5 [18] interstory drift ratios of structural damage states for high-rise steel moment frames with high-code design level.

Structural model Height range Design level Structural damage states

Slight Moderate Extensive Complete

Steel moment frame High-rise High-code 0.003 0.006 0.015 0.040

00.10.20.30.40.50.60.70.80.9

1

PGA (g)

Dam

age

prob

abili

ty

Slight

Moderate

Extensive

Complete

(a) MRF, damage states

0.20.30.40.50.60.70.80.9

1

Rep

air p

roba

bilit

y

RS1

RS2

RS3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Table 6Baldvins et al.s [6] recommended story drift ratios of structural repair states for SPSWs that meet certain seismic criteria.

Structural model Structural repair states

RS1 RS2 RS3 RS4 RS5

Steel plate shear wall 0.004 0.006 0.015 0.0275Description Cosmetic repair Replace web plate VBE repair HBE and connection repair Replace boundary elements or frame

202 J. Zhang, T. Zirakian / Engineering Structures 85 (2015) 195205ratios of structural damage states for high-rise steel momentframes with high-code design level, selected for the MRF model.Due to the lack of codied data for the case of structural damagestates for SPSW systems, recourse was made to the results of thestudy reported by Baldvins et al. [6], as discussed before. The verepair states and the associated story drift ratios proposed forSPSWs meeting certain seismic criteria were adopted in thisresearch, which are summarized in Table 6. As seen in the table,no story drift ratio was recommended for RS4 due to the lack ofexperimental data. Specication of a certain story drift ratio for thisrepair state is dependent upon availability and consideration ofadditional experimental data [6].

In addition, the HAZUS-MH MR5 [18] damage-state criteriaspecied for drift- and acceleration-sensitive nonstructural com-ponents and contents were adopted for development of the corre-sponding fragility curves for all three structural models. These areprovided in Tables 7 and 8, respectively.

4.4. Fragility curves of structural models

By selecting the effective EDPIM data pairs, determining log-normal distribution parameters, and considering the appropriatedamage and repair states, structural and nonstructural drift as wellcurves were developed in this study for the aforementioned struc-tural and nonstructural categories by adopting appropriate damageand repair states as discussed in the following.

HAZUS-MH MR5 [18] provides the average interstory driftratios of structural damage states for generic building types andas acceleration fragility curves were developed for the MRF,

Table 8HAZUS-MH MR5 [18] peak oor accelerations of nonstructural damage states foracceleration-sensitive components/contents of all building types with high-codedesign level.

Structural model Design level Nonstructural damage states

Slight Moderate Extensive Complete

All High-code 0.3 g 0.6 g 1.2 g 2.4 g

Table 7HAZUS-MH MR5 [18] interstory drift ratios of nonstructural damage states for drift-sensitive components of all building types.

Structural model Design level Nonstructural damage states

Slight Moderate Extensive Complete

All All 0.004 0.008 0.025 0.05000.1 RS5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5(b) GF-CSPSW, repair states

00.10.20.30.40.50.60.70.80.9

1

Rep

air p

roba

bilit

y

RS1

RS2

RS3

RS5

(c) GF-LYPSPSW2, repair states

PGA (g)

PGA (g)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Fig. 10. Fragility curves for predicting the probability of reaching or exceeding thedamage states of MRF and repair states of GF-CSPSW and GF-LYPSPSW2 structuralsystems.

0.4

age

0.8ty

ing S00.10.20.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5PGA (g)

Dam

(a) MRF

0.910.50.60.70.80.9

1

pro

babi

lity

Slight

Moderate

Extensive

Complete

J. Zhang, T. Zirakian / EngineerAs seen in Fig. 10(a), structural fragility curves were developedfor the Slight, Moderate, Extensive, and Complete damage statesfor the MRF model. Fig. 10(b) and (c) plot the structural fragilitycurves generated for the four repair states, i.e. RS1, RS2, RS3, andRS5 (Table 6), for the two respective GF-CSPSW and GF-LYPSPSW2models. The nonstructural drift and acceleration fragility curvesdeveloped for the Slight, Moderate, Extensive, and Complete dam-age states for the three structural models are also plotted in Figs. 11and 12, respectively.

5. Discussion of results

Quantitative assessment of risk to a structure from earthquakesis a multi-disciplinary and challenging problem, which involves: (i)quantication of the shaking that a structure might experience atits base, (ii) quantication of the structural response and resultingdamage, and (iii) cost estimation to help determine the social andeconomic consequences of the damage. Considering the uncertain-ties present in many aspects of this problem, it is important for any

00.10.20.30.40.50.60.70.8

Dam

age

prob

abili

ty

Slight

Moderate

Extensive

Complete

(b) GF-CSPSW

00.10.20.30.40.50.60.70.80.9

1

Dam

age

prob

abili

ty

Slight

Moderate

Extensive

Complete

(c) GF-LYPSPSW2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5PGA (g)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5PGA (g)

Fig. 11. Fragility curves for predicting the probability of reaching or exceeding thenonstructural damage states for drift-sensitive components of buildings.00.10.20.30.40.50.60.70.80.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5PGA (g)

Dam

age

prob

abili

ty

Slight

Moderate

Extensive

Complete

(a) MRF

0.91

tructures 85 (2015) 195205 203assessment to be made in terms of probabilities [7]. Hence, it isbelieved that the adopted probabilistic methodology can providea realistic and robust assessment of seismic performances of thestructural models.

The seismic vulnerability of the retrotted structures employ-ing SPSW systems and LYP steel material is evaluated in this sec-tion. Assessments are made by comparing the median (50thpercentile) PGA values of the fragility curves for all damage/repairstates of the MRF, GF-CSPSW, and GF-LYPSPSW2 models. In fact,consideration of the median values of probability of exceedanceallows the comparison of seismic vulnerabilities of different struc-tures to be made, given that the variations are similar for the struc-tures [23]. The higher the median PGA required, the better is thestructural response.

The median values of PGA obtained from the structural fragilitycurves (Fig. 10) for the damage/repair states of the MRF and SPSWmodels are shown in Fig. 13. Due to consideration of different cri-teria in developing the structural fragility curves for the MRF andthe SPSW systems, the seismic vulnerabilities of the two lateral

00.10.20.30.40.50.60.7

Dam

age

prob

abili

Slight

Moderate

Extensive

Complete

(b) GF-CSPSW

00.10.20.30.40.50.60.70.80.9

1

Dam

age

prob

abili

ty

Slight

Moderate

Extensive

Complete

(c) GF-LYPSPSW2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5PGA (g)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5PGA (g)

Fig. 12. Fragility curves for predicting the probability of reaching or exceeding thenonstructural damage states for acceleration-sensitive components/contents ofbuildings.

tive of superior seismic performance of the GF-LYPSPSW2 model.This is because for a given damage state, the GF-LYPSPSW2 modelis required to undergo higher levels of ground shaking in order toexperience the same amount of damage as experienced by theGF-CSPSW model. These ndings are consistent with the resultsshown in Fig. 7 in case of the acceleration performance.

It is important to note that employment of LYP steel with con-siderably low yield stress compared to that of conventional steelcan result in design of relatively thicker inll plates in SPSW sys-tems. This can improve the stiffness and buckling stability of SPSWsystems. Nevertheless, accurate assessment of the structural accel-eration performance and plate-frame interaction is required forcondent application of LYP steel inll plates in design of newand retrot of existing SPSWs.

The results of the nonlinear time-history analyses of the three

0.03 0.07

0.27

1.10

0

0.2

0.4

0.6

0.8

1

1.2

Slight Moderate Extensive Complete

Med

ian

PGA

(g)

MRF

(a) MRF system, damage states

Fig. 13. Median values of PGA from the fragility curves

204 J. Zhang, T. Zirakian / Engineering Sforce-resisting systems are evaluated separately. Fig. 13(a) demon-strates that the median PGA values for the MRF model increaseremarkably by moving from Slight to Complete damage states.Such a trend in general indicates that the structure will experiencemajor damages at higher levels of earthquake ground shaking.Comparison of the median PGA values for the two SPSW systemsshown in Fig. 13(b), on the other hand, demonstrates that theGF-CSPSW model is more vulnerable relative to the GF-LYPSPSW2model. In other words, the larger median values of PGA in case ofthe GF-LYPSPSW2 model are indicative of lower seismic vulnera-bility and consequently better performance.

The median PGA values from the nonstructural drift fragilitycurves (Fig. 11) for the Slight, Moderate, Extensive, and Completedamage states of the three structural models are shown inFig. 14. As it is observed in Fig. 14, the MRF and GF-LYPSPSW2models possess the smallest and the largest median PGA values,respectively, consistent with all four damage states. This indicatesthat the MRF model is the most vulnerable and the GF-LYPSPSW2model is the least vulnerable model among the three models.Accordingly, it can be concluded that the GF-LYPSPSW2 modelexhibits a better performance compared to the GF-CSPSW model.Also, the MRF model is expected to exhibit the weakest perfor-mance by experiencing damages at lower levels of ground shaking.These ndings are consistent with the results illustrated in Fig. 7,where the MRF and GF-LYPSPSW2 models were shown to havethe lowest and highest performances, respectively, in limiting thedrift response.

Fig. 15 shows the median values of PGA obtained from the non-structural acceleration fragility curves (Fig. 12) for the four distinctdamage states of the MRF, GF-CSPSW, and GF-LYPSPSW2 models.From the gure, it is found that the MRF model possesses the larg-est median values of PGA in cases of all damage states. This doesnot necessarily indicate better seismic performance of the MRFmodel, since from Fig. 7 it is quite evident that this model showsthe lowest drift performance due to its exibility compared to

the SPSW models. Further, it is found that retrotting of the

0.04 0.11

0.56

1.52

0.10 0.

23

0.91

2.07

0.15 0.

34

1.33

3.05

0

0.5

1

1.5

2

2.5

3

3.5

Slight Moderate Extensive Complete

Med

ian

PGA

(g)

MRFGF-CSPSWGF-LYPSPSW2

Fig. 14. Median values of PGA from the fragility curves for the damage states ofnonstructural drift-sensitive components.GF-CSPSW model with LYP steel inll plates of double thicknessappears to be effective in terms of reducing the probability of dam-age to the nonstructural acceleration-sensitive components andcontents. The larger median PGA values of the GF-LYPSPSW2model relative to those of the GF-CSPSW model are indeed indica-

0.10 0.17

0.50

1.02

0.15 0.

24

0.72

1.49

00.20.40.60.8

11.21.41.6

RS1 RS2 RS3 RS5

Med

ian

PGA

(g)

GF-CSPSWGF-LYPSPSW2

(b) SPSW systems, repair states

for the damage/repair states of structural systems.

0.09 0.

28

0.91

2.97

0.05 0.14 0

.38

1.04

0.09 0.

24

0.68

1.89

0

0.5

1

1.5

2

2.5

3

3.5

Slight Moderate Extensive CompleteM

edia

n PG

A (g

)

MRFGF-CSPSWGF-LYPSPSW2

Fig. 15. Median values of PGA from the fragility curves for the damage states ofnonstructural acceleration-sensitive components/contents.

tructures 85 (2015) 195205structural models were indicative of advantages of using relativelythicker LYP steel inll plates. In fact, application of LYP steel inllplates of double thickness was shown to improve the drift andacceleration performances of the retrotted code-designed andconventional steel SPSW frame by limiting the seismic responses.

It is also noted that application of LYP steel facilitates the designof SPSWs and results in a desirable plate and frame yieldingsequence by ensuring the early yielding of the inll plate comparedto those of HBE and VBE components. Further, the increase in web-plate thickness does not necessarily increase the overall systemdemand on the boundary frame members. Early yielding of a LYPsteel inll plate with high ductility and elongation capacity indeedsupplies a large source of energy dissipation, which in turn limitsthe plastic deformation demand to the primary structure.

In summary, the results of the adopted probabilistic methodol-ogy show that SPSWs in general and LYP steel shear walls in par-ticular are efcient lateral force-resisting systems. They can be

effectively used in controlling the seismic response and reducingthe vulnerability of structures. Findings of this study also demon-strate the effectiveness of using LYP steel in improving the seismicperformance of SPSW systems.

6. Conclusions

In spite of importance of the fragility methodology in perfor-mance-based earthquake engineering, little steps have been takentowards application of this methodology in seismic design, retrot,and performance assessment of SPSW systems. The major objec-tive of this study was to take an effective step towards addressingthis need by developing appropriate fragility functions and evalu-

References

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[3] Ghosh S, Adam F, Das A. Design of steel plate shear walls considering inelasticdrift demand. J Constr Steel Res 2009;65:14317.

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J. Zhang, T. Zirakian / Engineering Structures 85 (2015) 195205 205ating the seismic performances of code-designed and retrottedSPSW systems. This study also intended to demonstrate the effec-tiveness of using LYP steel in seismic design and retrot of SPSWsthrough system-level investigations. To achieve these objectives,nonlinear time-history analyses were performed on three 9-storystructural models including a code-designed moment-resistingframe, a code-designed and conventional steel shear wall frame,and a retrotted LYP steel shear wall frame.

The peak interstory drift ratio (PIDR) and peak oor acceleration(PFA) demand parameters were shown to be well-correlated withthe peak ground acceleration (PGA) intensity measure. Theseparameters were used for developing structural and nonstructuralfragility curves through probabilistic seismic demand analysis(PSDA) method. Comparison of the median (50th percentile) valuesof PGA obtained from the fragility curves showed that SPSW sys-tems in general are quite effective in controlling the seismicresponse and reducing the vulnerability of buildings. Moreover,application of LYP steel inll plates with double thickness wasfound to be quite effective in seismic retrot of the code-designedand conventional steel SPSWmodel. The retrotted LYP steel shearwall fame indeed exhibited higher performance in limiting thedrift and acceleration responses and lowering the seismic vulnera-bility relative to the original SPSW frame. Such an improvement inseismic performance is directly related to the application of LYPsteel with superb material properties, benecial for seismic hazardmitigation of structures.

Acknowledgements

The authors would like to express their sincere and profoundappreciations to Prof. Sheng-Jin Chen from National Taiwan Uni-versity of Science and Technology in Taiwan, Dr. Chyuan Jhangfrom the Sinotech Engineering Consultants in Taiwan, and Dr. In-Rak Choi from the Research Institute of Industrial Science andTechnology in South Korea, for their great support in providingexperimental data and details.344354.[6] Baldvins NM, Berman JW, Lowes LN, Janes TM, Low NA. Fragility functions for

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Probabilistic assessment of structures with SPSW systems and LYP steel infill plates using fragility function method1 Introduction2 Fragility function methodology3 Specifications and modeling of structural systems3.1 Selected structural models3.2 Finite element modeling and analysis3.3 Ground motion suite3.4 Seismic responses of structural models

4 Fragility analysis of structural systems4.1 Selection of appropriate EDPIM data pairs4.2 Determination of lognormal distribution parameters4.3 Considered damage and repair states4.4 Fragility curves of structural models

5 Discussion of results6 ConclusionsAcknowledgementsReferences