Engineering Structures 33 (2011) 77–89

Contents lists available at ScienceDirect

Engineering Structures

journal homepage: www.elsevier.com/locate/engstruct

Evaluation of buckling-restrained braced frame seismic performance consideringreserve strengthChristopher Ariyaratana a, Larry A. Fahnestock b,∗

a Arup, Edison, NJ 08837, USAb Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

a r t i c l e i n f o

Article history:Received 15 January 2010Received in revised form15 September 2010Accepted 16 September 2010Available online 2 November 2010

Keywords:Buckling-restrained braced frameDual systemReserve strengthSeismic performanceResidual drift

a b s t r a c t

Buckling-restrained braced frame (BRBF) systems are used extensively for resisting lateral forces in highseismic regions of the United States. Numerical and large-scale experimental studies of BRBFs have shownpredictable seismic performance with robust ductility and energy dissipation capacity. However, the lowpost-yield stiffness of buckling-restrained braces (BRBs) may cause BRBFs to exhibit large maximum andresidual drifts and allow the formation of soft stories. Thus, reserve strength provided by other elementsin the lateral-force-resisting system is critical to improving seismic performance of BRBFs. This reservestrength can be provided in two primary ways: (1) moment-resisting connections within the BRBF and(2) a steel special moment-resisting frame (SMRF) in parallel with the BRBF to create a dual systemconfiguration. These two approaches to providing reserve strength can be used together or separately,leading to a variety of potential system configurations. In addition, special attention must be given to theconnections within the BRBF since moment-resisting connections have been observed experimentally tolimit drift capacity due to undesirable connection-related failure modes. This paper presents nonlineardynamic analysis results and evaluates performance of BRBF and BRBF–SMRF systems using moment-resisting and non-moment-resisting beam–column connections within the BRBF. Reserve strength isshown to play a critical role in seismic behavior and performance of BRBFs.

© 2010 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Background

Tests of buckling-restrained braces (BRBs) have consistentlydemonstrated stable and robust behavior under cyclic load-ing [1,2]. Since the steel core of a BRB cannot buckle, it yields incompression as well as in tension and develops significant inelas-tic deformation and energy dissipation. These characteristics havemade BRBs an attractive alternative to conventional steel bracesin high seismic regions of the United States. In response to thewidespread interest in concentrically braced frames (CBFs) withBRBs, which are called buckling-restrained braced frames (BRBFs),BRBF design provisions are now included inMinimum Design Loadsfor Buildings and Other Structures: SEI/ASCE 7-05 [3] and the Amer-ican Institute of Steel Construction (AISC) Seismic Provisions forStructural Steel Buildings [4].

Although these provisions were developed to be both practicaland sufficiently rigorous to provide a level of reliability equivalent

∗ Corresponding author. Tel.: +1 217 265 0211; fax: +1 217 265 8040.E-mail address: fhnstck@illinois.edu (L.A. Fahnestock).

0141-0296/$ – see front matter© 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2010.09.020

to that of other earthquake-resistant structural systems [5], theydo not explicitly address the low post-yield stiffness of BRBs andthe resulting effect on residual drift and soft story formation. Afterthe BRBs in a given story have yielded under seismic excitation,their low post-yield stiffness provides minimal restoring force anddrift can easily concentrate in the story. As a result, residual driftis inherently unpredictable and highly dependent on the groundmotion characteristics. Numerical studies of BRBFs have shownresidual drift with a mean value greater than 0.005 rad for thedesign basis earthquake (DBE), which corresponds approximatelyto a seismic hazardwith 10% probability of exceedance in 50 years,and greater than 0.01 rad for themaximum considered earthquake(MCE), which corresponds to a seismic hazard with 2% probabilityof exceedance in 50 years [6,7]. Large-scale hybrid earthquakesimulations of BRBFs produced residual story drifts of 0.013 and0.027 rad for the DBE and MCE, respectively [8]. Although limitson residual drift are not clearly established, it is typically expectedthat residual drift less than 0.005 radwould be tolerable andwouldpermit a building to be returned to servicewith little difficulty (e.g.,doors, windows and elevatorswould still be functional). Given thatBRBF residual drift after a DBE could exceed this threshold, post-earthquake repair costs arising from residual driftmaymake BRBFsless attractive.

78 C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89

Recent research has demonstrated the influence thatbeam–column connections within BRBFs have on the overall sys-temperformance. Large-scale tests of a one-bay one-story BRBF [9]showed that, although the BRBs performed well, the moment-resisting beam–column connections induced unanticipated de-mands within the frame that eventually led to out-of-plane BRBfailure at a story drift around 0.025 rad. Similar undesirableBRB failure modes were observed in other large-scale BRBFtests [10,11]. Large-scale tests of a one-bay four-story BRBF [8]showed that creating a non-moment-resisting beam–column con-nection by introducing a bolted splice in the beam adjacent to thebeam–column connection significantly reduced demands and pre-vented out-of-plane BRB failure while still maintaining good seis-mic performance of the BRBF system. Wigle and Fahnestock [12]conducted parametric numerical studies that demonstrated thevariations in local and global behavior for BRBFs with moment-resisting and non-moment-resisting connections. The AISC SeismicProvisions [4] require stability to be considered when designinggusset plates in BRBFs, but the type of beam–column connection(moment-resisting or non-moment-resisting) is not identified asa critical parameter affecting behavior and performance, and noguidance is given for design.

1.2. Reserve strength and dual systems

Prior research has demonstrated the importance of reservestrength for reducing maximum and residual drift demands inbuildings. This reserve strength can be provided by column con-tinuity [13–15] or by secondarymoment-resisting frames [16–18].As defined in SEI/ASCE 7-05 [3], a dual system combines a stiff pri-mary seismic force-resisting system (a braced frame or shear wall)with special moment-resisting frames (SMRFs) capable of resist-ing at least 25% of prescribed seismic forces. In a dual system, thetotal seismic force resistance is to be provided by the combina-tion of the primary system and the SMRFs in proportion to theirrigidities. Since the primary system is much stiffer than the SM-RFs, the primary system is typically designed for the full seismicforce with the SMRFs providing reserve strength that enhancesseismic performance. Using this approach, Kiggins and Uang [16]investigated three-story and six-story BRBF–SMRF dual systemswith numerical earthquake simulations. This study built on a priorstudy by Sabelli et al. [6] that investigated isolated BRBFs. It wasshown that the BRBF–SMRF dual systems reduced residual storydrift by approximately 50% while maximum story drift was re-duced by approximately 10% when compared to the isolated BRBFsystems. Although the elastic stiffness of the dual systemswas onlyslightly larger than the isolated BRBFs due to the addition of theSMRFs, it was concluded that the additional global post-yield stiff-ness provided by the SMRFs introduced enough re-centering to sig-nificantly reduce the effect of the low inelastic BRBF stiffness.

A more novel system configuration, which was labeled a dualsystem by its developers, used BRBs on one side of a chevronCBF, whereas the other side of the CBF was designed to remainelastic and distribute inelastic demand (i.e., BRB yielding) over theheight of the frame [19]. This elastic–inelastic CBF dual systemconfiguration is much different from the BRBF–SMRF dual systemconfiguration described above since it is a braced frame withdistinct components that cannot support loads independently, butit appears to provide promising results. Numerical earthquakesimulations showed that by distributing inelastic demand, theelastic–inelastic CBF dual system developed 50% larger resistanceto collapse than an isolated BRBF. Residual drift comparisonswere not presented in this study. Although this new systemconfiguration is an important advance in the use of BRBs, it isa significant departure from the conventional BRBF–SMRF dualsystem configuration, which still requires further study.

1.3. Research motivation

Although numerical and experimental studies of BRBFs havedemonstrated reasonable seismic performance, the low post-yieldstiffness of BRBs may cause BRBFs to exhibit large maximum andresidual drifts and allow the formation of soft stories. In addition,premature failure of some types of beam–column connectionsmayhinder the performance of the BRBs and reduce the effectivenessof the BRBF system. Therefore, it is necessary to investigatesystem configurations that economically mitigate BRBF residualdrift, limit soft story formation, and prevent undesirable failuremodes in the beam–column connection regions. The researchdescribed in this paper explores the implications of reservestrength in the context of these needs. An investigation of isolatedBRBFs and BRBFs that are combined with SMRFs to form adual system was conducted with the objective of assessing theirseismic behavior and performance using numerical earthquakesimulations. Nonlinear time-history analysis for ground motionsscaled to two seismic hazard levels was conducted along withincremental dynamic analysis. BRBFs with moment-resisting andnon-moment-resisting beam–column connections were studied.Moment-resisting connections within a BRBF provide redundancyand reserve strength, butmay reduce the drift capacity of the BRBF.Conversely, non-moment-resisting connections within a BRBFreduce redundancy and reserve strength, but allow for larger driftcapacity since connection-related failure modes can be prevented.Thus, this research focuses on the impact of reserve strength inBRBF systems, whether provided by BRBF connections or parallelSMRFs, and assesses the design provision in SEI/ASCE 7-05 [3].

2. Prototype designs

2.1. Design provisions

SEI/ASCE 7-05 [3] includes provisions for isolated BRBF systemsand BRBF–SMRF dual systems. For isolated BRBF systems, two setsof design parameters are defined, with the variation based onthe type of beam–column connection. For a BRBF with moment-resisting beam–column connections, the response modificationcoefficient, R, system overstrength factor, Ω0, and deflectionamplification factor, Cd, are defined as R = 8, Ω0 = 2.5, andCd = 5. For a BRBF with non-moment-resisting beam–columnconnections, the system parameters are R = 7, Ω0 = 2, Cd = 5.5.When a BRBF is combined with a SMRF capable of resisting atleast 25% of the prescribed seismic forces, the system parametersare equivalent to those of an isolated BRBF with moment-resistingbeam–column connections.

2.2. Model building

A prototype building located in a high seismic region ofCalifornia was used as the basis for this research to assess theimpact of reserve strength on the performance of BRBFs. As notedabove, this reserve strength can be provided internally (i.e. throughflexural strength of BRBF beam–column connections) or externally(i.e. through parallel SMRFs). Fig. 1 shows frame elevations for theprototype building. The BRBF,whichwas extracted froma fictitiousseven-story building with a 37.3m×23.6m floor plan, representsone-half of the lateral-force-resisting system in one direction andis based on a prior BRBF design [20]. For the dual system (DS)configurations, the BRBFwas combinedwith a SMRF. These 7-storysystems are labeled BRBF7 andDS7,which is BRBF7 combinedwithSMRF7. In these frames, the beams and columns are A992 steelwide-flange sections and the BRB core plates are A36 steel.

The prototype designs were based on the equivalent-lateral-force procedure in SEI/ASCE 7 and the AISC Seismic Provisions. The

C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89 79

Table 1Prototype frame member sizes.

Level/story BRBF SMRFColumn Beam BRB (cm2) Column Beam

Roof – W16 × 50 – – W18 × 557 W14 × 74 W16 × 50 19.4 W24 × 76 W18 × 556 W14 × 74 W16 × 50 35.5 W24 × 76 W18 × 605 W14 × 74 W16 × 50 45.2 W24 × 76 W21 × 734 W14 × 145 W16 × 50 54.8 W24 × 94 W24 × 763 W14 × 145 W16 × 50 61.3 W24 × 94 W24 × 842 W14 × 211 W16 × 50 67.7 W24 × 131 W24 × 94Ground W14 × 211 – 71.0 W24 × 131 –

Fig. 1. Prototype frame elevations: (a) BRBF7-MR; (b) BRBF7-NMR; (c) DS7-MR;(d) DS7-NMR.

isolated BRBFs were sized for the design base shear and in thedual systems, the BRBF portions were also sized for the designbase shear with the SMRF portions sized for 25% of the designbase shear as required for dual systems in SEI/ASCE 7. The baseshear used to size the BRBF portion of a dual system is the fulldesign base shear since the BRBF portion is so much stiffer thanthe SMRF portion and in the elastic analysis of the equivalent-lateral-force procedure, the SMRF portion carries almost no baseshear. The equivalent lateral forceswere determinedusing a designspectra with short period design spectral response accelerationparameter, SDS , equal to 1.03g and one-second design spectralresponse acceleration parameter, SD1, equal to 0.89g . The ratio ofdesign base shear to building seismic weight was 0.13. Membersizes for the prototype designs are listed in Table 1 and thefundamental natural period, T1, for each system is listed in Table 2.For the isolated BRBF and the dual system, two configurationswere considered: moment-resisting and non-moment-resistingbeam–column connections within the BRBFs. Although SEI/ASCE7 specifies that BRBFs with non-moment-resisting connections bedesigned using R = 7, R = 8 was used for all designs consideredin this research. This decision was based on the prior findingsthat BRB demands varied little between designs with R = 6 and8 [6], and that a BRBF with non-moment-resisting connectionsdesigned using R = 8 performed well [7,8]. Fig. 1(a) shows theprototype BRBF with moment-resisting (MR) connections (BRBF7-MR), Fig. 1(b) shows the prototype BRBF with non-moment-resisting connections (BRBF7-NMR), Fig. 1(c) shows the prototypedual systemwithmoment-resisting connections in the BRBF (DS7-MR), and Fig. 1(d) shows the prototype dual system with non-moment-resisting connections in the BRBF (DS7-NMR).

3. Analysis framework

3.1. Numerical model

OpenSEES [21] was the analysis platform used for thisresearch. Nonlinear beam–column elements with fiber sectionswere used to model BRBF beams, columns, braces, and SMRFbeams and columns. The gusset plates in the beams and

Fig. 2. Calibrated OpenSEES stress–strain response.

columns were also incorporated in the fiber sections near thebeam–column connections. Beams were continuous betweencolumns for the BRBFs with moment-resisting beam–columnconnections, andpinswere introduced in the beams adjacent to thegusset plates for BRBFs with non-moment-resisting beam–columnconnections. In all BRBFs, the ends of the top floor beams werepinned to model the shear connections. These are simplifiedrepresentations of the non-moment-resisting connections sincethere is some rotational restraint due to the typical connectiondetails. Although connection-related failure modes can play a rolein BRBF performance, these localized failures were not includedin the models. Steel stress–strain properties were calibrated tocyclic test data [22] and implemented using the Menegotto–Pintomaterial model. Fig. 2 shows the cyclic stress–strain response forthe material that was assigned to the beams and columns in themodel along with the test data used for calibration [22]. Each BRBwas modeled with a truss element and the effect of the variousregions contained betweenbrace ends (e.g., BRB connection region,non-yielding BRB core region, and yielding BRB core region) wasrepresented by employing an equivalent elastic modulus. This wasbased on a BRB length that was taken as 70% of the work pointlength, a yielding core length that was taken as 70% of the BRBlength, and a non-yielding BRB core region that was assigned anarea three to six times that of the yielding core, which is consistentwith practice [6]. Thus, the truss element area was constant overthe BRB length and equal to the area of the yielding BRB core region.All of the BRB truss elements were attached to elastic elementsrepresenting the gusset plates. BRB force–deformation responsewas validated against large-scale test data [8] as illustrated inFig. 3(a). Fig. 3(b) shows the good agreement in energy dissipationbetween the BRB model and the test data. Kinematic hardening issmall since post-yield stiffness of BRBs is minimal and isotropichardening dominates the cyclic response. The isotropic hardeningparameter for the compression region is larger than that of thetension region to account for the higher compression strengthtypically observed in BRBs due to core confinement.

80 C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89

Fig. 3. Calibrated OpenSEES BRB response: (a) force–deformation; (b) energy dissipation.

Table 2Prototype system natural periods.

Frame T1 (s)Connection typeMR NMR

BRBF7 0.93 0.94DS7 0.89 0.90

A detailed model of the SMRFs used in the dual systemswas also created, including the effects of panel zone yieldingand potential strength degradation at the reduced beam sections.The panel zones were modeled using four rigid links with twobilinear rotational springs placed in parallel at one corner toobtain trilinear behavior. The elastic and inelastic properties ofthe panel zones were based on the adjacent members usingestablished procedures [23]. Strength degradation at the reducedbeam sections was based on test data and associated modelingrecommendations for SMRFs [24] and was implemented usinga fiber section beam–column element with negative isotropichardening to simulate the loss of strength in the member thatoccurs due to inelastic cycling. As recommended, the strengthdegradation ratio, which represents the loss of the strength at eachplastic excursion, was defined as 0.83 [24].

A pinned-base leaning column was included in all models toaccount for the second-order effects due to the prototype buildinggravity loads. The leaning columnwas modeled using fiber sectionbeam–column elements with properties based on the sum of thecross-sectional properties of the gravity columns associated withthe BRBF. The leaning columnwas connected to the primary frameat the floor levels by rigid links and gravity loads and masses werelumped at the floor-level nodes of the leaning column. These valueswere based on the structural self-weight, superimposed dead load,curtain wall load, and 25% of the live load. Rayleigh damping wasused with a viscous damping ratio of 2% assumed in the first andsecond modes.

The BRB models incorporated in the prototype frames includea remaining capacity model that tracks the cyclic deformationhistories of the BRBs and allows for the possibility of core fracturebased on accumulated damage. The remaining capacity modelis a function of BRB core geometric and material propertiesalong with a running count of cumulative and maximum ductilitydemands [25]. The remaining capacity model tracks BRB demandsduring the analysis and when the model indicates zero remainingcapacity for a BRB, it is considered to have fractured andthe element is removed from the model. Although fractureof the BRB core is not expected at the DBE or MCE hazardlevels, implementation of the remaining capacity model plays animportant role for incremental dynamic analysis, which evaluates

global collapse when ground motions are scaled beyond the MCE.Other potential BRB failure modes, such as internal bearing underextreme compressive deformation or out-of-plane buckling in theconnection region, are not included in the model.

3.2. Ground motion records

The selection of ground motions from the PEER Centerstrong motion database [26] was based on three fundamentalparameters: site class, source distance, and magnitude. These arethe parameters that are known to have the strongest influence onground motion characteristics [27]. Although recent research [28]has demonstrated the influence of epsilon on nonlinear structuralresponse, it was not considered in this research. Ground motionsassociatedwith site classD, as defined in SEI/ASCE 7-05 [3], a sourcedistance greater than 15 km, and amomentmagnitude in the range5.0 ≤ MW ≤ 7.5 were chosen. Table 3 summarizes the 31 groundmotion records that were used in this research.

4. Nonlinear time-history analysis

Nonlinear time-history analysis was conducted to assess theperformance of BRBF and BRBF–SMRF systems when subjectedto ground motion records scaled to DBE and MCE seismic hazardlevels. Scale factors for the 31 selected ground motion recordswere calculated so that the elastic response spectra for the recordsmatched the target spectra (DBE or MCE), which were defined bySEI/ASCE 7-05 [3], at the first natural period, T1, of the structuralsystem. The DBE scale factors are shown in Table 3, and the MCEscale factors are 50% larger.

4.1. Single time-history response case study

The responses of BRBF7 and DS7, with both moment-resisting(MR) and non-moment-resisting (NMR) beam–column connec-tions, to the Loma Prieta-57382 Gilroy Array #4 (G04000) groundmotion record scaled to the DBE hazard level have been selectedto highlight the behavioral characteristics of each system. Whenscaled to the DBE hazard level, the peak ground accelerationfor this record is approximately 0.5g , and it produces demandsthat are near the median level for the analysis suite describedbelow.

Fig. 4 illustrates the roof drift response of BRBF7 and DS7.Considering the difference between the moment-resisting andnon-moment-resisting connection cases, it is observed that BRBF7with moment-resisting connections (BRBF7-MR) exhibits a 13%smaller maximum roof drift and a 70% smaller residual roof

C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89 81

Fig. 4. Roof drift time histories for BRBF7 and DS7 under ground motion G04000 scaled to the DBE.

Table 3Ground motion record summary.

# Earthquake Station Component Mw R (km) PGA (g) DBE scale factor

1 Livermore 57187 San Ramon - Eastman Kodak KOD180 5.4 17.6 0.301 3.292 Loma prieta 1028 hollister city hall HCH090 6.9 28.2 0.247 1.543 Loma prieta 1028 hollister city hall HCH180 6.9 28.2 0.215 1.484 Loma prieta 57382 Gilroy array #4 G04000 6.9 16.1 0.417 2.915 Loma prieta 57382 Gilroy array #4 G04090 6.9 16.1 0.212 2.656 Loma prieta 57425 Gilroy array #7 GMR000 6.9 24.2 0.226 7.417 Loma prieta 57425 Gilroy array #7 GMR090 6.9 24.2 0.323 9.168 Loma prieta 1601 palo altoc - SLAC Lab SLC360 6.9 36.3 0.278 2.549 Loma prieta 1695 Sunnyvale - Colton Ave. SVL270 6.9 28.8 0.207 3.93

10 Loma prieta 1695 Sunnyvale - Colton Ave. SVL360 6.9 28.8 0.209 3.1611 Morgan Hill 47380 Gilroy array #2 G02090 6.2 15.1 0.212 8.0212 Northridge 24303 LA - hollywood stor FF HOL090 6.7 25.5 0.231 4.9313 Northridge 24,303 LA - hollywood stor FF HOL360 6.7 25.5 0.358 1.8614 Northridge 90053 Canoga park - topanga can CNP106 6.7 15.8 0.356 1.8515 Northridge 90053 Canoga park - topanga can CNP196 6.7 15.8 0.42 1.7216 Northridge 90063 glendale - las palmas GLP177 6.7 25.4 0.357 10.3617 Northridge 90054 LA - Centinela St CEN155 6.7 30.9 0.465 5.3618 Northridge 90054 LA - Centinela St CEN245 6.7 30.9 0.322 2.7819 Northridge 90091 LA - Saturn St STN020 6.7 30 0.474 2.5620 Northridge 90091 LA - Saturn St STN110 6.7 30 0.439 1.9421 Northridge 90095 Pasadena - N Sierra Madre SMV180 6.7 39.2 0.245 7.4422 San fernando 135 LA - hollywood stor lot PEL090 6.6 21.2 0.21 3.9923 Superstition hills 5061 Calipatria fire station CAL315 6.7 28.3 0.247 6.9224 Whittier narrows 90,078 Compton - castlegate St CAS000 6.0 16.9 0.332 2.0925 Whittier narrows 90,078 Compton - castlegate St CAS270 6.0 16.9 0.333 4.6126 Whittier narrows 90,063 Glendale - las palmas WHN177 6.0 19 0.296 10.0627 Whittier narrows 90,084 Lakewood - del amo blvd DEL000 6.0 20.9 0.277 2.1028 Chi-Chi, Taiwan NST CHNSTE 7.6 36.95 0.309 6.3629 Chi-Chi, Taiwan NS CHNSTN 7.6 36.95 0.388 4.0730 Duzce Bolu BOL000 7.1 17.6 0.728 1.1331 Duzce Bolu BOL090 7.1 17.6 0.822 0.73

drift than BRBF7 with non-moment-resisting connections (BRBF7-NMR). As noted in Table 2, the fundamental periods of theseframes are within 3% of one another, thus it is clear that thechange in elastic stiffness between these cases is not significantand the dominant effect is the reserve strength provided by thecontinuous beams (i.e., the configuration with moment-resistingconnections). Just as BRBF7-MR experienced smaller drifts thanBRBF7-NMR, drift reduction is observed when comparing the DS7configurations with moment-resisting and non-moment-resistingconnections to their isolated BRBF counterparts. In these cases, thereserve strength provided by the parallel SMRFs is the dominantfactor leading to drift reduction. There is only a slight increase inelastic stiffness between the isolated BRBFs and the correspondingBRBF–SMRF dual systems. However, DS7-MR almost completelyeliminates residual drift while DS7-NMR reduces residual driftby over 70% when compared to BRBF7-NMR. The SMRFs arestill elastic at drifts that yield the BRBF, leading to a slightly

higher yield base shear and increasing the post-yield stiffnessof the system, which creates a restoring force that re-centers it.These characteristics are depicted in Fig. 5, which illustrates thedifferences in cyclic behavior between the two frames with non-moment-resisting connections in the BRBF. Relative to BRBF7-NMR, DS7-NMR is slightly stronger and stiffer in the inelastic rangewhile the elastic stiffness is essentially equivalent. It should alsobe noted that the SMRF in DS7-NMR provides an excellent meansof compensating for the lower inelastic stiffness and strengththat result when moment releases are introduced in the BRBFbeams near the beam–column connections. Fig. 6, which depictsthe residual displacement profiles of the four frames, shows thatthe SMRF is capable of reducing residual drift for BRBF7-NMRto levels close to that for BRBF7-MR and, more importantly,to levels significantly less than 0.005 rad, which is commonlyaccepted as the threshold belowwhich residual drift should not beproblematic.

82 C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89

Fig. 5. Base shear vs. roof drift for BRBF7-NMR andDS7-NMR under groundmotionG04000 scaled to the DBE.

Fig. 6. Residual displacement profiles under ground motion G04000 scaled to theDBE.

4.2. Ground motion suite performance evaluation

Performance evaluation of the isolated BRBF systems andBRBF–SMRF dual systems is presented below in terms of themedian and 84th percentile response values under the DBE andMCE seismic hazard levels. These summaries for response to thefull suite of selected ground motion records further illustrate thetrends discussed above for the single ground motion case study.

4.2.1. Story driftTable 4 provides a statistical summary of the story drift

response under the DBE and MCE for all prototype systemsconsidered in this research. Figs. 7–10 plot maximum and residualstory drift under the 31 ground motion records scaled to the DBE.These plots also illustrate the median and 84th percentile valuesfor maximum and residual drift.

4.2.1.1. Residual drift. As discussed above, limiting residual storydrift after a large earthquake is critical for returning buildings toservice quickly and economically so that the impact on affectedcommunities is minimized. In this research, residual story drift of0.005 rad was used as a practical threshold below which residualdrift is deemed to be tolerable. This threshold was primarilyconsidered for the DBE. As seen in Table 4, under the DBE onlyBRBF7-NMR had median residual story drift exceeding 0.005rad. Comparing BRBF7-MR to BRBF7-NMR, median residual storydrift under the DBE was reduced by more than 50% and 84thpercentile residual story drift for BRBF7-MR was only slightlyabove 0.005 rad. Thus, these results indicate that BRBFs with

non-moment-resisting connections are likely to develop excessiveresidual drift under DBE-level ground shaking, whereas BRBFswith moment-resisting connections are much less susceptible toproblematic residual drift. Despite this clear advantage associatedwith moment-resisting connections in BRBFs, the difference inmaximum story drift capacity between moment-resisting andnon-moment-resisting connection configurations must also beconsidered to obtain a complete view of system performance.

For the BRBF–SMRF dual systems, appreciable reduction inresidual story drift is seen in comparison to the isolated BRBFsystems. Under the DBE, DS7-MR reduces median response byalmost 50% when compared to BRBF7-MR and DS7-NMR reducesmedian response by almost 60% when compared to BRBF7-NMR.84th percentile residual story drift response under the DBE isbelow 0.005 rad for BRBF7-NMR and below 0.004 rad for BRBF7-MR. Although residual drift under the MCE will typically not be acritical consideration, it is noteworthy that median residual storydrift under theMCE is below0.005 rad forDS7-MRandonly slightlyabove 0.005 rad for DS7-NMR.

4.2.1.2. Maximum drift. In current seismic design provisions [3],inelastic story drift is typically limited to 0.02 rad, which is also thethreshold above which BRBFs with moment-resisting connectionshave exhibited undesirable failuremodes in the connection region.As such, it is the primary criterion used for evaluating maximumstory drift in this research. Of the four cases considered, medianmaximum story drift response under the DBE exceeded 0.02 radonly for BRBF7-NMR. Although large-scale tests indicate that BRBFswith non-moment-resisting connections can easily sustain storydrift much greater than 0.02 rad [8], this level of response doesnot satisfy the typical code-based design criterion. 84th percentilemaximum story drift response exceeded 0.02 rad for all fourconfigurations, which is most notable for the configurations withmoment-resisting connections within the BRBF since large-scaletests indicate that connections limit states may become critical inthis range of demand.

Under the MCE, median maximum story drift is above 0.02rad for all systems. 84th percentile maximum story drift responseunder the MCE shows that isolated BRBFs with non-moment-resisting connections can experience drift greater than 0.04 radand that BRBFswithmoment-resisting connections can experiencedrift greater than 0.03 rad. Thus, based on large-scale test data [9–11], some connection-related failures are expected under MCE-level demands for BRBFs with moment-resisting connections.

Maximum story drift response is affected by changes inconnection type (moment-resisting vs. non-moment-resisting)and system type (isolated BRBF vs. BRBF–SMRF dual system)but not to the same degree that residual story drift is. Whenmoment-resisting connections were used in the isolated BRBFsinstead of non-moment-resisting connections, maximum storydrift reduction was in the range of 15%–20%. When isolated BRBFsystems are compared to the corresponding BRBF–SMRF dualsystems, maximum story drift reduction ranges widely dependingon the connection type and systemconfiguration, but the reductioncan be near 30%.

The BRBF–SMRF dual systems lead to more uniform driftprofiles when compared to the isolated BRBFs but do not alleviateconcentrations in drift demand. Fig. 11 depicts the medianmaximum story drift profiles for the four system configurations. Inall cases, the first story is subject to the least demand. The influenceof higher mode effects is seen, particularly for the isolated BRBFconfigurations, and these effects are exacerbated by the increasedflexibility of the top story due to shear connections between theroof beam and the columns. The large demands in the top story aresignificantly reduced by the dual systems. Although the traditionaldual system configuration reduces drift concentration, the morenovel configuration proposed by Tremblay and Poncet [19] appearsto provide the best resistance to soft story formation in BRBFs.

C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89 83

Fig. 7. BRBF7-MR story drift summary (records scaled to DBE).

Fig. 8. DS7-MR story drift summary (records scaled to DBE).

Fig. 9. BRBF7-NMR story drift summary (records scaled to DBE).

84 C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89

Table 4Story drift response summary.

Frame Connection type Maximum drift (rad) Residual drift (rad)DBE MCE DBE MCEMedian 84th perc. Median 84th perc. Median 84th perc. Median 84th perc.

BRBF7 MR 0.019 0.024 0.025 0.034 0.0031 0.0054 0.0059 0.013DS7 0.016 0.020 0.023 0.029 0.0016 0.0034 0.0036 0.0081BRBF7 NMR 0.022 0.030 0.030 0.042 0.0066 0.011 0.0099 0.025DS7 0.017 0.022 0.025 0.034 0.0027 0.0049 0.0052 0.0096

Fig. 10. DS7-NMR story drift summary (records scaled to DBE).

Fig. 11. Median maximum story drift profiles (records scaled to DBE).

4.2.2. System overstrengthQuantification of system overstrength, which is defined as the

ratio of maximum base shear to design base shear, is criticalfor seismic design since this ratio is used to capacity protectkey elements in the system when employing the equivalent-lateral-force procedure. SEI/ASCE 7-05 [3] specifies the followingvalues for system overstrength factor, Ω0: 2 for isolated BRBFswith non-moment-resisting beam–column connections, 2.5 forisolated BRBFs withmoment-resisting beam–column connections,and 2.5 for BRBF–SMRF dual systems regardless of beam–columnconnection type in the BRBF. As discussed above, the elasticproperties of a BRBF–SMRF dual system vary little in comparisonto the corresponding isolated BRBF, but inelastic response isappreciably different. Similarly, changes in connection type havelittle impact on elastic properties but also affect inelastic response.

The current system overstrength factors attempt to capture thevariation in maximum lateral force capacity due to connectionvariation, but do not treat the impact of dual systems onoverstrength.

Table 5 provides a statistical summary of system overstrengthfor the suite of analyses. The broad conclusion is that thecurrent values for Ω0 underestimate the potential overstrength.For BRBF7-MR the median system overstrength under the DBEis almost 15% greater than the code-prescribed value for Ω0.For BRBF7-NMR the median system overstrength under the DBEis over 30% greater than the code-prescribed value for Ω0.For the dual systems, the median system overstrength underthe DBE is around 30% greater than the code-prescribed valuefor Ω0. Although Ω0 is used to represent overstrength at theDBE, it is instructive to note that median system overstrengthis greater than 3.0 under the MCE, with the largest value ofmedian system overstrength equal to 3.9 for DS7-MR. Whilethese results do not cover the full range of potential BRBF andBRBF–SMRF system configurations, it is apparent that the currentsystemoverstrength factors are inadequate. Since underestimationof system overstrength may lead to unconservative design ofcritical elements such as connections and collectors, a thoroughreevaluation of system overstrength factors for isolated BRBFs andBRBF–SMRF dual systems is needed.

Table 5 also shows base shear ratios for the SMRF portions ofthe dual systems, which are calculated as SMRF base shear dividedby the BRBF base shear. This ratio is between 25% and 30%, whichis consistent with the design approach that proportions the SMRFcomponent of a BRBF–SMRF dual system for 25% of the BRBF baseshear.

4.2.3. Deflection amplification factorThe equivalent-lateral-force design procedure in SEI/ASCE 7-

05 [3] requires that inelastic displacements of the structure be

C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89 85

Table 5Base shear response summary.

Frame Connection type System overstrength Base shear ratio for SMRFDBE MCE DBE MCEMedian 84th perc. Median 84th perc. Median 84th perc. Median 84th perc.

BRBF7 MR 2.85 3.21 3.34 3.86 – – – –DS7 3.35 3.80 3.91 4.55 26.5 29.4 28.2 28.8

BRBF7 NMR 2.73 3.09 3.24 3.80 – – – –DS7 3.24 3.70 3.81 4.45 27.2 30.5 29.3 29.3

Table 6Roof deflection response summary under the DBE.

Frame Connection type Roof deflection amplification ratioMedian 84th percentile

BRBF7 MR 7.1 10.6DS7 6.6 8.9BRBF7 NMR 7.5 10.5DS7 6.8 8.9

estimated through the amplification of elastic displacements,which are obtained through linear analysis. The linear elastic staticapproximation of nonlinear dynamic response at the design levelgreatly simplifies calculations, but proper calibration of the factorsthat estimate nonlinear dynamic response are critical to ensurethat the structure remains stable and that it adheres to appropriatestory drift limits.

SEI/ASCE 7-05 [3] specifies the following values for deflec-tion amplification factor, Cd: 5.5 for isolated BRBFs with non-moment-resisting beam–column connections, 5 for isolated BRBFswith moment-resisting beam–column connections, and 5 forBRBF–SMRF dual systems regardless of beam–column connectiontype in the BRBF. Table 6 lists a statistical summary of the roof de-flection amplification ratio, which is defined as the maximum roofdeflection divided by the roof deflection under the force profileused to check drift in the equivalent-lateral-force procedure, forall system configurations under the DBE. The broad conclusion isthat the current values for Cd underestimate lateral deflections forboth isolated BRBFs and BRBF–SMRF dual systems. For BRBF7-MRthe median roof deflection amplification ratio at the DBE is almost30% greater than the code-prescribed value for Cd. For BRBF7-NMRthe median roof deflection amplification ratio at the DBE is 50%greater than the code-prescribed value for Cd. For the dual systems,the median roof deflection amplification ratio at the DBE is around20% greater than the code-prescribed value for Cd.

As a result of underestimating inelastic lateral displacements,the brace strains will subsequently be underestimated. An accu-rate approximation of brace deformations is a key parameterwhenevaluating brace overstrength factors, which are typically deter-mined using backbone force–deformation relationships developedfrom brace qualification tests [4]. Underestimating brace strainmay lead to inadequate capacity design of the gusset connectionregions, whichmay be especially problematic considering the sen-sitivity of these connection regions [9–11]. In addition, underesti-mation of brace forces may lead to beams being undersized, whichmay allow premature yielding and decrease the seismic perfor-mance of the system [6]. Considering the criticality of estimatinginelastic displacements, the deflection amplification factor for bothisolated BRBFs and BRBF–SMRF dual systems should be reevalu-ated. The results of the present research are consistent with priorresearch [8] and the latest guidelines [29], which recommend thatCd should be set equal to R.

4.2.4. BRB demandsBRB force and deformation demands are important parameters

for capacity design and estimation of BRB fatigue life [25]. Tables 7

and 8 provide statistical summaries of BRB force and ductilitydemands, respectively. The force and deformation demand ratiosare defined as follows: ω, which is called the strain hardeningadjustment factor in the AISC Seismic Provisions [4], is the ratioof maximum brace tension force to brace yield force; β , whichis called the compression strength adjustment factor in the AISCSeismic Provisions [4], is the ratio of maximum brace compressionforce to maximum brace tension force; µmax, maximum ductilitydemand, is the ratio of maximum absolute brace deformationto brace yield deformation; µc , cumulative ductility demand, isthe ratio of brace cumulative plastic deformation to brace yielddeformation.

As shown in Table 7, the impact of reserve strength on BRBforce demands is small. Moment-resisting connections in the BRBFslightly reduce BRB force demands compared to configurationswith non-moment-resisting connections in the BRBF, and dualsystems exhibit slightly lower BRB force demands compared toisolated BRBFs. For either source of reserve strength, themaximumobserved reduction in BRB force demand is around 5%, which hasminimal impact on design.

As shown in Table 8, the impact of reserve strength on BRBdeformation demands is more appreciable than on force demands.Using moment-resisting connections instead of non-moment-resisting connections or a dual system instead of an isolated BRBFsystem can reduce BRB maximum ductility demand by close to30% in some cases. However, the reduction in cumulative ductilitydemand is not as significant. The dual system configuration canreduce cumulative ductility demand by close to 15%, but the useof moment-resisting connections only provides a reduction of lessthan 5%. AlthoughBRBsmust have aminimumcumulative ductilitycapacity based on qualification testing [4], cumulative ductilitydemand is not checked in the design process. The remainingcapacity of a BRB after a seismic event is largely dependent uponcumulative ductility demand [25] and it can be concluded that thedual systemmay slightly increase the service life of BRBs. However,due to the very large cumulative ductility capacity that is typical forBRBs, this effect is minimal.

5. Incremental dynamic analysis

To assess system behavior across a wider range of seismicdemands and to evaluate seismic performance against criticallimit states, incremental dynamic analysis (IDA) was employed.A procedure similar to that described by Vamvatsikos andCornell [30,31] was used to perform the analysis and summarizethe data. Each of the 31 natural ground motion records that wasused in the nonlinear time-history analysis described above wasalso used for the IDA. The results from the IDA are presented in thesubsequent discussion.

5.1. Limit state definition

The IDAprocedure produces curveswhere a structural responsedamage measure (DM) is plotted as a function of a ground motionintensity measure (IM). Limit states are then defined to evaluate

86 C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89

Table 7Buckling-restrained brace force response summary.

Frame Connection type ω βω

DBE MCE DBE MCEMedian 84th perc. Median 84th perc. Median 84th perc. Median 84th perc.

BRBF7 MR 1.20 1.23 1.25 1.32 1.30 1.36 1.38 1.47DS7 1.17 1.21 1.23 1.28 1.25 1.32 1.35 1.43

BRBF7 NMR 1.21 1.27 1.28 1.35 1.34 1.41 1.42 1.53DS7 1.18 1.22 1.25 1.31 1.27 1.35 1.38 1.47

Table 8Buckling-restrained brace ductility response summary.

Frame Connection type µmax µc

DBE MCE DBE MCEMedian 84th perc. Median 84th perc. Median 84th perc. Median 84th perc.

BRBF7 MR 9.4 11.6 11.8 15.8 258 422 336 532DS7 7.3 9.7 10.5 13.9 223 366 299 489

BRBF7 NMR 11.2 14.9 14.4 20.0 259 419 340 533DS7 8.1 10.8 12.0 16.2 228 374 308 500

selected performance levels. In this research, the following twoperformance levels were considered: collapse prevention (CP)and immediate occupancy (IO). The CP performance level wasevaluated using story drift response. Per FEMA 450 [32], CP isdefined by the following:

• A structure has sustained nearly complete damage.• The structure has lost most of its original lateral stiffness and

strength and little resistance to collapse remains.• The structure may have significant residual displacements.• Nonstructural elements are non-functional and may pose a

threat to occupants.• The structure is not safe for continued occupancy and repairs

are not likely to be practical.

In IDA, there are two indicators for incipient collapse that aredefined in FEMA350 [33]. The first indicator is taken to be the pointwhere the slope of the IDA curve is less than or equal to 20% ofthe elastic slope of the IDA curve. The elastic slope is defined asthe slope of the IDA curve at intensity levels that produce elasticresponse. As the slope of the curve decreases, a small increasein intensity produces a significant increase in demand and thestructure is judged to be at incipient collapse due to global dynamicinstability. The second indicator for incipient collapse is when thedrift of the structure exceeds 0.1 rad. This limit originates fromstudies of SMRFs [33], however, it is extended to BRBFs for thisresearch with the assumption that any structure, regardless oflateral system, experiencing story drift of 0.1 rad would sustainheavy damage that could lead to global instability.

Although no specific guidelines exist for establishing residualdrift limit states and relating them to performance levels, theapproach for evaluating collapse prevention usingmaximum storydrift as the DM [32] is adapted for evaluating residual story drift.The IO performance level was used as the pertinent limit statelinked to the residual story drift response. A residual story driftlevel of 0.005 rad is related to the IO performance level since it isanticipated that buildings meeting this limit could be returned toservice without major repairs.

5.2. Single record case study

The response of BRBF7 and DS7, with both moment-resistingand non-moment-resisting beam–column connections in the

BRBFs, to the Loma Prieta-1695 Sunnyvale-Colton Avenue(SVL360) ground motion has been selected to highlight the behav-ioral characteristics of each frame as its response progresses to-wards collapse.

Figs. 12–15 show the drift profiles of the BRBF7 and DS7 sys-tems, with moment-resisting and non-moment-resisting connec-tions, as the seismic intensity is scaled to multiples of the DBElevel. The drift profiles for BRBF7-MR and DS7-MR in Figs. 12 and13 show that although the drifts are reduced in the dual systemat the 1.0 × DBE and 1.5 × DBE (MCE) levels, the drift profilesalong the height of the building are of similar shape with the mid-dle stories exhibiting larger drifts than the first and upper stories.The distinction between the two systems becomes more apparentat twice the MCE level (3.0 × DBE) where a concentration of driftis observed in the lower stories for the isolated BRBF compared tothe dual system, in which drift is more uniform over the height ofthe system. Although themaximumdrifts for the isolated BRBF andthe dual system at 3.0 × DBE are quite similar, the concentrationof drift in BRBF7-MR indicates a greater likelihood of dynamic in-stability [19]. While it was noted above that the dual system doesnot appreciably change the resistance to drift concentration underthe DBE, IDA reveals that at intensities greater than the DBE, thedual system effectively maintains relatively uniform drift over theheight of the system such that no story has significantly larger driftthan any other.

Figs. 14 and 15 show that BRBF7-NMR and DS7-NMR exhibitbehavioral trends similar to their counterparts with moment-resisting connections in the BRBFs, but the drift magnitudesare larger owing to the lack of rotational restraint at the BRBFconnections. Comparison of BRBF7-MR and DS7-NMR indicatesthat the dual system configuration with non-moment-resistingconnections in the BRBF distributes demand over the height ofthe structure at large seismic intensity more effectively than theisolated BRBF configurationwithmoment-resisting connections inthe BRBF. The performance improvement obtained by combining aSMRF with a BRBF to create a dual system is slightly greater for theBRBF with non-moment-resisting connections.

5.3. Response summary to full ground motion suite

The IDA response of the prototype frames to the full suiteof selected ground motion records is discussed in the followingsection. Since there is large variability between the individual IDAcurves for a given structure, the results are presented usingmediancurves.

C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89 87

Table 9Incremental dynamic analysis summary.

Frame Connection type Reference, IM Collapse prevention Immediate occupancySDS (g) SMS (g) θCP (rad) Sa,CP (g) Sa,CP/SMS θIO (rad) Sa,IO (g) Sa,IO/SDS

BRBF7 MR 1.03 1.55 0.099 3.76 2.43 0.005 1.02 0.99DS7 1.03 1.55 0.098 4.44 2.86 0.005 1.50 1.46BRBF7 NMR 1.03 1.55 0.096 3.34 2.15 0.005 0.54 0.52DS7 1.03 1.55 0.099 4.20 2.71 0.005 1.24 1.20

Fig. 12. BRBF7-MR maximum story drift profiles for ground motion SVL360.

5.3.1. Maximum story driftFig. 16 shows the median maximum story drift IDA curves for

all four system configurations, and Table 9 lists the drift values,θCP , from these curves where incipient collapse is indicated by theprocedure described above. Consistent with the results presentedabove, BRBF7-NMR is the most susceptible to collapse as a resultof the lack of reserve strength after the yielding of the BRBs.As shown in Table 9, BRBF7-NMR reaches the CP performancelevel at the lowest input intensity (Sa,CP) and the CP marginat the MCE, Sa,CP/SMS is 2.2. However, when the isolated BRBFis combined with a SMRF to create DS7-NMR, the values forSa,CP increase by 26% and the CP margin is increased to 2.7.Figs. 16 and 17 and Table 9 show that the performance of thedual system with non-moment-resisting connections is similar tothe isolated BRBF with moment-resisting connections. The bestperformance is observed in thedual systemwithmoment-resistingconnections. However, it should be noted that at higher seismicintensities, which produce drifts in excess of 0.02 rad, systemswithmoment-resisting beam–column connections in the BRBFwilllikely experience localized failure modes while the non-moment-resisting beam–column connection will not [8–12]. Despite thereduction in collapse capacity from DS7-NMR to DS7-MR, DS7-NMR still provides a significant improvement over BRBF7-NMR.Considering that non-moment-resisting connections eliminate theundesirable localized failure modes observed in isolated BRBFswith moment-resisting connections, BRBFs with non-moment-resisting connections are best suited for use in a dual systemconfiguration.

5.3.2. Residual story driftAs mentioned previously, there are no explicit guidelines

specifying residual drift limit states, therefore the IO performancelevel, which as discussed above is bounded by a residual story driftof 0.005 rad, is evaluated with respect to the design level intensitymeasure, Sa,DBE . This approach provides insight into the potentialfor returning a building to service after a DBE-level seismic event.

Fig. 17 shows median IDA curves of residual story drift for allfour systems’ configurations. Table 9 shows that the dual systems

Fig. 13. DS7-MR maximum story drift profile for ground motion SVL360.

Fig. 14. BRBF7-NMR maximum story drift profile for ground motion SVL360.

Fig. 15. DS7-NMR maximum story drift profile for ground motion SVL360.

significantly improve IOperformance, asmeasured by the intensitymeasure, Sa,IO, at which the IO residual drift limit is reached.

88 C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89

Fig. 16. Median maximum story drift IDA curves and collapse points.

Fig. 17. Median residual drift IDA curves.

The increase in Sa,IO as a result of the dual system is nearly 50%when the BRBF hasmoment-resisting connections and nearly 130%when the BRBF has non-moment-resisting connections. BRBF7-NMR exhibits the worst performance, with IO margin, Sa,IO/SDS ,of 0.5, indicating that the IO performance level is not met formedian response under the DBE. However, when BRBF7-NMR iscombinedwith a SMRF to create DS7-NMR, the IOmargin increasesto 1.2. BRBF7-MR has an IO margin similar to DS7-NMR. DS7-MR has the best residual drift performance, with an IO margin of1.5. Although a BRBF–SMRF dual system with moment-resistingconnections in the BRBF offers the best performance at the DBElevel, it likely would exhibit less favorable performance at theMCE level due to connection-related failuremodes at themoment-resisting connections in the BRBF.

6. Conclusions

The nonlinear dynamic analysis results presented in this papershow that reserve strength has a significant impact on seismicbehavior and performance of BRBFs. This reserve strength canbe provided by moment-resisting connections within the BRBFand/or a SMRF in parallel with the BRBF to create a dual systemconfiguration. However, potential limitations of moment-resistingconnection within BRBFs must be recognized. Nonlinear time-history analysis and incremental dynamic analysis of prototypeisolated BRBFs and BRBF–SMRF dual systems provide the keyconclusions summarized below. It should be noted that theseconclusions are based on the study of a single prototype building,which is regular in plan and elevation. Further studies considering

a broader range of prototype buildings with realistic variationswould be valuable to expand the findings from the currentresearch.• BRBFs with non-moment-resisting beam–column connections

experience the largest maximum and residual story drifts.Under the DBE, median and 84th percentile residual storydrift can be greater than 0.005 rad and 0.01 rad, respectively.Thus, residual story drift for this system configuration isexpected to make post-earthquake repair difficult and costly.However, no connection-related failure modes are anticipatedsince the non-moment-resisting beam–column connectionscan accommodate very large drift.

• BRBFs with moment-resisting beam–column connections ex-perience reduced residual story drifts. Under the DBE, medianresidual story drift is less than 0.004 rad and 84th percentileresidual story drift is slightly greater than 0.005 rad. Thus, resid-ual story drift for this system configuration is not expected tobe problematic. However, since 84th percentilemaximumstorydrift under the DBE andmedianmaximum story drift under theMCEare greater than0.02 rad, connection-related failuremodesmay occur under the DBE and will likely occur under the MCE.

• The dual system configurations reduced residual story driftappreciably, with 84th percentile response under the DBEbelow 0.005 rad. The reduction due to the dual systemwas greatest when the BRBF had non-moment-resistingconnections, but the smallest drifts occurred when the BRBFhad moment-resisting connections.

• Dual systems with moment-resisting connections in the BRBFhave 84th percentile maximum story drift less than or equal to0.02 rad under the DBE, so no connection-related failure modesare expected. Under the MCE, 84th percentile maximum storydrift can be greater than 0.025 rad, so connection-related failuremodes may occur.

• Dual systems with non-moment-resisting connections in theBRBF are judged to be the most favorable configuration sinceresidual drift is controlled effectively, even under the MCEwithmedian residual drift at worst only slightly greater than 0.005rad, and connection-related failure modes are not expectedowing to the small flexural demands in the connection region.

• System overstrength for both isolated BRBFs and BRBF–SMRFdual systems is under-predicted by current code provisions. Theisolated BRBFs had median base shear overstrength under theDBE greater than 2.7 and 2.8 for non-moment-resisting andmoment-resisting beam–column connections, respectively.The dual systems had median base shear overstrength underthe DBE greater than 3.2 and 3.3 for non-moment-resistingand moment-resisting beam–column connections in the BRBF,respectively.

• Estimation of inelastic lateral displacements using thedeflection amplification factor multiplied by elastic lateral dis-placements, as specified in current codeprovisions, is unconser-vative. The deflection amplification factor should be set equal tothe response modification coefficient.

• When a BRBF with non-moment-resisting connections is usedas part of a dual system, the collapse prevention margin underthe MCE is increased by more than 25% in comparison to thecorresponding isolated BRBF case. When a BRBF with non-moment-resisting connections is used as part of a dual system,the immediate occupancy margin under the DBE is increasedbymore than 100% in comparison to the corresponding isolatedBRBF cases.

Acknowledgements

The authors recognize the advice of Walterio Lopez, AssociatePrincipal at Rutherford & Chekene, in developing prototype systemdesigns. This research was supported by an allocation through theTeraGrid Advanced Support Program. All opinions, findings, andconclusions expressed are those of the authors.

C. Ariyaratana, L.A. Fahnestock / Engineering Structures 33 (2011) 77–89 89

References

[1] Black CJ, Makris N, Aiken ID. Component testing, seismic evaluation andcharacterization of BRBs. J Struct Eng 2002;130(6):880–94.

[2] Merritt S, Uang CM, Benzoni G. Subassemblage testing of star seismicBRBs. Structural systems research project report No. TR-2003/04. San Diego:University of California; 2003.

[3] ASCE. Minimum design loads for buildings and other structures. ASCE/SEI 7-05; 2005.

[4] AISC. Seismic provisions for structural steel buildings. Chicago (IL): AISC; 2005.[5] Sabelli R. Recommended provisions for buckling-restrained braced frames.

AISC Eng J 2004;(4th quarter):155–75.[6] Sabelli R, Mahin S, Chang C. Seismic demands on steel braced frame buildings

with buckling-restrained braces. Eng Struct 2003;25:655–66.[7] Fahnestock LA, Sause R, Ricles JM. Seismic response and performance of

buckling-restrained braced frames. J Struct Eng 2007;133(9):1195–204.[8] Fahnestock LA, Sause R, Ricles JM. Experimental evaluation of a large-scale

buckling-restrained braced frame. J Struct Eng 2007;133(9):1205–14.[9] Uriz P, Mahin SA. Toward earthquake-resistant design of concentrically-

braced steel-frame structures. PEER report 2008/08. Berkeley: University ofCalifornia; 2008.

[10] Tsai KC, Hsiao BC, Lai JW, Chen CH, Lin ML, Weng YT. Pseudo-dynamic ex-perimental response of a full-scale CFT/BRB composite frame. In: Proceedings.joint NCREE/JRC workshop. 2003.

[11] Christopulos AS. Improved seismic performance of BRBFs. M.S. thesis. Seattle:University of Washington; 2005.

[12] Wigle VR, Fahnestock LA. Buckling-restrained braced frame connectionperformance. J Constr Steel Res 2010;66:65–74.

[13] Tremblay R, Stiemer SF. Back-up stiffness for improving the stability of multi-story braced frames under seismic loading. In: Proceedings, structural stabilityresearch council annual technical session. 1994.

[14] MacRae GA, Kimura Y, Roeder C. Effect of column stiffness on braced frameseismic behavior. J Struct Eng 2004;130(3):381–91.

[15] Ji X, Kato M, Wang T, Hitaka T, Nakashima M. Effect of gravity columns onmitigation of drift concentration for braced frames. J Constr Steel Res 2009;65:2148–56.

[16] Kiggins S, Uang CM. Reducing residual drift of buckling-restrained bracedframes as a dual-system. Eng Struct 2006;28:1525–32.

[17] Pettinga D, Christopoulos C, Pampanin S, Priestley N. Effectiveness of simpleapproaches inmitigating residual deformations in buildings. Earthq Eng StructDyn 2007;36:1763–83.

[18] Xie Q. Dual system design of steel frames incorporating buckling-restrainedbraces. In: Proceedings, fourth international conference on advances in steelstructures. 2005.

[19] Tremblay R, Poncet L. Improving the seismic stability of concentrically-bracedsteel frames, In: Proceedings, structural stability research council annualtechnical session. 2004.

[20] Lopez WA, Sabelli R. Seismic design of buckling-restrained braced frames,Structural steel educational council steel tips; 2004.

[21] Mazzoni S, McKenna F, Scott MH, Fenves GL. Open system for earth-quake engineering simulation (OpenSEES) user command-language manual(opensees.berkeley.edu). Berkeley: Pacific Earthquake Engineering ResearchCenter, University of California; 2009.

[22] Kaufmann EJ, Pense AW. Characterization of cyclic inelastic strain behavior onproperties of A572 Gr. 50 and A913 rolled sections. AISC-PITA project progressreport. Bethlehem (PA): ATLSS Research Center, Lehigh University; 1999.

[23] Federal Emergency Management Agency. State of the art report on systemsperformance of steel moment resisting frames subject to earthquake groundshaking. FEMA 355C; 2000.

[24] Federal Emergency Management Agency. State of the art report on perfor-mance prediction and evaluation of steel moment resisting frame buildings.FEMA 355F; 2000.

[25] Andrews BM, Fahnestock LA, Song J. Ductility capacity models for buckling-restrained braces. J Constr Steel Res 2009;65:1712–20.

[26] PEER strong motion database (peer.berkeley.edu/smcat). Berkeley: PacificEarthquake Engineering Research Center, University of California; 2000.

[27] Bozorgnia Y, Bertero VV. Earthquake engineering: from engineering seismol-ogy to performance-based engineering. CRC Press; 2004.

[28] Baker JW, Cornell CA. A vector-valued ground motion intensity measureconsisting of spectral acceleration and epsilon. Earthq Eng Struct Dyn 2005;34:1193–217.

[29] Federal Emergency Management Agency. Quantification of building seismicperformance factors, FEMA P695; 2009.

[30] Vamvatsikos D, Cornell CA. Incremental dynamic analysis. Earthq Eng StructDyn 2002;31:491–514.

[31] Vamvatsikos D, Cornell CA. Applied incremental dynamic analysis. EERISpectra 20 (2) 523–553.

[32] Federal EmergencyManagement Agency. NEHRP recommended provisions forseismic regulations for buildings and other structures. FEMA 450; 2003.

[33] Federal Emergency Management Agency. recommended seismic designcriteria for new steel moment-frame buildings. FEMA 350; 2000.