Numerical comparison on the efficiency of conventional and hybrid bucklingrestrained braces for seismic protection of shorttomidrise steel buildings
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Abstract
Bucklingrestrained brace (BRB) is a specific kind of bracing system which has an acceptable energy dissipation behavior in a way that would not be buckled in compression forces. However, considerable residual deformations are noticed in strong ground motions as a result of the low postyield stiffness of the BRBs. The seismic performance of a modern lateral load resisting system, which is called the hybrid BRB, and its conventional counterpart are assessed and compared in this paper. Multiple plates with different stress–strain behavior are used in the core of this new innovative system, and this is its difference with the existent BRBs. Nonlinear static and incremental dynamic analyses are carried out for three building frames with different structural heights, which use conventional and hybrid BRB systems. To carry out response history analyses, the FEMA P695 farfield earthquake record set was adopted in different hazard levels. The hybrid BRBs are shown to have superior seismic performance in comparison with the conventional systems based on the response modification factor and the damage measures including residual displacements and interstory drift ratios.
Keywords
Seismic assessment Hybrid bucklingrestrained brace Performance factor Residual displacement Nonlinear analysisIntroduction
Steel concentric braced frame (CBF) is frequently applied as a lateral load resisting system, and it is highly effectual (López and Sabelli 2004). The lateral strength and the stiffness are boosted using the steel braces. This happens by inelastic deformation during earthquake ground motions, and an acceptable energy dissipation takes place (Kiggins and Uang 2006). When an earthquake happens, tension and compression loads influence the bracing members alternatively (Ariyaratana and Fahnestock 2011). Past researches indicate that the lateral response of CBFs is dependent on the inelastic behavior of these members (Broderick et al. 2008). Yielding and energy dissipation happen due to the postbuckling hysteresis behavior of braces and cyclic loading as well (Miller et al. 2012). Buckling of the braces causes limitation in the energy dissipation capacity in steel braced structures though (Tremblay et al. 2008).
The conventional bracing behavior, in nonlinear range of deformation, has several disadvantages: ductility is not acceptable, hysteresis curves are nonsymmetrical in tension and compression, strength is deteriorated, and stiffness is degraded due to buckling under cyclic loading. Therefore, modern CBF systems with stable hysteretic behaviors, considerable ductility, and excellent energy dissipation capacity are desirable, and researchers tried to advance CBF systems (Kumar et al. 2007). Bucklingrestrained brace (BRB) is a specific group of concentric bracing system, and it can be yielded under tension as well as compression (Sabelli et al. 2003). The BRB is made up of a steel core and a casing. The casing, which confines buckling of the core, is typically constructed of a mortar filled steel tube. The core and casing are isolated using a debounding material or a minimal air gap to ignore the transference of axial force to the casing (Bozorgnia and Bertero 2004). Unlike conventional CBFs, the BRB system has almost symmetrical behavior under tension and compression; therefore, energy dissipation capacity is much better, and unbalanced vertical forces are slight. Consequently, lighter beam sections are required compared to CBFs with V or invertedV bracing shapes (AISC 2010).
The most crucial problem of the ordinary bucklingrestrained braced frames (BRBFs) is the probable large residual deformations after severe earthquakes, and it has been described in the analytical and empirical study (Jarrett et al. 2015). Large residual lateral deformations in the last strong ground motions have shown that some structures did not face significant damage or partial collapse during the earthquake; nevertheless, they needed to be replaced by a new structure (Qiu and Zhu 2017). Sabelli et al. (2003) did numerical research on BRBF which demonstrated that the residual story drifts are approximately 40 to 60 percent of the highest drifts. Energy dissipation is acceptable in BRBFs, but the renovation cost could be high for a significant earthquake. This is because of the low postyield stiffness and not having a recentering mechanism. Reducing the residual deformations in BRBFs is the first purpose of improvements to BRBs. Having a higher performance standard than the life safety in structures is the other purpose that BRBs improvement focused on. Applying the backup moment frame system in a dualframe is another solution to alleviate the permanent deformation as well as to reach higher performance levels in the BRBFs (Kiggins and Uang 2006). They demonstrated that the residual drifts are lessened by more than 50% when a dual system is applied. Using the selfcentering energy dissipative bracing system is another way of removing the residual deformation of BRBFs (Miller et al. 2012; Tremblay et al. 2008; Kammula et al. 2014). Providing an elastic remaining element is the concept of this system. Obviously, the fuse element yields and consequently dissipates energy in this system. Increasing the cost of buildings is the main disadvantage of selfcentering systems. Hoveidae et al. (2015) studied a new type of BRB, in which a shorter core component was serially connected to a semirigid nonyielding member. They showed that the shortcore BRBs can considerably reduce the residual drifts of BRBFs. Dong et al. (2017) proposed an innovative selfcentering BRB system for mitigating the seismic response of bridge structures with double column piers. The research results indicated that the proposed system can reduce residual drifts and exhibited moderate energy dissipation capacity. A hybrid BRB (HBRB) is another innovative idea related to BRBs which uses a multicore BRB using various steel grades. Atlayan and Charney (2014) showed that the hybrid BRBF experiences significantly smaller residual drifts with the lowest modification to the regular BRBFs.
According to all the above findings, this research aims to gain an understanding of whether the use of the innovative hybrid BRBs can perform better than the conventional counterpart in steel buildings with various heights. The characteristics of the seismic sequences were examined considering performance factors, interstory drift ratio (IDR), and residual displacement. To do this, an extensive parametric study, with different approaches of analysis, is performed for assessing and comparing the seismic response of lowtomidrise conventional and hybrid steel BRBF buildings subjected to lateral static pushover loadings and earthquake ground motion records of different hazard levels. The numerical outcomes show that the new hybrid systems improve the seismic behavior of the conventional BRBFs, which is significantly important to the performancebased design of steel braced structures.
Building description
Material properties
A36  LYP100  HPS70W  HPS100W  

F_{y} (MPa)  290  107  503  745 
E (Gpa)  200  186  200  200 
Hybrid BRB combinations
Material  Conventional BRB  HBRB1  HBRB2  HBRB3  

Area ratios  A36 LYP100 HPS70 W HPS100 W  1.00 – – –  0.167 0.493 0.375 –  – 0.614 0.446 –  – 0.776 – 0.278 
Total stiffness (× A/L)  200,000  200,098  203,384  199,936  
Total strength (× A)  290.0  289.8  290.0  290.1 
Details of steel BRBF members
Story level  Brace area (cm^{2})  Beam section  Column section  

5Story model  Roof  –  W460 × 74  – 
5  19.4  W460 × 89  W360 × 110  
4  29.0  W530 × 109  W360 × 110  
3  38.7  W530 × 109  W360 × 110  
2  45.2  W530 × 123  W360 × 216  
Ground  51.6  –  W360 × 216  
8Story model  Roof  –  W530 × 123  – 
8  29  W530 × 123  W360 × 110  
7  29  W530 × 123  W360 × 110  
6  45.2  W530 × 123  W360 × 216  
5  45.2  W530 × 123  W360 × 216  
4  58.1  W530 × 123  W360 × 216  
3  58.1  W530 × 123  W360 × 347  
2  71  W530 × 123  W360 × 347  
Ground  71  –  W360 × 347  
12Story model  Roof  –  W530 × 123  – 
12  45.2  W530 × 123  W360 × 347  
11  45.2  W530 × 123  W360 × 347  
10  45.2  W530 × 123  W360 × 347  
9  45.2  W530 × 123  W360 × 347  
8  83.9  W530 × 123  W360 × 509  
7  83.9  W530 × 123  W360 × 509  
6  83.9  W530 × 123  W360 × 509  
5  83.9  W530 × 123  W360 × 509  
4  96.8  W530 × 123  W460 × 463  
3  96.8  W530 × 123  W460 × 463  
2  96.8  W530 × 123  W460 × 463  
Ground  96.8  –  W460 × 463 
The foundations and the superstructures have been commonly designed as two separated systems, and the superstructures were restricted at the bottom. As a result, the assessed seismic evaluation of the buildings only relies on the superstructures. This approach is useful and straightforward, but the flexibility of the foundation has to be considered; otherwise, the dynamic characteristics and seismic performance of structures may be considerably diverse from those of the real demands (Tahghighi and Rabiee 2017; Wolf 1985). Therefore, investigating the effect of foundation flexibility on the seismic behavior of steel braced frame structures is required as a further study.
Earthquake ground motions
The structural response can be different in a responsehistory analysis. Estimation of the structural seismic performance needs to be more precise. Therefore, the selection of earthquake ground motions is so important. By employing twentytwo farfield records suggested by the Applied Technology Council (FEMA P695 2009), the variety has been reduced and the randomness of the ground motions is kept in this paper. The FEMA P695 set has been applied for seismic performance assessment in many kinds of researches, for instance, ATC 76 (NIST 2010) and ATC 84 (NIST 2012). The considered set of ground motions is neither structure specific nor site specific and has ground motion records from the PEERNGA database (PEER 2015). The event moment magnitude is from 6.5 to 7.6. All motions have been recorded on medium soil site with the lowest distance to the fault rupture of more than 10 km except one with 7.1 km to the fault plane, having low to medium PGA from 0.21 g to 0.82 g, and the average value of 0.43 g.
Characteristics of considered FEMA P695 farfield earthquake records (PEER 2015)
No.  Earthquake  Year  Station  M _{ w}  d (km)  PGA_{max} (g) 

1  Northridge, USA  1994  Beverly HillsMulhol  6.7  17.2  0.52 
2  Northridge, USA  1994  Canyon CountryWLC  6.7  12.4  0.48 
3  Duzce, Turkey  1999  Bolu  7.1  12  0.82 
4  Hector Mine, USA  1999  Hector  7.1  11.7  0.34 
5  Imperial Valley, USA  1979  Delta  6.5  22  0.35 
6  Imperial Valley, USA  1979  El Centro Array #11  6.5  12.5  0.38 
7  Kobe, Japan  1995  NishiAkashi  6.9  7.1  0.51 
8  Kobe, Japan  1995  ShinOsaka  6.9  19.2  0.24 
9  Kocaeli, Turkey  1999  Duzce  7.5  15.4  0.36 
10  Kocaeli, Turkey  1999  Arcelik  7.5  13.5  0.22 
11  Landers, USA  1992  Yermo Fire Station  7.3  23.6  0.24 
12  Landers, USA  1992  Coolwater  7.3  19.7  0.42 
13  Loma Prieta, USA  1989  Capitola  6.9  15.2  0.53 
14  Loma Prieta, USA  1989  Gilroy Array#3  6.9  12.8  0.56 
15  Manjil, Iran  1990  Abbar  7.4  12.6  0.51 
16  Superstition Hills, USA  1987  El Centro Imp. Co.  6.5  18.2  0.36 
17  Superstition Hills, USA  1987  Poe Road (temp)  6.5  11.2  0.45 
18  Cape Mendocino, USA  1992  Rio Dell Overpass  7  14.3  0.55 
19  ChiChi, Taiwan  1999  CHY101  7.6  10  0.44 
20  ChiChi, Taiwan  1999  TCU045  7.6  26  0.51 
21  San Fernando, USA  1971  LAHollywood Stor  6.6  22.8  0.21 
22  Friuli, Italy  1976  Tolmezzo  6.5  15.8  0.35 
Numerical analysis
Nonlinear static analysis
Incremental dynamic analysis
The seismic behavior of structures needed to be assessed more precisely; therefore, an increasing analysis method called the incremental dynamic analysis (IDA) was promoted. IDA is a parametric analysis approach. A set of nonlinear analyses have to be constructed under multiple scaled earthquake records. The ground motion intensities are chosen in a way that can take the entire range from elasticity to global dynamic instability (Vamvatsikos and Cornell 2002).
Two fundamental quantities named Damage Measure (DM) and Intensity Measure (IM) are used for presenting IDA curves. DM is an observable quantity that is obtained from the outcomes of the nonlinear dynamic analysis. It is noteworthy that the suitable quantity for DM is chosen considering the type of problem or the intended structure. In this research, DM is described concerning residual roof displacement and maximum IDR which are known to connect well to structural damage during the seismic performancebased assessment of multistory buildings (Kiggins and Uang 2006; RuizGarcia and Miranda 2010; Atlayan 2013).
For the structural systems, the intensity measure (IM) is also defined using the relatively efficient 5% damped firstmode spectral acceleration, S_{a}(T_{1}, 5%) (In units of g). S_{a}(T_{1}, 5%) seems desirable to the structureindependent IM, i.e., PGA, producing lower dispersion in the IDA results (Vamvatsikos and Cornell 2005a, b). It is necessary to note that IDA can be significantly reliant on the selected record, so we need a suite of records to have acceptable precision in estimating seismic demands, S_{a}(T_{1}, 5%) (Shome and Cornell 1999). Accordingly, IDA was carried out by using the 22 progressively scaled records, listed in Table 4. Each selected acceleration record is scaled in from linear range (initial elastic) to nonlinear range with IM steps of 0.01 g for increasing the efficiency of the outcomes in incremental dynamic analyses. Therefore, the whole range of models’ behavior is covered from the elastic state until yield and collapse points. Finally, by inserting the taken pairs of S_{a}(T_{1}, 5%) and DM parameters, we get continuous IDA curves for each record, and the corresponding summarized median IDA curves for each conventional and hybrid multistory BRBF buildings.
Results and discussion
The purpose of this section is to investigate and compare the performance of hybrid and regular BRBF concerning seismic behavior factors, IDRs, and residual displacements. The OpenSees platform has been adopted to carry out nonlinear static pushover, nonlinear response history, and incremental dynamic analyses. The results of different cases are extracted, compared and discussed in the next sections.
Seismic performance factors
Response modification factor of hybrid BRBFs against conventional ones
Building model  V_{max} (kN)  V (kN)  δ_{u} (m)  δ_{y, eff} (m)  Ω  µ _{ T}  R _{ µ}  R 

HBRB3  
5 story  2293  1435  1.46  0.102  1.6  14.3  14.3  22.9 
8 story  2988  1992  1.46  0.207  1.5  7.1  7.1  10.6 
12 story  3960  2688  1.61  0.442  1.47  3.6  3.6  5.4 
HBRB2  
5 story  2273  1435  1.13  0.101  1.58  11.2  11.2  17.7 
8 story  2975  1977  1.24  0.207  1.5  6.0  6.0  9.0 
12 story  3949  2830  1.49  0.441  1.4  3.4  3.4  4.7 
HBRB1  
5 story  2269  1435  1.08  0.101  1.58  10.7  10.7  16.9 
8 story  2972  2014  1.21  0.206  1.48  5.9  5.9  8.7 
12 story  3947  2697  1.47  0.441  1.46  3.3  3.3  4.9 
Conventional BRB  
5 story  2265  1435  1.04  0.101  1.58  10.3  10.3  16.2 
8 story  2970  2003  1.18  0.206  1.48  5.7  5.7  8.5 
12 story  3944  2712  1.44  0.441  1.45  3.3  3.3  4.8 
In former studies, the seismic response modification factor for the conventional BRBFs has been suggested as 8.35 by Asgarian and Shokrgozar (2009). Another study revealed the value of R equal to 12.2 on average for BRBFs with various stories (Mahmoudi and Zaree 2010). Further, recent codecompliant seismic designs such as Standard No. 2800 (BHRC 2014); ASCE 7 (2010); and AISC (2010) recommend a constant value of response modification coefficient for conventional BRBF systems. According to these provisions, the R factor varies between 7 and 8. It is worth mentioning that the assessed response modification factors are various in this paper regarding both the brace type and the building height. Consequently, the BRB provisions included in seismic standards need to be modified and/or updated based on continuing research to be able to achieve a safer and more economic structural design.
Response history analysis results
Subsequent to the pushover analysis, the nonlinear dynamic response history analyses are performed applying the records in Table 4. They capture both geometrical (PΔ effects) and material nonlinearities. The transient analysis with the solution parameters of γ = 0.5 and β = 0.25 is carried out by applying the Newmark linear acceleration approach (Chopra 2012). The critical damping ratio is set to 2% at the first and third modes as it is commonly regarded in steel frame structures literature. The nonlinear equilibrium equations are solved by applying the modified Newton–Raphson algorithm with a convergence tolerance of 1.0E8 more than a maximum of 1000 repetitions. The stiffness matrixes are altered by limiting the restricted degrees of freedom in the transformation approach. This method is used in the analysis as a constraint handler. The size of the system for multipoint constraints is reduced employing this approach (OpenSees 2016).
Interstory drift ratio
The highest relative displacement between two consecutive stories divided by the height of that story is called the story drift ratio and is the most commonly used damage parameter. Applying hybrid frames improves the median performance regarding the highest IDR, and it is shown in Fig. 9. Based on the nonlinear dynamic response history analyses, the hybrid BRBs are not useful to reduce the IDR of 5 and 8story frames when compared to the conventional systems. However, as shown in Fig. 9, for the 12story models, the IDR is observed to be reduced by about 6% when the hybrid frames are subjected to the highest intensity motion (2% in 50 years).
Residual roof displacement
Residual displacement demand needs to be assessed for characterizing the technical and economical possibility of fixing and retrofitting the damaged structures after earthquakes (RuizGarcia and Miranda 2010). Furthermore, residual displacements might have a significant impact on earthquakeinduced economic losses since structures may be demolished due to extreme residual deformations even though they did not have moderatetosevere damage. Therefore, estimation of relevant seismic demands associated with residual displacements under various earthquake hazard levels is required in a contemporary performancebased seismic assessment procedure for the assessment of available structures.
The median performance advancement of hybrid BRBFs in comparison with the conventional frames regarding the residual roof displacement can be seen in Fig. 10. The residual roof displacement reduced as much as 20% for the 5 and 8story frames, by increasing the seismic intensities up to the collapse level. However, for 12story models, the residual displacement decreased as much as 17%, when the hybrid frame is considered. Hence, the advantage of hybridity is undeniable in residual roof displacement compared to IDR demand, and the most hybrid frame (the HBRB3 type) carried out the best.
IDA curves
To evaluate the seismic performance and the collapse capacity of each building model, IDA was implemented using the 22 gradually scaled records in Table 4 in the case of the conventional and the hybrid BRB conditions. IDA curves are obtained by interpolating the resulting DMIM discrete points in the IDA research. As explained before, IDA is strongly dependent on the record selected, so we have to resort to subjecting the structural model to an adequate number of seismic records. Such a study correspondingly produces sets of IDA curves which can be plotted on the same figure. Nonlinear response history analyses were performed from elasticity to building collapse level in small scaling increases to assess the behavior of the hybrid BRBFs versus conventional counterparts. Herein, some representative IDA curves are selected to study the general trend of seismic demands.
Figure 14a–c illustrates the comparison of the median IDA curves of the hybrid and conventional BRBFs regarding the residual roof displacement. It can be observed that hybrid frames carried out better than the other one at all intensities up to the collapse level, and the most hybrid frame which has the highest percentage of LYP100 performed the best. As shown in Fig. 14, for each constant value of intensity measure, the residual roof displacement rises with the number of stories. In other words, plastic hinges are developed at low ground motion intensities as the structural height increases.
Conclusions

Response modification factor for HBRB3, HBRB2, HBRB1, and conventional BRB models was suggested as 12.9, 10.5, 10.2 and 9.8 on average, respectively. It is noted that the R factor showed a significant decrease in frames as the number of stories increase. The increase in the R value of the hybrid BRBFs indicates the system performance enhancement and consequently will result in a more economical structural design.

Results show that hybrid frames yield sooner than typical frames. The early yielding and the delay in negative postyield stiffness drift ratio are becoming clear as the frames become more hybrid (from HBRB1 to HBRB3).

The median residual roof displacements reduced as much as 20% for hybrid BRBFs, which is a promising outcome in terms of overall seismic performance. Thus, repairing the buildings applying hybrid BRBFs is cheaper as a result of lower residual displacements.

The seismic performance of the lowrise hybrid BRBFs did not change substantially with respect to the maximum IDR. However, for the midrise frame (i.e., 12story models), the median drift ratio decreased by up to 6% when hybridity was considered.

According to the IDA curves, the HBRBs were observed to have considerable improvement over conventional systems regarding the studied damage measures as the ground motion intensities and the number of stories in the models increased. In other words, the use of HBRBs is more beneficial to the performance of tall buildings sitting in highseismicity sites where PΔ effects are more critical.
As mentioned, the results outlined in this paper will be helpful to quantify the beneficial effects of hybrid BRBs on the structural response so that the obtained information can provide guidance for developing the current seismic design codes. Yet, this study requires to be validated for further structures with a broader range of natural periods, various bracing configurations, an alternative combination of LYP and HPS materials, and the nearfield ground motions. The performance of this ductile lateral resistance system can be developed through more researches.
Notes
Acknowledgements
The authors would like to thank the anonymous reviewers for their constructive comments which helped to improve the manuscript.
References
 AISC (2010) Seismic provisions for structural steel buildings. ANSI/AISC 34110, American Institute of Steel Construction, ChicagoGoogle Scholar
 Alborzi Verki M, Tahghighi H (2019) Evaluation of seismic behavior of steel frames constrained with hybrid core bucklingrestrained braces. Amirkabir J Civ Eng. https://doi.org/10.22060/CEEJ.2018.13837.5486 in press (in Persian) CrossRefGoogle Scholar
 Ariyaratana C, Fahnestock LA (2011) Evaluation of bucklingrestrained brace frame seismic performance considering reserve strength. Eng Struct 33:77–89CrossRefGoogle Scholar
 ASCE 7 (2010) Minimum design loads for buildings and other structures. ASCE/SEI 710, American Society of Civil Engineers/Structural Engineering Institute, RestonGoogle Scholar
 Asgarian B, Shokrgozar H (2009) BRBF response modification factor. J Constr Steel Res 65(2):290–298CrossRefGoogle Scholar
 ATC 306 (1978) Tentative provisions for the development of seismic regulations for buildings. Applied Technology Council, Redwood CityGoogle Scholar
 Atlayan O (2013) Hybrid steel frames. PhD thesis, Virginia Polytechnic Institute and State University, USAGoogle Scholar
 Atlayan O, Charney FA (2014) Hybrid bucklingrestrained braced frames. J Constr Steel Res 96:95–105CrossRefGoogle Scholar
 BHRC (2014) Iranian code of practice for seismic resistant design of buildings (Standard No. 2800). Building and Housing Research Center, TehranGoogle Scholar
 Bozorgnia Y, Bertero VV (2004) Earthquake engineering: form engineering seismology to performance based design. CRC Press LLC, Boca RatonCrossRefGoogle Scholar
 Broderick BM, Elghazouli AY, Goggins J (2008) Earthquake testing and response analysis of concentricallybraced subframes. J Constr Steel Res 64(9):997–1007CrossRefGoogle Scholar
 Bruneau M, Uang CM, Sabelli R (2011) Ductile design of steel structures, 2nd edn. McGrawHill Professional, NYGoogle Scholar
 Chen CC, Chen SY, Liaw JJ (2001) Application of low yield strength steel on controlled plastification ductile concentrically braced frame. Can J Civ Eng 28(5):823–836CrossRefGoogle Scholar
 Chopra AK (2012) Dynamics of structures: theory and applications to earthquake engineering, 4th edn. Prentice Hall, NJGoogle Scholar
 Dong H, Du X, Han Q, Hao H, Bi K, Wang X (2017) Performance of an innovative selfcentering buckling restrained brace for mitigating seismic responses of bridge structures with doublecolumn piers. Eng Struct 148:47–62CrossRefGoogle Scholar
 FEMA 356 (2000) Prestandard and commentary for seismic rehabilitation of buildings. Prepared by the Applied Technology Council for the Federal Emergency Management Agency, Washington DCGoogle Scholar
 FEMA P695 (2009) Quantification of building seismic performance factors. Prepared by Applied Technology Council for the Federal Emergency Management Agency, Washington DCGoogle Scholar
 Günther HP, Raoul J (2005) Use and application of highperformance steels for steel structures. International Association for Bridge and Structural Engineering, ZürichGoogle Scholar
 Hoveidae N, Tremblay R, Rafezy B, Davaran A (2015) Numerical investigation of seismic behaviour of shortcore allsteel buckling restrained braces. J Constr Steel Res 114:89–99CrossRefGoogle Scholar
 Jarrett JA, Judd JP, Charney FA (2015) Comparative evaluation of innovative and traditional seismicresisting systems using the FEMA P58 procedure. J Constr Steel Res 105:107–118CrossRefGoogle Scholar
 Kammula V, Erochko J, Kwon OS, Christopoulos C (2014) Application of hybridsimulation to fragility assessment of the telescoping selfcentering energy dissipative bracing system. Earthquake Eng Struct Dynam 43(6):811–830CrossRefGoogle Scholar
 Kiggins S, Uang CM (2006) Reducing residual drift of bucklingrestrained braced frames as a dual system. Eng Struct 28(11):1525–1532CrossRefGoogle Scholar
 Kumar GR, Kumar SRS, Kalyanaraman V (2007) Behaviour of frames with nonbuckling bracings under earthquake loading. J Constr Steel Res 63(2):254–262CrossRefGoogle Scholar
 López WA, Sabelli R (2004) Seismic design of bucklingrestrained braced frames. Steel Tips, Structural Steel Educational Council (www.steeltips.org)
 Mahmoudi M, Zaree M (2010) Evaluating response modification factors of concentrically braced steel frames. J Constr Steel Res 66:1196–1204CrossRefGoogle Scholar
 MHUD (2013a) Iranian national building code for structural loadings (part 6). Ministry of Housing and Urban Development, TehranGoogle Scholar
 MHUD (2013b) Iranian national building code for steel structure design (part 10). Ministry of Housing and Urban Development, TehranGoogle Scholar
 Miller DJ, Fahnestock LA, Eatherton MR (2012) Development and experimental validation of a nickel–titanium shape memory alloy selfcentering bucklingrestrained brace. Eng Struct 40:288–298CrossRefGoogle Scholar
 Nakashima M, Iwai S, Iwata M, Takeuchi T, Konomi S, Akazawa T, Saburi K (1994) Energy dissipation behaviour of shear panels made of low yield steel. Earthquake Eng Struct Dynam 23(12):1299–1313CrossRefGoogle Scholar
 Newmark NM, Hall WJ (1982) Earthquake spectra and design. EERI Monograph Series EERI, OaklandGoogle Scholar
 Nippon Steel (2009) Steel plates. Nippon Steel Corporation, ChiyodaGoogle Scholar
 NIST (2010) Evaluation of the FEMA methodology for quantification of building seismic performance factors (NIST GCR 109178). Prepared by the NEHRP Consultants Joint Venture for the National Institute of Standards and Technology, MarylandGoogle Scholar
 NIST (2012) Tentative framework for development of advanced seismic design criteria for new buildings (NIST GCR 1291720). Prepared by the NEHRP Consultants Joint Venture for the National Institute of Standards and Technology, MarylandGoogle Scholar
 OpenSees (2016) Open system for earthquake engineering simulation. Pacific Earthquake Engineering Research Center, University of California, BerkeleyGoogle Scholar
 PEER (2015) Strong motion database, http://peer.berkeley.edu, Pacific Earthquake Engineering Research Center, University of California, Berkeley
 Qiu CX, Zhu S (2017) Performancebased seismic design of selfcentering steel frames with SMAbased braces. Eng Struct 130:67–82CrossRefGoogle Scholar
 RuizGarcia J, Miranda E (2010) Probabilistic estimation of residual drift demands for seismic assessment of multistory framed buildings. Eng Struct 32:11–20CrossRefGoogle Scholar
 Sabelli R, Mahin S, Chang C (2003) Seismic demands on steel braced frame buildings with bucklingrestrained braces. Eng Struct 25(5):655–666CrossRefGoogle Scholar
 Saeki E, Sugisawa M, Yamaguchi T, Wada A (1998) Mechanical properties of low yield point steels. J Mat Civ Eng 10(3):143–152CrossRefGoogle Scholar
 Shome N, Cornell CA (1999) Probabilistic seismic demand analysis of nonlinear structures. RMS Report35: Department of Civil Engineering, Stanford University, StanfordGoogle Scholar
 Sugisawa M, Nakamura H, Ichikawa Y, Hokari M, Saeki E, Hirabayashi R, Ueki M (1995) Development of earthquakeresistant, vibration control, and base isolation technology for building structures. Nippon Steel Tech Rep 66:37–46Google Scholar
 Systani A, Asgarian B, Jalaeefar A (2016) Incremental dynamic analysis of concentrically braced frames (CBFs) under near field ground motions. Modares Civ Eng J 2:135–145 (in Persian) Google Scholar
 Tahghighi H (2012) Simulation of strong ground motion using the stochastic method: application and validation for nearfault region. J Earthquake Eng 16:1230–1247CrossRefGoogle Scholar
 Tahghighi H, Rabiee M (2017) Influence of foundation flexibility on the seismic response of low tomidrise moment resisting frame buildings. Scientia Iranica 24(3):979–992CrossRefGoogle Scholar
 Tremblay R, Lacerte M, Christopoulos C (2008) Seismic response of multistory buildings with selfcentering energy dissipative steel braces. J Struct Eng 134(1):108–120CrossRefGoogle Scholar
 Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthquake Eng Struct Dynam 31(3):491–514CrossRefGoogle Scholar
 Vamvatsikos D, Cornell CA (2005a) Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information. Earthquake Eng Struct Dynam 34:1573–1600CrossRefGoogle Scholar
 Vamvatsikos D, Cornell CA (2005) Seismic performance, capacity and rellability of structures as seen through incremental dynamic analysis. Department of Civil and Environmental Engineering, Stanford University, Report No.151Google Scholar
 Vamvatsikos D, Fragiadakis M (2009) Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty. Earthquake Eng Struct Dynam 39(2):141–163Google Scholar
 Wolf JP (1985) Dynamic soilstructure interaction. PrenticeHall, New JerseyGoogle Scholar
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