Ninth International Conference on Advances in Steel Structures (ICASS’2018)

5-7 December 2018 - Hong Kong, China

Proceedings of the ninth international conference on Advances in Steel Structures

Edited by Siu-Lai Chan, Tak-Ming Chan and Songye Zhu. Copyright © 2018 by The Hong Kong Institute of Steel Construction.

SEISMIC PERFORMANCE ASSESSMENT OF HYBRID SELF-CENTERING BUCKLING-RESTRAINED BRACED FRAME SYSTEMS

Ahmad Fayeq Ghowsi *, and Dipti Ranjan Sahoo

Department of Civil Engineering, Indian Institute of Technology Delhi, New Delhi-110016, India E-mails: faieq.ghowsi@gmail.com, drsahoo@civil.iitd.ac.in

Abstract: Buckling-restrained braces (BRBs) are preferred to the conventional steel braces as lateral force-resisting elements in civil structures because of their nearly-symmetric hysteretic response, high displacement ductility, and good energy dissipation potential. However, the main disadvantage of buckling-restrained braced frames (BRBFs) is the excessive residual drift in the post-earthquake scenario. Self-centering buckling-restrained braced frames (SC-BRBFs) have been developed for the better energy dissipation capacity along with the reduced residual drift response. This study is focused on the evaluation of seismic response of BRBFs, SC-BRBFs, and hybrid frames. through non-linear time-history analyses. The study frames, (i.e., 3-story, 9-story, and 20-story) are designed as per the US seismic code AISC 341-2014 provisions by considering the SC-BRBs as the combination of BRBs and shape-memory alloy (SMA) rods. The main parameters investigated in the numerical analyses are drift response, energy dissipation potential, and hinge mechanisms. The analysis results showed the better seismic performance for the hybrid systems as compared to BRBFs and SC-BRBFs.

Keywords: Buckling-restrained braces; Drift response; Numerical modelling; Seismic analysis; Self-centering braces

DOI: 10.18057/ICASS2018.P.126

1 INTRODUCTION

Buckling restrained braces (BRBs) capable of exhibiting the symmetrical hysteretic behavior, the higher energy dissipation, and the better displacement ductility are preferred in structural systems to the conventional steel braces. Past studies [ e.g., 1-2] have shown that the lack of re-centering capability of BRBs may result in the excessive post-earthquake residual displacement of the braced frame, which may not be cost-effective for repair and retrofitting [3–5]. In order to minimize this effect, some modifications may be carried out in the development of BRBs so as to develop self-centering BRB (SC-BRB) systems which can provide the re-centering capability to the buckling-restrained braced frames (BRBFs) [6]–[8].

The use of post-tensioned (PT) to provide the self-centering capability has been proved to effectively control the residual drift of systems [9–14]. A self-centering energy dissipative (SCED) brace using friction devices and a dual tube self-centering with aramid-fiber PT tendons has been recently developed [3,15]. A lightweight dual-tube SC-BRB having basalt fiber-reinforced polymer as pretension tendons material showed the flag-shaped hysteretic response under quasi-static loading indicating the better self-centering capability [16,17]. Pretension tendons have also used to achieve the rocking behavior of structural systems, thereby providing the self-centering capability. However, the energy dissipation devices are also

Ghowsi et al.

required in such a system to dissipate the input seismic energy [18]. Xie et al. [19] conducted a finite element analysis of dual tube SC-BRB with composite tendons using polymer pretension. Zhou et al. [20] carried out a numerical study to evaluate the design parameters of SC-BRB using a rheological model.

The present study is focused on the evaluation of seismic performance of 3-, 9-, and 20- story steel building frames in which BRBs, SC-BRBs, and hybrid braces (i.e., combination of BRBs and SC-BRBs) are used as lateral force-resisting systems. Shape memory alloy (SMA) rods are used along with steel BRB core elements are adopted to provide self-centering capability in SC-BRBs. These buildings frames are designed in accordance with current American building codes. The numerical models of these study frames are developed in a computer software OpenSees Ver.2.5 [21] and analyzed under near-fault earthquake ground motions. The main parameters investigated are the interstory and residual drift response of the study frames.

2 CONCEPTS OF SC-BRB

In this study, SC-BRBs utilizing the shape-memory alloy (SMA) for re-centering has been considered in this study. These braces have shown to possess the better self-centering capability with the higher energy dissipation, symmetrical hysteresis, and high ductility. SC-BRB consists of (a) BRB element for hysteretic energy dissipation and displacement ductility, and (b) SMA rod to provide self-centering capability to the brace. SMA rods are arranged parallel to the BRB core element. Rigid rods along the SMA rods are adopted to reduce the length of SMA elements. Outer and inner tubes are used to transfer SMA forces to BRB core elements and vice-versa. The main function of these tubes is to keep the SMA rods under tension either in shortened or elongated configuration BRB core segments. There would be no gap between movable plate and outer/inner tubes when the braces do not carry any axial loading. The gap would appear when the BRB core carries either compressive or tensile forces. The schematic representation of different components of SC-BRB is shown in Figure 1. Figure 2 shows the basic concepts of force-displacement response of SC-BRB under cyclic loading. The hysteretic response of SC-BRB is a combination of force-deformation response of BRB and the SMA rods. Nearly-symmetric hysteretic response of BRB added with the flag-shaped force-deformation response of SMA rods results the hysteresis response of SC-BRB as shown in figure.

(a)

(c)

(b)

Figure 1: SC-BRB assembly showing arrangements of SMA rods and cross-section

Ghowsi et al.

(BRB) (SMA rod) (SC-BRB)

Figure 2: Hysteretic response of BRB, SMA rod, and SC-BRB.

3 STUDY BUILDINGS

3-, 9-, and 20-story benchmark buildings, originally used in the SAC Phase-II Steel Projects have been considered in this study. These buildings represent the low, medium and high-rise buildings located in Los Angeles, California, USA. All braced bays are symmetrically located along the exterior perimeter of the building as shown in Figure 3. A total of four braced bays are placed along the longer direction, whereas only two braced bays are placed in the other direction in 3-story building and four braced bays are on both directions of 9- and 20-story building. All interior frames are considered as the gravity-load resisting frames. The braced frame of (BF-2) shown in the elevation view of the building in Figure 3. The frames in the shorter directions of all three buildings are considered as the study frames. All braces are assumed to be arranged in the inverted-V (chevron) configurations with pined connections at both ends. Beam-to-column connections are assumed to be non-moment-resisting types. The building frames are redesigned for three cases, namely, (a) all braces are BRBs, (b) all braces are SC-BRBs, and (c) combination of BRBs and SC-BRBs. Accordingly, the buildings frames are referred to as BRBF, SC-BRBF and Hybrid frame, respectively.

Table 1 provides the floor weights of these buildings. The study frames are designed in accordance with ASCE 7-16 [22] provisions. Seismic coefficient method has been adopted for the design of low and medium-rise (i.e., 3-story and 6-story) building frames. Response spectrum analysis has been considered for the design of 20-story frame. Response reduction factor (R), overstrength factor (0), and deflection amplification factor (Cd) are assumed as 8.0, 2.5, and 5.0, respectively, in the design of all study frames. These buildings are assumed to be located in Downtown, Los Angeles with site characterization of deep stiff soil (site class-D). The design spectral acceleration parameters, SDS and SD1 [22], are considered as 1.39 g and 0.77 g, respectively.

Table 1: Floor weights of the buildings.

Level 3-Story 9-Story 20-Story

First floor (kN) 9636.3 10140.2 5728.7

Intermediate floor (kN) 9636.3 9625.8 5610.0

Roof (kN) 10445.5 10434.1 5936.5

Total 29718.1 87955.1 112645.2

Ghowsi et al.

3-story

9-story

20-story

Figure 3: Building plan and elevation view of study frames

Braces in study frames are designed assuming that these braces carry the entire story shear without any contribution of beams and columns. The design axial strength of BRBs is considered as follows:

yBRBBRBu pp (1)

Where, the yield strength (PyBRB) of BRB core is the product of minimum specified tensile yield stress (Fysc) of BRB material and the net cross-sectional area (Asc) of core element and strength reduction factor () is considered as 0.9. For this example, an average value of Fysc is assumed as 289.6 MPa with a tolerance of MPa6.27/ . Thus, for the required steel core area for strength consideration, the lower bound MPaFysc 262 is used. The preliminary area

of BRB core element placed at an angle of inclination () for a given value of story shear (Vu) can be estimated as follows:

)cos(//

BracesnF

VA

ysc

usc (2)

Once the BRB core sections are finalized for BRBFs, the compression yield strength and

ultimate strengths of BRBs are computed considering the compression adjustment factor ()

Ghowsi et al.

and strain-hardening factor (). The values of and are assumed as 1.04 and 1.56, respectively. The expected ultimate axial strengths of BRBs are used to determine the section sizes of beams and columns based on capacity-design approach. The unbalanced brace strengths in tension and compression as well as gravity load effects are considered to determine the design flexural demand on beams. Plastic/compact sections are chosen as beams such that their flexural yield strengths are higher than the design demand. Columns are designed as axial members considering the brace expected strengths and the beam shear.

Since the same design parameters are assumed for SC-BRBF systems, the SC-BRBs are designed for the same design story shear. The design axial strength of SC-BRBs can be expressed as the sum of the design strengths of BRB core and SMA rods as follows:

SMASMAicoreyscBRBSCu AFAFp 9.09.0 (3)

Where, Fi-SMA = initial pre-stress in the SMA, Acore = area of BRB steel core in SC-BRB, ASMA = area of SMA rods. The initial pre-stress in the SMA should be able to overcome the BRB core yield stress. The following condition has to be met for the adjacent brace strengths based on ANSI/AISC 341-16 [23] seismic provisions:

SMASMAiscyscBRBadj AFAFp (4)

Since the material yield stress is assumed to be obtained from the coupon tests, the material overstrength factor (Ry) is omitted from the adjusted brace strength equations. The cross-sectional area of BRB in SC-BRB can be calculated using the following expression:

1ysc

uSC

F

PA (5)

Similarly, the area of SMA in SC-BRB can be found as follows:

SMAi

scysc

SMAF

AFA

(6)

The value of SMAiF in this study has been considered as 200 MPa based on the results of a past experimental study [8]. The beams and columns are designed based on capacity-design approach to remain elastic prior to brace yielding as discussed earlier.

4 NUMERICAL MODELLING

The study frames are modelled and analysed using a computer software OpenSees [21]. In this study, SC-BRB (as shown in Figure 1) originally developed and tested by Miller et al. [8] has been considered for the numerical modelling and prediction to hysteretic response. The developed numerical model is validated by comparing the cyclic response of each component (BRB core and SMA rods) as well as the whole brace. The numerical modelling of SC-BRB assembly is shown in Figure 4. Individual section and material has been selected for each element. BRB core plate is modelled as displacement beam-column element with fibre sections with high moment of inertia to preventing element from buckling. Hysteretic material in Opensees [21] library has been adopted to capture the hardening as well as the degradation behaviour of material. The modelling of force-displacement behaviour of SMA material adopted by Taftali [24] did not consider the residual strain effect. Later, the material model was

Ghowsi et al.

modified by Eatherton [18] in order to capture the reversed loading and residual strain effects. This modelling approach has been adopted in the present study. A forced-based beam-column element has been selected for the modelling of SMA rod. Since, there is no prefect material in OpenSees library to match with real experimental result, a new material (UMAT) has been developed for the SMA for better prediction of material behaviour [6] and implemented to the OpenSees library.

Figure 4: Numerical modelling of SC-BRB system

The developed numerical model of SC-BRB is validated by comparing the predicted hysteretic response of SMA rods and BRB core elements with the test results reported by Miller et al. [8]. Figure 5 shows the axial force-strain response of SMA rods and BRB core elements. Both loading and unloading force-strain response of both components matched well with the test results. Numerical model successfully captured the material hardening behavior as well as axial resistance and corresponding strain levels of BRB core element and the SMA rods. While the modelling technique of BRBs is directly adopted in the BRBF systems, both SC-BRB and BRB elements are assembled in SC-BRB using the outer and inner tubes. These tubes are modelled as elastic beam-column elements and are connected to the elastic end zones of BRBs through the rigid multi-point constrain links at one end only as shown in Figure 4. The elastic rigid rods are also modelled along the SMA rods. The gap elements are modelled as zero link element between the SMA rod and the outer and inner tubes. These gap elements are assigned with elastic compression and small but non-zero tension characteristics.

(a) (b)

Figure 5: Comparison of predicted hysteretic response of SC-BRB components with test results, (a) SMA rods, (b) BRB.

-3 -2 -1 0 1 2 30

100

200

300

400

500

600

SM

A F

orc

e (

kN)

Strain (%)

Experiment Opensees

Ghowsi et al.

Figure 6(a) shows the degradation behaviour in axial resistance of BRB core after reaching the maximum core strain considered in the modelling. The degrading behavior is also reflected in the back-bone curves of SC-BRB system at assembled configuration. Figure 6(b) shown the comparison of the predicted force-deformation response of SC-BRB system with the test results. As shown in figure, the predicted results matched well with the experimental findings. This numerical modelling technique for braces is then adopted in all the study frames.

(a) (b)

Figure 7: (a) Backbone curve of BRB and SC-BRB with degradation (b) Numerical validation of SC-BRB assembly.

Beams and columns of study frames are modelled as nonlinear beam-column fibre elements with lumped plastic hinges at both ends and distributed plastic hinges in the middle segments [25]. A total six integration points has been considered for these elements, in which two integration points at hinges portions and two integration points at middle portions of the beam-column element. Columns are assumed to be perfectly fixed at their bases. The P-delta effect of gravity loads is included in the analysis by modelling elastic gravity columns with pinned base and connecting them with braced frames using rigid link beams. An elastic beam-column element has been selected for the panel-zone of beam-to-column connections. The width of panel zone is varying according to the depth of columns and the depth the panel zone is depends on the beam depth. Figure 8 shows the modelling of panel zone with rigid offset link adopted in this study. For the hybrid frames, SC-BRBs are used at the first story of 3-story frame, first to fourth stories of 9-story frame, and first to tenth stories of 20-story frame. Braces in the remaining stories of these hybrid frames are considered as conventional BRBs.

Figure 8: Modelling of panel-zone in beam-column joints

-80 -60 -40 -20 0 20 40 60 80-1000

-800

-600

-400

-200

0

200

400

600

800

1000

Bra

ce

Forc

e (

kN

)

Brace Deformation (mm)

SC-BRB BRB

-60 -40 -20 0 20 40 60-1000

-800

-600

-400

-200

0

200

400

600

800

1000

Bra

ce F

orc

e (

kN

)Brace Deformation (mm)

Expriment Opensees

Ghowsi et al.

5 SELECTION OF GROUND MOTIONS

A set of forty near-fault (NF) ground motions has been selected for nonlinear dynamic analyses. The selected ground motions were developed by Somerville et al. [26] for SAC steel projects. These NF ground motions contain two different types records, i.e., the first ten ground motions (NF01-20) are derived from the historical recordings, and the remaining ten ground motions (NF21-40) are derived from the physical simulations of fault rupture and seismic wave propagation through soil strata. The individual components of each ground motion is rotated 45 degrees away from the fault-normal and fault-parallel orientations. These ground motions represent the earthquakes of magnitude in range of 6.75 to 7.5 with a source-to-site distance range of 0-18 km. The selected ground motions provide a reasonable representation in which the median magnitude of 7.0 at a distance about 5 km are reflected. This magnitude and distance controls in many regions of California, USA with probability of 10% in 50-year. The individual ground motion contains the pulse-like and long-period spectral accelerations. Figure 9 shows the comparison of mean response spectra of the NF ground motions with the design spectrum at the building locations.

Figure 9: Comparison of mean response spectrum of ground motions and the design spectrum

6 ANALYSIS RESULTS

Nonlinear time-history analyses are carried out in this study for all three building frames (3-story, 9-story, and 20-story) with three types of braces (BRB, SC-BRB, and Hybrid bracing system) under the selected the forty near-field ground motions. The main parameters investigated are inter-story drift and residual drift response. Inter-story drift ratio (ISDR) is computed as the ratio of maximum transient displacement between two consecutive floor levels during the earthquake to the height of the particular story. Residual drift ratio (RDR) is computed as ratio of the interstory displacement at the end of the earthquake to the particular story height. Both ISDR and RDR are considered as the critical performance objectives for the acceptable criteria in the seismic design of building structures. RDR represents the re-usability or reparability of structural systems in the post-earthquake conditions. One of the main objectives of this study is to compare the RDR response of the study frames with three considered bracing systems.

In this study, the average of peak ISDR and RDR response of the study frames has been considered for the comparison purpose. Figure 10 shows the variation of ISDR and RDR response over the height of the 3-story frames. Since the 3-story frames exhibited complete collapse under NF23 ground motion, the results for this record are excluded in the plots In Both

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Sp

ectr

al

Acc

eler

ati

on

(g)

T (sec)

NF Design

Ghowsi et al.

BRBF and SC-BRBF systems exhibited nearly similar ISDR response in case of 3-story frames. However, the hybrid bracing system showed the relatively higher ISDR response. The maximum value of ISDR response is noted as 2.5% for the hybrid system and nearly 2% for BRBF and SC-BRBF systems. As shown in Figure 10(b), SC-BRBF exhibited the negligible RDR response, whereas both BRBF and hybrid frame exhibited the peak RDR value of about 0.35% at the third story level. This showed that the hybrid bracing system is not very effective in the low-rise frames in which SC-BRBs significantly reduced the post-earthquake residual drift response.

1

2

3

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Inter-storey Drift (%)

Sto

ry L

evel

BRBF SC-BRBF Hybrid frame

1

2

3

0.0 0.2 0.4 0.6 0.8 1.0

Residual Drift (%)

Sto

ry L

evel

BRBF SC-BRBF Hybrid frame

(a) (b)

Figure 10: Comparison of (a) ISDR and (b) RDR response of 3-story study frames

Figure 11(a) represents the variation in the mean ISDR response over the height of 9-story frame. BRBF exhibited the relatively smaller ISDR response as compared to SC-BRBF and hybrid frame. However, the peak values of ISDR response of BRBF, SC-BRBF and hybrid frame are computed as 0.8%, 1.5%, and 1.2%, respectively. Thus, all systems exhibited the peak ISDR response less than the design value of 2%. Figure 11(b) shows the RDR response 9-story study frames. SC-BRBF exhibited very negligible residual drift response. The maximum value of RDR is noted for BRBF which is calculated as 0.36%. The maximum value of RDR noted for the hybrid frame is found to be 0.22%. As expected, there is sudden increase in the RDR at the 5th story 9-story hybrid frame where SC-BRBs are replaced by conventional BRBs. Further studies are required in terms of design and placement of SC-BRBs in order to keep the RDR and ISDR response within the acceptable range.

1

2

3

4

5

6

7

8

9

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Inter-storey Drift (%)

Sto

ry L

evel

BRBF SC-BRBF Hybrid frame

1

2

3

4

5

6

7

8

9

0.0 0.2 0.4 0.6 0.8 1.0

Residual Drift (%)

Sto

ry L

evel

BRBF SC-BRBF Hybrid frame

(a) (b)

Figure 11: Comparison of (a) ISDR and (b) RDR response of 9-story study frames

Ghowsi et al.

Figure 12 shows the ISDR and RDR response of 20-story frames with BRBs, SC-BRBs and hybrid braces. All study frames exhibited the nearly-similar ISDR response over the height. The peak values of ISDR of all frames are found to be about 1.2%, which is less than the design value of 2%. Further, the higher mode effects is more pronounced in the ISDR response as shown in Figure 12(a). It is worth-mentioning that the 20-story frame was designed based response spectrum analysis approach, instead of equivalent lateral load approach as followed for 3-story and 9-story frames, which consider the modal response. Figure 13(b) represents the RDR response of the 9-story study frames. SC-BRBF system exhibited the negligible residual drift at all story levels, whereas the BRBF showed the relatively higher residual drift as compared to other systems at all story levels. The hybrid frame showed the much reduced RDR response at the lower ten stories having SC-BRBs. The peak values of RDR at the top two stories of the hybrid frame are found to be nearly same as that of BRBF.

4

8

12

16

20

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Inter-storey Drift (%)

Sto

ry L

evel

BRBF SC-BRBF Hybrid frame

4

8

12

16

20

0.0 0.2 0.4 0.6 0.8 1.0

Residual Drift (%)

Sto

ry L

evel

BRBF SC-BRBF Hybrid frame

(a) (b)

Figure 12: Comparison of (a) ISDR and (b) RDR response of 20-story study frames

7 CONCLUSIONS

This study presents a comparative performance analysis of 3-story, 9-story and 20-story frames representing the low-, medium-, and high-rise buildings under seismic loading conditions. Three different types of braces, namely, BRBs, SC-BRBs, and combinations of these two braces, are adopted for each study frame. All study frames are numerically modelled and analysed under forty near-fault ground motions using a computer software OpenSees.

Analysis results concluded that all study frames exhibited the negligible residual drift response if SC-BRBs are used at story levels. BRBFs exhibited the higher residual drift for all study frames. The ISDR response of SC-BRBFs is found to be higher or similar to those of BRBFs. The combination of BRBs and SC-BRBs (i.e., hybrid braces) showed promising seismic performance of study frames, particularly for medium and high-rise frames. However, further studies are required to utilize the SC-BRBs and BRBs in an efficient way.

REFERENCES

[1] P. W. Clark, I. D. Aiken, K. Kasai, and I. Kimura, “Large-Scale Testing of Steel Unbonded Braces for Energy Dissipation,” in Advanced Technology in Structural Engineering, 2000, pp. 1–5.

[2] A. F. Ghowsi and D. R. Sahoo, “Fragility assessment of buckling-restrained braced frames under near-field earthquakes,” Steel Compos. Struct., vol. 19, no. 1, 2015.

Ghowsi et al.

[3] C. Christopoulos, R. Tremblay, H. Kim, and M. Lacerte, “Self-Centering Energy Dissipative Bracing System for the Seismic Resistance of Structures :,” no. January, pp. 96–107, 2008.

[4] M. Dolce and D. Cardone, “Theoretical and Experimental Studies for the Application of Shape Memory Alloys in Civil Engineering,” J. Eng. Mater. Technol., vol. 128, no. 3, p. 302, 2006.

[5] S. Chao, M. Asce, N. B. Karki, a M. Asce, and D. R. Sahoo, “Seismic Behavior of Steel Buildings with Hybrid Braced Frames,” J. Struct. Eng., vol. 139, no. 6, pp. 1019–1032, 2013.

[6] M. R. Eatherton, L. A. Fahnestock, and D. J. Miller, “Self-centering buckling restrained brace development and application for seismic response mitigation,” NCEE 2014 - 10th U.S. Natl. Conf. Earthq. Eng. Front. Earthq. Eng., 2014.

[7] D. A. Roke and M. R. Hasan, “The Effect of Frame Geometry on the Seismic Response of Self-Centering Concentrically- Braced Frames,” 2012.

[8] D. J. Miller, L. a. Fahnestock, and M. R. Eatherton, “Development and experimental validation of a nickel–titanium shape memory alloy self-centering buckling-restrained brace,” Eng. Struct., vol. 40, pp. 288–298, Jul. 2012.

[9] M. J. N. Priestley, S. (Sri) Sritharan, J. R. Conley, and S. Stefano Pampanin, “Preliminary Results and Conclusions From the PRESSS Five-Story Precast Concrete Test Building,” PCI J., 1999.

[10] J. M. Ricles, R. Sause, M. M. Garlock, and C. Zhao, “Posttensioned Seismic-Resistant Connections for Steel Frames,” J. Struct. Eng., vol. 127, no. 2, pp. 113–121, Feb. 2001.

[11] H. Choi, J. Erochko, C. Christopoulos, and R. Tremblay, “Comparison of the Seismic Response of Steel Buildings Incorporating Self-Centering Energy Dissipative Braces , Buckling Restrained Braced and Moment Resisting Frames,” Buildings, vol. 1, p. 236, 2008.

[12] C. Christopoulos, A. Filiatrault, C. Uang, and B. Folz, “Posttensioned Energy Dissipating Connections for Moment-Resisting Steel Frames,” J. Struct. Eng., vol. 128, no. 9, pp. 1111–1120, Sep. 2002.

[13] M. M. Garlock, J. M. Ricles, R. Sause, and M. Asce, “Experimental Studies of Full-Scale Posttensioned Steel Connections,” no. March, pp. 438–448, 2005.

[14] H. Kim and C. Christopoulos, “Friction Damped Posttensioned Self-Centering Steel Moment-Resisting Frames,” J. Struct. Eng., vol. 134, no. 11, pp. 1768–1779, Nov. 2008.

[15] J. Erochko, C. Christopoulos, and R. Tremblay, “Design and Testing of an Enhanced-Elongation Telescoping Self-Centering Energy-Dissipative Brace,” J. Struct. Eng., vol. 141, no. 6, p. 04014163, Jun. 2015.

[16] Z. Zhou, X. T. He, J. Wu, C. L. Wang, and S. P. Meng, “Development of a novel self-centering buckling-restrained brace with BFRP composite tendons,” Steel Compos. Struct., vol. 16, no. 5, pp. 491–506, May 2014.

[17] Z. Zhou, Q. Xie, X. C. Lei, X. T. He, and S. P. Meng, “Experimental Investigation of the Hysteretic Performance of Dual-Tube Self-Centering Buckling-Restrained Braces with Composite Tendons,” J. Compos. Constr., vol. 19, no. 6, p. 04015011, Dec. 2015.

[18] M. R. Eatherton, X. Ma, H. Krawinkler, D. Mar, S. Billington, J. F. Hajjar, and G. G. Deierlein, “Design Concepts for Controlled Rocking of Self-Centering Steel-Braced Frames,” J. Struct. Eng., vol. 140, no. 11, p. 04014082, Nov. 2014.

[19] Q. Xie, Z. Zhou, J. H. Huang, D. P. Zhu, and S. P. Meng, “Finite-Element Analysis of Dual-Tube Self-Centering Buckling-Restrained Braces with Composite Tendons,” J. Compos. Constr., vol. 21, no. 3, p. 04016112, Jun. 2017.

[20] Z. Zhou, Q. Xie, S. P. Meng, W. Y. Wang, and X. T. He, “Hysteretic Performance Analysis of Self-Centering Buckling Restrained Braces Using a Rheological Model,” J. Eng. Mech., vol. 142, no. 6, p. 04016032, Jun. 2016.

Ghowsi et al.

[21] S. Mazzoni, F. McKenna, M. H. Scott, and G. L. Fenves, “OpenSees command language manual.,” 2006.

[22] ASCE 7-16, Minimum Design Loads for Buildings and Other Structures. Reston, VA: American Society of Civil Engineers, 2016.

[23] ANSI/AISC 341‐16. Seismic Provisions for Structural Steel Buildings. Chicago, Illinois: American Institute of Steel Construction; 2016.

[24] B. Taftali, “Probabilistic seismic demand assessment of steel frames with shape memory alloy connections.No Title,” Georgia Institute of Technology, 2007.

[25] M. H. Scott and G. L. Fenves, “Plastic Hinge Integration Methods for Force-Based Beam–Column Elements,” J. Struct. Eng., vol. 132, no. 2, pp. 244–252, 2006.

[26] P. G. Somerville, N. F. Smith, R. W. Graves, and N. A. Abrahamson, “Modification of Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity,” Seismol. Res. Lett., vol. 68, no. 1, pp. 199–222, Jan. 1997.