Self-centering cable brace with friction devices for enhancing seismic performance of RC frame structures

Engineering Structures 207 (2020) 110187

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Self-centering cable brace with friction devices for enhancing seismic performance of RC frame structures

T

⁎

Tong Guo , Jishuai Wang, Yongsheng Song, Weihong Xuan, Yuzhi Chen Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 210096, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Self-centering Cable brace Friction Seismic performance Strengthening

A novel self-centering cable brace (SCCB) with friction devices is developed to improve the seismic performance of existing RC frame structures. This paper presents the structural configuration and the theoretical load-displacement relationship of the SCCB. Cyclic loading tests are conducted to show the effectiveness of the SCCB, and a numerical model is established and validated based on the test results. A parametric analysis is made to investigate the influence of tendon stiffness and friction on hysteretic performance of the SCCB. Nonlinear dynamic analyses are further carried out on a nine-story RC frame, which is seismically deficient and enhanced with buckling restrained braces (BRBs) and SCCBs respectively for comparison. Inter-story and residual interstory drifts, base shear forces, load-axial elongation relationships and self-centering indexes of the bare and strengthened frames are obtained and compared. It is found that both the SCCBs and BRBs increase the seismic capacity, while the SCCBs can reduce the maximum story drifts more significantly and have much less residual story drifts than BRBs.

1. Introduction

braces have been investigated due to the ease of installation in existing buildings and the supplementary stiffness, which include the self-centering buckling restrained brace [13–16], the self-centering steel brace with pre-pressed disc springs [17–19], the shape memory alloy (SMA)based brace [20–23] and the seesaw system [24,25], etc. For self-centering buckling restrained braces, most of them use pre-stressed steel strands and FRP bars for self-centering, accordingly there may have shortcomings of insufficient elastic deformation capability and inevitable pre-stress loss owing to the high-level pre-stress and slippage of the anchorage system [26–28]; furthermore, in order to prevent compressive buckling and provide self-centering and energy dissipating capacity simultaneously, most of these SC braces have complex configuration, which undermines their potential for industrial application. For the seesaw system, the forces are transferred through two dampers and the pin support to the mid-span of the underneath beam, thus the beam needs to be strengthened. Besides, since no prestress is used, the self-centering capacity of the seesaw system is limited. For other tension-only SC braces [29–31], they adopt SMA rods or flexible steel strands instead of rigid braces; therefore, they have to be placed in two crossed directions. Besides, the SMA materials are usually costly and temperature sensitive [32]. Considering the above shortcomings of the existing SC systems, a novel self-centering cable brace (SCCB) with friction devices is

Strong ground motion in earthquakes has long been a primary cause of death and property loss, and society in seismic zones is responsible for evaluating vulnerability of their building stock. When evaluated as seismically deficient, the structures are in need of strengthening so as to mitigate the damage risk. For reinforced concrete (RC) frames, traditional seismic strengthening methods include the use of steel plates and angles [1], fiber reinforced polymer (FRP) composites [2,3], infilled RC walls [4], eccentrically braced frames with vertical fuse [5], steelconcrete shear walls [6,7], various dampers including fluid viscous dampers [8] and buckling-restrained braces (BRBs) [9–11], etc. However, though the maximum story drifts could be mitigated, excessive residual deformations after damaging earthquakes may still exist, resulting in enormous repair costs and down-time loss. For example, previous investigations showed that, when the residual inter-story drift exceeds 0.5%, the repair or retrofit may result in more costs than reconstruction [12]. In order to mitigate the residual seismic deformations, a number of self-centering (SC) systems have been developed in recent decades, which usually provide the re-centering capacity through prestressing elements and dissipate the seismic energy through various dampers. Among these SC systems, the self-centering energy dissipation (ED)

⁎

Corresponding author. E-mail address: [email protected] (T. Guo).

https://doi.org/10.1016/j.engstruct.2020.110187 Received 18 August 2019; Received in revised form 7 January 2020; Accepted 7 January 2020 0141-0296/ © 2020 Published by Elsevier Ltd.

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Fig. 1. Structural configuration of the SCCB.

that with high prestress. Besides, since the tendon is flexible, it does not introduce additional initial stiffness, which is beneficial to reducing seismic response. In addition, the disc springs are pre-compressed in factory, so that the field installation of the SCCB is easy, as compared with those self-centering devices which require field jacking. The outline of the paper is as follows. First, the structural configuration and theoretical load-displacement relationship of the SCCB are presented. Hysteretic load test results are presented to show the effectiveness of the SCCB, and a numerical model is established and validated based on test results. Thereafter, a parametric analysis is made to investigate the influence of tendon stiffness and friction on hysteretic performance of the SCCB. Nonlinear dynamic analyses are carried out on a seismically deficient 9-story RC frame, which is enhanced by using BRBs and SCCBs for comparison purposes, respectively.

Fig. 2. Theoretical load-displacement relationship of SCCB.

proposed. Compared with theses SC braces, the proposed brace only functions in one direction and does not buckle. Therefore, the configuration of the SCCB is simpler. The tendon of SCCB is only pre-tightened for installation and does not have high pretension stress (i.e. the self-centering capacity is mainly provided by the disc springs); therefore, the long-term stress relaxation in tendon becomes smaller than

2. Structural configuration and theoretical model 2.1. Structural configuration The proposed SCCB is assembled of three parts, i.e. the self2

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Fig. 3. Mechanical behavior of SCCB in various stages.

is realized. The friction force can be altered through changing the prestressed force of high-strength bolts. As compared with previous SC braces, the SCCB has the advantages of being light weight, buckling free, easy for installation, and having stable self-centering and energy dissipation capacity. Besides, since no pre-stressing is applied on the tendon of the SCCB, the elastic deformation capability of the SCCB is higher than the pre-stressed steel strands, and the loss in pre-tension force becomes smaller.

centering energy dissipation (SCED) unit, the cable unit and the end connectors, as shown in Fig. 1(a). The self-centering energy dissipation unit, as shown in Fig. 1(b) and (c), includes a series of disc springs, high-strength bolts, two slotted steel plates, two friction plates attached on the C steel, a screw with nut and a steel pipe with internal and external threads. The cable unit includes two tendon connectors (being externally and internally threaded, respectively) and a high-strength tendon with two extruding anchors, as shown in Fig. 1(d). Two end connectors are used to connect the SCCB to the building. As shown in Fig. 1(b), the pre-compression on disc springs is applied through the threaded steel pipe, screw and the nut, so as to provide the self-centering capacity, which can be adjusted through screw, the nut and the threaded steel pipe. The C steel with friction plates can move synchronously with the disc springs, and sliding of friction plates along the slotted holes occurs as friction is exceeded; thus, energy dissipation

2.2. Theoretical model for hysteretic behaviors The theoretical load-displacement relationship of the proposed SCCB can be described through the flag-shape hysteretic loop as shown in Fig. 2, where the pre-compression force of disc springs, friction force and axial load are labeled as Fn, Ff and F, respectively. The linear 3

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X1 =

Fn + Ff (1)

K1 2Ff

X2 = Xm −

X3 =

(2)

K1

Fn − Ff (3)

K1

The mechanical behavior of the SCCB in various stages in Fig. 2 can be described as follows. (1) Stage O-B: As shown in Fig. 3(a), the axial load F is smaller than the sum of pre-compression force of disc springs and static friction force, so that there is no sliding between the slotted steel plates and C steel. The deformation of the SCCB can only be induced by elastic deformation of the tendon; therefore, the axial load F is described as follows:

Fig. 4. Calculation of hysteretic energy dissipation of SCCB.

F = K1 x stiffness of steel tendon K1 = Ew∙Aw/ lw, where Ew, Aw and lw indicate the elastic modulus, cross-sectional area and length of tendon, respectively. The stiffness of the disc springs is labeled as K2, which determines the secondary stiffness of the SCCB as shown in Fig. 2. The displacement and maximum displacement are labeled as x and Xm, respectively. In Fig. 2, A, B, C and D are four characteristic points indicating the change in status of the SCCB. The corresponding X coordinates of X1, X2 and X3 can be defined through Eqs. (1), (2) and (3), respectively.

;

(0 < x < X1)

(4)

(2) Stage B-C: As shown in Fig. 3(b), when the axial load F is greater than the sum of pre-compression force of disc springs and sliding friction force, relative sliding occurs between the slotted steel plates and C steel, followed by the compressive deformation of the disc springs. In this stage, the axial load F is as follows:

F=

K1 (Fn + Ff ) K1 K2 x+ K1 + K2 K1 + K2

;

(X1 < x < Xm )

(5)

(3) Stage C-D: As shown in Fig. 3(c), when the axial load F begins to

Fig. 5. Test results of mechanical parameters of the SCCB. 4

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24

200 Ff =45kN

Displacement (mm)

20

Fn =45kN

150

Load (kN)

16

SCCB specimen

12 8

100

50

Test Theoretical

4 0

0

1

2

3

4

0

5

0

5

Serial number of cycles

10

(a) Loading protocol 200 Ff =45kN

Ff = 30kN

Fn =70kN

150

Fn =70kN

150

Load (kN)

Load (kN)

20

(b) Case 1

200

100

50

0

15

Displacement (mm)

50

Test Theoretical

0

5

10

15

100

0

20

Test Theoretical

0

5

Displacement (mm)

10

15

20

Displacement (mm)

(c) Case 2

(d) Case 3

Fig. 6. Loading protocol and tested hysteretic behavior.

2.3. Energy dissipation

Table 1 Parameters used in nine analysis cases. Load case

1

2

3

4

5

6

7

8

9

Pre-compression force of disc springs Fn (kN) Friction force Ff (kN) Stiffness of high-strength tendon K1 (kN/mm) Stiffness of disc springs K2 (kN/mm)

60

60

60

40

80

40

40

60

60

20 30

40 30

60 30

40 30

40 30

40 30

40 30

60 15

60 45

5

5

5

5

5

1

10

5

5

A hysteretic loop of the SCCB in a single load cycle is shown in Fig. 4, where Xm is the maximum displacement and X1 is the displacement at imminent sliding. It can be found that the actual hysteretic loop can be replaced equivalently by a rectangle with the same area. Therefore, the area of the hysteretic loop SABCD = SBEFH = lBH • lON. Consequently, the dissipated energy ED in this load cycle can be calculated by using Eqs. (8), (9), (10a) and (10b).

lBH = (Fn + Ff ) − (Fn − Ff ) = 2Ff decrease due to both reduction of seismic loading and reversal of seismic motion, the compression force of disc springs is still smaller than the sum of axial load F on SCCB and friction force Ff; therefore, no sliding occurs and the axial load F is as follows:

lON = Xm −

Fm K1

(9)

K1 Xm − Fn − Ff ⎞ F ED = lBH lON = 2Ff ⎛Xm − m ⎞ = 2Ff ⎛ K1 ⎠ K1 + K2 ⎝ ⎝ ⎠ ⎜

F = K1 x −

K12 K1 + K2

Xm +

K1 (Fn + Ff ) K1 + K2

;

(X2 < x < Xm )

F=

K1 K2 x+ K1 + K2

K1 + K2

;

(X3 < x < X2 )

⎟

⎜

⎟

;

(x > X1) (10a)

(6)

ED = 0 ;

(4) Stage D-A: As shown in Fig. 3(c), when the axial load F continues to decrease until the compression force of disc springs becomes smaller than the sum of F and friction force, relative sliding occurs and the highstrength tendon and disc springs deform consistently. The axial load F is expressed as follows:

K1 (Fn − Ff )

(8)

(0 < x < X1)

(10b)

3. Cyclic loading test According to the structural configuration depicted in Fig. 1, a SCCB specimen is fabricated. A seven-wire steel strand with a diameter of 15.2 mm and the cross-sectional area of 140 mm2 is used as the highstrength tendon, which has the nominal tensile strength of 1860 MPa.

(7) 5

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200

Case 1 Case 2 Case 3

Case 2 Case 4 Case 5

160

150

Load (kN)

Load (kN)

200

100

120 80

50

0

40

0

5

10

15

0

20

0

5

10 15 Displacement (mm)

Displacement (mm)

(b) Cases with different Fn

(a) Cases with different Ff

200

160

Load (kN)

Load (kN)

200

Case 3 Case 8 Case 9

160 120 80

Case 4 Case 6 Case 7

120 80

40 0

20

40

0

5

10

15

0

20

Displacement (mm)

0

5

10

15

20

Displacement (mm)

(c) Cases with different K1

(d) Cases with different K2

Fig. 7. Comparison of hysteretic loops of various load cases.

its elastic deformation. Fig. 6(b) to (d) present the comparison of test and theoretical analysis results, where good agreement is observed, demonstrating the accuracy of the proposed analytical model.

Twelve disc springs were installed in the specimen, each with the diameter and height of 150 mm and 10 mm, respectively. Two 1 mm-thick brass plates were used as friction plates. To obtain the basic mechanical parameters, i.e. the elastic modulus of tendon, axial stiffness of spring series and the relationship between friction force and bolt torque, low-frequency cyclic tests are conducted. According to Fig. 5(a), the elastic modulus of tendon is calculated as 205,500 MPa; besides, the elastic elongation of the tendon is measured as 0.75%. Similarly, Fig. 5(b) shows the load-displacement curves of the spring series, where the axial stiffness is estimated as 5.67kN/mm. According to Fig. 5(c) and (d), the sliding friction forces are 15kN and 30kN when the twisting torques are 50 N∙m and 100 N∙m, respectively. Thereafter, low cyclic tests are conducted on the SCCB specimen, where the displacement-based loading protocol is adopted, as shown in Fig. 6(a). In order to investigate the influence of different pre-compression force (Fn) and friction force (Ff) on the hysteretic behavior of the SCCB, three test cases are designed, as shown in Fig. 6(b), (c) and (d). It is observed that the SCCB has a typical flag shape under the cyclic loading, and comparison between Fig. 6(b) and (c) shows that higher pre-compression force resulted in higher imminent sliding force; according to Fig. 6(c) and (d), the energy dissipation capacity decreased as the friction force was reduced. It is worth noting that the friction force should not be too large, so as to avoid the reduction in self-centering capacity, as shown Fig. 6(b). In these tests, when the SCED unit returned to its original status (i.e. point A in Fig. 2), the tendon forces in Cases 1, 2 and 3 are 0kN, 20kN and 40kN, respectively. Therefore, the tendon also provides some re-centering capacity due to the recovery of

4. Parameter analysis on hysteretic performance of SCCB Based on the validated theoretical model, parameter analyses are conducted in order to investigate the influence of various design parameters on the hysteretic performance of SCCB. Nine cases were designed, where four typical parameters (i.e. Ff, Fn, K1 and K2) are involved, as presented in Table 1. The displacement-based load protocol in Fig. 6(a) was adopted in these analyses, and Figs. 7 and 8 show the hysteretic curves and the calculated ED, respectively. According to Fig. 7(a), as Ff increases from 20kN to 60kN, the imminent sliding load and displacement also increases, with larger energy dissipation, which can be quantitatively obtained as shown in Fig. 8(a). Besides, larger Ff results in smaller re-centering load of the SCED unit (see point A in Fig. 2), indicating that the re-centering capacity of the SCED unit is reduced. However, the initial and post sliding stiffness are basically the same in the three cases. The hysteretic loops of Cases 2, 4 and 5 are presented in Fig. 7(b) to investigate the influence of Fn. When Fn increases, the stiffness of SCCB remain constant while the imminent sliding force and displacement increase accordingly. In addition, as shown in Fig. 8(b), the energy dissipation capacity of SCCB decreases slightly as Fn increases, since sliding becomes more difficult to be started. As to the axial stiffness of tendon K1, Fig. 7(c) shows that when K1 6

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Fig. 8. Comparison of ED in different load cases.

The structure is arranged symmetrically and the torsional effect can be neglected; thus, instead of the three-dimensional structure, only a five-bay plane frame is taken for the subsequent seismic analyses. Seismic performance evaluation shows that the RC frame is seismically deficient in the Y direction; therefore, the SCCBs were designed to improve the seismic performance of the plane RC frame. For comparison purposes, the seismic strengthening by using the BRBs is also analyzed. The SCCBs and BRBs are designed with the same initial stiffness and energy dissipation excitation displacements. For the SCCB, the energy dissipation excitation displacement denotes X1 in Fig. 4, while for the BRB, it is the yield displacement of its metallic core. Fig. 9(c) and Fig. 9(d) show the layouts of the SCCBs and BRBs, respectively. Considering that there are five spans in Y direction, and the strengthening should be symmetric, the SCCB and BRBs are placed in the second and fourth spans. To avoid sudden change in inter-story stiffness, all stories are enhanced, though the placement could be further optimized. According to the trial analysis, primary design parameters of the SCCB and BRB are determined through Eqs. (11)–(17) [35], where θ, θt, D, Db and Ds represent the angle between BRB and beam, inter-story drift when the energy dissipation of the SCCB is triggered, inter-story stiffness of the bare RC frame, lateral stiffness contributed by the BRB and SCCB, respectively; ic, ib, lb, lw, Ab, Aw and hc represent the linear stiffness of column, linear stiffness of beam, length of BRB, length of SCCB, cross-sectional area of inner core of BRB, crosssectional area of high-strength tendon and height of column, respectively. Note that X1 in Eq. (1) equals hcθtcosθ, K1 is determined according to Eq. (16), and it is recommended that K2/K1 is no more than 1/3. In order to have enough re-centering capacity, Fn must be no less

increases, the imminent sliding load and re-centering load of ED unit remain unchanged, while the pre and post-sliding stiffness become higher. According to Fig. 8(c), ED increases significantly with the increase of K1. This is due to that the disc springs and tendon are connected in series, and to reach the same target displacement, larger K1 results in longer friction slippage, corresponding to more energy dissipation. On the other hand, as shown in Fig. 7(d), when the stiffness of disc springs K2 increases, the imminent sliding load, re-centering load of ED unit, and pre-sliding stiffness remain unchanged; however, post-sliding stiffness increases and the energy dissipation capacity of SCCB decreases slightly, as shown in Fig. 8(d), since the sliding becomes more difficult. 5. Case study 5.1. Project description A 9-story RC frame structure was built on the site with the seismic fortification intensity of seven and the soil category of II [33], and Fig. 9 shows the plan and elevation views. All these RC frames are lateral force resisting frames. The cross-section and area of reinforcing bars of beams and columns of the RC frame are shown in Table 2, where the C35 grade concrete with the nominal cubic compressive strength of 35 MPa and HRB335 steel with the nominal yield strength of 335 MPa are used [34]. The design dead and live loads of the stories and roof are 5 kN/m2 and 2 kN/m2, respectively, and the dead load of in-filled walls is 15 kN/m. 7

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Fig. 9. Plan and elevation views of the RC frames.

Table 2 Parameters of beams and columns of the RC frames. Story

Column/beam

Cross-section (mm)

Area of longitudinal reinforcing bars (mm2)

1 to 3

Column Beam Column Beam Column Beam

600 250 500 250 400 250

1401 (each side) 867 (top) × 636 (bottom) 1101 (each side) 867 (top) × 636 (bottom) 801 (each side) 735 (top) × 636 (bottom)

4 to 6 7 to 9

× × × × × ×

600 550 500 550 400 550

1–3 4–6 7–9

SCCB

Ab (mm2)

Fn(kN)

Ff (kN)

Aw (mm2)

K1 (kN/mm)

K2 (kN/mm)

4800 2400 960

720 360 144

720 360 144

4800 2400 960

130.08 65.04 26.016

43.36 21.68 8.672

∑ αc

12ic hc2

ib ic EAb

∑ ∑

(13)

(14)

cos2 θ (15)

lb cos2 θ

EAw lw

Fn = Ff =

=

∑ K1cos2 θ

Ew Aw hc θt cos θ 2l w

(16)

(17)

5.2. Numerical model Numerical models of the RC frames are developed in the finite element software ABAQUS, as shown in Fig. 10, where the beams and columns are simulated by using the B21 elements which are the firstorder Timoshenko beam elements, and each beam or column is divided into five elements. The constitutive models of concrete and reinforcing bars adopt the U-concrete02 and U-steel02 materials, respectively, as shown in Fig. 11, where E0, dc, dt, R, εre, and fy are the initial modulus of elasticity, compressive damage factor, tensile damage factor, virtual point R, residual strain and yield strength, respectively [36]. Note that when the two material models are used, the PQ-fiber subroutine [36] is called, which consists of a set of uniaxial material hysteretic constitutive models. In this paper, the axial compressive strength, peak compressive strain, ultimate compressive strength, ultimate compressive strain and axial tensile strength of unconfined concrete are 23.4 MPa, 0.0017, 19.89 MPa, 0.0038 and 2.20 MPa, respectively, and the parameters of confined concrete are calculated according to the Kent-Scott-Park concrete material model [37]. The ultimate strain of

than Ff, and ED is increasing with the increasing of Ff; therefore, “Fn = Ff” is recommended in the design of SCCB, as indicated in Eq. (17), so as to maximize ED and to have enough re-centering capacity. Assuming that the yield strength of the steel of BRB is 300 MPa, Table 3 summarizes the calculated design parameters of SCCB and BRB.

D=

K=

Ds =

BRB

Db D = s = 36% D D

0.5 + K 2+K

Db =

Table 3 Design parameters of the SCCB and BRB. Story

αc =

(11)

(12) 8

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Fig. 10. Numerical models of the strengthened frames.

Fig. 11. Constitutive models of concrete and reinforcing bars.

confined core concrete, εu, is calculated through εu = 0.004 + 0.9ρs(fyh/300) [37], where εu is the volume stirrup rate and fyh is the yield strength of stirrups. The elastic modulus and yield strength of reinforcing steel are 200000 MPa and 335 MPa, respectively. The low cycle fatigue degradation is considered in the adopted material model of reinforcing bars, as shown in Eqs. (1) and (2) [38].

Eeff , i ⎛ ⎞ f yi = f y1 ⎜1 − ⩾ 0.3f y1 3f y1 εf (1 − α ) ⎟ ⎝ ⎠

Eeff , i =

⎡

ε

2

(18)

⎤

∑ ⎢Ei ⎛⎜ ε i ⎞⎟ ⎥ f

concrete and spalling of concrete cover [38], while the inelastic buckling of reinforcing bars [39] and the slippage of longitudinal reinforcing bars at the adjacent of beam-column connection [40] are not considered, since the focus of this study is the seismic performance of SCCB and BRB-enhanced structures. Note that the BRB and SCCB are usually pin-connected to structures and are designed based on their axial force; therefore, they are simulated by using the truss element (i.e. the T2D2 element). Since the design of BRB usually does not consider the low cycle fatigue degradation of yielding segment [41] of BRB, the possibility of fatigue degradation of BRB is neglected in this study, as done in previous other finite element analyses of BRB-strengthened structures[42]. The constitutive model of the BRB is ideal elastic plastic, and according to the load-displacement relationship of SCCB, a user-defined material subroutine (UMAT) is developed in the ABAQUS and assigned to the truss element of the SCCB. According to the comparison of numerical simulation and test results, as shown in Fig. 12, good agreement is observed, showing the accuracy of the proposed the simulation method for the SCCB. For RC frames, the accuracy of the simulation method has been validated according to the test results [36].

⎣ ⎝ ⎠⎦

(19)

where Eeff,i is the effective accumulated hysteretic energy when loaded to the ith cycle; Ei and εi denote the dissipated energy and the maximum strain at the ith cycle, respectively; α is the post-yield stiffness coefficient and εf is the strain of reinforcing bar when failure of RC member occurs under monotonic loading. Such a strength degradation rule is depicted in Fig. 11(b), where fyi represents the yield strength of the ith loading cycle, and the signs of “+”and “−” indicate positive and negative loading, respectively. Note that the adopted material model of reinforcing steel accounts for the bond-slip effect of reinforcing bars in 9

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Fig. 12. Comparison of numerical simulation and test results.

Fourier transform. According to frequency analyses, the natural vibration periods of the bare frame, BRB-strengthened frame and SCCBstrengthened frame are 1.686 s, 1.186 s and 1.686 s, respectively, and the SCCB-strengthened frame has the same value with that of the bare frame. This is due to the SCCB is flexible and does not influence the initial structural stiffness of the frame. Fig. 13 shows the pseudo-acceleration spectra of individual ground motions and the design spectrum, where the mean spectrum matches well with the design one, especially at the natural periods of the SCCB-strengthened and BRBstrengthened RC frames.

Table 4 Characteristics of selected ground motions. Name

Duration (s)

Magnitude

Year

Epicentral distance (km)

Component

Iwate Superstition Hills-01 Superstition Hills-02 Chi-Chi Tabas Artificial-1 Artificial-2

79.32 29.835

6.9 6.22

2008 1987

16.26 17.59

IWT010NS A-IVW090

59.985

6.54

1987

13.03

B-WSM090

68.71 32.96 88.14 32.96

7.6 7.3 – –

1999 1978 – –

2.74 1.79

TCU076-E TAB-L1 – –

5.4. Seismic analysis results As shown in Fig. 14(a) and Fig. 14(b), prior to the strengthening, the bare RC frame shows excessive inter-story drifts, and some stories exceeded the threshold values indicated in the design code [33], which are 0.009 and 0.02 for the DBE and MCE, respectively. After strengthening, the inter-story drifts are significantly reduced and are all within the threshold values. To be more specific, the maximum inter-story drift are reduced by 35.81% and 37.78% respectively after strengthening with BRBs and SCCBs under the DBE, and reduced by 18.98% and 23.36% respectively under the MCE. As to the residual inter-story drifts, O’Reilly et al. [43] used a threshold value (i.e., 0.2%) as the “re-centering” criterion for the selfcentering concentrically braced RC frame systems, indicating that the structure with such small residual drifts can be regarded the same as the one prior to the earthquake. Based on a survey of damaged structures during past earthquakes, McCormick et al. suggested the 0.5% residual

5.3. Ground motions According to the Chinese code [33], five earthquake ground motion records and two artificial waves, as shown in Table 4, are selected according to the soil type of the construction site, and used for nonlinear dynamic time-history analyses of the frame before and after strengthening. Design dead and live loads are considered in analyses. For the seismic fortification intensity of seven [33], the peak acceleration of design-basis earthquake (DEB, with 10% probability of exceedance in 50 years) and the maximum considered earthquake (MCE, with 2% probability of exceedance in 50 years) are 100 Gal and 220 Gal, respectively. The peak accelerations of ground motions are therefore scaled to 100 Gal and 220 Gal, and the individual and mean earthquake response spectra at the DBE and MCE level can be acquired through the 10

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Fig. 13. Pseudo-acceleration spectra of selected ground motions and design spectrum.

Fig. 14. Seismic analysis results.

drift limit for the “Repairable” performance level [12]. According to Fig. 14(c), the bare RC frame under the DBE exceeded the “re-centering” criterion, while after strengthening with BRBs and SCCBs, the maximum residual inter-story drift are reduced by 50.22% and 64.02% respectively, so that the RC frame can be seismically resilient. For the MCE, as shown in Fig. 14(d), the maximum residual inter-story drift of

the bare RC frame is 0.55%, indicating the RC frame is no longer repairable. After strengthening with BRBs and SCCBs, the residual interstory drifts are significantly reduced, with the reduction rates of 51.99% and 72.29%, respectively, and the RC frame could be repairable even though the ground motions are strong. Fig. 15 illustrates the peak base shear forces of the bare, BRB-

11

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under the Superstition Hills-01 ground motion at the MCE level. In general, the BRB dissipates more seismic energy than the two SCCBs, while significant yielding of the BRB occurs during the earthquake. For the SCCBs, the maximum load reaches 370kN, while the stress is only 400 MPa, which is much lower than the nominal strength of highstrength tendon (i.e. 1860 MPa). In this regard, the SCCBs have higher seismic capacity than the BRB. To evaluate the seismic resilience of the frames, the self-centering index S1 is used, as shown in Eq. (20) [44,45], where FA and FD denote the loading and the unloading plateau forces, respectively, as illustrated through the flag-shaped hysteretic model in Fig. 17. Reversal cyclic loading is increasingly applied to the nine floors in an inverted triangle mode, until the roof displacements reach 1/50H (H denotes the building height). Fig. 18 illustrates the hysteretic loops of the bare, BRB-strengthened and SCCB-strengthened RC frames, where S1 of the three frames are 0.319, 0.113 and 0.894, respectively, indicating the SCCB can improve the self-centering capability of the RC frame, while the BRB may have the negative influence on self-centering capability due to yielding.

Fig. 15. Base shear forces under DBE and MCE.

S1 =

FA + FD FA − FD

(20)

6. Summary and conclusions This paper proposes a novel self-centering cable brace with friction devices, based on which theoretical, experimental and numerical studies are conducted. According to the presented work, the following conclusions can be drawn. (1) The proposed SCCB has the advantages of being light weight, buckling free, easy for installation, and having stable self-centering and energy dissipation capacity. This novel device can not only apply to the retrofit of existing RC frame structures, but also be used in the design of new structures. (2) Cyclic loading tests demonstrate the effectiveness of the proposed SCCB, which has stable self-centering and energy dissipation capacity. The theoretical and numerical results are in good agreement with cyclic loading test, indicating that the proposed theoretical and numerical models can accurately describe the mechanical behavior of SCCB. (3) The parametric analysis indicates that the SCCB is a highly variable damping device. The stiffness of SCCB can be increased by enlarging the linear tensile stiffness of high-strength tendons and the compressive stiffness of disc springs. The starting sliding force can be changed by changing the pre-tightening force of bolts and friction coefficient. In addition, with the increase of the linear stiffness of high-strength tendon and friction force, the energy dissipation capacity of SCCB is increased. (4) According to the nonlinear dynamic analyses, it is found that both the SCCBs and BRBs increase the seismic capacity of the bare RC frame, while the SCCBs can reduce the maximum story drifts more significantly and have much less residual story drifts than the BRBs.

Fig. 16. Load-axial elongation relationships.

Fig. 17. Flag-shaped hysteretic model.

CRediT authorship contribution statement

strengthened and SCCB-strengthened frames under DBE and MCE. As shown in Fig. 15, due to the added stiffness, the base shear forces of BRB-strengthened and SCCB-strengthened frame are both higher than the bare frame under DBE and MCE, and the base shearing force of SCCB-strengthened frame is slightly higher than the BRB-strengthened frame under DBE and significantly higher under DBE, indicating the SCCB-strengthened frame takes larger seismic loading than the BRBstrengthened RC frame under strong earthquake. Fig. 16 presents the load-axial elongation relationships of one BRB and two SCCBs (in positive and negative directions) in the 7th floor

Tong Guo: Conceptualization, Methodology, Writing - review & editing, Supervision. Jishuai Wang: Methodology, Software, Data curation, Writing - original draft, Validation, Investigation. Yongsheng Song: Methodology, Resources. Weihong Xuan: Project administration, Funding acquisition. Yuzhi Chen: Validation. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to 12

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Fig. 18. Hysteretic loops of the three frames.

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