Comparative study of steel plate shear walls with different types of unbonded stiffeners

Journal of Constructional Steel Research 159 (2019) 384–396

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Journal of Constructional Steel Research

Comparative study of steel plate shear walls with different types of unbonded stiffeners Jin-Guang Yu a,b, Li-Ming Liu a, Bo Li c,⁎, Ji-Ping Hao a, Xi Gao d, Xiao-Tian Feng a a

School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China State Key Laboratory of Western Architecture and Technology, Xi'an 710055, China Department of Civil Engineering, University of Nottingham Ningbo China, Ningbo 315100, China d School of Mathematical Sciences, University of Nottingham Ningbo China, Ningbo 315100, China b c

a r t i c l e

i n f o

Article history: Received 25 December 2018 Received in revised form 18 April 2019 Accepted 5 May 2019 Available online 16 May 2019 Keywords: Steel plate shear walls Stiffener Precast concrete panel Cyclic performance

a b s t r a c t This paper presents a comparative study of the steel plate shear walls (SPSWs) with different types of unbonded stiffeners. Multiple ribs and precast concrete panels are installed for restraining the out-of-plane deformation of steel plates. The effect of spacing of unbonded ribs on the behaviour of SPSWs is first investigated through a finite element analysis. Subsequently, three 1/3-scale one-bay, two-storey SPSW specimens, namely unstiffened SPSW (US-SPSW), partially restrained SPSW (PR-SPSW) and completely restrained SPSW (CR-SPSW), are tested under cyclic loading. Test results indicate that specimens PR-SPSW and CR-SPSW exhibit similar load-carrying capacity, energy dissipation capacity, and stiffness degradation. Out-of-plane deformations of infilled steel plates, inward deformation of columns, and rotation of beam-column connections in both specimens PR-SPSW and CR-SPSW are effectively restrained, which alleviates the pinching phenomenon of hysteretic curves and stiffness degradation. As compared to the complete restraints for steel plates, partial restraints can increase the buckling area of the infilled steel plates and subsequently enhance the ductility of SPSW structure. They can also convert the deformation mode of infilled steel panels from the high-wave-low order to the low-wave-high order. In general, specimen PR-SPSW stiffened by unbonded multiple ribs with an appropriate spacing shows the excellent structural behaviour and constructability. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction Steel plate shear wall (SPSW) structure, consisting of infilled steel plates and boundary frame members, has gained increasing popularity due to its excellent hysteretic performance, energy dissipation, and earthquake resistance [1–3]. The addition of steel plates has been also used to upgrade the existing reinforced concrete buildings by considering their excellent hysteretic properties [4–7]. Gholizadeh and Shahrezaei [8] adopted a meta-heuristic search algorithm to optimize the layout of steel frames with steel plate walls (SPWs), and demonstrated the effectiveness of the proposed method for optimization of steel frames with SPWs. However, there are several limitations for the SPSWs with thin infilled steel plates. For instance, the premature buckling of infilled steel plates in SPSWs at the elastic stage reduces their shear resistance. The out-of-plane deformation of steel plates (known as the breathing effect) causes loud noises and tremors which disturbs the occupants. Increasing the thickness of steel plates is one of the solutions usually adopted to reduce their out-of-plane deformation. Notwithstanding, buckling of infilled steel plates in SPSWs still occurs ⁎ Corresponding author. E-mail address: [email protected] (B. Li).

https://doi.org/10.1016/j.jcsr.2019.05.007 0143-974X/© 2019 Elsevier Ltd. All rights reserved.

when the structure is subjected to a moderate or strong earthquake. In addition, infilled steel plates in SPSWs are allowed to buckle under shear stress fields, and subsequently contribute to resist horizontal forces through diagonal tension fields. However, this characteristic would reduce the stability of columns due to the additional bending moments introduced by the tension fields in the steel plates. As a result, plastic hinges tend to form at both ends of columns, followed with the hourglass phenomenon, which negatively affects the performance of SPSWs [9]. The installation of stiffeners on steel plates has been recognized as an effective way to restrain the out-of-plane deformation of the infilled steel plates in SPSWs, and subsequently enhances their efficiency for shear resistance [10–22]. Among others, Guo et al. [10,11] demonstrated that the cross and diagonal stiffeners are effective to restrain the out-of-plane deformation of infilled steel plates in SPSWs, which enhances the loading capacity and stiffness of the SPSW structure. Alinia and Shirazi [12] reported the performance of SPSWs with different types of stiffeners, and highlighted that utilising unidirectional stiffeners is more effective to enhance the behaviour of SPSWs than the bidirectional cross stiffeners. Alinia [13] further optimized the stiffeners for steel plates, and recommended that the transverse stiffeners installed on steel plates

J.-G. Yu et al. / Journal of Constructional Steel Research 159 (2019) 384–396

should divide the length of the plate to portions equal or less than the width of steel plate. Yu et al. [14] conducted the dynamic analysis of SPSWs with non-welded multi-rib stiffeners, and concluded that the non-welded multi-rib stiffeners are effective in postponing the stiffness degeneration of SPSWs subjected to a moderate or strong earthquake. For the aluminium plate shear wall, the use of stiffeners has been proved to be effective in delaying the shear buckling of the aluminium plate, and then improves their hysteretic performance. This has been identified as a promising solution to protect moment resisting frame structures from earthquake attacks [15–17]. Zhao and Astaneh-asl [18] and Astaneh-asl [19] tested two types of composite SPSWs under cyclic loading. A gap between the reinforced concrete wall and the boundary frame members is reserved in the innovative composite SPSWs. Both composite SPSWs exhibit excellent ductility up to 5.0% drift. Afterward, Rahaia and Hatamib [20] and Arabzadeh and Soltani [21] investigated the influence of the spacing of shear studs, thickness of concrete panels and concrete strength on the performance of composite SPSWs. Guo et al. [22] proposed a buckling-restrained SPSW structure with reinforced concrete panels installed on the infilled steel plates. The reinforced concrete panels are prone to separate from the steel plates due to their weak bond. It is also difficult to install the precast concrete panel due to its heavy weight. Although the behaviour of SPSWs with different types of stiffeners has been widely investigated, there are limited studies focusing on the influence of out-of-plane restraining level on the performance of SPSW structure, e.g. the comparative study of SPSWs with different types of stiffeners. Therefore, this paper focuses on investigating the performance of SPSWs with different types of out-of-plane restraining stiffeners. The non-welded multi-rib stiffeners and the precast concrete panels are adopted to restrain the out-of-plane deformation of steel plates. In this study, the design methods for non-welded ribs and precast concrete panels are first proposed based on a finite element analysis. Afterwards, SPSWs without stiffeners, with non-welded multi-rib stiffeners and with precast concrete panels are tested and compared in terms of failure modes, hysteretic behaviour, energy dissipation and stiffness degradation. The out-of-plane deformation of infilled steel plates, inward deformation of columns, and rotation of beam-column connections are also examined.

385

2. Structural design 2.1. Stiffeners for infilled steel plates Fig. 1(a) shows the schematic view of infilled steel plate restrained by the non-welded multiple ribs in specimen PR-SPSW. Transverse and longitudinal steel belts with grooves are mutually embedded at the intersection of ribs in both directions as shown in Fig. 1(b). The formed multi-rib stiffeners are fixed on both sides of the steel plate by threaded bolts passing through the welded tubes at the intersection of the ribs. Here, the length of the tube is equal to the depth of the ribs. It should be noted that the non-welded multi-rib stiffeners are disconnected from the frame. The detailed assembly process of the nonwelded multi-rib stiffeners for SPSWs can be referred to Yu et al. [2]. For specimen CR-SPSW, the precast concrete cover is installed to provide a high level of restraint as shown in Fig. 1(c). The thickness of the precast concrete cover is identical to the depth of the ribs. Different from the non-welded multi-rib stiffeners, the precast concrete cover is able to restrain the buckling of the whole steel plate. To reduce the friction between concrete panel and steel plate, a 1.0 mm thick PTFE plate coated with 1.0 mm thick molybdenum disulphide grease is placed on concrete surface. The PTFE has excellent mechanical properties over a temperature range of −196 °C to 260 °C. The non-welded multi-rib stiffeners can overcome the disadvantages of the conventional welded stiffeners, e.g. large residual stress, welding distortion and installation difficulty. They can also avoid the premature buckling failure which is commonly existed in the conventional welded stiffeners. As a result, they can continuously restrain the out-of-plane deformation of steel plate in SPSWs. In addition, the nonwelded multi-rib stiffeners are ease of installation due to their light weight. The precast concrete panel in the form of non-welding exhibits the higher constraint stiffness as compared with the non-welded multirib stiffeners. This means that the precast concrete panel is more efficient to restraint the out-of-plane deformation of steel plate. Moreover, the precast concrete panel has the better fire resistance as compared with the multi-rib stiffeners. However, the precast concrete panel is much heavier than the non-welded multi-rib stiffeners, which probably leads to the difficulty of installation, large earthquake response and high foundation cost.

Fig. 1. Stiffeners for specimens PR-SPSW and CR-SPSW.

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2.2. Design methods for stiffeners 2.2.1. Flexural stiffness ratio of ribs to steel plate To reflect the strength of steel plate with out-of-plane deformation, flexural stiffness ratio of stiffeners per unit width Dr to the infilled steel plate per unit width D is adopted and is defined as Eq. (1). Dr η¼ D

ð1Þ

where η is the flexural stiffness ratio, Dr and D are the flexural stiffness of the stiffeners and the infilled steel plate, respectively. D can be calculated based on Eq. (2). D¼

Et3 12ð1−υ2 Þ

ð2Þ

where t, E and υ are the thickness, elastic modulus and Poisson's ratio of the steel plate, respectively. Dr can be computed based on Eqs. (3) and (4) for the multi-rib stiffeners and the precast concrete panel, respectively.

 . 2 kp ¼ 4:0 þ 5:34 d2 d1  . 2 d2 kp ¼ 5:34 þ 4:0 d1

ð3Þ

Dr ¼ Dc ¼

E t3
c c  12 1−υ2c

ð4Þ

where Ir is the moment of inertia of rib belts, in which the neutral axis is assumed at the middle plane of the steel plate. d is the spacing of rib belts. Dc is the flexural stiffness of the precast concrete panel. tc is the thickness of concrete panel. Ec and υc are the elastic module and Poisson's ratio of concrete, respectively. The elastic shear buckling loading capacity of specimen PR-SPSW can be determined by Eq. (5) [23,24]. π2 2

b t

1

3

D41 D42 ða≥bÞ

ð5Þ

where τcr,t is the shear buckling loading capacity of specimen PR-SPSW, a and b are the width and height of the infilled steel plate, respectively. kst is the shear buckling coefficient and is related to the dimensional ratio of the rib belts to the steel plates. This coefficient can be determined based on the theory of elastic stability [25]. A lower limit of shear buckling coefficient of 3.5 is adopted in accordance with JGJ99– 2015 [24]. D1 and D2 are the flexural stiffness corresponding to the bending moment Mx, and My, respectively. For the double-sided symmetrically arranged multi-rib stiffened steel plate, the flexural stiffness is averaged flexural stiffness of rib belts and infilled steel plates relative to the neutral axis, as expressed in Eq. (6). Et3 EI rx þ ¼ D þ Drx 12ð1‐υ2 Þ d1 3 Et EI ry þ D2 ¼ ¼ D þ Dry 12ð1‐υ2 Þ d2

D1 ¼

ð6Þ

where d1 and d2 are the ribs spacing in the longitudinal and transverse directions, respectively. Irx and Iry is the moment of inertia of rib belts corresponding to the bending moment Mx and My, respectively. The elastic shear buckling loading capacity of the cell plates can be calculated by Eq. (7). τcr;p ¼ χkp

π2 D 2

d2 t

ðd1 ≥d2 Þ

ð7Þ

where χ is the embedding coefficient. As the non-welded multiple ribs are connected to the steel plate at the intersections of ribs, the

ðd1 ≤d2 Þ

ð8Þ

ðd1 Nd2 Þ

As the length is almost identical to the width of the cell plate, the shear buckling coefficient kp is recommended to be 9.34. To achieve the local buckling of cell steel plate prior to the overall buckling of the whole steel plate, the following equation should be satisfied. τcr:t ≥τcr:p

ð9Þ

Substituting Eqs. (5)–(8) into Eq. (9), the flexural stiffness ratio of rib belts to steel plates can be calculated in Eq. (10).


EIr Dr ¼ d

τcr;t ¼ kst

embedding effect of the multi-rib on the infilled steel plate is marginal. Therefore, χ = 1.0 is adopted for specimen PR-SPSW. The shear buckling coefficient kp can be computed by Eq. (8).

1 þ ηx

14 

1 þ ηy

34

≥ ðn2 þ 1Þ2

χkp kst

ð10Þ

where ηx and ηy are the stiffness ratios corresponding to the bending moment Mx and My, respectively. n1 and n2 are the number of vertical and horizontal stiffeners, respectively. If the moment of inertia and the distance for the stiffeners are the identical (i.e. ηx = ηy = η), flexural stiffness ratio of rib belts to steel plates in Eq. (10) can be simplified to Eq. (11). η≥ ðn2 þ 1Þ2

χkp −1 kst

ð11Þ

2.2.2. Spacing of multiple ribs According to the yield criterion of distortion energy, the cell plates should fulfil Eq. (12) to avoid the occurrence of out-of-plane flexure at the elastic stage. τcr;p ≥ f vy

ð12Þ

Therefore, the relationship between the width and the thickness of the cell plates can be established in Eq. (13). d2 ≤π 

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ekp t 12f vy ð1−υ2 Þ

ð13Þ

Here, fvy is the shear yield strength of steel plate, and is assumed to be 0.577fy. Substituting materials properties and kp = 9.34 into Eq. (13), the spacing of rib belts can be defined in Eq. (14). sffiffiffiffiffiffiffiffiffi d2 235 ≤113:3 fy t

ð14Þ

2.2.3. Flexural stiffness ratio of precast concrete panel to steel plate The shear yield of the infilled steel plate occurs before the overall elastic buckling when the concrete cover of specimen CR-SPSW meets limit restrained stiffness. The occurrence of overall elastic buckling of steel plate in specimen CR-SPSW should fulfil Eq. (15). τcr ≥ f vy

ð15Þ

where τcr is the critical buckling shear stress of steel plate, and can be

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387

calculated according to the Eq. (16). τcr ¼

kp π2 ðD þ 2Dc Þ

ð16Þ

2

tb

Substituting stiffness ratio of concrete cover into Eq. (16), the following equation can be obtained. τcr ¼

kp π2 ð1 þ 2ηÞ 2

tb

D

ð17Þ

Based on the Eqs. (2), (15) and (17), flexural stiffness ratio of concrete panel to steel plate can be calculated in Eq. (18). 1 η≥ 2

f vy 


 12 1−υ2 Et 2

2

b  −1 kp π2

! ð18Þ

Fig. 2. FE model for specimens (a) PR-SPSW3 and (b) CR-SPSW.

1.2

3. Finite element analysis

1.0

3.1. Finite element model of SPSWs

0.8 V/fvyL t

The finite element (FE) models for the SPSW specimens are built and analysed using the finite element software ANSYS. FE model based on specimen C2-W3 in Yu et al. [2] is established to estimate the influence of the rib spacing on the out-of-plane restraining stiffness of the SPSW structure. Specimen C2-W3 is designed to allow the fully development of tension field in steel plates for lateral resistance. The dimension of the simplified FE model is 1200 mm × 1200 mm. The column flexibility coefficient, width-to-height ratio, and height-to-thickness ratio of specimen C2-W3 are fixed at 2.1, 1.0 and 400, respectively. Five FE models with different out-of-plane restraints are established as shown in Table 1, and are renamed US-SPSW, PR-SPSW1, PR-SPSW2, PR-SPSW3 and CR-SPSW, respectively. The out-of-plane restraint of specimens PR-SPSW1, PR-SPSW2 and PR-SPSW3 are non-welded multi-rib stiffeners. The restrained stiffness ratio of their rib belts is 2 times that in Eq. (11). According to the requirements of spacing-to-thickness for ribs in Eq. (14), three spacing of ribs are used for specimens PR-SPSW1, PR-SPSW2 and PR-SPSW3. To reflect the influence of the different restraints of the steel plates on the out-of-plane restraining stiffness, specimens US-SPSW and CR-SPSW are included for comparison. The restraining stiffness of precast concrete panel of specimen CRSPSW satisfies the requirement in Eq. (18). Fig. 2 shows the FE model of specimens PR-SPSW3 and CR-SPSW. For the out-of-plane restraining stiffeners, Solid 45 and Shell 181 are used to simulate the precast concrete panel and the rib belts, respectively. The friction element includes the contact element Conta 173 and the target unit Targe 169. For the specimens PR-SPSW3 and CR-SPSW, the out-ofplane degree of freedoms (DoFs) of the stiffeners and the steel plate, and the out-of-plane DoFs of the concrete cover and the steel plate are coupled at the location of threaded bolts, but their translational DoFs are released. Boundary members and infilled steel plates are modelled using the Beam188 and Shell181 elements, respectively. The initial imperfections caused by the fabrication process, the shrinkage of welding and the out-of-plane deformation could affect the performance SPSWs. Therefore, the buckling analysis of the structure was carried out to

0.6 0.4

US-SPSW PR-SPSW1 PR-SPSW2 PR-SPSW3 CR-SPSW

0.2 0.0 0.0

0.5

1.0 1.5 Drift raio (%)

2.0

2.5

Fig. 3. Shear strength of infilled steel plates under various drifts.

obtain the buckling mode of the SPSW under horizontal load, and subsequently 1/1000 of the first buckling mode was applied to the model as the initial defect of the SPSW. The residual stresses in SPSWs was not considered in the current FE model as discussed by Wang et al. [26]. Based on a preliminary mesh sensitivity study, a mesh of 50 mm × 50 mm has been chosen to compromise time of analysis with accuracy of simulation results [27]. The beam-column connections are idealized as the hinges, while the columns are hinged to the foundation. The ideal elastic-plastic model is used to model steel material. The yield strength and the elastic modulus of the steel are 235 MPa and 210 GPa. 3.2. Monotonic behaviour of SPSWs Fig. 3 shows the shear strength of infilled steel plates in SPSWs against the drift ratio. Summary of simulation results is given in Table 2. Here, V is the shear force taken by the infilled steel plate, fvy is shear yield strength of the infilled steel plate, and L and t are the width and thickness of the infilled steel plate, respectively. In the elastic stage, horizontal load in specimen US-SPSW is lower than that of other specimens. When the horizontal drift increases to 0.2%, the elastic

Table 1 Details of FE model of specimens. Specimen

Stiffeners

Stiffener size (mm)

Rib spacing (mm)

Restrained stiffness ratio

US-SPSW PR-SPSW1 PR-SPSW2 PR-SPSW3 CR-SPSW

N/A V3H3 ribs V4H4 ribs V5H5 ribs Steel & concrete panels

N/A −6 × 60 × 1100 −6 × 60 × 1100 −6 × 60 × 1100 −40 × 1100 × 1100

– 525.0 340.0 262.5 –

0 83.2 128.5 166.4 321.0

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Table 2 Comparison of loading capacity and out-of-plane deformation of steel plates. Stage

Drift

Elastic load (kN) Ultimate load (kN) Deformation of steel plate (mm)

0.2% 2.0% 2.0%

US-SPSW

PR-SPSW1

PR-SPSW2

PR-SPSW3

CR-SPSW

Loading ratios

(A)

(B)

(C)

(D)

(E)

(B-A)/A

(E-A)/A

(C\ \B)/B

323.84 432.28 30.10

416.07 439.25 13.61

433.87 449.74 12.61

436.27 455.04 11.01

439.60 460.45 4.17

28.50% 1.60% −54.80%

35.70% 6.50% −86.20%

4.30% 2.40% −7.30%

deformation modes of the infilled steel plates in specimens US-SPSW and CR-SPSW are overall buckling. Specimen US-SPSW has three large diagonal buckling belts with the maximum deformation in the middle of steel plate. Steel plate in specimen CR-SPSW exhibits the smallest deformation in the steel plate as compared with other specimens. Fig. 4(c), (d) and (e) show the out-of-plane deformations of steel plate of specimens PR-SPSW1, PR-SPSW2 and PR-SPSW3, which are mainly local buckling of the cell plates. With the increase of the number of ribs, the buckling form of infilled steel plate transforms from the high-wavelow order to the low-wave-high order. The deformation of steel plates tends to be more uniform and concentrates in the corner of steel plates. Fig. 4(f), (g) and (h) show the out-of-plane deformations of the rib belts. When the ribs are arranged in a sparse way, the out-of-plane deformation of the steel plate causes the obvious sliding of the restraining members. The non-welded multi-rib stiffened SPSWs satisfying the requirement of rib spacing can confine the maximum out-of-plane deformation at the corner of the steel plate. This is similar to the precast concrete panel stiffened SPSWs.

buckling loading capacities of specimens CR-SPSW and PR-SPSW1 are 35.7% and 28.5% higher than that of specimen US-SPSW, respectively. Besides, the elastic buckling loading capacity of specimen PR-SPSW2 is increased by 4.3% as compared with that of specimen PR-SPSW1. Subsequently, specimens PR-SPSW1, PR-SPSW2, PR-SPSW3 and CR-SPSW gradually enter the plastic stage, and the steel plates buckle inside the cells. At the drift ratio of 2.0%, the loading capacity of specimen CR-SPSW is 6.5% higher than that of specimen US-SPSW. It indicates that the out-of-plane restrained stiffness has a great influence on the yield loading capacity of SPSWs, but have marginal impact on the ultimate loading capacity of SPSWs. The ultimate out-of-plane deformation of infilled steel plate of specimen PR-SPSW1 is 54.8% lower than that of specimen US-SPSW. 3.3. Out-of-plane deformation of steel plates in FE model Fig. 4 shows the out-of-plane deformation contour of steel plates and rib belts at the drift ratio of 2.0%. As seen from Fig. 4(a) and (b),

MX

MN MX

Y Z

-.016354 -.011193 -.006031 -.870E-03 .004292 .009453 .014615 .019776 .024938 .030099

MN

Y Z

(a) US-SPSW

-.003863 -.002971 -.002079 -.001187 -.295E-03 .597E-03 .001489 .002381 .003273 .004165

(b) CR-SPSW MX MN

MN

MX

Y Z

-.012679 -.009758 -.006837 -.003915 -.994E-03 .004848 .007769 .01069 .013611

MX

Y Z

(c) PR-SPSW1

-.012613 -.009944 -.007275 -.004605 -.001936 .003402 .006071 .00874 .011409

(d) PR-SPSW2

-.011005 -.00862 -.006236 -.003852 -.001467 .917E-03 .003301 .005686 .00807 .010454

MN

Y Z

MX

(e) PR-SPSW3

MN MX

MX

MN

Y Z

(f) PR-SPSW1

-.348E-03 -.221E-03 -.944E-04 .322E-04 .159E-03 .412E-03 .538E-03 .665E-03 .792E-03

Y Z

-.267E-03 -.145E-03 -.233E-04 .988E-04 .221E-03 .465E-03 .587E-03 .709E-03 .831E-03

(g) PR-SPSW2 Fig. 4. The out-of-plane deformation contours of steel plates and ribs (unit: m).

MN

Y Z

(h) PR-SPSW3

-.519E-03 -.351E-03 -.184E-03 -.162E-04 .151E-03 .319E-03 .486E-03 .654E-03 .821E-03 .988E-03

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389

Fig. 5. Dimensions and details of the specimens (a) PR-SPSW and (b) CR-SPSW.

4. Experimental programme

Eqs. (19) and (20) [28,29].

4.1. Design of SPSW specimen

Ic ≥

0:0031tH 4 L

ð19Þ

Ib ≥

0:0031L4 H

ð20Þ

Three 1/3-scale single-bay, two-storey SPSW specimens are constructed and tested. According to the restraining level for the infilled steel plate, the specimens are categorized into unstiffened SPSW (USSPSW), non-welded multi-rib stiffened SPSW (PR-SPSW) and precast concrete panel restrained SPSW (CR-SPSW). Fig. 5 shows the dimensions and details of specimens PR-SPSW and CR-SPSW. The details of the SPSW specimens are summarized in Table 3. The mechanical properties of steel materials are tabulated in Table 4. The upper two stories of the frame are the main structure of the specimen, and the lower lowrise story serves as the fixed end of the upper two stories structure. This can avoid weld cracking-caused structural damage to the column bases. The lower story frame has a net height of 300 mm and the thickness of the steel plate of 5.0 mm. The beam and column sections are designed in accordance with the moment of inertia requirements in

Table 3 Details of SPSW specimens. Specimen

US-SPSW

Column Middle or bottom beam Top beam Beam-column connection Upper end plate Lower end plate Infilled steel plate Stiffener Thickness of stiffener (mm) Ratio of restrained stiffness Weight of stiffener (kg)

HW175 × 175 × 7.5 × 11 HN200 × 100 × 5.5 × 8 HN300 × 150 × 6.5 × 9 End plate −405 × 154 × 20 −250 × 145.5 × 12 3.3 N/A Multiple ribs N/A 60 0 130.5 0 22.0

PR-SPSW

CR-SPSW

where Ic and Ib are the moment of inertia of column and beam, respectively. t is the thickness of the infilled steel plate. H is the axial distance taken perpendicular to the plane of the column web, and L is the axial distance perpendicular to the plane of the beam web. The length of the column at each story is 1350 mm, and the total height is 3270 mm. The design of steel plate and sub-plate is based on the standard JGJ/T380 [30] and is also referred to De Matteis et al. [31]. For the design of bolts, the tensile force in bolts can be assumed to be about 3% of the ultimate in-plane panel shear force [32]. The steel is fabricated by Q235B, and frictional high-strength bolts of 10.9 class are used. The non-welded multiples ribs have a cross section of −60 mm × 6 mm. The lengths of transverse and vertical ribs are 975 mm and 850 mm, respectively. The rib stiffness (i.e. 130.5) fully satisfies the requirement (i.e. 65.7) in Eq. (11), indicating that the buckling of infilled steel plate is confined to cell plates. The infilled steel plates are stiffened by a grid consisting of vertical and horizontal ribs. The ribs form a square with a

Table 4 Mechanical properties of steel materials.

Precast concrete panel 60 813.9 131.2

Materials

fy (MPa)

fu (MPa)

Elongation

E (GPa)

Steel plate Rib Sub-plate Tube

345.27 335.07 276.30 294.39

521.80 463.07 399.90 492.59

36% 37% 50% 44%

210 192 200 205

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C30 concrete is used for precast concrete panels. The arrangement of bolt and reserved holes of the precast concrete panels is consistent with that in specimen PR-SPSW. The M12 bolts are adopting for fixing the precast concrete panels. The restraining stiffness of the concrete panel satisfies the requirement specified in Eq. (18). Thus, the overall elastic buckling of specimen CR-SPSW can occur only after the shear yielding of infilled steel plates. Based on the dimensions of stiffeners and their material properties, specimen PR-SPSW is 83.2% lighter than that of specimen CR-SPSW. Although it has a higher material cost, multi-rib stiffeners can save the installation cost and reduce the foundation cost due to their light weight. In addition, weight of SPSWs alters the seismic responses of the whole structure system, which may also affect the overall cost of SPSW structures.

4.2. Test setup and loading sequence

Fig. 6. Test setup and instrumentation for SPSWs.

side length of 230 mm, and a round tube with an inner diameter of 26 mm is welded to their corners. The spacing of ribs (i.e. 69.7) meets the requirement (i.e. 93.2) specified in Eq. (14). Thus, the out-of-plane buckling of the infilled steel plate is expected to be avoided in the elastic stage. The size of the precast concrete panel is 975 mm × 850 mm × 60 mm, and its thickness is equal to the width of the rib belt. The

The test setup and instrumentations for testing SPSW structure is shown in Fig. 6. Vertical loads are applied by two 2000 kN synchronous hydraulic jacks. To maintain the same shear force in the two-floor structure, the members are provided with a loading end matched to the size of the actuator at the one end of the top beam, and a 1000 kN actuator is used to apply a horizontal cyclic load (or displacement). The specimen was subjected to load control before yielding, and the displacement control was then adopted after yielding of specimen. For the vertical load, a load of 430 kN was applied to the top of each column. The loading was applied in two levels, i.e. 215 kN at each level. The horizontal load was applied by two stages, i.e. elastic and yielding stages. The horizontal load was first applied in force-control mode with a 100 kN increment at each level, and each level was cycled thrice. After the specimen yielded, horizontal loading was controlled through the displacement mode, and was applied at 1.0, 1.5, 2.0 … 0.5n times of the yield displacement, and each level was cycled twice [33]. The test was stopped when the horizontal load dropped to 85% of the maximum load.

Fig. 7. Failure modes of specimens (a) US-SPSW, (b) PR-SPSW, and (c) CR-SPSW.

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in Fig. 7(b). Specimen PR-SPSW failed with bending-torsional buckling of columns and in-plane shear of steel plates.

5. Test results and discussion 5.1. General behaviour and failure modes 5.1.1. Specimen US-SPSW The out-of-plane deformation of steel plate at the 1st floor occurs when the drift ratio reaches 0.16% in specimen US-SPSW. The tensile stress fields subsequently form along the diagonal direction in firststory steel plate at the drift ratio of 0.3%. When unloading to the zerodisplacement point, out-of-plane deformation of steel plate causes loud banging sounds and can be restored. When the drift ratio reaches 0.47%, the steel plate exhibits a slight residual deformation in the diagonal directions. Yield of column is found when the horizontal load reaches 439.02 kN at the drift ratio of 0.49%. After specimen US-SPSW enters the yielding stage with the development of residual deformation of steel plate, the sound of buckling of steel plate gradually weakens. The number of buckling waves keeps increasing as horizontal load increases. When the drift ratio reaches 1.1%, the west column at the 1st floor exhibits local bucking at inner flange. The specimen attains the loading capacity of 724.85 kN at the drift ratio of 1.3%–1.5%. The steel plate at the 1st floor is torn in many locations, and residual deformation of the steel plate at the 2nd floor is also observed. With increasing the horizontal load, the steel plate gradually yields under the action of tensile stress field. When the drift ratio increases to 2.0%, the plastic hinges form at the ends of columns, followed with the in-plane bending-shear failure of specimen US-SPSW as shown in Fig. 7(a). 5.1.2. Specimen PR-SPSW The column in specimen PR-SPSW enters the yielding stage at the horizontal load of 544.93 kN when the drift ratio reaches 0.61%. Local bucking of steel plate occurs in several cells at the drift ratio of 1.2%. At this stage, the low-amplitude buckling within the thickness of the multiple ribs can be effectively suppressed, while the loading capacity remains at a certain level. The steel plate continues to bear the increasing horizontal load with the action of tensile stress fields. The specimen PR-SPSW attains the loading capacity of 906.47 kN at the drift ratio of 1.7%. As compared with specimen US-SPSW, the loading capacity of specimen PR-SPSW is increased by 25.06%. A slight tear of steel plates is observed in the two upper corners of steel plate at the 1st story. Meanwhile, residual deformation of steel plate at the 2nd floor is obvious while the rotation of beam-column connections is marginal. With the increasing horizontal load, the steel plate gradually yields under the action of tensile stress filed. Similar to specimen US-SPSW, the plastic hinges form at the ends of columns at the drift ratio of 2.0% as shown

Load (kN)

500

-2.2

-1.1

Drift ratio (%) 0.0 1.1

2.2

3.3

US-SPSW PR-SPSW CR-SPSW

Fig. 8 shows the load-displacement hysteretic curves for all SPSW specimens. It is readily seen that the hysteretic curve of specimen USSPSW exhibits more obvious pinching phenomenon than those of specimens PR-SPSW and CR-SPSW. For specimen US-SPSW, the horizontal load in linear to horizontal displacement of the SPSW structure at the initial stage of loading. After the specimen US-SPSW yields, the unloading stiffness of the specimen is slightly lower than its elastic stiffness. The hysteretic loop shows an obvious reverse-S shape with a slight pinching phenomenon. With the contribution of infilled steel plate, the presence of cracks does not significantly decreases the loading capacity of SPSW structure. Under the combined action of axial load, bending and shear, the loading capacity of SPSWs decreases at the advanced stage of loading. Both specimens PR-SPSW and CR-SPSW have a similar hysteretic behaviour. Similar to specimen US-SPSW, the horizontal load is linear to the horizontal displacement at the initial stage of loading. The enclosed area of the hysteretic loop is very small, and the unloading stiffness of the specimens is almost the same as their elastic stiffness. As the drift ratio increases, both specimens enter the elasto-plastic stage and the

-3.3 1000

500

0

-500

-1000 -90

5.2. Hysteretic behaviour and loading capacity

Load (kN)

-3.3 1000

5.1.3. Specimen CR-SPSW At the elastic stage, the horizontal load is mainly resisted by the shear stress fields of the infilled steel plate in SPSWs. When the drift ratio increases to 0.5%, the steel plate at the 1st floor starts to yield. The column enters yielding stage at the horizontal load of 546.81 kN at the drift ratio of 0.61%. The elastic buckling of steel plate is restrained by the concrete panels, resulting in a low-amplitude bucking of steel plates. However, the loading capacity of specimen CR-SPSW keeps at the similar level as that of specimen PR-SPSW. The steel plate is able to bear the increased horizontal load with the effect of plane shear stress fields. The specimen CR-SPSW attains the maximum load of 895.89 kN at the drift ratio of 1.4%, which is increased by 23.60% as compared with that of specimen US-SPSW. The steel plate buckles at the nonrestrained area of the steel plate, e.g. the gap between concrete panel and the columns. This leads to the crushing and partial destruction of concrete panels. At the drift ratio of 1.9%, plastic hinges form at the ends of columns as shown in Fig. 7(c). The failure mode of specimen CR-SPSW is dominated by the bending-torsional buckling of columns and in-plane shear of steel plates.

-2.2

Drift ratio (%) 0.0 1.1

2.2

3.3

-30 0 30 Displacement (mm)

60

90

-1.1

US-SPSW PR-SPSW CR-SPSW

0

-500

-60

-30 0 30 Displacement (mm)

(a)

60

90

-1000 -90

-60

(b)

Fig. 8. Hysteretic curves of the samples: (a) whole loading cycles, and (b) first cycle.

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infilled steel plates start to yield. During the plastic stage of loading, the enveloped area of the hysteretic loops gradually expands, and the unloading rigidity is lower than the elastic rigidity. When unloading to zero and loading in the reverse direction, there is an obvious stiffness degradation of SPSWs. At the advanced stage of loading, the stiffness of specimens PR-SPSW and CR-SPSW degrade faster than that of specimen US-SPSW. In summary, specimen PR-SPSW can achieve a comparable hysteretic behaviour to specimen CR-SPSW. Envelops of hysteretic curves for specimens US-SPSW, PR-SPSW and CR-SPSW are plotted in Fig. 9. Summary of test results of the specimens are given in Table 5. Ductility of specimen is calculated as the ratio of ultimate drift to yield drift. The averaged ultimate drift of specimen USSPSW is 2.38% while that of specimen CR-SPSW is around 1.75%. This is mainly attributed to the installed stiffeners which postpone the buckling of steel plates, in turns to change the stress statuses of steel plates from tension to plane shear. As a result, the lateral loading capacity of SPSW structure is enhanced. However, this also increases the force demand on the columns as additional forces transfer to the columns. Premature buckling of columns decreases the deformation capacity of SPSW structures. As seen in Table 5, the yield capacity of specimen PR-SPSW is reduced by 1.3% as compared with that of specimen CR-SPSW and is increased by 18.8% as compared with that of specimen US-SPSW. The ultimate loading capacity of PR-SPSW is reduced by 1.0% and increased by 23.7% as compared with those of specimens CR-SPSW and US-SPSW, respectively. The loading capacity of specimen PR-SPSW is almost the same as that of specimen CR-SPSW. It can be concluded that the use of unbonded multiple ribs can contribute the similar enhancement to SPSWs as precast concrete panel. The installation of non-welded multi-rib stiffeners or precast concrete panel decreases the displacement ductility of SPSW structure. The displacement ductility coefficients of specimens PR-SPSW and

-1.1

Drift ration(%) 0.0 1.1

2.2

3.3

NR-SPSW PR-SPSW CR-SPSW

500 Load (kN)

-2.2

5.3. Energy dissipation and stiffness degradation Energy dissipation is calculated by the area enclosed in each load– displacement loop. Fig. 10 shows the cumulative energy dissipation of SPSWs under different drift ratios. At the initial stage of loading (e.g. before 1.0% drift), specimen CR-SPSW dissipates higher energy than other two specimens. This is mainly attributed to the more effective restraining effect of precast concrete panels for the steel plates. Afterwards, both specimens with stiffeners exhibit higher energy dissipation capacities than that without stiffener under the same drift. However, specimen CR-SPSW with precast concrete panel fails at the early stage and cannot dissipate energy at the advanced stage of loading (i.e. after 1.6% drift). The ultimate energy dissipation of specimen PR-SPSW is 47.8% higher than that of CR-SPSW and 47.3% higher than that of specimen US-SPSW. It indicates that specimen PR-SPSW possesses the best energy dissipation capacity as compared with specimens CR-SPSW and US-SPSW.

100000

Energy dissipation (kNmm)

-3.3 1000

CR-SPSW are 7.6% and 25.2% lower than that of specimen US-SPSW. This is mainly attributed to the rapid decrease in stiffness after reaching the peak load, which is caused by the buckling of multiple ribs and cracking of precast concrete panels. For the SPSWs with different degrees of restraints, specimen PR-SPSW exhibits the larger displacement ductility coefficient than that of specimen CR-SPSW. For instance, the ductility of specimen PR-SPSW is 23.6% higher than that of specimen CR-SPSW. Cracking of precast concrete panels accelerates the stiffness degradation of specimen CR-SPSW. Moreover, the columns in specimen PR-SPSW is prevented from completely buckling, which ensures the ductility of the structure. In summary, specimen PR-SPSW exhibits reasonable ductility and loading capacity as compared with other two SPSWs.

0

60000 40000 20000 0 0.0

-500

-1000 -90

-60

-30 0 30 Displacement (mm)

60

US-SPSW PR-SPSW CR-SPSW

80000

90

0.5

1.0 1.5 2.0 Drift angle (%)

70 US-SPSW PR-SPSW CR-SPSW

Table 5 Summary of test results of all specimens.

US-SPSW

PR-SPSW

CR-SPSW

Push Pull Ave. Push Pull Ave. Push Pull Ave.

Yield

Peak

Load (kN)

Drift

Load (kN)

Drift

493.90 487.59 490.75 580.06 585.91 582.99 592.82 587.94 590.38

0.46% 0.53% 0.49% 0.45% 0.48% 0.47% 0.52% 0.44% 0.48%

691.54 724.85 708.20 845.86 906.47 876.17 874.25 895.89 885.07

1.35% 1.52% 1.43% 1.45% 1.72% 1.59% 1.37% 1.38% 1.37%

Ultimate drift

2.27% 2.56% 2.38% 2.00% 2.17% 2.08% 1.79% 1.72% 1.75%

Ductility

4.98 4.79 4.88 4.44 4.59 4.51 3.43 3.87 3.65

Stiffness (kN/mm)

60

Dir.

3.0

Fig. 10. Energy dissipation of SPSWs.

Fig. 9. Envelops of hysteretic curves of SPSW structures.

Specimen

2.5

50 40 30 20 10 0 0.0

0.5

1.0 1.5 2.0 Drift angle (%)

Fig. 11. Stiffness degradation of SPSWs.

2.5

3.0

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(a) Deformed steel plate at the 1st floor of US-SPSW

(b) Deformed steel plate at the 1st floor of PR-SPSW

(c) Concrete cover panel at the 1st floor of CR-SPSW

(d) Concrete cover panel at the 2nd floor of CR-SPSW

(e) Deformed steel plate at the 1st floor of CR-SPSW

(f) Deformed steel plate at the 2nd floor of CR-SPSW

Fig. 12. Out-of-plane ultimate deformations of steel plates in specimens (a) US-SPSW, (b) PR-SPSW, and (c) CR-SPSW.

-1.0

-0.5

1.5

2.0

1.5 300kN 400kN 450kN

-40 -20 0 Column deflection (mm)

-1.5

-1.0

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0.0

0.0

3.0

2.0 1.5 300kN 400kN 450kN

1.0

2.0 1.5

300kN 400kN 450kN 500kN

1.0

0.0 -60

20 40 60 Column deflection (mm)

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(a) -2.0

3.0

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-0.5

1.5 1.0

0

0.0 0

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3.0

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2.5

1.5 1.0

300kN 400kN 500kN 600kN

1.0

1.5

2.0

2.0 1.5 1.0

300kN 400kN 500kN 600kN

0.5

0.5 0.0 -60

0.5

2.5

2.0

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0

(c)

0.0 0

1.5

2.0

2.0

(b) Drift ratio(%)

1.0

300kN 400kN 450kN 500kN

0.5

0.5

0.0 0

Drift ratio(%)

0.5

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2.5

0.5

0.5

Drift ratio(%)

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3.0

Column height (m)

Column height (m)

Column height (m)

1.0

2.5

2.0

0.0 -60

0.5

3.0

2.5

1.0

Drift ratio(%)

0.0

0.0

Column height (m)

Drift ratio(%)

-1.5

Column height (m)

-2.0

3.0

20 40 60 Column deflection (mm)

Fig. 13. Overall deformations of columns of specimens (a) US-SPSW, (b) PR-SPSW, and (c) CR-SPSW.

20 40 60 Column deflection (mm)

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Stiffness at different drift ratio is calculated based on the secant slope of a line passing through the peak loads in a hysteretic loop. Fig. 11 shows the peak stiffness degradation of SPSWs against drift. All of specimens have the similar initial stiffness and degrade rapidly when the drift ratio reaches 0.2%. However, both specimens with stiffeners show higher stiffness than specimen US-SPSW at various drift ratios. It demonstrates that both non-welded multi-rib stiffeners and precast concrete panels are effective in enhancing the stiffness of SPSW structure. Comparing with SPSW with non-welded multiple ribs, SPSW stiffened by precast concrete panel exhibits slightly higher stiffness at the drift ratio between 0.20% and 1.2%. Similarly, precast concrete panel attached to the steel plate is more effective to restraining stiffness degradation as compared with the non-weld multi-rib stiffeners. As the occurrence of concrete crushing, stiffness of specimen CR-SPSW degrades quickly and is equal to that of specimen PR-SPSW at the drift ratio of 1.5%. 5.4. Out-of-plane deformation of steel plates The out-of-plane deformed shapes of the infilled steel plates in specimens US-SPSW, CR-SPSW and PR-SPSW are shown in Fig. 12. Precast concrete panels in specimen CR-SPSW are also included in Fig. 12. As seen in Fig. 12(a), there are two diagonal buckling belts and several local tears in the steel plate of specimen US-SPSW. The out-of-plane deformation of the steel plate in specimen US-SPSW is 92 mm. For the specimen PR-SPSW, cross-type low-wave buckling deformation in 1.25

1.00

300kN 400kN 450kN

0.75 0.50 0.25

Column height (m)

Column height (m)

1.25

0.00 -10 -8 -6 -4 -2 0 Column deflection (mm)

1.00 0.75

0.25 0

2 4 6 8 10 Column deflection (mm)

0.75 0.50 0.25

Column height (m)

Column height (m)

1.25 300kN 400kN 450kN 500kN

0.00 -10 -8 -6 -4 -2 0 Column deflection (mm)

1.00 0.75 0.50 0.25 0.00

0

2 4 6 8 10 Column deflection (mm)

0

2 4 6 8 10 Column deflection (mm)

(b) 1.25

1.00

300kN 400kN 500kN 600kN

0.75 0.50 0.25 0.00 -10

Column height (m)

Column height (m)

1.25

1.00 0.75 0.50 0.25 0.00

-8 -6 -4 -2 0 Column deflection (mm)

Direction

Column

δi (mm)

δi/L

δi/δUS-SPSW

US-SPSW

Push Pull Push Pull Push Pull

East West East West East West

−7.69 7.38 −2.92 2.85 −2.51 1.05

−0.61% 0.59% −0.23% 0.23% −0.20% 0.08%

1.00 1.00 0.38 0.39 0.33 0.14

PR-SPSW CR-SPSW

each cell and single-oblique low-wave buckling deformation within the edge plates are observed as seen Fig. 12(b). The maximum out-ofplane deformation of the steel plate in specimen PR-SPSW is 28 mm. It can be found that the maximum out-of-deformation of steel plate is reduced by 69.6% after installing the non-welded multi-rib stiffeners. For specimen CR-SPSW, concrete crushing occurs at both bottom corners of the concrete panel at the 1st story (as shown in Fig. 12(c)) while minor cracks are observed at the bottom corner of concrete panel at the 2nd story (Fig. 12(d)). It implies that the concrete cover panels work well with the steel plates. The deformation of steel plate concentrates at the bottom corners and the maximum out-of-plane deformation is around 31 mm as shown in Fig. 12(e). This is slightly larger than that of specimen PR-SPSW. However, the deformation area in specimen CR-SPSW is much smaller than that in specimen PR-SPSW. For instance, the steel plate at the 2nd floor is almost without obvious out-of-plane deformation as shown in Fig. 12(c). The buckling form in SPSWs transforms from the high-wave-low order in specimen PR-SPSW to the low-wave-high order in specimen CR-SPSW.

5.5. Overall and local deformations of columns in SPSWs

(a) 1.00

Specimen

0.50

0.00

1.25

Table 6 Inward deformations of columns at the 1st floor.

(c) Fig. 14. Local deformations of the columns at the first story of specimens (a) US-SPSW, (b) PR-SPSW, (c) CR-SPSW.

Fig. 13 shows the overall deformation of the columns for specimens US-SPSW, PR-SPSW and CR-SPSW during the loading process. Fig. 14 presents the local deformation of columns during the loading stages. Here, the symbols “+” and “–” in figures represent the specimen subjected to push and pull loads, respectively. Both east and west columns in all specimens under push or pull load exhibit similar deformation as seen in Fig. 13. At the initial stage of loading, deformations of the columns increase linearly along the column height and are mainly shear deformation. When SPSW structure reaches the yielding displacement, the columns exhibit a certain level of inward deformation with increasing tension forces in the infilled steel plates. The overall deformation of the columns transforms from the shear type to the bending-shear type. When the SPSW structure reaches three times of yield displacement, deformation of columns in both specimen PR-SPSW and CR-SPSW are still linear and are dominated by the shear mode. Therefore, both non-welded multi-rib stiffeners and precast concrete panel have the similar influence on the overall deformation of columns in the SPSWs. As seen in Fig. 14, specimen US-SPSW exhibits significant local deformation in the columns as the infilled steel plates buckle at the horizontal load of 300 kN. This is mainly attributed to the forces transferred from tensile stress fields in the steel plate to the columns. Differently, there is no obvious inward deformations occurred in columns of specimens PR-SPSW and CR-SPSW. The use of non-welded multiple ribs and precast concrete panel restrain the buckling deformation of the steel plate, which minimizes the tensile forces transferred to the columns. Table 6 summaries the inward deformation of columns at the lateral drift of 2.0%. In general, the inward deformations of columns in both specimens PR-SPSW CR-SPSW are around 40% of those in specimen US-SPSW. This also confirms the serious buckling failure of columns in specimen US-SPSW. Both specimens with different stiffeners show similar inward deformations in the columns, demonstrating that non-welded multiple ribs and precast concrete panels have similar effect on controlling the inward deformation of columns.

J.-G. Yu et al. / Journal of Constructional Steel Research 159 (2019) 384–396

5.6. Rotations of beam-column connections in SPSWs

connections TW2, TW5 and TW7 are 0.027, 0.040 and 0.018 rad, respectively. It can be found that the maximum rotation of beam-column connection at the first story in specimen PR-SPSW is 50% lower than that of specimen US-SPSW. Similarly, the maximum rotation of beam-column connections TW2, TW5, and TW7 in specimen CR-SPSW are 0.02, 0.0055, and 0.0031 rad, respectively. The maximum rotation of beamcolumn connection at the first story in specimen CR-SPSW is 94% lower than that of specimen US-SPSW. It reflects that the beamcolumn connections in SPSWs with both types of stiffeners exhibit slightly degradation in stiffness. The installed non-welded multi-rib and precast concrete panel are effective in restraining the deformation of beam-column connections in the SPSWs. For SPSWs with stiffeners, rotations of beam-column connections in SPSWs with precast concrete panels are slightly larger than those in SPSWs with multi-rib stiffeners. This is mainly attributed to the partially existence of non-welded multi-rib stiffeners in specimen PR-SPSW. As the local buckling of the steel plate occurs, the multi-rib stiffeners in specimen PR-SPSW fail to bear the tension forces due to detachment of the multi-rib from the infilled steel plates. The tension forces in the steel plates are eventually transferred to the frame, causing a certain influence on the rotation of beam-column connections. Differently, the precast concrete panels in specimen CR-SPSW completely eliminate the tension forces transferred from the steel plate to the frame, which continuously exerts an axillary effect on the corner of steel plate to the beam-column connections. As a result, the rotations of beam-column

900

900

600

600

600

300

300

300

0 -300

Load (kN)

900

Load (kN)

Load (kN)

Fig. 15 shows the rotations of beam-column connections at each floor for specimens US-SPSW, PR-SPSW and CR-SPSW. Three typical beam-column connections at different stories are selected for analysis. It is readily seen that the deformations of beam-column connections in specimen US-SPSW are much higher than those in specimens PRSPSW and CR-SPSW. At the initial stage of loading, the rotations of beam-column connections are consistent and marginal. The infilled steel plates in SPSW structure are able to restrain the deformations beam-column connections, which is known as the axillary effect. At the advanced stage of loading, rotations of beam-column connections in SPSW structure increase as drift ratio increases, particularly for specimen US-SPSW. The maximum rotations of beam-column connection at the 1st, 2nd and 3rd floors in specimen US-SPSW are 0.11 rad, 0.084 rad and 0.041 rad, respectively. This is mainly attributed to the weakened axillary effect of the infilled steel plates on beam-column connections, associated with the buckling and cracking of infilled steel plates in specimen US-SPSW. In addition, formation of diagonal tension field in the steel plates causes additional forces applied to the beam-column connections, which also increases the rotations of beam-column connections. With the stiffeners installed on infill steel plates, rotations of beamcolumn connections in both specimens PR-SPSW and CR-SPSW are confined to 0.04 rad. For instance, the maximum rotations of beam-column

395

0 -300 -600

-600 -900 -0.12

TW2 -0.08

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0.08

0.12

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0.08

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0.12

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Load (kN)

Load (kN)

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TW7 0.12

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600

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0

TW5 -0.08

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0.08

0.12

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TW7 -0.08

(c) Fig. 15. Rotations of beam-column connections for specimens (a) US-SPSW, (b) PR-SPSW, and (c) CR-SPSW.

-0.04 0.00 0.04 Rotation angle (rad)

0.08

0.12

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connections are well restrained, even at the advanced stage of loading. Generally, precast concrete panels installed on the steel plates are more effective in restraining the rotations of beam-column connections in SPSWs than the multi-rib stiffeners. 6. Conclusions This paper investigated the cyclic performance of SPSWs with different levels of restraints. A finite element analysis and experimental study on the performance of SPSW structure with three levels of restraints are conducted. Based on the numerical and test results, the following conclusions can be drawn. (1) The out-of-plane deformation of steel plates in SPSW structure decreases as the restraining stiffness for steel plates increases. Both SPSWs with non-welded multi-rib stiffeners and precast concrete panels exhibit the similar out-of-plane deformations around 30 mm for the steel plates, which is 30% of that of SPSWs without stiffener. The deformation mode of steel plate transforms from the high-wave-low order to the low-wavehigh order, while the location of maximum deformation shifts from the middle to the corner of steel plates. (2) The installation of multi-rib stiffeners or precast concrete panels on steel plates can improve the seismic performance of SPSWs in terms of loading capacity, energy dissipation and stiffness degradation. The loading capacity of specimens PR-SPSW and CR-SPSW are 23.7% and 25.0% higher than that of specimen USSPSW, respectively. The specimen PR-SPSW exhibits the highest energy dissipation, which is 47.8% and 47.3% higher than those of specimens CR-SPSW and US-SPSW, respectively. (3) The use of multi-rib stiffeners or precast concrete panels on steel plates decreases the inward deformation of the columns and rotation of beam-column connections in SPSWs. The inward deformations of columns in specimens PR-SPSW and CR-SPSW are around 40% of those in specimen US-SPSW. The maximum rotations of beam-column connection at the first story in specimen CR-SPSW and PR-SPSW are 94% and 50% lower than that of specimen US-SPSW, respectively. Besides, the axillary effect on beam-column connections can be also strengthened by installing stiffeners on steel plates. (4) The ductility of specimen PR-SPSW is 23.6% higher than that of specimen CR-SPSW. The weight of multi-rib stiffeners is 83.2% lower than that of precast concrete panels, which is also beneficial to improve the seismic behaviour of SPSW structures. Thus, the use of non-welded multi-rib stiffeners is recommended for restraining the steel plates in SPSWs. Acknowledgements The authors wish to acknowledge the financial support from the National Natural Science Foundation of China, Young Scientists (Grant Nos.: 51708306 and 51408461), Zhejiang Provincial Natural Science Foundation of China (Grant No.: LGF19E080008) and Ningbo Natural Science Programme (Grant No: 2018A610354). Special thanks are also extended to the support of the State Key Laboratory at Xi'an University of Architecture & Technology. References [1] L.J. Thorburn, G.L. Kulak, C.J. Montgomery, Analysis of Steel Plate Shear Walls, Structural Engineering Report No. 107, University of Alberta, Canada, 1983. [2] J.G. Yu, X.T. Feng, B. Li, J.P. Hao, A. Elamin, M.L. Ge, Performance of steel plate shear walls with axially loaded vertical boundary elements, Thin Wall Struct. 125 (2018) 152–163.

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