Compressive behaviours of novel SCS sandwich composite walls with normal weight concrete

Thin-Walled Structures 141 (2019) 119–132

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Full length article

Compressive behaviours of novel SCS sandwich composite walls with normal weight concrete

T

Jia-Bao Yana, Zhe Wanga, Yun-Biao Luoa,∗, Tao Wangb a b

School of Civil Engineering / Key Laboratory of Coast Civil Structure Safety of Ministry of Education, Tianjin University, Tianjin, 300350, China Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, CEA, Harbin, 150080, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Composite shear wall Sandwich composite wall Immersed tunnel Arctic protective structure Compression test Theoretical analysis

Novel steel-concrete-steel (SCS) sandwich composite walls with normal weight concrete (NWC) and J-hook connectors have been proposed for shear walls in buildings and protective walls in Arctic offshore platforms. Eight SCS sandwich walls with J-hook connectors and NWC were tested under monotonic compression. Investigated parameters in this testing programme included thickness of steel faceplate, spacing of J-hook connectors, strength of NWC core, and different types of connectors. Based on the reported test results, the influences of these parameters were analysed and discussed. Theoretical models were developed to predict compressive resistance of SCS sandwich walls with different types of connectors. The developed analytical models considered the confinement of steel faceplate on compressive strength of concrete core and proposed new buckling length coefficient for steel faceplate in SCS sandwich wall. The accuracies of the proposed analytical models were checked through validations against 50 test results reported by authors and other researchers. Finally, step-by-step design procedures were proposed to determine compressive resistance of SCS sandwich walls with different types of shear connectors.

1. Introduction A typical steel-concrete-steel (SCS) sandwich composite structure usually consists of two external layers of steel faceplates and a sandwiched concrete core. Cohesive materials or shear connectors are widely used to connect external steel faceplates to the concrete core that maintain the composite action and integrity of the SCS sandwich structure. Extensive advantages received from SCS sandwich structures include savings of formwork and site construction labour force, increased construction efficiency, reductions in detailing of reinforcement, improvements on structural performances subjected to static and dynamic loadings [1–3]. This type of structure exhibits versatile engineering applications as shear walls in high-rise buildings, shielding walls in nuclear facilities, offshore platform decking, bridge decking, protective structures, immersed tunnels, and ice-resistant walls for the Arctic offshore structures (see Fig. 1) [2,3]. Different types of steel-concrete-steel (SCS) sandwich walls have been developed for engineering constructions. Wright [4] and Wright and Gallocher [5] developed the SCS sandwich walls using the profiled steel sheeting for low-story buildings. Their full-scale tests showed that the developed SCS sandwich walls offered excellent bending stiffness. However, the weak bonding at steel-concrete interface led to early

∗

buckling of the steel sheeting that compromised the compressive and bending resistances of the SCS sandwich walls. Xie et al. [6] developed the “Bi-steel” type of SCS sandwich wall that utilized the friction welding to connect the through-thickness-straight bars to the two external steel faceplates. These friction-welded connectors were proved to provide effective bonding between steel faceplates and the concrete core. However, the friction welding equipment limited the SCS sandwich wall within a thickness of 200–700 mm that limits its applications as the shear wall. Wright and Oduyemei [7] and Wright et al. [8] proposed SCS sandwich elements (beams and walls) with headed studs. They have carried out full-scale tests on the SCS sandwich elements with overlapped headed studs under compression and bending. The test results showed that this type of SCS sandwich structures exhibited good structural performances under compression and bending. Seo et al. [9], and Choi and Han [10] also developed the SCS sandwich walls with headed studs for nuclear facilities, and they have also studied compressive behaviours of these SCS sandwich walls by tests and analysis methods. Yan et al. [11] continued the studies on the compressive behaviours of the SCS sandwich walls with headed studs. Recently, SCS sandwich walls with headed studs have been developed for the nuclear power plant [12,13]. These nuclear SCS sandwich walls with a typical thickness of 0.6–1.5 m were used to resist the seismic forces, offer

Corresponding author. E-mail address: [email protected] (Y.-B. Luo).

https://doi.org/10.1016/j.tws.2019.01.051 Received 20 September 2018; Received in revised form 1 December 2018; Accepted 21 January 2019 Available online 17 April 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

fc f ys ts Δu Δ85%

= Bearing area of the headed stud under tension The projected area of conical concrete breakout failure surface Ac = Cross-sectional area of the concrete core = Cross sectional area of steel faceplate in SCS sandwich Ast wall = Thickness of concrete core in SCS sandwich wall Dc DI = Ductility index of SCS sandwich wall K e = P0.3/Δ0.3 initial stiffness of the SCS sandwich wall under compression = Ultimate compressive resistance of SCS sandwich wall Pu Nc = Ultimate compressive resistance of concrete core in sandwich wall by theoretical models Ns = Ultimate compressive resistance of steel faceplate in sandwich wall by theoretical models Nu = Ultimate compressive resistance of SCS sandwich wall by theoretical models S = Average spacing of the shear connectors in the SCS sandwich wall = Concrete breakout resistance of the shear connector TCB TH = Tensile resistance of the connectors = Pullout resistance of the shear connector Tpl Tps = Punching shear failure resistance of the steel face plate = Tensile fracture resistance of the steel shank of the Ts connector d Diameter of shear connector

Abrg AN

=

αs

εcr γc γM0 γM2 λ

σc σcr

σh

= Compressive strength of concrete cylinder = Yield strength of the steel plate = Thickness of the steel face plate in SCS sandwich wall = Deflections corresponding to Pu = Displacements corresponding to 85% Pu during the recession stage = shear yielding coefficient of concrete, and herein equals to 0.19 = Critical buckling strain of the steel faceplate under compression = Partial safety factor for concrete = Partial factor for steel = Partial factor for connector and may be taken as 1.25 = Strength enhancing coefficient varying from 1.15 to 1.30 = The ultimate compressive stress of the concrete = Critical buckling stress of the steel faceplate under compression = Confining stress acting on the concrete core side surface

Abbreviations COV DI SCS Stdev

coefficient of variation ductility index Steel-Concrete-Steel standard deviation

the ice-resistant walls with this novel SCS sandwich structure for the gravity based offshore platforms [30,31]. Considering these novel SCS sandwich walls are mainly developed for gravity based SCS sandwich platforms, normal weight concrete (NWC) is chosen for the novel SCS sandwich walls. However, the information on the novel SCS sandwich walls with NWC and J-hook connectors is still quite limited. Thus, compressive behaviours of this novel SCS sandwich walls need to be well understood. This paper makes efforts to develop ice-resistant walls for the Arctic platforms using novel SCS sandwich walls with J-hook connectors and NWC. The ultimate compressive behaviours of novel SCS sandwich walls with J-hook connectors and NWC were studied through an eightspecimen test program. The test results of the eight specimens reported the ultimate resistance and failure modes of SCS sandwich walls with Jhook connectors and NWC subjected to in-plane compression. This paper also reported the influences of different parameters on compressive behaviours of SCS sandwich walls with J-hook connectors and NWC. The investigated parameters included thickness of steel faceplate, compressive strength of the NWC core, spacing of the connectors, and different types of the connectors. Theoretical models were also developed to predict the ultimate compressive resistance of the novel SCS sandwich walls with J-hook connectors and NWC. Finally, conclusions were drawn based on these experimental and analytical studies.

shielding of radiation, and provide protections against impact and blast loads [12–16]. In these nuclear SCS sandwich walls, headed studs and linking steel bars were used to resist the steel-concrete interfacial shear force and separation, respectively. Nie et al. [17,18], Hu et al. [19,20], and Ji et al. [21,22] developed the SCS shear walls with headed studs for the high-rise buildings to resist the horizontal seismic force and wind loads. However, it should be noted that the composite action of SCS sandwich walls greatly depended on the tensile resistance of the headed stud embedded in the concrete [23]. If these overlapped headed studs were embedded with insufficient depth, they tend to fail in breakout or pullout mode that would resulted in splitting failure of the concrete core. Choi and Han [10] have also reported this splitting failure in the concrete core of the SCS sandwich walls. Novel SCS sandwich walls with J-hook connectors (see Fig. 1) overcome the separation problem in sandwich walls with headed studs and limitations on the thickness of Bi-steel type of SCS sandwich walls [24,25]. Moreover, the J-hook connectors were made of plain reinforcements that significantly reduces the costing of the SCS sandwich walls. Previous studies on novel SCS sandwich structures with J-hook connectors mainly focused on their offshore applications as slim platform deck and ship hulls [2,24,25]. Thus, lightweight concrete or ultralightweight composite materials with densities of 1200 kg/ m3∼1800 kg/m3 were used to reduce the self-weight of the SCS sandwich structures [24–27]. Liew and Sohel [25], Yan et al. [27], and Sohel et al. [28] carried out full-scale tests to investigate the static behaviours of this novel SCS sandwich beam under out-of-plane bending. The dynamic behaviours of SCS sandwich beams with J-hook connectors have been experimentally and analytically studied by Liew et al. [26]. Kang [3] and Dai and Liew [29] investigate their impact and fatigue behaviours. The dynamic behaviours of SCS sandwich walls with J-hook connectors were reported by Sohel and Liew [2]. It can be seen that most of these previous studies on the novel SCS sandwich walls with J-hook connectors mainly focused on their out-of-plane static or dynamic loadings. This paper continued previous studies on the novel SCS sandwich walls with J-hook connectors, and developed

2. Testing programme 2.1. Description of the specimens This test program consists of seven SCS sandwich walls with J-hook connectors, i.e., W1∼W7 and one specimen with overlapped headed studs, namely W8. Each specimen consists of two external steel faceplates with welded J-hook connectors or headed studs, concrete core, top and bottom endplate, and stiffeners. Fig. 2 shows the fabrication procedures of the SCS sandwich wall with J-hook connectors as the following; 120

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sandwich walls, W1-3 were designed with steel faceplates in different nominal thickness of 2.8 mm, 4.6 mm, and 5.9 mm that correspond to the cross-sectional steel content of 5.9%, 9.3%, and 11.6%, respectively. W1, W4, and W5 were designed with J-hook connectors in different spacing of 75 mm, 100 mm, and 150 mm that corresponds to the slenderness ratios of the steel faceplate of 26.8, 35.7, and 53.6, respectively. In addition, the spacing of connectors in steel faceplates determines the cross-sectional composite action of SCS sandwich wall and buckling resistances of steel faceplates. In order to study the influence of the strength of the concrete core on compressive behaviour of novel SCS sandwich walls, W1, W6, and W7 were designed with C40, C30, and C50 grade of NWC, respectively. Table 1 lists the mix proportions of these three grades of NWC. Finally, in order to check the influences of different types of connectors on compressive behaviours of novel SCS sandwich walls, W1 and W8 adopted J-hook connectors and overlapped headed studs, respectively. Grade Q235 mild steel plates were used in specimens W1eW8. Their elastic modulus, yield strength and ultimate strength are 202 GPa, 235 MPa, and 350 MPa, respectively. Mild steel plain reinforcements were used to fabricate the J-hook connectors in W1eW7, and Fig. 3 shows their geometric details. The elastic modulus, yield and ultimate strength of the J-hook connectors are 200 GPa, 330 MPa, and 450 MPa, respectively. Headed studs were used in W8, and their diameter and height are 10 mm and 90 mm, respectively. The elastic modulus, yield strength, and ultimate strength of headed studs are 200 GPa, 360 MPa, and 490 MPa, respectively. Three grades of normal weight concrete (i.e., C30, C40, and C50) were involved in this paper. More details of the specimens can be found in Table 1.

(a) Fabricating J-hook connector through bending straight steel reinforcements; (b) Welding J-hook connectors to the two external steel faceplate; (c) Performing bending tests to check the quality of the welding of Jhook connectors; (d) Preparing the steel skeleton that consists of two endplates; (e) Welding stiffeners between the two end plates and steel faceplates; (f) Casting of concrete into the steel skeleton and curing of the specimen. Fig. 3 shows the details of all prepared specimens. All the specimens measure 600 mm × 600 mm × 90 mm in height, width, and core thickness, respectively. In order to study the influence of the crosssectional steel content on compressive behaviour of the novel SCS

2.2. Test setup Fig. 4 shows the setup for the compression tests on novel SCS sandwich walls. It shows that all the specimens are put directly to the rigid support of a 1500 ton MTS testing machine. The positions for specimens need to be well controlled to minimize the eccentricity during the loading process. Displacement-controlled type of loading was applied to the top end of the SCS sandwich walls in a rate of 0.05 mm/min 12 linear varying displacement transducers (LVDTs) were installed on both top and bottom end of the specimen to measure their shortenings. Linear strain gauges were also installed on the steel faceplates to measure the strains developed in the steel faceplates. A load cell was attached between the loading frame and actuator to measure the reaction forces of SCS sandwich walls. After achieving the peak resistances, all the tests were terminated when the load carrying capacity of the specimen dropped to at least its 50% ultimate value or excessive shortening occurred. 3. Test results 3.1. Failure modes Fig. 5 shows the failure modes of the tested eight specimens. There were four types of failure modes that were observed from the tests, i.e., concrete crushing, concrete splitting, concrete pushed-out, and buckling of steel face plates. Global buckling failure mode was not observed in these short tested walls. Fig. 5 also shows that differences exist in the positions for the local buckling of the two side steel faceplates in most of the specimens, e.g., W2, W3, and W6, which is mainly caused by the eccentricities between the loading centre and geometric centre of the specimens. For specimen W1, the steel faceplates located at about 40% of its height started to buckle as W1 achieved its 90% ultimate resistance. Local buckling continued occurring to the steel faceplate strip at midheight as W1 achieved its ultimate resistances (see Fig. 5(a)). For specimen W2, as the applied displacement loading increases, concrete splitting crack was observed in the back side surface (see Fig. 5(b)) as

Fig. 1. Applications of SCS sandwich walls in buildings and offshore structures. 121

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Fig. 2. Fabrication procedures for SCS sandwich wall with J-hook and NWC.

Fig. 3. Details of the SCS sandwich wall.

specimen started to buckle as the specimen achieved its 50% ultimate resistance. Finally, W5 failed in local buckling of the steel faceplate. In addition, concrete pushed-out failure was also observed in the concrete core at final stage due to the splitting failure inside the concrete core. For specimen W6, local buckling started to develop in the steel faceplates at about its mid-height as shown in Fig. 5 (e). As W6 achieved its ultimate resistance, splitting in the concrete core and local buckling in the steel faceplates (see Fig. 5(f)) were observed. For specimen W7, steel faceplates started to buckle at 1/4 height from the bottom as the specimen achieved its 60% ultimate resistance. Gradually, steel faceplates at 3/4 height started to buckle, and finally W7 failed in concrete crushing and local buckling of the steel faceplate. Local buckling of the steel faceplate in specimen W8 was also observed as it achieved 50% of its ultimate resistance (see Fig. 5(g)). Finally, W8 failed in concrete

the reaction force of the sandwich wall, P, equals to about 90% its ultimate resistance. Local buckling and concrete crushing were, respectively, observed in the steel faceplates and concrete core (see Fig. 5(b)) as W2 achieved its ultimate resistances. As specimen W3 achieved its 50% ultimate resistance, cracks were observed at the root of the specimen. As W3 achieved its 90% ultimate resistance, local buckling of the steel faceplates started to develop. Finally, W3 failed in concrete crushing and local buckling of the steel faceplates as shown in Fig. 5 (c). For specimen W4, the strip of steel faceplate at the 70% height started to buckle as the specimen achieved its 50% ultimate resistance (see Fig. 5(d)). As the applied displacement load increased, the strip of steel faceplates at about 30% of its height started to buckle. Finally, W4 failed in splitting mode in the concrete core and local buckling of steel faceplates. For specimen W5, the steel faceplate near the root of the 122

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Fig. 3. (continued)

crushing mode and local buckling of the steel faceplate (see Fig. 5(g)).

Table 1 Mix proportions of normal weight concrete (kg/m3). Grade

Water

OPC

Mineral powder

Fly ash

Sand

Granite

SP

C30 C40 C50

165 165 165

195 276 333

56 96 102

87 68 65

945 817 725

923 978 1023

6.7 9.3 11

3.2. Load versus axial shortening behaviour Fig. 6 shows the load versus axial shortening of the SCS sandwich wall under pure compression. It shows that there are three working stages for the SCS sandwich wall under in-plane compression, i.e., elastic stage, non-elastic stage, and recession stage. During the first elastic stage, the reaction force of the SCS sandwich wall increased almost linearly with the increase of the axial shortening until the specimens achieved their 50%∼90% ultimate resistances. During the second nonlinear working stage, the load versus axial shortening curves of the SCS sandwich wall exhibit nonlinear behaviours. However, it should be noted that the nonlinear behaviours of the load versus axial

Note: OPC denotes ordinary Portland cement; SP denotes the superplasticizer.

Fig. 4. Test setup of SCS sandwich wall. 123

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Fig. 5. Failure modes of the SCS sandwich wall under in-plane compression.

buckling of the steel faceplate. After the peak resistance during the recession stage, the SCS sandwich wall exhibit a rapid decrease in the load carrying capacity. Local buckling of the steel faceplate and concrete crushing/splitting continued developing as the applied displacement loading increases.

shortening curves varies with different types of the concrete core, thickness of the steel faceplate, and spacing of the connectors. The SCS sandwich wall with lower strength concrete exhibit larger nonlinear portion in the load-displacement curves than that of specimen with higher strength concrete (see Fig. 6(c)). During this stage, concrete splitting or concrete crushing were developing in the concrete core whilst the strip in the steel faceplate between two rows of neighbouring connectors started to buckle. At the end of the second stage, the SCS sandwich wall achieved their ultimate compressive resistance and the specimen failed in crushing/splitting of concrete core and local

3.3. Load versus strain behaviour Fig. 7 depicts the load versus strain relationship for the steel faceplates of different specimens. It shows that at the initial loading stage 124

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Fig. 6. Compressive load versus shortening curves of SCS sandwich walls.

the strain increases almost linearly with the increasing loads. During this stage, the measured negative values of strain in steel faceplate implies that the steel faceplates were under compression. At the end of this stage, as the specimens achieved their ultimate resistances the strains in the steel faceplates exhibited threshold points of turning negative to positive values. This reflection point in the load-strain curves means that instability in the steel faceplate start to occur and local buckling of steel faceplates initiated after the SCS sandwich walls achieved their ultimate compressive resistances. Moreover, it can be also found from Fig. 7 that most of the strains at the point of occurrence of local buckling are close to or smaller than the yielding strains of the steel faceplates that implies the occurrences of elastic or inelastic buckling.

DI =

3.5. Discussions Ultimate compressive resistances of SCS sandwich walls with J-hook connectors, i.e., Pu, can be determined from the corresponding load versus axial shortening curves. Table 2 lists the ultimate compressive resistances of the tested eight specimens. Based on the test results, the influences of different parameters on the compressive behaviour of the SCS sandwich wall with J-hook connectors were herein discussed and analysed.

The experimental initial stiffness of the SCS sandwich wall, Ke, can be determined by the method recommended by Choi and Han [10] as the following;

P0.3 Δ0.3

(2)

where, Δ85% denotes the shortening as the reaction force of the SCS sandwich wall decreased to its 85% ultimate value during the recession stage; Δu denotes the shortening corresponding to ultimate resistance. The DI ratios for the tested eight specimens are listed in Table 2.

3.4. Initial stiffness and ductility index

Ke =

Δ85% Δu

3.5.1. Effect of the thickness of steel faceplate As shown in Fig. 8(a), increasing the thickness of the steel faceplate significantly influences the load versus shortening behaviours of SCS sandwich wall with J-hook connectors and NWC. Fig. 8(a) and (b) shows the influences of different thickness of steel faceplate on strength and ductility of the SCS sandwich wall with J-hook connectors and NWC. It shows that both ultimate compressive resistance, Pu, and initial stiffness, Ke, increase almost linearly with the increasing thickness of the steel faceplate. As the thickness of steel faceplate increases from 2.8 mm to 4.6 mm and 5.9 mm, Pu (or Ke) of the SCS sandwich wall were increased by 23% (9%) and 49% (31%), respectively. This is because that increasing the thickness of steel faceplate increases the steel

(1)

where, P0.3 denotes 30% ultimate resistance; Δ0.3 denotes shortening of SCS sandwich wall corresponding to P0.3. Table 2 lists the calculated initial stiffness for all the tested specimens. This paper adopted the methods using load versus shortening curves [32–34] to determine the ductility index (DI) as the following; 125

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content or equivalent area of cross section that resulted in increase of the ultimate resistance and initial stiffness. Moreover, with the same spacing of connectors, increasing the thickness of steel faceplate reduces its slenderness that further increases its compressive buckling resistance. Fig. 8(b) shows the influences of different thickness of steel faceplates on ductility of SCS sandwich wall with J-hook connectors and NWC. It shows that both DI ratio and shortening related to peak resistance,Δu, increases with the increasing thickness of the SCS sandwich wall, ts. As ts increases from 2.8 mm to 4.6 mm and 5.9 mm, DI ratio of the SCS sandwich wall increases from 1.30 to 1.48 and 1.40, respectively. Meanwhile, Δu increases almost linearly with the increasing ts from 2.34 mm to 2.83 mm and 2.98 mm, respectively. This is because increasing the thickness of the steel faceplate from 2.8 mm to 4.6 mm and 5.9 mm actually increases the steel content of the cross section from 5.9% to 9.3% and 11.6%, respectively. This increased steel content increases the ductility of the cross section since the steel materials are more ductile than the NWC. 3.5.2. Effect of spacing of connectors Fig. 9(a) shows the influence of spacing of connectors (i.e., S) on Pu and Ke of the SCS sandwich wall. It shows that as S increases the ultimate compressive resistance, Pu, of the SCS sandwich wall decreases almost linearly with the increasing S. As S increases from 75 mm to 100 mm and 150 mm, Pu is decreased by 10% and 22%, respectively. This is due to that increasing the spacing of the connectors, S, from 75 mm to 100 mm and 150 mm increase the slenderness ratio S/ts from 26.8 to 35.7 and 53.6 that significantly reduces the compressive buckling resistance of the steel faceplate. However, increasing S value exhibits marginal influence on the initial stiffness of the SCS sandwich walls. As S increases from 75 mm to 100 mm and 150 mm, Ke value is increased by 2% and 3%, respectively. Since Ke was determined by the ratio of 30% ultimate resistance to its corresponding shortening, the steel faceplate still behaves elastically and buckling could not occur at this point. Thus, spacing of the connectors exhibits marginal influence on the initial stiffness of the SCS sandwich walls. Fig. 9(b) shows the influences of the spacing of connectors, S, on DI ratio andΔu. It can be observed that increasing the spacing of connectors from 75 mm to 100 mm and 150 mm significantly reduces the DI ratio from 1.30 to 1.10 and 1.02, respectively. Increasing S from 75 mm to 100 mm and 150 mm actually increases the slenderness of the steel faceplate (i.e., S/ts ratio) from 26.8 to 35.7 and 53.6, respectively. The increased slenderness ratio accelerates the occurrence of buckling of steel faceplate that finally compromises the ductility of the SCS sandwich wall. This decreased ductility of the SCS sandwich wall is also reflected on the reducedΔu as S increases. As S increases from 75 mm to 100 mm and 150 mm,Δu was also reduced by 17% and 18%,

Fig. 7. Load versus strain curves of SCS sandwich walls under compression.

Table 2 Details and results of steel-concrete-steel sandwich walls with J-hook. Item

W1 W2 W3 W4 W5 W6 W7 W8 Mean Cov

ts (mm)

S (mm)

h mm

fc kN/mm

Ke kN/mm

Δu (mm)

Δ85% (mm)

DI Ratio

Pu (kN)

Nu (kN)

Pu/Nu

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(7)/(6)

(9)

(10)

(9)/(10)

2.8 4.6 5.9 2.8 2.8 2.8 2.8 2.8

75 75 75 100 150 75 75 75

53 53 53 53 53 53 53 90

43.9 43.9 43.9 43.9 43.9 28.0 46.0 43.9

1534 1667 2013 1510 1497 1112 1801 1731

2.34 2.83 2.98 1.94 1.92 2.42 2.90 2.67

3.05 4.20 4.17 2.14 1.96 3.35 3.39 3.47

1.30 1.48 1.40 1.10 1.02 1.39 1.17 1.30

3062 3779 4563 2769 2395 2038 3361 3001

2860 3356 3760 2683 2311 2129 2958 2874

1.08 1.13 1.21 1.03 1.04 0.96 1.14 1.04 1.12 0.17

ts denotes thickness of steel face plate; S denotes spacing of the connectors; h denotes height of the connectors; Ke denotes experimental elastic stiffness of SCS sandwich wall; Pu and Nu denote experimental and analytical ultimate compressive resistance, respectively; Δu denotes displacement related to Pu; Δ85% denotes displacement corresponding 85% Pu during the recession period; DI denotes ductility index. 126

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Fig. 8. Influences of thickness of steel faceplate on compressive behaviours.

Fig. 9. Influences of spacing of J-hook connectors on compressive behaviours.

increases Pu (or Ke) by 50% (or 39%) and 65% (or 63%), respectively. This is due to that increasing the grade of the used concrete core both increases its compressive strength and modulus of elasticity, which increases both Pu and Ke. Fig. 10(b) shows the influences of concrete-core strength fc on DI ratio andΔu of the SCS sandwich walls. It shows that increasing fc decreases the ductility of SCS sandwich wall. As fc increases from C30 to C40 and C50, the DI ratio is reduced by 6% and 16%, respectively. This is due to higher grade concrete becomes more brittle that compromises the ductility of SCS sandwich wall. However, As the strength of concrete increases from C30 to C40 and C50,Δu of SCS sandwich wall is increased by 3% and 20%, respectively. The strength of concrete for

respectively. Thus, increasing the spacing of the connector or slenderness ratio S/ ts of the specimens significantly reduces both the strength and ductility of SCS sandwich wall with J-hook connectors and NWC. 3.5.3. Effect of strength of concrete core Fig. 10(a) shows the influences of strength of concrete core, fc, on Pu and Ke of the SCS sandwich wall. It shows that increasing fc of the concrete core in the SCS sandwich walls improves both its ultimate compressive resistance and initial stiffness. It shows that Ke and Pu of the SCS sandwich walls almost increase linearly with the strength of concrete. Increasing fc from 28.0 MPa to 43.9 MPa and 46.0 MPa

Fig. 10. Influences of strength of concrete core on compressive behaviours. 127

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compressive resistance of steel faceplates, i.e.,

grade C30, C40, and C50 concrete is 28.0 MPa–43.9 MPa and 46.0 MPa, respectively. Thus, increasing the concrete from C30 to C40 and C50 leads to 57% and 64% increases of its strength of concrete that finally resulted in increased Δu of the SCS sandwich wall.

(3)

Nu = Nc + Ns

During the working stage, the concrete core work compositely with the two external steel faceplates. Previous studies [11] also showed that the steel faceplates working with shear connectors embedded in the concrete core provided certain degree of confinement. Thus, the compressive resistance of the concrete core, Nc, can be determined as the following;

3.5.4. Effect of the type of connectors There are two types of connectors involved in this testing programme, i.e., J-hook connector and headed stud. Specimen W1 and W8 were fabricated with Φ8 mm J-hook connectors and Φ10 mm headed studs (headed studs were only with certain diameter). Fig. 6(c) compares the load versus shortening curves of these two specimens. It shows that the load-shortening behaviours of these two specimens are very close. Fig. 11(a) and (b) shows the influences these two types of connectors on Ke, Pu, DI ratio andΔu. It shows that the differences of Ke, Pu, and DI ratio between the sandwich walls with these two types of connectors are only 13%, 2%, and 1%, respectively. This is because that the initial stiffness, ultimate compressive resistance, and ductility of the specimen are mainly determined by the steel content and strength of the materials if they were designed with fully composite action. Thus, it can be concluded that the developed J-hook connectors provide comparable composite action and structural performances of the cross section to the overlapped headed studs that were widely used in steelconcrete composite constructions. It can be also observed from Fig. 11(b) that Δu value of W8 with headed studs is 14% larger than that of W1 with J-hook connectors. This may be due to the larger diameter of headed studs used in W8. Thus, it can be concluded from above comparisons that the W1 with Φ8 mm J-hook connectors could offer comparable compressive behaviours to W8 with Φ10 mm headed studs in terms of load-shortening curves, ultimate compressive resistance, initial stiffness, and ductility. In addition, previous studies also proved that SCS sandwich structures with J-hook connectors exhibit excellent structural performances under impact and blast loads [35]. This may enhance the applications of the SCS sandwich walls with J-hook connectors as protective walls.

Nc = ϕAc σc

(4)

where, ϕ denotes partial safety factor and herein is adopted as 1.0 for the prediction purpose; Ac denotes the cross-section area of concrete core in SCS sandwich walls; σc is the compressive stress of concrete core that considers the confinement of steel faceplate. A method has been proposed by Yan et al. [11] to determine the σc as the following;

σc =

λ+

λ2 − 4(1 − αs2){σh2 − [(1 − αs ) fc + αs σh]2 } 2(1 − αs2)

λ = (1 + 2αs2) σh + 2(1 − αs ) αs fc

σh =

TH S2

(5) (6) (7)

where, fc denotes uni-axial compressive strength of NWC; αs is the shear yielding coefficient, and herein equals to 0.19; σh denotes confining stress provided by the steel faceplate; S denotes the spacing of the connectors; TH denotes tensile resistance of connectors used in the SCS sandwich wall. The tensile resistance of shear connectors in SCS sandwich walls is important that determines the degree of the confining stress acting on the concrete core. Its magnitude varies with the types of shear connectors. Fig. 12 shows the working mechanism of the confining effect of shear connectors on concrete core. Yan et al. [23,36] have categorized the shear connectors in SCS sandwich wall into three types, i.e., direct link, semi-direct link, and indirect link.

4. Analysis on ultimate compressive resistance of SCS sandwich walls

4.1.1. For direct link type of shear connector The working mechanism for direct link type of connectors is shown in Fig. 12. Through bolts or straight bars in Bi-steel structures are the representative type of direct link shear connectors. Their tensile resistances can be determined as the following [11];

4.1. Analytical model The SCS sandwich walls involved in this study are short, and global buckling was not observed in the tests. Thus, the compressive resistance of the short SCS sandwich walls is governed by the resistance of the cross section rather than global buckling. Since the main components in SCS sandwich walls are two external steel faceplates and the concrete core, the ultimate compressive resistance of the sandwich composite shear wall, Nu, consists of compressive resistance provided by the concrete core, Nc, and the

TH = min

Ts = Asd σu/ γM 2 ⎧ ⎫ ⎨Tps = πdt (f ys / 3 )/ γM 0 ⎬ ⎩ ⎭

(8)

where, Ts denotes tensile fracture resistance of the connector's shank; Tps denotes punching shear resistance of the steel faceplate where

Fig. 11. Influences of different types of connectors on compressive behaviours. 128

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Fig. 12. Failure modes of different types of connectors in SCS sandwich wall.

length of the J-hook; t denotes thickness of faceplate; AN denotes the projection area of concrete cone; σy denotes yield strength of reinforcement for J-hook; γM 2, γc , and γM 0 are partial safety factors, and are herein adopted as units for prediction purposes. As observed from the tests, local buckling occurred to steel faceplates in the locations between two neighbouring rows of connectors. Thus, based on Euler's buckling theory, the compressive buckling resistance of steel faceplate can be determined as the following;

connectors were welded; Asd and σu denotes cross-sectional area and ultimate strength of connectors, respectively; γM 2 and γM 0 are partial safety factors, and herein are adopted as units for the prediction on the test results. 4.1.2. For indirect link type of shear connector The working mechanism for indirect link type of connectors is shown in Fig. 12. Headed studs were the most widely used indirect link type of shear connector. Their tensile resistance in SCS sandwich wall can be determined as the following [11,23];

Ts = Asd σu/ γM 2 ⎧ ⎪ Tpl = 8Abrg fc / γc ⎪ TH = min ⎨ TCB = 0.333 fc AN / γc ⎪ ⎪Tps = πdts (f ys / 3 )/ γM 0 ⎩

π 2Es , fy ⎞ σcr = min ⎛ 2 (S / t ) 2 12 K s ⎠ ⎝

⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭

⎜

εcr = (9)

4.1.3. For semi-direct link type of shear connector The working mechanism for semi-direct link type of connectors is shown in Fig. 12. The J-hook connectors used in the SCS sandwich walls in this study is the representative type of semi-direct link type of shear connector. Their tensile resistances have been fully studied by Yan et al. [37], and can be determined as the following;

⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭

⎟

(12)

π2 12K 2 (S / ts )2

(13)

where, σcr , εcr denote critical elastic buckling stress and strain of steel faceplate, respectively; Ast denotes cross-sectional area of steel faceplate; K denotes coefficient on effective length for local buckling of steel faceplate, and varies with the restraints by the shear connectors; S denotes spacing of the connectors in SCS sandwich wall; ts denotes thickness of steel faceplate. The coefficient for buckling K in Eqn. (12) varies with different restraints related to slenderness ratio and layout of the connectors, e.g., 1.0 corresponds to pin-pin and 0.7 corresponds to pin-fixed boundary condition. Thus, using a proper K value is of importance to determine the buckling stress. Extensive previous experimental studies [38–44] have been reported to study the buckling strain versus slenderness ratio relationship. Fig. 13 summarizes the previous reported 62 test data including the reported test data in this paper on generalized buckling strain, εcr / εy versus generalized slenderness ratio, S / ts f ys / Es relationship. It can be found that most of the test data were distributed between the curves with K values of 0.7 and 1.0. Through regression analysis on the reported 62 test results, an average value of K = 0.825 (see Fig. 13) was proposed for the determination on elastic buckling strain of the steel faceplate in the SCS sandwich composite structure. Thus, the compressive resistance of the steel faceplate in SCS sandwich wall can be determined as the following;

where, Ts, Tpl, TCB, and Tps denotes tensile fracture strength of connector's shank, pullout resistance, concrete breakout resistance, and punching shear resistance of the steel faceplate, respectively; Asd denotes cross-sectional area of the shear connectors; Abrg denotes bearing area of the shear connectors under tension; AN denotes the projection area of concrete cone; d denotes diameter of the connector; ts denotes thickness of steel faceplate; fys denotes yield strength of steel faceplate; γM 2, γc , and γM 0 are partial safety factors, and are herein adopted as unit for the prediction on the test results.

Ts = Asd σu/ γM 2 ⎧ ⎪Tpl = (0.9f eh d + 0.116σy d 2)/γ c ⎪ ck TH = min TCB = 0.333 fc AN / γc ⎨ ⎪ ⎪ Tps = πdt (f ys / 3 )/ γM 0 ⎩

(11)

Ns = 2σcr Ast

(10)

π 2Es , f y ⎞ Ast Ns = min ⎛ 2 ⎝ 4.1(S / ts ) ⎠

where, Asd denotes cross-sectional area of the shear connectors; d denotes diameter of J-hook; eh is projection area of the top anchoring

⎜

129

⎟

(14)

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where, Es denotes elastic modulus of steel faceplate; S denotes spacing of connectors; ts denotes thickness of steel faceplate. 4.2. Validations The predicted ultimate compressive resistance are compared with the test results in Table 2. For the eight test results, the average test-toprediction ratio is 1.08 with a coefficient of variation (COV) of 0.07. The developed analytical models averagely underestimate the compressive resistance of SCS sandwich walls with NWC and J-hook connectors by 8%. In order to make more extensive validations of the developed analytical models, including the eight tests reported in this paper another 42 test results reported by Choi and Han [10], Choi et al. [41], Zhang et al. [42], Yang et al. [43], Zhang et al. [44], Liu et al. [44], Liu et al. [45], and Huang and Liew [46] were used in this paper for the validations of developed analytical models. Table 3 lists the details of these test details and results. Fig. 14 compares the predicted ultimate compressive resistances with the 50 test results. It can be seen that the average and COV for the 50 test-to-prediction ratios are 1.12 and 0.17, respectively. The developed analytical models averagely underestimate

Fig. 13. Normalized critical strain versus normalized slenderness ratio relationship.

Table 3 Details and results of SCS sandwich wall in Refs. [10,41,43–46]. Reference

Item

ts mm

fys MPa

Es GPa

d mm

h mm

S mm

fc MPa

Dc mm

S/ts

H mm

W mm

D mm

Pu kN

Nu kN

Pu/Nu

Choi & Han [10]

SS400eS SS400-M SS400-L SM490-S SM490-M SM490-L C24/490-T6B20 C24/490-T6B30 C24/490-T6B40 C16/490-T6B20 C16/490-T6B30 C16/490-T6B40 DSC4-150 DSC4-200 DSC4-250 DSC4-300 DSC4-150/300 DSC4-300/150 DSC6-240 DSC6-300 DSC6-360 SCW-1 SCW-2 SCW-3 SCW-4 DSW-1 DSW-2 DSW-3 DSW-4 SCSW-R1 SCSW-R2 SCSW-S1 SCSW-S2 SCSW-C1 SCSW-C2 SCSW-C30 SCSW-C45 SCSW-T8 SCSW-T12 SCSW-P1 SCSW-P2 SCSW-HS

6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 4.0 4.0 4.0 4.0 4.0 4.0 6.0 6.0 6.0 4.8 4.8 4.8 4.8 3.0 3.0 3.0 3.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 8.0 12.0 6.0 6.0 6.0

274 274 274 418 418 418 428 428 428 428 428 428 410 410 410 410 410 410 348 348 348 256 256 256 256 370 370 370 370 309 309 309 309 309 309 309 309 394 375 309 309 309

200 200 200 200 200 200 202 202 202 202 202 202 206 206 206 206 206 206 206 206 206 200 200 200 200 206 206 206 206 202 202 202 202 202 202 202 202 180 212 202 202 202

8 8 8 8 8 8 13 13 13 13 13 13 5 5 5 5 5 5 10 10 10 8 8 8 8 6 6 6 6 13 13 13 13 13 13 13 13 13 13 13 13 13

71 71 71 71 71 71 108 108 108 108 108 108 35 35 35 35 35 35 75 75 75 70 70 70 70 48 48 48 48 60 60 60 60 45 68 60 60 60 60 60 60 73

150 200 300 150 200 300 120 180 240 120 180 240 150 200 250 300 300 150 240 300 360 269 182 149 96 150 100 75 35 100 100 201 300 100 100 100 100 100 102 103 100 100

38 38 38 38 38 38 24 24 24 16 16 16 39 33 38 36 32 33 39 34 36 30 30 30 30 47 42 47 42 54 54 55 55 60 53 38 54 57 52 55 54 61

288 288 288 288 288 288 238 238 238 238 238 238 232 232 232 232 232 232 228 228 228 220 220 220 220 160 160 160 160 120 120 120 120 90 135 120 120 120 120 120 120 120

25.0 33.3 50.0 25.0 33.0 50.0 20.0 30.0 40.0 20.0 30.0 40.0 37.5 50.0 62.5 75.0 75.0 37.5 40.0 50.0 60.0 56.0 38.0 31.0 20.0 50.0 33.3 25.0 11.7 16.7 16.7 33.5 50.0 16.7 16.7 16.7 16.7 12.5 8.5 17.2 16.7 16.7

450 600 900 450 600 900 380 500 620 380 500 620 1200 1200 1200 1200 1200 1200 1200 1200 1200 1160 1160 1160 1160 800 800 800 800 400 400 500 700 400 400 400 400 400 400 400 400 400

380 480 680 380 480 680 280 370 460 280 370 460 1200 1200 1200 1200 1200 1200 1200 1200 1200 1100 1100 1100 1100 700 700 700 700 590 590 590 590 590 590 590 590 590 590 590 590 590

300 300 300 300 300 300 250 250 250 250 250 250 240 240 240 240 240 240 240 240 240 230 230 230 230 166 166 166 166 132 132 132 132 102 147 132 132 136 144 132 132 132

6282 7051 8956 6562 8069 8850 3052 3528 4164 2539 3055 3812 11249 10318 11230 11610 10122 9452 13525 11606 13033 9380 12123 9976 11433 6270 6390 6700 7780 4191 4906 4656 3670 4248 5467 3916 4689 6889 8418 5120 4933 5317

4884 5806 7201 5398 5806 7201 2864 3080 3132 2398 2455 2369 11097 8778 9747 9039 7895 9456 11358 9432 9513 7013 8011 8940 9137 4968 5054 6216 5734 5566 5566 4863 4018 4969 5871 4555 5572 7265 8539 5627 5536 5982

1.29 1.21 1.24 1.22 1.39 1.23 1.07 1.15 1.33 1.06 1.24 1.61 1.01 1.18 1.15 1.28 1.28 1.00 1.19 1.23 1.37 1.34 1.51 1.12 1.25 1.26 1.26 1.08 1.36 0.75 0.88 0.96 0.91 0.85 0.93 0.86 0.84 0.95 0.99 0.91 0.89 0.89 1.12 0.17

Choi et al. [41]

Yang et al. [43]

Zhang et al. [44]

Liu et al. [45]

Huang & Liew [46]

Mean Cov

ts, fys, and Es denote thickness, yield strength, and elastic modulus of steel faceplate, respectively; d and h denote diameter and height of shear connector; S denotes spacing of connector; Dc denotes thickness of concrete core; fc denotes compressive strength of concrete; H, W, and D denote height, weight, and depth of SCS sandwich wall, respectively. 130

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(2)

(3)

(4)

(5) Fig. 14. Comparisons of predictions with test results on Pu.

(6)

the ultimate compressive resistance of the SCS sandwich wall by 12%. In addition, it should be pointed out that the developed analytical models averagely overestimate 11 test results in Ref. [46] by 11%. This is due to that the specimens in Ref. [46] were designed with ultralightweight cement composite that is different from NWC used in this paper and the rest Ref. [10,41–45]. This implies further modifications are still required for the developed analytical models. In summary, the developed analytical models could offer reasonable and conservative estimations on the ultimate compressive resistance of the SCS sandwich walls with different types of shear connectors (including J-hook) and NWC. 4.3. Step-by-step predicting methods on compressive resistance of the SCS sandwich walls

faceplate. Global buckling of the SCS sandwich wall was not observed in the tests. The compressive resistance, initial stiffness, and ductility index ratio of SCS sandwich walls increase linearly with the increasing thickness of steel faceplate from 2.8 mm to 5.9 mm (corresponding steel content increasing from 5.9% to 11.9%). The spacing of J-hook shear connectors exhibited marginal influence on initial stiffness of the SCS sandwich wall with J-hook connectors and NWC. Ultimate compressive resistance of SCS sandwich wall with J-hook and NWC decreased almost linearly with the increasing spacing of the connectors from 75 mm to 150 mm. Increasing the spacing of the connectors from 75 mm to 100 mm and 150 mm significantly reduced the DI ratio from 1.30 to 1.10 and 1.02, respectively. Initial stiffness and ultimate compressive resistance of the SCS sandwich wall almost increases linearly with the grade of concrete. As fc increases from C30 to C40 and C50 the ductility of the sandwich wall was reduced by 7% and 16%, respectively. SCS sandwich walls with Φ8 mm J-hook connectors offered comparable ultimate compressive behaviours to the sandwich walls with Φ10 mm headed studs in terms of load-shorting behaviour, initial stiffness, ultimate compressive resistance, and ductility. Theoretical models were developed to predict ultimate compressive resistance of SCS sandwich walls with direct-link, indirect link and semi-direct link type of connectors. New buckling length coefficient 0.825 was proposed for predictions on ultimate compressive resistance of steel faceplates in SCS sandwich walls through regression analysis on 62 test results. Validations of predictions by developed theoretical models against 50 test results confirmed that the developed theoretical models averagely underestimated the test results by 12%. However, the developed models exhibited overestimations on compressive resistance of SCS sandwich walls with ultra-lightweight cement composite. Further modifications are still necessary.

Acknowledgments The authors would like to acknowledge the research grant 51608358 received from National Natural Science Foundation of China for the works reported herein. The authors gratefully express their gratitude for the financial supports.

Step I: Find the proper category of the shear connectors by the method as introduced, and using corresponding equations in Eqn. (8)∼(10) to determine the tensile resistance of shear connectors in SCS sandwich walls. Using Eqn. (7) to calculate the confining stress σh on the concrete core. Step II: Using Eqn. (5) to calculate compressive stress of concrete core, and using Eqn. (4) to calculate the compressive resistance contributed by the concrete core. Step III: Using Eqn. (14) to calculate the compressive resistance contributed by two steel faceplates in the SCS sandwich wall. Step IV: Using Eqn. (3) to calculate the compressive resistance of SCS sandwich walls.

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