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Tensile resistance of novel interlocked angle connectors used
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in steel-concrete-steel sandwich structures
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Zhaohui Zhoua,b, Yonghui Wanga,b,*, Ximei Zhaia,b
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a
Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin
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Institute of Technology, Harbin 150090, China
b
Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of
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Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China
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*Corresponding author Email: wangyonghui@hit.edu.cn
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Abstract
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This paper reports a new interlocked angle connector (IAC) for steel-concrete-
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steel sandwich structures, and the tensile behaviors of the IACs was also studied in
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detail by performing the tensile test. There were 14 specimens with different
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parameters being designed, including embedded depth of IACs, thicknesses of steel
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sheet, steel angle and bottom plate, side length of steel angle, diameter of steel tube
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and interlocking bolt. The failure modes and tensile resistances of the proposed IACs
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were obtained, and three failure modes were identified, including concrete breakout
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failure, tensile fracture failure of the steel angle and concrete direct shear failure. The
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main parameters affecting tensile resistance of the IACs were also discussed and
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analyzed. In addition, analytical models were proposed for predicting the tensile
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resistances of IACs and their accuracies were also verified via comparing the pre-
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dicted values with test results. Finally, the tensile resistances of IACs were compared
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with those of J-hook connectors, and improved tensile resistance could be observed
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for the proposed IACs.
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Keywords: Tensile test; Interlocked angle connectors; Shear connector; Tensile
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resistance of connector; Steel-concrete-steel sandwich structure.
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Nomenclature
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AS
Cross-sectional area of the steel angle of the IAC
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Ac
Area of concrete subjected to directly shear
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AN
Projected area of cone surface to free surface of the concrete
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b
Thickness of steel angle in IACs
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c
Cohesion coefficient of concrete
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D, DJ
Inner diameter of steel tube and hook, respectively
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d
Thickness of steel sheet in IACs
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dp
Distance from the center of the bolt hole to the plastic hinge line
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dJ
Diameter of J-hook connectors
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fc, fct
Compressive and tensile strength of the concrete
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fyp, fup
Yield and ultimate strength of steel sheet
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fya, fua
Yield and ultimate strength of steel angle
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hef
Embedded depth of connectors
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h
Side length of steel sheet
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hc
The height of concrete in specimens
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L
Side length of steel angle
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l
Distance from the center of bolt hole to free edge of steel sheet
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la
Diagonal length of steel angle
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M
Mass of connector in a specimen
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p
Thickness of bottom plate
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PT
Ultimate tensile resistance of IACs embedded in concrete
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PTest
Tensile resistances of connectors from tests
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PTB
Tensile resistance contributed by steel sheets
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PTC, PTC0
Concrete breakout resistance
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PTS
Tensile resistance of IACs failed in tensile fracture of steel angle
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PTF
Punching shear resistance of the steel faceplate
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T
Ultimate tensile resistance of J-hook failed in concrete breakout
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u
Critical section perimeter of concrete cone based on measured angle
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u0
Critical section perimeter of 45-degree concrete cone
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ua
Perimeter of the steel angle of the IAC
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θ
Inclination angle between conical surface and free surface of
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concrete
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η
The strength reduction factor
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τc
Ultimate shear stress at the concrete-to-concrete interface
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Ф
Tensile resistance per unit mass of the connector and also eliminates
the effect of concrete strength
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1. Introduction
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The interfacial bonding between steel and concrete plays essential roles in
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mechanical performances of steel-concrete-steel (SCS) sandwich structures, e.g.,
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providing longitudinal and transverse shear resistances as well as maintaining
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structural integrity [1]. In the past several decades, variant mechanical shear
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connectors were proposed as the steel-concrete interfacial bonding method, and they
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could be classified into three types according to their linking forms between two
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faceplates, including “direct link”, “indirect link”, and “semi-direct link” connectors
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[2].
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Some typical shear connectors are shown in Fig. 1. Direct-link shear connectors
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generally provide the strongest tensile resistance by directly connecting the two
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faceplates, like friction-welded connectors [3] and through bolt connectors [4], as
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shown in Figs. 1(a) and (b). However, these two types of connectors also have some
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disadvantages. For example, the friction-welding equipment needs a certain operating
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space, which limits the thickness of sandwich structures with friction-welded
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connectors in the range of 200-700 mm [5]. With regard to the through bolt
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connectors, the smoothness of the external faceplates cannot be assured, and the
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drilled holes on faceplates also weaken their strengths. Figs. 1(c) and (d) illustrate the
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indirect-link angles [6] and headed studs [7], which bond the concrete core and steel
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faceplates via embedding them into concrete. The disadvantage of indirect-link
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connectors may be that their tensile resistances are significantly reduced or lost once
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the concrete cracks. Fig. 1(e) shows the semi-direct-link J-hook connectors [8], which
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bond two faceplates through mechanical interlocking of two J-hooks and embedding
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in the concrete. Compared to indirect-link connectors, the interlocked J-hook
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connectors provided outperformed bonding behavior between concrete core and
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faceplates. Moreover, the J-hook connectors are also superior to the direct-link
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connectors in terms of smoothness of external faceplates (compared to through bolt
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connectors) and flexibility of thickness of SCS sandwich structures (compared to
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friction-welded connectors). However, the bonding strength of J-hook connectors
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might not be sufficient to assure the integrity of SCS sandwich structures under
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extreme loads [9-14]. In this study, a new semi-direct-link connector, which was
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named as interlocked angle connector (IAC) in Fig. 1(f), was proposed to enhance the
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bonding behavior of existing semi-direct-link connectors.
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In SCS sandwich structures, shear connectors can be employed for resisting the
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transverse shear force and diagonal shear cracks of concrete, having the similar
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function to shear links in reinforced concrete structures [15]. It is also required to
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prevent local bucking of the faceplates, separation between the concrete core and steel
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faceplates as well as enhance steel-concrete interfacial bonding [16,17]. Hence, the
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tensile resistance of shear connectors is crucial for the performances of SCS sandwich
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structures, which provides the motivation of the current work to study the tensile
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performance of proposed IACs.
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The tensile performances of shear connectors have been extensively studied in the
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past decades [15,18-31]. The friction-welded connectors exhibited five different
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failure modes from tensile tests, i.e., bar breaking, punching shear of the plate, bar-
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plate interface fracture, and some combinations of these basic modes [15,18-20][15].
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The influences of the collar developed after friction welding were also examined by
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employing finite element analysis [15]. It was reported by ACI 349 [21] that tensile
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resistance of the headed stud embedded into concrete was governed by the lowest
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resistances corresponding to the following failure modes, i.e., pullout failure, steel
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failure of connector, side-face blowout, concrete breakout failure, and concrete
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splitting. Several formulae were also developed to predict the tensile resistance of the
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headed stud embedded in concrete [21][21-29]. Sohel and Liew [12] investigated the
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behaviors of J-hook connectors subjected to direct tension, and obtained their tensile
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resistances and failure modes. Further studies on J-hook connectors were conducted
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by Yan et al. [16], and theoretical models were proposed for predicting their tensile
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resistances. Moreover, the effects of fibers in concrete and shear force applied to the
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connectors on the tensile resistance of J-hook connectors were reported in Refs. [30]
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and [31].
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In this paper, the tensile test on 14 specimens was conducted to study the tensile
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behaviors of IACs, and parameters affecting the tensile resistance of IACs were
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discussed. Theoretical modes were established for predicting tensile resistances and
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failure modes of IACs, and their accuracies were also validated with test data. Finally,
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the tensile resistances of IACs and interlocked J-hook connectors were compared.
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2. Test program
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2.1 Details of IACs
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Fig. 2 illustrates a pair of IACs which consists of two parts, i.e., an upper angle
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connector (including a steel angle, an interlocking bolt and a steel sheet) and a lower
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angle connector (including a steel angle and a steel sheet). For fabricating the upper
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angle connector, the steel sheet was firstly welded to the steel angle, and the
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interlocking bolt was subsequently passed through the hole and fixed to the steel sheet
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via spot welding (shown in Fig. 2(a)). As for the lower angle connector, it was
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fabricated via welding the steel sheet to the steel angle (shown in Fig. 2(b)). After the
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upper and lower angle connectors being fabricated, the interlocking bolt of the upper
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angle connector was passed through the reserved hole on the lower angle connector to
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realize the interlocking between the upper and lower angle connectors, as shown in
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Fig. 2(c).
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2.2 Test setup and instrumentation
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The tensile behavior of a pair of semi-direct-link connectors can be obtained
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through the tensile test, and there are two typical tensile test methods in the literature.
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One of the tensile test methods was proposed by Xie and Chapman [15], and a
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prefabricated steel frame was employed to apply tensile force to the shear connectors,
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as shown in Fig. 3(a) for the test setup. The steel frame is composed of top and
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bottom steel plates, bottom round steel bar and four linking bolts. During the test, the
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upper connector, extending from the hole reserved in the top steel plate, is applied
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with a tensile force by the testing machine, and the round steel bar at the bottom of the
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frame is fixed to the base of the testing machine. Another method was proposed by
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Sohel and Liew [12], and the test setup is illustrated in Fig. 3(b). In this method, a
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steel bar with the diameter of 18 mm is directly welded to the bottom of the specimen.
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During loading test, the steel bar is fixed to the base of the test machine, and the upper
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connector was directly clamped to the testing machine for applying tension. The
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tensile force between the testing machine and the specimen is transmitted by the steel
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bar. In the tensile test method proposed by Xie and Chapman [15], the concrete in the
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specimen is significantly confined, which results in larger tested tensile resistances of
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the connectors as compared to their true values. In addition, it is prone to introduce
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unexpected moment to the specimen due to the eccentricity of the frame during the
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test. In contrast, the tensile test method proposed by Sohel and Liew [12] is simpler,
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and the force transmission path is direct and clear. Moreover, the tensile resistance
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obtained from this test method is slightly lower as compared to the actual tensile
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resistance of the shear connector [16]. Hence, the tensile test method proposed by
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Sohel and Liew [12] was employed, and the test setup is given in Fig. 4. Since the
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steel angle of IACs cannot be directly clamped by the testing machine, a conversion
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device was designed and fabricated, as presented in Fig. 4(b). During the tensile test,
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the top steel bar of the conversion device was directly clamped to the testing machine,
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and the upper steel angle of IACs was fixed to the conversion device by two bolts
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(shown in Fig. 4(b)). For avoiding the fracture of upper steel angle occurred at the
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weakened zone with bolt holes, the additional 10 mm-thick steel plates were welded
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to the upper steel angle at the weakened zone (shown in Fig. 4(a)). Two Linear
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Variable Differential Transformers (LVDTs) were employed to measure the
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elongation of the IACs, as shown in Fig. 4(c). Moreover, in order to reduce the
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unexpected moment to the IACs, the applied tensile force was designed to pass
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through the center of the interlocking bolt of the IACs. Therefore, it is necessary to
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ensure that points A, B and C (shown in Fig. 4(b)) are coaxial when fabricating and
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installing the test specimen.
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A universal testing machine (loading capacity = 500 kN) was employed to
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conduct the tensile test on IACs. A displacement-controlled loading method was
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employed with the loading rate of 0.05 mm/min, and the tensile test was terminated
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once the load drops to 50% of the ultimate load.
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2.3 Test specimens
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The failure mode and tensile resistance of a semi-direct-link connector in SCS
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sandwich structure are strongly affected by the confinement magnitude from
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surrounding concrete [12,16], and the weaker confinement generally results in a lower
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tensile resistance of IACs. The confinement magnitude on shear connectors may be
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different for different types of SCS sandwich structures. For example, the shear
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connectors in SCS sandwich beam are weakly confined by the surrounding concrete
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owing to the smaller width of the beam. Moreover, through cracks are easily
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developed, which leads to weak tensile resistance of the shear connectors. In contrast,
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the shear connectors in SCS sandwich panel and shell generally experience higher
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confinement and through cracks of concrete can be generally prevented. Hence, the
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tensile resistance of shear connectors in SCS sandwich panel or shell is generally
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higher than that of SCS sandwich beam. In this study, two types of specimens were
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designed and fabricated to consider the different confinement magnitudes from
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concrete. Type A specimens were designed with outer steel tubes to consider the
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scenarios with strong confinement to IACs from the surrounding concrete, e.g., SCS
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sandwich panels and shells. Type B specimens were designed without outer steel tube
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to consider the weak confinement to IACs in the SCS sandwich beam. Type A and B
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specimens are shown in Fig. 5(e).
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A total of 14 specimens were designed and fabricated for tensile tests, including
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10 specimens of type A and 4 specimens of type B. Fig. 5 illustrates the fabrication
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procedures of the specimen, including (a) welding the lower angle connector to the
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bottom steel plate, (b) gluing the bottom steel plate and steel tube to a square plank,
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(c) fixing the upper angle connector via two steel bars that were welded to the upper
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steel angle and steel tube, and subsequently casting concrete, (d) removing the steel
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bars and square plank after hardening of concrete, and (e) welding the bottom round
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steel bar and removing the steel tube for type B specimens.
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Parameters influencing the tensile resistances of IACs in type A and B specimens
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were carefully chosen. For type A specimens, the following parameters that affect the
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tensile behaviors of IACs were experimentally investigated, including embedded
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depth of IACs (50, 75 and 100 mm), steel sheet thickness (2.9 and 4.5 mm), steel
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angle thickness (2.8, 3.6 and 4.5 mm), bottom plate thickness (2.9 and 7.8 mm),
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presence of interlocking bolt (the IACs without interlocking bolt is shown in Fig. 6)
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and diameter of steel tube (250 mm and 300 mm). With regard to type B specimens,
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the effects of side length of steel angle (45 and 56 mm) and interlocking bolt on the
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tensile resistance of IACs were experimentally studied. Table 1 summarizes the
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details of the fabricated specimens.
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In this study, Q235B mild steel was employed for steel angle and steel sheet, and
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tensile coupon tests were conducted to obtain their mechanical properties [32]. In
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addition, the normal weight concrete was employed for the specimens, and its
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mechanical properties were obtained via conducting uniaxial compression tests on
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concrete cylinders. The detailed mechanical properties of steel and concrete can be
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found in Table 1.
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3. Test results and discussions
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3.1 Failure modes
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Fig. 7 depicts the typical failure modes observed from the tensile tests. Two
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failure modes occurred to type A specimens, including concrete breakout failure and
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tensile fracture failure of the steel angle. With regard to type B specimens, only
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concrete direct shear failure was found.
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Fig. 7(a) shows the concrete breakout failure mode which are characterized by
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pulling a concrete cone out of the specimen and leaving a conical cavity in the
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remaining concrete. The inclination angle between conical surface and free surface of
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concrete is defined as 𝜃 (see Fig. 7(a)), and four values of 𝜃 were measured for
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each specimen and given in Table 2. It is noted that the values of 𝜃 are within a
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range of 23.4°~46.3°, and their average value is 29.2° with the coefficient of variance
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(COV) for the 36 measured data to be 0.08. The tensile fracture failure of the steel
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angle is presented in Fig. 7(b). The shank of the steel angle failed in fracture with
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evident necking being observed after the test. For this failure mode, there is no
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concrete cone being pulled out of the specimen, and only local damage of concrete
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occurs near the IACs. With regard to the concrete direct shear failure in Fig. 7(c), the
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IACs are found to split the surrounding concrete into two pieces, and the vertical
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fracture surface of concrete passes through the diagonal of the steel angle.
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Explanation for the concrete direct shear failure is that the type B specimen is not
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confined by the steel tube, and the concrete cracks propagate rapidly and form a
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vertical direct shear failure surface in the concrete once the concrete cracks appear.
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The failure modes and ultimate tensile resistances of the specimens are presented
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in Table 4. For type A specimens, most of them (8 out of 9) failed in concrete
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breakout, and only one specimen failed in tensile fracture failure of the steel angle.
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All type B specimens exhibited the failure mode of concrete direct shear.
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3.2 Parametric studies
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3.2.1 Embedded depth of IACs (ℎ𝑒𝑓)
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Fig 8(a) shows the influence of embedded depth of IACs (ℎef) on tensile
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resistances of IACs in type A specimens. The ultimate tensile resistance shows a
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growing tendency with increasing ℎef, i.e., the ultimate tensile resistance is increased
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by 29.3% and 67.5%, respectively, with an increase of ℎef from 50 mm to 75 mm
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and 100 mm. In addition, the failure modes of the specimens also change from
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concrete breakout failure (ℎ𝑒𝑓=50 and 75 mm) to tensile fracture failure of the steel
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angle (ℎ𝑒𝑓=100 mm) with the increase of ℎ𝑒𝑓. This can be attributed to improved
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concrete breakout resistance for higher value of ℎ𝑒𝑓. Thus, the concrete breakout
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failure mode before tensile fracture can be avoided if the embedded depth of IACs is
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sufficient.
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3.2.2 Steel sheet thickness (d)
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The effect of steel sheet thickness (d) on the ultimate tensile resistance of IACs in
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type A specimens is shown in Fig. 8(b). As the d increases from 2.9 mm to 4.5 mm,
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the ultimate tensile resistance is found to increase by 26%. Hence, the tensile
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resistances of IACs are evidently influenced by the variation of d. This is because the
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larger steel sheet thickness results in a larger tensile force being directly transmitted
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between the upper and lower angle connectors owing to enhanced interlocking
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behaviors.
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3.2.3 Steel angle thickness (b)
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Fig. 8(b) also shows the tensile test results of IACs in type A specimens with
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variation of steel angle thickness (b), and the ultimate tensile resistance is found to be
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slightly improved by increasing b from 2.8 mm to 3.6 mm and 4.5 mm, i.e., the
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ultimate tensile resistance of IACs is increased only by 1.7% and 4%, respectively.
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This is because all these specimens failed in concrete breakout, and the variation in b
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does not significantly influence the concrete breakout resistance.
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3.2.4 Bottom plate thickness (p)
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The effect of bottom plate thickness (p) on the ultimate tensile resistance of IACs
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in type A specimens is illustrated in Fig. 8(b), and the ultimate tensile resistance is
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nearly unaffected by the variation of p, i.e., the increment in p by 169% (increasing p
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from 2.9 to 7.8 mm) only leads to 7% increase in ultimate tensile resistance. This can
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be attributed to the same failure mode (concrete breakout failure) occurred to the two
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specimens. The test results herein also indicate that the variation of p exhibits minimal
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effect on the concrete breakout resistance. However, there is a possibility of punching
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shear failure of steel faceplate if further reducing the thickness of steel faceplate (i.e.,
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the bottom plate of the tensile test specimen). In addition, the punching shear failure
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mode was observed for the specimen with thin steel faceplate [12,13]. Therefore, it is
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necessary to consider the punching shear failure of the faceplate when developing the
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analytical models for calculating tensile resistances of IACs.
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3.2.5 Interlocking bolt
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There are two types of IACs being designed for the tensile tests, i.e., one with
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interlocking bolt and the other without interlocking bolt (shown in Fig. 6). Fig. 8(c)
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compares the ultimate tensile resistances of these two types of IACs in type A
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specimens. For the specimen TA1 with interlocking bolt and specimen TA9 without
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interlocking bolt, their ultimate tensile resistances are found to be close. However, for
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specimens TA3 and TA10, the ultimate tensile resistance of TA10 without
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interlocking bolt is 36.7% lower than that of TA3 with interlocking bolt. This is
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because the premature slipping between steel sheets may occur to the IACs without
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the interlocking bolt. The above comparisons indicate that the presence of
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interlocking bolts is generally beneficial to the tensile performance of IACs.
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3.2.6 Diameter of steel tube (D)
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Fig. 8(d) illustrates the influence of diameter of steel tube (D) on the ultimate
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tensile resistance of IACs in type A specimens, and it exhibits a slight decrease with
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increasing D. This is because the confinement magnitude on concrete provided by
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outer steel tube shows a decreasing trend with increasing D, and lower confinement
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magnitude on concrete leads to lower concrete breakout resistance.
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3.2.7 Comparison of tensile resistance of type B specimens
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Fig. 8(e) shows the influences of side length of steel angle (L) and interlocking
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bolt on the ultimate tensile resistance of IACs in type B specimens. The ultimate
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tensile resistances of the four type B specimens are found to be close. This is because
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all the four type B specimens exhibited the same failure mode (concrete direct shear),
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and their tensile resistances are governed by the area of concrete direct shear surface
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which is rarely affected by the variation of geometric parameters of IACs (i.e., side
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length of steel angle and interlocking bolt).
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4. Analytical model for tensile resistance of IACs
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The ultimate tensile resistance of a shear connector is the lowest resistances
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determined from all the possible failure modes [16,21,22]. For type A specimens,
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three failure modes may occur, including concrete breakout failure, tensile fracture
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failure of the steel angle, and punching shear failure of the faceplate. For type B
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specimens, only concrete direct shear failure occurs.
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4.1. Tensile resistance for IACs in type A specimens
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4.1.1. Tensile resistance of IACs with concrete breakout failure
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For a pair of IACs in type A specimen, the applied tensile force on the IACs (PT
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in Fig. 9) is partially resisted by the two steel angles which are interlocked by the steel
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sheets, and the rest is resisted by the surrounding concrete, as illustrated in Fig. 9.
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When the force applied to the concrete exceeds the concrete breakout resistance, a
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concrete cone will be pulled out of specimen, and the concrete breakout failure mode
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occurs. At the same time, the steel sheets also experience severe bending deformation
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(as shown in Fig. 12(a)), which also contributes to the tensile resistance of IACs.
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Hence, the ultimate tensile resistance of IACs with failure mode of concrete breakout
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consists of two parts, including concrete breakout resistance and resistance
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contributed by steel sheets.
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In this study, two methods for calculating concrete breakout resistance of IACs
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were proposed based on existing findings and current test results. One is 45-degree
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cone method according to ACI349 [21] and ACI318 [22] (shown in Fig. 10), and the
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other is to employ the measured angles of concrete cone (in Table 2) to modify the
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45-degree cone method.
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1) Concrete breakout resistance based on 45-degree cone method. The concrete
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breakout resistance is calculated based on the assumption that the slope of the conical
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surface is 45° (Fig. 10), i.e., θ is assumed to be 45°. In addition, a shear stress of
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0.33 fc is assumed to apply on the conical surface. For IACs embedded in concrete,
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the breakout resistance of concrete cone can be determined as:
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PTC0 = 0.33 fcu0ℎef
(1)
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where fc is the compressive strength of the concrete cylinder, u0 = 4(L +
345
the perimeter of critical section located at a distance
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concentrated load, and ℎef is the embedded depth of the IACs.
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ℎef
2
ℎef
2
) is
from the loading area of the
2) Concrete breakout resistance based on the measured angle of concrete cone.
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Table 2 presents the measured values of θ from the tensile tests on IACs, and
349
average value of θ is 29.2°, which is different from the value (45°) assumed in the
350
Eq. (1). In addition, test results also showed that the concrete cones are prone to be
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pulled out along the bottom edge of the steel tube for the specimens with a large ℎef
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of the IAC whose concrete cone with θ of 27° (recommended by EC 2 [32] and
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also close to the average measured value of θ) would exceed the boundary of steel
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tube (as illustrated in Fig. 11(b)). This leads to a large θ of the concrete cone, e.g.,
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specimen TA6. Based on above discussions, the values of θ for concrete cones in
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the Eq. (1) are modified as follows: when the concrete cone with θ=27° does not
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exceed the boundary of steel tube, the θ values of the concrete cones are taken as 27°
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(shown in Fig. 11(a)), otherwise, the θ values of the concrete cones are taken as the
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inclination angle of the line that passes the edge of the steel sheet to the bottom edge
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of the steel tube (Fig. 11(b)). Considering the variation of θ, the perimeter of the
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critical section u is obtained as follows:
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363
364
365
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4(L + 2ℎ ),
when θ = 27°
u = 2(D + L), ef otherwise
{
(2)
In the modified calculation method, the breakout resistance of concrete cone can
be determined as:
PTC = 0.33 fcuℎef
(3)
where the value of u is calculated according to Eq. (2).
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The resistance contributed by steel sheets is realized through interlocking
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behavior which transmits the tensile force between the two steel angles of IACs. It is
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observed from the test that evident plastic bending deformation of steel sheets
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occurred and plastic hinge lines was formed, as illustrated in Figs. 12(a) and (b). The
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plastic hinge line is assumed to pass the diagonal of the steel angle (see Fig. 12(b)) to
372
simplify the calculation. According to the free body diagram exhibited in Fig. 12(c),
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373
the tensile resistance contributed by steel sheets is obtained as:
𝑑2
𝑃𝑇𝐵 = 𝑓𝑦𝑝4𝑑 ( 2ℎ ‒ 𝑟)
374
𝑝
ℎ2
‒
2
(4)
375
where 𝑑𝑝 =
2𝑙 is the distance from the center of the bolt hole to the plastic
376
hinge line; 𝑙 is the distance from the center of bolt hole to free edge of steel sheet; 𝑓𝑦𝑝
377
is yield strength of steel sheet; 𝑑 and ℎ are the thickness and side length of steel
378
sheet, respectively; 𝑟 = 2 𝑅2 ‒ 𝑑𝑝2.
379
With regard to the IACs without interlocking bolt whose tensile resistance
380
contributed by steel sheets is lower owing to the weakened interlocking effect, the
381
reduction factor of 0.5 is introduced, and the tensile resistance contributed by steel
382
sheets can be finally given as:
2
𝑑2ℎ
383
𝑃𝑇𝐵 =
384
4.1.2 Tensile resistance of IACs with tensile fracture of steel angle
385
386
387
𝑓
8 𝑦𝑝 𝑑
𝑝
(5)
According to Ref. [33], the tensile resistance of a steel connector can be
calculated as:
𝑃𝑇𝑆 = Ф𝐴𝑆𝑓𝑢𝑎
(6)
388
where Ф = 0.75 is the reduction factor of the steel; 𝐴𝑆 is the cross-sectional area of
389
the steel angle of the IAC; 𝑓𝑢𝑎 is the ultimate tensile strength of steel angle.
390
4.1.3 Tensile resistance of IACs with punching shear failure of steel faceplate
391
When the steel faceplate welded with IACs is relatively thin, the punching shear
392
failure of the faceplate may occur. Based on EC 3 [34], the punching shear resistance
393
of the steel faceplate is obtained as:
394
395
𝑃𝑇𝐹 = 𝑢𝑎𝑝𝑓𝑢𝑝/ 3
(7)
where 𝑢𝑎 is the perimeter of the steel angle of the IAC; p is the thickness of the steel
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396
faceplate; 𝑓𝑢𝑝 is the ultimate tensile strength of the steel faceplate.
397
4.1.4 Summary of tensile resistance of IACs for type A specimens
The tensile resistance of IACs for type A specimens is determined according to
398
399
the corresponding failure modes and is summarized as followings:
(1) For concrete breakout failure, the tensile resistance of IACs can be obtained
400
401
as
402
403
404
405
PT = PTC0 + PTB (Based on 45-degree cone method)
(8)
PT = PTC + PTB (Based on the measured angle of concrete cone)
(9)
or
(2) For tensile fracture of connectors, the tensile resistance of IACs is given as
406
407
408
409
410
PT = PTS
(3) For punching shear failure of steel faceplate welded with IACs, the tensile
resistance of IACs is
PT = PTF
(11)
The lowest calculated value from Eqs. (8), (10) and (11) or Eqs. (9), (10) and (11)
411
is the ultimate tensile resistance of IACs for type A specimens.
412
𝑃𝑇 = min (𝑃𝑇𝐶0 + 𝑃𝑇𝐵 𝑜𝑟 𝑃𝑇𝐶 + 𝑃𝑇𝐵 , 𝑃𝑇𝑆, 𝑃𝑇𝐹)
413
(10)
(12)
4.2. Tensile resistance of IACs for Type B specimens
414
The concrete direct shear failure mode occurs to all the Type B specimens, as
415
shown Fig. 13(a), and the surrounding concrete of IACs is found to be split into two
416
pieces along the vertical plane passing through the diagonal of steel angles.
417
Meanwhile, the bending deformation of steel sheets is still minimal and plastic hinge
418
lines of steel sheets do not appear. Thus, only the direct shear resistance of concrete is
419
considered for the tensile resistance calculation of IACs. According to the free body
420
diagram shown in Fig. 13(b), the tensile resistance (PT) of IACs for type B specimens
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421
can be obtained as:
422
𝑃 𝑇 = 𝐴 𝑐𝜏 𝑐
(13)
423
424
where 𝐴𝑐 = ℎ𝑐(𝐷 ‒ 𝑙𝑎) is the area of concrete subjected to directly shear; ℎ𝑐 is the
425
height of concrete; 𝑙𝑎 is the diagonal length of steel angle; 𝜏𝑐 is the ultimate shear
426
stress at the concrete-to-concrete interface.
427
428
In EC 2 [35], the ultimate shear stress at the concrete-to-concrete interface is
obtained as:
429
𝜏𝑐 = 𝑐𝑓𝑐𝑡 ≤ 0.5𝜂𝑓𝑐
(14)
430
431
where 𝑐 is the cohesion coefficient; 𝜂 is the strength reduction factor and given by
432
0.6(1 ‒ 𝑓𝑐/250); 𝑓𝑐𝑡 and 𝑓𝑐 are the tensile and compressive strength of concrete.
433
In this study, c is determined as 0.5 for calculating the ultimate shear stress.
434
4.3. Verifications of the analytical model
435
4.3.1 Comparing two calculation methods of concrete breakout resistance
436
The test results of 9 specimens failed in concrete breakout mode are presented in
437
Table 3, and the analytical-predicted tensile resistances (by Eqs. (8) and (9)) are also
438
compared with the test data. Table 3 and Fig. 14 show that the tensile resistances
439
predicted by Eq. (8) and (9) are lower than the test values. It is noted that Eq. (9)
440
provides the predicted values closer to the test values, with the mean test-to-prediction
441
ratio of the 9 specimens to be 1.13. Moreover, a smaller COV of 0.08 is observed for
442
the predictions from Eq. (9). Hence, Eq. (9) offers more accurate predictions and
443
should be employed for calculating tensile resistance of IACs failed in concrete
444
breakout.
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445
4.3.2. Comparison with test results
446
The tensile resistances of IACs of type A and B specimens can be predicted by
447
Eq. (12) and Eq. (13), respectively. The comparisons of tensile resistances and failure
448
modes between the analytical models and test results are presented in Fig. 15 and
449
Table 4. The test-to-prediction ratio of tensile resistance for type A specimens is 1.13,
450
with a COV of 0.08. The over-prediction of analytical model (by an average 13%)
451
may be induced by the enhanced strength of confined concrete by the outer steel tube.
452
With regard to type B specimens, these two values are 1.03 and 0.09 respectively. The
453
predicted values for most test specimens are slightly lower than their test values
454
(except for specimen TB3). The aforementioned comparisons demonstrate the
455
accuracy of the proposed formulae for calculating the tensile resistance of IACs.
456
Moreover, the predicted failure modes for all specimens are found to be consistent
457
with those observed in the tests, which further demonstrates the applicability of the
458
analytical model.
459
5. Comparison of tensile resistances between IACs and J-
460
hook connectors
461
For semi-direct-link connectors such as J-hook connectors and IACs, the concrete
462
breakout failure mode is prone to occur. This is because semi-direct-link connectors
463
are generally more applicable for SCS sandwich structures with slim depth and
464
lightweight, and their concrete breakout resistance is low owing to the small
465
embedded depth of connectors. Herein, the comparison of tensile resistances between
466
IACs and J-hook connectors failed in concrete breakout is conducted.
467
Yan et al. [16] conducted the tensile test on J-hook connectors, and the similar
468
type A specimens were also employed in their tests. It was found that 30 specimens
469
exhibited the failure mode of concrete breakout, and their details and test results are
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470
listed in Table 5. In addition, the formula for predicting tensile resistance of J-hook
471
connectors failed in concrete breakout is given as:
T = 0.33 fcAN
472
d𝐽
473
2
where AN = πℎef
(1 +
474
concrete, and d𝐽 is the diameter of J-hook connectors.
(15)
) is the projected area of cone surface to free surface of the
ℎef
475
The tensile resistances of these two types of connectors failed in concrete
476
breakout are governed by geometries of the connectors as well as their dimensions
477
and strengths of materials. Hence, in order to fairly evaluate the superiority of the
478
proposed IACs, a parameter Ф, which represents the tensile resistance per unit mass
479
of the connector and also eliminates the effect of concrete strength, is defined as:
480
Ф=
𝑃𝑇𝑒𝑠𝑡
𝑓𝑐𝑀
(16)
481
where 𝑃𝑇𝑒𝑠𝑡 is the tensile resistances of connectors from tests, and 𝑀 is the mass of
482
connector in a specimen. For J-hook connectors, Eq. (15) shows that dividing the
483
tensile resistance by
484
strength on the tensile resistance of the connectors. With regard to IACs, their tensile
485
resistance is composed of two parts, including the breakout resistance of concrete (
486
P𝑇𝐶0 𝑜𝑟 P𝑇𝐶) and the resistance contributed by steel sheets (P𝑇𝐵), as given in Eq. (8)
487
or Eq. (9). However, the breakout resistance of concrete contributes the majority of
488
the total tensile resistance of IACs (77.7%-94.9%). Thus, it is also reasonable to
489
eliminate the influence of concrete strength on the tensile resistance of IACs by
490
dividing the tensile resistance by
491
tensile resistance is also divided by the mass of the connector (𝑀) in order to
492
evaluate the geometric superiority of the connectors, i.e., the higher value of Ф means
493
a superior geometry of the connector which offers higher tensile resistance per unit
𝑓𝑐 can theoretically eliminate the influence of concrete
𝑓𝑐 according to Eq. (1) or Eq. (3). In addition, the
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494
mass of steel material. The values of Ф for the specimens failed in concrete breakout
495
are shown in Table 5 and Fig. 16, and the average value of Ф of IACs is 55.9% higher
496
than that of J-hook connectors. This demonstrates the geometric superiority of IACs
497
as compared to J-hook connectors in terms of tensile resistance. In addition, the
498
specimens from Yan et al. [16] and current tests employed the dimensions and
499
materials of connectors that were commonly used in practical engineering. Hence, it is
500
of significance to directly compare their test values of tensile resistances. Fig. 16
501
shows that the average tensile resistance of IACs obtained from the current test is
502
303.1% higher than the tensile resistances of J-hook connectors.
503
6. Conclusions
504
In this paper, the tensile performances of the novel IACs embedded in concrete
505
were experimentally studied, and analytical models were developed to predict the
506
tensile resistances of IACs. The influences of embedded depth of IAC, thicknesses of
507
steel sheet, steel angle and bottom plate, side length of steel angle, steel tube diameter
508
and interlocking bolt on the tensile performances of the proposed IACs were also
509
experimentally investigated. The comparison of tensile resistances between the IACs
510
and J-hook connectors was conducted to evaluate the superiority of IACs. The main
511
findings from this work were summarized as follows:
512
(1) There were two failure modes for type A specimens, including concrete
513
breakout failure and tensile fracture failure of the steel angle. With regard to
514
type B specimens, only concrete direct shear failure was found. In the concrete
515
breakout failure, a concrete cone was pulled out of the specimen and leaving a
516
conical cavity in the remaining concrete. The tensile fracture failure of the
517
steel angle was characterized by the shank of the steel angle failed in fracture
518
with evident necking. With regard to the concrete direct shear failure, the
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519
surrounding concrete was split into two pieces by the IACs.
520
(2) The ultimate tensile resistance of type A specimens exhibited an evidently
521
growing tendency with increasing embedded depth of IACs (ℎef) and
522
thickness of steel sheet (d). The failure modes were also changed from the
523
concrete breakout failure to tensile fracture failure of the steel angle with the
524
increase of ℎef. The presence of interlocking bolts was found to enhance the
525
tensile resistance of IACs. Other parameters (i.e., the thickness of steel angle
526
and bottom plate as well as the diameter of steel tube) exhibited limited
527
influence on the tensile resistances of type A specimens
528
(3) The tensile resistances of IACs failed in concrete direct shear were determined
529
by the area of the concrete direct shear surface, and they are rarely affected by
530
the variation of the geometry of IACs. Thus, the tensile resistances of all type
531
B specimens were shown to be close.
532
(4) Analytical models were developed to predict the ultimate tensile resistances of
533
IACs for type A and B specimens. The mean test-to-prediction ratio for type A
534
specimens was 1.13 with a COV of 0.08, and these two values were 1.03 and
535
0.09 for type B specimens. This demonstrated the rationality of the proposed
536
formulae for tensile resistances of IACs.
537
(5) A parameter Ф was proposed to fairly evaluate the geometric superiority of
538
IACs in terms of tensile performance. The average value of Ф of IACs was
539
found to be 55.9% higher than that of J-hook connectors, which demonstrated
540
the improved tensile performance of the proposed IACs.
541
7. Acknowledgement
542
The research presented in this paper is financially supported by the National Key
543
Research and Development Project of China (Grant No. 2020YFB1901403), the
Electronic copy available at: https://ssrn.com/abstract=4070260
544
Funds for Creative Research Groups of National Natural Science Foundation of China
545
(Grant No. 51921006), the Fundamental Research Funds for the Central Universities
546
(Grant No. FRFCU5710051919) and Heilongjiang Postdoctoral Fund (Grant No.:
547
LBH-Q21099 and LBH-TZ1014).
548
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571
572
573
574
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577
578
579
580
581
582
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Electronic copy available at: https://ssrn.com/abstract=4070260
667
Tables
Table 1 Details of test specimens
668
Specime
n
Typ
e
D
(mm
)
L
(mm
)
b
(mm
)
d
(mm
)
hef
(mm
)
p
(mm
)
Bol
t
fc
(MPa
)
fct
(MPa
)
fyp
(MPa
)
fya
(MPa
)
fup
(MPa
)
fua
(MPa
)
TA1
TA2
TA3
TA4
TA5
TA6
TA7
TA8
TA9
TA10
TB1
TB2
TB3
TB4
A
A
A
A
A
A
A
A
A
A
B
B
B
B
250
300
250
250
250
250
250
250
250
250
250
250
250
250
50
50
50
50
50
50
50
50
50
50
50
45
56
50
2.8
2.8
2.8
3.6
4.5
2.8
2.8
4.5
2.8
2.8
2.8
2.8
2.8
2.8
2.9
2.9
4.5
2.9
2.9
2.9
2.9
2.9
2.9
4.5
3.8
2.9
2.9
3.8
50
50
50
50
50
75
100
50
50
50
50
50
50
50
7.8
7.8
7.8
7.8
7.8
7.8
7.8
2.9
7.8
7.8
7.8
7.8
7.8
7.8
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
Yes
Yes
Yes
No
50.6
50.6
50.6
50.6
50.6
50.6
50.6
50.6
50.6
50.6
50.6
50.6
50.6
50.6
3.62
3.62
3.62
3.62
3.62
3.62
3.62
3.62
3.62
3.62
3.62
3.62
3.62
3.62
278
278
307
278
278
278
278
278
278
307
284
278
278
284
353
353
353
303
383
353
353
383
353
353
353
353
353
353
522
522
526
522
522
522
522
522
522
526
508
522
522
508
630
630
630
555
673
630
630
673
630
630
630
630
630
630
669
Note: D is the inner diameter of the steel tube; L and b are the side length and
670
thickness of steel angle, respectively; d is the thickness of steel sheet; ℎ𝑒𝑓 is the
671
embedded depth of IACs (shown in Fig. 4(a)); p is the thickness of the bottom plate;
672
𝑓𝑐 and 𝑓𝑐𝑡 are the compressive and tensile strength of concrete, respectively; 𝑓𝑦𝑝 and
673
𝑓𝑢𝑝 are the yield and ultimate strength of steel sheet, respectively; 𝑓𝑦𝑎 and 𝑓𝑢𝑎 are
674
675
676
677
the yield and ultimate strength of steel angle, respectively.
Table 2 The angles of the concrete cones
Specimen
𝜽𝟏(deg.)
𝜽𝟐(deg.)
𝜽𝟑(deg.)
𝜽𝟒(deg.)
Average 𝜽𝒂(deg.)
TA1
TA2
TA3
TA4
TA5
TA6
TA8
TA9
TA10
Mean
Cov
26.0
25.7
30.8
23.5
31.2
39.9
26.4
25.4
27.7
25.9
26.2
25.4
46.3
29.9
32.5
31.4
38.9
27.1
27.5
23.4
32.4
25.3
29.5
40.5
28.4
23.9
26.7
26.6
35.7
26.2
25.6
33.5
28.4
30.1
24.6
26.9
26.5
27.7
28.7
30.2
31.0
35.33
29.1
28.2
27.1
29.2
0.08
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678
679
Note: θ1~θ4 are the angles between failure surface of concrete cone and free
concrete surface; θa is the average value of the θ1~θ4.
680
681
682
683
684
Table 3 Comparisons between predicted resistances and test data for specimens failed
in concrete breakout mode
Specimen
𝑃𝑇𝑒𝑠𝑡 (kN)
𝑃𝑇,𝑎1 (kN)
TA1
TA2
TA3
TA4
TA5
TA6
TA8
TA9
TA10
Mean
Cov
89.2
79.4
112.53
90.75
92.76
115.37
86.29
93.66
82.99
54.49
54.49
67.07
54.25
54.02
95.56
54.02
50.72
57.01
𝑃𝑇𝑒𝑠𝑡/
𝑃𝑇,𝑎1
1.64
1.46
1.68
1.67
1.72
1.21
1.60
1.85
1.46
1.59
0.12
𝑃𝑇,𝑎2 (kN)
77.96
77.96
90.54
77.73
77.49
113.17
77.49
74.19
80.48
𝑃𝑇𝑒𝑠𝑡/
𝑃𝑇,𝑎2
1.14
1.02
1.24
1.17
1.20
1.02
1.11
1.26
1.03
1.13
0.08
685
Note: 𝑃𝑇𝑒𝑠𝑡 are the test results of tensile resistance; 𝑃𝑇,𝑎1 is the predicted resistance
686
based on the 45-degee cone method; 𝑃𝑇,𝑎2 is the predicted resistance based on the
687
688
689
690
measured angles of concrete cone.
Table 4 Comparisons between predicted and experimental results for all specimens
Specimen
Test
failure
mode
Predicted
failure mode
𝑃𝑇𝑒𝑠𝑡 (kN)
𝑃𝑇,𝑎 (kN)
𝑃𝑇𝑒𝑠𝑡/𝑃𝑇,𝑎
TA1
TA2
TA3
TA4
TA5
TA6
TA7
TA8
TA9
TA10
Mean
Cov
CB
CB
CB
CB
CB
CB
STF
CB
CB
CB
CB
CB
CB
CB
CB
CB
STF
CB
CB
CB
89.2
79.4
112.53
90.75
92.76
115.37
149.41
86.29
93.66
82.99
77.96
77.96
90.54
77.73
77.49
113.17
140.33
77.49
74.19
80.48
1.14
1.02
1.24
1.17
1.2
1.02
1.06
1.11
1.26
1.03
1.13
0.08
TB1
CDS
CDS
32.86
32.80
1.00
Electronic copy available at: https://ssrn.com/abstract=4070260
TB2
TB3
TB4
Mean
Cov
CDS
CDS
CDS
CDS
CDS
CDS
35.63
29.06
37.91
34.09
31.25
32.80
1.05
0.93
1.16
1.03
0.09
691
Note: CB – concrete breakout failure; STF – tensile fracture failure of the steel angle;
692
CDS – concrete direct shear failure; 𝑃𝑇,𝑎 is the predicted resistance.
693
Table 5 Details and test results of the specimens with J-hook connectors and IACs
Details and test results of the specimens with J-hook connectors from ref. [13]
Specimen
hef (mm)
dJ (mm)
DJ / dJ
M (kg)
fc (MPa)
TUA1
TUA2
TUA3
TUA6
TUA7
TUA8
TUA13
TUA14
TLA5
TLA8
TLA10
TLA11
TNA9
TUB4
TUB5
TUB8
TUB9
TUB10
TLB7
TLB10
TLB11
TNB4
TNB7
TNB8
TNB11
TNB13
TNB14
TNB15
TNB16
Mean
Cov
50
50
50
50
50
50
50
50
50
50
50
50
50
100
50
50
50
50
50
50
50
50
47.5
47.5
62.5
50
50
50
50
12
12
12
16
16
16
16
12
16
16
12
16
12
12
16
12
16
12
12
12
12
12
12
16
20
16
12
12
12
2
3
4
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
4
2
2
2
2
2
2
2
2
2
0.17
0.19
0.21
0.35
0.35
0.35
0.35
0.17
0.35
0.35
0.17
0.35
0.17
0.26
0.35
0.17
0.35
0.17
0.19
0.21
0.17
0.17
0.16
0.34
0.67
0.35
0.17
0.17
0.17
55
55
55
55
55
55
47.86
60.62
60.62
33.11
48.73
48.73
54.67
54.67
54.67
66.51
66.51
57.75
57.75
57.75
53.1
66.07
57.75
65
65
26.65
47.86
60.62
54.67
PTest
(N)
21500
22100
23200
34600
34100
33400
29600
21300
36100
32300
26400
36200
25800
28900
35300
30150
33200
23400
25000
27700
30800
27100
26760
37810
57540
27410
19900
36800
28700
Details and test results of the specimens with IACs from present study
Electronic copy available at: https://ssrn.com/abstract=4070260
Ф
17282.30
15640.00
14664.61
13521.57
13326.17
13052.61
12400.45
16308.58
13437.90
16268.79
22545.00
15029.43
20801.26
15239.25
13836.70
22038.82
11798.50
18356.27
17265.92
17087.07
25196.95
19875.21
21562.35
13909.95
10590.47
15388.37
17147.91
28176.32
23139.39
17065.11
0.25
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
Specimen
hef (mm)
L(mm)
b(mm)
d(mm)
M(kg)
fc (Mpa)
TA1
TA2
TA3
TA4
TA5
TA6
TA8
TA9
Mean
Cov
50
50
50
50
50
75
50
50
50
50
50
50
50
50
50
50
3
3
3
4
5
3
5
3
3
3
5
3
3
3
3
3
0.44
0.44
0.50
0.52
0.61
0.55
0.61
0.39
50.59
50.59
50.59
50.59
50.59
50.59
50.59
50.59
PTest
(N)
89200
79400
112530
90750
92760
115370
86290
93660
Ф
28761.15
25601.30
31521.13
24365.57
21401.73
29477.77
19908.96
33602.96
26605.15
0.17
Note: hef is the embedded depth of the connector; dJ is the diameter of the J-hook shear
connectors; DJ is the inner diameter of the hook; M is the mass of a pair of connectors;
Ф is the tensile resistance per unit mass of the connector and also eliminates the effect
of concrete strength.
Electronic copy available at: https://ssrn.com/abstract=4070260
723
Figures
Steel faceplate Angle
Steel faceplate
Concrete Friction-welded bar
(a)
Steel faceplate
(b)
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
Concrete
Steel faceplate Headed stud
Through blot
(e)
Steel faceplate
Concrete
(d)
Direct-link connectors
Indirect-link connectors Semi-direct-link connectors
Fig. 1. Typical form of mechanical connectors (a) friction-welded bar connectors in
Bi-steel structure; (b) through blots; (c) angles; (d) headed studs; (e) J-hook
connectors; (f) Interlocked angle connectors (IACs).
Electronic copy available at: https://ssrn.com/abstract=4070260
J-h
Concrete
(c)
Concrete
Concrete
Steel faceplate
Interlocked a
(f)
𝐿
Steel angle
𝑏
Holes
Steel sheet
𝑑
Interlocking bolt
Components
742
Fillet welding
(1) Welding steel
sheet to steel angle
(2) Welding interlocking
bolt to steel sheet
Fabrication procedure
(a) Upper angle connector
743
Steel sheet
Holes
(1)Welding steel sheet
to steel angle
Steel angle
744
Fillet
welding
Fabrication procedure
Components
(b) Lower angle connector
745
Fillet welding
Upper angle
connector
Lower angle
connector
746
747
748
749
750
(c) Interlocked angle connectors
Fig. 2. Details of the IACs
Electronic copy available at: https://ssrn.com/abstract=4070260
Tensile Force
Tensile Force
Reserved hole
Connector
Connector
Top steel plate
Specimen
Linking
Bolts
Frame
Specimen
Bottom
steel plate
Bottom steel
bar
Tensile Force
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
Test setup
Frame
Bottom steel
bar
Tensile Force
Test setup
(a) Method proposed by Xie et al. [12]
(b) Method proposed by Sohel et al. [9]
Fig. 3. Typical tensile test methods
Electronic copy available at: https://ssrn.com/abstract=4070260
Concrete
Tensile Force
A
Top steel bar
Top view
Additional plate
Upper steel
angle
Bolt holes
ℎ��
Steel Tube
Conversion device
ℎ��
Bottom plate
783
784
Bolt
Interlocking bolt
B
Bottom steel bar
Tensile Force
Side view
(a) Details of specimen
C
(b) 3D view of test setup
LVDT
Conversion
device
Specimen
785
786
787
788
789
790
791
792
793
794
795
796
797
(c) Photo of test setup
Fig. 4. The tensile test method in present study
Electronic copy available at: https://ssrn.com/abstract=4070260
plank
Fillet welding
Adhesive
798
799
(a) Welding lower connector to bottom plate
Casting
concrete
800
801
(b) Gluing bottom plate and steel tube to square plank
Steel bar
(c) Fixing the upper angle connector and concreting
Type A
802
803
804
805
Steel bar
(d) Removing of plank and steel bar
Type B
(e) Welding bottom steel bar and cutting off steel tube of type B specimens
Fig. 5. Fabrication procedures of specimen
Upper angle connector
Fillet welding
Steel sheet
Lower angle connector
806
807
Fig. 6. The IACs without interlocking bolt
Electronic copy available at: https://ssrn.com/abstract=4070260
808
809
Bending
deformation
θ
θ
Concrete cone pulled out
810
811
Conical cavity
(a) Concrete breakout failure
Fracture
812
813
(b) Tensile
of the steel angle
Tension
failurefailure
after necking
Vatical through crack
814
815
816
817
818
819
820
821
822
823
824
825
826
Local damage
Vertical surface
(C) Concrete direct shear failure
Fig. 7. Failure modes of the tensile tests
Top view
Bottom view
Direct shear surface
Electronic copy available at: https://ssrn.com/abstract=4070260
827
160
120
PT versus b curves
110
120
100
TA1, hef = 50
TA6, hef = 75
TA7, hef = 100
80
60
50
25
50
75
100
Steel angle
thickness b
90
125
80
Bottom plate
thickness p
2
5
6
8
80
TA1, D = 250
TA2, D = 300
70
60
240
Without bolt
Connector type
(c) Effect of connector type on PT
250
260
270
280
290
300
Diameter D (mm)
(d) Effect of D on PT
50
PT (kN)
40
30
TB1, L=50, d=4, with bolt
TB2, L=45, d=3, with bolt
TB3, L=56, d=3, with bolt
TB4, L=50, d=4, without bolt
20
10
832
833
834
835
TB1
9
90
80
With bolt
7
100
TA1, d=3
TA3, d=5
TA9, d=3
TA10, d=5
PT (kN)
PT (kN)
4
(b) Effect of thickness on PT
100
60
3
Thickness value (mm)
(a) Effect of hef on PT
120
PT versus p curves
Steel sheet
thickness d
100
Depth hef (mm)
130
830
831
PT (kN)
PT (kN)
140
828
829
PT versus d curves
TB2
TB3
TB4
Specimen
(e) Comparison of tensile resistance of type B specimens
Fig. 8. Influences of different parameters on tensile resistance of IACs
Electronic copy available at: https://ssrn.com/abstract=4070260
310
𝑃�� Force transmitted directly
to the other IAC by steel
sheets
𝑃�� (𝑃��� )
𝑃�
836
837
838
Force transmitted to
concrete
Fig. 9. Force transmission path
L
L
Critical section
perimeter
ℎ��
𝑃�
45°
ℎ��
ℎ�� 2
2
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
Fig. 10. 45-degree cone method
Electronic copy available at: https://ssrn.com/abstract=4070260
Steel
tube
ℎ��
27°
ℎ��
θ = 27°
ℎ��
Critical section
𝑃�
854
855
Concrete
cone
(a) The concrete cone with θ=27° dose not exceed the boundary of steel tube
Steel
tube
27 ° concrete
cone
27°
ℎ��
θ
𝐷−𝐿
4
θ
27°
Actual concrete cone
pullled out along the
bottom edge of steel
tube
𝐷 − 𝐿 Critical section
4
856
𝑃�
857
858
859
(b) The concrete cone with θ=27° exceed the boundary of steel tube
Fig. 11. The 𝜃 values of the concrete cones
plastic hinge line
𝑃��
𝑃��
Bending
deformation
(b) Plastic hinge line position
𝑃��
ℎ
𝑙
𝑑�
r
𝑃�
860
861
862
(a) Deformation of steel sheets
(c) Free body diagram
Fig. 12. Bending deformation of steel sheets
Electronic copy available at: https://ssrn.com/abstract=4070260
𝑃�
𝑃�
Vertical shear
surface
Concrete
𝜏�
ℎ�
𝑃�
863
864
865
𝑙�
D
(a) The concrete split into two pieces
(b) Free body diagram
Fig. 13. Concrete direct shear failure
866
150
45° cone method
Meathod besed on the measured cone angle
Prediction (kN)
120
90
Unsafe side
60
Safe side
30
30
867
868
869
870
871
872
873
874
875
876
877
60
90
120
150
Test (kN)
Fig. 14. Comparisons of two calculation methods
Electronic copy available at: https://ssrn.com/abstract=4070260
160
Type A specimens
Type B specimens
Prediction (kN)
120
80
Unsafe side
40
Safe side
0
0
878
879
880
40
80
120
160
Test (kN)
Fig. 15. Comparisons between predicted resistance and test results
Ф(× 103 𝑁/𝑀 𝑃0.5
𝑎 /𝑘𝑔)
35
IACs
J-hook connectors
Mean of IACs
Mean of J-hook connectors
30
25
Mean test value of Jhook connectors
20
15
Mean test value of IACs
10
0
881
882
883
884
20
40
60
80
100
120
PTest (kN)
Fig. 16. Comparisons of tensile performances between IACs and J-hook connectors
Electronic copy available at: https://ssrn.com/abstract=4070260