Flexural Behavior of Insulated Concrete Sandwich Panels using FRP-Jacketed Steel-Composite Connectors

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Introduction
Precast concrete sandwich panels with an insulation layer are increasingly used as exterior walls in buildings because of their energy conservation, convenient installation, and excellent thermal efciencies [1]. A typical precast concrete wall-panel system consists of two reinforced concrete wythes, core insulation, and connectors penetrating through the insulation [2]. Precast concrete wall panels can be classifed as fully composite, noncomposite, or partially composite. Practically all precast concrete panels in use are partially composite with stifness depending on the confguration of the shear connectors [3]. To ensure sufcient composite action to meet design requirements of strength and stifness, connectors between wythes should provide adequate shear transfer ability [4]. Steel shear connectors have been widely employed to hold the wythes and foam core together. However, huge heat losses are noted in sandwich wall panels with steel connectors, due to the thermal bridging efect caused by the steel [5,6].
Nonmetallic connectors, such as fber-reinforced polymer (FRP) connectors and plastic connectors, have been developed as alternatives to steel connectors. FRP not only has high tensile strength, low thermal conductivity but also has low elastic modulus and poor ductility. Combining the advantages of FRP and steel, hybrid FRP/steel connectors are expected to have high elastic modulus and shear strength, good ductility, and be cost-efective. In this study, an innovative dumbbell-shaped steel-FRP composite connector was developed and the fexural behavior of sandwich panels with these novel connectors was investigated to understand composite action and failure mechanisms. Te efects of the confguration of connectors, axial compression ratio, loading direction, and content of vitrifed microspheres in the wythes were considered. Te resulting sandwich panels with these novel connectors were expected to be lightweight, have high composite action, and be energy-efcient for potential applications in prefabricated buildings in cold regions. Te process is shown in the graphical abstract.
Researchers have investigated the design and properties of various shapes of FRP connectors. For example, Woltman et al. [7] have investigated three diferent kinds of connectors produced from glass FRP (GFRP) bars, in comparison with steel and polymer connectors. Te shear strengths of these GFRP connectors (48-112 MPa) have been reported to be much higher than those of specialized polymer connectors (22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39), but lower than those of steel connectors (297-365 MPa). Chen et al. [8] compared the fexural behavior of concrete sandwich panels with diferent types of FRP plate connectors, in which the continuous and segmental connectors perform much better than discrete connectors. Tomlinson et al. [9] compared the behavior of basalt FRP (BFRP) and steel connectors under push-through loads. Teir results showed the BFRP and steel connectors had similar tensile strength for diameters of 6 mm, while the compressive strength of steel connectors was double than that of BFRP connectors. Lameiras et al. [10] investigated the infuence of diferent laminates and the number and geometry of holes of perforated GFRP plate connectors and found that the ultimate pull-out load capacities of connections with 3 holes (hole diameter and spacing at 30 and 45 mm, respectively) increased 49% compared with connections without holes. Choi et al. [11] investigated the inplane shear behavior of concrete sandwich panels with grid-type GFRP composites. Teir results showed reductions in panel stifness with increases in grid spacing of extruded polystyrene (XPS) insulation. Although sandwich wall panels with FRP grids or continuous connectors usually have a higher degree of composite action than wall panels with separate FRP connectors. A separate FRP connector has a relatively small cross section and can be simply designed and commercially constructed [12]. Terefore, separate FRP connectors have been recently used extensively in sandwich insulation wall panels. Separate FRP connectors usually adopt groove or angled features and both ends of FRP connectors can be grooved to increase friction between the connectors and concrete wythes [13]. Tis anchorage efect relies on construction quality [14], connectors arranged at an angle can better utilize the axial stifness of the materials [9], and the insertion angle and diameter of FRP connectors have signifcant efects on the ultimate capacity and stifness of sandwich wall panels. FRP plate and FRP tube connectors can use anchorage rebars passed through perforated plates and tubes to improve anchorage efects [12,15]. Although using FRP connectors is benefcial for thermal insulation purposes, the low elastic modulus and shear strength as well as the brittle failure type hinder the widespread application of FRP connectors.
Hybrid FRP/steel connectors combine the advantages of the two materials. Wu et al. [16] have developed a novel hybrid steel-FRP composite bar (SFCB) which consists of a steel core and FRP jacket. SFCBs exhibit bilinear tensile stress-strain curves before fracture and have stable post-yield stifness after yielding [16]. Cleary et al. [17] incorporated FRR plates into steel connections to correct thermal bridging issues. Dong et al. [18] investigated bond durability between SFCBs and sea sand concrete in an ocean environment. Teir test results indicated that chloride ions in sea sand improved SFCB bonding within the test duration (90 d) and the degree of corrosion in continuous immersion is greater than that in a wet-dry cycling environment. Seo et al. [19] compared the tensile properties of glass-type SFCBs with diferent steel cores, including a steel rod, a bunch of steel wires, or steel rebar in the core. SFCBs with a steel wire core exhibit the highest tensile strength than other composite bars. Zhi and Guo [20] stated that a reasonable design of W-shaped SFCB connectors could provide high composite action for Sandwich panels and enhance panel ductility due to steel cores in the connectors. Zhou et al. [21] examined SFCB durability by X-ray microcomputed tomography and found actual corrosion rates of carbon-type and glass-type SFCBs were less than 10 and 1% of the corrosion rate when compared with an ordinary steel bar, respectively. Yang et al. [22] reported the fexural behavior of concrete beams reinforced by SFCBs, in which SFCB-reinforced concrete beams display completely diferent failure modes compared with RC beams, depending on the reinforcement ratio and steel/FRP ratio [22]. Concrete beams reinforced with steel-BFRP composite bars exhibit better ductility and smaller crack widths compared with the beams reinforced with steel-GFRP composite bars [23]. Previous studies have indicated that SFCBs can be produced industrially and cost-efectively [24]. SFCB connectors possess superior performance in terms of stifness and load-carrying capacity [25]. However, because FRP adhesion to concrete is not as high as that of steel, some form of mechanical anchorage should be provided for SFCB connectors [26].
Te objective of this study was to develop an innovative dumbbell-shaped SFCB connector and study its efects on the fexural behavior of insulated concrete sandwich panels. FRP thickness, raised thickness of dumbbell ends of connectors, axial compression ratio, and content of vitrifed microspheres in the wythes were varied to investigate the structural behavior of these sandwich panels. Te incorporation of a certain content of vitrifed microspheres in concrete as lightweight aggregates was aimed to reduce the overall panel weight. Furthermore, when these sandwich panels are applied as external wall panels of high-rise buildings, they should have sufcient resistance against frontal wind pressure (positive pressure) and backwind suction (negative pressure). Tus, the fexural behavior of these panels under positive and negative loads was investigated. Ten, fnite-element (FE) models were constructed and the numerical results compared with the experimental data were gathered here. Te verifed FE model was fnally used to investigate the infuence of shear connector arrangement. In addition, an analytical model was developed and presented to predict the defection of these panels under combined axial-fexural loads.

Details of Proposed Connectors.
Connectors were designed based on hybrid GFRP-steel bars and fabricated by pultrusion. Crescent-rib steel rebar with an 8 mm diameter was used as the core material for the connectors. Te manufacturing process of the hybrid GFRP-steel bars has been previously described [16]. A 25 mm length at the top and bottom of the hybrid FRP-steel bars was wrapped with six or nine layers of GFRP to prevent slippage between the concrete wythe and shear connector. All shear connectors were of the same 250 mm length. Te diferences between the shear connectors were the thickness of GFRP and the raised thickness of the dumbbell ends. Te thickness of GFRP jackets of hybrid bars varied from 2 to 3 mm and the raised thickness of dumbbell ends varied also from 4 to 6 mm.

Material
Properties. E-glass rovings and vinyl ester resin were used to produce hybrid GFRP-steel bars. Moreover, the dumbbell ends were composed of E-glass woven fabric with vinyl ester resin. Te volume ratio of the glass fber was 65%. Te mechanical properties of glass fber obtained from the manufacturer were tensile strength 750 MPa, compression strength 725 MPa, and Young's modulus 45 GPa. Vinyl ester resin had physical performance indices of tensile strength 55 MPa, fracture elongation 2%, and fexural strength 105 MPa. Te tensile strength and Young's modulus of GFRP obtained from the manufacturer were 360 MPa and 25 GPa, respectively. HRB335 steel bars, with a yield strength of 335 MPa and Young's Modulus of 200 MPa, were used in the production of hybrid GFRP-steel bars.
Te tensile and shear properties of the hybrid GFRP-steel bars were measured in accordance with GB/T 228.1-2010 [27] and JG/T 406-2013 [28]. Te pull-out strength of the dumbbell-shaped SFCB connector to concrete was measured in accordance with GB/T 50081-2019 [29]. Te measured properties of shear connectors are given in Table 1.
Graphite polystyrene (GPS) foam was used as insulation, which could be efective against moderate fre exposure because of its low thermal conductivity and class B fre resistance (fame spread rating between 26 and 75). Te properties of GPS foam provided by the manufacturer were density 23.5 kg/m 3 , compressive strength 117 KPa, and thermal conductivity coefcient 0.034 W/(m·K).
Vitrifed microspheres are a type of inorganic insulation material with vitrifed irregular closed surfaces and porous microstructures, obtained from glass lava ore by vitrifcation. Teir particle size is in the range of 0.5-1.5 mm and their bulk density is 300 kg/m 3 . Te incorporation of vitrifed microspheres in concrete contributed to decreasing concrete density and thermal conductivity of concrete [30]. However, excessive vitrifed microspheres might lead to decreased concrete compressive strength and elasticity modulus. Previous research by Zhao et al. [31] indicated microcracks that occur around microspheres once the mass ratio increases to 2.8%. Terefore, the mass ratios of vitrifed microspheres to concrete mixture mass were chosen here as 0, 0.6, and 1.2% (corresponding volume fractions were 0, 10, and 20%, respectively). For concrete with certain microsphere content, fve 150 mm cubes were cast and cured under conditions similar to those of the related Sandwich panels. Te compressive properties of the concrete are shown in Table 2.
Wire mesh with a diameter of 8 mm was used for fexural reinforcement of the concrete wythe. Te yield strength and elastic modulus of the steel wire mesh were 400 MPa and 210 GPa, respectively.

Test Specimens.
Nine specimens were prepared to study the fexural responses of Sandwich panels with dumbbellshaped SFCB connectors. Te fabrication procedure of Sandwich panel specimens is shown in Figure 1. Two layers of steel wire mesh in the structural wythe were frst installed. Ten, the shear connectors were bound to the steel mesh at the design positions. After casting the concrete in the structural wythe, the insulation foam was installed, in which the shear connectors penetrated the foam. After that, the steel wire mesh in the facade wythe was installed, followed by casting the concrete in the façade wythe. Te Sandwich panel specimens and molds were covered with plastic flm to prevent moisture loss and then cured at room temperature for 24 h. After removal from their molds, the specimens were cured in a standard curing room at 20 ± 2°C at a relative humidity (RH) of 95% for 28 d.
Te proposed wall was a 2800 × 1000 mm Sandwich panel system with a total thickness of 310 mm. All specimens consisted of a 120-mm-thick structural wythe, a 60-mmthick facade wythe, and a 130-mm layer of GPS foam insulation between the two wythes. Tis thickness of insulation was aimed to achieve the desired thermal efciency in cold regions of China (heat transfer coefcient of external wall ≤0.35 W/(m 2 ·K)). Te facade and structural wythes were reinforced with one and two layers of 8 mmdiameter steel welded wire mesh (bar spacing of 250 mm in longitudinal direction and 150 mm in transverse direction), respectively. Te spacing of shear connectors was 600 mm in longitudinal and transverse directions. Te shear connectors of the control specimen had 2-mm-thickness of GFRP on the hybrid bars and 4 mm raised thickness of dumbbell ends. Te reference specimen was forced to yield a positive moment. Te arrangements of the steel reinforcements and connectors are shown in Figure 2. Note. Te thickness of FRP jacket and raised thickness of dumbbell ends of connector 1 are 2 mm and 4 mm, respectively, the thickness of FRP jacket and raised thickness of dumbbell ends of connector 2 are 3 mm and 4 mm, and the thickness of FRP jacket and raised thickness of dumbbell ends of connector 3 are 2 mm and 6 mm, respectively, and δ is coefcient of variation.  Te details of the test specimens are provided in Table 3. A list of the main parameters investigated are as follows: (1) GFRP thickness on the hybrid bars varied from 2 to 3 mm and raised thickness of the dumbbell from 4 mm to 6 mm. (2) Vitrifed microsphere volume fractions of concrete wythes varied between 0, 10, and 20%. (3) Axial loading was applied on two specimens under combinations of fexural and axial loads, with the axial compression ratio varying between 0/1, 0.2/1, and 0.4/1. Te axial compression ratio is n � C 0 / (f c A c + f ya A a ), with C 0 the applied axial compression force of Sandwich panels, f c the prismatic compressive strength of concrete, with f c � 0.76 f cu , f cu the cubic compressive strength of concrete, A c the gross cross-sectional area of concrete wythes, f ya the yield strength of steel reinforcements, and A a the cross-sectional area of steel reinforcements in the longitudinal direction in the facade and structural wythes. (4) Te loading direction of 7 specimens was loaded out of the plane on the facade wythe to simulate external wind pressure and two specimens were loaded out of the plane on the structural wythe to simulate suction pressure ( Figure 3).

Experimental Set-Up.
Specimens were tested under a four-point bending condition with load acting at one-third intervals of the span. Te experimental set-up consisted of a 200 kN load cell, which transferred the load to two load heads using a rigid steel spreading beam. Te clear span was kept at 2600 mm for each Sandwich wall panel. Linear variable displacement transducers (LVDTs) were used to monitor the defections at the supports and bottom defection at the midspan. Te test set-up of four points simply supported Sandwich panels ( Figure 4). Te stress state of the midspan cross section was monitored by strain gauges A1 to A5, which were bonded to the steel wires in the facade wythe, and strain gauges B1 to B5 and C1 to C5 were bonded to the steel wires in the structural wythe, with gauge 10 mm in length ( Figure 5). A load interval within one-ffteenth of the estimated failure load capacity was taken and maintained while testing for 10 min until the gauge readings became stable. Tests were stopped till the panels were fractured.

General Behavior and Failure
Mode. Typical failure modes are shown in Figure 6. Te reference specimen G24-I exhibited liner-elastic behavior in the early stage and, as the load increased up to ∼35% of the ultimate load, vertical cracks occurred on the facade wythe near the loading point. Further increased load up to 90% of the ultimate load caused several vertical cracks at the structural wythe of the midspan. Te facade wythe completely bonded with the foam core during the test, while an end slip occurred between the   Loading  direction  G24-I  2  4  0  0  Positive  G24-II  2  4  0  0  Negative  G24S10-I  2  4 10 In the frst column, the frst letter G means GFRP-steel hybrid connectors are used in Sandwich panels, the frst and second numbers mean the thickness of GFRP on hybrid bars and raised thickness of dumbbell ends, the second letter S and A mean vitrifed microspheres are added in concrete and axial compression load is applied on the panels, respectively, the numbers 10 and 20 after the letter S mean the volume fractions of vitrifed microspheres are 10% and 20%, respectively, the number 0.2 and 0.4 after the letter A mean the axial compression ratios of the panels, respectively, and the last number I and II mean the load results in positive and negative moments in the panels, respectively.

60-mm-wythe
120-mm-wythe Te specimens under the combined efects of axial and fexural loads and the specimen under negative loads exhibited diferent failures with specimen G24-I. Te axial compressive load contributed to the delay in the onset of concrete cracks. Te tensile crack occurred on the structural wythe of the specimen with an axial compression ratio of 0.2/1 while the vertical load increased up to ∼80% of the ultimate load. Tis was followed by cracks occurring on the facade wythe of the specimen and then failure by penetrating cracks on the face of the façade wythe of the midspan. For specimens with an axial compression ratio increased to 0.4/ 1façadefacade wythe peeled from the foam core and, then the end of the facade wythe was suddenly crushed. Te cracking load of the specimens subjected to negative loads was ∼60% of the ultimate loads and their failure modes were similar to those of specimens with an axial compression ratio of 0.2/1.

Load-Defection Responses.
Te load-defection curves for the test specimens at midspan showed that all specimens had high initial stifness followed by cracking and gradually reduced stifness before the ultimate load and onset of failure ( Figure 7). Tese Sandwich panels exhibited considerable ductility evidenced by a large amount of midspan defection.
Te increase in thickness of the GFRP jacket on hybrid bars from 2 to 3 mm (G24-I and G34-I) led to increased initial cracking load, ultimate load, and fexural stifness (slope of the load-defection curve in the linear-elastic phase) of the Sandwich panels by 75, 49, and 16%, respectively. Compared with specimen G24-I, the absorbed energy of G34-I increased by 22%, while the ductilities of these two specimens were almost identical. Herein, the absorbed energy was calculated from the area under the load-defection curve before a sudden drop in the load. Te ductility factor was defned as the maximum defection divided by the corresponding defection when yielding occurred [32]. Increasing the thickness of the GFRP jacket was found to increase load-carrying capacity and fexural stifness, as well as energy absorption because of thicker fber layers resulting in extra confnement to steel bars.
Te increased raised thickness of dumbbell ends from 4 to 6 mm (G24-I and G26-I) led to increased initial cracking load, ultimate load, and fexural stifness of the Sandwich panels of 18, 46, and 9%, respectively. Compared with specimen G24-I, the absorbed energy increased by 26% and ductility decreased by 14% for G26-I. Increasing the raised thickness of dumbbell ends contributed to improved integration performance of these panels.
Te increased volume fraction of vitrifed microspheres, from 0 to 10 and 20%, led to an increased initial cracking load of the panels by 49 and 72%, respectively, and an increase in ultimate load by 33 and 45%, increased fexural stifness by 25 and 50% and increased absorbed energy by 37 and 57%, respectively. However, the incorporation of vitrifed microspheres in concrete wythes led to decreased ductility, which might have been attributable to the brittle nature of these microspheres.
An increase in axial compression ratio from 0/1 to 0.2/1 led to increased initial cracking load, ultimate load, and absorbed energy of the Sandwich panels, by 205, 142, and 157%, respectively. Compressive loads contributed to decreased tensile stress in the bottom wythes, thus improving specimen crack resistance and load-carrying capacity. Before crack initiation in the concrete, axial compressive loads had no infuence on specimen fexural stifness. A clear decrease in ductility was observed in specimens under combined axial-fexural loading. After reaching the ultimate load, a load of specimens under combined axial-fexural loading decreased continuously. Consequently, the ratio of the ultimate defection to yield defection decreased and thus ductility decreased.
Te observed efects of loading direction on mechanical properties of the Sandwich panel specimens (G24-I vs. G24-II, and G26-I vs. G26-II) showed that specimens under negative loads had higher initial cracking load than specimens under positive loads. Tis was because the distance from the neutral axis to the bottom of panel specimens under negative loads was larger than that of specimens under positive loads, leading to lower tensile stress in the former. Consequently, the fexural capacity of specimens under negative loads was higher than that of specimens under positive loads, and the yield defection of the former was higher than that of the latter. Terefore, the ductility of specimens under negative loads was lower than that of specimens under positive loads. Specimen fexural stifnesses in the elastic phase were independent of the loading direction. Te absorbed energy of specimen G24-II was higher than that of G24-I, while the absorbed energy of G26-II was higher than that of G26-I. Te loading direction had an insignifcant efect on the ultimate load of specimens with a 6 mm raised thickness of dumbbell ends, while the maximum defection in G26-II was smaller than that of G26-I, resulting in lower absorbed energy in G26-II.
Both the increased thickness of FRP jackets and the thickness of dumbbell ends contributed to increasing the decrease in the slip between the two wythes, while increased vitrifed microsphere content led to a slight increase in the slip between the two wythes. No slip occurred in specimens under combined axial-fexural loading. Te test results are summarized in Table 4.

Load-Strain Responses.
Te progressive development of longitudinal strains of reinforcements at the midspan of typical specimens was examined. Te two layers of reinforcements in tension in the bottom wythe were consistently found to yield in specimens under positive loads, while the compressive strain of reinforcements in the upper wythe was small until specimen failure (Figures 8(a) and 8(b)). At the same loading level, the strain of the outermost reinforcements in tension was higher than that of the innermost reinforcements. For specimens under negative loads, reinforcements in tension yielded, while strains in the two layers of reinforcement in compression were small under fairly high loading levels (Figure 8(c)). 8 Advances in Materials Science and Engineering

Estimation of Degree of Composite Action.
Te degree of composite action for Sandwich wall panel specimens can be estimated in terms of the initial stifness and ultimate strength [33], expressed as and where, I exp , I c , and I nc are the experimentally-determined moment of inertia, theoretical moments of inertia for uncracked full and noncomposite action, respectively, and P exp , P c , and P nc are the experimental ultimate load, theoretical ultimate loads for full, and noncomposite action, respectively.   Advances in Materials Science and Engineering 9 Te estimated values of the degree of composite action in terms of initial stifness of the Sandwich panels with separate hybrid connections were in the range of 19 to 42. Tese were similar to those values of Sandwich panels with continuous GFRP grid connectors in Reference [34] (Table 5). Tis indicated that the facade and structural wythes behaved in a partially composite manner. Te values of the degree of composite action in terms of ultimate strength were higher than those of values in terms of initial stifness. Ticker FRP jackets and dumbbell end of connectors, the increased contents of vitrifed microspheres in concrete wythes, and applied axial compressive load led to higher degrees of composite action. Moreover, specimens under negative loading had a much higher degree of composite action in terms of ultimate strength than specimens under positive loading.

Finite Element Simulation
A three-dimensional (3D) FE model was developed using Abaqus/Explicit to simulate the fexural responses of test specimens. Ten, the verifed FE model was used to analyze the arrangement of dumbbell-shaped SFCB connectors.

Material Models.
Te damaged plasticity model was used for concrete and the compressive properties of concrete were obtained from coupon testing ( Table 2). Te tensile strength of the concrete was taken as 10% of the compressive strength. Te compressive and tensile stress-stain curves for concrete based on experimental results were determined according to GB 50010-2010 [35], and plotted in  10 Advances in Materials Science and Engineering factor (d t ), compressive inelastic strain (ε in c ), and tensile cracking strain (ε ck t ) were thus obtained according to [36] and incorporated in a damage plasticity model. Concrete mechanical parameters are listed in Table 6.
Te steel reinforcement and steel core in shear connectors were assumed as elastic-plastic materials with a yield strength of 400 MPa and elastic modulus of 210 GPa. Linear elastic models were used for the insulation and GFRP on shear connectors and Hashin's criterion was applied to predict GFRP failure.

FE Model Construction.
Eight-node reduced-integration continuum 3D solid elements (C3D8R) were used to model concrete panels, shear connectors, and insulation, and 3D 2node frst-order truss elements (T3D2) were used to model steel reinforcement. Based on the convergence study, the mesh sizes of the elements were 25 mm for the concrete panel, 13 mm for the connector, and 50 mm for the insulation and steel reinforcement. Te mesh at the contact zone between shear connectors and concrete wythe and insulation was set to be fner to capture interactions between these elements ( Figure 11).
Te load was applied step by step using the full Newton method with NLGEOM in, which large-defection efects were considered. Te test specimens were simply supported and surface-to-surface contact elements were used to simulate the interface between concrete wythe and insulation. Tis type of contact considers slip and separation. Hence, slip/debonding was displayed if either occurred between the concrete wythe and insulation. Godrich et al. [37] stated that the friction coefcient within the range of 0-0.5 had an insignifcant efect on the panel connection response. Jiang and Chorzepa [38] suggested that the friction coefcient for the contact surfaces of polymer composite and concrete can be taken as 0.22. Hence, the friction coefcient here was set as 0.22 for the contact surface of the wythe and insulation.

Comparison of Numerical and Experimental Results.
Te simulated failure modes and contours of stress, strain, and displacement of typical Sandwich panel specimens (i.e., G24-I and G24A0.2-I) are shown in Figures 12 and 13. For specimen G24-I, several tensile cracks occurred on the bottom wythe in the midspan, with a few cracks scattered at the loading point on the upper wythe and at supporting points on the bottom wythe. For G24A0.2-I, several tensile cracks occurred on the upper wythe due to the localized efect of the load applied at the midspan. Te tension damage in the bottom wythe of G24A0.2-I was more serious than that of G24-I. Te maximum Von Mises stress of the longitudinal rebars in the upper wythe and outermost longitudinal rebars in the bottom wythe was a little higher than the yield strength of rebar, indicating that these rebars   Note. x c is the ratio of the real compressive strain of concrete to the compressive strain of concrete corresponding to the compressive strength, and x t is the real tensile strain of concrete to the tensile strain of concrete corresponding to the tensile strength.     Te horizontal shear stress of the connectors of specimens G24-I and G24A0.2-I is shown in Figure 14. As mentioned in Reference [7], the shear strength was 20-25% of the tensile strength for GFRP bars, such that the shear strength of GFRP was taken as 95-119 MPa. Te maximum horizontal shear stress in GFRP jackets of connectors was 72 and 88 Mpa for G24-I and G24A0.2-I, respectively, which were lower than the GFRP shear strength. Moreover, the shear strength of steel is ∼50% of the tensile strength, such that the shear strength of the steel core was taken as 200 Mpa. Te maximum horizontal shear stress in the steel core of connectors was 71 and 87 Mpa for G24-I and G24A0.2-I, respectively, which was lower than the shear strength of the steel core. Tese simulated results indicated that GFRP-steel hybrid shear connectors did not fail during the test.

Advances in Materials Science and Engineering
A comparison between the experimental and numerical load-defection curves for test specimens showed that the FE model ofered a reasonable trend with the test data (Figure 15). Tat is to say that FE analyses were efective in capturing the shapes of the elastic and plastic phases of the measured load-defection curves. Te numerical ultimate loads were in good agreement with the test values (Table 7).

Infuence of Arrangement of Shear Connectors.
Te verifed FE model was used to analyze the infuence of the arrangement of shear connectors on the fexural behavior of Sandwich panels. Te spacing and number of shear connectors in Sandwich panel specimens were varied in the FE model, respectively (Figure 16). Tree diferent spacings (d � 550, 600, and 650 mm) of connectors were tried in G24-I specimens. Also, four diferent numbers of shear connectors (�10, 12, 13, and 14) were used in these specimens, with the shear connectors arranged symmetrically. Specimens with diferent connector spacing had almost identical load-defection curves (Figure 17(a)). Te number of connectors had an insignifcant infuence on the stifness of G24-I in the linear phase, while the ultimate loads of G24-I were enhanced up to 8% when the number of connectors increased from 10 (3.6/m 2 ) to 14 (5/m 2 , Figure 17(b)).

Analytical Model of Sandwich Panel Deflection
In this section, the defection of Sandwich panels with shear connectors under fexure was analysed based on the equilibrium equation of force, in which the efects of shear defection, axial compression load, and slippage between the structural and facade wythes were considered. Tis analysis was based on the following assumptions: (1) Te Sandwich panel section remains plane with respect to their neutral axes.
(2) Concrete in the tension region is ignored in the calculation of stifness of cracked Sandwich panels. (3) Tere is no relative slip between reinforcement and concrete in the compression region. (4) Te fexural resistance of the insulation foam core is ignored.

Stifness of Sandwich Wall Panels.
Te efective moment of inertia of reinforced concrete wythes was calculated by transforming the wythe into a single type of material. Herein, the cross section of reinforced wythes was transformed into the concrete using a multiplier factor of moduli ratio of α E � E s /E c (E s and E c are Young's moduli of steel and concrete, respectively). For cracked Sandwich sections, the contribution of concrete in the tensile region is ignored. Te depth of the neutral axis of cracked section y cr was generated by summing the frst moment of area about the neutral axis equal 0 ( Figure 18).
With reference to Figure 18, there were two possible locations of the neutral axis to be considered: Case 1. a ′ < y cr < h c1 . Te neutral axis lies inside the facade wythe. In this case, the following Equation can be applied: where b is the width of the section, a ′ is the depth of the compressive reinforcement, h is the depth of the section, h c1 is the thickness of the facade wythe, h 0 is the efective depth of the section, and A s and A s ′ are the areas of steel reinforcements in tension and compression regions, respectively. Te cracking moment of inertia of the section I cr can be obtained as follows: Case 2. H c1 ≤y cr ≤ h c1 +h e . Te neutral axis is located within the core. In this case, fexural stress in the core is ignored and the depth of the neutral axis of the cracked section y cr is given by Te cracking moment of inertia of the section I cr is thus given by Advances in Materials Science and Engineering Te efective shear modulus for the Sandwich section, G 0 , which includes the contribution of the wythes, can be defned based on the compliances of the constituent layers, as follows [39]: where, G c and G f are the shear moduli of the concrete and foam core, respectively, and h c2 and h f are the S, S13  Advances in Materials Science and Engineering thicknesses of the structural wythe and the foam core, respectively.

Equilibrium Equation of Sandwich Wall Panels under
Flexure. Due to the slippage between the structural and facade wythes, the sections of the structural and facade wythes are not in the same plane, so there is a neutral axis in either section of the structural and facade wythes. Te distribution of strain and forces of the Sandwich panels are shown in Figure 19. Te fexural of the section will induce a resultant compressive force C(x) in the concrete which acts through the centroid of the efective area of concrete in compression and a resultant tensile force T(x) in the reinforcing steel is expressed as follows: and where, A 1 is the area of the facade wythe, and d 1 and d 2 are the distances between the centroid of the facade and structural wythes to their neutral axes, respectively.
For equilibrium, the applied moment M(x) is balanced by the moment of resistance of the section and resultant force C(x) balanced by T(x), such that and where, I 1 is the moment of inertia of the facade wythe, d is the distance between the centroids of the facade and structural wythes, and d 0 is the distance between neutral axes of the facade and structural wythes. Due to the slippage between the facade and structural wythes, slip strain can be expressed as follows ( Figure 19): where, s is the relative slip of the facade and structural wythes.
Te relationship between the slip strain and curvature is as follows: Substituting (12) into (11) yielded where, C(x) is the axial force on the cross-section. Ten, substituting (8)-(10), (14) into (15) yielded, where α � (α E A s A 1 d 2 /(A 1 + α E A s )I 1 ). Te interface shear is proportional to the slip in the longitudinal direction, as given by where, q is the interface shear per unit length in the longitudinal direction and K the shear stifness of the connectors, as given by [40].
where, n s is the number of connectors in the section, N u is the shear capacity of the connector, and p is the distance of the connectors in the longitudinal direction of the panel.
Considering the element of facade wythe in Figure 20, the interface shear was equilibrated by the axial force, expressed as follows: Te substitution of (17) and (19) into (13) yielded Ten, substituting (20) into (16) yielded For specimens under four-point fexure, the applied moment of the section is as follows: and where L is the clear span of the panel and L 0 is the distance between two vertical loads.
Tere was no relative slip between the facade and structural wythes in the midspan section because the specimen was symmetric with respect to the midspan section, such that s(L/2) � q(L/2) � 0.

Advances in Materials Science and Engineering
Considering an element of the panel cut out by two adjacent cross-sections with a distance dx apart (Figure 21), the relationship between the shear defection and shear force was given by [41] where, y s is the shear defection, c 0 is the shear strain at the centroid of cross-sections, α s is a numerical factor with which the average shearing stress must be multiplied in order to obtain the shearing stress at the centroid of crosssections (α s � (3/2) for a rectangular cross-section and α s � (4/3) for a circular cross-section), V is the section shear force, and A is the section area. Te shear defection of the Sandwich panel was obtained by integrating (27) over half of the panel span and the shear defection of the midspan section thus given by Adding Eq. (28) to (26), the defection at the midspan of the Sandwich panels under fexure was expressed as follows: in which the efects of slipping and shear defection were included.

Defection of Sandwich Panels Under Combined Axial-Flexural Loading.
For specimens under the combined efects of fexure and compression, no slipping occurred between the facade and structural wythes. Hence, the defection of the mid-span section was given by [42] where u � (L/2) ������� � (C 0 /E c I), χ(u) � (3(tan u − u)/u 3 ), and C 0 are the applied axial compressive load.
Considering the efect of shear defection, the defection at the midspan of Sandwich panels subjected to combined axial-fexural loads was obtained by adding Equation (28) to (30), yielding

Comparison of Analytical and Experimental Results.
Equation (29) was used to calculate the defection at the ultimate load for the insulated concrete Sandwich panels under fexure. Equation (31) was used to calculate the defection at the ultimate load for the insulated concrete Sandwich panels under the combined efects of fexure and compression. Comparisons of the analytical and measured defections at the ultimate load at midspan of test specimens showed good agreement (Table 8).

Conclusions
Te structural responses of insulated concrete sandwiches with innovative dumbbell-shaped SFCB connectors under fexural load were investigated. Te results obtained from this study were summarized as follows: (1) Te failure modes of Sandwich panel specimens under positive fexure were governed by the yielding of the tension rebars and penetrating of the bottom wythe in the midspan. Te thickness of GFRP on the hybrid bars, raised thickness of the dumbbells, and the content of vitrifed microspheres have insignificant infuences on the failure modes of Sandwich panel specimens. Tese specimens, under combined axial-fexural loads, exhibited diferent failure modes from specimens without axial loads, in which the axial compressive load delayed crack onset in the bottom concrete wythe and prevented slipping between the facade and structural wythes. Te failure modes of specimens under negative fexure were similar to those of specimens with an axial compression ratio of 0.2/1. (2) Te increase in thickness of the GFRP jacket on the hybrid bar from 2 to 3 mm led to increased initial cracking load, ultimate load, and fexural stifness of specimens by 75, 49, and 16%, respectively. Te increase in raised thickness of dumbbell ends from 4 to 6 mm led to increased initial cracking load, ultimate load, and fexural stifness of specimens of 18, 46, and 9%, respectively. Both the increased thickness of the GFRP jacket and raised thickness of dumbbell ends contributed to decreased slip between the two wythes but had insignifcant infuence on ductility. Te incorporation of vitrifed microspheres in concrete wythes resulted in a remarkable increase in the load-carrying capacity of the Sandwich panels but decreased ductility. Increased axial compression ratio from 0/1 to 0.2/1 contributed in improving crack resistance and ultimate loads of these panels. No slip occurred in specimens under combined axial-fexural loading. Specimens under negative fexure had higher ultimate load and lower ductility than their counterpart under positive fexure. (3) Te FE model provided a reasonable simulation of the experimental results. Moreover, the verifed FE model was used to analyze the infuence of the arrangement of shear connectors. It is found that increasing the spacing of the connectors from 550 to 650 mm had an insignifcant infuence on the loaddefection responses and increasing the number of shear connectors per square meter from 3.6 to 5 led to a slight increase (∼8%) in the ultimate load. (4) Based on the relationship between slip strain and curvature and considering the relationship between interface shear and slip, the equilibrium equation of the composite section under fexure was solved to obtain the defection of sandwich panel specimens, in which the efect of shear defection and slipping between the two wythes were included. For specimens under the combined axial-fexural loads, no slipping efect was included in the analytical solution.
A comparison of analytical and test results showed that defection at the ultimate load was accurately predicted by the proposed theoretical model. (5) To promote the application of the sandwich wall panels with these innovative dumbbell-shaped SFCB connectors in building engineering, further research will be needed to optimize the confguration sandwich wall panels and investigate the thermal and seismic performances of the sandwich wall panel.

Data Availability
Data will be made available on request.

Conflicts of Interest
Te authors declare that they have no conficts of interest regarding the publication of this article.

Authors' Contributions
Yi Wang performed numerical analysis, validation, experimental study, and wrote the original draft. Jun Wang carried out conceptualization, formal analysis, resources, and project administration. Donghui Zhao performed data curation andinvestigation. Hota Gangarao carried out methodology and reviewed and edited the study. Ruifeng Liang performed the analysis of failure mode. David Hui visualized the study.