Experimental investigation and finite element analysis of flexural behavior of insulated concrete sandwich panels with FRP plate shear connectors

Engineering Structures 98 (2015) 95–108

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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct

Experimental investigation and finite element analysis of flexural behavior of insulated concrete sandwich panels with FRP plate shear connectors An Chen a,⇑, Thomas G. Norris b, Paul M. Hopkins b, Mostafa Yossef a a b

Department of Civil, Construction, and Environmental Engineering, Iowa State University, Ames, IA 50011, USA Department of Civil Engineering, University of Idaho, Moscow, ID 83844, USA

a r t i c l e

i n f o

Article history: Received 5 October 2014 Revised 10 April 2015 Accepted 13 April 2015

Keywords: Flexural behavior Insulated concrete sandwich panel FRP plate shear connector Experimental investigation Finite element analysis Partial composite action

a b s t r a c t Insulated concrete sandwich panels consist of two layers of concrete wythe separated by a foam insulation. The objective of this study is to develop an innovative fiber reinforced polymer (FRP) shear plate connector with specially designed anchoring schemes, and study its effects on the flexural behavior of insulated concrete sandwich panels, in terms of stiffness, strength, and applicability for roof/floor constructions, based on combined experimental investigation and Finite Element (FE) analysis. Three groups of 2743  610  254 mm3 (90  20  1000 ) concrete panels were constructed with continuous, segmental, and discrete FRP shear plate connectors, with two panels for each group. Additionally, two solid concrete panels were constructed as baselines. These specimens were tested under bending until failure. FE analysis was conducted on the panels. The accuracy of the FE model was proven through good correlations between test and FE results for two panels with continuous shear connectors, one solid panel and one panel with segmental shear connector. It can be concluded that the FRP plate can be used to transfer shear between the two concrete wythes, achieving a composite panel, which can meet ACI requirements for roof/floor applications. Different types of shear connectors, representing different degrees of composite action, affect both the strength and stiffness of the panels. This degree of composite action can be predicted with the FE model developed in this study. Continuous and segmental connectors perform much better than discrete connectors. The use of discrete shear connectors is not recommended. Unlike other proprietary FRP shear connectors, the FRP plate shear connectors developed in this study can be cut from commercially available FRP plates and are expected to be widely used for insulated concrete sandwich panels. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Reinforced concrete sandwich panels have been in use for several decades, first appearing in North America more than 50 years ago [1,2]. Interest in these panels has recently increased due to the publication of the state-of-the-art report by Precast/Prestressed Concrete Institute (PCI) [2,8]. There are many variations to their designs which are primarily regarded as trade secrets. As such, there are not many guidelines for the design of these panels. Generally, these panels are composed of two layers of concrete, known as wythes, separated by a layer of rigid foam plastic insulation [2,8]. The two wythes are connected by some form of shear transferring mechanism, generally using concrete webs, metal connectors, plastic connectors, or a combination of these elements [3,8,10]. ⇑ Corresponding author. E-mail address: [email protected] (A. Chen). http://dx.doi.org/10.1016/j.engstruct.2015.04.022 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved.

The panels provide dual function of transferring load and insulating the structure among other desirable characteristics of normal concrete panels, such as durable, economical and fire resistant. Studies have shown that R values of up to 12 can be achieved which can reduce peak heating and cooling loads of up to 30% as compared to insulated stud-wall systems [1,6,8]. R is a measure of thermal resistance used in building and construction industry. It is defined as

R¼

Temperature Difference  Area  Time Heat Loss

ð1Þ

R has a unit of h ft2 °F/Btu (customary unit) or K m2/W (SI unit). An R-12 means that it has a thermal resistance of 12 h ft2 °F/Btu (2.113 K m2/W). The panels are lighter comparing to solid slabs with comparable strength, due to the reduction in the amount of concrete. This lighter weight is beneficial to both transportation and construction, as most of these panels are pre-cast. The reduction in weight also has a substantial effect on the cost associated

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with these panels. Because the insulation is inside panels and the panels are lighter, the overall envelope of the structure, and therefore carbon footprint, can be reduced [6,8]. Because of these advantages, the panels have been used as shear walls, load bearing walls, retaining walls, beams, and general structural claddings [2]. 1.1. Wythe thickness and reinforcement Most sandwich panels are designed to be as thin as possible [2]. In the case of concrete sandwich panels, this thickness depends on the structural function, concrete cover, anchorage of connectors, stripping, and finish. The minimum recommended thickness of a structural wythe is 51 mm (2 in.) if prestressed and 76 mm (3 in.) if non-prestressed, however, a thickness as small as 19 mm (3/ 4 in.) has been used [8]. The concrete wythes can be reinforced in several ways, including prestressing strands, longitudinal reinforcing bars, wire mesh, or a combination thereof [8]. The reinforcement is typically located at the centroid of the wythe in order to minimize the tendency of the wythe to camber [2]. 1.2. Degree of composite action Early sandwich panels were designed as non-composite panels, generally with a thick, structural wythe and another non-structural wythe [2]. A wythe is considered structural if it significantly contributes to the resistance of the load applied to the panel. As such, in the case of non-composite panels, either one of the wythes is structural and the other wythe is non-structural, or each wythe can independently resist the applied load, such that they are both structural [8]. In the latter case, each wythe exhibits its own neutral axis, which is a characteristic of non-composite behavior [7,9]. Partially composite panels possess bending stiffness and strength between the stiffness and strength of fully composite panels (such as solid concrete slabs) and non-composite panels [2]. It was shown that partially composite panels are superior to noncomposite panels with regard to structural efficiency [1]. Degree of Composite Action (DCA) has been determined to be the best and most reliable way to determine the strength and stiffness of partially composite reinforced concrete sandwich panels. With a higher DCA, greater overall stiffness and strength are achieved. Non-composite panels can be described as DCA = 0%. Fully composite panels have a DCA of 100%, which act as a single unit in bending, accomplished by full shear transferring between the two wythes [2]. 1.3. Insulation and shear connectors At this time, although tests have shown that the panel stiffness is affected by the type of foam used, where a higher percentage of composite action can be achieved using expanded polystyrene (EPS) rather than extruded polystyrene (XPS) [1], the strength, stiffness and shear transferring mechanism of the foam insulation have not been established and are generally ignored and assumed to be zero [2,6]. Therefore, the ultimate strength and DCA of a panel depend on the stiffness of the shear connectors [9]. The purpose of the shear connectors within these reinforced concrete

76 mm (3”) 102 mm (4”) 76 mm (3”) Fig. 1. Sandwich panel.

sandwich panels is to transfer the shear, resulting from flexure in the panel, from one wythe to the other [8]. Many different types of connectors have been used in the past. These connectors include steel ties, wire trusses, bent wires, trussshaped connectors, and solid concrete zones [1,4,5,8], which have been proven to establish exceptional connections between the wythes. However, they can result in a thermal bridge (an area where a temperature gradient increases substantially with respect to other insulated areas) developing at the locations of the connectors, thus negating, or at least limiting the insulating benefits that could be gained through the use of the foam core. For this reason, carbon fiber-reinforced polymer (CFRP) materials, in both truss and mesh configurations, have begun to be incorporated as shear connectors. CFRP has a wide range of thermal conductivity. As reported by Gowayed and Hwang [18] and Mutnuri [19], the thermal conductivity of CFRP can be as low as 8 W/m K. The thermal conductivity for ASTM A572 Grade 50 Steel at 0 °F was reported to be 52 W/m K [20]. Franssen et al. [21] indicated that for typical carbon steel, this value was 54 W/m K. Therefore, CFRP has a thermal conductivity as low as 14% that of steel, and can significantly reduce thermal bridging [1,4,5]. For example, C-grid manufactured by Altus group has been reported to significantly reduce the thermal bridging. Glass FRP (GFRP) has a much lower thermal conductivity compared to CFPR, which was reported to be 0.5 W/m K in the two above studies [18,19]. Therefore, GFRP is more effective at reducing thermal bridging. Additionally, FRP exhibits high strength at low weight compared to steel and concrete. Although the initial material cost is comparatively higher than steel or concrete connectors, the use of FRP can reduce the long term building heating/cooling cost due to the reduction of thermal bridging. It should be noted that some form of mechanical anchorage should be provided for the FRP elements as their adhesion to concrete is not as high as that of steel [1,5]. Frankl et al. [17] tested four full-size precast sandwich panels, consisting of two wythes of prestressed concrete and an inner layer of rigid foam, under a combined vertical and lateral loads. CFRP grid, commercially known as C-grid, was used as shear connectors, with and without solid concrete zones. It was reported that, although solid concrete zones provided higher percent composite action than the use of C-grid alone, appropriate use of C-grid as a sole shear connector can provide significant composite action. In parallel to C-grid, Soriano and Rizkalla [15] studied G-grid, where the grid is made of GFRP. Their test plan included push-out tests on 38 doubled concrete sandwich wall panels, and flexural tests on the same types of sandwich panels. Test results indicated that when the foam thickness was increased, the shear strength of the panel increased. When EPS and sandblasted XPS foam layers were used, increasing the interface surface between foam and concrete increased the shear flow capacity. Only partial composite action was observed in the flexural tests because the panels were strengthened with CFRP sheets at the tension face, which prevented the specimens from behaving as typical insulated concrete sandwich panels. Woltman [16] studied the performance of sandwich concrete walls with GFRP bar connectors. Fourteen specimen were tested under shear test, considering various parameters such as bar types, number of connectors and end treatment. It was concluded that GFRP sand-coated bars had a great potential to be used as shear connectors. The adhesion between the insulating form and concrete provided significant shear resistance prior to engaging the GFRP connectors. However, most existing FRP shear connectors, for example, Cgrid from Chomarat [12], P24 Delta Tie from Dayton Superior [13,14], etc., are proprietary and require specialized equipment to manufacture. Therefore, it is the objective of this paper to develop an innovative FRP shear plate connector with specially designed anchoring schemes, which can be cut from commercially

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97

(a) Group 1: Panelss with Discrrete Shear Connector

(b) Group 2: Panels with Segmental Shearr Connector

(c) Group 3: Panels with w Contin nuous Sheaar Connectoor

(d) Group 1: Solid Coontrol Paneel Fig. 2. Shear connector layout (100 = 25.4 mm; 10 = 305 mm).

available FRP plates, and study its effects on the flexural behavior of insulated concrete sandwich panels. The effects of three different shear connector configurations were studied and compared with solid concrete control panels. The feasibility of using the developed FRP plate shear connectors in roof/floor applications was evaluated. 2. Experimental program 2.1. Specimen Details Four groups of 2743  610  254 mm3 (90  20  1000 ) concrete panels, with two panels for each group, were constructed and tested under bending until failure. The eight panels were divided into two types: solid and sandwich panels. The solid panels with

depths of 254 mm (1000 ) were prepared as controls. The sandwich panels consisted of three groups with identical reinforcement as solid panels and a wythe configuration of 76 mm + 102 mm + 76 mm (300 + 400 + 300 ; top wythe thickness, EPS foam core thickness, bottom wythe thickness; see Fig. 1); but with varying shear connector configurations, including discrete, segmental, and continuous FRP plates, as shown in Fig. 2(a)–(c). The panels were reinforced with two #5 [As = 200 mm2 (0.31 in2)] rebars at bottom and two #4 rebars [As = 129 mm2 (0.2 in2)] at top in the longitudinal direction. #4 rebars were used as temperature reinforcement in the transverse direction at 457 mm (1800 ) on center. The reinforcement layout and specimen details can be seen in Fig. 2(a)–(d). It is noted that the parameters of the test panels followed previous research or industrial practices, except that FRP plate shear connector was used in lieu of other types of

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Table 1 FRP material properties (provided by Crane Composites, Inc.). Typical values Property

EATR .08500 | 2.2 mm

Flexural strength Flexural modulus Tensile strength Tensile modulus Barcol hardness Coefficient of linear thermal expansion Thermal conductivity Water absorption Specific gravity

33  103 psi 1.0  106 psi 45  103 psi 2.0  106 psi 45 0.8  105 in./in./°F 0.4 Btu in./h ft2 °F 0.2%/24 h@77 °F 1.75

Test method 228 MPa 6895 MPa 310 MPa 13,790 MPa 45 14 lm/m/°C 5.0 cal cm/h m2 °C 0.2%/24 h@77 °F 1.75

ASTM-D790 ASTM-D790 ASTM-D638 ASTM-D638 ASTM-D2583 ASTM-D696 ASTM-C177 ASTM-D570 ASTM-D792

(a) Discrete Shear Connector

(b) Segmental Shear Connector

(c) Continuous Shear Connector Fig. 3. Shear connector configurations (100 = 25.4 mm; 10 = 305 mm).

connectors, which is the focus of this study. The configurations of the FRP shear connectors also followed existing practices, e.g., the continuous shear connector simulated continuous connectors such as C-grid; and the discrete shear connectors simulated discrete connectors, such as Delta tie.

2.2. Material properties The materials used in the construction of the panels were concrete, steel rebar, glass FRP, and expanded polystyrene (EPS) foam. Four cylinder compression tests conducted on 152 mm  305 mm

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(a) 6" Discrete Shear Connector Panel Fabrication

(b) Cage, Insulation, and Shear Connectors

(c) Continuous Shear Connectors

(d) Solid Panel Reinforcement Fig. 4. Panel fabrication.

(600  1200 ) specimens resulted in an average compressive strength of 28.4 MPa (4120 psi) with a standard deviation of 2.9 MPa (426 psi). The steel rebars used in the panels were ASTM A615 Grade 60 steel, with a yield strength of 414 MPa (60 ksi). The shear connectors were EATR, a type of GFRP provided by Crane Composites, Inc. It is made of chopped strand mat, and therefore, it can be treated as isotropic material and the material properties are the same in all directions. It has a Young’s modulus of 13.8 GPa (2.0  106 psi) and thickness of 2.2 mm (0.08500 ). Other properties of the FRP are provided in Table 1. The thermal insulation used in the sandwich panel was a Type II EPS with a Young’s modulus of 2.3 MPa (340 psi).

P

P 1,219 mm (4’)

Concrete Foam

2,438 mm (8’) 2,743 mm (9’)

Fig. 5. Schematic four-point bending test plan.

2.3. Specimen fabrication Three shear connectors were adopted in this study, with two different anchoring schemes. Fig. 3(a) displays the 600 discrete connector. The purpose of the holes with a diameter of 38 mm (1½00 ) is to allow concrete to flow through the connector at the center of each wythe in order to anchor the FRP plate and promote the integration of the shear connector within the concrete. The segmental and continuous shear connectors for the sandwich panels are displayed in Fig. 3(b) and (c), respectively. The small holes at the top and bottom of each segment allow for proper positioning of

610 mm (2’)

Fig. 6. Four-point bending test layout.

254 mm (10”)

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Table 2 Ultimate load summary.

*

Group

Load span (mm)

Test type

Moment arm (mm)

Cracking load (kN ⁄ mm)

Cracking moment (kN ⁄ mm)

Failure load (kN)

Failure moment (kN ⁄ mm)

Max load deflection (mm)

Adjusted max load deflection (mm)

1

2438 2438

4-Point 4-Point

792 792

13.3 13.3

441 441

60.9 61.8

2011 2042

37 16*

62 26*

2

2438 2743

3-Point 3-Point

1219 1372

17.8 13.3

904 763

69.3 75.1

3518 4290

30 37

43 –

3

2743 2743

3-Point 3-Point

1372 1372

13.3 13.3

763 763

75.6 74.9

4322 4282

43 34

– –

4

2743 2743

3-Point 3-Point

1372 1372

17.8 13.3

1017 763

81.7 91.6

4667 5237

56 54

–

Data Acquisition System quitted working before panel failed.

P Concrete Foam 254 mm 305 mm (1’)

2,743 mm (9’)

305 mm (1’)

610 mm (2’)

Fig. 7. Schematic three-point bending test plan.

Fig. 8. Three-point bending test layout.

(10”)

temperature steels, which double as anchors for the shear connectors within the concrete. The cut-offs at the top and bottom of the continuous shear connectors allow fresh concrete to move through freely during concrete pouring, forming a continuous concrete wythe with embedded FRP shear connectors. Panels with different FRP connectors required different installation procedures, as described next. 2.3.1. Group 1: Panels with discrete shear connectors The tension and temperature steel were first tied together. Chairs were provided for the rebar to sit on such that proper clear distances were maintained. The form was then oiled to assist in future stripping of the forms. After the tension reinforcement was placed, concrete was distributed throughout the form up to a level of 76 mm (300 ). This layer of concrete was vibrated in order to eliminate voids. The foam core with the 152 mm (600 ) discrete shear connectors was then lowered into position. Once the foam core was in position, the compression reinforcement was tied into place, as shown in Fig. 4(a). The final layer of concrete was then added and vibrated. Once the form had been filled, the surface was smoothed and edged to allow for easier stripping. 2.3.2. Group 2: Panels with segmental shear connectors The foam cores were marked where the shear connectors would pass through. They were then cut with a knife along these marks and widened with a file in order to allow easier insertion of the shear connectors. The shear connectors were then inserted into the foam at which point the temperature reinforcement passed through the holes in the connector. The tension and compression steel was then tied into place. Prior to positioning the

Fig. 9. Instrumentation layout.

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Deflection (mm) 18000 16000 14000 12000 10000 8000 6000 4000 2000 0

10

20

30

40

50 80 70 60 50 40 30 20 10 0

Panel #2

Panel #1

0

0.5

1

1.5

2

Load (kN)

Load (lbf)

0

Deflection (in) (a) Group 1 Load-Displacement Curves Deflection (mm) 0

reinforcement and foam, the first 76 mm (3 ) lift of concrete was poured into the oiled form and vibrated. Next, the complete cage, including the foam core and corresponding shear connectors as shown in Fig. 4(b) was lowered into position. It was placed such that the foam core, which was locked in place between the tension and compression reinforcement via shear connectors, could be seen to be properly positioned along the height of the form. When the foam core and cage were set, the final layer of concrete was added and vibrated.

10

20

30

40

50 80 70 60

9ft Effective Length

50

8ft Effective Length

40 30

Load (kN)

00

Load (lbf)

Fig. 10. Concrete strain gages.

18000 16000 14000 12000 10000 8000 6000 4000 2000 0

20 10 0

0.5

1

1.5

2

0

Deflection (inch) (b) Group 2 Load-Displacement Curves Deflection (mm) 18000 16000 14000 12000 10000 8000 6000 4000 2000 0

3. Test setup 3.1. Test layout As the first tests, two specimens from Group 1 were tested in four-point bending and one specimen from Group 2 was tested in three-point bending with 2438 mm (80 ) span, as shown in Figs. 5 and 6, extending 152 mm (600 ) over the supports. During the tests, it was observed that shear failure at the edge between the foam core and the solid zones occurred, as shown in Fig. 16, because the edge was too close to the support. Therefore, in order

20

30

40

50

60

Panel #1 Panel #2

0

0.5

1

1.5

2

2.5

80 70 60 50 40 30 20 10 0

Deflection (in) (c) Group 3 Load-Displacement Curves Deflection (mm) 0

10

20

30

40

50

25000 80 15000

60

Panel #1 10000

40

5000 0

Load (kN)

100

Panel #2

20000

Load (lbf)

2.3.4. Group 4: Solid panels The rebar cage was cut and tied together. Spacers were provided for the rebar to sit on such that proper clear distances were maintained, as shown in Fig. 4(d). The form was then oiled to assist in the future stripping of the forms. The cage was then positioned and the concrete was added and vibrated. As these were solid slabs, the concrete could be added in one 254 mm (1000 ) lift. All test specimens were allowed to cure for 28 days prior to the beginning of testing.

10

Load (kN)

0

Load (lbf)

2.3.3. Group 3: Panels with continuous shear connectors The temperature steel for the bottom wythe was first tied to the tension steel outside of the form. The tension steel and shear connectors were then placed within the oiled form, as shown in Fig. 4(c). The first 76 mm (300 ) lift of concrete was distributed throughout the form and vibrated. The foam core was segmented using a table saw into three pieces: two with 152 mm  2,134 mm  102 mm (600  70  400 ) and one with 305 mm  2134 mm  102 mm (10  70  400 ). The three sections of the foam core were then positioned, locking the shear connectors vertically in place. Next, the top wythe temperature steel and compression reinforcement were tied in place. The final layer of concrete was then added and vibrated.

20 0

0.5

1

1.5

2

2.5

0

Deflection (in) (d) Group 4 Load-Displacement Curves Fig. 11. Load–displacement curves.

to achieve bending failure, the following tests were changed to three-point bending and the load span was increased to 2743 mm (90 ). The loading condition and span for each specimen are listed in Table 2. Schematic plans of the test setup are shown in Figs. 5 and 7 with layouts represented in Figs. 6 and 8, respectively.

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Deflection (mm) 40 60

20

with no more inspection of cracks to ensure the safety of personnel.

80

25000 100 20000

Segmental 1

15000

60

Segmental 2 Continuous 1

10000

Load (kN)

80

Discrete 2

Load (lbf)

5. Experimental results

Discrete 1

40

Continuous 2 Solid 1

5000 0

20

Solid 2

0

0.5

1

1.5

2

2.5

3

3.5

Fig. 12. Slab comparison.

3.2. Instrumentation As shown in Fig. 9, three LVDTs were used to measure the vertical displacements at the quarter points and midpoint. The panels were supported at both ends and loaded using a hydraulic load cell. The load was applied until failure occurred. In order to monitor the strain of the steel reinforcement during testing, strain gages were bonded to the two #5 tension rebars at mid-span. After the specimens were cured, concrete strain gages were added. The strain gages were positioned at the top and bottom mid-spans along the center-line, and at the middle of the thicknesses of each wythe, also at mid-span, to record the strains along the depth of the panel. This scheme and layout are displayed in Figs. 9 and 10, respectively. 4. Test procedures Each panel was positioned at described locations on the supports and centered with respect to the load cell, and then was inspected for cracks prior to loading. If cracks existed, they were marked and noted. Load was then applied until a base-line load of 8.9 kN (2 kips) was reached using a ceiling mounted, hand pumped, hydraulic actuator with a capacity of 222 kN (50 kips). The panel was then inspected for cracking with all new cracks or extensions of existing cracks being marked. After each inspection, the load was increased by 4.4 kN (1 kip) and the process repeated until significant cracking was apparent and failure was deemed imminent. At this point, the panel was steadily loaded until failure

0.1

Fig. 11 displays load–displacement curves recorded for all specimens. As described above, loading condition and span were different for two specimens from Group 1 and one specimen from Group 2. Therefore, these curves were adjusted to be comparable to other specimens, as noted below.

0

Deflection (in)

0

5.1. Load–displacement

Deflection (mm) 0.2 0.3

5.1.1. Group 1: Discrete shear connectors With group 1, the data acquisition system experienced an error which caused the system to cease collecting data for the first specimen. However, the second test exhibited a similar load–deflection trend (see Fig. 11(a)). While the first specimen provides limited data, the initial loading of both specimens provides adequate data for later analysis. Since both specimens were tested under fourpoint bending with a load span of 2438 mm (80 ), the displacements were adjusted to exhibit the deflections that would have occurred had they been tested in three-point bending with a load span of 2743 mm (90 ) (see Fig. 12). 5.1.2. Group 2: Segmental shear connectors It can be seen from Fig. 11(b) that one specimen does not display the same degree of stiffness as the other initially, since one specimen was tested in three-point bending with a load span of 2438 mm (80 ), while the other was tested with a span of 2743 mm (90 ). To account for this difference, similar to Group 1, the displacement of the specimen tested at 2438 mm (80 ) was adjusted by applying a correction factor, calculated by comparing the theoretical deflections of a simply supported beam in threepoint bending at both load spans with all other variables equal. The results can be seen in Fig. 12. Once this correction factor was applied, it can be seen that both specimens behave more similarly. 5.1.3. Group 3: Continuous shear connectors Both specimens with the continuous connectors behaved similarly with one providing a greater overall stiffness and the other providing a greater overall strength (see Fig. 11(c)). 5.1.4. Group 4: Solid panels As with the specimens with the continuous connectors, the solid panels exhibited similar results, as shown in Fig. 11(d).

0.4

8

1600

7 Discrete 1

1400

Load (lbf)

0.5

1800

6

1200

5

1000 4 800 3

600 400

2

200

1

0

Discrete 2

Load (kN)

0

Segmental 1 Segmental 2 Continuous 1 Continuous 2 Solid 1 Solid 2 100% Composite

0

0.005

0.01

0.015

0 0.02

Deflection (in) Fig. 13. Linear Region comparison.

0% Composite

18000

80

16000

70

14000

60

12000

50

10000

40

8000

30

6000 4000

20

2000

10

0

0

500

1,000

1,500

2,000

2,500

Load (kN)

Load (lbs)

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0 3,000

80 70 60 40 30 20

Load (kN)

Load (lbs)

(a) Continuous Connectors - Top Surface Strain

50

10 0 1000 2000 3000 4000 5000 6000 7000 8000

0

Strain (x10-6)

80 70 60 50 40 30 20

Load (kN)

Load (lbs)

(b) Continuous Connectors - Tension Steel Strain 18000 16000 14000 12000 10000 8000 6000 4000 2000 0

10 300

800

1,300

0 1,800

70

14000

60

12000

50

10000 40

8000

30

6000 4000

20

2000

10

0

0

2000

4000

6000

8000

Strain

(x10-6)

Load (kN)

Load (lbs)

Strain (x10-6, Compression) (c) Solid Panel - Top Surface Strain 16000

panels. For reference, the load–deflection curves of 0% and 100% DCA are added. It can be seen from Fig. 13 that, as expected, all curves fall into the range between 0% and 100% DCAs. The specimens with discrete connectors do not exhibit stiffness as high as the majority of other specimens. 5.2. Strain 5.2.1. Load–strain Fig. 14 displays typical load–strain curves for the top surface and tension reinforcement for sandwich panels with continuous shear connector and solid panels. As expected, the top surface experienced compression and the reinforcement of bottom wythe experienced tension. The tension reinforcement yielded before the specimen failed.

Strain (x10-6, Compression)

18000 16000 14000 12000 10000 8000 6000 4000 2000 0

103

0 10000 12000 14000

5.2.2. Strain distribution The strain data collected were also used to plot the distribution of strain across each panel. Fig. 15 displays the strain distribution across the depth for various panels. In all cases, the panels were analyzed at loads which produced identical moments at mid-span. It is noted that the R2-value for the solid panel is 1, which is a statistical measure of how well data points fit a statistical model. In this case, a linear best-fit line for the collected strain data displays 100% DCA (see Fig. 15(a)). In the case of the discrete connectors (Fig. 15(b)), it can be seen that the strain profile crosses the neutral axis in each respective wythe. This behavior indicates less composite action between the two wythes. In the case of both the segmental and continuous connectors (Fig. 15(c) and (d), respectively), the strain profile displays a strain distribution that does not cross the neutral axis within either wythe. This is a mark of composite action. But as the lines (if extrapolated) do not perfectly line up with each other as shown in Fig. 15(a), it can be concluded that the wythes behaved in a partially composite manner. 5.3. Failure mode During the tests, various crack initiation and propagation was observed. When cracking began at the border between the solid concrete zone and the insulation, a shear failure resulted. In this case, the cracks began both on the top and bottom of the specimen. When cracking began on the bottom surface of the specimen near mid-span, propagating in a generally straight line across the width of the specimen, a bending failure occurred. When both of these crack initiations and propagations were present in a specimen, it resulted in a mixed failure mode, characterized by mid-span cracking which propagated in an angular fashion as opposed to straight across the width of the specimen. The failure mode experienced by each panel is presented in Table 3. Figs. 16 and 17 provide examples of shear and bending failures, respectively. 6. Finite element analysis

(d) Solid Panel - Tension Steel Strain 6.1. Finite element model Fig. 14. Load–strain curves.

5.1.5. Comparison Fig. 12 presents the comparison of the load–displacement curves from each group with necessary adjustment and Table 2 summarizes cracking loads, the maximum loads, and deflections corresponding to the maximum loads. It can be seen that, as expected, specimens with continuous and segmental connectors exhibit higher strength while those with discrete connectors exhibit lower strength. Fig. 13 represents the linear stage of all the

A Finite Element (FE) model was created using ABAQUSÓ (2011), a commercially available FE analysis software. The materials used were concrete, steel rebar, GFRP, and EPS foam, as shown in Fig. 18(a). As described in Section 2.2, the compressive strength of the concrete was fc0 = 28.4 MPa (4120 psi). The modulus of elasticity for concrete, Ec, can be calculated based on ACI building code [11] as:

qffiffiffiffi 0 Ec ¼ 57; 000 f c

ð2Þ

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Fig. 15. Strain distribution along depth.

Table 3 Failure Modes.

Fig. 16. Shear failure (profile view).

which results in Ec = 25.2 GPa (36.6  106 psi). The modulus of elasticity for steel was Es = 200 GPa (29  106 psi). As shown in Section 2.2, the FRP shear connectors had a Young’s modulus of 13.8 GPa (2.0  106 psi) and thickness of 2.16 mm (0.08500 ). The Young’s modulus for EPS was 2.344 MPa (340 psi). Concrete and EPS insulation were modeled using 3D deformable solid 8-point elements (C3D8R). The steel reinforcement was simulated using stringers, which were defined using 3D truss elements (T3D2). 3D deformable shell elements (S4R) were used to represent the FRP shear connectors. Based on a convergence study, the mesh

Group

Connector type

Initial failure mode

Secondary failure mode

1

Discrete Discrete

Shear Shear

– –

2

Segmental Segmental

Shear Bending

– Shear

3

Continuous Continuous

Bending Bending

Shear Shear

4

N/A N/A

Bending Bending

– –

size of 25.4 mm (1 in.) was used. Since this paper is focused on the degree of composite action at elastic stage, linear analyses were carried out. The self-weight and test load were simulated using a two-step loading process to more accurately represent the loading conditions. The self-weight was applied using ‘‘gravity load’’ while the test load was applied as pressure load, which were solved using a general static analysis. The boundary conditions were pinned at one end and roller at the other end. A typical FE mesh is shown in Fig. 18(b). Fig. 19 displays the contour plot of vertical deflection for a sandwich panel with continuous shear connector under bending, with and without concrete wythes. Load–displacement curves from FE analysis and test results are plotted in Fig. 20 for different types of panels. It can be seen that for Group 3 with continuous shear connector (Fig. 20(c)), good correlations can be observed between the FE and test results. For Groups 2 (with segmental shear connector, Fig. 20(b)) and 4 (solid panels, Fig. 20(d)), there is a good correlation between FE and test results for one panel. Therefore, it can

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discussed in next section. Therefore, it can be concluded that the performance of the shear connectors follow the order of continue, segmental, and discrete connectors. 7. Discussions 7.1. Degree of composite action The Degree of Composite Action (DCA) can be determined by the load and deflection of each specimen compared to that of the solid control specimens. The DCA was calculated using the following equation [1]:

1

Fig. 17. Bending failure (bottom of specimen).

DCA ¼

be concluded that the FE model can predict the behavior of various types of panels. However, one solid panel (Fig. 20(d)) and one panel with segmental shear connector (Fig. 20(b)) did not perform as expected, probably because of the construction practice. The FE model was further used to study the panels with discrete shear connector. As shown in Fig. 20(a), there is a big difference between FE and test results for both panels, indicating that the panels significantly under-performed. It is reasonable since misalignment is easy to occur for discrete shear connectors, while it is not a problem for continuous shear connector. For segmental shear connector, since they are connected at the bottom, the problem will less likely occur comparing to discrete shear connectors. The same trend can be observed for degree of composite action, as will be

EI1 0% EI 0%

 

1 EI1 Actual ð100%Þ

ð3Þ

EI 100%

      where EI1 0% , EI1 Actual and EI1 100% represent the values for panels with 0% DCA (non-composite); partial DCA; and solid control panels   with 100% DCA, respectively. In order to determine EI1 Actual , the following equations of a simply supported beam were applied for three point bending as:

D¼

PL3 48EI

ð4Þ

and four-point bending as:

D¼

Pa 3L2  a2 12EI 4

(a) Components of FE Model

(b) FE Mesh Fig. 18. FE model.

! ð5Þ

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(a) With Concrete Wythe

(b) Without Concrete Wythe

Fig. 19. Contour plot of vertical deflection.

Fig. 20. Test vs. FE results.

where D is the deflection at the mid-span, L is the span of the beam, a is the distance from the support to the loading point for four-point bending, and P is the load acting on the beam. By focusing on the data collected within the elastic region, best-fit lines were applied to the curves shown Fig. 13, such that the slope would be equal to DP , with details shown in Fig. 20. Given this load to deflection ratio, the moment of inertia I and EI values for each specimen can be calculated, based on which the DCA for each panel was determined, as shown in Table 4.

Using the theory of transformed section, the moment of inertias for 100% DCA based on a solid 610 mm  254 mm (2400  1000 ) cross-section, and 0% DCA based on two separate 610 mm  76 mm (2400  300 ) cross-sections are 8.86  108 mm4 (2129 in4) and 4.50  107 mm4 (108 in4), respectively. As expected, I values for all the panels fall into this range, as shown in Table 4. In particular, the I value for the first solid panel is 8.44  108 mm4 (2027 in4), which is close to Icomposite. The two panels with continuous connector exhibit similar results. There is a relatively large

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A. Chen et al. / Engineering Structures 98 (2015) 95–108 Table 4 Degree of Composite Action (DCA)a. Specimens Solid panels

Test results FE results

Panels with discrete connector

Test results

Panels with segmental connectorb

Test results

FE results

FE results Panels with continuous connector

Test results FE results

a b

P/D (kN/mm)

I (mm4)

EI (kN ⁄ mm2)

1/EI (1/(kN ⁄ mm2)

DCA (%)

Average DCA (%)

49.5 20.4 49.8

8.44E+08 3.47E+08 8.48E+08

2.13E+10 8.76E+09 2.14E+10

4.70E11 1.14E10 4.67E11

100 92 –

96

9.8 16.2 25.0

1.00E+08 1.65E+08 2.55E+08

2.53E+09 4.16E+09 6.42E+09

3.96E10 2.40E10 1.56E10

58 77 –

68

18.7 9.6 16.6

3.20E+08 1.64E+08 2.83E+08

8.06E+09 4.15E+09 7.15E+09

1.24E10 2.41E10 1.40E10

91 77 –

84

25.5 18.7 18.0

4.35E+08 3.18E+08 3.08E+08

1.10E+10 8.02E+09 7.76E+09

9.11E11 1.25E10 1.29E10

95 91 –

93

100

87

88

90

Calculations are based on 2.74 m (9 ft) span under 3-point bending unless otherwise noted. Calculations are based on 2.44 m (8 ft) span under 4-point bending.

Table 5 Strength comparison. Connector type

Strength (%)

First failure

Discrete Segmental Continuous

41 79 87

Shear Bending Bending

Table 6 Maximum allowable/failure uniformly distributed area loads. Connector type

Based on strength (kPa)

Based on stiffness (kPa)

Discrete Segmental Continuous

13 26 28

10 19 29

variance in the results for the panels with discrete and segmental shear connectors, probably because the segments for segmental and discrete shear connectors are not continuous. Any mis-alignment of the shear connectors might affect the global stiffness of the connectors. However, based on average DCA from Table 4, it can still be concluded that the DCA follows the order of the stiffness of the FRP connector, i.e., continuous and discrete connectors produce the highest and lowest DCAs, respectively. Following the same method as described above, the DCAs can be calculated based on FE results, as shown in Fig. 20 and Table 4, which indicates that Groups 2 through 4 performed as expected. However, both panels in Group 1 significantly underperformed. Therefore, discrete shear connectors are not effective as the other two types of shear connectors. The use of discrete connector is not recommended. 7.2. Strength The strengths of the panels with various connectors as compared to solid panels are presented in Table 5. The strength ratio was calculated by dividing the maximum moment applied to each group by the maximum moment sustained by the solid panels from Table 2. The failure mode provided by these connectors is also provided. It can be seen from Table 5 that a greater DCA results in a higher strength. 7.3. Applicability to roof/floor applications ACI 318-11 [11] specifies that the minimum thickness for a simply supported one-way slab is L/20. Therefore, the 254 mm (1000 ) panels considered in this study can have a span L of

4877 mm (160 ). The maximum loads that can be carried by the panels can be calculated based on the moment capacities shown in Table 2, as summarized in Table 6. It is noted that uniformly distributed area load is used in the calculations to be comparable with load requirement from applicable building codes. The limits for immediate deflection due to live load for floor and roof based on ACI 318-11 [11] are L/360 and L/180, respectively. Based on the criterion of L/360, the maximum allowable deflection for the given span is 14 mm (0.53300 ). Using the moment of inertial I from Table 4, the loads corresponding to this deflection for the sandwich panels are shown in Table 6. It should be noted that these value are based on the initial stiffness, i.e., assuming the sections are un-cracked. Further study needs to be conducted on how to determine the moment of inertial I of cracked sections for panels with 4877 mm (160 ) span, based on values from panels with 2743 mm (90 ) in this study, which will provide more accurate estimation of the maximum load that can be taken by the panels based on the deflection criterion. It can be seen from Table 6 that the failure load are higher than the live load for most of building applications. Therefore, the sandwich panels can be used for floor/roof applications. 8. Conclusions In this paper, bending tests and FE analyses were conducted on eight large-scale 2743  610  254 mm3 (90  20  1000 ) panels, including six sandwich panels consisting of discrete, segmental, and continuous shear connectors and two solid panels. The FRP plate, with specially designed anchoring schemes, can be successfully used as shear connectors to transfer shear force between the concrete wythes. Different types of FRP plate shear connector produce different degrees of composite action, which can affect both the strength and stiffness of the sandwich panels. This degree of composite action can be predicted with the FE model developed in this paper. The FRP connectors with greater stiffness have higher DCAs, which result in higher strength and stiffness. It is shown from this study that the sandwich panels can be used for roof/floor applications based on the criteria of static strength and immediate deflection. Continuous and segmental shear connectors performed better than discrete shear connector. The use of discrete shear connector is not recommended. However, other factors, such as creep, are also important factors that need to be considered for building applications. The results of the creep tests on the sandwich and solid concrete panels will be reported in another study. Fatigue and fire tests are important topics that need further research.

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Acknowledgments We gratefully acknowledge the Higher Education Research Council (HERC), Idaho State Board of Education for financial support; Missouri Structural Composites LLC for technical support; and Crane Composites Inc. for material donations. We thank Nicolas Pena, Michaela Peterson, and the Fall 2012 CE 441 students of University of Idaho for their help with the test. References [1] Frankl Bernard A, Lucier Gregory W, Hassan Tarek K, Rizkalla Sami H. Behavior of precast, prestressed concrete sandwich wall panels reinforced with CFRP shear grid. PCI J 2011;2011:42–54. Spring. [2] PCI Committee on Precast Sandwich Wall Panels. State of the art of precast/ prestressed concrete sandwich wall panels. PCI Committee report. Spring 2011; 2011. p. 131–42. [3] Bush Jr Thomas D, Wu Zhiqi. Flexural analysis of prestressed concrete sandwich panels with truss connectors. PCI J 1998;43 5:76–86. [4] Salmon David C, Einea Amin. Partially composite sandwich panel deflections. J Struct Eng 1995;121(4):778–83. [5] Einea Amin, Salmon David C, Tardos Maher K, Culp Todd. A new structurally and thermally efficient precast sandwich panel system. PCI J July–August 1994:90–101. [6] Bush Jr Thomas D, Stine Gregory L. Flexural behavior of composite precast concrete sandwich panels with continuous truss connectors. PCI J March–April 1994:112–21. [7] Lorenz Robert F, Stockwell Frank W. Concrete slab stresses in partially composite beams and girders. AISC Eng J 1984:185–8. 3rd Quarter. [8] Einea Amin, Salmon David C, Fogarasi Gyula J, Culp Todd D, Tardos Maher K. State-of-the-art of precast concrete sandwich panels. PCI J November– December 1991:78–98.

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