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Lumped GFRP star connector system for partial composite action in insulated precast concrete sandwich panels
Composite Structures 229 (2019) 111465
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Lumped GFRP star connector system for partial composite action in insulated precast concrete sandwich panels
T
Brandon Coxa, Parker Syndergaardb, Salam Al-Rubayec,d, Fray F. Pozo-Lorac, Raed Tawadrouse, ⁎ Marc Maguirec, a
Mountain View Engineering, Brigham City, UT, USA Calder Richards Structural Consulting Engineers, Salt Lake City, UT, USA c Department of Civil and Environmental Engineering, Utah State University, Logan, UT, USA d Department of Civil Engineering, Tikrit University, Salahuldean, Iraq e e.construct, Florida, Orlando, FL, USA b
ARTICLE INFO
ABSTRACT
Keywords: GFRP shear connectors Insulated sandwich panel Composite action Partially composite Precast concrete Thermal efficiency
This paper introduces a novel composite shear connectors system used to transfer interface shear forces in a precast concrete sandwich panel. The shear connectors consist of non-proprietary non-composite commercial glass fiber reinforced polymer (GFRP) pin connectors that are laid out in a star pattern and clustered at the top and bottom of the panels. The testing program consisted of thirty-four push-off, twenty-three pullout, and eight full-scale flexural specimens was conducted to evaluate the structural performance of the new shear connectors. The effect of concrete wythe thickness, insulation wythe thickness, and concrete compressive strength was investigated throughout these tests. Additionally, the effect of bond between insulation and concrete wythes was investigated using push-off tests. The flexural test results were compared with predicted fully composite, noncomposite, and partially composite values to evaluate the overall panel performance. The comparison showed satisfactory performance with a lower bound of 90% composite action for specimens with 100 mm thick insulation wythe and full composite action for most panels with 50 mm thick insulation. Idealized shear load-slip curves were also developed that account for various parameters to assist design engineers in designing insulated sandwich wall panels with the proposed shear connectors system.
1. Introduction Precast concrete sandwich panels (PCSPs) have become a popular building system due to their thermal and structural performance and the higher demand for energy efficient buildings [1]. These panels are commonly used as load bearing or non-load bearing (cladding) wall members in commercial buildings [2]. PCSPs consist of two exterior concrete layers (wythes) surrounding an insulation layer. Concrete wythe thickness vary between 50 and 150 mm depending on the expected loads, and fire and concrete cover requirements [3]. The insulation layer is typically composed of a 25 to 100 mm thick rigid foam such as expanded polystyrene (EPS) or extruded polystyrene (XPS) [3]. The structural behavior of PCSPs primarily depends on the shear transfer strength and stiffness of the connecting elements between the two exterior concrete wythes, which could be achieved by using various types of shear connectors such as discrete ties or solid concrete zones [4]. Connectors composed of various materials including steel, fiber
⁎
reinforced polymers (FRPs), and plastics [3]. PCSPs constructed using connectors with low strength and stiffness to transfer shear between the two concrete wythes, such that the wythes act independently, are considered non-composite. In cases where the strength and stiffness of the connectors are adequate to transfer the shear forces between the two concrete wythes act as one, the panel is considered fully composite. PCSPs with shear transfer strength that lie in between the two aforementioned extremes (non-composite and fully composite) are considered partially composite panels. Fully composite PCSPs usually utilize steel shear connectors or concrete solid zones when panel strength is of a primary concern, which results in reduced thermal efficiency due to thermal bridging through the highly conductive steel or concrete connectors. Fully composite panels are also more susceptible to thermal bowing, which is of particular concern in long-span walls [3,5]. Partially composite or noncomposite panels utilize variety of shapes such as plate, box, truss, or pin connector fabricated from various types of FRP such as glass FRP
Corresponding author. E-mail address: [email protected] (M. Maguire).
https://doi.org/10.1016/j.compstruct.2019.111465 Received 9 April 2019; Received in revised form 28 July 2019; Accepted 17 September 2019 Available online 19 September 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Star GFRP connectors configuration with 50 and 100 mm thick insulation (Note: dimensions shown are in mm). DtotalDtotal
400 400
70 tins 70 tins140 140 70 70 tins tins
SECTION SECTION A-A A-A EXTERIOR EXTERIOR WYTHES WYTHES
MAIN MAIN WYTHE WYTHE
267 267
Dtotal
200 INSULATION INSULATION LAYERS LAYERS SECTION A-A A-A SECTION
SECTION SECTION B-B B-B
SPC SECTION B-B
267 267
SECTION SECTION A-A A-A
a) Elevation
SHEAR CONNECTOR
400
535 535
200
1070
SHEAR SHEAR CONNECTOR CONNECTOR PROJECTION PROJECTION
1070
1070
1070
SHEAR SHEAR CONNECTOR CONNECTOR
EXTERIOR EXTERIOR WYTHES WYTHES
b) Side view
c) Plan view
Fig. 2. Typical push-off specimens’ geometry.
(GFRP), basalt FRP (BFRP), or carbon FRP (CFRP) and they are considerably more energy efficient due to the reduced thermal bridging between the two exterior concrete wythes [5–7]. Fully composite and non-composite PCSPs are easily analyzed using reinforced concrete sectional analysis, however, partially composite panels represent a challenging design problem to the design engineer. This is mainly due to the heavy reliance of the analysis on the experimental test results for
each connector type. Once the shear connectors resistance behavior is known, the design engineer will be able to accurately perform the partially composite panel design. GFRP shear connectors have been widely used during the last 30 years based on successfully conducted research programs that indicated their adequate structural performance with comparable composite action to steel connectors as well as their improved thermal 2
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production and uses fewer connectors for maximum effect.
Table 1 Push-off testing matrix. Specimen ID
Average f’c (MPa)
Insulation thickness (mm)
Bond condition
HS50P1-HS50P 5 HS100P1- HS100P5 LS50P1- LS50P6 LS100P1- LS100P6 HS50P1D-HS50P6D HS100P1D- HS100P6D
37.6 37.6 17.16 17.16 37.6 37.6
50 100 50 100 50 100
Bonded Bonded Bonded Bonded Debonded Debonded
2. Experimental program A comprehensive experimental program that consisted of push-off tests, pull-out tests, and large-scale flexural tests was conducted to investigate the composite action of insulated sandwich wall panels with the new clustered GFRP shear connectors. To develop partial composite action, the non-proprietary pin typically used for non-composite design were oriented in a “Star” pattern with two GFRP Pins inclined at 45 degrees (perpendicular to each other) and the third pin was inserted normal to the insulation in between the other two pins, as shown in Fig. 1. These pins are typically used individually and in the perpendicular orientation only and when doing so only allow non-composite behavior. Specifically, these pins are non-proprietary, but herein, the orientation of these pins in a star pattern, using three pins, partial composite action can be achieved. The modulus of elasticity for the GFRP Pin is 47988 MPa and the ultimate strength is 1200 Mpa based on manufacturer product testing. The two inclined connectors were intended to provide identical resistance when the panel is exposed to suction or pressure wind load and also to better utilize the axial stiffness of the connector material. All specimens were conventionally reinforced using 10 mm (#3) steel bars. The following sections present each of these experiments in details.
efficiency [2,4,8–12]. These research programs used various shear connector shapes, however, the uniform shear connector distribution along the entire length of the panel was common among all of them. Anecdotally, commercial panels have been attempted with lumped connectors near the ends, but this approach has resulted in delamination (tension) failure of the wythes due to inadequate tensile capacity. This paper investigates the validity of a newly developed GFRP shear connector system used to develop partial composite action in nonprestressed PCSPs. These connectors consist of non-proprietary pin connectors that are routinely used for non-composite wythe connection, oriented in a star pattern using three pins oriented around one location. The effect of different parameters such as insulation thickness, bond between concrete and insulation, and concrete compressive strength were investigated. The behavior of the new shear connectors system was studied using a series of push-off tests, pull-out tests, and largescale flexural tests. Large-scale flexural test results were compared with theoretically predicted values to quantify the level of composite action at the ultimate level. The new shear connectors utilize clustered shear connectors at each end of the panel, which significantly simplifies panel
2.1. Push-off tests Thirty-four push-off specimens were tested to evaluate the shear force-slip relationship. The new GFRP shear connectors were tested using double shear push-off specimens that were constructed using three concrete wythes and two XPS insulation wythes as shown in
Fig. 3. Push-off test setup. 3
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Fig. 4. Typical orthogonal views of pull-out specimens.
and 100 mm, which is the commonly used in practice [3]. Low and high concrete compressive strengths were used with average strengths of 17.16 and 37.6 MPa, respectively. Perimeter reinforcement was provided for handling and was centered in each wythe using 10 mm diameter reinforcement located 50 mm from each edge, ensuring no interaction with the shear connectors. The shear resistance contribution due to bond between concrete and the insulation layer is considered temporary and usually disregarded in composite action calculations for service loads because the bond is expected to degrade overtime [3]. Therefore, bond at the concrete-insulation interface in twelve push-off specimens was broken using thin plastic sheets to measure the shear stiffness of the shear connectors system without bond contribution. Table 1 provides a summary of the push-off testing matrix including concrete compressive strength, insulation thickness, and bond condition for each specimen. Bond was broken by placing a layer of 0.02 mm plastic around the insulation. As shown in Table 1, specimens are identified using concrete strength, insulation thickness, specimen number, and bond condition (letter “D” was added for debonded specimens). For example, specimen LS50P1, “LS” is for low strength concrete, “50” is for 50 mm foam insulation wythes, and “P1” is for specimen number one within the same group. 2.2. Double shear test setup and instrumentation Fig. 3 shows the test setup along with the instrumentation plan used in this study. The parameters measured during the experiments were applied load, and relative slip between the concrete wythes. The push-off specimens were tested by applying the load at the center concrete wythe with a hydraulic ram while the outer two wythes were supported by bearing on the concrete, as shown in Fig. 3, with polytetrafluoroethylene bearing pads at the interface to minimize any horizontal friction forces. The center wythe was recessed to allow for defomation. The applied load was measured at the ram location using an electrical resistance based full bridge 1300 kN load cell and 1300 kN hydraulic ram. Four total Linear Variable Differential Transducers (LVDTs) were used to measure the displacement of the center wythe relative to the outer concrete wythes on both sides of each wythe.
Fig. 5. Pull-out test setup.
Fig. 2. Note that XPS insulation has small contribution to shear strength [13–15], but bonded and debonded conditions were investigated because practicing engineers are often concerned with the different behaviors. All specimens contained two exterior and one interior concrete wythes with a thickness of 70 mm and 140 mm, respectively. The 70 mm wythes were selected because this is the typical minimum in practice and the center wythe is double that of the outer wythes to allow room for the connectors. The testing focused on investigating three main parameters: insulation thickness; bond between concrete and insulation; and concrete compressive strength. The specimens had four connectors each (two on each side) at a longitudinal spacing of 535 mm, as shown in Fig. 2. The insulation thickness varied between 50
2.3. Pull-out tests Twenty-three pull-out specimens were fabricated and tested to evaluate the pull-out capacity of the new GFRP shear connectors. Specimens were constructed to simulate insulated sandwich wall panel construction with 75 mm thick top and bottom concrete wythes, as shown in Fig. 4. Perimeter reinforcement was provided for handling 4
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Fig. 6. Typical panel geometry, reinforcement, and shear connectors of specimen 70-100-70. Table 2 Measured concrete material properties full scale flexure specimens. Panels ID
Span length (m)
Wythe
f’c (MPa)
Ec (MPa)
70-50-70
3.3
70-50-70
4.2
70-100-70
3.3
70-100-70
4.2
90-50-90
3.3
90-50-90
4.2
90-100-90
3.3
90-100-90
4.2
Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
29.0 51.9 40.0 54.6 34.7 40.0 45.8 44.5 34.7 34.7 44.5 44.5 29.0 47.3 40.0 54.6
21,201 31,325 21,201 32,032 32,961 21,201 26,958 32,553 32,962 32,962 32,554 32,554 21,201 31,783 24,201 32,032
and was centered in each wythe using 10 mm diameter reinforcement located 50 mm from each edge, ensuring no interaction with the shear connectors. The testing program focused on investigating the effect of insulation thickness and concrete compressive strength on the pull-out strength of the connectors. Low and high concrete compressive strengths were used with average strengths of 17.16 and 37.6 MPa, respectively. Insulation wythe thickness varied between 50 mm and 100 mm. Each specimen had one connector centered with the insulation and the top concrete wythe, while, the bottom concrete wythe was used to accommodate three pull-out specimens as shown in Fig. 4. Specimens are identified using concrete strength, insulation thickness, and specimen number. For example, specimen HS50T3, “HS” is for high strength concrete, “50” is for 50 mm foam insulation wythe, and “T1” is for specimen number one within the same group. The insulation and concrete bond was broken in a similar manner as with the double shear tests as engineers often prefer to not count on the bond.
Fig. 7. Flexure test setup and instrumentation a) sketch, and b) photo.
specimens were tested by applying the load to the top concrete wythe with a hydraulic ram while the bottom concrete wythe was tied down by two steel beams anchored to the strong floor, as shown in Fig. 5. The applied load was measured at the ram location using an electrical resistance based full bridge 440 kN load cell and 440 kN hydraulic ram. 2.5. Large-scale flexural tests Eight large-scale reinforced concrete, non-prestressed sandwich, panels were constructed and tested. The panels thickness and length were designed to bound their target market for low rise housing. The eight panels were constructed with four different panel thicknesses.
2.4. Pull-out test setup and instrumentation Fig. 5 shows the test setup used to test the pull-out specimens. The 5
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Fig. 8. Load-slip relationship for push-off tests (a) HS50P1-5 (b) HS100P1-5 (c) LS50P1-5 (d) LS100P1-6 (e) HS50P1-5D (f) HS100P1-5D.
Each designated panel thickness was constructed in two different lengths, 3300 and 4200 mm, and a width of 1800 mm. The four different wythe thicknesses were 70-50-70, 70-100-70, 90-50-90, and 90100-90 (values are in mm), where the outer two values refer to the exterior concrete wythes’ thicknesses and the middle value refer to the insulation thickness. For example, 90-100-90 means that the two outer concrete layers are 90 mm thick and the insulation has a thickness of 100 mm. Each concrete wythe was reinforced using five 10 mm (#3) Grade 410 (ASTM A615) conventional steel reinforcement bars. Two major parameters were investigated, insulation thickness and concrete wythe thickness, and their impact on strength and mode of failure. Fig. 6 shows an example of the typical insulated sandwich panel geometry, reinforcement, and shear connectors configuration for 70-10070 panel. The star pattern shear connectors were discretely clustered at each end of the panel and single pin connectors normal to the insulation surface were placed at 600 and 540 mm on center for 4200 and 3300 mm, respectively, along the interior zone, as shown in Fig. 6. Lifting locations used commercial 9kN pins suitable for stripping the panel from the forms, including transverse reinforcement, but did not penetrate the full thickness of the insulation. At these locations a 300 mm square recess into the insulation was created to achieve the proper embedment depth of 100 mm for the 50 mm and 100 mm insulation specimens. The bottom and the top concrete wythes were poured at different times using different concrete mixes because of fabrication constraints at the precast plant. Table 2 lists span length and the measured concrete properties including concrete compressive strength and modulus of elasticity for each concrete wythe measured at testing time. Specified yield and ultimate strengths of flexural steel reinforcement were 415 and 620 MPa, however, the average measured values using seven 10 mm (#3) rebar specimens were 453 and 767 MPa, respectively.
2.6. Large-scale flexural test setup and instrumentation Fig. 7 shows the test setup along with the instrumentation plan used in this study. The parameters measured during the experiments were applied load, deflection, and relative slip. Each span was loaded with four-point load using three spreader beams, which applied four equally spaced loads, to simulate the curvature distribution from a uniformly distributed loading condition, as shown in Fig. 7. The vertical deflection was measured using string potentiometers at mid-span on either side of the panel. A total of eight LVDTs were mounted on each specimen, one at each corner and four along the span length on one side of the panel, to measure the relative slip between the two exterior concrete wythes. The applied load was measured at the ram location using an electrical resistance based full bridge 1300 kN load cell and 1300 kN hydraulic ram. 3. Test results and discussion 3.1. Push-off test results Fig. 8 shows the load-slip relationships for the thirty-four specimens, where slip represents the relative movement between concrete wythes using the average of four LVDT readings for each specimen. The plots are divided into six sets to compare results of specimens with similar properties. All specimens exhibited an approximate bilinear loadslip relationship except specimens in groups 2 and 6 (with high strength concrete and 100 mm thick insulation wythe), which showed a nearly linear load-slip behavior. Table 3 lists load, slip, and calculated shear stiffness values at the end of the elastic and inelastic stages. The load values listed in Table 3 and shown in Fig. 8 represent 25% of the total applied load to account for the strength of one shear connector rather than the total number of shear connectors used in the push-off specimens. The results of seven specimens were excluded from Table 3 due 6
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Table 3 Summary of push-off test results. Group
Specimen ID
Elastic Load, FE (kN)
Elastic slip, ΔE (mm)
Elastic stiffness, KE (kN/ mm)
Ultimate Load, FU (kN)
Ultimate slip, ΔU (mm)
Ultimate stiffness, KIE (kN/ mm)
1
HS50P1 HS50P2 HS50P3 HS50P4 HS50P5 HS50P6 Mean COV HS100P1 HS100P2 HS100P3 HS100P4 HS100P5 Mean COV LS50P1 LS50P2 LS50P3 LS50P4 LS50P5 LS50P6 Mean COV LS100P1 LS100P2 LS100P3 LS100P4 LS100P5 LS100P6 Mean COV HS50P1D HS50P2D HS50P3D HS50P4D HS50P5D HS50P6D Mean COV HS100P1D HS100P2D HS100P3D HS100P4D HS100P5D HS100P6D Mean COV
20.88 – – 21.87 20.93 24.76 22.11 0.083 40.1 35.92 40.77 36.08 39.29 38.43 0.059 15.41 13.79 12.87 14.74 14.17 13.12 14.01 0.069 13.78 – – – 14.92 17.23 15.31 0.115 18.64 – 20.11 18.46 17.94 18.58 18.75 0.043 40.04 – 28.2 29.35 32.85 29.37 31.96 0.151
1.8 – – 1.47 1.88 1.65 1.7 0.106 6.35 5.08 6.35 5.08 6.35 5.842 0.119 1.93 1.8 2.24 1.91 1.83 1.55 1.88 0.119 1.41 – – – 1.78 1.52 1.57 0.121 1.1684 – 1.651 1.2954 1.778 1.4986 1.48 0.169 6.18388 – 3.49136 3.00585 4.07314 3.262 4 0.32
11.58 – – 14.85 11.13 15 13.14 0.157 6.31 7.07 6.42 7.1 6.19 6.62 0.066 7.98 7.65 5.76 7.74 7.75 8.47 7.56 0.123 9.79 – – – 8.39 11.3 9.83 0.148 15.95 – 12.18 14.25 10.09 12.4 12.98 0.171 6.47 – 8.08 9.76 8.06 9 8.28 0.149
41.76 – – 43.74 41.85 49.52 44.22 0.083 – – – – – –
5.51 – – 5.53 7.65 5.68 6.09 0.171 – – – – – –
5.63 – – 5.39 3.63 6.15 5.2 0.211 – – – – – –
30.82 27.58 25.74 29.47 28.33 26.23 28.03 0.069 27.55 – – – 29.85 34.45 30.62 0.115 37.28 – 40.22 36.93 35.87 37.17 37.49 0.043 – – – – – – – –
7.75 6.45 7.45 8.44 6.19 5.39 6.94 0.163 6.1 – – – 6.62 6.72 6.48 0.052 4.14503 – 4.94906 4.71615 4.83476 5.45313 4.82 0.098 – – – – – – – –
2.65 2.97 2.47 2.25 3.25 3.42 2.83 0.16 2.94 – – – 3.08 3.31 3.11 0.061 6.26 – 6.1 5.4 5.87 4.7 5.66 0.111 – – – – – – – –
2
3
4
5
6
The bolded values represent the mean and coefficient of variation for their group.
to the malfunctioning of the LVDT devices during the test. The main failure mode in all specimens was concrete breakout as shown in Fig. 9. Test results showed relatively high variability with a coefficient of variation (COV) ranging from 4.3 to 15.1% for elastic shear resistance, as shown in Table 3. The variation is believed to be attributed to the ability of the fabricator to install the pins in the appropriate orientation and the concrete material variability. Specimens with bonded contact between concrete and insulation wythes achieved the ultimate shear strength at relatively similar slip values with mean values ranging from 5.59 to 6.39 mm. However, unbonded specimens reached the ultimate load at slightly lower slip values with mean values ranging from 4 to 4.8 mm. These observations are similar to those from other commercial connectors [16]. Fig. 8a and c, and Fig. 8b and d show the difference in load-slip behavior between low and high strength concrete for specimens with 50 and 100 mm thick insulation, respectively. The failure load increased as the concrete compressive strength increased. For specimens with 50 mm thick insulation wythe, increasing the concrete strength from 17.16 to 37.6 MPa increased the failure load by 55%, while the increase
was 26% for specimens with 100 mm thick insulation. This difference is attributed to the increased unsupported length of the connectors in the latter group. It is worth noting that load-slip curve of HS100P series (Fig. 8b) showed linear relationship until failure, which is unlike HS50P, LS50P, and LS100P series that showed a bilinear relationship. It is believed that HS100P series behaved elastically due to simultaneous failure of concrete (breakout) and rupture of the tension GFRP pin connectors. Fig. 10 shows idealized shear load-slip relationships for low and high strengths concrete with 50 mm and 100 mm insulation thicknesses. These curves provide the base design values for designing PCSPs using the proposed shear connectors system. Comparing the load-slip curves of bonded and unbonded specimens with similar properties in Table 3 show tangible increase in the failure load due to bond contribution to the overall resistance. Bond contribution increased the failure load similarly for specimens with 50 and 100 mm thick insulation with an average of 17.6 and 16.3%, respectively. The difference between both groups was less than 1.5%. Unbonded specimens experienced less slip at failure when compared to 7
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Fig. 9. Typical concrete breakout failure of push-off tests.
Fig. 10. Idealized load-slip curves for high strength concrete (left) and low strength concrete (right).
bonded specimens with an average slip of 4 and 3.13 mm compared to 5.59 and 5.84 mm, respectively. This is evidence that bond at concreteinsulation interface failed after concrete and/or shear connectors failure took place and allowed for extra slip.
3.3. Flexural test results Fig. 12 shows the load–deflection curves for the specimens tested in this study. All tested specimens showed linear increase in the load–deflection relationship with approximately the same slope until cracking, then non-linear increase up to failure. The cracking load was not significantly affected by the insulation thickness for specimens with similar concrete wythe thicknesses, which indicates that the panels are having a low degree of composite action prior to cracking, as is typical [16]. Table 6 lists the measured cracking loads and moments for all panels except panel 70-100-70 with 3.3 m long span. The latter specimen experienced large cracks due to improper panel fabrication by the precaster, therefore the results of this specimen are disregarded. Additionally, Table 6 lists the predicted cracking moment for composite and non-composite section properties for comparison purposes. Prediction of cracking and deflections assumed fully non-composite and fully composite behavior using gross concrete properties and first principles. The comparison showed that the PCSP experienced a relatively low degree of composite action at cracking level with less than 7% composite as was expected. All specimens failed in a ductile manner by yielding the steel reinforcement in both bottom and top concrete wythes. As the load increased beyond yielding, excessive deflection
3.2. Pull-out test results Fig. 11 shows the observed failure mode for low and high strength concrete. In both cases, the failure was a combination of concrete breakout with no indication for rupture in the connectors. Tables 4 and 5 list a summary of pull-out test results for low strength and high strength concrete specimens, respectively. Low strength concrete specimens with 50 mm insulation thickness showed 36% higher tension resistance than those with 100 mm thick insulation wythe, with an average tension load resistance of 18 kN compared to 13.2 kN, with a COV of less than 13%. However, high strength concrete specimens showed relatively similar tension load resistance results regardless of the insulation wythe thickness with an average load resistance of 21.96 and 21.35 kN for HS50 and HS100 series, respectively. The reason for this difference is unclear. HS100 series showed the least COV value (4%) when compared to the other series. 8
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Fig. 11. Typical failure mode of pull-out specimens for a) low strength concrete and b) high strength concrete.
predicted using five methods: simplified elastic method [17]; the beamspring method [16]; a beam-truss method [18]; the Holmberg and Plem method [19]; and Bai and Davison method [20] and the results were compared with the observed behavior. The beam-spring and beam-truss methods are computational, relying on matrix models and the remaining methods variations of classical sandwich beam theory. A brief discussion of these methods is below, but full treatment of each method is contained in the appropriate reference. The simplified elastic method was proposed by Olsen et al. [17] and it is an iterative method that uses kinematic relationships to calculate the slip between the two exterior concrete wythes assuming linear loadslip relationship. The main advantage of this method, is that it allows for analysis of discrete connector locations. Once load-slip relationship for the shear connectors is identified and is iterated to equilibrium, the cracking moment and deflection can be calculated using fundamental statics equations. The beam-spring method was conducted using numerical analysis utilizing a commercial matrix analysis software package. This method is widely used by engineers in the United States to estimate elastic behavior of sandwich wall panels. Top and bottom concrete wythes were modeled using beam elements and shear connectors were modeled using spring elements, as shown in Fig. 14. Spring members were assigned shear and tension stiffness coefficients obtained from shear (push-off tests) and tension (pull-out tests). Beam elements were assigned the concrete properties of the top and bottom concrete wythes. The beam-truss method is similar to the beam-spring method with one difference. Shear connectors in the beam-truss method were modeled using truss members that resists only axial tension or compression forces and are assigned material properties consistent with those used for the GFRP material and cross sectional area. The Holmberg and Plem method [19] uses sandwich beam theory to predict both deflection and cracking load for the insulated wall panels. This method was originally developed by Granholm [21] for nailed timber structures, and subsequently extended to concrete sandwich wall panels of equal wythes by Holmberg and Plem. This method assumes that the connectors and concrete layers are made of isotropic, linearly elastic materials, with no connector axial deformation, but
Table 4 Summary of pull-out tests for low strength concrete. Specimen
Max Load (kN)
Specimen
Max Load (kN)
LS50T1 LS50T2 LS50T3 LS50T4 LS50T5 LS50T6 Mean COV
16.58 21.25 19.65 14.70 18.78 17.06 18.00 0.13
LS100T1 LS100T2 LS100T3 LS100T4 LS100T5 LS100T6 Mean COV
14.15 13.12 12.14 11.25 14.51 14.02 13.20 0.10
Table 5 Summary of pull-out tests for high strength concrete. Specimen
Max Load (kN)
Specimen
Max Load (kN)
HS50T1 HS50T2 HS50T3 HS50T4 HS50T5 HS50T6 Mean COV
24.38 22.95 24.03 19.06 18.78 22.55 21.96 0.11
HS100T1 HS100T2 HS100T3 HS100T4 HS100T5 – Mean COV
21.35 21.35 19.91 22.13 20.24 – 21.35 0.04
took place and concrete failure around the clustered shear connectors was observed and consequently larger slippage between the two concrete wythes, as shown in Fig. 13. The theoretical ultimate load is also shown in Fig. 12 for each specimen, which was calculated using the partially-composite strength prediction method developed by Olsen et al. [17]. More on this prediction will be discussed below. 4. Analytical comparison 4.1. Serviceability behavior Serviceability behavior of large-scale flexural specimens was 9
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Fig. 12. Load-deflection relationships (a) 70-50-70-3.3 (b) 70-50-70-4.2 (c) 70-100-70-4.2 (d) 90-50-90-3.3 (e) 90-50-90-4.2 (f) 90-100-90-4.2 and (g) 90-100-903.3. (Note: TUL = Theoretical ultimate load, TCL = Theoretical cracking load). Table 6 Measured cracking loads. Specimen ID
Cracking load (kN/ m2)
Measured Cracking Moment (kN*m)
Fully Composite Cracking Moment (kN*m)
Non-Composite Cracking Moment (kN*m)
Apparent Composite Action (%)
70-50-70-3.3 70-50-70-4.2 70-100-70-4.2 90-50-90-3.3 90-100-90-3.3 90-50-90-4.2 90-100-90-4.2
6.92 4.50 6.50 10.10 10.53 6.56 6.51
16.09 16.50 13.16 21.51 24.65 22.11 22.89
76.14 74.87 96.25 96.07 136.86 106.75 147.12
13.30 13.07 12.28 18.09 16.80 20.11 21.61
4.44 5.55 1.05 4.38 6.54 2.31 1.02
relative slip of those in the longitudinal direction of the sandwich panel, and no contribution of the insulation layer to the stiffness of the structure. Although this approach was not developed for wythes of different material properties and dimensions, the average of the
modulus of elasticity, thickness and panel stiffness (number of connectors multiplied by its stiffness divided by the area of the panel), were used to predict the behavior of the large-scale panels. Bai and Davison [20,22] modified Holmberg and Plem’s method to account for different 10
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most panels are controlled by cracking and designed for elastic second order effects, it is also considered less critical. This method uses first principles such as linear shear load-slip relationship for the shear connectors and the top and bottom concrete wythes bend with equal curvature when the panel is loaded in flexure. According to Olsen et al. [17], there are three failure conditions in partially composite sandwich panels: failure of shear connectors, rupture of tension reinforcement, and concrete crushing of the outermost compression fibers (i.e., εc1 = 0.003). In this method, each wythe of the panel is treated separately as an individual beam and the static equilibrium within each wythe is maintained. The unbalanced force in each concrete wythe is transferred to the other concrete wythe through the shear connectors, as shown in Eqs. (1) and (2). The top concrete wythe (compression wythe) was assigned wythe 1 and the bottom concrete wythe (tension wythe) was assigned wythe 2 in fully composite section, for calculations purposes, as shown in Fig. 14.
Fig. 13. Typical failure mode of flexural specimens.
wythe thicknesses and material properties and attempted to incorporate discrete connection placement using a discrete stiffness function. Table 7 lists the measured and predicted cracking loads and deflections of the tested large-scale sandwich panels. All predictions used the measured concrete material properties and the shear connector properties outlined above. The predicted cracking load and deflection values using the elastic method showed the most accurate results compared with the measured values with an average measured/predicted ratio of 1.04 and 1.04, respectively. This method also provided one of the least scattered prediction results with a coefficient of variation (COV) of 5.77% and 6.73% for cracking load and deflection, respectively. The beam-spring method showed the least scattered prediction results with COV values of 5.61% and 6.48% for cracking load and deflection, respectively. However, this method underestimated the cracking load and deflection by an average of 7% and 8%, respectively. The beam-truss method behaved in a similar manner to the beam-spring method for the predicted cracking load, however, this method significantly underestimated the deflection at cracking with an average measured/predicted ratio of 1.42. The Holmberg and Plem method overestimated both the cracking load and the deflection with an average measured/predicted cracking load and deflection of 0.81 and 0.72, respectively, which makes this method being the most unconservative prediction method. This was expected as it cannot account for the discrete placement of the connectors located at the ends of the panel. The COVs of cracking load and deflection were 10.37 and 7.96%, respectively, which are higher than the first three prediction methods. The Bai and Davison method provided the closest average measured/ predicted cracking load ratio to unity (0.98), however, this method yielded the most disperse cracking load prediction results with COV of 15.39%. The predicted deflection at cracking using this method was overestimated with and average measured/predicted ratio of 0.85 and COV of 9.42%.
Faxial,1 = T1
C1
Fsum = 0
(1)
Faxial,2 = T2
C2 + Fsum = 0
(2)
where, C1 and C2 = internal compression forces in the top and bottom wythes, respectively (See Fig. 15). T1 and T2 = internal tension forces in the top and bottom wythes, respectively (See Fig. 15). Whitney equivalent stress block is used to calculate the compression in the top concrete wythe when compression strain reaches 0.003. However, for partially composite panels, the compression force in the bottom concrete wythe, which may or may not be near failure, should be calculated using a concrete model that accounts for nonlinear concrete behavior before reaching its maximum strain. This method recommended using Hognestad model [23] to estimate the concrete compressive forces. The nominal moment of the partially composite panel is calculated using equation (3).
M = M1 + M2 + Fsum
twy1 + twy2 2
+ tins
(3)
where, M1 = moment in the top wythe created by C1 and T1 M2 = moment in the bottom wythe created by C2 and T2 Table 8 lists the shear resistance of provided shear connectors (Fprovided), required shear resistance to achieve full-composite action (Ffull-comp.), measured moment resistance at failure (Mtest), predicted moment resistance of partially composite section (Mpred.), predicted moment resistance of non-composite section (Mnon-comp.), and predicted moment resistance of full-composite section (Mfull-comp.). The required shear resistance of shear connectors to develop full-composite action between the two concrete wythes is equal to the yield strength of the steel reinforcement in the bottom concrete wythe in all specimens. By this definition, the experiments that allow the reinforcement to strain harden will exhibit higher than full-composite action, but is still consistent with design. The provided shear connector resistance varied between different specimens depending on insulation and concrete wythe thicknesses, as discussed in the push-off test results section. The analysis showed that the shear resistance of the shear
4.2. Ultimate strength behavior The theoretical flexural strengths of all tested specimens were predicted using strain compatibility and internal force equilibrium for partially composite sections, which is well documented in Olsen et al., [17]. There are considerably fewer methods available in the literature focusing on the ultimate strength of sandwich wall panels and because
Fig. 14. Beam-spring model geometry. 11
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Table 7 Measured and predicted serviceability behavior. Specimen ID
Elastic Method
Beam-Spring Deflection
Cracking load (KN/ m2)
Deflection (mm)
Cracking load Measured/ Predicted
Measure/ Predicted
Cracking load Measured/ Predicted
7.18 4.6 9.58 6.13 10.87 6.32 – –
3.18 6.1 2.01 3.61 3.23 5.08 – –
1.07 1 1.05 0.95 1.14 1.04 1.04 5.77%
1.08 1 1.05 0.94 1.15 1.04 1.04 6.73%
1.14 1.07 1.05 0.99 1.15 1.03 1.07 5.61%
Deflection
Beam-Truss
Holmberg & Plem
Bai and Davison
Deflection
Deflection
Measure/ Predicted
Cracking load Measured/ Predicted
0.64 0.65 0.79 0.74 0.75 0.76 0.72 7.96%
1.24 1.11 0.89 0.83 0.96 0.84 0.98 15.39%
0.82 0.84 0.79 0.74 0.97 0.93 0.85 9.42%
Deflection
Measured/ Predicted
Cracking load Measured/ Predicted
Measure/ Predicted
Cracking load Measured/ Predicted
1.15 1.08 1.05 0.99 1.16 1.03 1.08 6.48%
1.15 1.1 1.08 1.01 1.1 0.97 1.07 5.61%
1.53 1.54 1.4 1.34 1.44 1.27 1.42 7.75%
0.91 0.81 0.89 0.83 0.74 0.66 0.81 10.37%
Measure/ Predicted
Fsum = T1 - C1
C1
C1
70-50-70-3.3 70-50-70-4.2 90-50-90-3.3 90-50-90-4.2 90-100-90-3.3 90-100-90-4.2 Mean COV (%)
Experiment
T1 = AS1 x f S1 + APS1 x f PS1
C2
C2
Fsum = T2 - C2
T2 = AS2 x f S2 + APS2 x f PS2 Fig. 15. Stress and force distribution in a partially composite panel at failure. Table 8 Measured and predicted ultimate moments. Panel
Fprovided (kN)
Ffull-comp. (kN)
Fprovided/Ffull-comp.
Mtest (kN.m)
Mpred. (kN.m)
Mtest/Mpred.
Mfull-comp. (kN.m)
Mnon-comp. (kN.m)
K Mn (%)
70-50-70-3.3 70-100-70-4.2 70-50-70-4.2 90-50-90-3.3 90-100-90-3.3 90-50-90-4.2 90-100-90-4.2
146.8 128.3 146.8 146.8 115.3 146.8 128
146.8 146.8 146.8 146.8 146.8 146.8 146.8
1.0 0.874 1.0 1.0 0.785 1.0 0.872
27.76 33.2 26.29 46.96 37.29 43.72 40.31
26.85 31.46 27.37 34.6 34.51 35.15 38.76
1.03 1.06 0.96 1.36 1.08 1.24 1.04
27.33 34.48 27.74 34.65 39.87 35.15 42.2
9.62 9.7 9.98 14.51 12.52 14.92 14.61
102 94.83 92 126 90 142 93
connectors in panels with 50 mm insulation thickness is equivalent to the shear resistance required to develop full-composite action (Fprovided/ Ffull-comp. = 1.0). However, panels with 100 mm insulation thickness showed partial composite action with Fprovided/Ffull-comp. ratio of less than one. Nominal ultimate moment resistance (φ = 1.0) was predicted using the measured concrete compressive strength at testing time. Predicted nominal moment resistance (Mpred.) showed good agreement with the measured ultimate moment resistance (Mtest) with an average Mtest/Mpred. of 1.11 and a coefficient of variance (COV) of 0.13. All specimens showed higher Mtest than Mpred. values (Mtest/Mpred. > 1.0) except specimen 70-50-70-4.2, where the measured experimental value was 4% lower that the predicted value. The reason for this could be attributed to the concrete material property variability. Nominal predicted ultimate moment resistance for non-composite and full-composite sections were calculated using strain compatibility. Non-composite section was analyzed by summing the moment resistance of both wythes assuming equal curvature and deflection for both wythes. However, the full-composite section was analyzed as a single section consisting of the two concrete wythes separated by the thickness of insulation. The level of composite action was assessed at the ultimate level using Eq. (4) for all specimens. Table 8 lists the calculated composite action (K Mn ). Generally, calculated composite
action using measured ultimate moment resistance showed higher level of composite action than that indicated by Fprovided/Ffull-comp. ratios. For example, specimen 90-50-90-3.3 shows a value of K Mn of 126%, while Fprovided/Ffull-comp. shows a value of 1.0 (100% composite action). The reason for the observed difference is chiefly caused by the definition of full composite action neglecting strain hardening of the reinforcing steel, which was not considered in predicting the moment resistance values as discussed above.
K Mn =
Mn, test Mn, C
Mn, NC × 100 Mn, NC
(4)
where, Mn, test = experimental maximum moment of the sandwich panel Mn, NC = theoretical maximum moment for non-composite sandwich panel Mn, C = theoretical maximum moment for fully composite sandwich panel 5. Conclusions This paper establishes the structural behavior of precast concrete sandwich panels using lumped GFRP shear connectors at each end of 12
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the panel. A comprehensive experimental testing program was conducted to investigate the behavior of a new shear connector derived from commercial non-composite connectors. The testing program consisted of 34 push-off, 23 pullout, and eight large-scale flexural specimens. The effect of concrete wythe thickness, insulation wythe thickness, and concrete compressive strength was investigated throughout these tests. Additionally, bond effect at the insulation-concrete interface was investigated using push-off tests. The flexural test results were compared with predicted fully composite, non-composite, and partially composite values. The following conclusions can be made from the experimental and analytical investigations:
Concrete Sandwich Wall Panels. ASCE Congr. Tech. Adv., Duluth, MN.: 2017. [2] Salmon DC, Einea A, Tadros MK, Culp TD. Full Scale Testing of Precast Concrete Sandwich Panels. ACI Struct J 1997;94:354–62. https://doi.org/10.14359/486. [3] Losch ED, Hynes PW, Andrews Jr. R, Browning R, Cardone P, Devalapura R, et al. State of the art of precast/prestressed concrete sandwich wall panels. PCI J 2011. [4] Maximos HN, Pong WA, Tadros MK, Martin LD. Behavior and Design of Composite Precast Prestressed Concrete Sandwich Panels with NU-Tie. NE: Lincoln; 2007. [5] Tomlinson D, Fam A. Flexural behavior of precast concrete sandwich wall panels with basalt FRP and steel reinforcement. PCI J 2015. https://doi.org/10.15554/ pcij.11012015.51.71. [6] Huang JQ, Dai JG. Direct shear tests of glass fiber reinforced polymer connectors for use in precast concrete sandwich panels. Compos Struct 2019;207:136–47. https:// doi.org/10.1016/j.compstruct.2018.09.017. [7] Lameiras R, Barros J, Azenha M, Valente IB. Development of sandwich panels combining fibre reinforced concrete layers and fibre reinforced polymer connectors. Part II: evaluation of mechanical behaviour. Compos Struct 2013. https://doi.org/ 10.1016/j.compstruct.2013.06.015. [8] Wade T, Porter M, Jacobs D. Glass-Fiber Composite Connectors for Insulated Concrete Sandwich Walls. IA: Ames; 1988. [9] Einea A, Salmon D, Tadros MK, Culp T. A New Structurally and Thermally Efficient Precast Sandwich Panel System. PCI J 1994;39:90–101. [10] Lameiras R, Barros J, Valente IB, Azenha M. Development of sandwich panels combining fibre reinforced concrete layers and fibre reinforced polymer connectors. Part I: Conception and pull-out tests. Compos Struct 2013. https://doi.org/10. 1016/j.compstruct.2013.06.022. [11] Naito C, Hoemann J, Beacraft M, Bewick B. Performance and Characterization of Shear Ties for Use in Insulated Precast Concrete Sandwich Wall Panels. J Struct Eng 2012. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000430. [12] Woltman G, Tomlinson D, Fam A. Investigation of Various GFRP Shear Connectors for Insulated Precast Concrete Sandwich Wall Panels. J Compos Constr 2013. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000373. [13] Frankl BA, Lucier GW, Hassan TK, Rizkalla SH. Behavior of precast, prestressed concrete sandwich wall panels reinforced with CFRP shear grid. PCI J 2011. https://doi.org/10.15554/pcij.03012011.42.54. [14] Bunn WG. CFRP Grid/Rigid Foam Shear Transfer Mechanism for Precast. NC: Prestressed Concrete Sandwich Wall Panels. North Carolina State University at Raleigh; 2011. [15] Hassan TK, Rizkalla SH. Analysis and design guidelines of precast, prestressed concrete, sandwich wall panels reinforced with CFRP grid. PCI J 2010. [16] Al-Rubaye S, Olsen J, Sorenson T, Maguire M. Evaluating elastic behavior for partially composite precast concrete sandwich wall panels. PCI J 2018;63:71–88. [17] Olsen J, Al-Rubaye S, Sorensen T, Maguire M. Developing a General Methodology for Evaluating Composite Action in Insulation. Wall Panels 2017. [18] Morcous G, Tadros MK, Lafferty M, Gremel D. Optimized Nu sandwich panel system for energy, composite action and production efficiency. 3rd Int. fib Congr. Exhib. Inc. PCI Annu. Conv. Bridg. Conf. Think Glob. Build Locally, Proc. 2010. [19] Holmberg A, Plem E. Behaviour of Load-bearing Sandwich-type Structures. Byggforskningen 1965. [20] Bai F, Davidson JS. Analysis of partially composite foam insulated concrete sandwich structures. Eng Struct 2015;91:197–209. https://doi.org/10.1016/j.engstruct. 2015.02.033. [21] Granholm H. Om sammansatta balkar och pelare med särskild hänsyn till spikade träkonstruktioner: on composite beams and columns with particular regard to nailed timber structures. Elanders boktryckeri aktiebolag 1949. [22] Bai F, Davidson JS. Theory for composite sandwich structures with unsymmetrical wythes and transverse interaction. Eng Struct 2016;116:178–91. [23] Hognestad E. A Study of Combined Bending and Axial Load in Reinforced Concrete Members. Bull Ser No 399 1951. doi:10.14359/7785. [24] Huang J, Jiang Q, Chong X, Ye X, Wang D. Experimental study on precast concrete sandwich panel with cross-shaped GFRP connectors. Mag Concr Res 2018:1–49. https://doi.org/10.1680/jmacr.18.00258. [25] Teixeira N, Tomlinson DG, Fam A. Precast concrete sandwich wall panels with bolted angle connections tested in flexure under simulated wind pressure and suction. PCI J 2016:65–83.
• Push-off test results were used to develop idealized shear load-slip • •
• • • •
relationships for different cases to assist design engineers in designing insulated sandwich wall panels with the proposed shear connectors system. The insulation contribution to shear resistance was the same for both 50 mm and 100 mm thick insulation layers. An average shear strength increase of 17% was observed relative to unbonded insulation-concrete interface cases. Large-scale flexural test results showed lower percentage of composite action (less than 6.5%) at cracking level, as is typical of sandwich wall panels with flexible connectors [16,24,25], especially in short panels like those tested. The analysis techniques investigated imply that adding additional connectors could increase this apparent composite action. The Elastic Method by Olsen et al. [17] for predicting serviceability behavior of PCSPs showed the most accurate prediction results when compared with the other four methods evaluated in this study with an average measured-to-predicted value of 1.04 for cracking load and deflection with COV of less than 7%. A method that can incorporate the discrete position of the shear connectors is critical to the prediction of lumped connector placement as evidenced by the poor performance of the Holmberg and Plem [19] sandwich beam theory (measured-to-predicted ratio of 0.81 and 0.72 for cracking and deflection prediction, respectively). Large-scale flexural test results showed that the shear connectors system provides at least 90% composite action at ultimate level, which could be increased if additional rows of connectors are provided. The strength prediction model developed by Olsen et al. [17] provided an average measured-to-predicted value of 1.11 with a coefficient of variation of 0.13.
Acknowledgement This research was funded by ITW Construction Systems, International. The support of Paul Gaiardo, Abdelrahman Khodier and Bob Connell is greatly appreciated. References: [1] Sorensen T, Dorafshan S, Maguire M. Investigating Thermal Efficiency of In Service
13
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Lumped GFRP star connector system for partial composite action in insulated precast concrete sandwich panels
T
Brandon Coxa, Parker Syndergaardb, Salam Al-Rubayec,d, Fray F. Pozo-Lorac, Raed Tawadrouse, ⁎ Marc Maguirec, a
Mountain View Engineering, Brigham City, UT, USA Calder Richards Structural Consulting Engineers, Salt Lake City, UT, USA c Department of Civil and Environmental Engineering, Utah State University, Logan, UT, USA d Department of Civil Engineering, Tikrit University, Salahuldean, Iraq e e.construct, Florida, Orlando, FL, USA b
ARTICLE INFO
ABSTRACT
Keywords: GFRP shear connectors Insulated sandwich panel Composite action Partially composite Precast concrete Thermal efficiency
This paper introduces a novel composite shear connectors system used to transfer interface shear forces in a precast concrete sandwich panel. The shear connectors consist of non-proprietary non-composite commercial glass fiber reinforced polymer (GFRP) pin connectors that are laid out in a star pattern and clustered at the top and bottom of the panels. The testing program consisted of thirty-four push-off, twenty-three pullout, and eight full-scale flexural specimens was conducted to evaluate the structural performance of the new shear connectors. The effect of concrete wythe thickness, insulation wythe thickness, and concrete compressive strength was investigated throughout these tests. Additionally, the effect of bond between insulation and concrete wythes was investigated using push-off tests. The flexural test results were compared with predicted fully composite, noncomposite, and partially composite values to evaluate the overall panel performance. The comparison showed satisfactory performance with a lower bound of 90% composite action for specimens with 100 mm thick insulation wythe and full composite action for most panels with 50 mm thick insulation. Idealized shear load-slip curves were also developed that account for various parameters to assist design engineers in designing insulated sandwich wall panels with the proposed shear connectors system.
1. Introduction Precast concrete sandwich panels (PCSPs) have become a popular building system due to their thermal and structural performance and the higher demand for energy efficient buildings [1]. These panels are commonly used as load bearing or non-load bearing (cladding) wall members in commercial buildings [2]. PCSPs consist of two exterior concrete layers (wythes) surrounding an insulation layer. Concrete wythe thickness vary between 50 and 150 mm depending on the expected loads, and fire and concrete cover requirements [3]. The insulation layer is typically composed of a 25 to 100 mm thick rigid foam such as expanded polystyrene (EPS) or extruded polystyrene (XPS) [3]. The structural behavior of PCSPs primarily depends on the shear transfer strength and stiffness of the connecting elements between the two exterior concrete wythes, which could be achieved by using various types of shear connectors such as discrete ties or solid concrete zones [4]. Connectors composed of various materials including steel, fiber
⁎
reinforced polymers (FRPs), and plastics [3]. PCSPs constructed using connectors with low strength and stiffness to transfer shear between the two concrete wythes, such that the wythes act independently, are considered non-composite. In cases where the strength and stiffness of the connectors are adequate to transfer the shear forces between the two concrete wythes act as one, the panel is considered fully composite. PCSPs with shear transfer strength that lie in between the two aforementioned extremes (non-composite and fully composite) are considered partially composite panels. Fully composite PCSPs usually utilize steel shear connectors or concrete solid zones when panel strength is of a primary concern, which results in reduced thermal efficiency due to thermal bridging through the highly conductive steel or concrete connectors. Fully composite panels are also more susceptible to thermal bowing, which is of particular concern in long-span walls [3,5]. Partially composite or noncomposite panels utilize variety of shapes such as plate, box, truss, or pin connector fabricated from various types of FRP such as glass FRP
Corresponding author. E-mail address: [email protected] (M. Maguire).
https://doi.org/10.1016/j.compstruct.2019.111465 Received 9 April 2019; Received in revised form 28 July 2019; Accepted 17 September 2019 Available online 19 September 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Star GFRP connectors configuration with 50 and 100 mm thick insulation (Note: dimensions shown are in mm). DtotalDtotal
400 400
70 tins 70 tins140 140 70 70 tins tins
SECTION SECTION A-A A-A EXTERIOR EXTERIOR WYTHES WYTHES
MAIN MAIN WYTHE WYTHE
267 267
Dtotal
200 INSULATION INSULATION LAYERS LAYERS SECTION A-A A-A SECTION
SECTION SECTION B-B B-B
SPC SECTION B-B
267 267
SECTION SECTION A-A A-A
a) Elevation
SHEAR CONNECTOR
400
535 535
200
1070
SHEAR SHEAR CONNECTOR CONNECTOR PROJECTION PROJECTION
1070
1070
1070
SHEAR SHEAR CONNECTOR CONNECTOR
EXTERIOR EXTERIOR WYTHES WYTHES
b) Side view
c) Plan view
Fig. 2. Typical push-off specimens’ geometry.
(GFRP), basalt FRP (BFRP), or carbon FRP (CFRP) and they are considerably more energy efficient due to the reduced thermal bridging between the two exterior concrete wythes [5–7]. Fully composite and non-composite PCSPs are easily analyzed using reinforced concrete sectional analysis, however, partially composite panels represent a challenging design problem to the design engineer. This is mainly due to the heavy reliance of the analysis on the experimental test results for
each connector type. Once the shear connectors resistance behavior is known, the design engineer will be able to accurately perform the partially composite panel design. GFRP shear connectors have been widely used during the last 30 years based on successfully conducted research programs that indicated their adequate structural performance with comparable composite action to steel connectors as well as their improved thermal 2
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production and uses fewer connectors for maximum effect.
Table 1 Push-off testing matrix. Specimen ID
Average f’c (MPa)
Insulation thickness (mm)
Bond condition
HS50P1-HS50P 5 HS100P1- HS100P5 LS50P1- LS50P6 LS100P1- LS100P6 HS50P1D-HS50P6D HS100P1D- HS100P6D
37.6 37.6 17.16 17.16 37.6 37.6
50 100 50 100 50 100
Bonded Bonded Bonded Bonded Debonded Debonded
2. Experimental program A comprehensive experimental program that consisted of push-off tests, pull-out tests, and large-scale flexural tests was conducted to investigate the composite action of insulated sandwich wall panels with the new clustered GFRP shear connectors. To develop partial composite action, the non-proprietary pin typically used for non-composite design were oriented in a “Star” pattern with two GFRP Pins inclined at 45 degrees (perpendicular to each other) and the third pin was inserted normal to the insulation in between the other two pins, as shown in Fig. 1. These pins are typically used individually and in the perpendicular orientation only and when doing so only allow non-composite behavior. Specifically, these pins are non-proprietary, but herein, the orientation of these pins in a star pattern, using three pins, partial composite action can be achieved. The modulus of elasticity for the GFRP Pin is 47988 MPa and the ultimate strength is 1200 Mpa based on manufacturer product testing. The two inclined connectors were intended to provide identical resistance when the panel is exposed to suction or pressure wind load and also to better utilize the axial stiffness of the connector material. All specimens were conventionally reinforced using 10 mm (#3) steel bars. The following sections present each of these experiments in details.
efficiency [2,4,8–12]. These research programs used various shear connector shapes, however, the uniform shear connector distribution along the entire length of the panel was common among all of them. Anecdotally, commercial panels have been attempted with lumped connectors near the ends, but this approach has resulted in delamination (tension) failure of the wythes due to inadequate tensile capacity. This paper investigates the validity of a newly developed GFRP shear connector system used to develop partial composite action in nonprestressed PCSPs. These connectors consist of non-proprietary pin connectors that are routinely used for non-composite wythe connection, oriented in a star pattern using three pins oriented around one location. The effect of different parameters such as insulation thickness, bond between concrete and insulation, and concrete compressive strength were investigated. The behavior of the new shear connectors system was studied using a series of push-off tests, pull-out tests, and largescale flexural tests. Large-scale flexural test results were compared with theoretically predicted values to quantify the level of composite action at the ultimate level. The new shear connectors utilize clustered shear connectors at each end of the panel, which significantly simplifies panel
2.1. Push-off tests Thirty-four push-off specimens were tested to evaluate the shear force-slip relationship. The new GFRP shear connectors were tested using double shear push-off specimens that were constructed using three concrete wythes and two XPS insulation wythes as shown in
Fig. 3. Push-off test setup. 3
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Fig. 4. Typical orthogonal views of pull-out specimens.
and 100 mm, which is the commonly used in practice [3]. Low and high concrete compressive strengths were used with average strengths of 17.16 and 37.6 MPa, respectively. Perimeter reinforcement was provided for handling and was centered in each wythe using 10 mm diameter reinforcement located 50 mm from each edge, ensuring no interaction with the shear connectors. The shear resistance contribution due to bond between concrete and the insulation layer is considered temporary and usually disregarded in composite action calculations for service loads because the bond is expected to degrade overtime [3]. Therefore, bond at the concrete-insulation interface in twelve push-off specimens was broken using thin plastic sheets to measure the shear stiffness of the shear connectors system without bond contribution. Table 1 provides a summary of the push-off testing matrix including concrete compressive strength, insulation thickness, and bond condition for each specimen. Bond was broken by placing a layer of 0.02 mm plastic around the insulation. As shown in Table 1, specimens are identified using concrete strength, insulation thickness, specimen number, and bond condition (letter “D” was added for debonded specimens). For example, specimen LS50P1, “LS” is for low strength concrete, “50” is for 50 mm foam insulation wythes, and “P1” is for specimen number one within the same group. 2.2. Double shear test setup and instrumentation Fig. 3 shows the test setup along with the instrumentation plan used in this study. The parameters measured during the experiments were applied load, and relative slip between the concrete wythes. The push-off specimens were tested by applying the load at the center concrete wythe with a hydraulic ram while the outer two wythes were supported by bearing on the concrete, as shown in Fig. 3, with polytetrafluoroethylene bearing pads at the interface to minimize any horizontal friction forces. The center wythe was recessed to allow for defomation. The applied load was measured at the ram location using an electrical resistance based full bridge 1300 kN load cell and 1300 kN hydraulic ram. Four total Linear Variable Differential Transducers (LVDTs) were used to measure the displacement of the center wythe relative to the outer concrete wythes on both sides of each wythe.
Fig. 5. Pull-out test setup.
Fig. 2. Note that XPS insulation has small contribution to shear strength [13–15], but bonded and debonded conditions were investigated because practicing engineers are often concerned with the different behaviors. All specimens contained two exterior and one interior concrete wythes with a thickness of 70 mm and 140 mm, respectively. The 70 mm wythes were selected because this is the typical minimum in practice and the center wythe is double that of the outer wythes to allow room for the connectors. The testing focused on investigating three main parameters: insulation thickness; bond between concrete and insulation; and concrete compressive strength. The specimens had four connectors each (two on each side) at a longitudinal spacing of 535 mm, as shown in Fig. 2. The insulation thickness varied between 50
2.3. Pull-out tests Twenty-three pull-out specimens were fabricated and tested to evaluate the pull-out capacity of the new GFRP shear connectors. Specimens were constructed to simulate insulated sandwich wall panel construction with 75 mm thick top and bottom concrete wythes, as shown in Fig. 4. Perimeter reinforcement was provided for handling 4
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Fig. 6. Typical panel geometry, reinforcement, and shear connectors of specimen 70-100-70. Table 2 Measured concrete material properties full scale flexure specimens. Panels ID
Span length (m)
Wythe
f’c (MPa)
Ec (MPa)
70-50-70
3.3
70-50-70
4.2
70-100-70
3.3
70-100-70
4.2
90-50-90
3.3
90-50-90
4.2
90-100-90
3.3
90-100-90
4.2
Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
29.0 51.9 40.0 54.6 34.7 40.0 45.8 44.5 34.7 34.7 44.5 44.5 29.0 47.3 40.0 54.6
21,201 31,325 21,201 32,032 32,961 21,201 26,958 32,553 32,962 32,962 32,554 32,554 21,201 31,783 24,201 32,032
and was centered in each wythe using 10 mm diameter reinforcement located 50 mm from each edge, ensuring no interaction with the shear connectors. The testing program focused on investigating the effect of insulation thickness and concrete compressive strength on the pull-out strength of the connectors. Low and high concrete compressive strengths were used with average strengths of 17.16 and 37.6 MPa, respectively. Insulation wythe thickness varied between 50 mm and 100 mm. Each specimen had one connector centered with the insulation and the top concrete wythe, while, the bottom concrete wythe was used to accommodate three pull-out specimens as shown in Fig. 4. Specimens are identified using concrete strength, insulation thickness, and specimen number. For example, specimen HS50T3, “HS” is for high strength concrete, “50” is for 50 mm foam insulation wythe, and “T1” is for specimen number one within the same group. The insulation and concrete bond was broken in a similar manner as with the double shear tests as engineers often prefer to not count on the bond.
Fig. 7. Flexure test setup and instrumentation a) sketch, and b) photo.
specimens were tested by applying the load to the top concrete wythe with a hydraulic ram while the bottom concrete wythe was tied down by two steel beams anchored to the strong floor, as shown in Fig. 5. The applied load was measured at the ram location using an electrical resistance based full bridge 440 kN load cell and 440 kN hydraulic ram. 2.5. Large-scale flexural tests Eight large-scale reinforced concrete, non-prestressed sandwich, panels were constructed and tested. The panels thickness and length were designed to bound their target market for low rise housing. The eight panels were constructed with four different panel thicknesses.
2.4. Pull-out test setup and instrumentation Fig. 5 shows the test setup used to test the pull-out specimens. The 5
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Fig. 8. Load-slip relationship for push-off tests (a) HS50P1-5 (b) HS100P1-5 (c) LS50P1-5 (d) LS100P1-6 (e) HS50P1-5D (f) HS100P1-5D.
Each designated panel thickness was constructed in two different lengths, 3300 and 4200 mm, and a width of 1800 mm. The four different wythe thicknesses were 70-50-70, 70-100-70, 90-50-90, and 90100-90 (values are in mm), where the outer two values refer to the exterior concrete wythes’ thicknesses and the middle value refer to the insulation thickness. For example, 90-100-90 means that the two outer concrete layers are 90 mm thick and the insulation has a thickness of 100 mm. Each concrete wythe was reinforced using five 10 mm (#3) Grade 410 (ASTM A615) conventional steel reinforcement bars. Two major parameters were investigated, insulation thickness and concrete wythe thickness, and their impact on strength and mode of failure. Fig. 6 shows an example of the typical insulated sandwich panel geometry, reinforcement, and shear connectors configuration for 70-10070 panel. The star pattern shear connectors were discretely clustered at each end of the panel and single pin connectors normal to the insulation surface were placed at 600 and 540 mm on center for 4200 and 3300 mm, respectively, along the interior zone, as shown in Fig. 6. Lifting locations used commercial 9kN pins suitable for stripping the panel from the forms, including transverse reinforcement, but did not penetrate the full thickness of the insulation. At these locations a 300 mm square recess into the insulation was created to achieve the proper embedment depth of 100 mm for the 50 mm and 100 mm insulation specimens. The bottom and the top concrete wythes were poured at different times using different concrete mixes because of fabrication constraints at the precast plant. Table 2 lists span length and the measured concrete properties including concrete compressive strength and modulus of elasticity for each concrete wythe measured at testing time. Specified yield and ultimate strengths of flexural steel reinforcement were 415 and 620 MPa, however, the average measured values using seven 10 mm (#3) rebar specimens were 453 and 767 MPa, respectively.
2.6. Large-scale flexural test setup and instrumentation Fig. 7 shows the test setup along with the instrumentation plan used in this study. The parameters measured during the experiments were applied load, deflection, and relative slip. Each span was loaded with four-point load using three spreader beams, which applied four equally spaced loads, to simulate the curvature distribution from a uniformly distributed loading condition, as shown in Fig. 7. The vertical deflection was measured using string potentiometers at mid-span on either side of the panel. A total of eight LVDTs were mounted on each specimen, one at each corner and four along the span length on one side of the panel, to measure the relative slip between the two exterior concrete wythes. The applied load was measured at the ram location using an electrical resistance based full bridge 1300 kN load cell and 1300 kN hydraulic ram. 3. Test results and discussion 3.1. Push-off test results Fig. 8 shows the load-slip relationships for the thirty-four specimens, where slip represents the relative movement between concrete wythes using the average of four LVDT readings for each specimen. The plots are divided into six sets to compare results of specimens with similar properties. All specimens exhibited an approximate bilinear loadslip relationship except specimens in groups 2 and 6 (with high strength concrete and 100 mm thick insulation wythe), which showed a nearly linear load-slip behavior. Table 3 lists load, slip, and calculated shear stiffness values at the end of the elastic and inelastic stages. The load values listed in Table 3 and shown in Fig. 8 represent 25% of the total applied load to account for the strength of one shear connector rather than the total number of shear connectors used in the push-off specimens. The results of seven specimens were excluded from Table 3 due 6
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Table 3 Summary of push-off test results. Group
Specimen ID
Elastic Load, FE (kN)
Elastic slip, ΔE (mm)
Elastic stiffness, KE (kN/ mm)
Ultimate Load, FU (kN)
Ultimate slip, ΔU (mm)
Ultimate stiffness, KIE (kN/ mm)
1
HS50P1 HS50P2 HS50P3 HS50P4 HS50P5 HS50P6 Mean COV HS100P1 HS100P2 HS100P3 HS100P4 HS100P5 Mean COV LS50P1 LS50P2 LS50P3 LS50P4 LS50P5 LS50P6 Mean COV LS100P1 LS100P2 LS100P3 LS100P4 LS100P5 LS100P6 Mean COV HS50P1D HS50P2D HS50P3D HS50P4D HS50P5D HS50P6D Mean COV HS100P1D HS100P2D HS100P3D HS100P4D HS100P5D HS100P6D Mean COV
20.88 – – 21.87 20.93 24.76 22.11 0.083 40.1 35.92 40.77 36.08 39.29 38.43 0.059 15.41 13.79 12.87 14.74 14.17 13.12 14.01 0.069 13.78 – – – 14.92 17.23 15.31 0.115 18.64 – 20.11 18.46 17.94 18.58 18.75 0.043 40.04 – 28.2 29.35 32.85 29.37 31.96 0.151
1.8 – – 1.47 1.88 1.65 1.7 0.106 6.35 5.08 6.35 5.08 6.35 5.842 0.119 1.93 1.8 2.24 1.91 1.83 1.55 1.88 0.119 1.41 – – – 1.78 1.52 1.57 0.121 1.1684 – 1.651 1.2954 1.778 1.4986 1.48 0.169 6.18388 – 3.49136 3.00585 4.07314 3.262 4 0.32
11.58 – – 14.85 11.13 15 13.14 0.157 6.31 7.07 6.42 7.1 6.19 6.62 0.066 7.98 7.65 5.76 7.74 7.75 8.47 7.56 0.123 9.79 – – – 8.39 11.3 9.83 0.148 15.95 – 12.18 14.25 10.09 12.4 12.98 0.171 6.47 – 8.08 9.76 8.06 9 8.28 0.149
41.76 – – 43.74 41.85 49.52 44.22 0.083 – – – – – –
5.51 – – 5.53 7.65 5.68 6.09 0.171 – – – – – –
5.63 – – 5.39 3.63 6.15 5.2 0.211 – – – – – –
30.82 27.58 25.74 29.47 28.33 26.23 28.03 0.069 27.55 – – – 29.85 34.45 30.62 0.115 37.28 – 40.22 36.93 35.87 37.17 37.49 0.043 – – – – – – – –
7.75 6.45 7.45 8.44 6.19 5.39 6.94 0.163 6.1 – – – 6.62 6.72 6.48 0.052 4.14503 – 4.94906 4.71615 4.83476 5.45313 4.82 0.098 – – – – – – – –
2.65 2.97 2.47 2.25 3.25 3.42 2.83 0.16 2.94 – – – 3.08 3.31 3.11 0.061 6.26 – 6.1 5.4 5.87 4.7 5.66 0.111 – – – – – – – –
2
3
4
5
6
The bolded values represent the mean and coefficient of variation for their group.
to the malfunctioning of the LVDT devices during the test. The main failure mode in all specimens was concrete breakout as shown in Fig. 9. Test results showed relatively high variability with a coefficient of variation (COV) ranging from 4.3 to 15.1% for elastic shear resistance, as shown in Table 3. The variation is believed to be attributed to the ability of the fabricator to install the pins in the appropriate orientation and the concrete material variability. Specimens with bonded contact between concrete and insulation wythes achieved the ultimate shear strength at relatively similar slip values with mean values ranging from 5.59 to 6.39 mm. However, unbonded specimens reached the ultimate load at slightly lower slip values with mean values ranging from 4 to 4.8 mm. These observations are similar to those from other commercial connectors [16]. Fig. 8a and c, and Fig. 8b and d show the difference in load-slip behavior between low and high strength concrete for specimens with 50 and 100 mm thick insulation, respectively. The failure load increased as the concrete compressive strength increased. For specimens with 50 mm thick insulation wythe, increasing the concrete strength from 17.16 to 37.6 MPa increased the failure load by 55%, while the increase
was 26% for specimens with 100 mm thick insulation. This difference is attributed to the increased unsupported length of the connectors in the latter group. It is worth noting that load-slip curve of HS100P series (Fig. 8b) showed linear relationship until failure, which is unlike HS50P, LS50P, and LS100P series that showed a bilinear relationship. It is believed that HS100P series behaved elastically due to simultaneous failure of concrete (breakout) and rupture of the tension GFRP pin connectors. Fig. 10 shows idealized shear load-slip relationships for low and high strengths concrete with 50 mm and 100 mm insulation thicknesses. These curves provide the base design values for designing PCSPs using the proposed shear connectors system. Comparing the load-slip curves of bonded and unbonded specimens with similar properties in Table 3 show tangible increase in the failure load due to bond contribution to the overall resistance. Bond contribution increased the failure load similarly for specimens with 50 and 100 mm thick insulation with an average of 17.6 and 16.3%, respectively. The difference between both groups was less than 1.5%. Unbonded specimens experienced less slip at failure when compared to 7
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Fig. 9. Typical concrete breakout failure of push-off tests.
Fig. 10. Idealized load-slip curves for high strength concrete (left) and low strength concrete (right).
bonded specimens with an average slip of 4 and 3.13 mm compared to 5.59 and 5.84 mm, respectively. This is evidence that bond at concreteinsulation interface failed after concrete and/or shear connectors failure took place and allowed for extra slip.
3.3. Flexural test results Fig. 12 shows the load–deflection curves for the specimens tested in this study. All tested specimens showed linear increase in the load–deflection relationship with approximately the same slope until cracking, then non-linear increase up to failure. The cracking load was not significantly affected by the insulation thickness for specimens with similar concrete wythe thicknesses, which indicates that the panels are having a low degree of composite action prior to cracking, as is typical [16]. Table 6 lists the measured cracking loads and moments for all panels except panel 70-100-70 with 3.3 m long span. The latter specimen experienced large cracks due to improper panel fabrication by the precaster, therefore the results of this specimen are disregarded. Additionally, Table 6 lists the predicted cracking moment for composite and non-composite section properties for comparison purposes. Prediction of cracking and deflections assumed fully non-composite and fully composite behavior using gross concrete properties and first principles. The comparison showed that the PCSP experienced a relatively low degree of composite action at cracking level with less than 7% composite as was expected. All specimens failed in a ductile manner by yielding the steel reinforcement in both bottom and top concrete wythes. As the load increased beyond yielding, excessive deflection
3.2. Pull-out test results Fig. 11 shows the observed failure mode for low and high strength concrete. In both cases, the failure was a combination of concrete breakout with no indication for rupture in the connectors. Tables 4 and 5 list a summary of pull-out test results for low strength and high strength concrete specimens, respectively. Low strength concrete specimens with 50 mm insulation thickness showed 36% higher tension resistance than those with 100 mm thick insulation wythe, with an average tension load resistance of 18 kN compared to 13.2 kN, with a COV of less than 13%. However, high strength concrete specimens showed relatively similar tension load resistance results regardless of the insulation wythe thickness with an average load resistance of 21.96 and 21.35 kN for HS50 and HS100 series, respectively. The reason for this difference is unclear. HS100 series showed the least COV value (4%) when compared to the other series. 8
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Fig. 11. Typical failure mode of pull-out specimens for a) low strength concrete and b) high strength concrete.
predicted using five methods: simplified elastic method [17]; the beamspring method [16]; a beam-truss method [18]; the Holmberg and Plem method [19]; and Bai and Davison method [20] and the results were compared with the observed behavior. The beam-spring and beam-truss methods are computational, relying on matrix models and the remaining methods variations of classical sandwich beam theory. A brief discussion of these methods is below, but full treatment of each method is contained in the appropriate reference. The simplified elastic method was proposed by Olsen et al. [17] and it is an iterative method that uses kinematic relationships to calculate the slip between the two exterior concrete wythes assuming linear loadslip relationship. The main advantage of this method, is that it allows for analysis of discrete connector locations. Once load-slip relationship for the shear connectors is identified and is iterated to equilibrium, the cracking moment and deflection can be calculated using fundamental statics equations. The beam-spring method was conducted using numerical analysis utilizing a commercial matrix analysis software package. This method is widely used by engineers in the United States to estimate elastic behavior of sandwich wall panels. Top and bottom concrete wythes were modeled using beam elements and shear connectors were modeled using spring elements, as shown in Fig. 14. Spring members were assigned shear and tension stiffness coefficients obtained from shear (push-off tests) and tension (pull-out tests). Beam elements were assigned the concrete properties of the top and bottom concrete wythes. The beam-truss method is similar to the beam-spring method with one difference. Shear connectors in the beam-truss method were modeled using truss members that resists only axial tension or compression forces and are assigned material properties consistent with those used for the GFRP material and cross sectional area. The Holmberg and Plem method [19] uses sandwich beam theory to predict both deflection and cracking load for the insulated wall panels. This method was originally developed by Granholm [21] for nailed timber structures, and subsequently extended to concrete sandwich wall panels of equal wythes by Holmberg and Plem. This method assumes that the connectors and concrete layers are made of isotropic, linearly elastic materials, with no connector axial deformation, but
Table 4 Summary of pull-out tests for low strength concrete. Specimen
Max Load (kN)
Specimen
Max Load (kN)
LS50T1 LS50T2 LS50T3 LS50T4 LS50T5 LS50T6 Mean COV
16.58 21.25 19.65 14.70 18.78 17.06 18.00 0.13
LS100T1 LS100T2 LS100T3 LS100T4 LS100T5 LS100T6 Mean COV
14.15 13.12 12.14 11.25 14.51 14.02 13.20 0.10
Table 5 Summary of pull-out tests for high strength concrete. Specimen
Max Load (kN)
Specimen
Max Load (kN)
HS50T1 HS50T2 HS50T3 HS50T4 HS50T5 HS50T6 Mean COV
24.38 22.95 24.03 19.06 18.78 22.55 21.96 0.11
HS100T1 HS100T2 HS100T3 HS100T4 HS100T5 – Mean COV
21.35 21.35 19.91 22.13 20.24 – 21.35 0.04
took place and concrete failure around the clustered shear connectors was observed and consequently larger slippage between the two concrete wythes, as shown in Fig. 13. The theoretical ultimate load is also shown in Fig. 12 for each specimen, which was calculated using the partially-composite strength prediction method developed by Olsen et al. [17]. More on this prediction will be discussed below. 4. Analytical comparison 4.1. Serviceability behavior Serviceability behavior of large-scale flexural specimens was 9
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Fig. 12. Load-deflection relationships (a) 70-50-70-3.3 (b) 70-50-70-4.2 (c) 70-100-70-4.2 (d) 90-50-90-3.3 (e) 90-50-90-4.2 (f) 90-100-90-4.2 and (g) 90-100-903.3. (Note: TUL = Theoretical ultimate load, TCL = Theoretical cracking load). Table 6 Measured cracking loads. Specimen ID
Cracking load (kN/ m2)
Measured Cracking Moment (kN*m)
Fully Composite Cracking Moment (kN*m)
Non-Composite Cracking Moment (kN*m)
Apparent Composite Action (%)
70-50-70-3.3 70-50-70-4.2 70-100-70-4.2 90-50-90-3.3 90-100-90-3.3 90-50-90-4.2 90-100-90-4.2
6.92 4.50 6.50 10.10 10.53 6.56 6.51
16.09 16.50 13.16 21.51 24.65 22.11 22.89
76.14 74.87 96.25 96.07 136.86 106.75 147.12
13.30 13.07 12.28 18.09 16.80 20.11 21.61
4.44 5.55 1.05 4.38 6.54 2.31 1.02
relative slip of those in the longitudinal direction of the sandwich panel, and no contribution of the insulation layer to the stiffness of the structure. Although this approach was not developed for wythes of different material properties and dimensions, the average of the
modulus of elasticity, thickness and panel stiffness (number of connectors multiplied by its stiffness divided by the area of the panel), were used to predict the behavior of the large-scale panels. Bai and Davison [20,22] modified Holmberg and Plem’s method to account for different 10
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most panels are controlled by cracking and designed for elastic second order effects, it is also considered less critical. This method uses first principles such as linear shear load-slip relationship for the shear connectors and the top and bottom concrete wythes bend with equal curvature when the panel is loaded in flexure. According to Olsen et al. [17], there are three failure conditions in partially composite sandwich panels: failure of shear connectors, rupture of tension reinforcement, and concrete crushing of the outermost compression fibers (i.e., εc1 = 0.003). In this method, each wythe of the panel is treated separately as an individual beam and the static equilibrium within each wythe is maintained. The unbalanced force in each concrete wythe is transferred to the other concrete wythe through the shear connectors, as shown in Eqs. (1) and (2). The top concrete wythe (compression wythe) was assigned wythe 1 and the bottom concrete wythe (tension wythe) was assigned wythe 2 in fully composite section, for calculations purposes, as shown in Fig. 14.
Fig. 13. Typical failure mode of flexural specimens.
wythe thicknesses and material properties and attempted to incorporate discrete connection placement using a discrete stiffness function. Table 7 lists the measured and predicted cracking loads and deflections of the tested large-scale sandwich panels. All predictions used the measured concrete material properties and the shear connector properties outlined above. The predicted cracking load and deflection values using the elastic method showed the most accurate results compared with the measured values with an average measured/predicted ratio of 1.04 and 1.04, respectively. This method also provided one of the least scattered prediction results with a coefficient of variation (COV) of 5.77% and 6.73% for cracking load and deflection, respectively. The beam-spring method showed the least scattered prediction results with COV values of 5.61% and 6.48% for cracking load and deflection, respectively. However, this method underestimated the cracking load and deflection by an average of 7% and 8%, respectively. The beam-truss method behaved in a similar manner to the beam-spring method for the predicted cracking load, however, this method significantly underestimated the deflection at cracking with an average measured/predicted ratio of 1.42. The Holmberg and Plem method overestimated both the cracking load and the deflection with an average measured/predicted cracking load and deflection of 0.81 and 0.72, respectively, which makes this method being the most unconservative prediction method. This was expected as it cannot account for the discrete placement of the connectors located at the ends of the panel. The COVs of cracking load and deflection were 10.37 and 7.96%, respectively, which are higher than the first three prediction methods. The Bai and Davison method provided the closest average measured/ predicted cracking load ratio to unity (0.98), however, this method yielded the most disperse cracking load prediction results with COV of 15.39%. The predicted deflection at cracking using this method was overestimated with and average measured/predicted ratio of 0.85 and COV of 9.42%.
Faxial,1 = T1
C1
Fsum = 0
(1)
Faxial,2 = T2
C2 + Fsum = 0
(2)
where, C1 and C2 = internal compression forces in the top and bottom wythes, respectively (See Fig. 15). T1 and T2 = internal tension forces in the top and bottom wythes, respectively (See Fig. 15). Whitney equivalent stress block is used to calculate the compression in the top concrete wythe when compression strain reaches 0.003. However, for partially composite panels, the compression force in the bottom concrete wythe, which may or may not be near failure, should be calculated using a concrete model that accounts for nonlinear concrete behavior before reaching its maximum strain. This method recommended using Hognestad model [23] to estimate the concrete compressive forces. The nominal moment of the partially composite panel is calculated using equation (3).
M = M1 + M2 + Fsum
twy1 + twy2 2
+ tins
(3)
where, M1 = moment in the top wythe created by C1 and T1 M2 = moment in the bottom wythe created by C2 and T2 Table 8 lists the shear resistance of provided shear connectors (Fprovided), required shear resistance to achieve full-composite action (Ffull-comp.), measured moment resistance at failure (Mtest), predicted moment resistance of partially composite section (Mpred.), predicted moment resistance of non-composite section (Mnon-comp.), and predicted moment resistance of full-composite section (Mfull-comp.). The required shear resistance of shear connectors to develop full-composite action between the two concrete wythes is equal to the yield strength of the steel reinforcement in the bottom concrete wythe in all specimens. By this definition, the experiments that allow the reinforcement to strain harden will exhibit higher than full-composite action, but is still consistent with design. The provided shear connector resistance varied between different specimens depending on insulation and concrete wythe thicknesses, as discussed in the push-off test results section. The analysis showed that the shear resistance of the shear
4.2. Ultimate strength behavior The theoretical flexural strengths of all tested specimens were predicted using strain compatibility and internal force equilibrium for partially composite sections, which is well documented in Olsen et al., [17]. There are considerably fewer methods available in the literature focusing on the ultimate strength of sandwich wall panels and because
Fig. 14. Beam-spring model geometry. 11
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Table 7 Measured and predicted serviceability behavior. Specimen ID
Elastic Method
Beam-Spring Deflection
Cracking load (KN/ m2)
Deflection (mm)
Cracking load Measured/ Predicted
Measure/ Predicted
Cracking load Measured/ Predicted
7.18 4.6 9.58 6.13 10.87 6.32 – –
3.18 6.1 2.01 3.61 3.23 5.08 – –
1.07 1 1.05 0.95 1.14 1.04 1.04 5.77%
1.08 1 1.05 0.94 1.15 1.04 1.04 6.73%
1.14 1.07 1.05 0.99 1.15 1.03 1.07 5.61%
Deflection
Beam-Truss
Holmberg & Plem
Bai and Davison
Deflection
Deflection
Measure/ Predicted
Cracking load Measured/ Predicted
0.64 0.65 0.79 0.74 0.75 0.76 0.72 7.96%
1.24 1.11 0.89 0.83 0.96 0.84 0.98 15.39%
0.82 0.84 0.79 0.74 0.97 0.93 0.85 9.42%
Deflection
Measured/ Predicted
Cracking load Measured/ Predicted
Measure/ Predicted
Cracking load Measured/ Predicted
1.15 1.08 1.05 0.99 1.16 1.03 1.08 6.48%
1.15 1.1 1.08 1.01 1.1 0.97 1.07 5.61%
1.53 1.54 1.4 1.34 1.44 1.27 1.42 7.75%
0.91 0.81 0.89 0.83 0.74 0.66 0.81 10.37%
Measure/ Predicted
Fsum = T1 - C1
C1
C1
70-50-70-3.3 70-50-70-4.2 90-50-90-3.3 90-50-90-4.2 90-100-90-3.3 90-100-90-4.2 Mean COV (%)
Experiment
T1 = AS1 x f S1 + APS1 x f PS1
C2
C2
Fsum = T2 - C2
T2 = AS2 x f S2 + APS2 x f PS2 Fig. 15. Stress and force distribution in a partially composite panel at failure. Table 8 Measured and predicted ultimate moments. Panel
Fprovided (kN)
Ffull-comp. (kN)
Fprovided/Ffull-comp.
Mtest (kN.m)
Mpred. (kN.m)
Mtest/Mpred.
Mfull-comp. (kN.m)
Mnon-comp. (kN.m)
K Mn (%)
70-50-70-3.3 70-100-70-4.2 70-50-70-4.2 90-50-90-3.3 90-100-90-3.3 90-50-90-4.2 90-100-90-4.2
146.8 128.3 146.8 146.8 115.3 146.8 128
146.8 146.8 146.8 146.8 146.8 146.8 146.8
1.0 0.874 1.0 1.0 0.785 1.0 0.872
27.76 33.2 26.29 46.96 37.29 43.72 40.31
26.85 31.46 27.37 34.6 34.51 35.15 38.76
1.03 1.06 0.96 1.36 1.08 1.24 1.04
27.33 34.48 27.74 34.65 39.87 35.15 42.2
9.62 9.7 9.98 14.51 12.52 14.92 14.61
102 94.83 92 126 90 142 93
connectors in panels with 50 mm insulation thickness is equivalent to the shear resistance required to develop full-composite action (Fprovided/ Ffull-comp. = 1.0). However, panels with 100 mm insulation thickness showed partial composite action with Fprovided/Ffull-comp. ratio of less than one. Nominal ultimate moment resistance (φ = 1.0) was predicted using the measured concrete compressive strength at testing time. Predicted nominal moment resistance (Mpred.) showed good agreement with the measured ultimate moment resistance (Mtest) with an average Mtest/Mpred. of 1.11 and a coefficient of variance (COV) of 0.13. All specimens showed higher Mtest than Mpred. values (Mtest/Mpred. > 1.0) except specimen 70-50-70-4.2, where the measured experimental value was 4% lower that the predicted value. The reason for this could be attributed to the concrete material property variability. Nominal predicted ultimate moment resistance for non-composite and full-composite sections were calculated using strain compatibility. Non-composite section was analyzed by summing the moment resistance of both wythes assuming equal curvature and deflection for both wythes. However, the full-composite section was analyzed as a single section consisting of the two concrete wythes separated by the thickness of insulation. The level of composite action was assessed at the ultimate level using Eq. (4) for all specimens. Table 8 lists the calculated composite action (K Mn ). Generally, calculated composite
action using measured ultimate moment resistance showed higher level of composite action than that indicated by Fprovided/Ffull-comp. ratios. For example, specimen 90-50-90-3.3 shows a value of K Mn of 126%, while Fprovided/Ffull-comp. shows a value of 1.0 (100% composite action). The reason for the observed difference is chiefly caused by the definition of full composite action neglecting strain hardening of the reinforcing steel, which was not considered in predicting the moment resistance values as discussed above.
K Mn =
Mn, test Mn, C
Mn, NC × 100 Mn, NC
(4)
where, Mn, test = experimental maximum moment of the sandwich panel Mn, NC = theoretical maximum moment for non-composite sandwich panel Mn, C = theoretical maximum moment for fully composite sandwich panel 5. Conclusions This paper establishes the structural behavior of precast concrete sandwich panels using lumped GFRP shear connectors at each end of 12
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the panel. A comprehensive experimental testing program was conducted to investigate the behavior of a new shear connector derived from commercial non-composite connectors. The testing program consisted of 34 push-off, 23 pullout, and eight large-scale flexural specimens. The effect of concrete wythe thickness, insulation wythe thickness, and concrete compressive strength was investigated throughout these tests. Additionally, bond effect at the insulation-concrete interface was investigated using push-off tests. The flexural test results were compared with predicted fully composite, non-composite, and partially composite values. The following conclusions can be made from the experimental and analytical investigations:
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• Push-off test results were used to develop idealized shear load-slip • •
• • • •
relationships for different cases to assist design engineers in designing insulated sandwich wall panels with the proposed shear connectors system. The insulation contribution to shear resistance was the same for both 50 mm and 100 mm thick insulation layers. An average shear strength increase of 17% was observed relative to unbonded insulation-concrete interface cases. Large-scale flexural test results showed lower percentage of composite action (less than 6.5%) at cracking level, as is typical of sandwich wall panels with flexible connectors [16,24,25], especially in short panels like those tested. The analysis techniques investigated imply that adding additional connectors could increase this apparent composite action. The Elastic Method by Olsen et al. [17] for predicting serviceability behavior of PCSPs showed the most accurate prediction results when compared with the other four methods evaluated in this study with an average measured-to-predicted value of 1.04 for cracking load and deflection with COV of less than 7%. A method that can incorporate the discrete position of the shear connectors is critical to the prediction of lumped connector placement as evidenced by the poor performance of the Holmberg and Plem [19] sandwich beam theory (measured-to-predicted ratio of 0.81 and 0.72 for cracking and deflection prediction, respectively). Large-scale flexural test results showed that the shear connectors system provides at least 90% composite action at ultimate level, which could be increased if additional rows of connectors are provided. The strength prediction model developed by Olsen et al. [17] provided an average measured-to-predicted value of 1.11 with a coefficient of variation of 0.13.
Acknowledgement This research was funded by ITW Construction Systems, International. The support of Paul Gaiardo, Abdelrahman Khodier and Bob Connell is greatly appreciated. References: [1] Sorensen T, Dorafshan S, Maguire M. Investigating Thermal Efficiency of In Service
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