Experimental and numerical studies on the behaviour of concrete sandwich panels

EJECE. Volume 15 – No. 10/2011, pages 1465 to 1481

Experimental and numerical studies on the behaviour of concrete sandwich panels Giovanni Metelli — Nicola Bettini — Giovanni Plizzari

Department of Civil Engineering, Architecture, Land and Environment University of Brescia Via Branze 43, 25123 Brescia, Italy {gmetelli, nicola.bettini, plizzari}@ing.unibs.it

ABSTRACT. Precast concrete panels are often used for the façades of modern warehouses and commercial malls. During the last two decades, they have generally been made of two concrete layers with interposed thermal insulating polystyrene boards. Traditionally, perimeter concrete ribs allow the weight of the external concrete layer to be transferred to the internal thus causing unavoidable thermal bridges which reduce the energy performance of the building. In the sandwich cladding panel, the two concrete layers can be linked by low-conductivity shear connectors crossing through the insulation layer, thus ensuring the overall thermal efficiency of the building. In this paper, the results of a wide numerical study on the behaviour of concrete sandwich panels realized with glass fibre-composite pultruded connectors are presented, focusing on the stresses and deformations caused by dead load, thermal actions and shrinkage. RÉSUMÉ. Les panneaux préfabriqués en béton sont souvent utilisés pour les façades des entrepôts modernes et les centres commerciaux. Au cours des deux dernières décennies, elles ont généralement été faite de deux couches de béton avec interposition des panneaux de polystyrène thermiquement isolant, les nervures de béton périmètre permettent le poids de la couche externe en béton pour être transférés à l’interne ce qui provoque inévitablement des ponts thermiques qui réduisent la performance énergétique du bâtiment. Dans le panneau sandwich bardage, les deux couches de béton peuvent être reliées par des connecteurs de cisaillement à faible conductivité traversant la couche isolante, assurant ainsi efficacité thermique globale du bâtiment. Dans ce papier, les résultats d’une vaste étude numérique sur le comportement des panneaux sandwich en béton réalisé avec des fibres de verre composites par pultrusion connecteurs sont présentés, en se concentrant sur les contraintes et les déformations causées par la charge morte, les actions thermiques et de retrait. KEYWORDS: precast concrete structures, façade panel, thermal insulation. MOTS-CLÉS : structures préfabriquées en béton, panneau de façade, isolation thermique.

DOI:10.3166/EJECE.15.1465-1481 © 2011 Lavoisier, Paris

1466 EJECE. Volume 15 – No. 10/2011

1. Introduction

Since the last two decades, the increasing demand for thermally efficient structures has made the precast industry develop thermally broken concrete sandwich panels. They are generally made up of two outside layers surrounding an insulation layer. Traditionally, perimeter concrete ribs connecting the two r.c. concrete wythes allowed the weight of the external concrete to be transferred to the internal one, thus ensuring a full composite action of the panel (Pessiki, 2003). As a result, unavoidable thermal bridges occurred, thus reducing the energy performance of the building and raising risk of surface condensation. Some experimental studies on precast concrete sandwich wall panels (Lee et al., 2007; Lee et al., 2008) show that the concrete ribs can be replaced by several steel anchors to allow an adequate level of shear action to be transferred between the two concrete layers; however, they create local thermal bridges which reduce the energy efficiency of the cladding.

The development of thermally efficient concrete sandwich panels (CSP) is mainly due to the improvement of the manufacturing process and the use of advanced material, such as fiber-reinforced polymers (FRP), which can ensure the structural and the thermal performance of the cladding panels by means of their low thermal conductivity. In fact, in CSPs the two concrete layers can be linked by discrete shear connectors crossing through the insulation layer, without affecting precast construction technique. As a result, the overall thermal efficiency of the building is enhanced. As far as the internal actions in a CSP are concerned, the amount of shear transferred by the connection system between the wythes determines the level of composite flexural response of the panel. In the case of full composite action, achieved if the connection system is infinitely stiff, the concrete panel behaves as a monolithic element. In the case of non composite action (zero stiffness connection system), the concrete wythes behave independently under flexural loads. A low-connecting stiffness results in a partially composite action (Figure 1).

F

Non-composite action

F

Partially-composite action

F

Fully-composite action

Concrete layers

slipp.c.

(< slipn.c.)

slipn.c.

Insulating layer Shear connectors

Figure 1. Composite action of sandwich panels

In the design of a full composite panel, the shear force can be generated by the longitudinal bending due to wind and thermal loads, while in the case of non-composite walls, the shear connectors act as supports and transfer only the weight of the external (non-structural) wythe to the inner (structural) one (PCI, 1997). The

Behaviour of concrete sandwich panels 1467

former solution requires high strength and stiffness of the connectors, while the latter is based on flexible connectors which allow the free in-plane deformation of the architectural wythe to occur, due to both the thermal gradients and the differential shrinkage of the two concrete layers (Figure 1). As a result, with an increasing shear stiffness of the connectors, the composite action of the two concrete wythes increases and the deflection of the panel due to transversal load decreases. At the same time, the thermal gradient and the differential shrinkage can cause a greater transversal deformation in comparison with flexible connectors which, on the contrary, allow a free in plane deformation of the facing to occur without any out of plane deformation of the panel.

Several experimental and theoretical studies (Tarek et al., 2010; Benayoune et al., 2008; Salmon et al., 1997) show the good performance in term of strength and stiffness of precast concrete sandwich panels realized with FRP or steel shear grids, subjected to axial and lateral loads. The truss shaped connectors allow a composite action of the two connected layers to occur by means of their diagonal members, and their efficiency is not affected even by fatigue loads (Bush et al., 1994). It is also known that the bond between the insulation board and concrete layer provides a contribution on the composite action of the CSP (PCI, 1997; Bush et al., 1994) but its behaviour and its degradation during cycling loads have not been well investigated yet. Analytical studies on partially composite sandwich panels using truss-type connection (Salmon et al., 1995) provide design equations to calculate the panel thermal bowing which seems to be insensitive to the connector stiffness for long panel.

Several types of discrete FRP connectors are also available on the markets but few noteworthy studies have been published. It is known that CSPs with discrete V-shaped FRP connectors need large amount of connectors if a full composite behaviour is required (Pong et al., 2005); at the same time, there is a lack of experimental studies on the behaviour of these discrete connectors loaded by bending, shear and tension acting at the same time.

The research study presented in the paper aims to better understand the behaviour of a CSP realized by the use of pultruded glass fibre connectors. A wide numerical research program is presented, focusing on the stresses and deformations caused by dead load, thermal gradient and differential concrete shrinkage through the panel thickness. Material properties and local shear behaviour of the connector were experimentally studied with preliminary tests.

2. Connector and CSP details

Figure 2 shows the details of the horizontal CSP studied in the present work. The panel is 12.5 m long, 2.5 m high and 0.30 m thick. The concrete wythes are 6 cm thick. The internal wythe is stiffened by eight vertical and two horizontal 12 cm thick ribs to provide both the adequate strength and stiffness to the CSP. The facing

1468 EJECE. Volume 15 – No. 10/2011

outer concrete layer is connected to the inner ribs by means of 36 FRP shear inserts crossing through the insulating layer, whose thickness ranges between 6 cm and 18 cm (Figure 2). The connector are 216 mm long, 70 mm depth and 2.5 mm thick and they are made of pultruded glass fiber-vinylesther layers, woven mainly in two perpendicular directions in order to provide an homogeneous mechanical behaviour of the whole connector along different load directions (Figure 3a). The insert is fixed to the steel wire mesh of the external layer by its end hook and embedded in the horizontal concrete rib of the internal layer (Figure 2). The adopted connectors allow for an easy assembly and a reduced time construction of the panel, without the formation of discontinuity in the insulating layer. The low thermal conductivity (λ<0.231 W/m K-1) of the insert avoids the formation of a local thermal bridge. Furthermore, the inserts are oriented in order to allow free cyclic deformations of the outer concrete layer along its longitudinal dimension (X in Figure 2). As a result, the CSP is characterized by a non-composite behaviour for loads acting perpendicularly to the panel (Z in Figure 2) as well as by a partially-composite behaviour for the dead load acting in the panel plane and for thermal and shrinkage deformations acting along the lowest panel dimension (Y in Figure 2).

625

250

2525

250

X

Y

Z

20 20 2020

1 2 3 4 5 6 7 8 9 10

11 13 14 15 1612 17 18

Units in centimeters7

25

186

66 18

6

Figure 2. Geometry of a CSP with the detail of the connection

(a) (b)

Figure 3. FRP connectors (a); connectors fixed to the steel wire before the concrete casting of the outer layer (b)


Typical CSPs are manufactured in long line steel form according to the following phases (PCI, 1997): i) manufacturing of the external façade coating using natural stone, terracotta tiles or bricks on the bottom surface of the steel formwork; ii) placing of the steel wire mesh which also facilitates the anchoring of connectors (Figure 3b); iii) casting of the external concrete layer; iv) placing of the insulating elements; v) placing of the steel reinforcement and wire mesh of the internal wythe; vi) casting of the inner concrete layer.

The cladding panels is often fixed to the support structure at the bottom of the inner (structural) layer by means of two connections carrying the gravity loads and by two tie-back connections at the top of the panels, avoiding the out-of-plane movement of the panel (Figure 4). The four panel connections are designed to carry the same amount of the horizontal (parallel or perpendicular to the panel surface) loads due to wind or earthquake.

(a) (b) (c)

tie-back system

Z

Y

support systemX

inne

r w

ythe

oute

r w

ythe

Figure 4. CSP constraints (a); support system (b); tie-back system (c)

3. Mechanical properties of the connectors

(a) (b)

Figure 5. Reduction of modulus of elasticity (a) and tensile strength (b) relative to 25° values versus temperature curves (Pandini et al., 2010)

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A wide experimental campaign was carried out at the Material Laboratory of the University of Brescia in order to better understand the uniaxial tensile behaviour of the connector (Pandini et al., 2010). Several small specimens (2.5 mm thick, 15 mm wide and 140 mm long) were cut from the connector and tested along two main directions (90° and 45° with the respect to the axis shown in Figure 3a). The specimens were tested under displacement control at different temperatures, ranging from 23°C to 100°C.

Figure 5a shows that the modulus of elasticity is not significantly dependent on the load direction while it decreases only by 33% for an increase of temperature from 23°C to 100°C. At 23°C, the modulus of elasticity is equal to 13 GPa or 12.2 GPa, respectively for 45° or 90° load direction. The tensile strength is not affected by the temperature up to 100°C for 90° load direction while for 45° load direction there is a 12% strength reduction above 80°C (Figure 5b). The behaviour of the connector is mainly elastic and brittle, with a stiffness reduction for a tensile strength greater than 40 MPa. The ultimate deformation (εu) at 23°C is generally larger than 3 % for both directions (Pandini et al., 2010).

(a) (b)

600120 60 140

Figure 6. Scheme of the push-off test (a); connector failure (b)

(a) (b)

Figure 7. Test results: shear force Fy versus relative displacement δy (insulating layer of 60 mm) (a); tensile stress-strain relationship adopted in the FE model (b)

0

40

80

120

160

200

0 1 2 3 4 5

σ (MPa)

ε (%)

elas

tic ra

nge


The shear behaviour of several types of connector was experimentally investigated by four push-off tests. A steel bench was designed to test small prototype specimens (150 x 150 mm section and 600mm long), representing a portion of concrete wythes connected by one FRP insert. For practical reasons of symmetry, a pair of specimens were tested at the same time (Figure 6a).

The connectors were placed (with an inclination of about 10°) in order to simulate the shear behaviour of the inserts placed in the lower horizontal rib of the panel. The tests were carried out by using an universal testing machine of the Structural Laboratory of the University of Brescia; an increasing relative displacement δ between the inner and the two outer concrete blocks was applied with a speed rate of 0.1 mm/min. More details of the shear tests can be found in Bettini et al. (2010). The shear action Fy is transferred by a strut-tie mechanism within the connector, as the ratio between insulating layer and the connector depth is equal 0.85 (Figure 6a). As an example, Figure 7.a shows the experimental results for specimens with an insulating layer having a thickness of 60 mm. A shear strength greater than 8.0 kN was measured (Figure 7.a), assuming that the load is equally shared by the two symmetric connectors. Furthermore, the shear strength is greater than 6 times the action due to the gravity load of an outer concrete wythe having a thickness of 60 mm, assuming an uniform distribution of the load among all the connectors. The specimen failure occurred in the connector due to the buckling of the compressed strut that provoked the delamination of the connector layers (Figure 6b). As in the tensile tests, the shear behaviour of the connector is mainly elastic with a brittle failure.

4. Numerical study

4.1 Finite Element model

A three dimensional Finite Element (FE) model was carried out as the main goal of this study is to understand the role of concrete shrinkage and thermal gradient on the CSP deformation and on the internal action rate in the FRP connectors. Particular attention was devoted to the effect of differential shrinkage through wythe thickness (Z-direction in Figure 8). This component is due to the concrete wythe ageing in environments characterized by different moisture content (PCI, 1997): the faces in contact with the external environment age at a lower humidity content in comparison with the faces in contact with (polystyrene) insulating layer characterized by low-permeability. The non linear analyses were carried out with the FE program ABAQUS 6.9.

A 3D Finite Element (FE) model was carried out by adopting 20-node second-order brick elements for all the components forming the CSP. Over 18000 elements, with a dimension varying from 2.5 mm to 150 mm (away from the diffusion zone) were used (Figure 8a); only half of the panel was modelled due to its symmetry. The

1472 EJECE. Volume 15 – No. 10/2011

boundary conditions consisted of a rigid support in Y and Z direction and an elastic support in the longitudinal X direction at the lower corner of the inner concrete wythe; the tie-back system at the top corners avoid the out of plane movements of the panel and they behaves elastically in X and Z direction (Figure 8b). As few studies are available on the mechanical behaviour of the support system for precast concrete panels, a very conservative high-stiffness for the support system in X direction, equal to 100kN/mm, was supposed on the basis of numerical and experimental studies conducted at the University of Brescia (Metelli et al., 2007); a 30 kN/mm stiffness in both direction was assumed for the upper tie-back systems. More details of the effect of constraint stiffness are shown and discussed in (Bettini et al., 2010).

Concrete and polystyrene are modelled as elastic materials with the mechanical properties shown in Table 1. To take into account a possible concrete cracking due to differential shrinkage or transversal loads, the concrete (C25/30) Young modulus of the internal wythe was reduced by 25%, while that of the external one was reduced by 50%. The material of the connectors is supposed to be elasto-plastic and homogeneous, because the orientation of the woven layered glass fibres provides a good degree of isotropy, as shown by the experimental study specifically focused on the material (Figure 5). The non-linear behaviour observed in the experimental tests was not significant with respect to global fragility of collapse; however, a tri-linear tensile behaviour of the FRP connectors was adopted to understand the progressive, slight loss of stiffness of the connection system. The FRP constitutive law adopted in the analysis is shown in Figure 7b.

A unidirectional compressive contact surface between polystyrene layers was assumed with a friction coefficient µ equal to 0.5. Perfect bond was assumed at the interface between insulation and concrete, although cycling thermal loads could degrade the adhesion between concrete and insulation.

(a) (b)

Figure 8. Mesh (a) and boundary conditions (b) for the numerical model


Table 1. Material properties

E [GPa] υ f

[MPa] αT

[10-6/°C] internal RC wythe 24.75 0.2 25 10 external RC wythe 16.5 0.2 25 10 insulting layer 0.01 0.02 0.1 65 FRP connectors 6.7 0.1 120 f: material strength; αT: thermal expansion coefficient; E: modulus of elasticity; υ: Poisson’s ratio.

In the FE model, the following loads were applied progressively to the CSP: self weight, shrinkage, heating (+45 °C) or cooling (-25 °C) of the external concrete wythe in contact with the outside environment, positive (up to +2.0 kN/m2) or negative (up to -1.0 kN/m2) pressure generated by wind. As already mentioned, the differential shrinkage in the direction of thickness of the wythes (Z-direction) was based on the assumption that the external faces of the panels lie in an environment with low humidity content (RHext = 50%), while the inner concrete faces are in contact with polystyrene insulation characterized by an higher humidity rate (RHint = 90%), at least for 1 year concrete ageing. It is noteworthy that over 1 year time, the assumption on moisture content distribution may no longer be realistic, while shrinkage can be largely exhausted (Figure 9). A linear humidity distribution was assumed through the wythe thickness (Z direction).

Shrinkage strain were calculated according to the Eurocode 2 (2004) formulation, which distinguishes between autogenous (εca) and drying shrinkage (εcd), expressed by the following equations:

( ) ( ) ( )[ ]506 201101052 ,ckca t,expf,t −−⋅⋅−⋅=ε [1]

( ) ( )( ) 03

0040,cdh

s

scd k

h,tt

ttt εε ⋅⋅

⋅+−

−= [2]

( ) RHcm

cmdsds,cd f

fexp, βααε ⋅⋅

⋅−⋅−⋅= −6

0210 10110220850 [3]

−⋅=

3

0

1551RHRH,RHβ [4]

where t is the time at the moment considered (in days), ts is the age of concrete at the beginning of drying shrinkage (generally beginning at the end of the curing), h0 is the notional size of the cross section (2Ac/u, where Ac is the cross sectional area and u is the perimeter of that part of the cross section exposed to drying), k varies between 1.0 and 0.75 as a function of the notional size, fcm is the compressive strength, fcm0 is equal to 10MPa, RH is the environmental relative humidity, RH0 is equal to 100%; αds1 and αds2 are respectively equal to 4 and 0.12 for Class N cement. In particular, autogenous shrinkage can be neglected in case of precast elements

1474 EJECE. Volume 15 – No. 10/2011

subjected to heat curing (Eurocode 2, 2004, §10.3.1.2). The comparison of the drying and autogenous shrinkage for RHext = 50% and RHint = 90% are shown in Figure 9a.

Thermal loads were applied only to the external wythe, according to the scheme depicted in Figure 9b, which is based on a superposition of thermal and shrinkage eigen-strains applied to the concrete elements. In the FE model the shrinkage strains are applied in terms of equivalent temperature.

The FE model of the overall CSP was validated by FE numerical analysis of push-off shear test carried out on the connectors (Bettini et al., 2010).

(a) (b)

Figure 9. Autogenous and drying shrinkage according to EC2 formulation (a); superposition of equivalent thermal and shrinkage eigen-strains (b)

4.2 Numerical results

The first remarkable outcome concerns with the shear action Fy on the connector due to the dead load of the outer concrete whyte. Figure 10b shows that the external connectors are loaded by a shear action Fy close to 3.2 kN which is much higher than the value calculated assuming the classical uniform distribution of the load among the 36 connectors (1.3 kN). This behaviour is mainly due to the position and to the stiffness of support and tie-back restraints placed at the corners of the inner wythe that drive the dead load towards the outermost connectors (which carry most of the external layer weight). The numerical results also show a tensile action (Fz) ranging from 0.2 kN to 1.0 kN in the connectors due to the eccentricity between the external wythe and the inner one supported by the columns (Figure 10c). The position of the connectors is numbered from 1 to 10 in the superior rib and form 11 to 18 in the bottom rib of the panel, as shown in Figure 2.

The differential shrinkage (between inner and outer faces) causes opposite curvatures of the two CSP wythes thus increasing the tensile action Fz up to a value of 4.89 kN in the outermost connector (n.°1 in Figure 2); as a result, compressive strength in the insulation (equal to 0.06 MPa) are generated to equilibrate the tensile actions on the connectors. Figure 10d shows the results of several elastic analysis


with uncracked concrete concerning the effects of moisture content on the CSP out-of-plane deformation: the higher the difference of the humidity rate between the atmosphere and the concrete-to-insulation interface, the greater the Fz force occurs in the connectors. For example for an atmosphere humidity (RHext) equal to 40% and an humidity (RHint) equal to 90% at the concrete-to insulating layer, the Fz force is equal to 9.3 kN and it increases by 30% (up to 12.3kN) for an internal humidity (RHint) equal to 100%. Similarly, an increase of the external humidity rate by 50% causes a reduction of the tensile force (Fz) of about 60%. This phenomenon is also pointed out by the 11.1mm CSP out-of-plane deformation and by the relative displacement (1.2 mm) of the concrete wythes at the panel edges (with 100% RHint and 40% RHext moisture content; Figure 11).

(a) (b)

(c) (d)

Figure 10. Distribution of the internal actions in the connectors due to the dead load, 1 year drying shrinkage and thermal cooling gradient: transversal shear action Fx (a); vertical shear action Fy (b); tensile action Fz (c); tensile action Fz versus atmosphere humidity curve due to shrinkage from the elastic analyses (d)

The nonlinear analyses were carried out with RHint = 90% and RHext = 50%. The numerical results evidence that the differential shrinkage is beneficial for the lower connectors while it is detrimental for the upper ones. As far as the Fy shear action is concerned, the shrinkage due to 1 year concrete ageing does not remarkably change the pick value (7% increase) at the n.1 outermost connector, while it causes an increase by 73% of the mean value in the internal upper connectors (from 1.3 kN to

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2.28 kN, Figure 10b). Shrinkage strongly affects the Fz tensile action ranging from 1.9 kN to 4.0 kN in the internal connectors and with a pick value equal to 4.89 kN in the upper (n.°1 in Figure 2) outermost connector (Figure 10c). The transversal shear force (Fx) is very low, with a maximum value close to 0.022 kN, because of the lower stiffness of the connector along the longitudinal panel direction. In the Table 2 the relative displacements between the two concrete wythes at the external connectors (n.°1 and n.°11) are shown along the three directions. The maximum longitudinal relative displacement (δx), due to the dead load and 1 year differential shrinkage, is equal to 0.52 mm; it occurs at the outermost top connector and it is equal to the maximum relative vertical displacement (δy = 0.51 mm). The relative displacement (δz) between the two concrete wythes is 0.27 mm at the n.°11 connector position of lower panel rib.

The second main issue of the present numerical research concerns the effects of thermal gradient due to heating or cooling of the external concrete layer. As the thermal loads can be studied like eigen-strain developing in the plane of the external wythe subjected to cyclic temperature range, they mainly affect the Fx and Fy shear actions of the outermost connector without any variations in the Fz tensile action (Figure 10a, b). Furthermore, the results of several numerical analyses carried out with a thermal heating equal to 45°C or a thermal cooling of -25°C after a drying shrinkage action ranging from 15 days to 1 year time, evidence that the critical load combination for the connectors corresponds to a +45°C thermal heating of the external wythe after a 15 days shrinkage action (Table 2). The vertical shear action reaches a value close to 5.1 kN, equal to 73% the mean shear strength, evaluated by means of push-off tests. Figure 12a shows the effects on shear action Fy of the concrete shrinkage time: the longer the concrete ageing time the greater the effects of wythe cooling (-25°C) rather than heating (+45°C). The tensile action Fz is not dependent on the thermal gradient. What emerges from the numerical study is that the connectors in young CSPs (i.e. 15 days concrete ageing time) suffer from external wythe heating, while they suffers from cooling in older ones (i.e. 1 year concrete ageing time). As far as the panel deformation is concerned, the maximum longitudinal relative displacement (δx) is equal to 2.48 mm at the upper outermost connector while the vertical displacement (δy) is 1.10 mm for the combination of dead load, 15 days concrete shrinkage and thermal heating.

The effect of a wind depression equal to 1.0 kN/m2, acting perpendicularly to the panel, has been evaluated after 1 year of concrete curing time. The worst configuration is due to a wind direction towards the outer wythe, whose effects provoke an increase by 15% of Fz and by 12% of the shear action (Fy). The longitudinal relative displacements (δx) are comparable to those of thermal gradient while the vertical relative displacements (δy) are unchanged (Table 2).


Table 2. Relative displacements between the two wythes at the outermost connectors

n.° connector

δx δy δz Fx Fy Fz u [mm] [mm] [mm] [kN] [kN] [kN] [mm]

- dead load 1 0.11 0.56 0.01 0.005 3.20 0.97

3.4 11 0.12 0.60 0.06 0.004 3.27 0.13

- dead load - 1 year shrinkage

1 0.52 0.51 0.22 0.020 3.42 4.89 11.7

11 0.49 0.30 0.27 0.020 0.96 4.21

- dead load - 1 year shrinkage - cooling

1 1.86 0.80 0.22 0.056 4.64 5.02

8.1 11 1.85 0.01 0.25 0.062 0.23 4.36

- dead load - 15 days shrinkage - heating

1 2.48 0.21 0.05 0.078 1.32 1.40

5.77 11 2.48 1.10 0.16 0.069 5.12 0.38

- dead load - 1 year shrinkage - wind (-1.0kN/m2)

1 2.61 0.60 0.27 0.102 3.84 5.61

63.4 11 2.58 0.31 0.33 0.106 0.67 5.10

δx: longitudinal relative displacement; δy: vertical relative displacement; δz: transversal relative displacement; Fx: longitudinal shear action; Fx: vertical shear action; Fz: tensile force; u: panel bowing

(a) (b)

Figure 11. Global panel deformation (a); relative displacement between inner and outer wythe due to shrinkage (b)

It is worth pointing out that, although the magnitude of transversal shear action Fx is about 1÷2% of the vertical shear Fy or tensile force Fz, the three-dimensional stress state of the connector and the large longitudinal relative displacement due to the thermal and shrinkage gradients could cause an early failure of the connectors.

δz=

1478 EJECE. Volume 15 – No. 10/2011

As there are no available test data on the layered FRP inserts (adopted herein) under transversal bending, a Von-Mises plasticity domain has been assumed to evaluate the damage state in the connector. On the basis of preliminary numerical analysis (Bettini et al., 2010), aimed to model the tensile and shear push-off tests, an equivalent (σeq) von Mises was assumed:

(a) (b)

Figure 12. Elastic analyses: maximum cooling and heating effects on the Fy shear action (a) or Fz tensile action (b) on the outermost connector for increasing concrete ageing time

( ) ( ) ( ) eqIIIIIIIIIIII σσσσσσσ =−+−+− 222

21

21

21 [5]

where σI, σII and σIII are the principal stresses in the connector.

Figure 13 shows the number of Gauss points of all connectors where the equivalent Von Mises stress (σeq) lies within four ranges: i) σeq < 40 MPa (elastic range); ii) 40 MPa <σeq < 80 MPa; iii) 80 MPa <σeq < 120 MPa; iv) σeq > 120 MPa. Most of the connectors are in the elastic range, while only 4 Gauss points in the outermost connector (n.°1 and n.°11 in Figure 2) show a stress (σeq) ranging between 80 and 120 MPa for +45°C heating acting after 15 days of concrete shrinkage time.

The numerical results show that the FRP connectors, arranged according to a typical design layout for CSPs, are able to carry high thermal gradient, severe drying shrinkage of the concrete wythes and wind load without any damage. However, the distribution of shear and tensile force among the connectors is remarkably heterogeneous, with the outermost connectors stressed by peak loads remarkably higher than the inner ones (Figure 10), because shrinkage and thermal gradient act like eigen-strains applied to wythes without being affected by the position and by the number of connectors arranged in the panel. An increase in the number of outer connector in the CSP panel does not reduce the shear load Fy, whose maximum value remains unchanged at about 5.0 kN, also when failure of the outer connectors occurs (Bettini et al., 2010).


(a) (b)

Figure 13. Distribution of the equivalent Von Mises stress (σeq) in the connector Gauss points under: 1 year drying shrinkage and -25°C cooling (a); 15 days shrinkage and +45°C heating (b)

5. Concluding remarks

The present paper deals with the numerical studies on the behavior of concrete sandwich panels (CSP) made with FRP connectors in order to provide high energy-efficient cladding for precast buildings. The research work focused on the effects of dead load, thermal actions and drying shrinkage on the shear and tensile forces developing in the connectors as well as on the deformation of the CSPs.

The preliminary experimental campaign on the mechanical behavior of FRP connector shows that the tensile strength is weakly affected by the temperature with a decrease by 25% when temperature rises up to 100°C from 23°C.

A 3D FEM analyses show the remarkable role of the position of the panel constraints (to the structure) on the shear action distribution among the connectors: when only the dead load is present, the outermost connectors are stressed by greatest shear force (that is reduced in the inner ones), thus confirming that the typical uniform distribution of the dead load among the connectors cannot be adopted for design purposes. Results of several numerical analyses carried out with a thermal heating equal to 45°C or a thermal cooling of -25°C after a drying shrinkage actions ranging from 15 days to 1 year time, show that a young CSP could suffer from external wythe heating while an older one from cooling. The vertical shear action (Fy) on the outermost connectors reaches a value close to 73% of the maximum shear strength under the effects of dead load, 15 days shrinkage and +45°C heating of external concrete wythe.

As the thermal gradient and drying shrinkage act like eigen-strains applied to the concrete wythes, an increase of the connector number at the outer panel ends does not markedly reduce the stress in the connectors. Furthermore, the presented 3D numerical model shows that the differential drying shrinkage (within the wythe thickness) due to the different humidity between the environment and the concrete-to-insulation interface, is responsible of out of plane imperfection of the CSP. The drying shrinkage model suggested by the Eurocode 2, in case of precast elements

1480 EJECE. Volume 15 – No. 10/2011

subjected to heat curing, can be an effective tool to evaluate both the connector actions and CSP deformations during the whole concrete ageing process.

Finally, in order to validate the results from linear and nonlinear analyses performed herein, experimental studies on the multi-axial and cyclic behaviour of the CSP connector should be performed. However, the numerically determined displacements can provide noteworthy information on the amplitude of cyclic deformation to be experimentally applied to the connector along the three directions.

Acknowledgements

The Authors gratefully acknowledge the support of Chryso Italia S.p.A. (Lallio (BG), Italy) for financing this research project on the behaviour of precast concrete sandwich panels stressed by thermal and shrinkage actions.

The cooperation of Mr. Andrea Delbarba of the structural Laboratory of the University of Brescia, in carrying out the tests, is also gratefully acknowledged.

A special thank goes to Professor Paolo Riva of the University of Bergamo for the useful suggestions.

6. References

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Bettini N., Metelli G., Plizzari G.A., Numerical study on the structural behaviour of concrete sandwich panel. Technical Report, DICATA, University of Brescia, Italy (in Italian), vol. 12, 2010, p. 1-166.

Bush T. D., Stine G. L., “Flexural Behavior of Composite Precast Concrete Sandwich Panels with Continuous Truss Connectors”, PCI Journal, March-April, 1994, p. 112-121.

Eurocode 2, “Design of concrete structures - Part 1-1: General Rules, and Rules for Buildings”, UNI-ENV 1992-1-1, European Committee for Standardization, 2004.

Hassan T. K., Rizkalla S. H., “Analysis and design guidelines of precast, prestressed concrete, composite load-bearing sandwich wall panels reinforced with CFRP grid”, PCI Journal, Vol. 55, No. 2, 2010, p. 147-162.

Lee B., Pessiki S., “Design and Analysis of Precast, Prestressed Concrete Three- Wythe Sandwich Wall Panels”, PCI Journal, Vol. 52, No. 4, 2007, p. 70-83.

Lee B., Pessiki S., “Experimental Evaluation of Precast, Prestressed Concrete, Three-Wythe Sandwich Wall Panels”, PCI Journal, Vol. 53, No. 2, 2008, p. 95-115.


Metelli G., Riva P., “Behaviour of a support system for pre-cast concrete panels”, FRAMCOS, Vol. 6, 2007.

Pandini S., Riccò T., Characterization of the mechanical properties of the Chryso composite materials. Internal Report, p. 1-12, Department of Mechanical and Industrial Engineering, University of Brescia, Italy, 2010.

PCI Committee Report, “State-of-the-Art of Precast/Prestressed Sandwich Wall Panels”, PCI Journal, Vol. 42, No. 2, 1997, p. 1-61.

Pessiki S., Mlynarczyk A., “Experimental Evaluation of Composite Behavior of Precast Concrete Sandwich Wall Panels”, PCI Journal, Vol. 48, No. 2, 2003, p. 54-71.

Pong W. A., Morgan Girgis A. F., Tadros M. K., “Proposed GFRP connectors in sandwich panels”, special publication, ACI, Vol. 230-2, 2005, p.21-38.

Salmon D. C., Einea A. A., “Partially composite sandwich panel deflections”, Journal of Structural Engineering, No. 121, April 1995.

Salmon D. C., Einea A., Tadros M. K., Culp T. D., “Full Scale Testing of Precast Concrete Sandwich Panels”, ACI Structural Journal, Vol. 94, No. 4, 1997, p. 354-362.

Received: 3 May 2011 Accepted: 6 July 2011

Experimental and numerical studies on the behaviour of concrete sandwich panels

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