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Experimental tests and numerical modelling of wall sandwich panels
Engineering Structures 37 (2012) 193–204
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Experimental tests and numerical modelling of wall sandwich panels Fabrizio Gara ⇑, Laura Ragni, Davide Roia, Luigino Dezi Dept. of Civil and Construction Engineering and Architecture, Università Politecnica delle Marche, via Brecce Bianche, 60131 Ancona, Italy
a r t i c l e
i n f o
Article history: Received 23 July 2011 Revised 15 November 2011 Accepted 2 December 2011 Available online 4 February 2012 Keywords: Sandwich panels Bearing wall panels Full scale compression test Diagonal compression test Finite element analysis
a b s t r a c t This paper presents the first part of an experimental investigation carried out on a construction system based on completed in situ sandwich panels with non-shear connectors, concerning the study of vertical panels used as structural walls. Compression tests with axial and eccentric loads were carried out on several full scale panel specimens with different slenderness ratios in order to study the behaviour of panels under vertical in-plane forces. Additionally, diagonal compression tests were performed on square specimens in different configurations in order to study the behaviour of panels under horizontal in-plane forces. The most significant load–displacement diagrams for increasing load are illustrated and the failure modalities are discussed. The semi-composite behaviour of the panels, guaranteed by the internal layer of polystyrene and the reinforced concrete beams at the panel ends, is highlighted. Finally, some numerical simulations are performed with non-linear finite element models and some useful design indications are given. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Construction systems based on sandwich panels are commonly used worldwide for intensive building production. Sandwich panels are typically constituted by two concrete layers which are separated by an internal insulation layer of various materials (i.e. expanded and extruded polystyrene, rigid polyurethane foam) and are usually joined with ‘‘shear connectors’’ (i.e. truss connectors) able to transfer the longitudinal interface shear between the layers so as to ensure a fully-composite or a semi-composite behaviour of the sandwich panel. This paper deals with a construction system that utilises sandwich panels, both for structural walls and floors, which are obtained by self-supporting reinforced insulation layers completed in situ with spritz-beton. The prefabricated modular elements are made of an undulated (corrugated) layer of expanded polystyrene, with suitable density, reinforced by two metallic meshes connected by means of orthogonal steel wires welded to the meshes (steel connectors). Thanks to the easy and fast mounting procedures, this construction system presents some technical advantages that make it often competitive in comparison with traditional methods or precast systems. From a structural point of view these panels are characterised by orthogonal connectors (‘‘no-shear connectors’’) so that their semi-composite behaviour depends on the shear stiffness of the expanded polystyrene layer and, above all,
⇑ Corresponding author. Tel.: +39 071 2204550; fax: +39 071 2204576. E-mail addresses: [email protected] (F. Gara), [email protected] (L. Ragni), [email protected] (D. Roia), [email protected] (L. Dezi). 0141-0296/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2011.12.027
on construction details, such as reinforced concrete regions at the panel ends. The structural behaviour of such a sandwich panel can be theoretically studied by means of analytical models which are usually referred to in the literature as models for multilayered beams [1,2] or two-layers composite beams [3,4] with deformable interlayer connection. As this paper deals with experimental investigation, a literature review of theoretical models is beyond the scope of this paper and only some of the most recent works are cited as example from which a comprehensive list of references describing these models may be founded. However the behaviour of single sandwich panels is obviously much easier to predict than the behaviour of panels constituting real building walls. To evaluate the structural performances of buildings constructed with this kind of construction system, in addition to specific modelling taking into account the semi-composite behaviour of the sandwich panels, other aspects need to be considered in the numerical evaluations, like (i) the restrain degree of wall-floor node depending on the connection details and (ii) the bi-dimensional behaviour of the panels which are each-other connected in real buildings. For this purpose, experimental results of full scale tests, are an essential instrument to calibrate both theoretical methods and numerical models. In the technical literature several experimental campaigns on precast sandwich panels with shear connectors can be found [5–13]. On the contrary, very few experimental tests have been performed on sandwich panels with in situ sprayed concrete and no-shear connectors [14,15] and on 3D full scale mock-up [16] in order to study the behaviour of the panels in real structures. Consequently, general conclusions on the structural behaviour of this
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construction system cannot be drawn and further experimental investigations are needed. For this reason, an extensive experimental campaign, including a large number of tests on floor and wall panels, cyclic tests on wall-floor connections and a load test on the floor of a full scale 3D mock-up, has been carried out. This first paper refers only to tests performed on wall panels. In particular, the results of compression tests with axial and eccentric loads carried out on panels with an internal layer of different thickness, are presented. After that, the experimental results obtained on panels with non-undulated polystyrene sheet and on panels with undulated polystyrene sheet and half the number of connectors are discussed. Additionally, the results of diagonal compression tests carried out on square specimens of different configurations in order to study the behaviour of panels under horizontal in-plane forces are illustrated: wall standard panels, as well as wall panels externally prestressed to simulate the effects of vertical loads and panels stiffened with four orthogonal walls to simulate the behaviour of the wall in a real building are considered. For each test, the load–displacement diagram and the failure modalities are examined. Finally some numerical simulations, performed with non-linear finite element models, are also reported and some useful design indications are given. 2. Experimental campaign The sandwich panels considered in this study are made of a sheet of polystyrene reinforced by two 80 mm 75 mm metallic meshes assembled by means of steel connectors. The sheet of polystyrene has an undulated profile and density of about 15–25 kg/ m3. The galvanised welded wire meshes and the connectors welded orthogonally to the meshes, are made with U3 wires of high yield steel. Wall panels (WP) were completed simply by spraying concrete onto the external surfaces of the sheet, first up to the metallic mesh and then up to the final thickness of the concrete layer, using manual tools or pumps (Fig. 1). A ready-mixed concrete, with sand no greater than 3 mm and specific additives to improve adhesion and workability, was used. 2.1. Mechanical properties of materials In order to evaluate the mechanical properties of the used materials, several tests were carried out on concrete, metallic meshes and internal layer consisting of a polystyrene sheet and metallic connectors.
wire meshes
Table 1 Mean values of material properties. Prismatic specimens (MPa)
Cored specimens (MPa)
Metallic meshes (MPa)
fcu = 21.95 fcfm = 5.52
fcu = 25.10 fct = 2.40
fm = 769.00 Agt = 7.62
The concrete was characterised by means of tests on 40 40 160 mm specimens sampled during the cast, and tests on cored specimens with a diameter of 94 mm and length of 250 mm sampled from the reinforced concrete beams at the ends of the panel after the concrete curing. In accordance with EN ISO 12504-1 [17], bending tests were first carried out to evaluate the flexural strength of the rectangular specimens, then the two resultant parts of the specimens were used for compression tests. A total number of eight specimens were prepared so that eight flexural tensile tests and sixteen compression tests were performed. Table 1 reports the mean values of the compression (fcu) and flexural tensile concrete strength (fcfm). The cored specimens were divided into two sets, one of which was subjected to the compression test and the other to the indirect tensile splitting test, in accordance with EN 12390-6 [18]. Four cored specimens were sampled and, consequently, four compression tests and four tensile splitting tests were performed. The average values of compression strength (fcu) and tensile concrete strength (fct) are reported in Table 1. From these specimens, a mean value of 10500 MPa for the concrete elastic modulus (Ec) was also estimated. Tensile tests and weld shear strength tests were carried out on six samples of metallic meshes following EN ISO 15630-2 [19]. Four samples reached the yield stress showing a very low ductility (less than 2). The mean values of tensile strength (fm) and percentage elongation at failure (Agt) are reported in Table 1. The other two samples showed a brittle fracture and a strength value which was about 20% lower than the yielding strength. It is worth noticing that the failure of all the mesh samples occurred at a welded joint as a consequence of the welding disturbs. Finally, the weld shear strength tests gave an average shear force of 2.64 kN, which is 1.25 times greater than the wire yielding force, as prescribed by the code. The mechanical properties of the internal layer were obtained by means of shear tests according to the Standard Test Method for Shear Properties of Sandwich Core Materials [20]. Samples with dimensions of 400 445 mm made of three concrete layers and two internal layers were tested. In
concrete layers
steel connectors polystyrene
(a)
(b)
(c)
Fig. 1. ‘‘Concrewall’’ wall sandwich panels: (a) schematic sketch of the components; (b) concrete spraying onto the external surfaces up to the metallic mesh and (c) up to the final thickness.
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(a) 30
3S (160 mm)
1S (80 mm)
5S (160 mm)
Load [kN]
1S (80 mm)
Load [kN]
30
0
Displacement [mm]
0
5
Displacement [mm]
5
(b) Fig. 2. Shear tests: (a) test configuration and (b) load–displacement cycles.
particular, eight samples were considered with internal layers of different thickness and with a different number of connectors. Subsequently, the polystyrene sheets of four samples were dissolved in order to obtain samples with metallic connectors only. Load and unload cycles were performed up to failure (Fig. 2a). Slipping between the concrete layers was measured by means of two LVDTs and the applied load was determined by means a pressure transducer. In Fig. 2b load–displacement graphs are illustrated with reference to samples 1S and 3S, with polystyrene sheet thickness of 80 mm and 160 mm respectively, and sample 5S which is similar to sample 1S but without the polystyrene sheets. By comparing the results of the tests on 1S and 3S samples it is evident that the stiffness decreases considerably when the thickness of the internal layer increases, whereas by comparing the results of 1S and 5S samples it can be observed that the contribution of connectors is negligible with respect to the contribution of the polystyrene. For each test the initial shear modulus was calculated by means of
Gi ¼
Ki hi 2Ai
ð1Þ
where Ki is the initial stiffness of the sample, and hi and Ai the thickness and the area of each internal layer. Table 2 shows all the obtained results.
Table 2 Shear tests: samples and results. Sample
hi (mm)
Polystyrene
Connectors
Ki (kN/mm)
Gi (N/mm2)
1S 2S 3S 4S 5S 6S 7S 8S
80 120 160 80 80 120 160 80
Yes Yes Yes Yes No No No No
Double Double Double Single Double Double Double Single
15.70 9.20 7.30 12.80 0.47 0.15 0.07 0.20
3.45 3.03 3.20 2.81 0.10 0.04 0.03 0.04
2.2. Panel geometry A total of twenty two panels were built: sixteen for compression tests with axial and eccentric load and six for diagonal compression tests. The panels for compression tests had a total height of 2940 mm, a width of 1120 mm and concrete layer thickness of 35 mm. To avoid stress concentrations and to facilitate the handling operations two reinforced concrete beams were built at the ends of the panels by dissolving a portion of the polystyrene sheet in order to obtain a proper anchorage of the meshes (Fig. 3). For the compression tests, wall panels (WP) with three different
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120
Table 3 Geometric characteristics of panels for compression tests.
4φ8 φ6/200mm
A
120
2700 mm
2940 mm
A
35 1120 mm
35 mm c h
Fig. 3. Panel for compression tests.
thicknesses of the internal layer, 80 mm (WP08), 120 mm (WP12) and 160 mm (WP16), were built. For each thickness, two panels were tested under axial load and two under eccentric load. In addition, two different kinds of wall panel were prepared for the compression tests: the WPN panel with a non-undulated polystyrene layer and the WPH panel with half the number of connectors (Fig. 4). In these cases only one compression test with axial load
Specimen
Panel
Compression loading
c (mm)
h (mm)
2a.1 2a.2 3a.1 3a.2 4a.1 4a.2 X.2 Y.2 2b.1 2b.2 3b.1 3b.2 4b.1 4b.2 X.1 Y.1
WP08 WP08 WP12 WP12 WP16 WP16 WPN08 WPH8 WP08 WP08 WP12 WP12 WP16 WP16 WPN08 WPH08
Axial Axial Axial Axial Axial Axial Axial Axial Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric
80 80 120 120 160 160 80 80 80 80 120 120 160 160 80 80
150 150 190 190 230 230 150 150 150 150 190 190 230 230 150 150
and one with eccentric load were performed for each kind of panel. The list of all the panels with the overall thickness (h), the internal layer thickness (c), and the kind of test performed are reported in Table 3. For the diagonal compression tests, only 1120 mm 1120 mm WP08 panels were considered since the thickness of the internal layer does not influence the panel behaviour under in-plane forces. In addition, prestressed and transversally stiffened panels were considered in order to simulate the effects of vertical load and the stiffening contribution of walls and floors orthogonal to the panels, respectively. To better distribute the compression load, two triangular reinforced concrete regions at two opposite corners of the standard wall panels (Fig. 5a) and two reinforced concrete L-shaped beams in the stiffened panels (Fig. 5b) were built. In the prestressed panels two steel threaded bars are applied with prestressing loads of 30 kN and 90 kN. The list of all the specimens with overall thickness (h), internal layer thickness (c), prestressing forces and loading type are reported in Table 4.
Section B-B WP08
B A
WPH08
A
40
B
80 15
wire meshes φ3 150
WP08
150
Section A-A
80
polystyrene
80
80
concrete
40 1120 1245
WPN08
Fig. 4. Details of WP, WPN and WPH panels.
150
150
75
20
20
φ3
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1120 mm
1120 mm
Section A-A
4φ8 φ6/200mm
Section A-A
1420 mm
A A
A 1120 mm
A
150
(a)
1120 mm
(b)
Fig. 5. Panels for diagonal compression tests: (a) wall panel and (b) transversally stiffened panel.
Table 4 Geometric characteristics of panels for diagonal compression tests.
a
Specimen
Panel
Compression loading
Prestressing load (kN)
c (mm)
h (mm)
5.1 5.2 5.3 5.4 C.1 C.2
WP08 WP08 WP08 WP08 WP08a WP08a
Diagonal Diagonal Diagonal Diagonal Diagonal Diagonal
– – 30 90 – –
80 80 80 80 80 80
150 150 150 150 150 150
With traversal stiffening walls.
2.3. Test configuration and instrumentation For the compression tests the configuration of Fig. 6 was adopted: panels were placed vertically with the bottom end pinned (cylindrical pin) and the top end restrained so as to prevent lateral
displacement. This static scheme simulates the restraint condition of panels in real multi-storey buildings when connections between floor and wall panels produce negligible bending moments. In the axial compression tests the load is applied at the panel axis, while in the eccentric compression test the load is applied
reaction frame S4
hydraulic jacks
S5 S1 Svf
Svb Sf
S2
S3 cylindrical pin
axial load
eccentric load
Fig. 6. Compression tests with axial and eccentric load: test configuration and instrumentation.
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Svf Shf
Svf Shf
Fig. 7. Compression tests: overview and details of the top and bottom restraints.
at the axis of an external concrete layer. In both cases the load is applied by means of four hydraulic jacks of 500 kN fixed to a reaction frame (Figs. 6 and 7). The hydraulic jacks are managed by means of a hydraulic control unit equipped with a pressure transducer to measure the applied load. A steel plate is placed between the panel and the actuators in order to distribute the load uniformly. Furthermore, metallic profiles are used to confine the reinforced concrete beams at the panel ends. Each panel is instrumented with two LVDTs (Svf and Svb), working in a range of ±50 mm, applied in an extensometric configuration to measure strain over a base length of 0.9 m. Three other transducers (S1, S2, S3) are placed horizontally at 1/4, 1/2 and 3/4 of the panel height to measure horizontal displacement. Finally, two transducers (S4, S5) are placed within the panel thickness, at an angle of 45° with respect to the vertical direction, at 3/4 of the panel height, in order to measure the relative displacement between the concrete layers (Fig. 6). Diagonal compression tests are carried out by means of a slide pushed by six hydraulic jacks. The panels, rotated 45°, are placed between the slide and the reaction frame (Figs. 8 and 9). To avoid any stress concentration, metallic L-shaped profiles are used to distribute the load at the panel corners. Also in this case the applied
Fig. 9. Diagonal compression test without and with prestressing load: test configuration and instrumentation.
load is measured using a pressure transducer. Each panel is instrumented with four LVDTs, working in a range of ±50 mm, placed vertically (Svf and Svb) and horizontally (Shf and Shb) on the front and back panel surfaces, in an extensometric configuration to measure strain over a base length of 500 mm. 2.4. Test results In this section the main results of the tests carried out on the wall panels are illustrated: first the results of the axial and eccentric compression tests and then the results of the diagonal compression tests are reported and discussed. As regards the compression tests, Fig. 10 shows the lateral deflections recorded by the LVDT at mid-height of the panels (S2) on the sixteen panel specimens under axial (continuous lines) and eccentric (dashed lines) increasing load. The firsts three graphs report the results of four
Fig. 8. Diagonal compression tests of panels without and with prestressing load.
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WP08
500 2a.1 2a.2
0 1000
2b.1 2b.2
WP16
500 4a.1 4a.2
0
5
10 15 20 Lateral deflection [mm]
4b.1 4b.2 25
WP12
500 3a.1 3a.2
0 1000
Load [kN]
Load [kN]
1000 Load [kN]
Load [kN]
1000
3b.1 3b.2
WPN08 WPH08
500 Y.2 X.2
0
5
Y.1 X.1
10 15 20 Lateral deflection [mm]
25
Fig. 10. Axial and eccentric compression tests: load-lateral deflection diagrams at mid-height of the panel.
Table 5 Compression tests with axial and eccentric loading: ultimate loads. Specimen
Panel type
Loading
Ultimate Load (kN)
Mean U.L. (kN)
Mean U.U.D.L. (kN/m)
2a.1 2a.2 3a.1 3a.2 4a.1 4a.2 X.2 Y.2 2b.1 2b.2 3b.1 3b.2 4b.1 4b.2 X.1 Y.1
WP08 WP08 WP12 WP12 WP16 WP16 WPN08 WPH08 WP08 WP08 WP12 WP12 WP16 WP16 WPN08 WPH08
Axial Axial Axial Axial Axial Axial Axial Axial Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric
701 783 806 844 855 907 736 765 375 401 460 545 524 630 461 591
742
662.5
825
736.6
881
786.6
388
657.1 683.0 346.4
503
448.7
577
515.2 411.6 527.7
1000
Ultimate Load [kN]
compression tests, two with axial and two with eccentric load, carried out on specimens of the same typology (standard panels) WP08, WP12, and WP16, respectively. The fourth graph shows the results of tests on panels with non-undulated polystyrene sheet (WPN08) and half a number of connectors (WPH08), one under axial load and the other under eccentric load. The maximum load (Ultimate Load) achieved in each test is reported in Table 5, together with the mean value of the ultimate load (Mean U.L.) reached by two specimens of the same typology, and the mean ultimate uniformly distributed load (Mean U.U.D.L.), i.e. the ultimate load divided by the panel width. In both the cases, with axial and eccentric load, the ultimate loads decrease by increasing the panel slenderness ratios, defined as L/h, where L is the total height and h the overall thickness of the panel, as shown in Fig. 11. It is worth noticing that in the case of the axial compression test the ultimate load of the panels is strongly influenced by any small undesired eccentricity due to imperfections in the specimen and test set-up (load, restraints, etc.). However, due to the large difference between the values of undesired and imposed eccentricity, the behaviour of the axially and eccentrically loaded panels are significantly dissimilar. In particular, as regards axially loaded specimens, the lateral deflection of the panel remains generally small under increasing loading (Figs. 10 and 12a) up to load values close to the ultimate load. Failure occurs as a result of overall buckling of the specimen,
axial load eccentric load
650
300 12
14
16
18
20
Slenderness ratio L/h Fig. 11. Influence of panel slenderness ratio on axial and eccentric ultimate loads.
due to compression, followed by the crushing of the concrete layer in compression and the rupture of the metallic mesh inside the other concrete layer, subjected to tension (Fig. 13a). As regards the eccentrically loaded specimens, Fig. 10 shows that the load vs lateral deflection plots are nearly linear at the earlier stages of loading; later, after the first crack has appeared, the panels exhibit a non-linear behaviour. The failure of the panel occurs, in this case, because of the rupture of the metallic mesh in the concrete layer in tension. However, a not very ductile behaviour was observed, since mesh failure occurs at the joints where the effective cross-section of the metallic wires may be reduced and the steel strength and ductility are lower due to welding (Fig. 13b and c). The different behaviour and different failure modes between wall panels under axial and eccentric loading are also shown in Fig. 14a which reports the displacement measured by the transducers Svf and Svb placed in a vertical position on the front and back faces of specimens 2a.1 and 2b.2. Continuous lines refer to tests with axial load (2a.1), dashed lines to tests with eccentric load (2b.2). In the case of axially loaded specimens, the two concrete layers initially behave in the same way, both characterised by shortening deformations; only during a second phase does the behaviour of the two concrete layers become different, with one concrete layer characterised by shortening deformation and the other by elongation. In the case of eccentrically loaded specimens a different behaviour is observed from the beginning of the test. In fact, with a low load level, the two concrete layers behave differently, one with shortening deformation and the other with elongation, and this denotes a predominant flexural behaviour of the panel. In Fig. 14b the longitudinal (slip) and transversal (separation) components of the relative displacement between the two
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3.0
150 kN 300 kN 450 kN 600 kN
3.0
150kN 300kN 450kN 600kN
4b.2
Wall height [mm]
Wall height [mm]
4a.2
0
0 20
0
20
20
Lateral deflection [mm]
0
20
Lateral deflection [mm]
(a)
(b)
Fig. 12. Lateral deflection at different load stages: (a) axial load and (b) eccentric load.
Fig. 13. Specimens after failure (a) axially and (b) eccentrically loaded; (c) mesh failure.
800
Svb 400
0 -3
Svf
Load [kN]
Load [kN]
800
Svf
Svb
2a.1 2b.2 0 Displacement [mm]
3
(a)
400
0 -0.5
2a.1 2b.2 0
Displacement [mm]
2
(b)
Fig. 14. (a) Vertical deformation of the two concrete layers and (b) slip and separation between the concrete layers in axially and eccentrically loaded specimens.
concrete layers of the above mentioned specimens 2a.1 and 2b.2 are plotted, for increasing axial (continuous line) and eccentric (dashed line) loadings. These components are calculated from the vectorial decomposition of the displacement recorded by transducers S4 and S5. The
longitudinal slip exhibits an initial nearly linear behaviour followed by a non-linear behaviour until ultimate values of about 1.5 mm. Compared to the slip, the separation is characterised by much lower values, which are practically negligible, meaning that the two concrete layers deflect together.
F. Gara et al. / Engineering Structures 37 (2012) 193–204 Table 6 Diagonal compression tests: cracking load, ultimate load, and failure modes. Specimen
First cracking load (kN)
Failure load (kN)
Failure modes
5.1 5.2 5.3 5.4 C1 C2
144 129 118 168 103 137
302 342 332 306 341 225
a* a a a b b*
a – localised concrete crushing; b – failure due to diagonal tension. * Failure of one of the two concrete layers.
The high values of the ultimate loads obtained, the influence of the slenderness ratio on the ultimate loads as well as the low values of relative displacement between the concrete layers confirm that these wall panels behave as semi-composite elements. However, some aspects deserve to be discussed. First of all, it is worth noticing that the slip between the two concrete layers is restricted not only by the shear deformable internal layer but also by the solid reinforced concrete beams at the bottom and top ends of the panels. Consequently, the results of the tests presented in this paper may be considered as representative only for real buildings in which the connections between floor and wall panels are built with solid reinforced concrete regions. Furthermore, it is important to underline that the reinforced concrete beams at the panel ends also cause a higher degree of flexural restraint between the floor and wall panels, which may lead to high values of vertical load eccentricity and, thus, to ultimate loads significantly lower than the values obtained in the tests. With regard to the tests on WPN08 and WPH08 wall panels, under both axial and eccentric load, the values of ultimate loads are similar to or higher than those obtained by standard panels WP08. These panels can therefore be considered as valid alternatives for standard panels even if a greater number of specimens should be tested to arrive at some general conclusions. As regards the diagonal compression tests, Table 6 reports the first cracking load, the failure load and the failure modes. It is worth noticing that specimens 5.1 and C2 were characterised by premature failure of one of the two concrete layers of the panels, due to a small undesired eccentricity of the axial load. For this reason, these results are not taken into consideration in the following comments. High first cracking loads were observed for all the specimens, while concerning the ultimate load the only significant result is that provided by specimen C1, which is the only one
201
reaching a diagonal tensile failure. In fact, for the other specimens concrete crushing occurred at the load application point. Specimen C1, which is similar to specimen 5.2 but with transversal stiffening walls, nearly simulates a pure shear test thanks to the diffusion of the vertical load along the panel perimeter guarantee by the transversal walls. The highest stress values are reached in the central part of panel C1, where tensile and compression stress values are similar. Diagonal tensile failure occurred with a load of 341 kN. In Fig. 15a the largest crack is marked with a thick dashed line. On the contrary, for specimen 5.2, a concentration of the compression stresses occurred around the load application point, causing the crushing of the concrete at a load value of 342 kN, as shown in Fig. 15b. The influence of transversal walls can also clearly be seen in Fig. 16 where both the vertical shortening deformation (Svf and Svb) and the horizontal elongation (Sof and Sob) measured on the two sides of specimen C1 (with transversal walls) (Fig. 16a) and specimen 5.2 (without transversal walls) (Fig. 16b) are reported. In the panel with transversal walls, at the first stage of loading, the average horizontal elongation is nearly equal to the vertical shortening deformation; later, after the cracking of the concrete layer, it becomes larger. On the contrary, in panels without transversal walls, at the first stage of loading, the average horizontal elongation is lower than the vertical shortening and becomes similar after concrete cracking. The effects of prestressing can be observed in the results of tests on specimens 5.3 and 5.4, prestressed with forces of 30 kN and 90 kN respectively. The first concrete cracking appeared at a slightly higher load for specimen 5.4 than for specimen 5.3. However, a lower failure load was achieved by specimen 5.4 than by specimen 5.3, since the prestressing force incremented the compression stresses around the load application point where the failure occurred. Finally, it may be noticed that in all the tests performed, failure did not occur suddenly but was always preceded by extensive diffuse concrete cracking. All the specimens were in fact already micro-cracked before the tests, due to concrete shrinkage and specimen handling. The micro-cracks constitute weak zones in the concrete where cracks may preferentially occur. Nevertheless, the specimens revealed a high capacity for stress redistribution thanks to the metallic mesh inside the concrete layers. However, it should be underlined that the results considered here are relevant to tests on symmetrically loaded panels, with the two concrete layers equally loaded; in reality this is an ideal condition
Fig. 15. Diagonal compression test: crack pattern at failure for panels (a) with and (b) without transversal stiffening walls.
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400
Sof 200
0
Sof
Svf Sob
Load [kN]
Load [kN]
400
Svb
0
Sob
200
C1 -4
0
2
Svf Svb
5.2 0
-4
Displacement [mm]
2
Displacement [mm]
(a)
(b)
Fig. 16. Diagonal compression test: vertical shortening and transversal elongation of panels with (C1) and without (5.2) transversal stiffening walls.
that can only occur when concrete layers are connected by reinforced concrete beams.
3. Numerical simulation Compression tests were numerically simulated with a displacement based non-linear static analysis taking into account both geometrical and material non-linearities, performed with the structural analysis programme Seismostruct [21]. Specimens were modelled with non-linear finite element models. In particular 20 beam elements were used for each concrete layer. The nodes at each end of the two concrete layers were joined with two rigid elements to simulate the reinforced concrete beams while the internal nodes were joined with shear elastic links. The links are axially rigid and shear deformable with the shear stiffness provided by the internal layer (Fig. 17). The specimen is restrained with a cylindrical pin at the base and a horizontal support at the top. In simulating axial compression tests a small eccentricity of the vertical was considered in order to simulate geometrical imperfections of panels and uncertainties of the load position. To simulate eccentric compression tests the load was applied at the axis of a concrete layer (Fig. 17). In both cases the vertical load was applied incrementally until failure of the sample was reached.
axial load
eccentric load
15 15 300 cm
beam element
shear deformable link ( Kl)
rigid link hl
hl
Fig. 17. Finite element model for compression tests.
A non-linear constitutive law [22] was considered for the concrete and a symmetric elasto-perfectly-plastic bilinear model for the steel. The values of the mechanical parameters were determined from the results of the tests performed on the materials (paragraph 2.1). In particular the shear stiffness of the links joining the two concrete layers was calculated by the equation
Ki ¼
GAl hl c c
ð2Þ
where G = 3.2 N/mm2 is the mean value among those obtained with the shear tests for material characterisation, Al is the influence area of the links, c is the internal layer thickness and the factor hl/c takes into account the difference between the length (hl) of the links and c (Table 7). In Fig. 18 the load vs lateral deflection graphs obtained from compression tests are compared with the results obtained from the numerical analysis. The behaviour of eccentrically loaded panels is well-approximated by the numerical model while for axially loaded panels a lower agreement between experimental and numerical results is achieved. In fact, the behaviour and the ultimate loads of real panels are largely influenced by geometrical imperfections (not perfectly flat concrete layers, variability of thicknesses, etc.) that are difficult to evaluate and take into consideration in a numerical model. However the numerical simulations may be considered satisfactory. Furthermore, in order to evaluate the critical load Pb1 of panels, a buckling analysis was also carried out using the same numerical model but considering a linear elastic behaviour of the materials. Values of the buckling loads obtained with these analyses (Pb1) are reported in Table 8 and also in Fig. 18. It can be observed that the Pb1 values seem to be approached by the curves obtained with the non-linear models, considering approximately axial loads. In order to highlight the semi-composite behaviour of the panels, the values of the Euler buckling load (Pb2), calculated in the hypothesis of zero shear stiffness of the links are reported in Table 8 (values of Pb2 are twice the Euler buckling load for a single concrete layer). Furthermore, the buckling load Pb3 are reported in the same table, where Pb3 was calculated by considering the panel to be entirely made of concrete. The coefficient a = Pb1/Pb3 was introduced to easily estimate the buckling load of the panels. As expected, the values of this coefficient are less than 1 and decrease as the thickness of the internal layer increases. However, only in the case of undesired eccentricity, buckling loads are close to the ultimate loads. In fact, due to the pronounced non-linear behaviour of the materials, the ultimate load of the eccentrically loaded panels is significantly lower than the buckling load and can be estimated only with a non-linear analysis which considers both geometrical and material non-linearities. Obviously the reduction in the ultimate load will be more significant for greater values of load eccentricity. As already mentioned, the value
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F. Gara et al. / Engineering Structures 37 (2012) 193–204 Table 7 Characteristics of the numerical model. WP08
WP12
WP16
115 9660
155 5786
195 4095
experimental
Load [kN]
hl (mm) Kl (N/mm)
400
200
f.e.m. (Ec) f.e.m. (0.4Ec)
C1
0
1300
Displacement [mm]
2
Load [kN]
Pb1 = αPb3 Fig. 19. Diagonal compression tests: comparison between experimental and numerical results.
f.e.m. 2a.1 650
2a.1
2b.2
well-simulated by the model with the original concrete elastic modulus Ec. At this load a first crack appeared which was associated with a distinct horizontal segment in the load and displacement plot. After the first crack, the experimental curve is non-linear due to the progressive cracking of the concrete. The numerical model with a reduced elastic modulus (0.4Ec) simulates quite well the global behaviour of the cracked panel. The ultimate load may be estimated by simplified formulas found in technical scientific literature. In particular for the diagonal compression test the following formula may be used:
f.e.m. 2b.2 0 1300
Load [kN]
Pb1 = αPb3 3a.2 f.e.m. 3a.2 3b.2
650
f.e.m. 3b.2
Load [kN]
0 1300
Pb1 = αPb3
f.e.m. 4a.1 4a.1
Pu ¼ 2Bstot fct ¼ 4b.2
650
f.e.m. 4b.2
0
5
10
15
20
25
Displacement [mm] Fig. 18. Axial and eccentric load tests: comparison between experimental and numerical results.
Table 8 Critical loads and reduction coefficient. Specimen
Mean U.L. (kN)
Pb1 (kN)
Pb2 (kN)
Pb3 (kN)
a
WP08 WP12 WP16
742 825 881
931 1082 1221
92.8 92.8 92.8
3653 7424 13,169
0.25 0.15 0.09
of the load eccentricity depends on the rotational restraint between the wall and floor panels. With regard to the diagonal compression tests, the behaviour of the specimen with the transversal concrete wall (C1) was numerically simulated with an elastic finite element model using the structural analysis programme SAP2000 [23]. The panel was modelled with shell elements with a thickness equal to the overall thickness of the two concrete layers and with an elastic modulus equal to that of the concrete used. The transversal concrete walls were modelled with beam elements. Vertical static loads were applied on several nodes for a total force equal to the ultimate load experimentally obtained (341 kN). The value of the horizontal tension in the central node of the model is 2.3 N/mm2 which is nearly equal to the ultimate tensile strength of the concrete. In Fig. 19 the load-shortening plot experimentally obtained is compared with the results obtained with the numerical model, considering an elastic modulus Ec and a reduced modulus 0.4Ec to take into account the cracking of the concrete. Up to a load of about 100 kN the behaviour of the specimen is typically linear elastic and is
2 1120 70 2:3 ¼ 360 kN 1000
ð3Þ
where B is the width of the panel and stot is the overall thickness of the concrete layers. The result is close to the ultimate load experimentally evaluated for specimen C1. However, in real buildings, the strength of panels under vertical and horizontal forces involves not only the shear resistance but also the bending resistance, depending on the overall dimensions of the wall. Moreover, the influence of openings for doors and windows must be considered. 4. Conclusions The results of an experimental campaign on completed in situ sandwich panels with no-shear connectors, used as wall panels, have been presented. In particular, compression tests with axial and eccentric load and diagonal compression tests were performed. Some numerical simulations with linear and non-linear finite element models were also carried out. As regards compression tests, wall panels with different internal layer thickness (WP08, WP12, WP16) and with two different configurations (WPN and WPH) were tested. High ultimate loads, decreasing for increasing values of the slenderness ratios, were obtained. The numerical simulations indicated that the ultimate loads of axially loaded panels are close to the buckling loads which can be determined by performing a linear buckling analysis or by using the coefficient a. Differently, the ultimate loads of eccentrically loaded panels, which are significantly lower than the buckling loads, can be simulated only by performing a non-linear analysis. Additional research is needed to develop simple, effective and rational methods for predicting the ultimate load of wall panels for different values of load eccentricity. The results of the experimental tests and numerical simulations indicated that a partial degree of composite behaviour was attained by the tested panels even if non-shear connectors are used in the interior layer. However, this semi-composite behaviour is due not only to the internal layer, but also to the reinforced concrete beams at the ends of the panels. Additional investigations are needed to develop simple, effective and rational methods for predicting the ultimate load of wall panels for different values of load eccentricity and to study the behaviour of panels without reinforced concrete beams.
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As regards diagonal compression tests, simple wall panels, prestressed wall panels and panels with transversal stiffening walls were tested. In all these cases high cracking loads were observed. The panels also showed a high capacity for stress redistribution thanks to the metallic mesh inside the concrete layers. However, only one specimen with transversal stiffening walls showed a tensile diagonal rupture while the other specimens showed a compression failure at the load application region. The numerical simulation of the test reaching the tensile diagonal rupture showed that an effective concrete modulus of elasticity may be considered to simulate the global behaviour of the cracked panel and that the ultimate load may be estimated on the basis of the tensile strength of the concrete. However, since in real buildings the behaviour of the panels under vertical and horizontal in-plane forces is strongly influenced by the overall dimensions of the wall and by openings for doors and windows, further investigations on panels with different configurations are recommended. Acknowledgments The financial support provided by ‘‘Schnell House’’ S.p.A., based in San Marino, is gratefully acknowledged. The technical support of the laboratory staff at the Dept. of Architecture, Construction and Structures, Università Politecnica delle Marche, is greatly appreciated. The opinions, findings and conclusions contained in this paper are those of the authors, and do not necessarily reflect the views of the sponsors. References [1] Ranzi G. Locking problems in the partial interaction analysis of multi-layered composite beams. Eng Struct 2008;30:2009–911. [2] Sousa Jr JBM, da Silva AR. Analytical and numerical analysis of multilayered beams with interlayer slip. Eng Struct 2010;32:1671–80. [3] Gara F, Ranzi G, Leoni G. Displacement-based formulations for composite beams with longitudinal slip and vertical uplift. Int J Numer Methods Eng 2006;65:1197–220. [4] Schnabl S, Saje M, Turk G, Planinc I. Analytical solution of two-layer beam taking into account interlayer slip and shear deformation. J Struct Eng, ASCE 2007;133(6):886–95.
[5] PCI Committee on Precast Concrete Sandwich Wall Panels. State of the art of precast/prestressed sandwich wall panels. PCI J 1997;42(2):92–133. [6] Benayoune A, Aziz A, Samad A, Trikha DN, Abdullah Abang Ali A, Ashrabov AA. Structural behaviour of eccentrically loaded precast sandwich panels. J Constr Build Mater 2006;20:713–24. [7] Benayoune A, Samad AA, Abang Ali AA, Trikha DN. Response of pre-cast reinforced composite sandwich panels to axial loading. J Constr Build Mater 2007;21:677–85. [8] Benayoune A, Abdul Samad AA, Trikha DN, Abang Ali AA, Ellinna SHM. Flexural behaviour of pre-cast concrete sandwich composite panel – experimental and theoretical investigations. J Constr Build Mater 2008;22:580–92. [9] Salmon DC, Einea MK, Tadros A, Culp TD. Full scale testing of precast concrete sandwich panels. ACI J 1997;94:354–62. [10] Einea A, Salmon DC, Tadros MK, Culp TD. A new structurally and thermally efficient precast sandwich panel system. PCI J 1994;39(4):90–101. [11] Bush TD, Stine GL. Flexural behaviour of composite precast sandwich panels with continuous truss connectors. PCI J 1994;39(2):112–21. [12] Kabir MZ. Mechanical properties of 3D wall panels under shear and flexural loading. In: 4th Structural specialty conference of the Canadian society for civil engineering, Montreal; 2002. [13] Giacchetti R, Menditto G. Indagini sperimentali su pannelli sandwiches realizzati con la tecnica dello spritzbeton. Atti V Convegno CTE, Firenze; 1984. p. b.13–b.24 [in Italian]. [14] Ceccoli C, Mazzotti C, Savoia M, Dallavalle G, Perazzini G, Tomassoni C. Indagini sperimentali su una tipologia di pannelli in c.a. alleggeriti gettati in opera. Atti XIV Convegno CTE, Mantova; 2002. p. 557–67 [in Italian]. [15] Bassotti O, Ricci M. Caratteristiche di pannelli sandwich in cls. alleggerito e loro applicazioni costruttive. Atti XIV Convegno CTE, Mantova; 2002. p. 579– 87 [in Italian]. [16] Refaifar O, Kabir MZ, Taribakhsh M, Tehranian A. Dynamic behaviour of 3Dpanel single-storey system using shaking table testing. Eng Struct 2008;30:318–37. [17] EN ISO 12504-1. Testing concrete in structures. Cored specimens. Taking, examining and testing in compression. CEN European Committee for Standardization; 2000. [18] EN 12390-6. Testing hardened concrete. Tensile splitting strength of test specimens. CEN European Committee for Standardization; 2000. [19] EN ISO 15630-2. Steel for the reinforcement and prestressing of concrete – test methods – part 2: welded fabric. CEN European Committee for Standardization; 2002. [20] ASTM C273/C273M-07. A standard test method for shear properties of sandwich core materials. Committee D30.09 on Sandwich Construction; 2007. [21] Seimosoft Seimostruct. A computer program for static and dynamic nonlinear analysis of framed structures; 2004.
Contents lists available at SciVerse ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Experimental tests and numerical modelling of wall sandwich panels Fabrizio Gara ⇑, Laura Ragni, Davide Roia, Luigino Dezi Dept. of Civil and Construction Engineering and Architecture, Università Politecnica delle Marche, via Brecce Bianche, 60131 Ancona, Italy
a r t i c l e
i n f o
Article history: Received 23 July 2011 Revised 15 November 2011 Accepted 2 December 2011 Available online 4 February 2012 Keywords: Sandwich panels Bearing wall panels Full scale compression test Diagonal compression test Finite element analysis
a b s t r a c t This paper presents the first part of an experimental investigation carried out on a construction system based on completed in situ sandwich panels with non-shear connectors, concerning the study of vertical panels used as structural walls. Compression tests with axial and eccentric loads were carried out on several full scale panel specimens with different slenderness ratios in order to study the behaviour of panels under vertical in-plane forces. Additionally, diagonal compression tests were performed on square specimens in different configurations in order to study the behaviour of panels under horizontal in-plane forces. The most significant load–displacement diagrams for increasing load are illustrated and the failure modalities are discussed. The semi-composite behaviour of the panels, guaranteed by the internal layer of polystyrene and the reinforced concrete beams at the panel ends, is highlighted. Finally, some numerical simulations are performed with non-linear finite element models and some useful design indications are given. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Construction systems based on sandwich panels are commonly used worldwide for intensive building production. Sandwich panels are typically constituted by two concrete layers which are separated by an internal insulation layer of various materials (i.e. expanded and extruded polystyrene, rigid polyurethane foam) and are usually joined with ‘‘shear connectors’’ (i.e. truss connectors) able to transfer the longitudinal interface shear between the layers so as to ensure a fully-composite or a semi-composite behaviour of the sandwich panel. This paper deals with a construction system that utilises sandwich panels, both for structural walls and floors, which are obtained by self-supporting reinforced insulation layers completed in situ with spritz-beton. The prefabricated modular elements are made of an undulated (corrugated) layer of expanded polystyrene, with suitable density, reinforced by two metallic meshes connected by means of orthogonal steel wires welded to the meshes (steel connectors). Thanks to the easy and fast mounting procedures, this construction system presents some technical advantages that make it often competitive in comparison with traditional methods or precast systems. From a structural point of view these panels are characterised by orthogonal connectors (‘‘no-shear connectors’’) so that their semi-composite behaviour depends on the shear stiffness of the expanded polystyrene layer and, above all,
⇑ Corresponding author. Tel.: +39 071 2204550; fax: +39 071 2204576. E-mail addresses: [email protected] (F. Gara), [email protected] (L. Ragni), [email protected] (D. Roia), [email protected] (L. Dezi). 0141-0296/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2011.12.027
on construction details, such as reinforced concrete regions at the panel ends. The structural behaviour of such a sandwich panel can be theoretically studied by means of analytical models which are usually referred to in the literature as models for multilayered beams [1,2] or two-layers composite beams [3,4] with deformable interlayer connection. As this paper deals with experimental investigation, a literature review of theoretical models is beyond the scope of this paper and only some of the most recent works are cited as example from which a comprehensive list of references describing these models may be founded. However the behaviour of single sandwich panels is obviously much easier to predict than the behaviour of panels constituting real building walls. To evaluate the structural performances of buildings constructed with this kind of construction system, in addition to specific modelling taking into account the semi-composite behaviour of the sandwich panels, other aspects need to be considered in the numerical evaluations, like (i) the restrain degree of wall-floor node depending on the connection details and (ii) the bi-dimensional behaviour of the panels which are each-other connected in real buildings. For this purpose, experimental results of full scale tests, are an essential instrument to calibrate both theoretical methods and numerical models. In the technical literature several experimental campaigns on precast sandwich panels with shear connectors can be found [5–13]. On the contrary, very few experimental tests have been performed on sandwich panels with in situ sprayed concrete and no-shear connectors [14,15] and on 3D full scale mock-up [16] in order to study the behaviour of the panels in real structures. Consequently, general conclusions on the structural behaviour of this
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F. Gara et al. / Engineering Structures 37 (2012) 193–204
construction system cannot be drawn and further experimental investigations are needed. For this reason, an extensive experimental campaign, including a large number of tests on floor and wall panels, cyclic tests on wall-floor connections and a load test on the floor of a full scale 3D mock-up, has been carried out. This first paper refers only to tests performed on wall panels. In particular, the results of compression tests with axial and eccentric loads carried out on panels with an internal layer of different thickness, are presented. After that, the experimental results obtained on panels with non-undulated polystyrene sheet and on panels with undulated polystyrene sheet and half the number of connectors are discussed. Additionally, the results of diagonal compression tests carried out on square specimens of different configurations in order to study the behaviour of panels under horizontal in-plane forces are illustrated: wall standard panels, as well as wall panels externally prestressed to simulate the effects of vertical loads and panels stiffened with four orthogonal walls to simulate the behaviour of the wall in a real building are considered. For each test, the load–displacement diagram and the failure modalities are examined. Finally some numerical simulations, performed with non-linear finite element models, are also reported and some useful design indications are given. 2. Experimental campaign The sandwich panels considered in this study are made of a sheet of polystyrene reinforced by two 80 mm 75 mm metallic meshes assembled by means of steel connectors. The sheet of polystyrene has an undulated profile and density of about 15–25 kg/ m3. The galvanised welded wire meshes and the connectors welded orthogonally to the meshes, are made with U3 wires of high yield steel. Wall panels (WP) were completed simply by spraying concrete onto the external surfaces of the sheet, first up to the metallic mesh and then up to the final thickness of the concrete layer, using manual tools or pumps (Fig. 1). A ready-mixed concrete, with sand no greater than 3 mm and specific additives to improve adhesion and workability, was used. 2.1. Mechanical properties of materials In order to evaluate the mechanical properties of the used materials, several tests were carried out on concrete, metallic meshes and internal layer consisting of a polystyrene sheet and metallic connectors.
wire meshes
Table 1 Mean values of material properties. Prismatic specimens (MPa)
Cored specimens (MPa)
Metallic meshes (MPa)
fcu = 21.95 fcfm = 5.52
fcu = 25.10 fct = 2.40
fm = 769.00 Agt = 7.62
The concrete was characterised by means of tests on 40 40 160 mm specimens sampled during the cast, and tests on cored specimens with a diameter of 94 mm and length of 250 mm sampled from the reinforced concrete beams at the ends of the panel after the concrete curing. In accordance with EN ISO 12504-1 [17], bending tests were first carried out to evaluate the flexural strength of the rectangular specimens, then the two resultant parts of the specimens were used for compression tests. A total number of eight specimens were prepared so that eight flexural tensile tests and sixteen compression tests were performed. Table 1 reports the mean values of the compression (fcu) and flexural tensile concrete strength (fcfm). The cored specimens were divided into two sets, one of which was subjected to the compression test and the other to the indirect tensile splitting test, in accordance with EN 12390-6 [18]. Four cored specimens were sampled and, consequently, four compression tests and four tensile splitting tests were performed. The average values of compression strength (fcu) and tensile concrete strength (fct) are reported in Table 1. From these specimens, a mean value of 10500 MPa for the concrete elastic modulus (Ec) was also estimated. Tensile tests and weld shear strength tests were carried out on six samples of metallic meshes following EN ISO 15630-2 [19]. Four samples reached the yield stress showing a very low ductility (less than 2). The mean values of tensile strength (fm) and percentage elongation at failure (Agt) are reported in Table 1. The other two samples showed a brittle fracture and a strength value which was about 20% lower than the yielding strength. It is worth noticing that the failure of all the mesh samples occurred at a welded joint as a consequence of the welding disturbs. Finally, the weld shear strength tests gave an average shear force of 2.64 kN, which is 1.25 times greater than the wire yielding force, as prescribed by the code. The mechanical properties of the internal layer were obtained by means of shear tests according to the Standard Test Method for Shear Properties of Sandwich Core Materials [20]. Samples with dimensions of 400 445 mm made of three concrete layers and two internal layers were tested. In
concrete layers
steel connectors polystyrene
(a)
(b)
(c)
Fig. 1. ‘‘Concrewall’’ wall sandwich panels: (a) schematic sketch of the components; (b) concrete spraying onto the external surfaces up to the metallic mesh and (c) up to the final thickness.
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(a) 30
3S (160 mm)
1S (80 mm)
5S (160 mm)
Load [kN]
1S (80 mm)
Load [kN]
30
0
Displacement [mm]
0
5
Displacement [mm]
5
(b) Fig. 2. Shear tests: (a) test configuration and (b) load–displacement cycles.
particular, eight samples were considered with internal layers of different thickness and with a different number of connectors. Subsequently, the polystyrene sheets of four samples were dissolved in order to obtain samples with metallic connectors only. Load and unload cycles were performed up to failure (Fig. 2a). Slipping between the concrete layers was measured by means of two LVDTs and the applied load was determined by means a pressure transducer. In Fig. 2b load–displacement graphs are illustrated with reference to samples 1S and 3S, with polystyrene sheet thickness of 80 mm and 160 mm respectively, and sample 5S which is similar to sample 1S but without the polystyrene sheets. By comparing the results of the tests on 1S and 3S samples it is evident that the stiffness decreases considerably when the thickness of the internal layer increases, whereas by comparing the results of 1S and 5S samples it can be observed that the contribution of connectors is negligible with respect to the contribution of the polystyrene. For each test the initial shear modulus was calculated by means of
Gi ¼
Ki hi 2Ai
ð1Þ
where Ki is the initial stiffness of the sample, and hi and Ai the thickness and the area of each internal layer. Table 2 shows all the obtained results.
Table 2 Shear tests: samples and results. Sample
hi (mm)
Polystyrene
Connectors
Ki (kN/mm)
Gi (N/mm2)
1S 2S 3S 4S 5S 6S 7S 8S
80 120 160 80 80 120 160 80
Yes Yes Yes Yes No No No No
Double Double Double Single Double Double Double Single
15.70 9.20 7.30 12.80 0.47 0.15 0.07 0.20
3.45 3.03 3.20 2.81 0.10 0.04 0.03 0.04
2.2. Panel geometry A total of twenty two panels were built: sixteen for compression tests with axial and eccentric load and six for diagonal compression tests. The panels for compression tests had a total height of 2940 mm, a width of 1120 mm and concrete layer thickness of 35 mm. To avoid stress concentrations and to facilitate the handling operations two reinforced concrete beams were built at the ends of the panels by dissolving a portion of the polystyrene sheet in order to obtain a proper anchorage of the meshes (Fig. 3). For the compression tests, wall panels (WP) with three different
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120
Table 3 Geometric characteristics of panels for compression tests.
4φ8 φ6/200mm
A
120
2700 mm
2940 mm
A
35 1120 mm
35 mm c h
Fig. 3. Panel for compression tests.
thicknesses of the internal layer, 80 mm (WP08), 120 mm (WP12) and 160 mm (WP16), were built. For each thickness, two panels were tested under axial load and two under eccentric load. In addition, two different kinds of wall panel were prepared for the compression tests: the WPN panel with a non-undulated polystyrene layer and the WPH panel with half the number of connectors (Fig. 4). In these cases only one compression test with axial load
Specimen
Panel
Compression loading
c (mm)
h (mm)
2a.1 2a.2 3a.1 3a.2 4a.1 4a.2 X.2 Y.2 2b.1 2b.2 3b.1 3b.2 4b.1 4b.2 X.1 Y.1
WP08 WP08 WP12 WP12 WP16 WP16 WPN08 WPH8 WP08 WP08 WP12 WP12 WP16 WP16 WPN08 WPH08
Axial Axial Axial Axial Axial Axial Axial Axial Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric
80 80 120 120 160 160 80 80 80 80 120 120 160 160 80 80
150 150 190 190 230 230 150 150 150 150 190 190 230 230 150 150
and one with eccentric load were performed for each kind of panel. The list of all the panels with the overall thickness (h), the internal layer thickness (c), and the kind of test performed are reported in Table 3. For the diagonal compression tests, only 1120 mm 1120 mm WP08 panels were considered since the thickness of the internal layer does not influence the panel behaviour under in-plane forces. In addition, prestressed and transversally stiffened panels were considered in order to simulate the effects of vertical load and the stiffening contribution of walls and floors orthogonal to the panels, respectively. To better distribute the compression load, two triangular reinforced concrete regions at two opposite corners of the standard wall panels (Fig. 5a) and two reinforced concrete L-shaped beams in the stiffened panels (Fig. 5b) were built. In the prestressed panels two steel threaded bars are applied with prestressing loads of 30 kN and 90 kN. The list of all the specimens with overall thickness (h), internal layer thickness (c), prestressing forces and loading type are reported in Table 4.
Section B-B WP08
B A
WPH08
A
40
B
80 15
wire meshes φ3 150
WP08
150
Section A-A
80
polystyrene
80
80
concrete
40 1120 1245
WPN08
Fig. 4. Details of WP, WPN and WPH panels.
150
150
75
20
20
φ3
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1120 mm
1120 mm
Section A-A
4φ8 φ6/200mm
Section A-A
1420 mm
A A
A 1120 mm
A
150
(a)
1120 mm
(b)
Fig. 5. Panels for diagonal compression tests: (a) wall panel and (b) transversally stiffened panel.
Table 4 Geometric characteristics of panels for diagonal compression tests.
a
Specimen
Panel
Compression loading
Prestressing load (kN)
c (mm)
h (mm)
5.1 5.2 5.3 5.4 C.1 C.2
WP08 WP08 WP08 WP08 WP08a WP08a
Diagonal Diagonal Diagonal Diagonal Diagonal Diagonal
– – 30 90 – –
80 80 80 80 80 80
150 150 150 150 150 150
With traversal stiffening walls.
2.3. Test configuration and instrumentation For the compression tests the configuration of Fig. 6 was adopted: panels were placed vertically with the bottom end pinned (cylindrical pin) and the top end restrained so as to prevent lateral
displacement. This static scheme simulates the restraint condition of panels in real multi-storey buildings when connections between floor and wall panels produce negligible bending moments. In the axial compression tests the load is applied at the panel axis, while in the eccentric compression test the load is applied
reaction frame S4
hydraulic jacks
S5 S1 Svf
Svb Sf
S2
S3 cylindrical pin
axial load
eccentric load
Fig. 6. Compression tests with axial and eccentric load: test configuration and instrumentation.
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Svf Shf
Svf Shf
Fig. 7. Compression tests: overview and details of the top and bottom restraints.
at the axis of an external concrete layer. In both cases the load is applied by means of four hydraulic jacks of 500 kN fixed to a reaction frame (Figs. 6 and 7). The hydraulic jacks are managed by means of a hydraulic control unit equipped with a pressure transducer to measure the applied load. A steel plate is placed between the panel and the actuators in order to distribute the load uniformly. Furthermore, metallic profiles are used to confine the reinforced concrete beams at the panel ends. Each panel is instrumented with two LVDTs (Svf and Svb), working in a range of ±50 mm, applied in an extensometric configuration to measure strain over a base length of 0.9 m. Three other transducers (S1, S2, S3) are placed horizontally at 1/4, 1/2 and 3/4 of the panel height to measure horizontal displacement. Finally, two transducers (S4, S5) are placed within the panel thickness, at an angle of 45° with respect to the vertical direction, at 3/4 of the panel height, in order to measure the relative displacement between the concrete layers (Fig. 6). Diagonal compression tests are carried out by means of a slide pushed by six hydraulic jacks. The panels, rotated 45°, are placed between the slide and the reaction frame (Figs. 8 and 9). To avoid any stress concentration, metallic L-shaped profiles are used to distribute the load at the panel corners. Also in this case the applied
Fig. 9. Diagonal compression test without and with prestressing load: test configuration and instrumentation.
load is measured using a pressure transducer. Each panel is instrumented with four LVDTs, working in a range of ±50 mm, placed vertically (Svf and Svb) and horizontally (Shf and Shb) on the front and back panel surfaces, in an extensometric configuration to measure strain over a base length of 500 mm. 2.4. Test results In this section the main results of the tests carried out on the wall panels are illustrated: first the results of the axial and eccentric compression tests and then the results of the diagonal compression tests are reported and discussed. As regards the compression tests, Fig. 10 shows the lateral deflections recorded by the LVDT at mid-height of the panels (S2) on the sixteen panel specimens under axial (continuous lines) and eccentric (dashed lines) increasing load. The firsts three graphs report the results of four
Fig. 8. Diagonal compression tests of panels without and with prestressing load.
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WP08
500 2a.1 2a.2
0 1000
2b.1 2b.2
WP16
500 4a.1 4a.2
0
5
10 15 20 Lateral deflection [mm]
4b.1 4b.2 25
WP12
500 3a.1 3a.2
0 1000
Load [kN]
Load [kN]
1000 Load [kN]
Load [kN]
1000
3b.1 3b.2
WPN08 WPH08
500 Y.2 X.2
0
5
Y.1 X.1
10 15 20 Lateral deflection [mm]
25
Fig. 10. Axial and eccentric compression tests: load-lateral deflection diagrams at mid-height of the panel.
Table 5 Compression tests with axial and eccentric loading: ultimate loads. Specimen
Panel type
Loading
Ultimate Load (kN)
Mean U.L. (kN)
Mean U.U.D.L. (kN/m)
2a.1 2a.2 3a.1 3a.2 4a.1 4a.2 X.2 Y.2 2b.1 2b.2 3b.1 3b.2 4b.1 4b.2 X.1 Y.1
WP08 WP08 WP12 WP12 WP16 WP16 WPN08 WPH08 WP08 WP08 WP12 WP12 WP16 WP16 WPN08 WPH08
Axial Axial Axial Axial Axial Axial Axial Axial Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric Eccentric
701 783 806 844 855 907 736 765 375 401 460 545 524 630 461 591
742
662.5
825
736.6
881
786.6
388
657.1 683.0 346.4
503
448.7
577
515.2 411.6 527.7
1000
Ultimate Load [kN]
compression tests, two with axial and two with eccentric load, carried out on specimens of the same typology (standard panels) WP08, WP12, and WP16, respectively. The fourth graph shows the results of tests on panels with non-undulated polystyrene sheet (WPN08) and half a number of connectors (WPH08), one under axial load and the other under eccentric load. The maximum load (Ultimate Load) achieved in each test is reported in Table 5, together with the mean value of the ultimate load (Mean U.L.) reached by two specimens of the same typology, and the mean ultimate uniformly distributed load (Mean U.U.D.L.), i.e. the ultimate load divided by the panel width. In both the cases, with axial and eccentric load, the ultimate loads decrease by increasing the panel slenderness ratios, defined as L/h, where L is the total height and h the overall thickness of the panel, as shown in Fig. 11. It is worth noticing that in the case of the axial compression test the ultimate load of the panels is strongly influenced by any small undesired eccentricity due to imperfections in the specimen and test set-up (load, restraints, etc.). However, due to the large difference between the values of undesired and imposed eccentricity, the behaviour of the axially and eccentrically loaded panels are significantly dissimilar. In particular, as regards axially loaded specimens, the lateral deflection of the panel remains generally small under increasing loading (Figs. 10 and 12a) up to load values close to the ultimate load. Failure occurs as a result of overall buckling of the specimen,
axial load eccentric load
650
300 12
14
16
18
20
Slenderness ratio L/h Fig. 11. Influence of panel slenderness ratio on axial and eccentric ultimate loads.
due to compression, followed by the crushing of the concrete layer in compression and the rupture of the metallic mesh inside the other concrete layer, subjected to tension (Fig. 13a). As regards the eccentrically loaded specimens, Fig. 10 shows that the load vs lateral deflection plots are nearly linear at the earlier stages of loading; later, after the first crack has appeared, the panels exhibit a non-linear behaviour. The failure of the panel occurs, in this case, because of the rupture of the metallic mesh in the concrete layer in tension. However, a not very ductile behaviour was observed, since mesh failure occurs at the joints where the effective cross-section of the metallic wires may be reduced and the steel strength and ductility are lower due to welding (Fig. 13b and c). The different behaviour and different failure modes between wall panels under axial and eccentric loading are also shown in Fig. 14a which reports the displacement measured by the transducers Svf and Svb placed in a vertical position on the front and back faces of specimens 2a.1 and 2b.2. Continuous lines refer to tests with axial load (2a.1), dashed lines to tests with eccentric load (2b.2). In the case of axially loaded specimens, the two concrete layers initially behave in the same way, both characterised by shortening deformations; only during a second phase does the behaviour of the two concrete layers become different, with one concrete layer characterised by shortening deformation and the other by elongation. In the case of eccentrically loaded specimens a different behaviour is observed from the beginning of the test. In fact, with a low load level, the two concrete layers behave differently, one with shortening deformation and the other with elongation, and this denotes a predominant flexural behaviour of the panel. In Fig. 14b the longitudinal (slip) and transversal (separation) components of the relative displacement between the two
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3.0
150 kN 300 kN 450 kN 600 kN
3.0
150kN 300kN 450kN 600kN
4b.2
Wall height [mm]
Wall height [mm]
4a.2
0
0 20
0
20
20
Lateral deflection [mm]
0
20
Lateral deflection [mm]
(a)
(b)
Fig. 12. Lateral deflection at different load stages: (a) axial load and (b) eccentric load.
Fig. 13. Specimens after failure (a) axially and (b) eccentrically loaded; (c) mesh failure.
800
Svb 400
0 -3
Svf
Load [kN]
Load [kN]
800
Svf
Svb
2a.1 2b.2 0 Displacement [mm]
3
(a)
400
0 -0.5
2a.1 2b.2 0
Displacement [mm]
2
(b)
Fig. 14. (a) Vertical deformation of the two concrete layers and (b) slip and separation between the concrete layers in axially and eccentrically loaded specimens.
concrete layers of the above mentioned specimens 2a.1 and 2b.2 are plotted, for increasing axial (continuous line) and eccentric (dashed line) loadings. These components are calculated from the vectorial decomposition of the displacement recorded by transducers S4 and S5. The
longitudinal slip exhibits an initial nearly linear behaviour followed by a non-linear behaviour until ultimate values of about 1.5 mm. Compared to the slip, the separation is characterised by much lower values, which are practically negligible, meaning that the two concrete layers deflect together.
F. Gara et al. / Engineering Structures 37 (2012) 193–204 Table 6 Diagonal compression tests: cracking load, ultimate load, and failure modes. Specimen
First cracking load (kN)
Failure load (kN)
Failure modes
5.1 5.2 5.3 5.4 C1 C2
144 129 118 168 103 137
302 342 332 306 341 225
a* a a a b b*
a – localised concrete crushing; b – failure due to diagonal tension. * Failure of one of the two concrete layers.
The high values of the ultimate loads obtained, the influence of the slenderness ratio on the ultimate loads as well as the low values of relative displacement between the concrete layers confirm that these wall panels behave as semi-composite elements. However, some aspects deserve to be discussed. First of all, it is worth noticing that the slip between the two concrete layers is restricted not only by the shear deformable internal layer but also by the solid reinforced concrete beams at the bottom and top ends of the panels. Consequently, the results of the tests presented in this paper may be considered as representative only for real buildings in which the connections between floor and wall panels are built with solid reinforced concrete regions. Furthermore, it is important to underline that the reinforced concrete beams at the panel ends also cause a higher degree of flexural restraint between the floor and wall panels, which may lead to high values of vertical load eccentricity and, thus, to ultimate loads significantly lower than the values obtained in the tests. With regard to the tests on WPN08 and WPH08 wall panels, under both axial and eccentric load, the values of ultimate loads are similar to or higher than those obtained by standard panels WP08. These panels can therefore be considered as valid alternatives for standard panels even if a greater number of specimens should be tested to arrive at some general conclusions. As regards the diagonal compression tests, Table 6 reports the first cracking load, the failure load and the failure modes. It is worth noticing that specimens 5.1 and C2 were characterised by premature failure of one of the two concrete layers of the panels, due to a small undesired eccentricity of the axial load. For this reason, these results are not taken into consideration in the following comments. High first cracking loads were observed for all the specimens, while concerning the ultimate load the only significant result is that provided by specimen C1, which is the only one
201
reaching a diagonal tensile failure. In fact, for the other specimens concrete crushing occurred at the load application point. Specimen C1, which is similar to specimen 5.2 but with transversal stiffening walls, nearly simulates a pure shear test thanks to the diffusion of the vertical load along the panel perimeter guarantee by the transversal walls. The highest stress values are reached in the central part of panel C1, where tensile and compression stress values are similar. Diagonal tensile failure occurred with a load of 341 kN. In Fig. 15a the largest crack is marked with a thick dashed line. On the contrary, for specimen 5.2, a concentration of the compression stresses occurred around the load application point, causing the crushing of the concrete at a load value of 342 kN, as shown in Fig. 15b. The influence of transversal walls can also clearly be seen in Fig. 16 where both the vertical shortening deformation (Svf and Svb) and the horizontal elongation (Sof and Sob) measured on the two sides of specimen C1 (with transversal walls) (Fig. 16a) and specimen 5.2 (without transversal walls) (Fig. 16b) are reported. In the panel with transversal walls, at the first stage of loading, the average horizontal elongation is nearly equal to the vertical shortening deformation; later, after the cracking of the concrete layer, it becomes larger. On the contrary, in panels without transversal walls, at the first stage of loading, the average horizontal elongation is lower than the vertical shortening and becomes similar after concrete cracking. The effects of prestressing can be observed in the results of tests on specimens 5.3 and 5.4, prestressed with forces of 30 kN and 90 kN respectively. The first concrete cracking appeared at a slightly higher load for specimen 5.4 than for specimen 5.3. However, a lower failure load was achieved by specimen 5.4 than by specimen 5.3, since the prestressing force incremented the compression stresses around the load application point where the failure occurred. Finally, it may be noticed that in all the tests performed, failure did not occur suddenly but was always preceded by extensive diffuse concrete cracking. All the specimens were in fact already micro-cracked before the tests, due to concrete shrinkage and specimen handling. The micro-cracks constitute weak zones in the concrete where cracks may preferentially occur. Nevertheless, the specimens revealed a high capacity for stress redistribution thanks to the metallic mesh inside the concrete layers. However, it should be underlined that the results considered here are relevant to tests on symmetrically loaded panels, with the two concrete layers equally loaded; in reality this is an ideal condition
Fig. 15. Diagonal compression test: crack pattern at failure for panels (a) with and (b) without transversal stiffening walls.
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400
Sof 200
0
Sof
Svf Sob
Load [kN]
Load [kN]
400
Svb
0
Sob
200
C1 -4
0
2
Svf Svb
5.2 0
-4
Displacement [mm]
2
Displacement [mm]
(a)
(b)
Fig. 16. Diagonal compression test: vertical shortening and transversal elongation of panels with (C1) and without (5.2) transversal stiffening walls.
that can only occur when concrete layers are connected by reinforced concrete beams.
3. Numerical simulation Compression tests were numerically simulated with a displacement based non-linear static analysis taking into account both geometrical and material non-linearities, performed with the structural analysis programme Seismostruct [21]. Specimens were modelled with non-linear finite element models. In particular 20 beam elements were used for each concrete layer. The nodes at each end of the two concrete layers were joined with two rigid elements to simulate the reinforced concrete beams while the internal nodes were joined with shear elastic links. The links are axially rigid and shear deformable with the shear stiffness provided by the internal layer (Fig. 17). The specimen is restrained with a cylindrical pin at the base and a horizontal support at the top. In simulating axial compression tests a small eccentricity of the vertical was considered in order to simulate geometrical imperfections of panels and uncertainties of the load position. To simulate eccentric compression tests the load was applied at the axis of a concrete layer (Fig. 17). In both cases the vertical load was applied incrementally until failure of the sample was reached.
axial load
eccentric load
15 15 300 cm
beam element
shear deformable link ( Kl)
rigid link hl
hl
Fig. 17. Finite element model for compression tests.
A non-linear constitutive law [22] was considered for the concrete and a symmetric elasto-perfectly-plastic bilinear model for the steel. The values of the mechanical parameters were determined from the results of the tests performed on the materials (paragraph 2.1). In particular the shear stiffness of the links joining the two concrete layers was calculated by the equation
Ki ¼
GAl hl c c
ð2Þ
where G = 3.2 N/mm2 is the mean value among those obtained with the shear tests for material characterisation, Al is the influence area of the links, c is the internal layer thickness and the factor hl/c takes into account the difference between the length (hl) of the links and c (Table 7). In Fig. 18 the load vs lateral deflection graphs obtained from compression tests are compared with the results obtained from the numerical analysis. The behaviour of eccentrically loaded panels is well-approximated by the numerical model while for axially loaded panels a lower agreement between experimental and numerical results is achieved. In fact, the behaviour and the ultimate loads of real panels are largely influenced by geometrical imperfections (not perfectly flat concrete layers, variability of thicknesses, etc.) that are difficult to evaluate and take into consideration in a numerical model. However the numerical simulations may be considered satisfactory. Furthermore, in order to evaluate the critical load Pb1 of panels, a buckling analysis was also carried out using the same numerical model but considering a linear elastic behaviour of the materials. Values of the buckling loads obtained with these analyses (Pb1) are reported in Table 8 and also in Fig. 18. It can be observed that the Pb1 values seem to be approached by the curves obtained with the non-linear models, considering approximately axial loads. In order to highlight the semi-composite behaviour of the panels, the values of the Euler buckling load (Pb2), calculated in the hypothesis of zero shear stiffness of the links are reported in Table 8 (values of Pb2 are twice the Euler buckling load for a single concrete layer). Furthermore, the buckling load Pb3 are reported in the same table, where Pb3 was calculated by considering the panel to be entirely made of concrete. The coefficient a = Pb1/Pb3 was introduced to easily estimate the buckling load of the panels. As expected, the values of this coefficient are less than 1 and decrease as the thickness of the internal layer increases. However, only in the case of undesired eccentricity, buckling loads are close to the ultimate loads. In fact, due to the pronounced non-linear behaviour of the materials, the ultimate load of the eccentrically loaded panels is significantly lower than the buckling load and can be estimated only with a non-linear analysis which considers both geometrical and material non-linearities. Obviously the reduction in the ultimate load will be more significant for greater values of load eccentricity. As already mentioned, the value
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F. Gara et al. / Engineering Structures 37 (2012) 193–204 Table 7 Characteristics of the numerical model. WP08
WP12
WP16
115 9660
155 5786
195 4095
experimental
Load [kN]
hl (mm) Kl (N/mm)
400
200
f.e.m. (Ec) f.e.m. (0.4Ec)
C1
0
1300
Displacement [mm]
2
Load [kN]
Pb1 = αPb3 Fig. 19. Diagonal compression tests: comparison between experimental and numerical results.
f.e.m. 2a.1 650
2a.1
2b.2
well-simulated by the model with the original concrete elastic modulus Ec. At this load a first crack appeared which was associated with a distinct horizontal segment in the load and displacement plot. After the first crack, the experimental curve is non-linear due to the progressive cracking of the concrete. The numerical model with a reduced elastic modulus (0.4Ec) simulates quite well the global behaviour of the cracked panel. The ultimate load may be estimated by simplified formulas found in technical scientific literature. In particular for the diagonal compression test the following formula may be used:
f.e.m. 2b.2 0 1300
Load [kN]
Pb1 = αPb3 3a.2 f.e.m. 3a.2 3b.2
650
f.e.m. 3b.2
Load [kN]
0 1300
Pb1 = αPb3
f.e.m. 4a.1 4a.1
Pu ¼ 2Bstot fct ¼ 4b.2
650
f.e.m. 4b.2
0
5
10
15
20
25
Displacement [mm] Fig. 18. Axial and eccentric load tests: comparison between experimental and numerical results.
Table 8 Critical loads and reduction coefficient. Specimen
Mean U.L. (kN)
Pb1 (kN)
Pb2 (kN)
Pb3 (kN)
a
WP08 WP12 WP16
742 825 881
931 1082 1221
92.8 92.8 92.8
3653 7424 13,169
0.25 0.15 0.09
of the load eccentricity depends on the rotational restraint between the wall and floor panels. With regard to the diagonal compression tests, the behaviour of the specimen with the transversal concrete wall (C1) was numerically simulated with an elastic finite element model using the structural analysis programme SAP2000 [23]. The panel was modelled with shell elements with a thickness equal to the overall thickness of the two concrete layers and with an elastic modulus equal to that of the concrete used. The transversal concrete walls were modelled with beam elements. Vertical static loads were applied on several nodes for a total force equal to the ultimate load experimentally obtained (341 kN). The value of the horizontal tension in the central node of the model is 2.3 N/mm2 which is nearly equal to the ultimate tensile strength of the concrete. In Fig. 19 the load-shortening plot experimentally obtained is compared with the results obtained with the numerical model, considering an elastic modulus Ec and a reduced modulus 0.4Ec to take into account the cracking of the concrete. Up to a load of about 100 kN the behaviour of the specimen is typically linear elastic and is
2 1120 70 2:3 ¼ 360 kN 1000
ð3Þ
where B is the width of the panel and stot is the overall thickness of the concrete layers. The result is close to the ultimate load experimentally evaluated for specimen C1. However, in real buildings, the strength of panels under vertical and horizontal forces involves not only the shear resistance but also the bending resistance, depending on the overall dimensions of the wall. Moreover, the influence of openings for doors and windows must be considered. 4. Conclusions The results of an experimental campaign on completed in situ sandwich panels with no-shear connectors, used as wall panels, have been presented. In particular, compression tests with axial and eccentric load and diagonal compression tests were performed. Some numerical simulations with linear and non-linear finite element models were also carried out. As regards compression tests, wall panels with different internal layer thickness (WP08, WP12, WP16) and with two different configurations (WPN and WPH) were tested. High ultimate loads, decreasing for increasing values of the slenderness ratios, were obtained. The numerical simulations indicated that the ultimate loads of axially loaded panels are close to the buckling loads which can be determined by performing a linear buckling analysis or by using the coefficient a. Differently, the ultimate loads of eccentrically loaded panels, which are significantly lower than the buckling loads, can be simulated only by performing a non-linear analysis. Additional research is needed to develop simple, effective and rational methods for predicting the ultimate load of wall panels for different values of load eccentricity. The results of the experimental tests and numerical simulations indicated that a partial degree of composite behaviour was attained by the tested panels even if non-shear connectors are used in the interior layer. However, this semi-composite behaviour is due not only to the internal layer, but also to the reinforced concrete beams at the ends of the panels. Additional investigations are needed to develop simple, effective and rational methods for predicting the ultimate load of wall panels for different values of load eccentricity and to study the behaviour of panels without reinforced concrete beams.
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As regards diagonal compression tests, simple wall panels, prestressed wall panels and panels with transversal stiffening walls were tested. In all these cases high cracking loads were observed. The panels also showed a high capacity for stress redistribution thanks to the metallic mesh inside the concrete layers. However, only one specimen with transversal stiffening walls showed a tensile diagonal rupture while the other specimens showed a compression failure at the load application region. The numerical simulation of the test reaching the tensile diagonal rupture showed that an effective concrete modulus of elasticity may be considered to simulate the global behaviour of the cracked panel and that the ultimate load may be estimated on the basis of the tensile strength of the concrete. However, since in real buildings the behaviour of the panels under vertical and horizontal in-plane forces is strongly influenced by the overall dimensions of the wall and by openings for doors and windows, further investigations on panels with different configurations are recommended. Acknowledgments The financial support provided by ‘‘Schnell House’’ S.p.A., based in San Marino, is gratefully acknowledged. The technical support of the laboratory staff at the Dept. of Architecture, Construction and Structures, Università Politecnica delle Marche, is greatly appreciated. The opinions, findings and conclusions contained in this paper are those of the authors, and do not necessarily reflect the views of the sponsors. References [1] Ranzi G. Locking problems in the partial interaction analysis of multi-layered composite beams. Eng Struct 2008;30:2009–911. [2] Sousa Jr JBM, da Silva AR. Analytical and numerical analysis of multilayered beams with interlayer slip. Eng Struct 2010;32:1671–80. [3] Gara F, Ranzi G, Leoni G. Displacement-based formulations for composite beams with longitudinal slip and vertical uplift. Int J Numer Methods Eng 2006;65:1197–220. [4] Schnabl S, Saje M, Turk G, Planinc I. Analytical solution of two-layer beam taking into account interlayer slip and shear deformation. J Struct Eng, ASCE 2007;133(6):886–95.
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