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Experimental analysis and structural modelling of the punching behaviour of continuous two-way CLT flat slabs
Engineering Structures 205 (2020) 110046
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Experimental analysis and structural modelling of the punching behaviour of continuous two-way CLT flat slabs
T
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M. Muster , A. Frangi ETH Zurich, Chair of Structural Engineering – Timber Structures, Stefano-Franscini-Platz 5, CH-8093 Zurich, Switzerland
A R T I C LE I N FO
A B S T R A C T
Keywords: Punching Rolling shear Stress concentration Cross-laminated timber (CLT)
A newly developed bonding technology makes it possible to rigidly connect timber elements parallel to the grain. This technology allows to build two-way and point-supported flat slabs in cross-laminated timber (CLT). In such a structure high loads have to be transferred from the slab into the columns. This paper presents punching tests on different CLT plates. The results of these tests allow for a better understanding of the important parameters of a point-supported CLT slab and should help create the basic design criteria for these connections. To transfer vertical forces from higher storeys through the CLT slab without subjecting it to stresses perpendicular to the grain, the columns are directly connected to each other through an opening in the slab. Even though the opening leads to a stress concentration in the CLT plate, the rolling shear failure was the governing failure mode during the tests. With numerical models the behaviour of the tested plates was simulated and the strains around the opening were calculated. The results show good correlation with the measured strains. After the punching tests, every plate was cut in cubes and the visible failures were recorded. In addition, material samples were cut out of the plates and tested to determine the rolling shear strength of single boards. The achieved shear resistance in the punching tests was 1.4 times higher, than the rolling shear strength determined in shear tests on single boards would allow. An additional rolling shear test series showed that an anchoring effect contributes to the increased rolling shear resistance in punching tests. The results of the punching tests confirm the potential of CLT slabs to be used as biaxial, continuous, point-supported floor slabs.
1. Introduction Since 2009, the company Timber Structures 3.0 has been developing a bonded butt joint for timber elements. In contrast to a finger joint, a bonded butt joint needs no external applied pressure and both connected surfaces are plane. Therefore, it can be carried out directly on construction sites. As CLT plates are limited in size, the rigid connection of several CLT elements enables the slab to carry loads not only in one, but in two ways, while having longer spans than a single CLT plate. Fig. 1 shows a multi storey skeleton structure as it is possible to build by gluing CLT slabs together [1]. As CLT slabs are only point-supported, the punching behaviour of slabs has to be considered. A special feature of this CLT slab system is an opening in the slab on top of the column, as it can be seen in Fig. 2. This opening is necessary to lead vertical loads from upper storeys through the slab without subjecting the CLT slab to stresses perpendicular to the grain. However, this opening is unfavourably located at the point where the highest bending moment occurs. Point-supported slabs are often used for office or industry buildings.
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For such structures, a column grid of 6–8 m is required and live loads of 3–5 kN/m2 have to be considered [2]. These requirements lead to vertical design loads varying from 380 kN up to 1050 kN which have to be transferred from the slab into the interior columns. In 2012, Boccadoro tested the punching behaviour of six full scale plates at ETH Zurich [3]. The tested plates had dimensions of 2.5 m by 2.5 m and were 240 mm, 320 mm and 400 mm thick. The plates had a central opening with a diameter of 300 mm. Three of these plates were made of beech plywood and three were made of a combination of beech plywood and spruce boards. The measured load carrying capacity of all the plates was higher than the required resistance. Nevertheless, the cost of production for such slabs is not competitive compared to common CLT slabs. Punching tests on CLT plates performed by Mestek [4], Hochreiner [5] and Bogensperger [6] have shown that the shear resistance of common CLT slabs could be sufficient to achieve the required load carrying capacity. However, all these tests on CLT plates were performed without an opening in the plate. For the student apartment building Brock Commons at UBC in Vancouver, corner and edge supported CLT plates with openings in the plates were tested. As
Corresponding author. E-mail addresses: [email protected] (M. Muster), [email protected] (A. Frangi).
https://doi.org/10.1016/j.engstruct.2019.110046 Received 12 March 2019; Received in revised form 4 December 2019; Accepted 4 December 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Timber skeleton structure.
Fig. 3. The six tested CLT plates viewed from the loaded side.
always a six-layer 180 mm thick CLT plate and the single boards were not glued together at the side faces. Specimens 1 and 2 consisted of CLT alone with opening diameters of 300 mm and 200 mm respectively. On specimen 3 an additional 60 mm thick load distribution ring made of beech plywood was placed. Specimen 4 was tested with 30 mm thick glued on beech plywood plates on both sides. Specimens 5 and 6 consisted of both, a placed on load distribution ring and glued on beech plywood plates, but with different opening diameters. The CLT plates had the same bending stiffness in both directions and so did the beech plywood reinforcement plates. The area covered by the beech plywood plates was chosen in such a way, that the critical circumference for the shear stresses is in the reinforced area. The critical circumference is discussed in detail in Section 2.2.1. The two different diameters of the openings (200 mm and 300 mm) were chosen such that high loads from upper storeys in a multi-storey building can be transferred through this opening by a glued laminated timber column according to Fig. 2. The boards used for the CLT were graded for C24 as stated in SN EN 338:2016 [11] and the beech plywood plates were produced by Hess & Co AG having strength class F40/30 E70/60 according to EN 636:2012 [12]. To achieve a simple support without any restraints, the plates were positioned vertically. The experimental setup is illustrated in Fig. 4. The hydraulic jack with a load application diameter of 380 mm is shown at the right and the supporting steel frame is shown at the left. After the first test (specimen 1), an additional steel plate with a diameter of 400 mm was mounted on the hydraulic jack to protect a measurement device. The plates were supported on all four sides over one meter with a hinged support. With this setup, an equivalent bending moment and shear force distribution could be achieved, as it occurs around an interior column in a biaxial, continuous slab. The displacements were measured with LVDT (Linear Variable Differential Transformer) sensors on the side of the hydraulic jack. On the other side of the plate, the tension side, the displacements in all three directions were recorded with 52 light emitting diodes (LED) glued onto the surface of the plate as shown in Figs. 9 and 10. The 3D measurement system used was
Fig. 2. Section through the column-to-slab connection.
the column grid was rather small, no inner supports were used [7]. At the University of Innsbruck a system, which reinforces CLT plates at the inner supports with metal plates and screws is being developed [8]. Since in this project no metallic fasteners should be used, further research has been conducted. Possible reinforcement to reach the desired load carrying capacity are beech plywood plates to locally increase the cross section. This paper presents the results of the punching tests performed on reinforced and unreinforced CLT plates with an opening and the accompanying structural modelling. 2. Materials and methods 2.1. Punching tests Six CLT plates with dimensions of 2.1 m by 2.1 m, as illustrated in Fig. 3, were tested. The span of 2.0 m in the experiment represents approximately a column grid of 5.0 m by 5.0 m, as the distance from the column to the point of zero bending moment is a fifth of the distance between the columns [9,10]. In contrast to previous analyses, the tested CLT had an asymmetric layout, thus the top and bottom layer are not orientated in the same direction. This was chosen to have the same bending stiffness in both in-plane directions. The basic element was 2
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Fig. 6. 2D FEM model of the punching tests for specimens 1–3.
2.2.2. FEM model with 2D elements The tested plates were modelled as 2D plates with Dlubal’s finite element software RFEM [17]. The load was applied around the opening at the effective support area shown in Fig. 6, which was determined as explained in Section 2.2.1. The supports at the edges are modelled as roller line supports with locked in-plane deformations in the direction of the line supports. The strains parallel to the grain were simulated at the same location and over the same length as they were measured in the experiments. Due to the distance between the LED markers of 100 mm, the strains are average over this length (see also Figs. 9 and 10). The interpretation of simulated strains at an opening can be difficult. Therefore, averaging of strains over a certain distance is a good approach to avoid this problem. With a mesh size of 25 mm, four elements were within the measuring length of 100 mm. A sensitivity analysis showed that the averaged strains do not increase significantly with mesh sizes smaller than 25 mm. To implement the CLT and the beech plywood the add-on module RF-Laminate of RFEM was used. The glue line between the CLT boards and also between the CLT and the beech plywood was modelled as a rigid interaction with no slip between the layers. From the single layers a global stiffness matrix was derived and with the plate theory of Mindlin–Reissner the deformations and strains could be calculated. The material parameters were determined with tests as stated in Section 3.2, or taken from the according Swiss code [11].
Fig. 4. Test configuration of specimen 5.
Optotrak Certus from Northern Digital Inc. It has an accuracy of 0.3 mm, a resolution of 0.01 mm and coordinates were recorded with a frequency of 10 Hz [13]. The force was measured through the hydraulic oil pressure. The load path was controlled by a servo-hydraulic device and consisted of two loading and unloading cycles, before the load was increased until failure occurred or until the maximum possible displacement was achieved. The test procedure followed the general principles for static load testing in DIN EN 380:1993 [14]. The first load level was 200 kN and the second was 300 kN. 2.2. Simulations To describe the load-bearing behaviour of the tested plates, three different approaches were used. These three approaches had different levels of complexity. With a simplified model it is possible to calculate the shear stress in the plates. Including this approach into a FEM model with 2D elements the bending stresses can also be calculated. Finally, the plates were modelled with 3D elements to validate the other approaches and to analyse further phenomena.
2.2.3. FEM model with 3D elements The tested plates were modelled as 3D plates in Simulia’s finite element software Abaqus [18]. The CLT was modelled as a partitioned element with assigned orientation of material properties for every layer. Therefore, the interaction between the CLT layers was rigid without slip. Even though the boards were not glued together at the side faces in the experiments, the modelling was done without implementation of gaps between the boards, as a preliminary study showed that this has a negligible effect on the simulated rolling shear stresses. The influence on the stress concentration around the opening will be discussed in Sections 3.3 and 3.6. The interaction between the glued on beech plywood and the CLT was modelled as a rough interaction with hard contact. The interaction with the placed on beech plywood ring was modelled in tangential direction with a friction coefficient of 0.2 [19] and in normal direction as a hard contact. The material properties are listed in Table 1. The plywood was implemented as an orthotropic material without modelling every single layer. The used elements in Abaqus were cubes C3D8R solid elements and the mesh size was 25 mm.
2.2.1. Simplified model In line with Mestek [4], the effective area where the load is introduced can be determined. From the support area, we assume a load spread angle of 35° in the CLT as shown by Brandner [15] and of 45° in the beech plywood as derived by Walker [16]. As it is shown in Fig. 5 for specimen 3, at the intersection point between the load spreading cone and the axis of the cross section, a critical circumference around the support area is defined and the shear stresses are calculated there with Eq. (1).
τR =
1.5 × F ucrit × hCLT
(1)
3. Results 3.1. Load-displacement behaviour Fig. 5. Critical circumference in the simplified model for specimen 3.
In Figs. 7 and 8, the load-displacement curves of the tested plates 3
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3.2. Material tests
Table 1 Material properties for the solid FEM simulation.
E1 [N/mm2] E2 [N/mm2] E3 [N/mm2] G12 [N/mm2] G13 [N/mm2] G23 [N/mm2] v12 v13 v23
Spruce boards
Beech plywood
11000 370 370 690 690 69 0.42 0.37 0.47
7665 7665 1000 1000 550 550 0.52 0.46 0.46
In order to gain more information about the mechanical properties of the tested plates, smaller specimens were cut out of specimens 1–6. At first, a series of shear tests was performed to determine the rolling shear strength and then bending tests were performed to gain information about the bending strength and stiffness [20]. The rolling shear tests were performed following the rules of Ehrhart [21] and the grain pattern of all the boards was flat grain. The measured mean rolling shear strength was 1.5 N/mm2 and the mean rolling shear stiffness was 69 N/mm2. In four-point bending tests, a mean Young’s modulus of 11209 N/mm2 was determined. Out of the five tested specimens, three failed due to rolling shear failure and two due to bending failure. The determined mean bending strength of these two specimens was 44.4 N/mm2. The span in the bending tests was 2.0 m and the specimens were 250 mm wide and consisted of three 30 mm thick layers.
3.3. Strain measurement The three-dimensional displacements, recorded with the LED markers, were used to calculate the strains parallel to the grain on the tension side of the plates. Figs. 9 and 10 show the location of section 1-1 and the location of the LED markers. The vertical distance between the LED markers in section 1-1 was 100 mm. The applied reinforcements lead to different strain peaks. In Fig. 11, all specimens with their specific features are illustrated together with the measured and calculated strains. From previous tests with beech plywood plates, similar data could be extracted [3], as shown in Fig. 12. The calculated and measured values are shown at a load level of 130 kN and were taken from the 2D FEM simulation. The difference between spruce CLT (Fig. 11) and beech plywood plates (Fig. 12) is due to the different measurement location and length. The measuring location was 15 mm away from the opening in the beech plywood compared to 5 mm in the CLT and the measurement distance was 200 mm compared to 100 mm. Fig. 13 compares the measured and calculated strains from the 2D FEM model of all specimens. The values shown are the first ones next to the opening. Due to cracks or knots, the right value of specimen 2 and the left value of specimen 3 in Fig. 11 were not considered. The mean difference between calculated and measured strains was −2% for the spruce CLT plates and +6% for the beech plywood plates. Furthermore, it is interesting to analyse whether the measured and calculated strains lead to an accurate prediction of the tensile cracks in the boards next to the opening. Table 2 summarises the calculated tensile stresses when the first cracks were observed. Additionally, the measured values are compared to the calculated values from the 2D and
Fig. 7. Load – displacement behaviour of specimens 1–3.
Fig. 8. Load – displacement behaviour of specimens 4–6.
are shown. The details of these plates can also be seen in Figs. 3 and 11. Specimen 1 showed early deformations due to the narrow support area, which led to a crushing of the timber perpendicular to the grain. Specimen 3 had a 60 mm thick additional load distribution ring placed on the hydraulic jack and therefore a higher ultimate load. The tests were stopped after 75 mm of deformation to prevent damaging the measuring devices. Specimens 4–6 had additional glued on 30 mm thick beech plywood plates on both sides. These specimens achieved about 1.5 times higher ultimate loads than the plates with just CLT. The tests were stopped after the load fell under 80% of the maximum load. All the specimens showed a quasi-ductile global structural behaviour. Specimens 5 and 6 showed a significant drop of load at 600 kN and 640 kN respectively. This happened when the beech plywood at the tension side detached (see also Section 3.5). Fig. 9. LED markers in specimens 1–3. 4
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from bending tests as shown in Section 3.2 was 44.4 N/mm2. As both of these values were calculated with a small number of tests, they have to be treated with caution. Nevertheless, it can be seen that the extrapolated calculated values given in Table 2 are close to the estimated strength at the moment when the first crack appears. As mentioned before, the gaps between the boards were not included in the simulations.
3.4. Rolling shear Table 3 shows the maximum load of every specimen together with the corresponding calculated rolling shear stress at this moment. The three models described in Section 2.2 are compared to each other. The back-calculated values are 30 to 40% higher, than those determined in the shear tests (1.5 N/mm2) in Section 3.2. The simplified model and the 3D solid model show good agreement. The rolling shear stresses calculated in the 3D solid simulation are about 2% higher compared to the simplified model. The results from the 2D plane FEM simulation, which uses the same critical circumference as the simplified model, show a bigger difference to those calculated in the 3D solid FEM simulation. In Fig. 14, a section through the 3D solid FEM simulation of specimen 3 is shown, with the existing rolling shear stresses in both directions at maximum load.
Fig. 10. LED markers in specimens 4–6.
the 3D FEM model. The values in brackets in the column “3D FEM” are the maximum bending stresses at the opening. The strains from the simulation are averaged values between the same locations as in the measurements and are multiplied with the Young’s modulus of the respective material. For spruce it is 11000 N/mm2 and for beech plywood it is 15530 N/mm2, which is the Young’s modulus parallel to the grain or twice the value considered for the plywood in the simulations. The mean bending strength of the beech plywood was 123.7 N/mm2 [22]. The mean bending strength of the CLT specimens determined
Fig. 11. Support details and averaged strains at 130 kN for CLT. 5
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Fig. 12. Support details and averaged strains at 130 kN for beech plywood.
Table 3 Back-calculated rolling shear stress (values in [N/mm2]). Nr.
Max. Load
Simplified
FEM plane
FEM solid
1 2 3 4 5 6
380 408 455 605 620 666
2.0 2.1 1.9 2.1 2.1 2.2
1.8 1.9 1.8 1.9 2.0 2.0
2.0 2.1 2.1 2.2 2.0 2.2
a b
Fig. 13. Measured vs calculated strains next to the opening.
kN kN kN kN kN kN
a b b
Including beech plywood besides bending failure at 557 kN. Not including beech plywood plates on tension side (detaching).
Fig. 14. Rolling shear stresses in the 3D solid FEM model of specimen 3.
Table 2 Calculated stress at first crack (values in [N/mm2]). Specimen 1 2 3 4 5 6 F240 F320 F400
First Crack
Test
2D FEM
3D FEM (max)
Material
200 kN 243 kN 364 kN 557 kN – – 1155 kN 2100 kN 2878 kN
36.7 39.8 47.9 89.8 detaching detaching 100.8 100.4 86.0
39.4 41.4 63.6 81.2
34.4 (44.54) 38.9 (52.2) 58.1 (71.8) 97.4 (113.2)
spruce spruce spruce beech beech beech beech beech beech
Fig. 15. Cut out cube of specimen 5 with detaching failure.
3.5. Detaching of beech plywood plates During the tests on specimens 5 and 6, the glued on beech plywood detached from the spruce CLT at high loads. As the cross section has a discontinuity where the beech plywood plate ends, high stresses appear.
If the grain direction of the top layer of the CLT is parallel to the edge of the plywood, this layer is subjected to rolling shear stresses. At the same time, tensile stresses perpendicular to the grain occur at the tension side 6
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Fig. 17. First tensile failure in specimen 1. Fig. 16. Stress ratio of specimen 6 at 640 kN.
due to the bending shape of the glued on beech plywood. Fig. 15 shows a cut out cube of specimen 5 at the location where detaching occurred. The governing failure which is responsible for detaching is therefore a combination of shear and tension perpendicular to the grain. The identified failure criterion is given by Eq. (2).
σt ,90 τ + R > 1.0 ft ,90 fR
(2)
The rolling shear strength of single spruce boards was determined in Section 3.2 as 1.5 N/mm2. In standardisation, the strength of timber in tension perpendicular to the grain is normally very low. Tests done by Blass and Schmid [23] showed that the mean tensile strength perpendicular to the grain is 1.89 N/mm2 for small specimen volume. In the 3D solid FEM model, rolling shear stresses and tensile stresses perpendicular to the grain were simulated. Along the line of discontinuity the stress ratio from Eq. (2) was observed at the load level of detaching. The horizontal line in Fig. 16 indicates this failure criterion, the dots are simulated points and the dashed line is a second order polynomial fit of these simulated values for specimen 6. At the moment when the bending failure in specimen 4 occurred the maximum stress ratio of Eq. (2) was 1.11. For specimen 5 the maximum stress ratio was 1.00 at the moment of detaching. Specimen 6 had a maximum stress ratio of 1.17 at the moment of detaching. The simulated stress ratios are within the right magnitude so that one can state that the failure of detaching can be described by the approach here presented. Nevertheless, the number of specimens with this observed failure (two out of three) is very limited and therefore further investigations have to be done to confirm this finding.
Fig. 18. First tensile failure in specimen 2.
3.6. Failures on the tension side Interval photo shootings at the tension side of the plate together with the load-displacement curves allow the detection of tensile failure in the outermost lamellae. For specimen 1, a tensile failure next to the opening during the linear elastic phase was observed. At a load level of 200 kN, the first board to the right of the opening failed. Fig. 17 shows the plate just before the failure happens (left) and the crack indicated by an arrow (right). The load-displacement curve in Fig. 7 shows just a minor drop during this failure. The next visible failure is a tensile failure of the first board on the left next to the opening at a load level of 360 kN. In specimen 2 at a load level of 243 kN the first crack in the left board next to the opening appeared, as shown in Fig. 18. The load was subsequently raised up to 400 kN when this crack started growing and the board on the right side of the opening failed as well.
Fig. 19. First tensile failure in specimen 3.
Specimen 3 in Fig. 19 showed no failure until the board at the right side cracked at a load level of 364 kN, which is also visible in the load displacement curve. After that, no further failures were visible until the displacement reached 50 mm. Then the boards at the left side showed tensile failure, too. The specimens with the two-sided glued on beech plywood plates (4–6) showed two different failures. The first failure in specimen 4, shown in Fig. 20, was a tensile failure of the beech plywood plate. It occurred at the tension side and the fibre direction of the outermost layer of the plywood was perpendicular to the crack, which 7
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4.2. Materials and methods To determine the effect of continuous boards on the rolling shear stress distribution, an additional, independent test series was performed. 52 specimens as illustrated in Fig. 22 were tested. The defining difference between the specimens was the overhang of the horizontal boards at the sides of the vertical boards indicated by the parameter ”o” in Fig. 22. The range of the overhang was from 0 mm up to 75 mm. The horizontal boards were always 30 mm thick and 120 mm wide. The vertical boards were either 120 mm or 60 mm wide and either 20 mm or 30 mm thick. All tested specimens are listed in Table 4. The used spruce boards were graded for C24 as stated in SN EN 338:2016 [11]. Additionally, the dynamic Young’s modulus and the density were determined by using the system Timber Grader MTG. The mean dynamic Young’s modulus was 12517 N/mm2 and the mean density was 461 kg/m3. The tested boards had flat grain orientation.
Fig. 20. First tensile failure in specimen 4.
started at a load level of 557 kN. After the whole plywood plate was torn apart, no other failures were visible but the load could still be increased. In specimens 5 and 6, the first failure occurred in the connection between the beech plywood and the CLT. The plywood detached at a load of 640 kN (specimen 6) and 600 kN (specimen 5). This failure is indicated by a large drop in the load-displacement curve. Nevertheless, this failure did no mark the maximum load of these two plates. The load could be increased again with no visible failures from the outside.
4.3. Results In Fig. 23, the y-axis shows the ratio of the achieved load carrying capacity to the mean load carrying capacity of all specimens without overhang. The x-axis shows the ratio (r) between the total width of the overhang to the width of the loaded section.
r = o / wl
(3)
where o and wl can be seen in Fig. 22. Even though the correlation coefficient between the ratio of load carrying capacity of all specimens and r is only 0.33, an increasing load bearing capacity with a rising r is visible. The load carrying capacity can be increased up to 20% when there is an overhang. In order to verify if the mean load carrying capacity of specimens with r > 0 is significantly higher, a one-tailed t-test was performed. On a significance level of 5%, the test showed that the mean load carrying capacity of specimens with r ⩾ 0.5 is significantly higher than the mean load carrying capacity of specimens without overhang.
3.7. Internal failures In order to find areas of rolling shear failures or internal tensile failures, the plates were cut into cubes and all the cracks were recorded. The grey shaded area in Fig. 21 represents the area of rolling shear failure due to shear forces, whereas the black shaded fields show areas with rolling shear failure due to detaching. The jagged lines show tensile failures due to bending. The numbering of the layers starts at the tension side. So the first layer is the outermost layer on the tension side. For example, the jagged line on the right of the opening in specimen 1, reaching from the middle to a location above the opening, represents the tensile failure illustrated in Fig. 17. From the analysis of the internal failures, it was observed that tensile failures occurred often just next to the opening. In contrast to the tensile failures, the rolling shear failures were not locally limited. Some of the plates were almost separated due to the widespread rolling shear failures. In specimens 5 and 6, detaching of the glued on beech plywood plates on the tension side was observed. However, these failures did not mark the ultimate load: widespread rolling shear failures occurred after the detaching. All these observations lead to the conclusion that the rolling shear failure was the governing failure and limited the load carrying capacity of the plates. At the same time, the rolling shear failure provides the capability to achieve large deformations as the shear cracks are growing steadily away from the support area. These continuous failures were clearly audible after the linear elastic phase, as no other failures could be observed from the outside.
5. Discussion The following chapter discusses three topics which are essential for the detailed understanding of the load-bearing behaviour of a two-way, point-supported CLT slab: rolling shear, stress concentration and simulations. 5.1. Rolling shear The calculated rolling shear stress in the punching tests is obviously higher than the measured strength for single boards. This conclusion was already shown by Mestek and others by testing CLT plates without openings [4]. The measured increase was 50% between the punching tests and the shear tests. One reason for this increase is the simultaneously acting compression stress perpendicular to the grain, which increases the rolling shear strength up to 20%. This was proven in shear tests, where specimens were exposed to external compression stress perpendicular to the grain (0.0, 0.3 and 0.8 N/mm2). According to Mestek, a stress redistribution and an anchoring effect due to the continuous boards could be responsible for the additional 25% increase. A simulated distribution of the rolling shear stress and the compression stress perpendicular to the grain for specimen 1 is shown in Fig. 25. The section is in the 4th layer and 10 cm away from the opening as illustrated in Fig. 24 and the considered load level is 130 kN. The grey dashed line shows the shear stress distribution and the black line shows the compression perpendicular to the grain stress distribution. These results were simulated with the 3D solid FEM model. In the additional shear tests two phenomena occurred. First, the increased shear area due to an overhang and second a clamping or
4. Additional rolling shear tests 4.1. Motivation Rolling shear tests, where the whole board is subjected to rolling shear show a nonlinear load-deformation behaviour [20]. These deformations before ultimate failure allow a stress redistribution in only locally loaded or continuous boards. In this case, boards with a highly stressed part show a clamping or anchoring effect and therefore a local reduction of shear stresses. In CLT subjected to concentrated loads, this effect could increase the rolling shear resistance. 8
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Fig. 21. Recorded internal failures.
5.2. Stress concentration
anchoring effect due to large deformations in the middle. Both phenomena lead to a higher ultimate load. The load bearing capacity was increased up to 20% dependent on the overhang. Furthermore, the horizontal boards failed over the whole length and not only at a central part. As the rolling shear distribution in a plate differs from the one in the performed additional rolling shear tests, it is not possible to quantify this anchoring effect in a CLT plate simply based on this test series. Nevertheless, it is likely that the anchoring effect is responsible for an additional increase in rolling shear resistance.
As a result of the point support and the opening in the plate, a strain and consequentially a stress concentration occurs as shown in Figs. 11 and 12. This concentration is influenced of course by the material properties, but also by the area of support, the diameter of the opening and the thickness of the plate. Another point is the arrangement of the boards next to the opening. A board cannot be cut at all or can be cut almost over the whole width. The more of the cross section is cut out due to the opening, the higher is the strain in the residual cross section. It was observed that boards with a small residual cross section already 9
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Fig. 22. Additional rolling shear specimens. Table 4 Number of additional rolling shear specimens. tl [mm]/ wl [mm] overhang 0 mm 15 mm 30 mm 45 mm 60 mm 75 mm
20/ 60
20/ 120
30/ 120
6 3 3 3
11 3 3 3 3 2
6 3 3 3 3 3
Fig. 24. Section for stress distribution through specimen 1.
Fig. 25. Stress distribution around the support for specimen 1.
FEM model, which shows stresses in the same magnitude as the simpler model. The approach to measure and simulate the tensile stresses not directly at the opening, but 5 mm away was also confirmed by the test results. The shear stresses are more difficult to verify. The area of support in the 2D plane FEM model was chosen due to assumptions in terms of load distribution and led to satisfying results for the bending stresses described above. As no nonlinearities were considered in the simulations and as there is so far no conclusive definition of an increase in rolling shear strength for CLT subjected to concentrated load, the calculated rolling shear stresses remain questionable. However, considering that there is a 50% resistance increase, all the models were able to predict the rolling shear failure accurately. Independently of this uncertainty, the three different calculation approaches showed good agreement. Compared to the 3D solid FEM model, the 2D plane model showed lower values. A comparison of the location of the highest shear stresses revealed that the assumption of the load distribution is too big and therefore the critical circumference is too big as well. The
Fig. 23. Rolling shear behaviour of continuous boards.
failed at an early stage of the test, but the neighbouring boards were able to sustain the stresses from the failed boards. Results from the punching tests demonstrate that the occurred tensile failures were not limiting the load-bearing capacity. Nevertheless, the correlation between several geometrical parameters is still not known. Therefore, an additional test series was performed at ETH Zurich, which is currently being evaluated. This series should also evaluate the actual bending resistance of CLT plates with a central opening. 5.3. Simulations The rather simple 2D plane FEM model for simulating the punching tests was able to calculate the tensile and bending stresses accurately. This is confirmed by the comparison of measured and calculated values both for spruce CLT and for beech plywood and also by the 3D solid 10
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References
simplified model compensates this mistake with a shear stress calculation on the safe side. For the critical circumference or effective support area used in the 2D plane FEM simulations, the outermost cross layer should be excluded. In general, the plane FEM model allows designing such column to slab connections, but there is a need for a simple solution to include the detaching failure of the glued on beech plates from the CLT. The results from the solid FEM model are promising, but need verification first.
[1] Zöllig S, Frangi A, Franke S, Muster M. Timber structures 3.0 – new technology for multi-axial, slim, high performance timber structures. World conference on timber engineering (WCTE 2016), Vienna, Austria. 2016. [2] SIA 261:2014. Einwirkung auf Tragwerke; 2014. [3] Boccadoro L. Experimentelle Untersuchungen zum Durchstanzen von Holzdecken (Flachdecke) [Master’s thesis]. ETH Zurich; 2012. [4] Mestek P. Punktgestützte Flächentragwerke aus Brettsperrholz (BSP) – Schubbemessung unter Berücksichtigung von Schubverstärkungen [Doctoral thesis]. TU München; 2011. [5] Hochreiner G, Füssl J, Eberhardsteiner J. Cross-laminated timber plates subjected to concentrated loading: experimental identification of failure mechanisms. Strain 2013;50(1):68–81. [6] Bogensperger T, Jöbstl R, Augustin M. Concentrated load introduction in CLT elements perpendicular to plane. World conference on timber engineering (WCTE 2016), Vienna, Austria. 2016. [7] Popovski M, Chen Z, Gafner B. Structural behaviour of point-supported CLT floor systems. World conference on timber engineering (WCTE 2016), Vienna, Austria. 2016. [8] Maurer B, Maderebner R, Zingerle P, Färberböck I, Flach M. Point-Supported flat slabs with CLT panels. World conference on timber engineering (WCTE 2018), Seoul, Korea. 2018. [9] Kinnunen S, Nylander H. Punching of concrete slabs without shear reinforcement. Transactions of the Royal Institute of Technology, Nr. 158; 1960. [10] SIA 262:2013. Concrete structures; 2013. [11] SN EN 338:2016. Structural timber - Strength classes; 2016. [12] EN 636:2012+A1:2015. Plywood – Specifications; 2012. [13] Northern Digital Inc. Optotrak Certus motion capture system. Retrieved August 07, 2019, from https://www.ndigital.com/msci/products/optotrak-certus/. [14] DIN EN 380:1993. Timber structures; test methods; general principles for static load testing; German version; 1993. [15] Brandner R. Cross laminated timber (CLT) in compression perpendicular to plane: testing, properties, design and recommendations for harmonizing design provisions for structural timber products. Eng Struct 2018;171(15):944–60. [16] Walker D. Untersuchungen zum Tragverhalten von punktgelagerten, zweiachsig tragenden Massivholzplatten [Master’s thesis]. ETH Zurich; 2017. [17] Dlubal Software GmbH. RFEM 5; 2018. [18] Simulia. Abaqus - Finite Element Modelling Programme and Standard User’s Manual. Version 6.11; 2011. [19] Maissen A. Festkörperreibung: Reibungszahlen verschiedener Werkstoffe. Schweizer Ingenieur und Architekt 1993;111(3):25–9. [20] Muster M, Frangi A. Punching behaviour of continuous two-way CLT flat slabs at interior connections to columns. World conference on timber engineering (WCTE 2018), Seoul, Korea. 2018. [21] Ehrhart T, Brandner R, Schickhofer G, Frangi A. Rolling shear properties of some European timber species with focus on cross laminated timber (CLT): test configuration and parameter study. 2nd meeting of the international network on timber engineering research (INTER), Sibenik, Croatia, August 24–27. 2015. p. 61–76. [22] Grüter B. Untersuchungen zum Tragverhalten von Holzplatten aus Buche [Master’s thesis]. ETH Zürich; 2013. [23] Blaß HJ, Schmid M. Querzugfestigkeit von Vollholz und Brettschichtholz. Holz als Roh- und Werkstoff 2002;58(6):456–66.
6. Conclusion The punching tests showed that the chosen slabs are able to transfer high shear forces into the column and can resist high bending moments. The load-displacement behaviour has already been observed in many other studies. Bogensperger et al. [6] stated that the rolling shear softening at material level leads to a global elastic plastic load-displacement behaviour. With an increase of the thickness of the slab it is also possible to fulfil the requirements defined in Section 1. The opening in the plate has no influence on the shear resistance. The same increase in rolling shear resistance was observed in other studies with concentrated loads but without openings. The shear tests with overhanging horizontal boards showed that the anchoring effect is likely responsible for the additional increase in rolling shear resistance. Despite the large opening, none of the specimens failed due to a bending failure even though local tensile failures were observed. As a limited number of plates were tested it is yet not possible to quantify the bending resistance of such CLT slab to column connections. More tests have already been performed and will reveal the relations of the geometric parameters and therefore help to quantify the bending resistance. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The presented research project is funded by Innosuisse. The project partners are Timber Structures 3.0 AG, Timbatec Holzbauingenieure Schweiz AG, Schilliger Holz AG and Henkel & Cie AG. The research project is a collaboration between the ETH Zurich and the Bern University of Applied Sciences.
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Experimental analysis and structural modelling of the punching behaviour of continuous two-way CLT flat slabs
T
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M. Muster , A. Frangi ETH Zurich, Chair of Structural Engineering – Timber Structures, Stefano-Franscini-Platz 5, CH-8093 Zurich, Switzerland
A R T I C LE I N FO
A B S T R A C T
Keywords: Punching Rolling shear Stress concentration Cross-laminated timber (CLT)
A newly developed bonding technology makes it possible to rigidly connect timber elements parallel to the grain. This technology allows to build two-way and point-supported flat slabs in cross-laminated timber (CLT). In such a structure high loads have to be transferred from the slab into the columns. This paper presents punching tests on different CLT plates. The results of these tests allow for a better understanding of the important parameters of a point-supported CLT slab and should help create the basic design criteria for these connections. To transfer vertical forces from higher storeys through the CLT slab without subjecting it to stresses perpendicular to the grain, the columns are directly connected to each other through an opening in the slab. Even though the opening leads to a stress concentration in the CLT plate, the rolling shear failure was the governing failure mode during the tests. With numerical models the behaviour of the tested plates was simulated and the strains around the opening were calculated. The results show good correlation with the measured strains. After the punching tests, every plate was cut in cubes and the visible failures were recorded. In addition, material samples were cut out of the plates and tested to determine the rolling shear strength of single boards. The achieved shear resistance in the punching tests was 1.4 times higher, than the rolling shear strength determined in shear tests on single boards would allow. An additional rolling shear test series showed that an anchoring effect contributes to the increased rolling shear resistance in punching tests. The results of the punching tests confirm the potential of CLT slabs to be used as biaxial, continuous, point-supported floor slabs.
1. Introduction Since 2009, the company Timber Structures 3.0 has been developing a bonded butt joint for timber elements. In contrast to a finger joint, a bonded butt joint needs no external applied pressure and both connected surfaces are plane. Therefore, it can be carried out directly on construction sites. As CLT plates are limited in size, the rigid connection of several CLT elements enables the slab to carry loads not only in one, but in two ways, while having longer spans than a single CLT plate. Fig. 1 shows a multi storey skeleton structure as it is possible to build by gluing CLT slabs together [1]. As CLT slabs are only point-supported, the punching behaviour of slabs has to be considered. A special feature of this CLT slab system is an opening in the slab on top of the column, as it can be seen in Fig. 2. This opening is necessary to lead vertical loads from upper storeys through the slab without subjecting the CLT slab to stresses perpendicular to the grain. However, this opening is unfavourably located at the point where the highest bending moment occurs. Point-supported slabs are often used for office or industry buildings.
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For such structures, a column grid of 6–8 m is required and live loads of 3–5 kN/m2 have to be considered [2]. These requirements lead to vertical design loads varying from 380 kN up to 1050 kN which have to be transferred from the slab into the interior columns. In 2012, Boccadoro tested the punching behaviour of six full scale plates at ETH Zurich [3]. The tested plates had dimensions of 2.5 m by 2.5 m and were 240 mm, 320 mm and 400 mm thick. The plates had a central opening with a diameter of 300 mm. Three of these plates were made of beech plywood and three were made of a combination of beech plywood and spruce boards. The measured load carrying capacity of all the plates was higher than the required resistance. Nevertheless, the cost of production for such slabs is not competitive compared to common CLT slabs. Punching tests on CLT plates performed by Mestek [4], Hochreiner [5] and Bogensperger [6] have shown that the shear resistance of common CLT slabs could be sufficient to achieve the required load carrying capacity. However, all these tests on CLT plates were performed without an opening in the plate. For the student apartment building Brock Commons at UBC in Vancouver, corner and edge supported CLT plates with openings in the plates were tested. As
Corresponding author. E-mail addresses: [email protected] (M. Muster), [email protected] (A. Frangi).
https://doi.org/10.1016/j.engstruct.2019.110046 Received 12 March 2019; Received in revised form 4 December 2019; Accepted 4 December 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Timber skeleton structure.
Fig. 3. The six tested CLT plates viewed from the loaded side.
always a six-layer 180 mm thick CLT plate and the single boards were not glued together at the side faces. Specimens 1 and 2 consisted of CLT alone with opening diameters of 300 mm and 200 mm respectively. On specimen 3 an additional 60 mm thick load distribution ring made of beech plywood was placed. Specimen 4 was tested with 30 mm thick glued on beech plywood plates on both sides. Specimens 5 and 6 consisted of both, a placed on load distribution ring and glued on beech plywood plates, but with different opening diameters. The CLT plates had the same bending stiffness in both directions and so did the beech plywood reinforcement plates. The area covered by the beech plywood plates was chosen in such a way, that the critical circumference for the shear stresses is in the reinforced area. The critical circumference is discussed in detail in Section 2.2.1. The two different diameters of the openings (200 mm and 300 mm) were chosen such that high loads from upper storeys in a multi-storey building can be transferred through this opening by a glued laminated timber column according to Fig. 2. The boards used for the CLT were graded for C24 as stated in SN EN 338:2016 [11] and the beech plywood plates were produced by Hess & Co AG having strength class F40/30 E70/60 according to EN 636:2012 [12]. To achieve a simple support without any restraints, the plates were positioned vertically. The experimental setup is illustrated in Fig. 4. The hydraulic jack with a load application diameter of 380 mm is shown at the right and the supporting steel frame is shown at the left. After the first test (specimen 1), an additional steel plate with a diameter of 400 mm was mounted on the hydraulic jack to protect a measurement device. The plates were supported on all four sides over one meter with a hinged support. With this setup, an equivalent bending moment and shear force distribution could be achieved, as it occurs around an interior column in a biaxial, continuous slab. The displacements were measured with LVDT (Linear Variable Differential Transformer) sensors on the side of the hydraulic jack. On the other side of the plate, the tension side, the displacements in all three directions were recorded with 52 light emitting diodes (LED) glued onto the surface of the plate as shown in Figs. 9 and 10. The 3D measurement system used was
Fig. 2. Section through the column-to-slab connection.
the column grid was rather small, no inner supports were used [7]. At the University of Innsbruck a system, which reinforces CLT plates at the inner supports with metal plates and screws is being developed [8]. Since in this project no metallic fasteners should be used, further research has been conducted. Possible reinforcement to reach the desired load carrying capacity are beech plywood plates to locally increase the cross section. This paper presents the results of the punching tests performed on reinforced and unreinforced CLT plates with an opening and the accompanying structural modelling. 2. Materials and methods 2.1. Punching tests Six CLT plates with dimensions of 2.1 m by 2.1 m, as illustrated in Fig. 3, were tested. The span of 2.0 m in the experiment represents approximately a column grid of 5.0 m by 5.0 m, as the distance from the column to the point of zero bending moment is a fifth of the distance between the columns [9,10]. In contrast to previous analyses, the tested CLT had an asymmetric layout, thus the top and bottom layer are not orientated in the same direction. This was chosen to have the same bending stiffness in both in-plane directions. The basic element was 2
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Fig. 6. 2D FEM model of the punching tests for specimens 1–3.
2.2.2. FEM model with 2D elements The tested plates were modelled as 2D plates with Dlubal’s finite element software RFEM [17]. The load was applied around the opening at the effective support area shown in Fig. 6, which was determined as explained in Section 2.2.1. The supports at the edges are modelled as roller line supports with locked in-plane deformations in the direction of the line supports. The strains parallel to the grain were simulated at the same location and over the same length as they were measured in the experiments. Due to the distance between the LED markers of 100 mm, the strains are average over this length (see also Figs. 9 and 10). The interpretation of simulated strains at an opening can be difficult. Therefore, averaging of strains over a certain distance is a good approach to avoid this problem. With a mesh size of 25 mm, four elements were within the measuring length of 100 mm. A sensitivity analysis showed that the averaged strains do not increase significantly with mesh sizes smaller than 25 mm. To implement the CLT and the beech plywood the add-on module RF-Laminate of RFEM was used. The glue line between the CLT boards and also between the CLT and the beech plywood was modelled as a rigid interaction with no slip between the layers. From the single layers a global stiffness matrix was derived and with the plate theory of Mindlin–Reissner the deformations and strains could be calculated. The material parameters were determined with tests as stated in Section 3.2, or taken from the according Swiss code [11].
Fig. 4. Test configuration of specimen 5.
Optotrak Certus from Northern Digital Inc. It has an accuracy of 0.3 mm, a resolution of 0.01 mm and coordinates were recorded with a frequency of 10 Hz [13]. The force was measured through the hydraulic oil pressure. The load path was controlled by a servo-hydraulic device and consisted of two loading and unloading cycles, before the load was increased until failure occurred or until the maximum possible displacement was achieved. The test procedure followed the general principles for static load testing in DIN EN 380:1993 [14]. The first load level was 200 kN and the second was 300 kN. 2.2. Simulations To describe the load-bearing behaviour of the tested plates, three different approaches were used. These three approaches had different levels of complexity. With a simplified model it is possible to calculate the shear stress in the plates. Including this approach into a FEM model with 2D elements the bending stresses can also be calculated. Finally, the plates were modelled with 3D elements to validate the other approaches and to analyse further phenomena.
2.2.3. FEM model with 3D elements The tested plates were modelled as 3D plates in Simulia’s finite element software Abaqus [18]. The CLT was modelled as a partitioned element with assigned orientation of material properties for every layer. Therefore, the interaction between the CLT layers was rigid without slip. Even though the boards were not glued together at the side faces in the experiments, the modelling was done without implementation of gaps between the boards, as a preliminary study showed that this has a negligible effect on the simulated rolling shear stresses. The influence on the stress concentration around the opening will be discussed in Sections 3.3 and 3.6. The interaction between the glued on beech plywood and the CLT was modelled as a rough interaction with hard contact. The interaction with the placed on beech plywood ring was modelled in tangential direction with a friction coefficient of 0.2 [19] and in normal direction as a hard contact. The material properties are listed in Table 1. The plywood was implemented as an orthotropic material without modelling every single layer. The used elements in Abaqus were cubes C3D8R solid elements and the mesh size was 25 mm.
2.2.1. Simplified model In line with Mestek [4], the effective area where the load is introduced can be determined. From the support area, we assume a load spread angle of 35° in the CLT as shown by Brandner [15] and of 45° in the beech plywood as derived by Walker [16]. As it is shown in Fig. 5 for specimen 3, at the intersection point between the load spreading cone and the axis of the cross section, a critical circumference around the support area is defined and the shear stresses are calculated there with Eq. (1).
τR =
1.5 × F ucrit × hCLT
(1)
3. Results 3.1. Load-displacement behaviour Fig. 5. Critical circumference in the simplified model for specimen 3.
In Figs. 7 and 8, the load-displacement curves of the tested plates 3
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3.2. Material tests
Table 1 Material properties for the solid FEM simulation.
E1 [N/mm2] E2 [N/mm2] E3 [N/mm2] G12 [N/mm2] G13 [N/mm2] G23 [N/mm2] v12 v13 v23
Spruce boards
Beech plywood
11000 370 370 690 690 69 0.42 0.37 0.47
7665 7665 1000 1000 550 550 0.52 0.46 0.46
In order to gain more information about the mechanical properties of the tested plates, smaller specimens were cut out of specimens 1–6. At first, a series of shear tests was performed to determine the rolling shear strength and then bending tests were performed to gain information about the bending strength and stiffness [20]. The rolling shear tests were performed following the rules of Ehrhart [21] and the grain pattern of all the boards was flat grain. The measured mean rolling shear strength was 1.5 N/mm2 and the mean rolling shear stiffness was 69 N/mm2. In four-point bending tests, a mean Young’s modulus of 11209 N/mm2 was determined. Out of the five tested specimens, three failed due to rolling shear failure and two due to bending failure. The determined mean bending strength of these two specimens was 44.4 N/mm2. The span in the bending tests was 2.0 m and the specimens were 250 mm wide and consisted of three 30 mm thick layers.
3.3. Strain measurement The three-dimensional displacements, recorded with the LED markers, were used to calculate the strains parallel to the grain on the tension side of the plates. Figs. 9 and 10 show the location of section 1-1 and the location of the LED markers. The vertical distance between the LED markers in section 1-1 was 100 mm. The applied reinforcements lead to different strain peaks. In Fig. 11, all specimens with their specific features are illustrated together with the measured and calculated strains. From previous tests with beech plywood plates, similar data could be extracted [3], as shown in Fig. 12. The calculated and measured values are shown at a load level of 130 kN and were taken from the 2D FEM simulation. The difference between spruce CLT (Fig. 11) and beech plywood plates (Fig. 12) is due to the different measurement location and length. The measuring location was 15 mm away from the opening in the beech plywood compared to 5 mm in the CLT and the measurement distance was 200 mm compared to 100 mm. Fig. 13 compares the measured and calculated strains from the 2D FEM model of all specimens. The values shown are the first ones next to the opening. Due to cracks or knots, the right value of specimen 2 and the left value of specimen 3 in Fig. 11 were not considered. The mean difference between calculated and measured strains was −2% for the spruce CLT plates and +6% for the beech plywood plates. Furthermore, it is interesting to analyse whether the measured and calculated strains lead to an accurate prediction of the tensile cracks in the boards next to the opening. Table 2 summarises the calculated tensile stresses when the first cracks were observed. Additionally, the measured values are compared to the calculated values from the 2D and
Fig. 7. Load – displacement behaviour of specimens 1–3.
Fig. 8. Load – displacement behaviour of specimens 4–6.
are shown. The details of these plates can also be seen in Figs. 3 and 11. Specimen 1 showed early deformations due to the narrow support area, which led to a crushing of the timber perpendicular to the grain. Specimen 3 had a 60 mm thick additional load distribution ring placed on the hydraulic jack and therefore a higher ultimate load. The tests were stopped after 75 mm of deformation to prevent damaging the measuring devices. Specimens 4–6 had additional glued on 30 mm thick beech plywood plates on both sides. These specimens achieved about 1.5 times higher ultimate loads than the plates with just CLT. The tests were stopped after the load fell under 80% of the maximum load. All the specimens showed a quasi-ductile global structural behaviour. Specimens 5 and 6 showed a significant drop of load at 600 kN and 640 kN respectively. This happened when the beech plywood at the tension side detached (see also Section 3.5). Fig. 9. LED markers in specimens 1–3. 4
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from bending tests as shown in Section 3.2 was 44.4 N/mm2. As both of these values were calculated with a small number of tests, they have to be treated with caution. Nevertheless, it can be seen that the extrapolated calculated values given in Table 2 are close to the estimated strength at the moment when the first crack appears. As mentioned before, the gaps between the boards were not included in the simulations.
3.4. Rolling shear Table 3 shows the maximum load of every specimen together with the corresponding calculated rolling shear stress at this moment. The three models described in Section 2.2 are compared to each other. The back-calculated values are 30 to 40% higher, than those determined in the shear tests (1.5 N/mm2) in Section 3.2. The simplified model and the 3D solid model show good agreement. The rolling shear stresses calculated in the 3D solid simulation are about 2% higher compared to the simplified model. The results from the 2D plane FEM simulation, which uses the same critical circumference as the simplified model, show a bigger difference to those calculated in the 3D solid FEM simulation. In Fig. 14, a section through the 3D solid FEM simulation of specimen 3 is shown, with the existing rolling shear stresses in both directions at maximum load.
Fig. 10. LED markers in specimens 4–6.
the 3D FEM model. The values in brackets in the column “3D FEM” are the maximum bending stresses at the opening. The strains from the simulation are averaged values between the same locations as in the measurements and are multiplied with the Young’s modulus of the respective material. For spruce it is 11000 N/mm2 and for beech plywood it is 15530 N/mm2, which is the Young’s modulus parallel to the grain or twice the value considered for the plywood in the simulations. The mean bending strength of the beech plywood was 123.7 N/mm2 [22]. The mean bending strength of the CLT specimens determined
Fig. 11. Support details and averaged strains at 130 kN for CLT. 5
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Fig. 12. Support details and averaged strains at 130 kN for beech plywood.
Table 3 Back-calculated rolling shear stress (values in [N/mm2]). Nr.
Max. Load
Simplified
FEM plane
FEM solid
1 2 3 4 5 6
380 408 455 605 620 666
2.0 2.1 1.9 2.1 2.1 2.2
1.8 1.9 1.8 1.9 2.0 2.0
2.0 2.1 2.1 2.2 2.0 2.2
a b
Fig. 13. Measured vs calculated strains next to the opening.
kN kN kN kN kN kN
a b b
Including beech plywood besides bending failure at 557 kN. Not including beech plywood plates on tension side (detaching).
Fig. 14. Rolling shear stresses in the 3D solid FEM model of specimen 3.
Table 2 Calculated stress at first crack (values in [N/mm2]). Specimen 1 2 3 4 5 6 F240 F320 F400
First Crack
Test
2D FEM
3D FEM (max)
Material
200 kN 243 kN 364 kN 557 kN – – 1155 kN 2100 kN 2878 kN
36.7 39.8 47.9 89.8 detaching detaching 100.8 100.4 86.0
39.4 41.4 63.6 81.2
34.4 (44.54) 38.9 (52.2) 58.1 (71.8) 97.4 (113.2)
spruce spruce spruce beech beech beech beech beech beech
Fig. 15. Cut out cube of specimen 5 with detaching failure.
3.5. Detaching of beech plywood plates During the tests on specimens 5 and 6, the glued on beech plywood detached from the spruce CLT at high loads. As the cross section has a discontinuity where the beech plywood plate ends, high stresses appear.
If the grain direction of the top layer of the CLT is parallel to the edge of the plywood, this layer is subjected to rolling shear stresses. At the same time, tensile stresses perpendicular to the grain occur at the tension side 6
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Fig. 17. First tensile failure in specimen 1. Fig. 16. Stress ratio of specimen 6 at 640 kN.
due to the bending shape of the glued on beech plywood. Fig. 15 shows a cut out cube of specimen 5 at the location where detaching occurred. The governing failure which is responsible for detaching is therefore a combination of shear and tension perpendicular to the grain. The identified failure criterion is given by Eq. (2).
σt ,90 τ + R > 1.0 ft ,90 fR
(2)
The rolling shear strength of single spruce boards was determined in Section 3.2 as 1.5 N/mm2. In standardisation, the strength of timber in tension perpendicular to the grain is normally very low. Tests done by Blass and Schmid [23] showed that the mean tensile strength perpendicular to the grain is 1.89 N/mm2 for small specimen volume. In the 3D solid FEM model, rolling shear stresses and tensile stresses perpendicular to the grain were simulated. Along the line of discontinuity the stress ratio from Eq. (2) was observed at the load level of detaching. The horizontal line in Fig. 16 indicates this failure criterion, the dots are simulated points and the dashed line is a second order polynomial fit of these simulated values for specimen 6. At the moment when the bending failure in specimen 4 occurred the maximum stress ratio of Eq. (2) was 1.11. For specimen 5 the maximum stress ratio was 1.00 at the moment of detaching. Specimen 6 had a maximum stress ratio of 1.17 at the moment of detaching. The simulated stress ratios are within the right magnitude so that one can state that the failure of detaching can be described by the approach here presented. Nevertheless, the number of specimens with this observed failure (two out of three) is very limited and therefore further investigations have to be done to confirm this finding.
Fig. 18. First tensile failure in specimen 2.
3.6. Failures on the tension side Interval photo shootings at the tension side of the plate together with the load-displacement curves allow the detection of tensile failure in the outermost lamellae. For specimen 1, a tensile failure next to the opening during the linear elastic phase was observed. At a load level of 200 kN, the first board to the right of the opening failed. Fig. 17 shows the plate just before the failure happens (left) and the crack indicated by an arrow (right). The load-displacement curve in Fig. 7 shows just a minor drop during this failure. The next visible failure is a tensile failure of the first board on the left next to the opening at a load level of 360 kN. In specimen 2 at a load level of 243 kN the first crack in the left board next to the opening appeared, as shown in Fig. 18. The load was subsequently raised up to 400 kN when this crack started growing and the board on the right side of the opening failed as well.
Fig. 19. First tensile failure in specimen 3.
Specimen 3 in Fig. 19 showed no failure until the board at the right side cracked at a load level of 364 kN, which is also visible in the load displacement curve. After that, no further failures were visible until the displacement reached 50 mm. Then the boards at the left side showed tensile failure, too. The specimens with the two-sided glued on beech plywood plates (4–6) showed two different failures. The first failure in specimen 4, shown in Fig. 20, was a tensile failure of the beech plywood plate. It occurred at the tension side and the fibre direction of the outermost layer of the plywood was perpendicular to the crack, which 7
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4.2. Materials and methods To determine the effect of continuous boards on the rolling shear stress distribution, an additional, independent test series was performed. 52 specimens as illustrated in Fig. 22 were tested. The defining difference between the specimens was the overhang of the horizontal boards at the sides of the vertical boards indicated by the parameter ”o” in Fig. 22. The range of the overhang was from 0 mm up to 75 mm. The horizontal boards were always 30 mm thick and 120 mm wide. The vertical boards were either 120 mm or 60 mm wide and either 20 mm or 30 mm thick. All tested specimens are listed in Table 4. The used spruce boards were graded for C24 as stated in SN EN 338:2016 [11]. Additionally, the dynamic Young’s modulus and the density were determined by using the system Timber Grader MTG. The mean dynamic Young’s modulus was 12517 N/mm2 and the mean density was 461 kg/m3. The tested boards had flat grain orientation.
Fig. 20. First tensile failure in specimen 4.
started at a load level of 557 kN. After the whole plywood plate was torn apart, no other failures were visible but the load could still be increased. In specimens 5 and 6, the first failure occurred in the connection between the beech plywood and the CLT. The plywood detached at a load of 640 kN (specimen 6) and 600 kN (specimen 5). This failure is indicated by a large drop in the load-displacement curve. Nevertheless, this failure did no mark the maximum load of these two plates. The load could be increased again with no visible failures from the outside.
4.3. Results In Fig. 23, the y-axis shows the ratio of the achieved load carrying capacity to the mean load carrying capacity of all specimens without overhang. The x-axis shows the ratio (r) between the total width of the overhang to the width of the loaded section.
r = o / wl
(3)
where o and wl can be seen in Fig. 22. Even though the correlation coefficient between the ratio of load carrying capacity of all specimens and r is only 0.33, an increasing load bearing capacity with a rising r is visible. The load carrying capacity can be increased up to 20% when there is an overhang. In order to verify if the mean load carrying capacity of specimens with r > 0 is significantly higher, a one-tailed t-test was performed. On a significance level of 5%, the test showed that the mean load carrying capacity of specimens with r ⩾ 0.5 is significantly higher than the mean load carrying capacity of specimens without overhang.
3.7. Internal failures In order to find areas of rolling shear failures or internal tensile failures, the plates were cut into cubes and all the cracks were recorded. The grey shaded area in Fig. 21 represents the area of rolling shear failure due to shear forces, whereas the black shaded fields show areas with rolling shear failure due to detaching. The jagged lines show tensile failures due to bending. The numbering of the layers starts at the tension side. So the first layer is the outermost layer on the tension side. For example, the jagged line on the right of the opening in specimen 1, reaching from the middle to a location above the opening, represents the tensile failure illustrated in Fig. 17. From the analysis of the internal failures, it was observed that tensile failures occurred often just next to the opening. In contrast to the tensile failures, the rolling shear failures were not locally limited. Some of the plates were almost separated due to the widespread rolling shear failures. In specimens 5 and 6, detaching of the glued on beech plywood plates on the tension side was observed. However, these failures did not mark the ultimate load: widespread rolling shear failures occurred after the detaching. All these observations lead to the conclusion that the rolling shear failure was the governing failure and limited the load carrying capacity of the plates. At the same time, the rolling shear failure provides the capability to achieve large deformations as the shear cracks are growing steadily away from the support area. These continuous failures were clearly audible after the linear elastic phase, as no other failures could be observed from the outside.
5. Discussion The following chapter discusses three topics which are essential for the detailed understanding of the load-bearing behaviour of a two-way, point-supported CLT slab: rolling shear, stress concentration and simulations. 5.1. Rolling shear The calculated rolling shear stress in the punching tests is obviously higher than the measured strength for single boards. This conclusion was already shown by Mestek and others by testing CLT plates without openings [4]. The measured increase was 50% between the punching tests and the shear tests. One reason for this increase is the simultaneously acting compression stress perpendicular to the grain, which increases the rolling shear strength up to 20%. This was proven in shear tests, where specimens were exposed to external compression stress perpendicular to the grain (0.0, 0.3 and 0.8 N/mm2). According to Mestek, a stress redistribution and an anchoring effect due to the continuous boards could be responsible for the additional 25% increase. A simulated distribution of the rolling shear stress and the compression stress perpendicular to the grain for specimen 1 is shown in Fig. 25. The section is in the 4th layer and 10 cm away from the opening as illustrated in Fig. 24 and the considered load level is 130 kN. The grey dashed line shows the shear stress distribution and the black line shows the compression perpendicular to the grain stress distribution. These results were simulated with the 3D solid FEM model. In the additional shear tests two phenomena occurred. First, the increased shear area due to an overhang and second a clamping or
4. Additional rolling shear tests 4.1. Motivation Rolling shear tests, where the whole board is subjected to rolling shear show a nonlinear load-deformation behaviour [20]. These deformations before ultimate failure allow a stress redistribution in only locally loaded or continuous boards. In this case, boards with a highly stressed part show a clamping or anchoring effect and therefore a local reduction of shear stresses. In CLT subjected to concentrated loads, this effect could increase the rolling shear resistance. 8
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Fig. 21. Recorded internal failures.
5.2. Stress concentration
anchoring effect due to large deformations in the middle. Both phenomena lead to a higher ultimate load. The load bearing capacity was increased up to 20% dependent on the overhang. Furthermore, the horizontal boards failed over the whole length and not only at a central part. As the rolling shear distribution in a plate differs from the one in the performed additional rolling shear tests, it is not possible to quantify this anchoring effect in a CLT plate simply based on this test series. Nevertheless, it is likely that the anchoring effect is responsible for an additional increase in rolling shear resistance.
As a result of the point support and the opening in the plate, a strain and consequentially a stress concentration occurs as shown in Figs. 11 and 12. This concentration is influenced of course by the material properties, but also by the area of support, the diameter of the opening and the thickness of the plate. Another point is the arrangement of the boards next to the opening. A board cannot be cut at all or can be cut almost over the whole width. The more of the cross section is cut out due to the opening, the higher is the strain in the residual cross section. It was observed that boards with a small residual cross section already 9
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Fig. 22. Additional rolling shear specimens. Table 4 Number of additional rolling shear specimens. tl [mm]/ wl [mm] overhang 0 mm 15 mm 30 mm 45 mm 60 mm 75 mm
20/ 60
20/ 120
30/ 120
6 3 3 3
11 3 3 3 3 2
6 3 3 3 3 3
Fig. 24. Section for stress distribution through specimen 1.
Fig. 25. Stress distribution around the support for specimen 1.
FEM model, which shows stresses in the same magnitude as the simpler model. The approach to measure and simulate the tensile stresses not directly at the opening, but 5 mm away was also confirmed by the test results. The shear stresses are more difficult to verify. The area of support in the 2D plane FEM model was chosen due to assumptions in terms of load distribution and led to satisfying results for the bending stresses described above. As no nonlinearities were considered in the simulations and as there is so far no conclusive definition of an increase in rolling shear strength for CLT subjected to concentrated load, the calculated rolling shear stresses remain questionable. However, considering that there is a 50% resistance increase, all the models were able to predict the rolling shear failure accurately. Independently of this uncertainty, the three different calculation approaches showed good agreement. Compared to the 3D solid FEM model, the 2D plane model showed lower values. A comparison of the location of the highest shear stresses revealed that the assumption of the load distribution is too big and therefore the critical circumference is too big as well. The
Fig. 23. Rolling shear behaviour of continuous boards.
failed at an early stage of the test, but the neighbouring boards were able to sustain the stresses from the failed boards. Results from the punching tests demonstrate that the occurred tensile failures were not limiting the load-bearing capacity. Nevertheless, the correlation between several geometrical parameters is still not known. Therefore, an additional test series was performed at ETH Zurich, which is currently being evaluated. This series should also evaluate the actual bending resistance of CLT plates with a central opening. 5.3. Simulations The rather simple 2D plane FEM model for simulating the punching tests was able to calculate the tensile and bending stresses accurately. This is confirmed by the comparison of measured and calculated values both for spruce CLT and for beech plywood and also by the 3D solid 10
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References
simplified model compensates this mistake with a shear stress calculation on the safe side. For the critical circumference or effective support area used in the 2D plane FEM simulations, the outermost cross layer should be excluded. In general, the plane FEM model allows designing such column to slab connections, but there is a need for a simple solution to include the detaching failure of the glued on beech plates from the CLT. The results from the solid FEM model are promising, but need verification first.
[1] Zöllig S, Frangi A, Franke S, Muster M. Timber structures 3.0 – new technology for multi-axial, slim, high performance timber structures. World conference on timber engineering (WCTE 2016), Vienna, Austria. 2016. [2] SIA 261:2014. Einwirkung auf Tragwerke; 2014. [3] Boccadoro L. Experimentelle Untersuchungen zum Durchstanzen von Holzdecken (Flachdecke) [Master’s thesis]. ETH Zurich; 2012. [4] Mestek P. Punktgestützte Flächentragwerke aus Brettsperrholz (BSP) – Schubbemessung unter Berücksichtigung von Schubverstärkungen [Doctoral thesis]. TU München; 2011. [5] Hochreiner G, Füssl J, Eberhardsteiner J. Cross-laminated timber plates subjected to concentrated loading: experimental identification of failure mechanisms. Strain 2013;50(1):68–81. [6] Bogensperger T, Jöbstl R, Augustin M. Concentrated load introduction in CLT elements perpendicular to plane. World conference on timber engineering (WCTE 2016), Vienna, Austria. 2016. [7] Popovski M, Chen Z, Gafner B. Structural behaviour of point-supported CLT floor systems. World conference on timber engineering (WCTE 2016), Vienna, Austria. 2016. [8] Maurer B, Maderebner R, Zingerle P, Färberböck I, Flach M. Point-Supported flat slabs with CLT panels. World conference on timber engineering (WCTE 2018), Seoul, Korea. 2018. [9] Kinnunen S, Nylander H. Punching of concrete slabs without shear reinforcement. Transactions of the Royal Institute of Technology, Nr. 158; 1960. [10] SIA 262:2013. Concrete structures; 2013. [11] SN EN 338:2016. Structural timber - Strength classes; 2016. [12] EN 636:2012+A1:2015. Plywood – Specifications; 2012. [13] Northern Digital Inc. Optotrak Certus motion capture system. Retrieved August 07, 2019, from https://www.ndigital.com/msci/products/optotrak-certus/. [14] DIN EN 380:1993. Timber structures; test methods; general principles for static load testing; German version; 1993. [15] Brandner R. Cross laminated timber (CLT) in compression perpendicular to plane: testing, properties, design and recommendations for harmonizing design provisions for structural timber products. Eng Struct 2018;171(15):944–60. [16] Walker D. Untersuchungen zum Tragverhalten von punktgelagerten, zweiachsig tragenden Massivholzplatten [Master’s thesis]. ETH Zurich; 2017. [17] Dlubal Software GmbH. RFEM 5; 2018. [18] Simulia. Abaqus - Finite Element Modelling Programme and Standard User’s Manual. Version 6.11; 2011. [19] Maissen A. Festkörperreibung: Reibungszahlen verschiedener Werkstoffe. Schweizer Ingenieur und Architekt 1993;111(3):25–9. [20] Muster M, Frangi A. Punching behaviour of continuous two-way CLT flat slabs at interior connections to columns. World conference on timber engineering (WCTE 2018), Seoul, Korea. 2018. [21] Ehrhart T, Brandner R, Schickhofer G, Frangi A. Rolling shear properties of some European timber species with focus on cross laminated timber (CLT): test configuration and parameter study. 2nd meeting of the international network on timber engineering research (INTER), Sibenik, Croatia, August 24–27. 2015. p. 61–76. [22] Grüter B. Untersuchungen zum Tragverhalten von Holzplatten aus Buche [Master’s thesis]. ETH Zürich; 2013. [23] Blaß HJ, Schmid M. Querzugfestigkeit von Vollholz und Brettschichtholz. Holz als Roh- und Werkstoff 2002;58(6):456–66.
6. Conclusion The punching tests showed that the chosen slabs are able to transfer high shear forces into the column and can resist high bending moments. The load-displacement behaviour has already been observed in many other studies. Bogensperger et al. [6] stated that the rolling shear softening at material level leads to a global elastic plastic load-displacement behaviour. With an increase of the thickness of the slab it is also possible to fulfil the requirements defined in Section 1. The opening in the plate has no influence on the shear resistance. The same increase in rolling shear resistance was observed in other studies with concentrated loads but without openings. The shear tests with overhanging horizontal boards showed that the anchoring effect is likely responsible for the additional increase in rolling shear resistance. Despite the large opening, none of the specimens failed due to a bending failure even though local tensile failures were observed. As a limited number of plates were tested it is yet not possible to quantify the bending resistance of such CLT slab to column connections. More tests have already been performed and will reveal the relations of the geometric parameters and therefore help to quantify the bending resistance. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The presented research project is funded by Innosuisse. The project partners are Timber Structures 3.0 AG, Timbatec Holzbauingenieure Schweiz AG, Schilliger Holz AG and Henkel & Cie AG. The research project is a collaboration between the ETH Zurich and the Bern University of Applied Sciences.
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