Numerical analysis of the influence of layer number and thickness on CLT panels under bending

Nuernberg Junior, Claudio; Miotto, José Luiz

doi:10.1590/s1678-86212025000100848

Abstract

In the production of Cross-Laminated Timber (CLT), different geometrical configurations can be adopted. This work analyzed, using Finite Element simulations developed in software Abaqus, the influence of layer geometry in the performance of CLT panels subjected to bending perpendicular to plane and in one direction. The wood was simulated considering an elastoplastic behavior, using the Hill Failure Criterion. The calibration of the simulations was based on experimental results of other authors. Then, the geometry of the panels was changed, varying the number and thickness of the layers, in seven different configurations. The Load x Displacement curves resulted from the simulations were compared and the bending stiffness was calculated using the Mechanically Jointed Beam Theory (Gamma Method). The magnitude and distribution of stress within the panels were also evaluated. Generally, panels with thicker layers oriented in the main direction presented higher bearing capacity and stiffness. A tendency for higher rolling shear stresses was observed on the panels with thicker layers perpendicular to the main direction. The work that was carried out, within its limitations, made it possible to analyze the influence of the layer geometry on the behavior of the CLT panels, therefore fulfilling the research objectives.

Keywords
CLT; Mechanical Properties; Bending; Simulation; Abaqus

Resumo

Na produção de Madeira Lamelada Colada Cruzada (MLCC), diferentes geometrias podem ser adotadas. Esta pesquisa analisou, usando simulações de Elementos Finitos desenvolvidas no software Abaqus, a influência da geometria das camadas no desempenho de painéis de MLCC submetidos à flexão perpendicular ao plano e unidirecional. A madeira foi simulada considerando-se um comportamento elastoplástico, utilizando-se o Critério de Falha de Hill. A calibração das simulações foi baseada em resultados experimentais de outros autores. Então, a geometria dos painéis foi alterada, variando-se o número e a espessura das camadas, em sete diferentes configurações. As curvas de Carga x Deslocamento resultantes das simulações foram comparadas e a rigidez à flexão foi calculada pela Teoria das Vigas Mecanicamente Unidas (Método Gama). A magnitude e a distribuição de tensões nos painéis também foram avaliadas. Em geral, painéis com camadas mais espessas na direção principal apresentaram maior capacidade de carga e rigidez. Verificou-se uma tendência de ocorrerem maiores tensões de rolling shear nos painéis com camadas mais espessas perpendiculares à direção principal. O trabalho realizado, dentro de suas limitações, permitiu a análise da influência da geometria das camadas no comportamento dos painéis de MLCC, atendendo assim os objetivos da pesquisa.

Palavras-chave
MLCC; Propriedades mecânicas; Flexão; Simulações; Abaqus

Introduction

Cross-laminated timber (CLT) is a novel engineered wood material, developed in the 1990s in Central Europe. It consists of panels made of orthogonally glued wooden boards, with variable sizes and layups. CLT panels can be used as structural walls or slabs, and allow the construction of high-rise wood buildings. In Brazil, despite the enormous potential of wood production, mass-timber systems are not as widespread as in Europe and North America.

As an innovative material, the mechanical behavior of CLT panels is constantly subject of research. Variables like material grading and even the wood species used in the manufacturing process can influence the performance of CLT. Usually, engineered wood products are made of softwood species but, recently, the possibility of using hardwood species as raw material for CLT has been evaluated in works like the ones of Das (2023) and Azambuja (2023).

The influence of panel lay-up on the structural performance of CLT has also been investigated. Whenever used on slabs, CLT panels are subjected mainly to bending and shear stresses. Sikora, McPolin and Harte (2016) and O’Ceallaigh, Sikora and Harte (2018) realized bending and shear tests on full scale panels, varying the thickness and number of layers, as well as the total thickness of the panels, evaluating the mechanical performance in terms of stiffness, bending and shear strength and failure modes. Gong (2019) and Kong (2024) also carried out bending tests with different lay ups, as well as rolling shear investigations. Pang and Jeong (2019) studied the effects of the thickness and the distance between supports on the bearing capacity and failure modes of panels subjected to out of plane loads. The influence of the number and thickness of the layers was also investigated by Wang (2018) by means of bending tests.

As rolling shear strength of wood is of major importance in CLT panels and still do not have universally standardized test configuration and methods, it has been subject of several studies, usually considering the variability of panel geometry. Sun, He and Li (2022) and Shahnewaz (2023) performed rolling shear tests to investigate the influence of the thickness of the lamellae on the rolling shear strength and failure mode of wood. Franke (2016) also studied the influence of lamellae thickness on the rolling shear strength and stress distribution of panels.

Even aspects like the orientation of the layers has been investigated. Buck (2016) and Furtmüller, Giger and Adam (2018) produced panels in which the layers were not oriented perpendicular to each other. After bending tests, the authors evaluated the effects of layer orientation on the bending strength, stiffness and failure modes of the panels.

Given that cross-laminated timber is a relatively new material with several application possibilities, it is important to conduct experimental tests, such as those carried out by the researchers previously mentioned, to analyze the performance of CLT panels. However, since different wood species, strength classes, and geometric configurations can be used, incorporating all these variables into experimental procedures can prove costly and time-consuming, especially considering the need to manufacture panels for testing. Thus, the use of computational simulations is highly opportune, as they enable the analysis of different panel types in an agile and economical manner.

This work aims precisely to develop and calibrate a Finite Element modeling, using Abaqus software, capable of representing the mechanical behavior of CLT panels subjected to bending perpendicular to the plane in one direction. From this modeling, differences in the mechanical behavior of the panels resulting from modifications in their number of layers and layer thickness were analyzed.

The Hill Failure Criterion

Due to the complexity of the wood behavior, the pursuit of an adequate failure criterion has been subject of several investigations, as presented in the research of Cabrero (2012).

The Hill Failure Criterion enables the setting of different plastic material properties in each direction, which is suitable to the orthotropic behavior of wood. This criterion was used in Miotto (2009) and Furtmüller, Giger and Adam (2018) to simulate the behavior of timber. One of its major limitations is that there is no distinction between the material properties under compressive or tensile stress for each direction. However, as pointed by Furtmüller, Giger and Adam (2018), this limitation is acceptable, since the differences related to the orthotropic behavior of timber are more significant than the ones between compression or tensile stress.

Dassault Systèmes (2014), on the Analysis User’s Guide of Abaqus, presents the Equation 1, corresponding to the Hill Failure Criterion:

f (σ) = \sqrt{F {(σ_{22} - σ_{33})}^{2} + G {(σ_{33} - σ_{11})}^{2} + H {(σ_{11} - σ_{22})}^{2} + 2 L σ_{23}^{2} + 2 M {σ_{31}}^{2} + 2 N σ_{12}^{2}}

Eq. 1

In this equation, each value of σij corresponds to a stress to which the solid is subjected and F, G, H, L, M and N are constant values obtained by testing the material on different directions. To calculate these constants, Dassault Systèmes (2014) indicates Equations 2 to 8:

F = \frac{{(σ^{0})}^{2}}{2} (\frac{1}{{\bar{σ}}_{22}^{2}} + \frac{1}{{\bar{σ}}_{33}^{2}} - \frac{1}{{\bar{σ}}_{11}^{2}}) = \frac{1}{2} (\frac{1}{R_{22}^{2}} + \frac{1}{R_{33}^{2}} - \frac{1}{R_{11}^{2}})

Eq. 2

G = \frac{{(σ^{0})}^{2}}{2} (\frac{1}{{\bar{σ}}_{33}^{2}} + \frac{1}{{\bar{σ}}_{11}^{2}} - \frac{1}{{\bar{σ}}_{22}^{2}}) = \frac{1}{2} (\frac{1}{R_{33}^{2}} + \frac{1}{R_{11}^{2}} - \frac{1}{R_{22}^{2}})

Eq. 3

H = \frac{{(σ^{0})}^{2}}{2} (\frac{1}{{\bar{σ}}_{11}^{2}} + \frac{1}{{\bar{σ}}_{22}^{2}} - \frac{1}{{\bar{σ}}_{33}^{2}}) = \frac{1}{2} (\frac{1}{R_{11}^{2}} + \frac{1}{R_{22}^{2}} - \frac{1}{R_{33}^{2}})

Eq. 4

L = \frac{3}{2} {(\frac{τ^{0}}{{\bar{σ}}_{23}})}^{2} = \frac{3}{2 R_{23}^{2}}

Eq. 5

M = \frac{3}{2} {(\frac{τ^{0}}{{\bar{σ}}_{13}})}^{2} = \frac{3}{2 R_{13}^{2}}

Eq. 6

N = \frac{3}{2} {(\frac{τ^{0}}{{\bar{σ}}_{13}})}^{2} = \frac{3}{2 R_{13}^{2}}

Eq. 7

τ^{0} = \frac{σ^{0}}{\sqrt{3}}

Eq. 8

In these equations, each value of 𝜎̅ij is the measured yield stress value when σij is applied as the only nonzero stress component, σ0 is a yield stress of reference and τ0 is a shear stress of reference.

Another limitation of the Hill Failure Criterion is related to the fact that the material behavior should be considered the same in all three directions, even though differentiation regarding the level of stresses associated with its plasticization and rupture is possible. That is not the case in wood, as yielding does not occur in tension parallel to the grain, but that was considered a minor limitation for the simulations and analysis purposed in the present work.

Methodological procedures

Research strategy

The Finite Element modeling was implemented in the software Abaqus, version 14.5 in two steps. At first, a calibration phase was necessary to verify if the purposed modeling was adequate to simulate the behavior of the CLT panels and to define how refined the mesh should be. In order to do so, data from O’Ceallaigh, Sikora and Harte (2018) were used in modellings intended to simulate their tests for two different panel layups. Then, the outputs of the simulations were compared to the results of the authors.

Since the comparisons between experimental and simulated results were considered adequate in the calibration phase, it was possible to simulate CLT panels of different layups submitted to bending perpendicular to the main direction. Table 1 presents the geometrical characteristics of the panels simulated in this second phase of the research.

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Table 1
Geometrical characteristics of the panels simulated

After the simulations, the results were discussed based on the comparison between the numerical results and the consulted literature.

Simulating the mechanical properties of wood in Abaqus

O’Ceallaigh, Sikora and Harte (2018) studied the use of Sitka spruce timber in the production of CLT panels, considering it is a fast growing species and the most-widely grown in Ireland. During their experimental procedure, the authors evaluated the mechanical properties of the timber and found that the material could be classified as C16, according to the strength classes included in standard EN 338, from European Committee for Standardization (2009). This standard states the strength and stiffness properties for this class of wood, as presented in Table 2.

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Table 2
Strength and Stiffness properties of C16 wood species according to CEN EN

Besides this information, it was also necessary to obtain a value for the Rolling Shear Modulus. That was obtained from the work of Fellmoser and Blass (2004), who suggested that, for softwood, Rolling Shear Modulus values are on the order of 10% of the value found for the Shear Modulus. Thus, considering a wood of Strength Class C16, it is possible to estimate the Rolling Shear Modulus at 50 MPa.

Another necessary piece of information concerns the Poisson’s Ratio for the analyzed material. Since the reference experiments were conducted with Sitka Spruce wood, efforts were made to obtain values for this same species. Kretschmann (2010) provide these values as νLR= 0.372, νLR= 0.467, and νRT= 0.435.

The rolling shear strength (fr) for the analyzed species was another crucial data for conducting the simulations. This value was obtained from the work of Brandner (2016), who suggest a characteristic value of fr= 0.80 MPa for CLT lamellae produced with a thickness up to four times smaller than the width and 1.40 MPa for lamellae with a thickness-to-width ratio greater than that. So, a characteristic value of 0.80 was considered for rolling shear strength, except for panel B-11-9 and the thinner layers of panels B-30-5-30-5-30 and B-24-14-24-14-24, in which the characteristic value considered was 1.40 MPa.

After obtaining the values for the strength and stiffness properties of the wood used, it was necessary to perform an adjustment to transform the characteristic values of the properties into mean values. For this, the information presented in D2555-06 (ASTM, 2006) standard was consulted, regarding the standard deviation existing between the mean values and the characteristic values of the mechanical properties of wood. The coefficient of variation presented for shear strength was also used to adjust the rolling shear strength.

Therefore, the mean values of the strength properties adopted were those presented in Table 3.

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Table 3
Mean values of the strength properties of wood used in the simulations, considering the adjusted characteristic values

Abaqus allowed the insertion of different elastic properties in each direction of the materials. This was a key factor in order to simulate the orthotropic behavior of wood.

For modeling purposes, in addition to the strength and stiffness properties of the wood, it was also necessary to incorporate information about its behavior under stresses that exceeded the elastic regime. The Hill Failure Criterion was available in the software and enabled the setting of different plastic material properties in each direction.

Porteus and Kermani (2007) present a relationship between the maximum compressive stress (fc,0,m) and the stress at compressive failure (fc,0,u), that fc,0,u = 0.85 fc,0,m. In turn, Johansson (2016) presents typical values of εc ranging from 0.8% to 1.2% and values of εu approximately three times larger than that.

To represent the behavior of the wood after the yield point, stress and strain information were used, considering the parallel to grain direction, that is illustrated by the diagram in Figure 1.

In this diagram, a simplification is presented, which is the consideration that the stress representing the onset of plastic behavior (fc,0,a) has the same value as fc,0,u. The shaded area corresponds to the elastic regime. It is worth noting that the values presented on the horizontal axis correspond only to specific strains in the plastic regime. This explains why the strain associated with the first value of fc,0,a is presented with a value equal to zero on the graphic.

A simplification of the model was that the differences between the elastic and plastic properties and behavior of the material in tension and compression could not be set into the models, which represents a limitation of the simulations. Therefore, the values and behavior associated to tension parallel to the grain had to be considered the same of those associated to compression. Also, the mechanical behavior of wood in compression perpendicular to the grain, shear and rolling shear had to be considered the same associated to compression parallel to the grain, although it was possible to set different stresses associated to these phenomena.

Figure 1
Stress x Strain diagram with the values used in the simulations, considering the parallel to grain direction

The usage of the Hill Failure Criterion in software Abaqus is associated to six yield stress ratios, which are variables presented in Equations 2 to 7. Dassault Systèmes (2014) indicates these ratios in Equations 9 to 14:

R_{11} = \frac{{\bar{σ}}_{11}}{σ^{0}}

Eq. 9

R_{22} = \frac{{\bar{σ}}_{22}}{σ^{0}}

Eq. 10

R_{33} = \frac{{\bar{σ}}_{33}}{σ^{0}}

Eq. 11

R_{12} = \frac{{\bar{σ}}_{12}}{τ^{0}}

Eq. 12

R_{13} = \frac{{\bar{σ}}_{13}}{τ^{0}}

Eq. 13

R_{23} = \frac{{\bar{σ}}_{23}}{τ^{0}}

Eq. 14

The yield stress fc,0,a, of 20.35 MPa was adopted as the stress of reference σ0. The shear stress of reference τ0 was calculated using to Equation 8, resulting in 11.75 MPa. The same adjustment made for fc,0,a, considering its value as 85% of fc,0,m, was made for all the mean values presented in Table 3. Then, the information entered into the software as properties of Sitka Spruce wood is presented in Table 4.

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Table 4
Mechanical properties attributed to Sitka Spruce wood and variables corresponding to the Hill Failure Criterion used in the simulations

Calibration phase: arrangement of the test and construction of numerical model

After defining the properties of the wood used in the simulations, details were sought regarding the geometry of the panels and the tests conducted by O’Ceallaigh, Sikora, and Harte (2018). The panels used in the bending tests simulated for the first calibration consisted of five layers of wood, each with a thickness of 20 mm (therefore referred to as B-5-20), with a width of 584 mm. The span between the supports for the test was 2,400 mm, while the distance between the load points was equal to six times the panel thickness, in this case, 600 mm. Figure 2 illustrates the test setup used by O’Ceallaigh, Sikora, and Harte (2018) and implemented in Abaqus for the first calibration.

Figura 2
Graphical representation of the bending test set-up used by O’Ceallaigh, Sikora and Harte (2018) for the B-5-20 panels

One important aspect of the simulations was the account of boundary conditions to reduce their computational cost. Since the tests were symmetrical, the modeling was divided into two identical parts, considering they would behave in the same way, and only one half was simulated. The model implemented in Abaqus is illustrated in Figure 3.

Figura 3
Model implemented in Abaqus for the B-5-20 panel

Other important aspects of the models were simplifications related to the contact between elements. Since in the experiment the lamellae of each layer were not glued together, an interaction property considering a friction coefficient equal to 0.1 was used between them. The same consideration was adopted in the surface of contact between the timber and steel elements, as recommended by Furtmüller, Giger and Adam (2018). On the other hand, another interaction property was adopted in the surface of contact between the different wood layers, which were glued together in the manufacturing of the panels. In Abaqus, this property was set as a “Constraint” of the “Tie” type, which means that the layers were considered perfectly glued together.

As previously mentioned, Abaqus allowed to inform the orthotropic material properties. In order to do so, it was necessary to assign a material orientation. Figure 4 illustrates the material orientation used, considering the direction 1 as parallel the wood grain.

Figura 4
Material orientation used for wood in Abaqus

The material properties of the steel elements were set as elastic, with E= 200,000.00 MPa and ν= 0.3.

Besides their experimental tests, Furtmüller, Giger and Adam (2018) had also conducted Finite Element Methods simulations. The authors used a mesh of 5 mm hexagonal elements, with outcomes consistent with the experimental results. Using that as a parameter, for the first calibration, two different simulations were held in order to obtain a model capable to reproduce the results of the bending tests with an acceptable computational cost. The difference between them consisted on the size of the elements used, and the computational cost was evaluated based on the simulation duration time.

Second phase: numerical model for panels of different layup

Since the results of the calibrations were regarded as successful, new models were assembled for the seven different panel layups presented on Table 1, using the same methodology. When the simulations were completed, a Load x Displacement curve for each panel was plotted. The theoretical bending stiffness of the panels was calculated using the Mechanically Jointed Beam Theory (Gamma Method), presented in Popovski (2019). Also, the stress level and distribution of the panels were analyzed to understand the influence of the layups on their mechanical behavior.

Results and discussion

Calibration phase: comparison between experimental and simulation results

For the first calibration, two simulations were held, differing on the size of the elements used, a fact that influenced their time span. The first simulation was carried out using a mesh consisting of 117,912 hexagonal elements (C3D8), each one measuring 10 x 10 x 10 mm, and 212,762 nodes, taking 7,629 seconds to be completed. The second simulation was carried out using a mesh consisting of 38.934 hexagonal elements (C3D8), each one measuring 20 x 20 x 10 mm, with 76,508 nodes, taking 1,274 seconds to be completed.

Both the simulations presented similar outcomes. Since the experimental results from O’Ceallaigh, Sikora and Harte (2018) varied from one specimen to another, the simulations were considered adequate as their outcomes were extremely similar and represented the general trend of the bending tests. Figure 5 illustrates the Load x Displacement curves of five bending tests of the referred article and the two simulations conducted in Abaqus.

Figura 5
Load x Displacement curves corresponding to Calibration 1

Therefore, for the second calibration, another simulation was carried out, using the same material properties and considerations of its two predecessors. The model was built using a mesh consisting of 11,768 hexagonal elements (C3D8), each one measuring 20 x 20 x 10 mm, and 21,601 nodes, lasting 269 seconds. The simulation was considered adequate, since its outcomes represented the general trend of the experimental results, as illustrated in Figure 6, with the Load x Displacement curve of the tests and the simulation.

Figura 6
Load x Displacement curves corresponding to Calibration 2

This calibration process assured that the material properties and considerations adopted in the models resulted on simulations capable of reproducing the behavior of different CLT panels. Therefore, the next step was to use the same method to simulate the behavior of CLT panels varying some aspects of their geometry.

Second phase: influence of different layups on the mechanical behavior

After the calibration phase, the same material properties and considerations were used to simulate CLT panels of different layups. The panels simulated were 585 mm width and had practically the same total thickness, of 100 mm. They were subjected to four points bending tests, with a 2,100 mm span, and load applied on two different points, spaced 600 mm from the center of the panels. The differences between the panels were related to the number of layers and their individual thickness, as already showed in Table 1.

A model was assembled according to the geometry of each panel, and then the bending test was simulated. Data related to the progressive load application and the corresponding displacement at the center part of the panel, such as the ones obtained in the bending tests and the abovementioned simulations, were plotted, resulting on the Load x Displacement curves of Figure 7.

Figura 7
Load x Displacement curves for the CLT panels simulated

Since the tests simulated had equal spans and the cross section of the panels had practically the same total size, a direct comparison of their bending stiffness was possible based on the Load x Displacement curves of Figure 7. Considering the slope of the linear segment of the curve, panel B-30-5-30-5-30 presented the highest bending stiffness, since its deformation was lower for an equal load. On the contrary, B-10-35-10-35-10 presented the lowest bending stiffness.

Considering that both the geometry of the panels and the elastic properties of the material were known, it was possible to calculate the theoretical bending stiffness of the panels using the Mechanically Jointed Beam Theory (Gamma Method), presented in Popovski (2019). Figure 8 illustrates the values of bending stiffness calculated according to this method.

Figura 8
Theoretical bending stiffness of CLT panels according to Mechanically Jointed Beam Theory

The comparison between the Load x Displacement curves and the theoretical bending stiffness for the panels demonstrates that the simulations outcomes are consistent with the calculated values. Also, it is noticeable that the sequence of the panels with highest to lowest stiffness is the same in both cases, as well as the similarities between them.

A higher bending stiffness is associated to a larger cross-sectional area of the lamellae oriented parallel to the main direction. It is a consequence of the much larger Modulus of Elasticity of wood in the parallel to the grain direction (in this case, Ec,0= 8,000.0 MPa) compared to the Modulus of Elasticity in the perpendicular to grain direction (Ec,90= 270.0 MPa). These results are in accordance with the experimental works of Furtmüller, Giger and Adam (2018) and Gong (2019). Also, considering only the panels with layers of equal thickness, the bending stiffness seems to have decreased as the lamination thickness decreased, in accordance with Wang (2018) and Kong (2024).

Therefore, although the volume of material used in all the panels is the same, the amount of wood grain oriented on the main direction has a significant impact on its bending stiffness. For instance, panel B-30-5-30-5-30 had 90% of its cross-section made of lamellae oriented in the parallel to main direction, while panel B-10-35-10-35-10 had only 30%, resulting on substantial differences regarding to their bending stiffness.

However, it is noteworthy that this is not the only variable that interferes in the panel bending stiffness, since panel B-3-33 (with 66.7% of cross section oriented on the main direction) and panel B-24-14-24-14-24 (with 72.0%) had an almost identical elastic behavior in the Load x Displacement curve and similar calculated bending stiffness. The same is observed comparing panel B-16-26-16-26-16 (with 48%) and panel B-11-9 (with 54.6%), with the first being slightly stiffer.

That is explained by the fact that the bending stiffness is influenced by both the moment of inertia of each layer and its modulus of elasticity. The moment of inertia of the outermost layers of panel B-3-33, which are oriented parallel to the main direction and therefore have larger modulus of elasticity, is higher than that of panel B-24-14-24-14, which results in higher bending stiffness. In the case of panel B-11-9, since it is composed of many thin layers, the moment of inertia of those oriented parallel to the main direction is smaller than that of panel B-16-26-16-26, resulting in a similar bending stiffness, even though panel B-11-9 has a larger amount of wood oriented parallel to the main direction.

Another tool of the software enables the visualization of the stress distribution on each load increment, in which the load was progressively being increased, and the deformed shape of the panels. The stresses acting in each direction of the material could be visualized, and by setting an adequate range of colors, it was possible to compare the stresses to the reference values presented on Tables 3 and 4.

Figure 9 illustrates results for panel B-5-20, showing the stresses acting in the bottom part of the panel. There, the red and gray color represent the bottom parts of the panel where the maximum tensile stress of 23.94 MPa was reached, with an applied load of 60.5 kN, on the 23rd increment of the simulation. Therefore, when the maximum tensile stress parallel to the grain direction was reached, this was associated to the failure mode of the panel.

Figura 9
Maximum tensile stress in the parallel to the grain direction reached under a 60.5 kN load (panel B-5-20)

Figure 10 also illustrates results for panel B-5-20, in the 12nd increment of the same simulation. There, the elements in black color represent the wood in the top layer reaching a 20.35 MPa compressive stress in the parallel to the grain direction, which was considered the elastic limit for the material. Therefore, this was considered the beginning of the plastic deformations and yielding associated to the compression in this direction.

Figura 10
Compression yield stress reached under a 45.7 kN load (panel B-5-20)

All the panels have reached the compressive yield stress of 20.35 MPa in the top layers, which means that the material achieved the plastic regime. Subsequently, after increments on the load, all the panels reached the maximum tensile stress of 23.94 MPa in the bottom layers. No panel had reached the maximum compressive, rolling shear or shear stress prior to maximum tensile stress, in these simulations.

The tensile rupture of the lamellae of the bottom layer was exactly the behavior expected in these bending tests. It has also been considered the predominant failure mode for the panels tested in Sikora, McPolin and Harte (2016), O’Ceallaigh, Sikora and Harte (2018) and Pang and Jeong (2019). Therefore, although the models did not allow the simulation of the precise rupture of the panels, the methodology, supported by the literature, indicated the tensile stress as their failure mode, since the maximum tensile stresses were observed in the bottom layers.

That being said, it is noteworthy that the value attributed to the maximum tensile stress was considered conservative, as the tensile strength of wood is higher than its compressive strength. The values related to compression were attributed as the material properties in the parallel to grain direction, since the software did not allow the usage of different properties in compression and tension.

Another question is that, under tension parallel to the grain, wood presents a brittle failure, instead of yielding. Once more, since the behavior of the material, set as the stress strain diagram of Figure 1, was necessarily the same for each direction (although with variable stress levels), on both tension and compression, it represents another limitation of this study. However, this was considered a minor limitation, as the analysis were made by comparing the distribution and level of stress acting on the panels to the reference values Tables 3 and 4.

Figure 11 illustrates the loads associated to the compression yielding and the maximum tensile stress of each simulated panel. The percentage of lamellae oriented on the main direction on each panel is also presented.

Figura 11
Loads associated to reaching the maximum tensile strength (Fmax) and compressive yielding (Fcy) on each panel

Considering the methodology utilized, the size of the increments in the simulation was another limitation that could possibly affect the accuracy of the loads associated with the maximum tensile stress and compressive yielding. Since the images of consecutive increments were analyzed and associated to its respective load, and each increment corresponded to one image, the size of the increments in the simulation could cause and overestimation of the load associated to one of these phenomena, which could have begun at a point between the current increment and its predecessor.

These results followed the same pattern observed in the stiffness analysis, with a better performance of panels with a larger amount of wood grains oriented parallel to the main direction. As seen, panel B-30-5-30-5-30 presented the highest loads associated to maximum tensile stress and compression yielding (79.40 kN and 58.40 kN, respectively), while panel B-10-35-10-35-10 presented the lowest (36.00 kN and 29.30 kN, respectively). This result is in accordance with Wang (2018) and Gong (2019).

However, that was not observed in all panels, as we compare the results for panel B-16-26-16-26-16 to those of panel B-11-9 and the results for panel B-3-33 to those of panel B-24-14-24-14-24, in which larger amounts of wood grains oriented parallel to the main direction did not result in higher bearing capacities. That indicates that the thickness of the layers oriented to the main direction is also an important variable associated to the bearing capacity of the panels.

On the other hand, it is noteworthy that an increasing number of layers did not represent an overall advantage, considering the performance of the panels. That might not be the case in mechanical tests, since the higher number of layers would represent a discontinuity of defects such as knots, as a homogenization effect that could increase the performance of the panels, according to O’Ceallaigh, Sikora and Harte (2018). The material properties used on the simulations, however, considered wood as a homogeneous material, without defects, and therefore this advantage could not be simulated.

For all the panel configurations, the loads associated to the maximum tensile stress were between 23% and 36% higher than those responsible for the compressive yielding. Once more, no relation between this range and the number of layers was found.

The stress distribution within the panels was also studied. Concerning the normal stresses, it was observed that the higher values were concentrated in the top and bottom layers for every single panel, as expected, except for B-11-9. In this panel, not only the outer layers, but also the third and the ninth layers, also oriented parallel to the main direction, reached a similar level of stress. That can be explained by the fact that, since the layers are thinner in this panel, the distance between the neutral axis and the geometric center of the outer layers is similar to that of the third and ninth layers. This could be a point of concern when producing panels with thin layers and wood of different grades, since in this situation usually only the outer layers are fabricated with higher graded wood. Considering that a similar level of stress was observed in other layers, using higher graded wood also in these areas should be considered in the manufacturing of CLT panels of thinner layers.

As stated, rolling shear strength was not reached in any simulation. In order to better analyze the influence of the geometry of the panels on the rolling shear stresses, a fixed load was applied on all the panels, and then the magnitude and distribution of the rolling shear stresses were observed. A 30 kN load was adopted in these simulations, since it was approximately the load associated to the beginning of inelastic behavior on panel B-10-35-10-35-10, the lowest among all the panels, according to the data presented in Figure 11. Figure 12 illustrates the rolling shear stresses for panel B-5-20.

Figura 12
Rolling shear stresses under a 30.0 kN load (panel B-5-20)

The maximum rolling shear stress for a 30 kN load was registered for each of the panels. Table 5 shows these data, as well as the comparison between the maximum stresses and the estimated rolling shear strengths.

The rolling shear strength of panels B-11-9, B-30-5-30-5-30 and B-24-14-24-14-24 was considered higher because they had thinner orthogonal layers, and so their width to thickness ratio was more than 4. The value was obtained considering the characteristic strength as 1.40 MPa, and not 0.80 MPa, according to Brandner (2016), and the mean value was obtained using the coefficient of variation of 14% presented in Table 3.

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Table 5
Maximum rolling shear stress for a 30 kN load and comparison to estimated rolling shear strength for each panel

It was expected that a higher number of layers led to an attenuation of rolling shear stresses, according to Franke (2016). That was not found when data of all panels were compared, since panel B-11-9 did not present the lowest values. One explanation for that is the fact that the highest shear and rolling shear values are generally observed in the central layers of CLT panels. Given that the rolling shear occurs in the layers oriented perpendicular to the main direction, and that the five layers panels had their central layer oriented parallel to the main direction, it may had led, in some cases, to lower rolling shear stresses than observed in panel B-11-9, which had its central layer oriented perpendicular to the main direction. Considering that, the rolling shear performance of the panels seemed to be improved by reducing the lamination thickness, in accordance with Kong (2024).

Generally, higher rolling shear stresses were observed on the panels with thicker layers oriented perpendicular to the main direction. This indicates that whenever these layers are thinner, two advantages are found, since that for the same load they present lower stresses and also higher strength. To illustrate that, panel B-10-35-10-35-10 (orthogonal layer of 35 mm) reached 39.23% of the rolling shear strength, while panel B-30-5-30-5-30 (orthogonal layer of 5 mm) reached only 20.35%. Naturally, this is not the only relevant mechanical property to be considered in a design situation and, on the other hand, this panel had the lowest stiffness. However, this fact can be taken into account to produce the most suitable panels to be used in a structural solution.

Conclusions

Based on the investigations presented, the following conclusions can be formulated:

a Finite Element Method modeling using software Abaqus, according to the adopted methodology, was capable of simulating the behavior of CLT panels under perpendicular to the plane bending, with satisfactory computational cost;
the Load x Displacement curves for panels of variable geometry were in accordance with experimental results from other authors and the theoretical bending stiffness calculated using the Mechanically Jointed Beam Theory, allowing an analysis regarding the effect of the number and thickness of the layers of CLT panels on their stiffness;
according to the Load x Displacement curves obtained, panels composed with a greater amount of wood oriented parallel to the main direction revealed higher stiffness, an effect that was more pronounced in panels with thicker layers oriented in this direction, although other variables, such as the moment of inertia of the layers oriented parallel to the grain direction also influenced the bending stiffness;
although the simulation did not represent the exact failure of the panels, the analysis resulted on an estimated tensile failure of the bottom layers, which was in accordance with the experimental results for bending tests, and the maximum tensile stresses occurred under loads 23-36% higher than those associated to the compressive plastic yielding;
considering the level of stresses associated with the maximum tensile stress of the material and the load applied, panels composed with a greater amount of wood oriented parallel to the main direction presented higher bearing capacities (ranging from 79.40 kN for panel B-30-5-30-5-30 to 36 kN for panel B-10-35-10-35-10), an effect that was more pronounced in panels with thicker layers with this orientation;
the distribution of normal stresses observed in panel B-11-9 indicated that, since the level of stress in the outermost layers is similar to that found in other layers distant from the neutral axis, whenever producing panels with thin layers and wood of different grades, using higher graded wood also in these areas should be considered;
generally, for a fixed load of 30 kN, higher rolling shear stresses were observed on the panels with thicker layers oriented perpendicular to the main direction, which indicates that whenever these layers are thinner, they present both lower stresses and also higher strength, depending on the width to thickness relation of their lamellae; and
the results obtained must be considered with reservations, since the models were unable to precisely simulate the wood failure, the mechanical behavior of wood was considered the same under tension and compression, wood was considered a material with no defects and the accuracy of the loads associated to the compressive yielding and tensile failure were influenced by the size of the increments used in the simulation.

Acknowledgments

The second co-author, tutor of the Tutorial Education Program (PET) of the Civil Engineering course at the State University of Maringá (UEM), thanks the Ministry of Education for granting a scholarship during the period of completion of this work.

References

AMERICAN SOCIETY FOR TESTING AND MATERIALS. D-2555-6: standard practice for establishing clear wood strength values. West Conshohocken, 2006.
AZAMBUJA, R. R. Cross-laminated timber panels produced from low-grade yellow-poplar sorted by structural visual grade. Forest Products Journal, v. 73, n. 2, p. 104-112, 2023.
BRANDNER, R. Cross Laminated Timber (CLT): overview and development. European Journal of Wood and Wood Products, Berlin, v. 4, n. 3, p. 331-351, 2016.
BUCK, D. Bending properties of Cross Laminated Timber (CLT) with a 45° alternating layer configuration. BioResources, Raleigh, v. 11, n. 2, p. 4633-4644, 2016.
CABRERO, J. M. Assessment of phenomenological failure criteria for wood. European Journal of Wood and -Wood Products, Berlin, v. 70, n. 6, p. 871-882, 2012.
DAS, S. Suitability of aspen (populous tremula l.) for cross-laminated timber (CLT). Wood Research, v. 68, n. 3, p. 502-520, 2023.
DASSAULT SYSTEMES. Abaqus 6.14: analysis user’s guide. Providence: Dassault Systèmes Simulia Corp., 2014.
EUROPEAN COMMITTEE FOR STANDARDIZATION. EN 338: structural timber: strength classes. Brussels, 2009.
FELLMOSER, P.; BLASS, H. J. Influence of rolling shear modulus on strength and stiffness of structural bonded timber elements. In: International Council for Research and Innovation in Building and Construction, 37., Edinburgh, 2004. Proceedings […] Edinburgh, 2004.
FRANKE, S. Mechanical properties of beech CLT. In: WORLD CONFERENCE ON TIMBER ENGINEERING, Wien, 2016. Proceedings […] Wien: Technische Universität Wien, 2016.
FURTMÜLLER, T.; GIGER, B.; ADAM, C. General shell section properties and failure model for cross-laminated timber obtained by numerical homogenization. Engineering Structures, v. 163, p. 77-92, 2018.
GONG, Y. Evaluation of mechanical properties of cross-laminated timber with different lay-ups using japanese larch. Journal of Renewable Materials, v. 17, n. 10, p. 941-956, 2019.
JOHANSSON, M. Structural properties of sawn timber and engineered wood products. In: SWEDISH FOREST INDUSTRIES FEDERATION. Design of timber structures – volume 1: structural aspects of timber construction. 2^nd ed. Estocolmo: Timber Development UK, 2016.
KONG, F. Experimental investigation on mechanical properties of Chinese fir composites as cross-laminated timber. Industrial Crops & Products, v. 213, 2024.
KRETSCHMANN, D. E. Mechanical properties of wood. In: FOREST PRODUCTS LABORATORY. Wood Handbook: wood as an engineering material. Wisconsin: University Press of the Pacific, 2010.
MIOTTO, J. L. Estruturas mistas de madeira-concreto: avaliação das vigas de madeira laminada colada reforçadas com fibras de vidro. São Carlos, 2009. 325f . Tese (Doutorado em Engenharia de Estruturas) – Escola de Engenharia de São Carlos, Universidade de São Paulo, São Carlos, 2009.
O’CEALLAIGH, C.; SIKORA, K.; HARTE, A. M. The influence of panel lay-up on the characteristic bending and rolling shear Strength of CLT. Buildings, v. 8, n. 9, 2018.
PANG, S. J.; JEONG, G. Y. Effects of combinations of lamina grade and thickness, and span-to-depth ratios on bending properties of cross-laminated timber (CLT) floor. Construction and Building Materials, v. 222, p. 142-141, 2019.
POPOVSKI, M. Structural design of cross-laminated timber elements. In: KARACABEYLI, E.; GAGNON, S. (ed.). Canadian CLT handbook: volume 1. Pointe-Claire: FPInnovations, 2019.
PORTEOUS, J.; KERMANI, A. Structural timber design to Eurocode 5 Oxford: Blackwell Publishing, 2007.
SHAHNEWAZ, M. Experimental research on point-supported CLT panels: phase 1: rolling shear strength. In: WORLD CONFERENCE ON TIMBER ENGINEERING, 13., Oslo, 2023. Proceedings […] Oslo, 2023.
SIKORA, K. S.; MCPOLIN, D. O.; HARTE, A. M. Effects of the thickness of cross laminated timber (CLT) panels made from Irish Sitka spruce on mechanical performance in bending and shear. Construction and Building Materials, v. 116, p. 141-150, 2016.
SUN, X.; HE, M.; LI, Z. Experimental investigation on the influence of lamination aspect ratios on rolling shear strength of cross-laminated timber. Archives of Civil and Mechanical Engineering, v. 22, 2022.
WANG, X. Effect of different thickness of the layers of cross-laminated timber made from chinese fir on the mechanical performance. Bioresources, v. 13, n. 3, p. 7002-7016, 2018.

Edited by

Editores
Marcelo Henrique Farias de Medeiros e Julio Molina Julio Cesar Molina

Publication Dates

Publication in this collection
17 Mar 2025
Date of issue
Jan-Dec 2025

History

Received
01 May 2024
Accepted
16 July 2024

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] AMERICAN SOCIETY FOR TESTING AND MATERIALS. D-2555-6: standard practice for establishing clear wood strength values. West Conshohocken, 2006.

[2] AZAMBUJA, R. R. Cross-laminated timber panels produced from low-grade yellow-poplar sorted by structural visual grade. Forest Products Journal, v. 73, n. 2, p. 104-112, 2023.

[3] BRANDNER, R. Cross Laminated Timber (CLT): overview and development. European Journal of Wood and Wood Products, Berlin, v. 4, n. 3, p. 331-351, 2016.

[4] BUCK, D. Bending properties of Cross Laminated Timber (CLT) with a 45° alternating layer configuration. BioResources, Raleigh, v. 11, n. 2, p. 4633-4644, 2016.

[5] CABRERO, J. M. Assessment of phenomenological failure criteria for wood. European Journal of Wood and -Wood Products, Berlin, v. 70, n. 6, p. 871-882, 2012.

[6] DAS, S. Suitability of aspen (populous tremula l.) for cross-laminated timber (CLT). Wood Research, v. 68, n. 3, p. 502-520, 2023.

[7] DASSAULT SYSTEMES. Abaqus 6.14: analysis user’s guide. Providence: Dassault Systèmes Simulia Corp., 2014.

[8] EUROPEAN COMMITTEE FOR STANDARDIZATION. EN 338: structural timber: strength classes. Brussels, 2009.

[9] FELLMOSER, P.; BLASS, H. J. Influence of rolling shear modulus on strength and stiffness of structural bonded timber elements. In: International Council for Research and Innovation in Building and Construction, 37., Edinburgh, 2004. Proceedings […] Edinburgh, 2004.

[10] FRANKE, S. Mechanical properties of beech CLT. In: WORLD CONFERENCE ON TIMBER ENGINEERING, Wien, 2016. Proceedings […] Wien: Technische Universität Wien, 2016.

[11] FURTMÜLLER, T.; GIGER, B.; ADAM, C. General shell section properties and failure model for cross-laminated timber obtained by numerical homogenization. Engineering Structures, v. 163, p. 77-92, 2018.

[12] GONG, Y. Evaluation of mechanical properties of cross-laminated timber with different lay-ups using japanese larch. Journal of Renewable Materials, v. 17, n. 10, p. 941-956, 2019.

[13] JOHANSSON, M. Structural properties of sawn timber and engineered wood products. In: SWEDISH FOREST INDUSTRIES FEDERATION. Design of timber structures – volume 1: structural aspects of timber construction. 2^nd ed. Estocolmo: Timber Development UK, 2016.

[14] KONG, F. Experimental investigation on mechanical properties of Chinese fir composites as cross-laminated timber. Industrial Crops & Products, v. 213, 2024.

[15] KRETSCHMANN, D. E. Mechanical properties of wood. In: FOREST PRODUCTS LABORATORY. Wood Handbook: wood as an engineering material. Wisconsin: University Press of the Pacific, 2010.

[16] MIOTTO, J. L. Estruturas mistas de madeira-concreto: avaliação das vigas de madeira laminada colada reforçadas com fibras de vidro. São Carlos, 2009. 325f . Tese (Doutorado em Engenharia de Estruturas) – Escola de Engenharia de São Carlos, Universidade de São Paulo, São Carlos, 2009.

[17] O’CEALLAIGH, C.; SIKORA, K.; HARTE, A. M. The influence of panel lay-up on the characteristic bending and rolling shear Strength of CLT. Buildings, v. 8, n. 9, 2018.

[18] PANG, S. J.; JEONG, G. Y. Effects of combinations of lamina grade and thickness, and span-to-depth ratios on bending properties of cross-laminated timber (CLT) floor. Construction and Building Materials, v. 222, p. 142-141, 2019.

[19] POPOVSKI, M. Structural design of cross-laminated timber elements. In: KARACABEYLI, E.; GAGNON, S. (ed.). Canadian CLT handbook: volume 1. Pointe-Claire: FPInnovations, 2019.

[20] PORTEOUS, J.; KERMANI, A. Structural timber design to Eurocode 5 Oxford: Blackwell Publishing, 2007.

[21] SHAHNEWAZ, M. Experimental research on point-supported CLT panels: phase 1: rolling shear strength. In: WORLD CONFERENCE ON TIMBER ENGINEERING, 13., Oslo, 2023. Proceedings […] Oslo, 2023.

[22] SIKORA, K. S.; MCPOLIN, D. O.; HARTE, A. M. Effects of the thickness of cross laminated timber (CLT) panels made from Irish Sitka spruce on mechanical performance in bending and shear. Construction and Building Materials, v. 116, p. 141-150, 2016.

[23] SUN, X.; HE, M.; LI, Z. Experimental investigation on the influence of lamination aspect ratios on rolling shear strength of cross-laminated timber. Archives of Civil and Mechanical Engineering, v. 22, 2022.

[24] WANG, X. Effect of different thickness of the layers of cross-laminated timber made from chinese fir on the mechanical performance. Bioresources, v. 13, n. 3, p. 7002-7016, 2018.

Strength Properties – Characteristic Values (MPa)
Bending (fm,k)	Tension Parallel (ft,0,k)	Tension Perpendicular (ft,90,k)	Compression Parallel (fc,0,k)	Compression Perpendicular (fc,90,k)	Shear (fv,k)
16.00	10.00	0.40	17.00	2.20	3.20
Stiffness Properties (MPa)
Mean Modulus of Elasticity Parallel (E0,mean)		Mean Modulus of Elasticity Perpendicular (E90,mean)		Mean Shear Modulus (Gmean)
8,000.00		270.00		500.00

Property	Coefficient of variation (ASTM D2555-06)	fwk / fm	Characteristic value (MPa)	Mean value (MPa)
Compression strength parallel to the grain (fc,0)	18%	0.71	17.00	23.94
Shear strength parallel to the grain (fv,0)	14%	0.77	3.20	4.16
Compression strength parallel to the grain (fc,90)	28%	0.54	2.20	4.07
Rolling shear strength	14%	0.77	0.80	1.04

Mechanical Property	Mean Value (MPa)	Value associated to onset of plastic behavior (MPa)	Variable of the Hill Failure Criterion	Value attributed
Normal stress parallel to the grain (fc,0)	23.94	20.35	R11	1.00
Normal stress perpendicular to the grain (fc,90)	4.07	3.46	R22	0.17015
Normal stress perpendicular to the grain (fc,90)	4.07	3.46	R33	0.17015
Shear stress perpendicular to the grain (fv,90)	4.36	3.53	R12	0.3006
Shear stress perpendicular to the grain (fv,90)	4.36	3.53	R13	0.3006
Rolling shear stress (fr)	1.04	0.883	R23	0.0752

Panel	Maximum rolling shear stress for a 30 kN load (MPa)	Estimated Rolling Shear strength (MPa)	Percentage of Rolling Shear strength achieved (%)
B-3-33	0.459	1.040	44.13
B-5-20	0.392	1.040	37.69
B-30-5-30-5-30	0.370	1.818	20.35
B-24-14-24-14-24	0.356	1.818	19.58
B-16-26-16-26-16	0.395	1.040	37.98
B-10-35-10-35-10	0.408	1.040	39.23
B-11-9	0.394	1.818	21.67

Numerical analysis of the influence of layer number and thickness on CLT panels under bending

Análise numérica da influência do número e espessura das camadas em painéis de MLCC sob flexão

Abstract

Resumo

Introduction

The Hill Failure Criterion

Methodological procedures

Research strategy

Simulating the mechanical properties of wood in Abaqus

Calibration phase: arrangement of the test and construction of numerical model

Second phase: numerical model for panels of different layup

Results and discussion

Calibration phase: comparison between experimental and simulation results

Second phase: influence of different layups on the mechanical behavior

Conclusions

Acknowledgments

References

Edited by

Publication Dates

History