# Effect of Layer Arrangement on Bending Strength of Cross-Laminated Timber (CLT) Manufactured from Poplar (Populus deltoides L.)

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}(Length, Width, Thickness) were fabricated in five configurations: 0/30/0, 0/45/0, 0/90/0, 45/0/45, and 45/45/45. The apparent modulus of elasticity (MOE

_{app}), modulus of rupture (MOR) and apparent bending stiffness (EI

_{app}) values in major and minor axes of CLT panels were calculated using experimental bending testing. In the major axis, the highest values of MOR, MOE

_{app}, and EI

_{app}were obtained from the 0/30/0 arrangement, while the least values resulted from the arrangements of 90/60/90 and 90/45/90 in the minor axis. Besides, in all arrangements, the average of the experimental apparent bending stiffness values (EI

_{app,exp}) of specimens was higher than that of the shear analogy apparent bending stiffness values (EI

_{app,shear}). The bending and shear stress distribution values over the cross section of samples were also estimated using the finite element method. Moreover, the numerical apparent bending stiffness (EI

_{app,fem}) values of samples were compared to experimental apparent bending stiffness (EI

_{app,exp}) values. Based on experimental and finite element method results, in all groups of layer arrangements, the EI

_{app,fem}values concurred well with the EI

_{app,exp}values.

## 1. Introduction

_{eff}) value of the CLT panel and the stress distribution in the laminae depend meaningfully on the rolling shear modulus of the transvers layers of CLT [19]. Several research papers have employed FEM and the shear analogy methodology as two valid methodologies for predicting flexural properties of the CLTs, comparing numerical and analytical data to experimentally test data. The apparent and effective bending stiffness values of innovative multi-layer composite laminated panels predicted by the shear analogy approach were in good concurrence with values recorded by experimental bending testing, according to Niederwestberg et al. [20]. Using the 3D finite element approach, Li et al. [21] estimated the flexural strength of CLT plates under centered loading. The numerical results were found to be in good agreement with the experimental data. Mahamid and Torra-Bilal [22] studied the analysis and design of CLT mats and revealed that the finite element prediction corresponded to the experimental results of maximum displacement, shear, and normal stresses in bending. He et al. [23] evaluated the bending and compression strength of CLT panels constructed with Canadian hemlock at a span to depth ratio of 30. They reported that the finite element method was able to estimate the ultimate deflection and load in the bending test. The global bending stiffness (EI

_{m,g}) and local bending stiffness (EI

_{m,l}) values of the CLT panel could also be determined relatively accurately using the shear analogy approach in the major axis. Besides, they observed that in the major axis, the dominant failure modes of CLT panel were tensile occurred in the bottom outer lamina, and rolling shear occurred in the middle cross lamina of CLT panel. In contrast, in the minor axis, the prevalent failure mode was tensile and occurred in the bottom outer lamina. The bending and shear properties of Australian radiata pine CLT panels were investigated by Navaratnam et al. [24]. They found that experimental bending stiffness values were higher than those obtained by shear analogy, and the bending and shear strength of CLT panels predicted by FEM matched those measured in experiments. In major and minor strength directions, Li et al. [25] examined the engineering performance of two types of 3-ply composite CLT panels made from bamboo mat-curtain panel (BMCP) and hem-fir lumber. They explained that for Composite CLT with the outer layer of bamboo and the inner layer of hem-fir lumber (BWB-CCLT), the MOE and bending strength of the minor strength direction were 96.0% and 104.0% of the major strength direction, respectively. A pilot testing on the flexural behavior of cross-laminated bamboo and wood (CLBT) beams was conducted by Xiao et al. [26]. The testing parameters of the CLBT specimens included two types of inner timber layers spruce-pine-fir (SPF) or poplar wood, and two types of surface engineered bamboo layers (thin-strip glulam or thick-strip glulam). CLBT specimens built with locally available poplar wood had equivalent, if not greater, capabilities than those made with SPF, according to the findings. Hematabadi et al. [27] used experimental and theoretical approaches to investigate the structural performance of hybrid poplar-beech CLT in both major and minor strength directions, comparing the findings to hybrid CLT produced entirely from poplar species. They mentioned that the bending and shear performances of hybrid poplar-beech CLT were superior to those of poplar CLT in all span-to-thickness ratios for both major and minor orientations, based on experimental and theoretical results. In addition, the bending and shear stress distributions of the specimens showed that the hybrid poplar-beech CLT had greater load-carrying capacity than poplar CLT, in both orientations.

- -
- The feasibility of poplar as a raw material for CLT production was investigated
- -
- The effect of layer arrangement on bending strength of CLT panel was investigated
- -
- The dominant failure modes in the major axis were rolling shear and delamination
- -
- The experimental results were in good concurrence with the finite element method

## 2. Materials and Methods

#### 2.1. Materials

^{3}(Length, Width, Thickness). Afterwards, the boards were air-dried for two months at 20 °C and 60% relative humidity to achieve a moisture content (MC) of 12%, as required by ASTM D198 [30]. Different laboratory tests were used to analyze the material properties. More information on evaluating material attributes was presented by Hematabadi et al. [10].

^{3}.

#### 2.2. CLT Panel Production

^{2}(WT), then glued with a 400 g/m

^{2}spread rate of polyurethane adhesive. All of the boards were also edge-glued. The lamellae were then arranged according to the orientations listed in Table 2 to manufacture three-layer CLT panels. Finally, panels were pressed for 90 min at a pressure of 0.8 MPa and a temperature of 40 °C. According to the manufacturer’s specifications, the glue assembly and curing times were 20 and 90 min, respectively. A total of 36 CLT panels with dimensions of 1300 × 360 × 48 mm

^{3}(LWT) were produced. According to the ASTM D198 standard [30], CLT panels were set at 20 °C with a relative humidity of 65% to achieve a moisture content of roughly 12%. Then, in the major and minor axes, CLTs were cut to final dimensions of 1300 × 75 × 48 mm

^{3}. Four CLT samples were tested in each recognized configuration listed in Table 2 to determine their bending strength. Due to the similar layer orientation (45/45/45) at the major and minor axes, only four samples were examined in group E.

#### 2.3. Out-of-Plane Bending Test of CLTs

#### 2.3.1. Experimental Bending Test

_{app}), the apparent bending stiffness (EI

_{app,exp}), and the modulus of rupture (MOR) values of samples were calculated based on the following Equations according to the ASTM D198 standard [30].

_{max}—Maximum moment occurred in the center of the beam (N.mm).

_{max}—the maximum loading (kN).

^{3})

^{4}) computed based on Equation (6)

_{o}terms are the moments of inertia of the individual sections; the f and c indexes are related to the facial and core layers; the A terms are the areas of the individual sections; and the d terms are the distances between the individual section centroids to the composite section centroid.

#### 2.3.2. Apparent Bending Stiffness (EI_{app}) of CLT

_{app}) value of CLT beams was obtained based on three different methods, firstly by experimental study (EI

_{app,exp}) using the Equation (2), secondly based on shear analogy theory (EI

_{app,shear}) using the Equation (7) recommended in CLT Handbook [2], and finally according to numerical analysis using FEM method by ABAQUS [31].

_{eff}is the effective bending stiffness of CLT estimated by the shear analogy approach using Equation (8), K

_{s}is a factor based on a ratio of deflection (14.4 for concentrated loading at mid-span), GA

_{eff}is the effective shear stiffness of CLT estimated by the shear analogy approach using Equation (9), and L is the span length (mm).

_{i}is the modulus of elasticity for the ith lamina (MPa), I

_{i}is the moment of inertia for the ith lamina (mm

^{3}), and n is the number of CLT laminae.

_{i}is the height of each lamina (mm), G

_{i}is the shear modulus of each lamina, b

_{i}is the width of each lamina (mm), and a is the space between the neutral axis of outer laminae (mm), the elastic parameters of poplar species at fiber inclination angles of 30, 45, and 60 degrees were computed according to Hankinson’s Equation (10) [32]. Then, they were used respectively in Equations (8) and (9) for calculating the EI

_{eff,shear}, and GA

_{eff,shear}values of CLT panels at various arrangements of layers. According to the shear analogy approach suggested in CLT Handbook [2], the modulus of elasticity of lumber in the perpendicular to grain axis, E

_{90}, is 1/30 of the modulus of elasticity of lumber in the parallel to grain axis, E

_{0}; the modulus of shear rigidity of lumber in the parallel to grain axis, G

_{0}, is 1/16 of the modulus of elasticity of lumber in the parallel to grain axis, E

_{0}. Furthermore, the modulus of shear rigidity of lumber in the perpendicular to grain axis, G

_{90}, is 1/10 of the modulus of shear rigidity of lumber in the parallel to grain axis, G

_{0}. Table 3 shows the modulus of elasticity and modulus of rigidity (shear modulus) of the poplar’s lamina in various angles of 30, 45, and 60 degrees computed using Equation (10).

_{1}is the strength parallel to the grain, E

_{2}is the strength perpendicular to the grain, and θ is the angle of fiber axis

#### 2.4. Finite Element Modeling of CLT

_{app,fem}) of CLT panels was predicted using finite element modeling, and the bending and shear stress values were compared across the cross-section of CLT panels at various layer arrangements. All groups of CLT specimens were modeled by the finite element method using ABAQUS software Version 6.14 [31]. CLTs were modeled as a rectangular three-layer cross-section beam model in which the layers were connected together by a rigid tie. No lamination gap was considered in modeling because the boards were glued side by side in the CLT manufacturing process. The input elastic properties of wood material used in models were presented in Table 1. In the meshing of the models, a 20-node quadratic hex-structured reduced integration (C3D20R) was considered. There was no difference between the results obtained through the full integration and reduced integration methods; consequently, in this research for faster post-processing, the reduced integration method was selected for all models. Furthermore, the sensitivity analysis of mesh size of the modeling was considered less than 5% difference between the results of each model. The final mesh size for each modeled specimen was considered 5 × 5 × 5 (mm

^{3}).

#### Loading and Boundary Conditions

^{2}area in the center of the beam length in the modeling of the samples, just as it was in the experimental tests. One hardpoint was modeled and connected in the center of the loading surface to apply the concentrated vertical forces in this location. Then the force was input into the hardpoint. Each CLT was modeled with one hinged or pin support and one roller support at the end of the beam length, the same as the experimental tests. The loading and boundary conditions for each model were identical to those used in the experiments. All models were investigated using a static-general solver.

#### 2.5. Bending and Shear Stress Distribution over the Cross-Section of CLT Panel

## 3. Results and Discussion

#### 3.1. Experimental Bending Test Results

#### 3.1.1. Force–Displacement Response

#### 3.1.2. Apparent Modulus of Elasticity (MOE_{app})

_{app}of CLTs manufactured in various configurations in major and minor axes are presented in Figure 3. The highest value of MOE

_{app}of CLT panels was observed at the 0/30/0 configuration, followed by 0/45/0, 0/90/0, 45/0/45, and 45/45/45. The results showed that with alteration of middle layer angle from 30° to 45° or 30° to 90°, the average MOE

_{app}value decreased by 2.4% and 13.6%, respectively, while the maximum value of MOE

_{app}in the minor axis of CLT was obtained at the 45/45/45 arrangement, followed by 45/90/45, 90/0/90, 90/45/90, and 90/60/90. In the minor axis, the CLTs with a surface layer angle of 45° presented higher MOE

_{app}than those with a 90° angle as the maximum value of MOE

_{app}was measured at about 1150 MPa for 45/45/45 configuration. This decreasing trend of MOE

_{app}values was due to the lower stiffness of wood in the middle layer at a greater inclination angle from the beam length axis under bending loading. As a result, the higher the fiber inclination angle from the beam length axis, the lower the bending strength of CLTs. In other words, the MOE

_{app}values of CLT were highly affected when the middle layer angle altered from 30° to 45° or 90°. The results showed that in the major axis, the MOE

_{app}values of specimens were more dependent on the changing angle of surface layers rather than the middle layer. The lowest MOE

_{app}values of CLTs in the major axis were seen at the orientations of 45/0/45 and 45/45/45. Based on the results, the average MOE

_{app}value of CLTs with 45/0/45 orientation was calculated 21% higher than that with 45/45/45 orientation. In addition, the average value of MOE

_{app}of CLTs with 0/90/0 configuration was 511% greater than that with 45/45/45. As a general rule, the higher the total sum of the fiber inclination angle of all layers of the CLT panel, the lower the stiffness of the CLT panel in the minor and major axes.

#### 3.1.3. Modulus of Rupture (MOR) of CLT

_{app}and MOR in the major axis were obtained in 0/30/0, 0/45/0, and 0/90/0 arrangements, respectively (Figure 3 and Figure 4).

#### 3.1.4. Relationship between MOE and MOR of CLTs

#### 3.1.5. Finding the Optimal CLT Construction Based on Mechanical Properties

#### 3.1.6. Failure Modes of CLTs

#### 3.2. Analytical and Numerical Bending and Shear Stress Distribution of CLT

#### 3.2.1. Bending Stress Distribution of CLT

#### 3.2.2. Shear Stress Distribution of CLT

#### 3.3. Apparent Bending Stiffness (EI_{app})

_{app}) value of CLT panels was calculated experimentally (EI

_{app,exp}) using Equation (2) according to the ASTM D198 standard, theoretically according to shear analogy approach (EI

_{app,shear}) using Equation (7), and numerically (EI

_{app,fem}) using load/deflection parameters computed from modeling of CLTs by Abaqus software and using Equation (2).

_{app}values of CLT using experimental, shear analogy, and FEM in various configurations were depicted in Figure 10 and Figure 11. According to the three methods, the major axis of CLT with a 0/30/0 configuration had the highest bending stiffness value, followed by 0/45/0, 0/90/0, 45/0/45, and 45/45/45. This behavior of CLTs was in agreement with the apparent bending stiffness found by Bahmanzad et al. [34]. They reported that the apparent bending stiffness value of CLT with a 30° cross layer was higher than those with 45° and 90°. In contrast, the 45/45/45, 45/90/45, 90/0/90, 90/45/90, and 90/60/90 configurations in the minor axis showed the highest value of bending stiffness, respectively. The natural stiffness of wood layers at different fibers’ inclination angles affects the whole bending stiffness of CLT panels. Consequently, the panels with a higher fibers’ inclination angle along the beam showed lower bending stiffness. Comparing the experimental and shear analogy methods for the arrangements of 0/30/0, 0/45/0, 0/90/0, 45/0/45, 45/45/45, 90/60/90, 90/45/90, 90/0/90, and 45/90/45, the average EI

_{app,exp}values were, respectively, 21.38%, 20.74%, 23.34%, 20.03%, 33.18%, 33.45%, 33%, 26%, and 29.4% greater than EI

_{app,shear}value. Crovellaet al. [36] investigated the EI

_{app}values by the experimental test and shear analogy method for CLT manufactured from Eastern White Pine, Red Maple, and White Ash. They revealed that the shear analogy approach predicted the EI

_{app}value of the softwood and hardwood CLTs by 5% and 25% less than that of the experimental tests. In this research, there was a good agreement between the experimental tests and the FE method for calculating the EI

_{app}of CLTs. Comparing the experimental and FEM results, the EI

_{app,exp}values were 2.17%, 4.16%, 3.4, 6.57%, 6.93%, 8.81%, 7.57%, 3.28%, and 5.88%, less than EI

_{app,fem}, respectively, for the arrangements of 0/30/0, 0/45/0, 0/90/0, 45/0/45, 45/45/45, 90/60/90, 90/45/90, 90/0/90, and 45/90/45.

## 4. Conclusions

- Based on both average MOE and MOR values in both major and minor direction, the optimal CLT was constructed in 0/30/0 orientation. However, based on average MOE values, the optimal construction of CLT was in 0/30/0, 0/45,0, and 0/90/0 orientations, while according to average MOR, the optimal construction of CLTs was in 0/30/0, 0/90,0, and 0/45/0, respectively. Moreover, the 45/45/45 orientation indicated the least CLT construction.
- The dominant failure modes in the major axis were rolling shear and delamination, however, the dominant failure modes in the minor axis were observed as tensile failures and cracks.
- Under an equal loading, both FE and theoretical methods indicated that the maximum bending and shear stress values occurred in middle layers of CLT panels with orientations 90/0/90 and 45/0/45, respectively.
- Comparing the experimental, shear analogy, and FE methods, the EI
_{app,exp}value in all arrangements was at least 20% greater than EI_{app,shear}value of CLTs. However, the EI_{app,fem}value was maximally 8% greater than the EI_{app,exp}value.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**The types of failure modes of CLTs in the various arrangement (

**a**–

**d**) under out-of-plane bending test.

**Figure 10.**Comparison of apparent bending stiffness (EI

_{app}) values estimated by the experimental test, shear analogy, and FEM methods in major axis of CLT.

**Figure 11.**Comparison of apparent bending stiffness (EI

_{app}) values using the experimental test, shear analogy, and FEM approaches in minor axis of CLT.

**Table 1.**Elastic parameters of poplar species at 12% moisture content [10].

Density (g/cm^{3}) | E_{L} (MPa) | E_{R} (MPa) | E_{T} (MPa) | ν_{LR} | ν_{LT} | ν_{RT} | G_{LR} (MPa) | G_{LT} (MPa) | G_{RT} (MPa) |
---|---|---|---|---|---|---|---|---|---|

0.38 | 8900 | 739 | 418 | 0.344 | 0.42 | 0.875 | 676 | 463 | 134 |

Group Name | Layer Arrangement in Major Axis (Degree) | Group Name | Layer Arrangement in Minor Axis (Degree) |
---|---|---|---|

A | 0/30/0 | F | 90/60/90 |

B | 0/45/0 | G | 90/45/90 |

C | 0/90/0 | H | 90/0/90 |

D | 45/0/45 | I | 45/90/45 |

E | 45/45/45 | E | 45/45/45 |

**Table 3.**Modulus of elasticity and modulus of rigidity of the poplar wood at various degrees in accordance with shear analogy approach using Hannkinson’s Equation.

Grain Axis θ (Degree) | 0 | 30 | 45 | 60 | 90 |
---|---|---|---|---|---|

Modulus of Elasticity (MPa) | 8900 | 1079.9 | 574.8 | 391.6 | 297 |

Modulus of rigidity (MPa) | 556.25 | 171.15 | 101.14 | 71.78 | 55.62 |

Orientatios | MOE Major | MOE Minor | Average MOE | MOR Major | MOR Minor | Average MOR |
---|---|---|---|---|---|---|

0/30/0 | 7988 | 440 | 4214 | 65.5 | 6.5 | 36 |

0/45/0 | 7797 | 481 | 4139 | 60.8 | 6.6 | 33.7 |

0/90/0 | 7031 | 740 | 3885.5 | 57.4 | 13 | 35.2 |

45/0/45 | 1400 | 1010 | 1205 | 19.1 | 10.7 | 14.9 |

45/45/45 | 1146 | 1146 | 1146 | 12.2 | 12.2 | 12.2 |

Layers Orientations (Major Axis) | Failure Modes in Major Axis | Layers Orientations (Minor Axis) | Failure Modes in Minor Axis |
---|---|---|---|

0/30/0 | Tensile and Delamination | 90/60/90 | Tensile |

0/45/0 | Tensile and Delamination | 90/45/90 | Tensile |

0/90/0 | Tensile and Delamination | 90/0/90 | Tensile |

45/0/45 | Tensile | 45/90/45 | Tensile and Delamination |

45/45/45 | Tensile, Shear and Delamination | 45/45/45 | Tensile, Shear and Delamination |

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## Share and Cite

**MDPI and ACS Style**

Rostampour Haftkhani, A.; Hematabadi, H.
Effect of Layer Arrangement on Bending Strength of Cross-Laminated Timber (CLT) Manufactured from Poplar (*Populus deltoides* L.). *Buildings* **2022**, *12*, 608.
https://doi.org/10.3390/buildings12050608

**AMA Style**

Rostampour Haftkhani A, Hematabadi H.
Effect of Layer Arrangement on Bending Strength of Cross-Laminated Timber (CLT) Manufactured from Poplar (*Populus deltoides* L.). *Buildings*. 2022; 12(5):608.
https://doi.org/10.3390/buildings12050608

**Chicago/Turabian Style**

Rostampour Haftkhani, Akbar, and Hojat Hematabadi.
2022. "Effect of Layer Arrangement on Bending Strength of Cross-Laminated Timber (CLT) Manufactured from Poplar (*Populus deltoides* L.)" *Buildings* 12, no. 5: 608.
https://doi.org/10.3390/buildings12050608