Evaluating the Shear Stiffness of Asymmetric Angle-Ply Layers in Diagonal Cross-laminated Timber

doi:10.21203/rs.3.rs-3001955/v1

The perpendicular orientation of the cross-layer (s) makes Cross-laminated Timber (CLT) susceptible to rolling shear failure and reduced stiffness in bending. Under out-of-plane bending, rolling shear failure occurs in the cross layers along the radial-tangential plane. This weakness in CLT panels could be improved by varying the grain orientation of the cross-layers away from perpendicular-to-grain (90°), and closer to parallel-to-grain (0°). This paper studies the shear stiffness of a pair of asymmetric angle-ply layers rotated at angles from 90° to 70°, 40°, 20°, 10°, and 0°. These two layers with varying grain orientations were assumed to be representative of the inner layers of a four-ply Diagonal Cross-laminated Timber (DCLT) panel. For this purpose, Hankinson’s formula was applied in addition to two-plate shear tests and numerical modeling. The experimental testing and FE model results were compared with the theoretical values to evaluate the theory for shear stiffness prediction of the asymmetric angle-ply layers. The results of the three methods showed an agreement in predicting an increase in shear stiffness when the angle-ply orientation of the layers decreases from 90° to 0°. The results indicated that Hankinson’s formula seems to be a conservative theoretical predictor for the shear stiffness of diagonal layers. Regarding the experimental results, orienting the cross layers to an angle between 70° and 40° was shown to improve the rolling shear stiffness by 10% and 46% respectively. This research provides insights into innovations towards CLT development with improved rolling shear stiffness using diagonally-oriented layers.

Cross-laminated Timber

Diagonal cross-laminated timber

Shear Stiffness

Grain orientation of wood

Two-plate (Planar) Shear Test

Finite Element Analysis

The building and construction sector plays an important role in battling the global climate crisis since it contributes up to 40% of annual worldwide greenhouse gas emissions [1]. Over the last two decades, the construction industry has been increasingly interested in using ecologically friendly renewable materials and a shift towards using timber products for long-span structural elements and in high-rise buildings. Methods to improve mass timber competitiveness and structural reliability will ensure its future use as a sustainable, low-carbon-footprint material and a major contributor to affordable structures [2].

Cross-laminated Timber (CLT) is a relatively new mass timber product consisting of layers of timber boards that are stacked and glued crosswise together. Using CLT for floor systems is a growing interest due to its environmental benefits over traditional concrete and steel alternatives. CLT as an orthogonal laminar structure has shown acceptable structural properties and promising dimensional stability compared to unidirectional timber composites such as Glued-laminated Timber (GLT or Glulam). When considering the out-of-plane behavior of a CLT panel, there are parallel and perpendicular-oriented layers that present very different responses. This is because wood is an orthotropic material, meaning that it has different mechanical properties in three principal directions: longitudinal, radial, and tangential. The inner layers orientation in CLT panels exposes timber’s weaker radial and tangential structure to the bending and shear stresses [3]. One of the challenges with using CLT in floor systems is the planar shear properties of wood in the perpendicular-to-grain direction (also called rolling shear). Rolling shear is a unique property of wood due to its anisotropic cellular structure. Rolling shear as shown in Fig. 1 is defined as shear stress leading to shear strains in a plane perpendicular to the main beam axis [4].

Given the orientation of the cross layers with lower shear stiffness properties in the perpendicular-to-grain direction, CLT panels have been identified to be prone to rolling shear failure under out-of-plane loads and this issue can lead the system to relatively large shear deformation and corresponding vertical deflection in CLT floors when subjected to transverse loading.

There have been few studies on the underlying factors influencing rolling shear failure in CLT panels. Among these factors, Nero et al.[3] investigated the effect of aspect ratio and the annual ring orientation on the rolling shear properties of CLT. To investigate these effects, two types of shear tests, the planar shear test, and the short-span four-point bending test were performed on CLT blocks fabricated from Australian-grown Eucalyptus nitens, radiata pine, and European-grown Norway spruce. The tests on these species were performed with annual ring orientations of 0°-30°, 30°-60°, and 60°-90° and with three different aspect ratios (width-to-thickness) of 2, 4, and 6. The width-to-thickness ratio of the test specimen was found to have a strong positive relationship with rolling shear strength. Also, they found that the rolling shear modulus did not have a similar correlation with the aspect ratio. Rather it was shown that the rolling shear modulus is more strongly influenced by the annual ring orientation. The specimens with larger percentages of the smaller ring angles showed larger rolling shear modulus values. Their findings indicated that the orientation of annual rings is more influential in predicting the rolling shear modulus than the aspect ratio.

Aicher et al. [5] investigated the rolling shear modulus dependency on sawing patterns of the wood layers of Norway Spruce by quantitative evaluation using the Finite Element Method. They found that the rolling shear modulus strongly depends on the growth ring orientation of the lamina. When the growth ring of the cross-layer is 45°, the rolling shear modulus is at a maximum value of approximately four times stiffer than the layers with 0° annual rings.

One of the other factors that potentially impacts both the shear and bending properties of the CLT panel, is the grain orientation of the inner layer. When the cross layers are placed diagonally (instead of perpendicularly at 90°) to the major grain direction of the outer plies, the panel’s stiffness properties are improved. Previously, the effect of the grain angle on the shear properties of a solid timber board of Douglas-fir board was studied by Gupta et al. [6]. They tested a total of 85 small specimens with 10 different grain angle orientations ranging from 0° to 90° (10° increments) under two-plate (planar) shear tests. The objective of their study was to find a relationship between shear strength and grain angle orientation. Based on the comparison they did between the actual experimental results and the assessed theories, the modified root-mean-square equation was found to be suitable to predict the relationship between the grain angle and shear strength, while Hankinson’s formula and the Tsai-Wu criteria were less effective compared to their experimental test results.

In another similar study, Bahmanzad et al. [7] hypothesized that reorienting the cross layers of laminations can improve the rolling shear properties of conventional CLT panels. They tested 75 small eastern hemlock specimens with grain orientations of 0°, 30°, 45°, 60°, and 90° (15 replicates of each orientation) under two-plate planar shear tests. They also validated their results using Hankinson’s criterion to examine the accuracy of this theory. Their results from the planar shear tests confirmed that the rolling shear properties of CLT panels could be improved by using angled cross layers compared with traditional layups. For specimens with cross-layer grain orientations of 30° and 45°, their data showed an increase of 98% and 59% higher values for rolling shear strength values and shear modulus values. These results support the reorientation of the inner layers as an alternative candidate for use in the layups of CLT panels to improve their rolling shear properties. Regarding their acquired data and their evaluation of Hankinson’s formula, they found out that this theory can provide an acceptable prediction method for the off-axis shear strength and modulus of wood.

This study evaluates the effect of grain orientation of asymmetric layers on shear stiffness. The specimens under investigation were fabricated from a local softwood species, eastern white pine (Pinus strobus), and tested to determine their performance as the inner layers of Diagonal-Cross-laminated Timber (DCLT) panels. DCLT is a composite timber product, consisting of inner cross layers rotated at different angle-ply orientations between 0 and 90 degrees. These shear specimens were tested under a two-plate (planar) shear test in accordance with ASTM 2718 [8] and their shear properties were recorded and compared to modeled results. A Finite Element Analysis (FEA) was performed to simulate the two-plate (planar) shear test. Finally, Hankinson’s formula and the RMS method were assessed and compared with the results of both experimental data and the finite element method. Exploring the methods to predict the CLT and DCLT mechanical properties allows the industry to consider new non-standard species and orientations for the fabrication of these products.

2.1. Shear Specimens Preparation and Fabrication

Seven flatsawn eastern white pine (Pinus strobus) boards obtained from a local timber supplier near Syracuse, NY were used for this project. The boards were NeLMA [9] finish grade with actual dimensions of 22 mm thickness, 197 mm width, and 3.65 m length. These boards had been kiln-dried and planed. They were stored in ambient conditions in the testing laboratory for 30 days, and the moisture content of all the boards was measured with a Delmhorst (BD 2100) pin-type moisture meter before fabrication. The average measured moisture content of the boards was approximately 11 ± 1%. These boards were planed to the desired thickness of 19 mm to assure uniform thickness and a fresh surface for correct adhesive performance. The boards were then cut to the desired length and orientation for the angled layers.

First, six two-layer panels with 19mm-thick layers, a width of 197mm, and a length of 3.65m with angle-ply orientations of 0°, ± 10°, ± 20°, ± 40°, ± 70°, and 90° were fabricated. The layers were cut to the desired size from the straight grain and defect-free parts of the boards to eliminate the possible effects of knots on the results. However, because of the NeLMA finish grade’s allowance of small knots, and the process of cutting the boards in different grain orientations, a minimal number of knots were included in some of the test specimens. Next, three replicates of each grain orientation panel were cut from the full-size panels to 38mm thickness, 152mm width, and 457mm length (Fig. 2). The width and length of the specimens in this study followed ASTM D2718 [8]. Loctite HB X452 Purbond adhesive (Henkel Corporation, Bridgewater, NJ) with a recommended spread rate of 180 g/m² was used to glue the top and bottom of the lamina (face-glued). The grain orientations of the boards were alternated in the adjacent layer to equalize the effect of shear failure on the overall performance. A vacuum press set to maintain a negative pressure of 0.82 MPa (24 in Hg) was used to apply sufficient pressure for the gluing process. This pressure was found to be sufficient based on previously tested specimens showing no glue failures. The boards were under pressure for 42 hours meeting the minimum requirement of 24 hours and were then released and cut to the final dimension shear blocks.

As Fig. 3 illustrates, to perform the two-plate shear tests, the shear specimens were glued to two steel plates with dimensions of 13- mm thickness, 152- mm width, and 559- mm length with one side knife-edged at 20° on the top and bottom layers.

The steel plates were first heated in an oven at 150°C for one hour to provide dry metal surfaces and to improve the gluing process. Then a Loctite PL Premium Fast Grab Polyurethane adhesive with an approximate spread rate of 1500 g/m² and an assembly time of 20 minutes was used to glue the specimens to the steel plates. As shown in Fig. 4, the specimens glued to the steel plates were placed under a pressure of 1.03 MPa using a Tinius Olsen universal testing machine for 48 hours at 25°C to ensure sufficient bonding.

After each test, the steel plates were prepared by removing wood residue from the previous test. Then they were scrubbed with a clean bristle brush with acetone solvent and then washed under cold running tap water and then placed in the oven again as described above.

2.2. Two-plate Planar Shear Test

The planar shear test, as defined in the European CLT standard EN 16351 − 2021 [11] and as a modified method of the shear compression test in ASTM D2718 [8], was conducted using a compression test fixture configuration with a Young Universal Mechanical Testing Machine. The test was performed to measure the angled and rolling shear modulus (G_α relative to the grain orientation of the angle-ply layers). As shown in Fig. 5, the experimental setup provides uniform shear stress in the layers and guarantees angled and rolling shear failure. The 10° angle (ϴ) of inclination was determined based on the length and thickness of the specimens [12]. Each shear specimen was loaded in compression until failure and the load-displacement curve was recorded to calculate the shear modulus (G_α). The shear modulus (G_α) was calculated using the slope between 40% and 50% of the peak load using Eq. 1,

\({\text{G}}_{{\alpha }}=\frac{t}{\text{l}\times \text{b}} \times \frac{\text{P}}{\varDelta } \times \text{cos}\text{ϴ}\) Eq. 1

where l is the length of inclined height and b is the width of the specimen, t is the thickness of the cross-layer, P/Δ is the slope of the load-displacement linear curve between 40% and 50% range from the first loading step (zero point) to max load, and ϴ is the angle between the shear plane and force direction which here is 10°.

2.3. Finite Element Method

The research version of the software ANSYS® Workbench 2022 [13] was used to provide numerical finite element analysis (FEA) for insight into the shear stress distribution in each specimen during the two-plate (planar) shear test. The boundary conditions of one of the knife-edge steel plates were assumed fixed and the other knife-edge of the steel plate was subjected to the compressive load in the form of displacement.

The specimens were modeled using linear elastic orthotropic wood materials. The nine independent elastic constants are required to define the mechanical response of an orthotropic material in the simulation. These constants are three elastic moduli (E), three Poisson’s ratios (ν), and three shear moduli (G). The actual test configuration was modeled for each shear specimen with two steel plates with a modulus of elasticity and Poisson’s ratio respectively set to 200 GPa and 0.30. For the wood material property values input in the simulations, the longitudinal elastic modulus value (MoE, E_L) for eastern white pine was obtained from non-destructive simply supported bending tests on three eastern white pine boards (span to depth ratio > 15 [8]). The values for two constants of G_LR (G₀) and G_TR (G₉₀) were also acquired from the two-plate shear tests in the study. The USDA Wood Handbook[14] provides elastic ratios with respect to the longitudinal elastic modulus (E_L) for some softwood and hardwood species. However, there are no available published values or elastic ratios for the constants of E_R, G_TL, E_T, and the three required Poisson’s ratios for eastern white pine. To predict these elastic constants using the measured longitudinal (parallel to the grain) modulus of elasticity, linear regressions (confidence level of 95%) were performed on each constant of the species in the USDA Wood Handbook with available elastic ratios. The regressions were performed with Microsoft Excel[14] using the longitudinal MoE as the predictor. The regressions showed R² ranging from 80–99% P < 0.05), indicating a statistically significant correlation between MoE and the response elastic constant (Appendix). Final elastic ratios and values for the material in FEM simulations have been reported in Table 1 and Table 2.

Table 1. Investigated Ratios of Eastern White Pine Mechanical Properties for the ANSYS Simulations Input

Species	Poisson's ratio			Shear Modulus	Young’s Modulus
Species	ν_LT	ν_LR	ν_TR	G_LT/ E_L	E_T/ E_L	E_R/ E_L
Eastern White Pine	0.233	0.223	0.220	0.0693	0.0547	0.0896

Table 2. Final Material Properties of Eastern White Pine for ANSYS Simulations

Species

Poisson's ratio

Shear Modulus (MPa)

Young’s Modulus (MPa)

Specific Gravity

ν_LT

ν_LR

ν_TR

G_LR

G_LT

G_TR

E_T

E_R

E_L

SG

Eastern White Pine

0.233

0.223

0.220

465.0

520.8

37.5

411.1

673.4

7,515.3

0.35

FEM ANSYS Workbench [13] simulations were performed under the “Static Structural” analysis system on a 3D model of each shear specimen with grain orientations of 0°, ± 10°, ± 20°, ± 40°, ± 70°, and 90°. The shear blocks were modeled with the properties and configurations such as material, loading, and boundary conditions identical to those tested. Mesh development was performed under mechanical physics preference (program-controlled element order) by subdividing the mesh size to the rectangular elements with the size of 3.5mm for each solid geometry. The mesh elements used for the sample specimens were higher order elements: SOLID186, a 3-D 20-node element was used for solids, TARGE170, a 3-D target surface for the associated contact element of CONTA174, a 3-D 8-node surface-to-surface element. The mesh size was refined to ensure mesh convergence. Table 3 shows the details of the mesh sizing and the refinement quality of the models.

Table 3

Mesh Sizing and Details for ANSYS Modeling
Group	Bounding Box Diagonal Size (mm)	Average Surface Area (cm²)	Minimum Edge Length Size (mm)	Numbers of Nodes	Number of Elements
Specimen 0°	607	292	12.7	572,624	121,432
Specimen ± 10°	574	151	12.7	541,574	113,460
Specimen ± 20°	566	150	12.7	536,634	112,416
Specimen ± 40°	566	150	12.7	566,792	119,460
Specimen ± 70°	566	121	12.7	560,352	117,672
Specimen 90°	607	135	12.7	576,989	121,432

For each simulation, four coordinate systems were defined: one global coordinate system aligned with the testing machine load heads) two local coordinate systems aligned to the two diagonal layers with ± α° rotation, and one additional coordinate system parallel to the 10° angle of inclination (theta symbol here) of the test set-up. The absolute shear strain was measured with respect to this last coordinate system. The simulation’s details and the details of different coordinate systems designed in the modeling are shown in Fig. 6.

2.4. Evaluating the Shear Stiffness of Specimens Using Analytical Models

Finally, theoretical investigations were performed to evaluate the accuracy of Hankinson’s criterion and the RMS method by experimental and FEM results. The first tested model (Eq. 2) was initially developed by Hankinson in 1921 [16] and is still commonly used to describe uniaxial strength and/or stiffness with respect to the grain angle. Hankinson’s formula has been one of the most useful theories to predict the mechanical properties of solid wood when its grain orientation is at a diagonal angle. Also, a modified model was assessed using the Root-Mean-Square (RMS) method as shown in Eq. 3, which was applied by Gupta et al [6] to find the relationship between the shear strength and the grain angle.

\({\text{G}}_{{\alpha }}= \frac{{\text{G}}_{0 }\times {\text{G}}_{90}}{{\text{G}}_{0}\times {\text{sin}}^{2}{\alpha } +{\text{G}}_{90}\times {\text{cos}}^{2}{\alpha }}\) Eq. 2

\({\text{G}}_{{\alpha }}=\sqrt{{G}_{0}^{2}\times {\text{cos}}^{2}{\alpha }+{G}_{90}^{2}\times {\text{sin}}^{2}{\alpha } }\) Eq. 3

where, α is the angle of the grain orientation off the main axis, G_α is the shear modulus of the diagonal layer, G₀, and G₉₀ are shear moduli parallel and perpendicular to the grain.

This study has evaluated the accuracy of analytical models for predicting the shear stiffness values of angle-ply layers compared to the experimental tests and FEM results. Because these theoretical models use different methods to interpolate intermediate values, it is unclear which theory can provide an accurate relationship over the entire grain angle range [17].

3.1. Two-Plate (Planar) Shear Test Results

For a better understanding of the two-plate (planar) shear test results, the load-deflection curves of all the tested specimens are presented and then values for the shear stiffness of the specimens are presented.

3.1.1. Load-Deflection Curves

The load-displacement curves of the tested shear blocks are illustrated in Fig. 7. The slope (P/Δ) of the specimens (stiffness) decreases as the grain orientation angle in the shear specimens’ layers increases. Therefore, the rolling shear stiffness (G₉₀) is weaker than the longitudinal shear stiffness (G₀). In between these two “pure” shear stress states, the shear in ± α° specimens is a mixed stress state that is part longitudinal shear and part rolling shear. Moreover, the 90° shear specimens are more ductile with larger deformations and a lower value of peak load than the angle-ply ± α° shear specimens. Most of the ± α° shear specimens failed more consistently in an abrupt and brittle manner, with shear specimens at 0° having the largest value of ultimate load and steepest slope of the specimens.

3.1.2. Measured Shear Modulus from the Two-Plate Shear Tests

The shear modulus values of the tested angle-ply eastern white pine shear specimens from two-plate (planar) tests are reported in Table 4. As shown, the mean rolling shear modulus G₉₀ (37.5 MPa) was 1/12.4 of the mean longitudinal shear modulus G₀ (465 MPa). This ratio is approximately 20% less than the assumed ratio suggested in ANSI/APA PRG-320-2019 [10] for rolling shear to longitudinal shear moduli (G₉₀/G₀ = 1/10). Also, considering the measured longitudinal modulus of elasticity (MoE, E₀) of eastern white pine (reported previously in Table 2 to be 7,515.3 MPa), the measured longitudinal shear modulus (G₀) of eastern white pine is 1/16.1 of its measured longitudinal modulus of elasticity (MoE, E₀), which is in agreement with the ANSI/APA PRG 320 [9] suggested ratio of G₀/E₀ = 1/16 for softwoods.

Meanwhile, the mean G_α values of the ± 70°, ± 40°, ± 20°, and ± 10° shear specimens were respectively 10%, 46%, 75%, and 84% higher than the rolling shear value, G₉₀, indicating a progressive increase in shear modulus stiffness when the grain orientation decreases relative to the major grain direction.

Table 4

± α° Specimens Mean Shear Stiffness from Two-Plate (Planar) Shear Test
Mechanical Property (MPa)	Grain Orientation
Mechanical Property (MPa)	0°	10°	20°	40°	70°	90°
Mean Shear Modulus G_α	465.0	230.6	147.5	69.5	41.7	37.5

3.2. Finite Element Analysis

As noted in section ‎2.3, the test configuration was modeled for each shear specimen with two steel plates based on the actual two-plate shear tests. Shear stress and shear strain results from FEM models were evaluated. The maximum shear stress-shear strain linear curves were plotted for each angle-ply shear specimen model. The slopes of the curves were measured as the shear modulus of the angle-ply shear specimens. Figure 8 shows the shear stress distribution in the specimens with two different grain orientations. As shown, the shear stress distribution is uniform over the specimen when the maximum shear stress occurs in the top and bottom parts of the specimen that are in contact with the applied load and the support.

The mean shear modulus values of the FEM models are presented in Table 5. The FEM configuration models the pure shear for the longitudinal (parallel to the grain) and rolling (perpendicular to the grain) shear modulus. The FEM analysis values for the longitudinal shear modulus (G₀) and rolling shear (G₉₀) correspond to the input values for the material properties in the modeling.

Table 5

Shear Modulus Values of ± α° Specimens from the FEM Simulations
Mechanical Property (MPa)	Grain Orientation
Mechanical Property (MPa)	0°	10°	20°	40°	70°	90°
Shear Modulus G_α	465.0	276.7	153.0	89.5	50.7	37.5

3.3. Effect of Angle-Ply Grain Orientation on Shear Modulus

To compare the methods studied for predicting the shear properties in different angle-ply grain orientations, Fig. 9 illustrates the relationship between the grain orientation and the shear modulus from FEM and two-plate (planar) shear tests. Also plotted on this graph are the results from Hankinson’s formula and the modified RMS model to assess the effectiveness of the two theoretical approaches in predicting shear modulus based on grain orientation. As shown, the RMS method significantly overpredicts values from experimental and numerical results. Regarding the shear modulus difference (%) of the RMS method to the experimental values in Table 6, this model appears to be a poor theoretical shear stiffness indicator. However, Hankinson’s equation seems to be a conservative theoretical predictor and it provides a closer fit for the shear modulus results for grain orientations between 40° and 90°. The largest difference between the shear moduli calculated from three methods of two-plate shear tests, FEM, and Hankinson’s formula belongs to the ± 10° and ± 20° specimens. As reported in Table 6, for the shear modulus at ± 10°, the predicted value from Hankinson’s equation, which is 346 MPa, is 50% and 25% higher than the experimental and FEM results respectively. The shear modulus at ± 10° from the FEM simulation is also 20% higher than the experimental result. For the shear modulus at ± 20°, the results from the experimental and FEM are within 4%, while the predicted value from Hankinson’s Eq. (200 MPa) is approximately 35% higher than both the experimental and FEM results. These results seem to agree with the study by Bahmanzad et al. [7] that showed the predicted shear modulus from Hankinson’s equation for the tested specimen with the angle-ply of 30° (the only tested ± α angle-ply specimen with a grain orientation (α) less than 40°) has a larger difference from the experimental result compared to the other angle-ply specimens with grain orientations of 45°, 60° and 90°.

Table 6

The Difference Percentage of the Shear Modulus Between the Assessed Prediction Methods
Prediction Method	Shear Modulus (G_α) Difference %
Prediction Method	10°	20°	40°	70°
Hankinson vs Two-Plate Shear Test	+ 50%	+ 35%	+ 17%	+ 0.7%
FEM vs Two-Plate Shear Test	+ 20%	+ 4%	+ 29%	+ 21%
RMS vs Two-Plate Shear Test	+ 98%	+ 196%	+ 413%	+ 290%

The effect on the shear modulus of varying the grain orientation of eastern white pine has been evaluated in this study. For this purpose, 18 shear specimens with asymmetric angle-ply layers oriented at 0°, ± 10°, ± 20°, ± 40°, ± 70°, and 90° were tested under the two-plate (planar) shear test. Also, one sample of each ± α specimen was modeled in FEM ANSYS Workbench [13] software to provide a comparison to the experimental results. In addition to these two methods, Hankinson’s criterion and a modified RMS model were applied and used to predict the shear moduli. The following conclusions can be drawn from the results of three methods:

Decreasing the angle of the grain orientation in the asymmetric layers from 90° to 0° increases the shear stiffness.
The (rolling) shear stiffness of the inner lamina in CLT panels can be improved by using diagonal layers orientated at an angle less than 90° compared to the traditional layups.
From the two-plate (planar) shear test, orienting the cross layers to an angle between 70° and 40° can improve rolling shear stiffness by 10–46%.
The results from two investigated theoretical models; Hankinson’s formula and the modified RMS model, showed that Hankinson’s criterion provided closer values to the experimental and numerical results. The study shows that RMS is a poor predictor of shear stiffness for angle-ply layers although previous studies showed its effectiveness for measuring the shear strength of layers with a grain angle between 0° and 90°.
It was also shown that Hankinson’s formula provides non-conservative predictions for the shear stiffness of diagonal layers when the angle-ply of the layers is at 10° or 20° and between.
While the North American CLT standard, ANSI/APA PRG 320 [10], predicts the rolling shear (perpendicular to the grain) of softwoods to be 1/10 of the longitudinal shear modulus (parallel to the grain), the results of this study found this ratio to be 1/12.4 for eastern white pine.
The results of this study show that the measured longitudinal shear modulus (G₀, parallel to the grain) of eastern white pine is 1/16.1 of its measured longitudinal modulus of elasticity (MoE, E₀) which is in agreement with the ANSI/APA PRG 320 [10] suggested ratio of G₀/E₀ = 1/16 for softwoods.

Acknowledgement

This research was generously supported by a USDA Wood Innovation Grant, grant number: 20-DG-11094200-179.

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Evaluating the Shear Stiffness of Asymmetric Angle-Ply Layers in Diagonal Cross-laminated Timber

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Materials and Methodology