Abstract
In this study , torque loading tests on small shear blocks were performed to evaluate the rolling shear strength of crosslaminated timber (CLT). The CLT plates in the tests were manufactured with Mountain Pine Beetleafflicted lumber boards and glued with polyurethane adhesive; two types of layups (fivelayer and threelayer) with a clamping pressure 0.4 MPa were studied. The small block specimens were sampled from fullsize CLT plates and the cross layers were processed to have an annular cross section. These specimens were tested under torque loading until brittle shear failure occurred in the middle cross layers. Based on the test results, the brittle shear failure in the specimens was evaluated by detailed finite element models to confirm the observed failure mode was rolling shear. Furthermore, a Monte Carlo simulation procedure was performed to investigate the occurrence probability of different shear failure modes in the tests considering the randomness of the rolling shear strength and longitudinal shear strength properties in the wood material. The result also suggested the probability of rolling shear failure is very high, which gives more confident proof that the specimens failed dominantly in rolling shear. It was also found that the torque loading test method yielded different rolling shear strength values compared to the previous research from shortspan beam bending tests; such a difference may mainly be due to the different stressed volumes of material under different testing methods, which can be further investigated using the size effect theory in the future.
Introduction
Rolling shear stress in wood is defined as the shear stress in the radial–tangential plane perpendicular to the grain direction; rolling shear strength and stiffness of wood are much lower than its longitudinal shear strength and stiffness [1]. According to the literature [1–6], rolling shear strength normally varies between 18 and 28 % of paralleltograin shear strength based on limited test data. In Eurocode 5 [7], a characteristic rolling shear strength value of 1.0 MPa is used for wood independent of its strength class. In timber design, high rolling shear stresses should always be avoided due to the low rolling shear strength of wood.
Crosslaminated timber (CLT) consists of crosswise oriented layers of wood boards that are either glued by adhesives or fastened with aluminum nails or wooden dowels [8]. For general timber design, rolling shear strength and stiffness are not major design properties. For CLT, however, rolling shear strength and stiffness must be considered in some loading scenarios due to the existing cross layers. For example, when a CLT floor panel is supported by columns, highly concentrated loads in the supporting area may cause high rolling shear stresses in cross layers; the same concerns may arise for designing shortspan floors or beams. Therefore, there is a need to evaluate the rolling shear strength and stiffness properties for more practical applications of CLT structures.
ASTM D271800 stipulates two test methods (shortspan bending test and planar shear test) to evaluate shear properties of wood products [9]. The shortspan bending test is to load the specimen with small spandepth ratios to encourage shear failure mechanism; in the planar shear test, shear loads are applied by two metal plates faceglued onto the specimen. Norlin et al. [10] used a shortspan bending test to study longitudinal and rolling shear strength properties of a laminated veneer product. Using nondestructive bending vibration tests, Fellmoser and Blass [4] studied the influence of rolling shear modulus on CLT stiffness as well as the relationship between shear deformations and beam spandepth ratios. Mestek et al. [11] studied the influence of shear deformations in cross layers on the loadcarrying capacity of CLT beams. Zhou et al. [12] used both planar shear tests and shortspan bending tests to study rolling shear strength and stiffness properties of CLT specimens made by black spruce. Li [6] performed shortterm ramp loading tests in the research of the rolling shear behaviour of CLT; fivelayer and threelayer CLT products were investigated in the tests. In this research, basic shortterm rolling shear strength distribution was established by shortterm ramp loading.
The objective of this study is to evaluate the rolling shear strength properties of nonedgeglued CLT plates by the torque loading tests. The CLT plates were manufactured mainly by Mountain Pine Beetlekilled lodgepole pine, which is one of the major species in the SprucePineFir group in Canada. Another important reason to study CLT made out of the beetleafflicted wood is to utilize the trees from the beetleattacked forests [6].
In this study, torque loading tests were performed on CLT tube specimens. Brittle shear failure mode was observed in the CLT tube specimens. To further investigate the observed failure mode and the shear stress distribution in the cross layers, a detailed finiteelement method was then adopted to simulate the structural behaviour of the CLT tube specimens under the testing conditions. A Monte Carlo simulation procedure was further performed to investigate the probability of different shear failure modes in the tests considering the randomness of the rolling shear strength and longitudinal shear strength in wood material.
Experimental methods
CLT test specimens are shown in Fig. 1, and two categories of the nonedgeglued CLT plates laminated with polyurethane adhesive, i.e., fivelayer SprucePineFir (SPF5) plates and threelayer SprucePineFir (SPF3) plates, were studied. Within each category, one rigid mechanical clamping pressure level (i.e., 0.4 MPa) was applied for manufacturing [13]. For convenience, a fivelayer SprucePineFir plate is simply denoted as an SPF5 plate. Considering the 0.4 MPa pressure applied, this plate is further denoted as SPF50.4. Similarly, a threelayer SprucePineFir plate pressed under 0.4 MPa is denoted as an SPF30.4 plate. Table 1 shows the configurations of these CLT plates, including the board grades, the thickness of laminations, the width of laminations, and the plate dimensions [13, 14]. The grade of lamination in Table 1 follows the NLGA (National Lumber Grade Authority) Standard Grading Rules for Canadian Lumber [15], and the Mountain Pine Beetleafflicted lumber boards in both No.2 and stud grades in Table 1 were used for the CLT manufacturing.
To investigate the rolling shear failure, CLT tube specimens were prepared for the torque loading test, as shown in Fig. 2.
The torque tube specimen included three layers of laminated wood. First, small CLT cubic block specimens were sampled from fullsize CLT plates. Then, the middle cross layer was cut and shaped into cylinder volume with an outer diameter of 52 mm by a computer numerical control (CNC) machine. The whole cylinder middle layer came from one piece of crosslaminated board, and this middle layer was continuous with no gaps guaranteed by the quality control process. Then, one hole with an inner diameter of 19.0 mm was drilled throughout the torque specimen crossing all the three layers of laminated wood. Table 2 shows the detailed information for the CLT torque tube specimens.
After one torque tube specimen was fixed on the loading machine platform, the upper layer of the specimen was locked on a steel frame with lever welded, as shown in Fig. 3. Then, vertical load was applied to the other end of the lever. The force arm from the centre of test specimen to the loading point is 0.5 m. The jack kept loading vertically at a constant loading rate until the specimens failed. The vertical load on the lever transformed into the torque load on the specimen, leaving the middle cylinder layer in a shear status. The loading test adopted the displacement control method, and the speed was about 4.8 mm/min (0.2 inch/min). The total time to failure for one tube specimen was about 4 min. The specimen would fail when the shear stress from the torque loading exceeded the rolling shear strength in the timber material, as further discussed in following sections investigating the failure modes in the torque tests. In the test, the loading history and the failure modes for the specimens were recorded.
Finiteelement model
To investigate the stress distributions in the torque tube specimens, further modeling work was performed and summarized as follows with consideration of different shear stress components (longitudinal shear).
Considering the anisotropic material property in timber material and the grain influences on strength, the evaluation of the stress status of CLT torque tube specimens requires finiteelement method for further investigation, since the elementary mechanical torque theory equations (calculated by hand) are not able to accurately evaluate the structural response of the tube specimens. Therefore, a linear elastic finiteelement analysis was carried out.
The finiteelement model, as shown in Fig. 4, was developed in ANSYS platform [16], considering the glue line shear stiffness and anisotropic wood properties. Dimensions of the tube models are the same as those in the CLT specimens, as introduced in Tables 1 and 2. Table 3 gives the input elastic orthotropic properties of wood material [6, 13]. Poisson’s ratios for SprucePineFir were obtained from the Wood Handbook [2].
Solid volume elements were used to model the wood boards. The metal part of the test jig was also simulated. The fibre direction of the cross layer in the model was the same as that in the test setup, i.e., the grain direction (Y direction) was perpendicular to the longitudinal direction of the steel lever (X direction in Figs. 3 and 4).
For modeling the glue line strength between different layers, the glue line shear stiffness was obtained from one test database [17]. In Schaaf’s study, torsional shear tests were conducted to study the shear strength and stiffness properties of glue lines in threelayered wood composites glued by polyurethane adhesive, as shown in Fig. 5. Table 4 shows the input shear line stiffness value for the finiteelement models. COMBIN14 linear x–y–z spring pairs were used to model the glue line bonding stiffness. The xsprings and ysprings considered the glue line shear stiffness, and the zsprings were assigned with high stiffness value representing rigid vertical bonding between wood layers. The boundary condition for the model was the same as the support condition in the test setup.
Test results and data analysis
There were two failure modes in the torque tests, shown in Figs. 6 and 7; blue stains in the beetleafflicted lumber boards may also be found in Fig. 6. Most of the tube specimens failed in brittle shear failure mode; the shear failure showed the typical brittle failure behaviour with 45° inclined angle observing from the top or bottom face of the tube specimen. The resistance of the specimens to carry load suddenly dropped to zero, when the failure occurred. The other specimens (two specimens at SPF504 group and eight specimens at SPF304 group) showed the glue strength failure in the tests; the average glue failure peak loads for the two specimens at SPF504 group and the eight specimens at SPF304 group are 52,258 and 52,117 N × mm. Only those specimens with the shear failure were included in the analysis in Table 5. The typical curve between the recorded applied load and displacement at the lever end is given in Fig. 8.
In Table 5, the mean value, standard deviation, and coefficient of variation of the measured torque failure loads are given. Table 5 also includes the Weibull fitting parameters for the cumulative distribution of the torque test results. Shear strength τ can be calculated using equation τ = T/I _{p} × r, where τ is the shear strength in N/mm^{2}, T is the peak failure torque load in N × mm from Table 5, I _{p} = πD ^{4}_{outer} /32 − πD ^{4}_{inner} /32 is the polar moment of area in mm^{4}, D _{outer} is the outer diameter, D _{inner} is the inner diameter, and r = D _{outer}/2 is the outer radius in mm. Table 5 gives the mean value of the calculated shear strength τ; the given shear strength τ in Table 5 from equation τ = T/I _{p} × r is based on the assumption of isotropic material property which is not true for timber, and more accurate results can be evaluated based on the developed finiteelement models introduced in the next section.
Analysis and discussion on the rolling shear failure in torque loading tests
Finiteelement model results
In the torque loading tests, most of the CLT tube specimens had brittle shear failure. Once failure occurred, the resistance to carry load sharply dropped to zero. The cracks were developed at an inclined angle in the middle layer of the specimen. The brittle shear failure mechanism in the torque tube specimens was not as clear as the rolling shear failure observed in the shortspan beam specimens [6]. To investigate and confirm that the observed shear failure mode was rolling shear failure in the torque tube specimens, a linear elastic finiteelement analysis was performed to evaluate the rolling shear stress distribution with consideration of the orthotropic wood material properties; the results were summarized as follows with consideration of different shear stress components (longitudinal shear and rolling shear).
Figures 9, 10, and 11 show the shear stress (\( \tau_{\text{xz}} , \tau_{\text{xy}} , \tau_{\text{yz}} \) in Pa in the figures) distributions in the cross layer of threelayer CLT tube specimens, when the applied load level is the mean peak failure load (84,561 N × mm from Table 5) for threelayer CLT. The shear stress \( \tau_{\text{xz}} \) (the same as engineering definitions in Cartesian coordinate system in terms of directions) is the shear stress directed parallel to a given plane (YZ plane) which is perpendicular to the X direction, and this \( \tau_{\text{xz}} \) is parallel to the Z direction. Therefore, since rolling shear is defined as a shear stress leading to the shear strain in the planes perpendicular to the grain, \( \tau_{\text{xz}} \) is the rolling shear stress, and \( \tau_{\text{xy}} \) and \( \tau_{\text{yz}} \) are the longitudinal shear stresses. These two longitudinal shear stresses (\( \tau_{\text{xy}} \) and \( \tau_{\text{yz}} \)) are also uncoupled according to the defined wood orthotropic material property [18]. The maximum value of the shear stress (\( \tau_{\text{xz}} , \tau_{\text{xy}}\,{\text{or}}\,\tau_{\text{yz}} \)) is also given in the figures (in Pa).
Figure 9 shows that the maximum rolling shear stress (3.86 MPa) occurred near the ringedge of the cross layer volume close to the top or bottom layer of the tube specimen, where the initial shear crack typically started in the tests (brittle shear failure mode as given in Fig. 7). As shown in Fig. 10, the maximum longitudinal shear stress is 7.04 MPa.
Similarly, when the applied load level is the mean value of peak failure load (103,989 N × mm from Table 5) for fivelayer CLT, the maximum rolling shear stress (4.83 MPa) occurred near the ringedge of the cross layer volume; the maximum longitudinal shear stress was 10.30 MPa.
In Table 5, the calculated mean shear strength for the threelayer CLT from equation τ = T/I _{p} × r is 3.36 MPa and the calculated mean shear strength for the fivelayer CLT is 3.79 MPa. In the developed finiteelement models, the evaluated mean rolling shear strength is 3.86 MPa for the threelayer CLT and is 4.83 MPa for the fivelayer CLT. The results are close but different; the difference is due to that the finiteelement modeling can simulate the timber anisotropic material property, and it can give more accurate results in terms of shear stress concentrations and distributions in volumes by considering both longitudinal and rolling shear components. The results in Table 5 are based on the assumption of isotropic material property which is different in timber; the finiteelement result shows the shear stress distribution is highly nonuniform by simulating the specimens’ detailed geometry giving a better understanding of the structural behaviour of specimens.
For the threelayer CLT tube specimens, the ratio between the maximum rolling shear stress and longitudinal shear stress is \( R_{\text{Shear}}^{{{\text{Three}}  {\text{layer}}}} = \frac{{\tau_{\text{xz}}^{\hbox{max} } }}{{\tau_{\text{yz}}^{\hbox{max} } }} = \frac{3.86}{7.04} = 0.55 \approx 1/1.82. \) For the fivelayer CLT tube specimens, the ratio between the maximum rolling shear stress and longitudinal shear stress is \( R_{\text{Shear}}^{{{\text{Five}}  {\text{layer}}}} = \frac{{\tau_{\text{xz}}^{\hbox{max} } }}{{\tau_{\text{yz}}^{\hbox{max} } }} = \frac{4.83}{10.30} = 0.47 \approx 1/2.13. \)
Rolling shear strength and stiffness of wood are much lower than its longitudinal shear strength and stiffness. According to limited test data [1–6], rolling shear strength is typically between 18 and 28 % of paralleltograin shear strength. In this study, the ratio \( R_{\text{Shear}} = 0.47 \approx 1/2.13 \) (i.e., the minimum of \( R_{\text{Shear}}^{{{\text{Three}}  {\text{layer}}}} \) and \( R_{\text{Shear}}^{{{\text{Five}}  {\text{layer}}}} \)) is much higher than the ratio of rolling shear strength and longitudinal shear strength (18–28 %, which is about 1/5–1/3). Therefore, in the torque loading tests, the rolling shear stress should reach the material strength limit earlier than longitudinal shear and the brittle failure mode observed in the cross layers of the CLT tube specimens should be rolling shear failure. The calculation from the finiteelement models under applied peak torque load from the experiments shows the longitudinal shear stress not failed meaning that the failure is not longitudinal shear failure; therefore, the ratio \( R_{\text{Shear}} \) shows much higher than the reference data.
Further investigation on the shear failure mode in torque loading tests based on a Monte Carlo simulation procedure
Test results show that the longitudinal shear strength of SprucePineFir, a Canadian softwood species category, ranges from 6.94 to 8.08 MPa [5]. SprucePineFir species comprises timber from white spruce, engelmann spruce, lodgepole pine, and alpine fir species in western Canada (British Columbia and Alberta states, Canada). According to the Wood Handbook [2], the longitudinal shear strength of lodgepole pine grown in Canada is 8.50 MPa in 12 % moisture content, and the white spruce grown in Canada has the lowest longitudinal shear strength (mean value of 6.80 MPa in 12 % moisture content) among SprucePineFir species. There is also research informing the average longitudinal shear strength (mean value of 7.27 MPa) of Mountain Pine Beetleafflicted lodgepole pine, based on the test data [19]. Therefore, the values of 6.80 and 7.27 MPa were selected in the following simulation process.
In this section, a Monte Carlo simulation procedure was performed as follows to investigate the probability of different shear failure modes in torque loading tests, considering the randomness of the rolling shear strength and longitudinal shear strength in wood material, and this process was as follows:

1.
The mean values of rolling shear strength \( \tau_{\text{RS}}^{\text{m}} \) (for example, \( \tau_{\text{RS}}^{\text{m}} = 1.0 \, {\text{MPa}} \)) and longitudinal shear strength \( \tau_{\text{LS}}^{\text{m}} \) (for example, a lower longitudinal shear mean strength \( \tau_{\text{LS}}^{\text{m}} = 6.80 \, {\text{MPa}} \)) were chosen, and a coefficient of variation of 18 % was also chosen.

2.
Assume the rolling shear strength and longitudinal shear strength were lognormally distributed, and based on the initial distribution parameters chosen in step 1), a random sample size of \( N_{\text{Rnd}} = 1000 \) sets of \( \tau_{\text{RS}} \) and \( \tau_{\text{LS}} \) was generated. \( \tau_{\text{RS}} \) and \( \tau_{\text{LS}} \) represent the rolling shear strength and longitudinal shear strength in wood material of this given random set.

3.
For each random set, the ratio (i.e., \( {\text{Ratio}}_{\text{Random}} \)) between \( \tau_{\text{RS}} \) and \( \tau_{\text{LS}} \) was calculated as \( {\text{Ratio}}_{\text{Random}} = \tau_{\text{RS}} /\tau_{\text{LS}} \).

4.
As investigated in the previous section, if \( {\text{Ratio}}_{\text{Random}} < { \hbox{min} }\left( {R_{\text{Shear}}^{{{\text{Three}}  {\text{layer}}}} , R_{\text{Shear}}^{{{\text{Five}}  {\text{layer}}}} } \right), \) where
there is rolling shear failure occurred in this random set; otherwise, the failure mode will be longitudinal shear failure.

5.
The probability of rolling shear failure \( p_{f}^{\text{RS}} \) can be evaluated based on the number of sets with rolling shear failure mode.
In the simulation, different variables were also included and investigated, considering the variable mean values of rolling shear strength \( \tau_{\text{RS}}^{\text{m}} \) (1.0, 1.5, 2.0, 2.5, and 3.0 MPa) and longitudinal shear strength \( \tau_{\text{LS}}^{\text{m}} \) (6.80 and 7.27 MPa), and the coefficient of variation (16 and 18 %).
It needs to be emphasized that the selected longitudinal shear strength category of 6.80 MPa in step (1) of the simulation has already been an underestimation, considering the longitudinal shear strength of lodgepole pine grown in Canada is 8.50 MPa, and considering that the lodgepole pine, rather than white spruce species, was mainly adopted in the related CLT manufacture process [13].
Table 6 shows the probability of rolling shear failure \( p_{f}^{\text{RS}} \) based on different ratios (\( \tau_{\text{RS}}^{\text{m}} /\tau_{\text{LS}}^{\text{m}} \)) between the chosen mean values of rolling shear strength \( \tau_{\text{RS}}^{\text{m}} \) and longitudinal shear strength \( \tau_{\text{LS}}^{\text{m}} \). Although the criterion was strict in the longitudinal shear strength simulation, in most cases, it still shows \( p_{f}^{\text{RS}} > 94\;\% \), and this gives more confidence on the observed rolling shear failure mode in the tube specimens. The cases with \( p_{f}^{\text{RS}} \le 94\;{\text{\% }} \) only occurred when the ratio between \( \tau_{\text{RS}}^{\text{m}} \) and \( \tau_{\text{LS}}^{\text{m}} \) was larger than 1/3. This is not realistic considering rolling shear strength is recognized to be between 18 and 28 % (about 1/5–1/3) of longitudinal shear strength. When the ratio \( \tau_{\text{RS}}^{\text{m}} /\tau_{\text{LS}}^{\text{m}} \) is between 1/5 and 1/3, the \( p_{f}^{\text{RS}} > 97\;\% \). Even when the ratio \( \tau_{\text{RS}}^{\text{m}} /\tau_{\text{LS}}^{\text{m}} \) is impractically larger than 1/3 (\( \tau_{\text{RS}}^{\text{m}} /\tau_{\text{LS}}^{\text{m}} = 1/2.4 \) and with assumed rolling shear strength to be 3 MPa), \( p_{f}^{\text{RS}} \) is still in a high confidence level (75.4 %).
Conclusions
In this study, the rolling shear behaviour of CLT was investigated by the torsional shear tests on CLT shear blocks with processed tubular cross layers. The rolling shear strength values were evaluated by finiteelement modeling of the test specimens subjected to the failure loads. Simple analytical equations to calculate the rolling shear strength is not applicable in this study due to the complicated orthotropic wood properties and the torsional shear loading scheme. A Monte Carlo simulation procedure was performed to investigate the occurrence probability of longitudinal shear and rolling shear failure modes in the specimens considering the randomness of the rolling shear strength and longitudinal shear strength of wood material. The simulation results further confirmed that the observed brittle shear failure was indeed rolling shear. Therefore, the torque loading test is a viable method to investigate the rolling shear behaviour of the CLT specimens.
The evaluated rolling shear strength values by the finiteelement modeling results were very different from other test results from bending tests or planar shear tests available in literature. In this study, much higher rolling shear strength values were obtained, i.e., 3.86 and 4.83 MPa, for the threelayer and the fivelayer CLT tube specimens, respectively. Apparently, these values cannot be directly used for design purpose, because it involved a significant size effect and rolling shear stress concentration was observed in the cross layers. However, together with shortspan bending test results, these test results can be a useful data source to study the size effect on rolling shear strength properties of CLT with common structural sizes under normal loading scenarios. In addition, to consider the size dependence and to explain the strength differences between the CLT beam bending tests and the torque loading tests, Weibull’s weakest link theory will be applied to evaluate the size effect on the rolling shear strength of CLT in the future.
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Acknowledgments
The authors would like to thank NSERC strategic network for engineered woodbased building systems for supporting this research. Special thanks also go to Dr. Ricardo O. Foschi for his advice and guidance in the research.
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Lam, F., Li, Y. & Li, M. Torque loading tests on the rolling shear strength of crosslaminated timber. J Wood Sci 62, 407–415 (2016). https://doi.org/10.1007/s1008601615672
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Keywords
 Torque loading test
 Rolling shear
 Crosslaminated timber
 Brittle fracture
 Finite element model