Measurement of the Poisson’s Ratio of Materials Based on the Bending Mode of the Cantilever Plate

To explore in-plane shear failure mode of cross-laminated timber (CLT) panel, this paper carried out relevant research work from the perspective of stress analysis and combined with the crack morphology of the specimen after planar shear. In this study, the load–displacement curve of the hemlock [Tsuga canadensis (L.) Carrière] CLT specimen was obtained by a three-point bending test or an improved planar shear test, the crack morphology of the CLT vertical layer and the azimuth angle of the crack surface were observed and recorded synchronously. The shear strength values of CLT specimens under the two tests were obtained by corresponding calculation. Then the stress analysis of the CLT vertical layer was combined with the azimuth angle of the crack surface to discuss the failure mode of the CLT vertical layer in planar shear. The results showed that the planar shear strength measured by the three-point bending test and the improved planar shear test was in good agreement, and the results measured by the improved planar shear test were more dispersed than those measured by the three-point bending test; Considering the approximation that the in-plane shear of the CLT vertical layer could be treated as pure shear, the three-point bending test was better than the improved planar shear test; For the vertical layer of 63.3% CLT specimens, the azimuth of the crack surface was near the azimuth of the first principal plane obtained by stress analysis; There were two failure modes in the CLT vertical layer in-plane shear: tension failure and shear failure.

In this work, according to the first-order torsional mode shape function computed by ANSYS software and the optimization principle, the relationship between the shear modulus of materials and the first-order torsional frequency of the free plate was established in terms of the energy method. Mode shape coefficients of orthotropic materials (lumbers of Sitka spruce, Scots pine, Beech, et al.) and isotropic materials (steel, aluminum, and glass) were calculated. The correlation between the mode shape coefficients of lumbers in tangential, radial, and cross sections and length-width and width-thickness ratios of the free plate was obtained. Also, the correlation between the mode shape coefficients of isotropic materials and the length-width ratio of the free plate were achieved. The correctness of these correlations was verified by mathematical simulation, dynamic testing, and static testing for shear modulus. The transient excitation method can be used to measure the spectrum of free plates. With the aid of the cross-power spectrum based on the frequency spectrum, the first-order torsional frequency of the free plate can be directly identified. The free-plate torsional mode shape method proposed in this work is applicable not only to testing the shear modulus of isotropic materials such as steel but also to testing shear modulus in the three main sections (G_TL, G_LR, and G_RT) of orthotropic materials such as lumber.

The interlaminar shear stresses of the three-layer, five-layer, and seven-layer cross laminated timber (CLT) and those of the oriented laminated beams were calculated according to Hooke’s law and the differential relationship between the beam bending moment and shear force. The interlaminar and maximum shear stresses of the CLT beam are related to the number of CLT layers and to the elastic modulus ratio EL/ET (or EL/ER) of the parallel and perpendicular layers. The interlaminar shear strength of the Hemlock CLT was positively correlated with the elastic modulus of its parallel layer. The results showed that the CLT short-span beams had three failure modes when subjected to a three-point bending test, namely perpendicular layer rolling shear failure, CLT interlaminar shear failure, and parallel layer bending failure. The shear stress of the oriented laminated beam followed a parabolic distribution along the height of the section, while the shear stress of the orthogonally laminated beams tended to be balanced, rather than parabolically distributed along the height of section. The short beam three-point bending method was able to effectively test the interlaminar shear strength of CLT due to its stable and readable load.