Anisotropic shear modulus of wood-based composite

By using stress function methods and the conversion theories from isotropy to anisotropy, the torsional rigidity was analyzed, and the theoretical formulas for the anisotropic shear moduli in width and thickness directions were given for 3-ply composite. According to the theoretical analysis, the anisotropic shear moduli in width and thickness directions, and the anisotropic coefficients were obtained from Eq. (36), (37) and (41). The shear modulus in width direction was not related to that in the thickness direction of each ply, and could be calculated by Eq. (42) including secondary moment. There was an effect of the shear moduli in width direction of each ply on the shear modulus in thickness direction for composite, but it was little.In addition, the variations of shear stress distribution factors, which appear as the correction coefficient to shear modulus in the Timoshenko's beam theory including secondary shear deformation effects, were estimated for the composite materials. Using the mixture law of shear modulus obtained herein and the well-known mixture law of Young's modulus in bending, the shear stress distribution factors in thickness direction for 3-ply composite were about 1.0-1.35 except for 90° plywood. There were still the errors between the theoretical shear moduli and the those estimated from the distribution factors (κ44).