Elasticity of Wood-Based Materials

All of the materials presented above have three mutually perpendicular principal axes, defining their orthogonal anisotropy. Usually, it is assumed, however, that the thickness of boards is small in relation to other dimensions, and the elastic prop­erties of the wood-based materials in question adopt extreme values in the mutually orthogonal directions, while perpendicular to the thickness of the board. In other words, in two mutually perpendicular directions, the elastic properties of wood-based materials assume extreme values that is the largest in one direction and the smallest in the other direction. These directions correspond to the axes of symmetry of elastic properties, and it has been adopted to call them the main directions of anisotropy. Materials with such properties are called orthotropic. Therefore, Hooke’s law for the orthotropic body in a system of rectangular Cartesian coordinates, overlapping with the main directions of anisotropy (Fig. 4.20), can be written in the form:

where

Ex, Ey linear elasticity modules in the main directions of anisotropy, vx, vy Poisson’s ratios in the main directions of anisotropy,

Gxy shear elasticity module in the anisotropic plane,

ex, sy normal strains in the main directions of anisotropy and

Yxy shear strains in the anisotropic plane,

whereby the following dependency applies here

mxy myx

EX= Ey;

Tables 4.5, 4.6 and 4.7 show examples of values of mechanical properties of different types of wood-based materials.