TRANSFORMATION OF ELASTIC PROPERTIES FOR LUMBER WITH CROSS GRAIN

Application of orthotropic constitutive models to lumber with cross gr ain requires transformation of coordinates when material axes are not aligned with board axes. This paper presents a procedure to construct the coordinate transformation matrix using angles measured on the surf ace of a board for any orientation of wood fibers and growth rings wit hin the board. Procedures in the literature are limited to special ori entations of the wood material, although their authors have not always recognized the limitations. The key to the present method is the reco gnition that for each set of three independent surface angles there co rresponds a set of Euler angles that can be used in the coordinate tra nsformation matrix. Numerical examples show that the procedure identif ies significant variations in board elastic properties for changes in the grain and ring angles. The examples also reveal potentially critic al material shear stresses in uniaxial situations following stress tra nsformations associated with combinations of seemingly small angles.