Effect of Polar Anisotropy of Wood Loaded Perpendicular to Grain

Abstract

This paper reports on an analysis and experimental verification of the effect of cylindrical an- isotropy of softwood loaded in the radial r and tangential t growth plane, i.e., perpendicular to grain. This off- axis loading mode is especially design-relevant for curved and tapered glulam beams. The very low shear stiffness in the r,t on-axis growth plane, together with a complex shear coupling effect in polar coordinates, contributes essentially to extremely variable off-axis strain and stress fields. Thus far, no explicit empiric proof exists for these effects with considerable consequences on damage-relevant stresses. The exemplary off-axis investigations were performed with a cross-sectional slab of a spruce board loaded in tension parallel to the longer edges. True on-axis stiffnesses were determined for the simulations from two on-axis specimens cut from the test volume. Throughout a good agreement between the finite-element predictions and the measured results was obtained. The experiments, for example, proved that off-axis strains parallel and normal to load axes may vary along specimen length by factors of about 4.5 and 9, respectively. The natural fiber-composite material, wood, globally shows a cylindrical anisotropy of stiffness and strength properties. The three principal axes of the cylindrical material anisotropy are (1) the stem (rotation) axis, termed pith, being parallel to the fiber direction; (2) the radial; and (3) tangential directions in the cross section normal to pith. In the radial-tangential plane the constitutive law thus is polar anisotropic. The as- sumption of a cylindrical material anisotropy represents, strictly speaking, an approximation of the actual conical an- isotropy bound to the conical shape of a stem. Growth bound, a periodically layered built-up material, exists in the radial direction with discontinuous stiffness changes at the interfaces of late and early wood of adjacent annual rings. When the regarded size scale covers several annual rings the material may however be approximated as smeared homogeneous in the radial and in the other principal directions. Consequently this homogenization excludes local effects of defects such as knots and resin pockets. The stiffness properties in the three principal material di- rections differ considerably. For most softwoods the stiffness in the fiber direction is about 10-15 times higher compared to radial stiffness, the latter being about 1.5-2 times higher than tangential stiffness. Due to the thin wall thickness of early wood cells within the aforementioned periodical buildup in the radial direction the shear stiffness in the radial-tangential plane is very low for most softwood species; the shear modulus is in the range of about 1/20 of the radial stiffness. Boards and dimension lumber are sawn parallel to the stem axis whereby the rectangular cross section breaks the cylin- drical symmetry according to respective cross-sectional size and position in the stem. Generally, a continuum analysis of bar or plate-shaped in-plane loaded wooden members is per- formed by plane 2D computations based on a rhombic or polar orthotropic material law for straight resp. curved beams. Hereby one of both principal material axes is the fiber direc-