A three-dimensional paradigm of fiber orientation in timber

Knowledge of the three-dimensional orthogonal directions of wood material a t any position within a tree is necessary for the understanding of strength reducing effects of knots and essential for the continuation of research i n areas which relate small clear wood specimen behavior to the behavior of full size structural timber. A complete three-dimensional paradigm describi ng the geometry of knots and related fiber distortion, initially derived to predict the strength-reducing behavior of knots in structural timber of No rway Spruce with the finite element method, is presented in this article. B esides strength prediction analyses, it is believed that the paradigm may b e useful in other areas of research on structural timber that are effected by fiber orientation, such as drying and form change of structural timber. The paradigm generates fiber orientation in any position within a log or lu mber from assumed fiber patterns in planes parallel to the longitudinal dir ection of the original tree. Fiber patterns in the radial and tangential di rections are derived from physical restraints related to fiber production w ithin the annual increase surfaces of the tree and from theories of knot fo rmation. The adaptability of the paradigm allows practically any softwood k not to be modeled with an accuracy that is limited only by input-data. The knot-axis may be non-linear, and the knot cross-section oval with its verti cal and horizontal axis increasing from the pith of the stem at chosen rate s. Spiral grain may also be included in the paradigm and vary with the annu al growth layers. Investigations presented in this article showed that gene rated fiber orientations for Picea abies complied well with measured fiber distortions, and that the general trends of fiber orientation, explained by the applied knot formation theory, is reflected in the measured specimens.