Spatial correlation of tensile perpendicular to grain properties in Norway spruce timber

Tensile strength perpendicular to grain constitutes one of the most vulnerable properties of timber. Due to versatile influencing parameters this property exhibits a high amount of uncertainty. Thus, progress in modeling, in particular by considering stochastics, is seen as worthwhile. This increases the reliability estimates of timber constructions but also their economic efficiency. Test data of tensile properties determined on consecutive board segments of Norway spruce are analyzed. The data consists of four subgroups, classified in regard to segment length and radial position within the log. The correlation in longitudinal direction of perpendicular to grain tensile strength and elastic modulus as well as of density is examined. This is done depending on the radial position of structural timber within the log. A second-order hierarchical model together with equicorrelation is used. The results outline the applicability of the model and allow the quantification of equicorrelation coefficients of all three properties. The outcome provides a valuable and necessary input for state-of-the-art mechanics-stochastic modeling of the resistance perpendicular to grain tensile strength and elastic modulus of unjointed and jointed structural timber, but in particular of products available in large dimensions, like glued and cross-laminated timber. Additionally, the spatial correlation of density is discussed which is seen as worthwhile for the estimation of group action of fasteners. The necessity to differentiate between the variability within and between segments of structural timber is clearly demonstrated.