Modeling the effects of knots in Structural Timber
Sammanfattning: The main purpose of the pursued research is to increase knowledge of the effects of knots in structural timber so that characteristics of weaker timber may be determined and applied to improve current grading techniques. In the process, a three-dimensional fiber paradigm was established, which describes variations of local principle material axes in timber containing knots. The adaptability of the paradigm allows practically any softwood knot and its effect on surrounding wood material to be modeled with an accuracy that is limited only by input data. In the description of the fiber paradigm, considerations are given to Shigo’s knot formation theory, which predicts two separate patterns of fiber direction within annual growth layers related to live knots. In order to determine the possibility to practically and non-destructively predict local material directions in structural timber with the three-dimensional fiber paradigm, variations of knot and knot bump geometry and related fiber disturbance of eleven knots from two trees of Nordic Spruce (Picea Abies) grown in Southern Sweden were analyzed. Results showed that the paradigm could be calibrated to describe measured projected fiber orientations in the radial and tangential planes from two visual knot parameters with a coefficient of correlation R2=0.88. Spiral grain was considered in the investigation, and was shown to correspond well to results from previous research on Nordic Spruce. When modeling the mechanical behavior of timber containing knots, variation of material properties within the stem wood, and the effect of altering fiber patterns within a single annual growth layer were modeled with the principles of homogenization and assumed constant material properties of the earlywood, transientwood, and latewood. Flatwise bending stiffness along a timber beam was predicted numerically with the model and compared to measured values. The results indicated that the proposed model of the effect of knots on sawn timber, and the assumed properties of earlywood, transientwood, and latewood in relation to variations of annual ring thickness throughout the beam account for the measured variations of stiffness. The results also suggest that variation of annual ring thickness may cause larger variations in stiffness than the distribution and properties of knots along the beam. The derived and verified model of knot effects on sawn timber was applied to predict the severity of stress states for various knot positions in tensile loaded timber members. From these results a definition of a critical knot was derived. The applicability of the critical knot definition was analyzed in relation to actual tensile load carrying capacities experimentally determined for structural timber. Based on these results it is concluded that the derived critical knot definition offers an efficient method to sort out particularly weak members (tensile capacity less than 20 MPa).
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