Estimating the influence of knots on the local longitudinal stiffness in radiata pine structural timber

A theoretical model is developed to evaluate the negative effect of knots on the local longitudinal stiffness (elastic modulus) in radiata pine structural timber. The parameters in the compliance matrices for knotwood in branches are estimated by extending the mechanical formula for clearwood also to knotwood, assuming a structural similarity for stem and branch. The stiffness of knots in the longitudinal direction of sawn boards is then obtained by coordinate transformation. The effective local longitudinal stiffness in a mixture of wood (a combination of knotwood and stem wood) is estimated in terms of the elastic moduli and volume fractions of all phases using a modified rule of mixtures. The effects of branch angle and volume fraction of a knot on the local longitudinal stiffness of structural timber are simulated under different scenarios. Experimental observations also demonstrate similar trends to those shown in the simulations.