THEORETICAL-ANALYSIS ON BENDING OF LUMBER CONTAINING KNOTS BY USING FINITE-ELEMENT METHOD

The influences of knot sizes and knot positions on the MOE (moduli of elasticity) and MOR (moduli of rupture) of lumber were investigated th eoretically by using the Finite Element Method (FEM). The FEM mesh was basically made by using a flow-grain analogy which was modified accor ding to the measured results. The FEM mesh of each beam consisted of 4 104 elements. The computed results were as follows: (i) Edge knots dim inish MOE more than center knots do ; for example, in the case of a lu mber containing an edge knot whose diameter is 44% (22%) of the lumber depth and the knot center is on the edge line, MOE decreases 23% (11% ) while it is 11% (2%) for a center knot under a central concentrated load. (ii) In the case of central concentrated loading (three-point lo ading), reduction of the MOE caused by a knot is nearly twice that of four-point (trisection) bending. (iii) The MOE is influenced greatly b y the distance between the knot and the central loading point. The inf luence curve was computed. (iv) The analysis of stress distribution of lumber containing a knot made it clear that the existence of a knot c auses large stresses perpendicular to the grain near the knot. The max imum stress near an edge knot is 6-7 times greater than that near a ce nter-located knot of the same size. This great perpendicular stress in duces a crack near the edge knot at small bending loads; for example, in the case of an edge knot whose diameter is 33% of the lumber depth and the center of the knot is on the edge line, the ultimate load, tha t is, the MOR varies from 1/10 to 1/2 of that of clear lumber.