The influences of knot sizes and knot positions on the MOE (moduli of elasticity) and MOR (moduli of rupture) of lumber were investigated theoretically by using the Finite Element Method (FEM). The FEM mesh was basically made by using a flow-grain analogy which was modified according to the measured results. The FEM mesh of each beam consisted of 4104 elements. The computed results were as follows: (i) Edge knots diminish MOE more than center knots do ; for example, in the case of a lumber 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 loading), reduction of the MOE caused by a knot is nearly twice that of four-point (trisection) bending. (iii) The MOE is influenced greatly by the distance between the knot and the central loading point. The influence curve was computed. (iv) The analysis of stress distribution of lumber containing a knot made it clear that the existence of a knot causes large stresses perpendicular to the grain near the knot. The maximum stress near an edge knot is 6-7 times greater than that near a center-located knot of the same size. This great perpendicular stress induces 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, that is, the MOR varies from 1/10 to 1/2 of that of clear lumber.
