Strength of Wood Beams With End Splits

A method of analysis for determining crack propagation loads on wood beams with end splits is presented. The method is based on (1) linear elastic orthotropic fracture mechanics concepts, (2) theory of complex variables, and (3) least squares boundary value collocation (BVC). Using this method, the critical stress intensity factor, Kllc of Douglas-fir beams with end splits is determined to be 2,035 psi √in. Also, a simple failure equation for end split beams is proposed. Acknowledgment The author is indebted to B. Norris and E. O. Erickson, who conducted the experimental studies reported herein in 1951. They reported their results in an unpublished report. Their results have been reevaluated in the light of fracture mechanics theory in the preparation of this paper. United States Department of Agriculture Forest Service Forest Products Laboratory1 Research Paper FPL 347 1979 Strength of Wood Beams With End Splits By JOSEPH MURPHY, Engineer Introduction three independent modes as shown in figure 1. The first mode. or In the grading of timber for beams opening mode, has the crack surit is useful to have a quantitative faces move in a normal direction with measure of the effect of end splits on respect to the surface planes. The the strength of such beams. The second, sliding. or forward shear, al. ( 15 ): method presented gives a way of mode has the surfaces move in their predicting when an end crack will respective planes in the direction propagate resulting in a loss of parallel to collinear crack propagastiffness and strength. Linear elastic tion. The third, tearing, or transverse fracture mechanics has been applied shear, mode has the surfaces moving in their respective planes but Although the title problem has been propagation. The opening mode examined ( 2 ), this report uses a results from (a plane different method of solution and perpendicular to the crack front) loading while the sliding mode loading. The third mode results from out of or antiplane loading conditions (loading parallel to crack front). The theoretical stresses (see 2 for positive stresses) for a small region directly ahead of the crack (the crack surfaces coincident with the negative x, z half plane) for the three modes are reduced from Sih et successfully to predict brittle failure (crack propagation) in wood ( 2 , 8 , 14 ).2 perpendicular to collinear crack simplifies the results while investigatsymmetric about the ing the effect of different orthotropic plane between crack plane surfaces) parameters. fracture mechanics will be overviewed. The propagation of a planar crack can be described, in the most general case, by the combination of Before proceeding, linear elastic results from skew-symmetric 1 Maintained at Madison, Wis., in cooperation 2 Underlined numbers in refer to with the University of Wisconsin. literature cited at end of report.