Timber Beams with Holes: Fracture Mechanics Approach

Abstract

Timber beams with holes have been analyzed with linear elastic fracture mechanics. The energy release rate corresponding to the beginning of the crack growth is set equal to the external work done by the loading of the beam. Further, this fracture energy is partitioned into a mode I and a mode II component. Stress intensities at the hole corner are calculated from the strain energy release rates, and the orthotropicity of the material is taken into account. If the hole is near to the support or the point load, a correction term is given for the basic solution. The equations are derived for a rectangular hole, but a circular hole can be modeled with a rectangular one. Solutions for special cases as beam with cracks are given. The method can be extended to other load and support conditions, crack sources, and other orthotropic materials. The analytical solution was experimentally evaluated. Wu's fracture criterion was found to be applicable for beams with known material properties. For small clear beams, the measured capacity was 0.97 times the predicted one. For glulam beams, the measured capacity was 1.04 times the predicted one.