System Effects Influencing the Bending Strength of Timber Beams

A stochastic model of hierarchical series system type for the bending strength of spruce beams is defined from the anticipation that the bending failure takes place at a cross-section with a defect cluster formed by knots or grain irregularities. The parameters of the model are estimated from measurements of the strengths of a large number of short test pieces cut from the beams such that judgementally each test piece contains only a single defect cluster. The test piece is spliced to stronger wood beam shafts in both ends. Due to the occurrence of a substantial number of splice failures in the total test series of 197 tests a special maximum likelihood estimation procedure is applied to estimate the parameters. Assuming that the estimated parameters are applicable in the series system model for the full uncut beams a theoretical bending strength distribution function is obtained in dependence of number of defect clusters within the span of constant bending moment loading. A strong test of the predictional power of the model is established by experiments with 54 long beams from the same population of beams from which the small test pieces were cut.