System effects influencing the bending strength of timber beams

A stochastic model of hierarchical series system type for the bending strength of spruce beams isdefined 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 shorttest pieces cut from the beams such that judgementally each test piece contains only a single defect cluster. The testpiece is spliced to stronger wood beam shafts in both ends. Due to the occurrence of a substantial number of splicefailures in the total test series of 197 tests a special maximum likelihood estimation procedure is applied to estimate theparameters. Assuming that the estimated parameters are applicable in the series system model for the full uncutbeams a theoretical bending strength distribution function is obtained in dependence of number of defect clusterswithin the span of constant bending moment loading. A strong test of the predictional power of the model is establishedby experiments with 54 long beams from the same population of beams from which the small test pieces were cut.