Probabilistic Modelling of Bending Strength of Timber Beams with the Help of Weak Zones Model

The variability of longitudinal bending strength of timber beams due to the presence of knots and other defects is analyzed. The weak zones model of timber beam bending strength used in the analysis consists of short weak zones (knots or group of them) and strong sections of clear wood. The load bearing capacity of timber beams is defined as an extreme (minimum) value problem or as a first downcrossing problem. Assuming a marked Poisson random field with zero correlation between all random variables, cumulative probability distribution functions of the load carrying capacity of timber beams were determined by analytical methods for typical load cases: pure bending, midspan point load and one-third point load. These results, as well as the marked Poisson random field as a model of longitudinal variability of the bending strength of timber beams, can be applied in the reliability analysis of timber structures. Furthermore, the analytical formulae for the cumulative distribution functions of load carrying capacity of timber beams can provide a good reference for numerical analysis conducted with Monte Carlo simulation to determined statistics for specific timber members.