Loss in Moment Capacity of Tree Stems Induced by Decay

Abstract

We model varying decay in tree cross-sections by considering bending theory to estimate moment capacity loss (MCL) for the sections. We compare MCL with experiments on selected oak trees. Tree failures can damage property and injure people, sometimes with fatal consequences. Arborists assess the likelihood of failure by examining many factors, including strength loss in the stem or branch due to decay. Current methods for assessing strength loss due to decay are limited by not accounting for offset areas of decay and assuming that the neutral axis of the cross-section corresponds to the centroidal axis. This paper considers that strength loss of a tree can be related to moment capacity loss (MCL) of the decayed tree cross-section, because tree failures are assumed to occur when induced moments exceed the moment capacity of the tree cross-section. An estimation of MCL is theoretically derived to account for offset areas of decay and for differences in properties of wood under compressive and tensile stresses. Field measurements are used to validate the theoretical approach, and predictions of loss in moment capacity are plotted for a range of scenarios of decayed stems or branches. Results show that the location and size of decay in the cross-section and relative to the direction of sway are important to determine MCL. The effect of wood properties on MCL was most evident for concentric decay and decreased as the location of decay moved to the periphery of the stem. The effect of the ratio of tensile to compressive moduli of elasticity on calculations of MCL was negligible. Practitioners are cautioned against using certain existing methods because the degree to which they over- or underestimate the likelihood of failure depended on the amount and location of decay in the cross-section.