A deterministic model combining NDT to estimate permissible bending loads on trees

The stability of trees is the subject of numerous studies, as their loss poses a threat to life and limb. Bending loads are responsible for the two most common failure modes: uprooting and stem break. Uprooting is strongly related to soil conditions, water saturation and the root system itself. These parameters are difficult to measure in situ. Since both failure modes result in loss of vitality, arguments from evolutionary theory suggest that roots and stems should have similar load limits under normal conditions. Therefore, we propose a deterministic model to estimate the allowable bending load in the stem of European beech (Fagus sylvatica). The model assumes a non‐linear stress distribution in the cross section. Destructive bending tests show that damage progresses in three stages. Furthermore, the local compressive and tensile strength in fibre direction are crucial parameters to determine the ultimate load. Since the tensile strength cannot be measured by NDT, the experimental data from the large‐scale tests are used to relate this parameter to the compressive strength from the NDT data. This provides a method for determining the risk of a tree, for example in urban areas. It is also useful for estimating the allowable limit of engineering loads on trees.