Force Distribution Along Tree Branch – Static Analysis

Abstract

The standard approach of tree stability assessment assumes that wind force is applied in a unique point (centre of gravity). Such a description of the loading brings a significant simplification of the reality, where the tree stem is submitted to multiple forces distributed from higher-order branches to lower order one. The aim of this study is to describe the influence of the simplification by comparison of branch response (deflection curve, bending moment) in the case of single-and the multi-point loading. Four beam-like models were built in ANSYS APDL according to geometry (tapered beams with realistic elliptical cross-sections) and material properties (shear included) of real tested branches. The models were experimentally validated in the case of single-point loading and consequently used for simulations of various loading scenarios. The distribution of force along the branches, by weighted division of total wind force according to different properties of branches, was applied. The branch response differs between single-and multi-point loading in the case of deflection curve, whereas the bending moment at branch anchorage is comparable.

Effect of Geometry Precision and Load Distribution on Branch Mechanical Response

“…As there is a functional relationship between stem or branch diameter and leaf area or mass [40][41][42][43], the diameter could replace the frontal area as the weighting factor for force distribution. The correlations between measured mass (m sj ), area (A sj ), and diameter (d sj ) were verified by Spearman correlation coefficients (0.68-0.89) [26]. Scenarios 6 (ACEL) and 7 (ACEL and EP diameter) worked with the ACEL command, which allowed the entire object to be loaded in a distributed way by the elements' mass and global acceleration.…”

“…Furthermore, the bending moment is a useful and measurable parameter for static and dynamic analyses [22,25,26]. The emergence of tree structure (crown and stem) creation provides the option to apply, for example, (a) beam-shaped geometry based on directly measured and 3D scan-based parameters [20,27]; (b) solid geometry, which can be generated from a 3D scan by cylinders [28,29]; or (c) solid geometry, precisely extracted by Poisson surface reconstruction [30][31][32].…”

“…The models provided can be subsequently used for the analysis of static loading scenarios with different force distributions. Analysis of loading scenarios freely followed previous work [26].…”