Tree Trunk Fracture Assessment Using Directional Section Modulus
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Solution Overview
Problem
Existing methods for assessing the fracture safety of urban trees, such as VTA and SIA, are inadequate due to their reliance on circular cross-section assumptions and isotropic material properties, leading to incorrect evaluations of non-circular and anisotropic tree trunks, resulting in unnecessary tree removals and increased costs.
Innovation Solution
A method and device for determining fracture safety by calculating relative direction-dependent load-bearing capacity using geometric quantities, such as moments of resistance, and considering anisotropy of wood, without requiring material strength measurements, and incorporating factors like height and diameter changes over time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If the one-third rule (t/R > 1/3) is used to assess fracture safety, then the assessment is simple and quick, but it gives incorrect results for non-circular cross-sections and edge-located decay
Solution Approach 1:
The patent changes the assessment parameters from the simplified t/R ratio to direction-dependent parameters including the distance from the extreme fiber to the neutral axis (e), the moment of resistance (WM), and the section modulus (W). These parameters are calculated for multiple directions around the cross-section to accurately capture the anisotropic nature of wood and non-circular geometries, replacing the single scalar t/R metric with a set of direction-specific parameters that reflect actual load-bearing capacity.
Solution Approach 2:
The patent applies local quality by evaluating the cross-section at multiple angular positions (e.g., every 10 or 15 degrees) around the circumference. Each position has its own moment of resistance and section modulus calculated based on local geometry and decay conditions. This allows the assessment to capture local variations in wood properties, decay distribution, and geometric characteristics, providing a detailed map of load-bearing capacity around the cross-section rather than a single averaged value.
2Ease of manufacture
If VTA methods are used for fracture safety assessment, then the procedure is straightforward, but it relies on incorrect assumptions of circular cross-sections and isotropic material properties
Solution Approach 1:
The patent explicitly accounts for asymmetry in both geometry and material properties. The cross-section is modeled as non-circular with varying dimensions around the circumference. Material properties such as modulus of elasticity and strength are assigned different values in different directions (radial, tangential, longitudinal) to reflect the anisotropic nature of wood. The calculation of moments of resistance and section moduli is performed for each angular position, capturing the asymmetric distribution of load-bearing capacity caused by non-uniform decay patterns and irregular cross-sectional shapes.
3Measurement precision
If SIA methods are used to calculate load-bearing capacity, then absolute values can be determined, but material strength measurements are required which increase complexity
Solution Approach 1:
The patent extracts and isolates the geometric factors from the material strength factors in the load-bearing capacity calculation. By formulating the moment of resistance (WM) and section modulus (W) as purely geometric quantities that can be calculated from cross-sectional dimensions and decay patterns, the method separates the structural geometry assessment from material property measurement. This allows the geometric framework to be established without requiring complex material testing equipment, while still providing a basis for load-bearing capacity evaluation that can be later combined with material strength data if available.
Data Source
AI summary
A method is provided for determining the fracture safety of a tree. The method includes: determining a trunk cross-section of the tree to be assessed; detecting at least a largest and a smallest diameter in the trunk cross-section as well as a shape with possibly existing damages of the trunk cross-section; calculating a percentage relative direction-dependent load-bearing capacity in a plurality of definable directions via moments of resistance respectively associated with the trunk cross-section and specifically determined in accordance with anisotropy of the material, wherein, in order to calculate a respective percentage relative direction-dependent load-bearing capacity for each of the plurality of definable directions, a section modulus determined in each case in the trunk cross-section to be assessed and possibly damaged is divided by a determined section modulus of the same trunk cross-section in an assumed undamaged state; and merging the calculated relative directional load-carrying capacities.