Wrapped Curves Around Cross-Sections

Diameter and Stability When a tree is impacted by a wind force, its cells in the trunk on the windward (wind-exposed) side are stretched, while those on the leeward (wind-sheltered) side are compressed (Figure 1). Furthermore, the tree crown’s own weight has to be added as well, which results in an even higher compression load on the leeward cells and a correspondingly lower tension on the opposite side. To describe the tree’s ability to withstand such bending loads, the so called “moment of resistance,” represented by the symbol “W” (for the German word Widerstandsmoment) is used. It characterizes the mechanical stability of a cross-section as far as it depends on size and geometrical shape. The resistance moment of a circular cross-section with a diameter D can be summarized with a simple formula: