Cracking failure of curved hollow tree trunks

Area of Science:

• Biomechanics of trees
• Structural analysis of natural materials
• Wood science and engineering

Background:

• Failure modes of curved hollow tree trunks are critical for safety and conservation.
• Existing research lacks theoretical analysis incorporating initial curvature and orthotropic properties.
• The precise mechanism of cracking failure in these structures remains unclear.

Purpose of the Study:

• To derive mathematical expressions for predicting cracking failure in curved hollow tree trunks.
• To determine failure modes based on trunk geometry and material properties.
• To provide insights for tree management and conservation efforts.

Main Methods:

• Derivation of new mathematical expressions for bending moment at cracking failure (M_crack).
• Comparison of M_crack with conventional bending failure moment (M_bend).
• Analysis of 11 tree species using data from 66 hardwoods and 43 softwoods.

Main Results:

• M_crack is proportional to tangential tensile strength, increases with t/R, and decreases with cR.
• Hardwoods favor conventional bending failure; softwoods are more prone to cracking failure.
• Cracking failure is more likely in curvature-decreasing bending for larger cR; bending failure for smaller cR.

Conclusions:

• The developed formulae accurately predict cracking failure moments in curved hollow beams.
• Findings differentiate failure modes between hardwoods and softwoods based on material properties.
• The study offers valuable insights for urban tree management and conservation of hollow-dependent fauna.