Transverse stresses and modes of failure in tree branches and other beams

Abstract

The longitudinal stresses in beams subjected to bending also set up transverse stresses within them; they compress the cross section when the beam's curvature is being increased and stretch it when its curvature is being reduced. Analysis shows that transverse stresses rise to a maximum at the neutral axis and increase with both the bending moment applied and the curvature of the beam. These stresses can qualitatively explain the fracture behaviour of tree branches. Curved 'hazard beams' that are being straightened split down the middle because of the low transverse tensile strength of wood. By contrast, straight branches of light wood buckle when they are bent because of its low transverse compressive strength. Branches of denser wood break, but the low transverse tensile strength diverts the crack longitudinally when the fracture has only run half-way across the beam, to produce their characteristic 'greenstick fracture'. The bones of young mammals and uniaxially reinforced composite beams may also be prone to greenstick fracture because of their lower transverse tensile strength.