A.R. Ennos

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

The longitudinal stresses in beams subjected to bending also set up transverse stresses within them; they compress the cross section when the beams 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.

Why don’t branches snap? The mechanics of bending failure in three temperate angiosperm trees

Living tree branches are almost impossible to snap. Some show “greenstick fracture”, breaking halfway across before splitting along their length, while others simply buckle. In this study we investigated the bending failure of coppice branches of three temperate angiosperm trees: ash, Fraxinus excelsior; hazel, Corylus avellana; and white willow, Salix alba. We carried out bending tests, and made a series of observations on the structure, density and tensile and compressive strength of their wood to understand the pattern of failure. The three species showed contrasting behaviour; willow buckled whereas ash showed clean greenstick fracture and hazel a more diffuse greenstick fracture. These differences could be related to their wood properties. Willow buckled because its light wood had very low transverse compressive strength, particularly tangentially and was crushed by transverse stresses. Though the other species yielded in longitudinal compression on the concave side, they ultimately failed in tension on the convex side when bent because their higher density wood resisted transverse compression better. However, the crack was diverted down the midline because of the low tangential tensile strength of their wood. Differences in fracture between ash and hazel are related to fine-scale differences in their wood anatomy and mechanics.

Sonation in the male common snipe (Capella gallinago gallinago L.) is achieved by a flag-like fluttering of their tail feathers and consequent vortex shedding

SUMMARY Male common snipe (Capella gallinago gallinago) produce a ‘drumming’ sound with their outer tail feathers during their mating dives, but little is known about how this is achieved. We investigated the movements and sound producing capabilities of the outer tail feathers. Using a wind tunnel, we compared observations of the frequencies of sound produced with the predictions from aerodynamic theory. The feathers were also filmed in an air-flow with a high speed video camera, and subjected to morphological examination and biomechanical testing. We propose a mechanistic hypothesis of how the modified outer feathers of the male common snipe generate sound, and the adaptations that facilitate this. Video and audio analysis of the feather demonstrated that a fluttering of the trailing vane generated the sound. The flutter of the vane is facilitated by the rearward curvature of the feather shaft, reduced branching angles of the barbs in the trailing vane and the lack of hooks on the barbs along a hinge region, all of which increase its flexural compliance. Sound production occurred at the same frequency as the vane movements, at frequencies consistent with it being produced by a fluttering flag mechanism powered by vortex shedding.

Failure of forks in clonal varieties of Platanus x acerifolia

Established plantings of clonal London Planes (Platanus x acerifolia (Aiton) Willd.) in Bristol city centre have suffered such a high proportion of failures at their forks and branch junctions that many semi-mature trees have been removed on the grounds of safety. This issue of “Problem Planes” has been noted in arboricultural literature (Tubby & Rose, 2008), but the phenomenon has up until now not been subject to rigorous scientific investigation. Young plane forks harvested from a modern problematic clonal type and from traditional non-problematic clonal stock were compared in relation to the size of their growth increments, wood density, load-bearing capacity and load-bearing capacity of the smaller branch arising from the bifurcation. Based on two-dimensional (2D) images taken of each fork, finite element analysis (FEA) software was used to estimate the relative stress concentration levels of the harvested forks if the two branches arising from the bifurcation were bent apart. The stems of the modern problematic clones situated just below the junctions tested were found to be growing 79% faster than the traditional non-problematic clones by analysis of transverse growth increments of the test samples collected. However, wood density was not found to be significantly different between these clonal types. Forks of modern problematic clones which were each subjected to an in-plane static tensile test had only 50.5% of the bending strength of their smaller arising branches which were subjected to a three-point bending test, whereas the forks of traditional non-problematic clones were 68.6% as strong as their smaller branches. Finite element analysis predicted that the shapes of the forks formed on the problematic clones would lead to around 16% higher stress concentrations at their fork apices when compared with the shapes of the junctions found on the non-problematic clone samples. From this evidence, the authors find that at least part of the explanation as to why the junctions of these modern problematic clones of Platanus x acerifolia are failing is that they develop more “V-shaped” junctions that lead to greater stress concentrations on the inside of the fork when the branches arising from the bifurcation sway apart in windy conditions. Selection of planting stock of London Plane by arboriculturists should include an assessment of the shape of their branch junctions and forks, to avoid perpetuation of this problem.