The model on the previous page depicted the branch as a straight cylinder .
If the model is altered to depict the branch with a regular taper , the graph of bending moment remains similar . The bending moment is lowest near the tip of the branch , and highest near the union with the trunk .
The graph of bending stress , on the other hand , becomes a flat line . Because the branch diameter is thickest where the force is high , and thinnest where the force is low , the stress ( force divided by cross-sectional area ) remains constant .
An arborist and physicist called Claus Mattheck stated that the growth of new wood tends to eliminate any stress concentrations [ in the tree structure ], maintaining a uniform stress distribution . Mattheck described this as the axiom of uniform stress . This can be seen in the image above : the stress in the tree is shown as a straight ( uniform ) line .
According to Mattheck ’ s model , the amount of wood at any given point in the tree is considered to be roughly proportional to the load that it bears .
As a rule of thumb , the axiom of uniform stress may help to describe the relationship between branch length , load and taper , and to identify parts of the tree structure where insufficient taper or reductions in diameter may result in local concentrations of bending stress .
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