Shape of tree stems-a re-examination of the uniform stress hypothesis

The transfer matrix method of structural analysis was used to examine the hypothesis that tree stems grow to a shape that tends to equalize the average bending plus axial stresses to which they are subjected along their length. The method and computational procedures were checked by comparing computed height-diameter profiles with those calculated using elementary stress theory for trees with simple force distributions in the crown. Measured height-diameter profiles for trees were then taken from the literature and shown to be well-fitted by profiles calculated to give uniform stress along the stems, using the most realistic average forces and force distributions within the crowns. At high wind speeds, the height-diameter profile giving uniform stress was more tapered than the profile giving uniform stress at low wind speeds. The profile giving uniform stress was similar over the normal range of average wind speeds of 2.5 to 10.0 m s(-1) (at the top of the canopy). But a tree that had grown to give uniform stress along its stem in an average wind of 5 m s(-1) showed markedly decreased stress with height at wind speeds of about 15 m s(-1) or more, and increased stress with height (to the crown base) at wind speeds of about 1.25 m s(-1) or less. The fact that tree stems develop shapes in response to average conditions, but show varying stress distribution in extreme conditions, may help to explain some of the apparent evidence for non-uniform stress distribution in the literature. In general, our analysis supports the above hypothesis for the stem region above the butt swell.