SHAPE OF TREE STEMS - A REEXAMINATION 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 al ong 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 distributio ns in the crown. Measured height-diameter profiles for trees were then taken from the literature and shown to be well-fitted by profiles cal culated to give uniform stress along the stems, using the most realist ic average forces and force distributions within the crowns. At high w ind speeds, the height-diameter profile giving uniform stress was more tapered than the profile giving uniform stress at low wind speeds. Th e profile giving uniform stress was similar over the normal range of a verage wind speeds of 2.5 to 10.0 m s-1 (at the top of the canopy). Bu t a tree that had grown to give uniform stress along its stem in an av erage 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 heigh t (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 distributions in extreme conditions, may help to explain some of the apparent evidence for non-uniform stress distr ibution in the literature. In general, our analysis supports the above hypothesis for the stem region above the butt swell.