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.