Changes in the factor of safety within the superstructure of a dicot tree

The objective of this study was to determine whether the factor of safety f or mechanical stability varied among stems differing in size and age within the superstructure of a large dicot tree. Two factors of safety were selec ted for study: the quotient of the critical buckling height and the actual length of stems, Herit/L, and the quotient of the modulus of rupture (the f orce per unit area required to break a stem) and the working stress (the fo rce per unit area resulting from the biomass measured distal to a stem). M, lo,. These two dimensionless safety factors were determined for a total of 420 shoot segments comprising much of the aboveground biomass of a Robinia pseudoacacia (Fabaceae) tree measuring 18.7 m in height and 1347 kg in mass , and 0.46 m in diameter (40 yr old) at 1.2 m from the ground. An S-shaped trend was observed when each of the two factors of safety was p lotted as a function of stern age. Each factor decreased from a local maxim um for the most distal (peripheral) stems in the canopy to a local minimum value for sterns similar to 10 yr old; each factor increased again to anoth er local maximum for stems 11-18 yr old, and then decreased steadily toward the base of the trunk. This trend was the result of the allometric relatio nships among stem diamcter, length, biomass, and material properties (stiff ness and strength) with respect to stem age, Although they were disproporti onately more slender than their older counterparts, peripheral stems were s ufficiently stiff and strong:: to sustain the stresses resulting from their weight and that of foliage without deflecting under these lends, yet they were sufficiently flexible to easily bend and thereby presumably provide a mechanism to reduce the drag forces acting on the entire tree. In contrast, the internally imposed mechanical forces acting on progressively older ste ms increased at a greater rate than the observed rate of increase in stem s tiffness, strength, or diameter. The probability of mechanical failure, whi ch must be considered from a demographic perspective (i.e., an age-dependen t phenomenon), thus increased from older branches to the base of the trunk. Reports of similar allometric trends based on interspecific comparisons am ong diverse dicot species comply with the allometry observed for the R. pse udoacacia tree and suggest that the S-shaped trend for the factor of safety holds for stems differing in age drawn from individual trees and for the t runks of conspecifics differing in age drawn from a dense population.