MECHANICS OF STANDING TREES - MODELING A GROWING STRUCTURE SUBMITTED TO CONTINUOUS AND FLUCTUATING LOADS .1. ANALYSIS OF SUPPORT STRESSES

A general analysis of mechanical stresses which develop in stems as the tree grows in weight and volume is presented and applied to the study of the distribution of longitudinal stresses due to the self weight supported. Compressive and bending loads, the main loads due to weight supported, are analysed using simple concepts of beam theory. The effect of radial growth is taken into account. Compared to the classical distribution of stresses in a non-growing initially straight cantilever beam and fully loaded at a given moment in time, the stress patterns so calculated are totally unconventional: on the one hand, stress values are very low everywhere at the stem surface where young wood has been loaded for a short time; on the other hand, the positions and values of maximal tensile or compressive stresses depend not only on the actual state but on the entire history of the tree. The intuitive concepts of "tensile or compressive face" must be reconsidered. These conclusions are shown by several realistic numerical simulations: in the case of the symmetrical straight tree (fig 3), near the pith where the wood is older, compressive stresses can be 3-6 times greater than the uniform stresses calculated from the standard distribution of the whole weight on the final cross-section. In the case of the tree which offsets its crown eccentrically in a fixed direction (fig 4), the greater stress is not at the surface: the more recent the offset is, the nearer to the surface is the position of greater stress. The case of the tree which straightens its eccentric crown in a fixed direction (fig 5), clearly shows that a tree which is straight at the present time can undergo quite high tensile or compressive stresses inside. In the case of the tree with an eccentric twisting crown (fig 6), the position of greater tensile or compressive stresses is not in the axis of the bending observed at present, but depends on the history of twisting.