On the distribution of tree growth stresses

Summary Growth stress distributions in trees are derived using the hypothesis that longitudinal and circumferential growth strains are continuously induced at the periphery of the growing stem. A plane strain combined with pure torsion model is used to compute the internal stresses and strains due to forces and moments caused by the new growth increment. The twisting angle of the pure torsion model is caused by the shear stresses set up in the growth increment as the growth strains are induced along the grain axis and the coupling of axial and torsional effects due to the elastic constants for the inclined grain material. Detailed stress distributions are derived for a range of constant grain angle cases. The extreme sensitivity of the torsional shear distribution to small grain angles is noteworthy.This work was supported in part by NSF Grant ENG 74-02428