Shrinkage effect on radial and tangential direction stresses in cylindrical wood pieces of Pinus taeda

Abstract

Shrinkage is a key factor in generating internal stresses and deformations within wood structures, especially due to the anisotropic nature of wood, which causes direction-dependent stress responses and must be considered to accurately predict the mechanical behaviour of cylindrical elements. However, its influence on the stress distribution in cylindrical wood elements remains insufficiently explored. This study addresses this gap by formulating a theoretical model to evaluate the development of internal stresses resulting from the shrinkage of wood specimens.

Shrinkage was determined based on the stress–strain relationship of a cylindrical piece of wood, in the absence of external forces, within a cylindrical coordinate system. Due to its radial symmetry, the displacement field is a function of the radius, and the angular displacement is null. Assuming constant longitudinal strains, the strain components can be described as a function of Lekhnitskii’s reduced strain coefficients and the associated coefficient, denoted by k, where the coefficients depend on the material's elastic properties. Thus, the governing equation of the problem becomes a function of the strain coefficients and, consequently, of shrinkage.

To demonstrate the effects of shrinkage and to show how stresses in the radial and tangential directions are influenced, the elastic coefficients of the wood species Pinus taeda (loblolly pine) were experimentally obtained, and the coefficient k was determined. Overall, the results emphasise the importance of considering shrinkage and anisotropy when evaluating radial and tangential stresses, as well as radial displacements, in cylindrical wood elements.