Twist of wood studs: dependence on spiral grain gradient

Abstract

Distortions due to moisture changes during drying or in service are a major problem for construction timber. Twist, caused mainly by the cylindrical geometry, the orthotropic nature of the wood material, and the tendency of the wood fibers to grow in a spiral around the stem, is often regarded as the most detrimental distortion of sawn timber. There is a need for a basic mechanical understanding of how the twist distortion arises and also a need for a simple formula to predict the amount of twist distortion. In this article such a formula is proposed, and theory and experimental data that indicate the validity of the formula are shown. The first term in the formula is a modification of a traditional expression which is proportional to the mean value of the spiral grain angle in the cross section in question. The second term in the formula is new and is proportional to the gradient of the spiral grain angle, and this term normally counteracts the first term so that a stud with a left-handed spiral grain might achieve a right-handed twist. Linear elastic finite element method (FEM) results and comparisons with experimental data show that the formula works well and that linear FEM calculations exaggerate the twist, which is probably partly due to nonlinear effects. The formula could be used to predict the twist of sawn timber from measured spiral grain angles on the log surface.