The significance of coupling between shear and extension in the elastic behaviour of wood and plywood

The effect on the elastic behaviour of wood and plywood of coefficients such as s ' 16 (coupling coefficients) in the generalized Hooke's Law is considered. It is shown that for specimens cut at angles to the principal directions, these coefficients may differ from zero. This implies a difference between "pure" and "free" elastic constants for such specimens, a difference which is verified experimentally. The existence of coupling coefficients introduces uncertainties into the calculation of the free Young's and rigidity moduli from the frequencies of flexural and torsional vibrations, but it is shown that the free constants can be measured to sufficient accuracy by working on specimens of suitable length. Finally, it is shown that the elastic behaviour of plywood cut at an angle to the grain may be determined as much by the pure elastic constants of the individual plies as by the free constants.