Part 3: Modelling bow and spring

This paper clarifies the extent to which models based on two- and three-dimensional material descrip- tions can predict bow and spring deformation. Changes in longitudinal shrinkage and swelling and their varia- tions over cross-sections of studs cause these studs to develop distortion in terms of spring and/or bow. Radial variation from pith to bark (two-dimensional) of the longitudinal shrinkage in the cross-section is often as- sumed to be the only physical data needed to predict spring and bow in a stud. However, using measurements from 240 studs of Norway spruce (fast-grown and one slow-grown stand), it was found that there was no correlation between shrinkage gradients measured at one longitudinal position and three-dimensional bending distortion (spring and bow). As a result, two studs, one with large spring (and no bow or twist) and one with large bow (and no spring or twist), were cut longitudi- nally in sections 200 mm long. From these sections, sticks were cut and the longitudinal shrinkage was measured twice on all sticks, when the climate was 90% relative humidity (RH) and 30% RH, in order to pro- duce data which correspond to changes in moisture content in the studs, roughly between 15% and 7.5%. The difference in the longitudinal shrinkage between two faces of the studs explained spring or bow far better when the variation in shrinkage along the stud was considered. The longitudinal variation in shrinkage was very large; i.e. strains varied from 0.062% to 0.290% along one stud. Knowing the three-dimensional shrink- age variation, it appears to be possible to predict bending distortion with very good accuracy, as shown in this paper. It is clearly demonstrated that knowledge of the three-dimensional variation in longitudinal shrinkage is needed in order to predict bow and spring more accurately.