Hygroscopic Swelling
The moisture concentration is assumed to vary linearly across the beam’s cross section. For the 3D beam it becomes
where cm is the concentration at the beam centerline while cgz and cgy are the concentration gradients in the two local transversal directions. The strain from hygroscopic swelling is then
where βh is the coefficient of hygroscopic swelling, and cmo,ref is the strain-free reference moisture concentration.
For the 2D beam, the term depending on zl disappears.