Strain-Displacement/Rotation Relation
The axial strain depends on the rotation derivative (curvature) and axial displacement derivative defined by the shape function and the transversal coordinate in the beam. For the 3D case it becomes
where s is the local coordinate along the beam axis, and uaxi is the axial displacement. The coordinates from the beam centerline in the local transversal directions are denoted zl and yl respectively. In the 2D case, the first term is omitted, and the local z direction is always directed out of the plane.
The total strain ε consists of thermal (εth), hygroscopic (εhs), initial (εi), and elastic strains(εel)