From my understanding, the Euler Bernoulli Beam theory is mostly used for small angle displacements, and an implication of this assumption is that the length of the beam is subject to distortion and stretching, meaning that when the beam is bent, its length is greater than when relaxed, due to the fact that the end of the rod always remains in line with the end of the rod at equilibrium. The theory thus fails for larger displacements when the change in length of the beam actually affects the result.
Does Timoshenko beam theory suffer from this issue as well? Do beams in Timoshenko theory have consistent length? Are there simple ways of conserving the length of the beam in these theories? Or is the only way to use Geometrically Exact Beam theory and do finite element methods?
