I was going through the basic assumptions made by Bernoulli beam theory. I realized that one of the most important assumption in this theory is that the deformations and rotations of the beams are supposed to be small, not large. I couldn't understand that how is this important and if it could invalidate the Bernoulli beam theory if they are not small? In some places, its written that it is to make the calculations easier and reach to a more understandable form, while some sites write that it is because if the deformations/rotations are large then significant shear deformations develop on the cross section. I don't know what is the actual reason behind it. I mean even if the shear deformations develop, then isn't it possible to super impose the deformations from Bernoulli beam equation onto the ones coming from shear? Or does it completely invalidates the Bernoulli beam theory results if deformations are large?
Plus, how would we decide that this deformation is small and this deformation is large?