In case of theory of simple bending there are the following assumptions (approximations): (i) Only pure bending can occur - there’s no shear force, torsion nor axial load (ii) We consider isotropic or orthotropic homogenous material (iii)Only linear elasticity (up to proportionality limit) is analyzed (iv) Initially there’s no deformation and there’s no varying cross section (v) Beam is equilibrium in the plane along which bending occurs (vi)Appropriate proportions make it impossible for the beam to fail in any other way than because of bending (no buckling and so on) (vii)Cross-section of the beam is still plane after (and during) bending - that’s the main assumption of Euler-Bernoulli beam theory.