The exact theory of deep beams without ad hoc assumptions

Based on the loadings subjected on the top and bottom surfaces of beams, the general deformation of beams can be decomposed into two independent parts: the bending of a beam and the extension or compression of a beam. Without employing ad hoc assumptions, the exact theory of deep beams with the two deformations is explicitly established from the Boussinesq–Galerkin solution and the Lur’e method. Meanwhile, as a classical example, it is shown that the solution based on the present theory is the elasticity solution, and provides better results than those of other beam theories.