A refined 1D beam theory built on 3D Saint-Venant’s solution to compute homogeneous and composite beams

This paper proposes a refined 1D beam theory (RBT) built on the 3D Saint-Venant (SV) solution established for arbitrary composite cross-section.In this theory (RBT/SV), the displacement model introduces sectional out-of-plane warpings, Poisson's effects and distortions.For a given cross-section, the sectional displacement modes are extracted from the computation of the correspondent 3D SV's solution.These sectional modes, which reflect the mechanical behavior of the cross-section, lead to a beam theory that really fits the section nature (shape and material(s)).As a result, RBT/SV allows to recover a more realistic spatial behavior for the beam, to catch a significant part of the edge effects, and hence to compute a relatively short beam.In order to apply RBT/SV, a package (named CSB) of two complementary numerical Matlab tools have been developed: CSection and CBeam.CSection computes by 2D-FEM the deformation modes of the cross-section, and CBeam uses these sectional modes to generate the correspondent beam theory and compute by 1D-FEM the beam.A significant set of homogeneous/composite beams have been computed and, to show the efficiency of such a theory, 3D RBT/SV results have been systematically compared with those provided by full 3D-FEM computations.