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.
