Computation of internal stress resultants in beam elements with constrained torsional warping

Abstract

The computation of stress in beam elements requires the internal stress resultants like axial force and bending moments. For displacement-based beam elements, these resultants can be obtained 1) based on equilibrium, 2) consistent to the constitutive law or 3) based on load interpolation functions. Although the methods give similar results in case of small deformation, the discrepancies in case of large deformation are significant. This paper shows that the method based on equilibrium gives the most accurate results. Torsion of beam elements causes warping of the cross section. This warping is constrained at clamped ends of beam elements, causing extra stress. This paper shows a method to accurately obtain the corresponding internal stress resultants, i.e. the Saint-Venant torsion moment and bimoment.