A mixed beam model with non-uniform warpings derived from the Saint Venànt rod

•The beam model takes into account the non-uniform warping effects due to shear and torsion.•The model is generated through a mixed formulation with an independent description of displacement and stress fields.•Two different descriptions for the stress field are proposed and tested.•The model exactly contains the classical Saint Venànt solution.•A mixed finite element based on exact shape functions has been used to validate the beam model.

A new linear model for beams with compact or thin-walled section is presented. The formulation is based on the Hellinger–Reissner principle with independent descriptions of the stress and displacement fields. The kinematics is constituted by a rigid section motion and non uniform out-of-plane warpings related to shear and torsion. The stress field is built on the basis of the Saint-Venànt (SV) solution and with a new part to describe the variable warping.The formulation of a finite element with exact shape functions made possible to validate the beam model avoiding discretization errors.