A higher order beam finite element with warping eigenmodes

► We develop a new kinematic for beams based on eigenwarping modes. ► New equilibrium equations are obtained and an exact solution is given. ► Very accurate and mesh independent results are obtained for restrained warping. ► We can constitute bridges models with one exact beam finite element. In this paper, a new beam finite element is presented, with an accurate representation of normal stresses caused by “shear lag” or restrained torsion. This is achieved using an enriched kinematics, representing cross-section warping as the superposition of “warping modes”. Detailed definitions and computational methods are given for these associated “warping functions”. The exact solution of the equilibrium equations is given for a user-defined number of warping modes, though elastic results are totally mesh-independent.