A shear warping kinematic enhancement for fiber beam elements with a damaging cross-section

The present paper is dedicated to the modeling of the non-linear behavior of reinforced concrete structures subject to transverse shear or torsion under monotonic and cyclic loading. The fiber beam element approach has been proved to be an interesting modeling strategy, but needs to be improved for shear effects. This can be achieved by enhancing the cross-section kinematics with a warping displacement field. This field must be free from the cross-section rigid body motions, for the problem to be well posed. This condition can be enforced by projecting the warping displacements orthogonally to the space of the plane cross-section displacements. The present contribution proposes a kinematic enhancement for a Timoshenko fiber beam element with a new formulation of the projection functions. The warping shape of the cross-section is computed along with the beam displacements and rotations by an implicit solution procedure. The proposed formulation takes into account the possible material heterogeneity of the cross-section. It enables the warping profile to evolve in time with the material damage state, as may occur in reinforced concrete structures. The element formulation is validated using an analytical solution in the case of transverse shear, and 3D simulations of beams subject to shear and torsion. To address nonlinear behavior, a comparison to experimental results is performed. The first case study shows that including warping in the model drastically improves the prediction of the experimental behavior of concrete beams in torsion. The second case study shows the ability of the model to deal with cyclic bending of a reinforced concrete column.