Displacement-based and two-field mixed variational formulations for composite beams with shear lag

Displacement-based and two-field mixed beam elements are proposed for the linear analysis of steel-concrete composite beams with shear lag and deformable shear connection. The kinematics of the shear lag relies on a parabolic shear warping function of uniform shape along the slab. These assumptions are verified by comparing a closed-form solution of the composite beam problem with the results provided by the ABAQUS code. Moreover, three displacement-based finite elements and two mixed elements where both variables, forces, and displacements are approximated within the elements are developed especially for very coarse discretizations. All models neglect uplift and consider shear connectors using distributed interface elements. Locking problems that arise in the 10 degrees-of-freedom (DOF) displacement-based element which ensures the lowest regularity required by the problem are detected. Then, a locking-free element which relies on a reduced integration and a scaling factor method is proposed and analyzed for fine mesh discretizations. Energy errors and convergence rates of the proposed elements are illustrated while numerical examples dealing with a fixed-end steel-concrete composite beam and a simply supported concrete Tee beam are considered to confirm the validity of the closed-form solution and illustrate the performance of the proposed elements, especially of the ones with 10 and 13 DOF.