Mixed formulation frame element for shear critical steel and reinforced concrete members

This study describes the formulation of a two dimensional frame finite element model for the analysis of shear critical steel and reinforced concrete structural members under monotonic and cyclic loading conditions involving the interaction of axial force, shear and bending moment.; The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. The interpolation functions for the stress resultants satisfy the element equilibrium exactly, and discontinuous functions are used for the interpolation of section deformations. Under linear geometry, no approximation is necessary for the transverse displacement field. Large displacements are accommodated by transforming the force-displacement response of the basic element without rigid body modes to the complete force/displacement set in global coordinates with the corotational formulation. The nonlinear response of the basic system results from the integration of the response at control sections along the element axis. The later is obtained by integration of the multi-axial material response at integration points in each section. With the use of a three dimensional material model at each material point the interaction of the longitudinal normal stress and shear stress is explicitly included in the beam model. The transverse normal stress is used to satisfy the equations of transverse equilibrium at each control section.; A 3d generalized plasticity model is implemented for structural steel and a 3d plastic-damage model is used for the simulation of concrete. The consistent implementation of these material models in the beam finite element is discussed.; Numerical validation studies of the proposed beam model show excellent agreement with theoretical results without any "shear locking" problems, even for a single element discretization for each structural member.; The validity of the proposed beam element is confirmed by correlation studies of its nonlinear response with experimental results from steel shear links, slender RC beams and columns, and RC shear walls of moderate to low span to depth. In these studies the model proves capable of representing very accurately the global response, the failure mode, and several local response measures of each specimen.