Fiber element for cyclic bending and shear of r.c. structures. I:Theory

After a few years of successful application of the fiber beam element to the analysis of reinforced concrete (RC) frames, the introduction of the mechanisms of shear deformation and strength appears to be the next necessary step toward a realistic description of the ultimate behavior of shear sensitive structures. This paper presents a new finite-beam element for modeling the shear behavior and its interaction with the axial force and the bending moment in RC beams and columns. This new element, based on the fiber section discretization, shares many features with the traditional fiber beam element to which it reduces, as a limit case, when the shear forces are negligible. The element basic concept is to model the shear mechanism at each concrete fiber of the cross sections, assuming the strain field of the section as given by the superposition of the classical plane section hypothesis for the longitudinal strain field with an assigned distribution over the cross section for the shear strain field. Transverse strains are instead determined by imposing the equilibrium between the concrete and the transverse steel reinforcement. The nonlinear solution algorithm for the element uses an innovative equilibrium-based iterative procedure. The resulting model, although computationally more demanding than the traditional fiber element, has proved to be very efficient in the analysis of shear sensitive RC structures under cyclic loads where the full 2D and 3D models are often too onerous.