A flexure-shear Timoshenko fiber beam element based on softened damage-plasticity model

In this paper, a displacement-based fiber beam element including flexure-shear interaction is developed. The element is based on the conventional Timoshenko beam theory, and the section behavior is modeled with the well-known fiber section approach, where the section is divided into steel fibers and concrete fibers. The Menegotto-Pinto model is used for steel fibers and a multi-dimensional softened damage-plasticity model, which accounts for the compression-softening effect of reinforced concrete, is adopted for concrete fibers. The axial-flexure-shear interaction can be well reflected in both section level and material level since the normal-shear coupling is reflected naturally in the multi-dimensional material constitutive law. Besides, the concrete material parameters are related to fracture energy to avoid mesh-sensitivity issue of softening problems. The numerical implementation of the proposed element, including the finite element approximation and fiber state determination, is also discussed in detail. The element is validated through the test results for a series of simply supported reinforced concrete beams under monotonic loading and reinforced concrete columns and wall under cyclic loading, and the results indicate that the element is capable to reproduce the shear behaviors of reinforced concrete members under different loading cases.