A regularized force-based Timoshenko fiber element including flexure-shear interaction for cyclic analysis of RC structures

Reinforced concrete (RC) columns are the most critical structural components in buildings/bridges. For those with small span-to-depth ratios and/or insufficient transverse reinforcing details, it will suffer from shear type or flexure-shear type failure modes, which are challenge to be represented in numerical simulation. For instance, conventional fiber element employs the Euler Bernoulli beam theory which neglects the shear deformation, thus it will over-estimate the structural responses of flexure-shear and shear-critical columns. This paper presents a new fiber element to include the flexure-shear interaction for cyclic analysis of RC structures. The element adopts a force-based formulation and extends the original fiber element from the Euler-Bernoulli theory basis to the Timoshenko theory basis by introducing shear deformations at the section level. Then the multi-axial softened damage-plasticity model is used for concrete fibers and the uniaxial modified Menegotto Pinto model is used for reinforcement fibers. The concrete-steel coupling effect that is typical for reinforced concrete subjected to shear, i.e., tension-stiffening and compression softening, are also considered through modifying the material constitutive laws. To overcome the difficulties in force-based element state determination and enhance the computational efficiency, the non-iterative state determination strategy is adopted for the element implementation. Meanwhile, to avoid the localization issue (i.e., integration point-dependency) arising from strain-softening behavior, an interpolatory quadrature is used for the numerical integration of the element. Finally, the element is validated through numerical simulations of a series of column tests under cyclic loadings. The results indicate that the element can retain the performance in modeling flexure-critical columns as conventional Euler Bernoulli fiber element, while demonstrating significant superiors in modeling flexure-shear and shear-critical columns.