Non-linear model for reinforced concrete under cyclic loading

Most of the available shear models for reinforced concrete rely on empirical formulations. In this study, a rational shear stress function is used to define the shear stress-strain envelope for reinforced concrete. Cyclic rules are proposed to define the loading, unloading and reloading relationships for reinforced concrete under shear stress reversals. A normal stress function describing the cyclic relationship of concrete under axial stress is also introduced. The proposed functions are verified using experimental data of reinforced concrete panels tested under monotonic and cyclic loading. Subsequently, the normal and shear stress functions along with their cyclic rules are integrated in a non-linear finite element analysis code. The resulting model accounts for tension stiffening, crack opening and closing, compression hardening and softening, degradation of concrete strength and stiffness in the direction parallel to the crack, compression unloading and reloading, as well as non-linear steel behaviour (strain hardening and Bauschinger effect). The finite element model is then used to analyse two Portland Cement Association shear walls with different geometries tested under cyclic loading. The results show a good agreement between analytical and experimental data. The model showed an excellent capacity of predicting shear deformations of reinforced concrete elements under cyclic loading with minimal computational efforts.