Dynamic analysis of the elasto-plastic behaviour of buildings and structures in the SCAD ++ software package

Abstract

The problem formulation of nonlinear equations of motion obtained by the finite element method applying to the dynamic analysis of buildings and structures is presented. The elasto-plastic behaviour of reinforced concrete structural elements is described using the plastic flow theory, moreover, for concrete, the Drucker-Prager yield criterion is used for bending elements, and the yield surface, which coincides in shape with the Geniev strength surface, for compressed-bending elements. Concrete degradation due to crack opening is simulated by the descending branch of the σ − ε diagram. The plastic flow theory with von Mises yield criterion describes the behaviour of reinforcement. Using the aforementioned constitutive models, a finite element library was developed, including plane shell quadrilateral and triangular finite elements based on the Mindlin-Reissner shear theory as well as a two-node spatial frame finite element based on the Timoshenko shear theory. The seismic analysis of the 3-D model of multi-storey building is considered as an example.