Convex and effective yield surfaces for numerical rigid plastic limit analysis of reinforced concrete structures with in-plane forces

Many reinforced concrete structures are validated in the ultimate limit state (ULS) using analysis methods based on the theorems of plasticity and the rigid-plastic material model.The rigid-plastic material model significantly simplifies the actual stress-strain relationship of reinforced concrete. However, good agreement with capacities found from experiments has been shown when a reduced or so-called effective concrete compressive strength is used. The effective strength is mainly dependent on the transverse tensile strain when a single material point is considered, and well-accepted expressions are given in the codes. The Modified Mohr-Coulomb yield criterion with an effective strength is combined with the elasto-plastic behavior of the reinforcement to create an effective yield surface for reinforced concrete for plane stress states. Based on this, the paper presents an approximate convex effective yield surface, which can be used for Finite Element Limit Analysis (FELA) calculations. The convex effective yield surface is based on auxiliary strains linked to the reinforcement stresses on a material point level. The effective yield surface is tested on a material point level using an experimental database for reinforced concrete panels and on a structural level with an example of a reinforced concrete deep beam with holes. Both tests yield satisfactory results.