Design of reinforced concrete structures based on three‐dimensional stress fields

Abstract The ultimate limit state design of reinforced concrete members usually derives from the analyses of structural models composed of unidimensional or bidimensional elements (bar and shell elements, respectively). Less recurrent in these structural models is the use of solid elements, which may be ascribed to the difficulties arising when dimensioning the structure for the complete stress field with six stress components ( σ x , σ y , σ z , τ xy , τ xz , τ yz ) derived from the analyses. In the present work, the design method for three‐dimensional stress fields combining linear analysis and limit design is revisited, with the description of the resisting mechanism in which the applied stresses are balanced with stresses in the concrete and in the reinforcement. Expressions for the verification of concrete crushing and the evaluation of the required reinforcement are deduced analytically and interpreted physically. The design process is organized into four design cases, according to the internal stresses mobilized in concrete. The proposed equations are presented in a framework for direct application to engineering practice, as demonstrated in noted design examples for selected stress states.