Closed-form approximations of interaction diagrams for assessment and design of reinforced concrete columns and concrete-filled steel tubes with circular cross-section

This paper proposes closed-form approximations of the axial force-bending moment interaction diagrams for reinforced concrete columns and concrete-filled steel tubes with circular cross-section. For reinforced concrete columns, this simplified formulation is obtained by assuming an elastic-perfectly plastic behavior of the reinforcing steel and the parabola-rectangular strain-stress relation for the concrete in compression. As regards concrete-filled steel tubes, full plasticity conditions are considered. Interestingly, a single closed-form expression is provided for both cases, wherein only one parameter (which depends on the mechanical ratio of the reinforcing steel) is calibrated by means of a numerical optimization procedure. The accuracy of the formulation is demonstrated through several numerical applications. Finally, a simple design procedure based on the approximated interaction diagrams is developed.