A simple method for N-M interaction diagrams of circular reinforced concrete cross-sections

A novel closed-form expression is derived for the ultimate capacity interaction diagram (i.e., axial compression-bending moment resistance in N-M space) of reinforced concrete (RC) columns with circular cross-section. To this aim, the longitudinal rebar arrangement is replaced with a thin steel ring equivalent to the total steel area; moreover, according to modern design approaches, simplified stress-strain relationships for concrete and reinforcing steel are used. Illustrative applications demonstrate that the ultimate capacity computed by the proposed analytical approach agrees well with the results obtained by rigorous methods based on consolidated numerical algorithms. The new solution allows rapid, accurate assessments of cross-section capacity by means of hand calculations; this is especially useful at the conceptual design stage of various structural and geotechnical systems. The solution can be extended to more general configurations, such as multiple steel rings and composite concrete-steel sections.