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Significant research efforts have been devoted in recent years to the development of displacement-based seismic assessment and design methodology, recognising the shortcomings of traditional, code-specified force-based procedures. Recent advances in direct displacement-based seismic design of columns rely on the estimates of yield curvature for determining seismic design forces to satisfy the specified seismic performance levels. This paper presents simple expressions for estimating the effective yield curvature for normal-and high-strength circular reinforced concrete columns based on moment-curvature analyses of a large number of column sections. Such expressions can be programmed into spreadsheet format and can be used for the direct displacement-based design of circular reinforced concrete columns. Influences of different parameters on the effective yield curvature have been quantified. Effective yield curvature is presented in terms of the gross diameter of the section and the yield strain of longitudinal reinforcement together with three modification factors that take into account the effects of the strength of concrete, axial load ratio and the amount of longitudinal reinforcement. An example illustrating the preliminary design of bridge columns based on the developed expressions is presented

Yield curvature for seismic design of circular reinforced concrete columns