With the concrete treated as unconfined, semi-empirical equations for curvature ductility ratios of doubly reinforced beam sections were derived. Based on the resulted semi-empirical equations, design formulas for curvature ductility ratios, which take into account the effect of tension and compression reinforcement ratios and strengths of reinforcement and concrete, are established and calibrated. The proposed design formulas are fairly simple with reasonable accuracy. The proposed design formulas enable the designer to design beam sections for selected ductility ratios, and, consequently, to acquire better control of concrete spalling during major earthquakes. From the aspect of performance based design, the proposed formulas can facilitate beam design for concrete spalling limit state.
