Deflection ductility of RC beams under mid-span load

Ductility is very important parameter in seismic design of RC members such as beams where it allows RC beams to dissipate the seismic energy. In this field, the curvature ductility has taken a large part of interest compared to the deflection ductility. For this reason, the present paper aims to propose a general formula for predicting the deflection ductility factor of RC beams under mid-span load. Firstly, the moment area theorem is used to develop a model in order to calculate the yield and the ultimate deflections; then this model is validated by using some results extracted from previous researches. Secondly, a general formula of deflection ductility factor is written based on the developed deflection expressions. The new formula is depended on curvature ductility factor, beam length, and plastic hinge length. To facilitate the use of this formula, a parametric study on the curvature ductility factor is conducted in order to write it in simple manner without the need for curvature calculations. Therefore, the deflection ductility factor can be directly calculated based on beam length, plastic hinge length, concrete strength, reinforcement ratios, and yield strength of steel reinforcement. Finally, the new formula of deflection ductility factor is compared with the model previously developed based on the moment area theorem. The results show the good performance of the new formula.