Closed-Form Solutions for Quantifying the Ductility of Concrete Beams with Passively Restrained Concrete

Abstract

The ductility of a beam is important in reinforced concrete member design at the ultimate limit state, especially in resisting dynamic loads such as those from earthquakes or blasts. Concrete confinement reinforcement, such as stirrups or tubes, are widely used in structures and can significantly enhance the ductility of concrete beams. However, this confinement effect is normally ignored in current design standards, limiting the ability to design specifically for ductility or to estimate the ductility of existing structures. In this paper, a novel concrete passive stress/strain relationship based on the application of partial interaction and shear friction theories is simplified to a rectangular stress block for flexural analyses. This confined concrete stress block is then applied to quantify the moment/rotation of a hinge where both the confinement of the concrete and hinge lengths are quantified through mechanics. The aim of this paper is to provide a mechanics based approach for quantifying the ductility of RC beams that can be used to develop simple design rules without the need for large amounts of member testing.