Strain-Based Quantification of Ductility Reserve in Eurocode 2 Minimum-Reinforced Singly Reinforced Concrete Beams

Eurocode 2 (EC2) minimum longitudinal reinforcement provisions for singly reinforced concrete beams are widely applied to ensure crack control and avoid brittle failure; however, compliance with these requirements is often assumed to imply adequate ductility without explicit quantification. This paper presents a strain-based parametric assessment of the sectional ductility reserve of singly reinforced concrete beams designed at and modestly above the EC2 minimum reinforcement level. Ductility is quantified using a ductility reserve ratio (DRR), defined as the normalized post-yield tensile strain capacity of the reinforcement between first yield and the onset of concrete crushing. Sectional analyses within the EC2 framework examine the influence of effective beam depth, concrete strength class (C25/30, C30/37, and C40/50), and reinforcement ratio expressed relative to the EC2 minimum requirement (ρ/ρₘᵢₙ = 1.0–1.50). Results show that effective depth has no influence on strain-based sectional ductility, while increasing reinforcement ratio systematically reduces ductility reserve. Higher concrete strength increases ductility at a fixed reinforcement level; however, beams with lower-strength concrete at the EC2 minimum reinforcement level may exhibit greater ductility reserve than higher-strength concrete beams with modestly increased reinforcement. The findings provide quantitative insight into ductility behavior relevant to deformation-controlled design.