Failure-mode scale transitions in RC and PC beams

Abstract

Current design Standards for reinforced concrete beams prescribe to respect a minimum, ρmin, and a maximum, ρmax, reinforcement ratio in the design of structures. Below ρmin a brittle failure due to unstable crack propagation is expected. On the other hand, for ρ > ρmax a brittle failure due to concrete crushing is obtained. In this framework, a reinforced concrete element with ρmin < ρ < ρmax presents yielded steel at Ultimate Limite State (ULS) with a stable behaviour and no catastrophic loss of bearing capacity. Design Standards define ρmin and ρmax limits on the basis of the Bernoulli’s hypothesis of plane sections, and completely disregard size-scale effects. Within the present paper, Dimensional Analysis is used to determine the Brittleness Numbers that govern the behaviour of reinforced concrete (RC) as well as of prestressed reinforced concrete (PC) beams. Therefore, parametric analyses carried out by means of the Cohesive/Overlapping Crack Model (COCM) are used to study the ductile-to-brittle transitions in RC and PC beams, and to highlight the size-scale dependency of the two above-mentioned reinforcement limits.