Fracture and Size Effect Suppression by Mesh Reinforcement of Concrete and Justification of Empirical Shrinkage and Temperature Reinforcement in Design Codes

A minimum mesh reinforcement, called the shrinkage and temperature reinforcement, has been required by ACI design code for 92 years to attain ductility with no formation of large localized cracks. The required steel ratio, which is 0.18%, has been empirical. In this paper, it is shown that it can be explained theoretically and justified approximately by finite-element analysis of the size effect and crack growth based on quasibrittle fracture mechanics, in which the microplane model M7 and crack band model are used. The premise, which simplifies the analysis, is that the cracking would localize into wider cracks if and only if there is a size effect. The size effect can be completely avoided only if, for the same cross-section area, the tensile strength of yielding reinforcement is greater that the tensile strength of concrete. The effect of increasing the reinforcement ratio is also explored. The calculations indicate that fracture mechanics can, and should, be used to check ductility and size effect implications in the two-sided reinforced members, boundary beams, and more complicated designs such as in shear walls.