On reformulating the theory of critical distances to predict strength of notched plain concrete beams under mode I and mixed mode loading

Abstract

The theory of critical distances (TCD), due to its appealing characteristics, has been successfully used in the past to predict the strength of brittle as well as ductile materials, weakened by the presence of stress risers, under both static and fatigue loading. In this work, the TCD’s unique features are exploited and the point method is reformulated to predict the strength of notched plain concrete beams of different sizes under mode I and mixed mode quasi-static loading. The fracture process zone, which is responsible for the non-linearity of concrete, is considered through the concept of an effective elastic crack. A power law is proposed to relate the effective crack length to the geometrical properties. The material characteristic length, required for application of TCD, is correlated with the maximum aggregate size. The resulting formulation is found to yield satisfactory prediction of static strength of notched plain concrete beams, wherein the geometric dimensions of the beam, tensile strength and maximum aggregate size of the concrete mix are the only input parameters. The proposed formulation is validated using a probabilistic analysis of various experimental results available in the literature.