The Theory of Critical Distances to estimate static and dynamic strength of notched plain concrete

Abstract

The Theory of Critical Distances (TCD) is a well-known design method allowing the strength of notched/cracked components to be estimated accurately by directly post-processing the entire linear-elastic stress fields damaging the material in the vicinity of the stress concentrators being designed. By taking full advantage of the TCD’s unique features, in the present study this powerful theory was reformulated to make it suitable for designing notched plain concrete against static and dynamic loading. The accuracy and reliability of the proposed reformulation of the TCD was checked against a set of experimental results generated by testing, under different displacement rates, square section beams of plain concrete containing notches of different sharpness. This validation exercise has demonstrated that the proposed reformulation of the TCD is capable of accurately assessing the static and dynamic strength of notched unreinforced concrete, with the estimates falling within an error interval of ±20%. The level of accuracy that was obtained is certainly satisfactory, especially in light of the fact that static and dynamic strength was estimated without explicitly modelling the stress vs. strain dynamic behaviour of the concrete being tested.