High-performance reinforced concrete structures: brittleness size-scale effects

The present paper deals with the brittle behaviours of high-performance reinforced concrete beams for rather low or high reinforcement percentages. In the former case, the loading drop is due to tensile concrete cracking, whereas in the latter it is due to compression concrete crushing at the opposite beam edge. For the former case, an analytical model is introduced (the Bridged Crack Model) that is able, through a peculiar rotational compatibility condition, to deduce the redundant closing forces applied by the longitudinal reinforcement to the crack faces. This model is conceptually relevant, since it permits to find the minimum reinforcement condition. The linear elasticity of the matrix and the LEFM stress-singularity at the crack tip provide a power-law for the reinforcement percentage as a function of the beam depth raised to –1/2. On the other hand, introducing a numerical model where concrete is considered as a cohesive softening material both in tension and compression, we can obtain a double size-scale brittle-to-ductile-to-brittle transition. By applying Dimensional Analysis and a best-fitting procedure, both in tension and compression, it is possible to find the scaling laws for minimum and maximum reinforcement percentages, respectively. The two exponents become equal to –0.15 and –0.25, respectively. The absolute values of both these exponents are lower than the absolute value of the reference LEFM exponent 0.50 (scaling of extreme severity) and agree with the available experimental results very well. The first has recently been assumed as the reference value in the AASHTO Guidelines for the minimum flexural reinforcement. Unfortunately, we can not affirm the same for the most well-known National and International Standard Codes.