Minimum flexural reinforcement in rectangular and T-section concrete beams

The prescriptions provided by codes of practice for assessing the minimum reinforcement amount for strength purposes in reinforced concrete beams usually disregard the non-linear contribution of concrete in tension and size-scale effects. In the present paper, these phenomena are taken into account correctly in the description of the flexural failure in lightly reinforced concrete beams by means of a numerical algorithm based on non-linear fracture mechanics. In this context, the application of dimensional analysis permits a reduction in the number of governing parameters. In particular, it is demonstrated analytically that only two dimensionless parameters, referred to as reinforcement brittleness number and stress brittleness number, are responsible for the brittle-to-ductile transition in the mechanical response. According to this approach, new formulae suitable for evaluating the minimum reinforcement in practical applications is proposed for both rectangular and T-sections. A comparison with experimental results demonstrates the effectiveness of the proposed model for different reinforcement percentages and beam depths.