Limits to Plastic Analysis due to Size-Scale Effects on the Rotational Capacity of Reinforced Concrete Cross Sections

Reinforced concrete (RC) structures are usually designed to provide a ductile response under bending loadings. To this aim, most codes of practice impose lower and upper limits to the steel ratio in order to prevent unstable crack propagation and to avoid brittle failure due to concrete crushing without steel yielding. Within these limitations, elastic analysis with moment redistribution or even plastic analysis can be adopted for RC structures. In this context, size-scale effects are usually disregarded, leading to unsafe design conditions in the case of large structures.

In the present study, the limitations of the prescriptions provided by the European and American building codes concerning the admissible plastic rotation and moment redistribution are highlighted. In particular, using a numerical algorithm based on the finite element method and on nonlinear fracture mechanics concepts recently developed by the present authors, the mechanical behaviour of the plastic hinge region of RC beams in bending is simulated. The results show that the effect of the structural dimension should be explicitly introduced in the code prescriptions for a safe structural design, by considering different design curves depending on the size-scale of the beams.