Reinforced concrete elements are susceptible to various failure modes especially when subjected to seismic loads. Therefore, different computational methods used in safety assessment have to put into consideration geometrical behavior, external loads and constitutive nonlinearities of the concrete. Presently, Eurocode-compliant ultimate limit state (ULS)method is widely used in structural analysis to perform safety checks, by means of capacity domains. To this end, it is necessary to compute ULS limit surfaces defined as boundaries for bending moments and axial forces. However, several limitations associated with USL technique have limited their use especially in cases involving numerous load combinations that require a great number of safety checks. For instance, it is difficult to determine whether the type of USL capacity check analysis is either plastic type of nonlinear elastic. To this end, an alternative method to overcome the drawbacks that hinder the use of traditional methods like USL are needed and limit analysis technique have been identified as a promising solution.
Dr. Salvatore Sessa, Dr. Francesco Marmo and Professor Luciano Rosati at the University of Naples Federico II in collaboration with Dr. Leonardo Leonetti, Professor Giovanni Garcea and Professor Raffaele Casciaro at the University of Calabria developed a comparison between the capacity domains of two reinforced concrete sections obtained from limit analysis and ultimate limit state analysis technique. A sufficient ductility of the structural members to permitted stress redistribution and ensured collapse mechanism determined by the limit analysis. Also, they formulated modeling assumptions to reproduce the physical behaviors with respect to the ductility of the cross-sectional area of the reinforced concrete such as ignoring the contribution of the concrete cover in the computation of the yield surface. Their research work, published in the journal, Meccanica, aimed at investigating the relationship between the design procedure and the plasticity theory.
The authors observed that confined ratios produced sufficient ductility enough to make the yield surface computed by limit analysis to be equivalent to the ultimate limit state domain. Therefore, for force-based safety checks in reinforced concrete, the ULS can be accurately approximated by the yield surface due to the limited error average obtained. In addition, the authors pointed out that for a generalized strain value, the yield surface can be used to surrogate the response of the reinforced concrete section and in particular for plastic analyses. This was attributed to the comparison that was based on the consistent strain mechanism that resulted in a limited relative error calculated for both the yield and the ultimate limit state.
The researchers successfully evaluated the capacity surfaces of the reinforced concrete sections through the ultimate limit state and limit analysis approaches. Both the theoretical investigation and the numerical experiments proved that the proposed limit analysis approach provided accurate results. Furthermore, the proposed strategy permits the evaluation of the material strength and of the load limit values. Owing to its simplicity, effectiveness and cost, the authors are optimistic that the limit analysis will advance several design practices as it is capable of determining structural safety factors by proving the essential information concerning the design process. It also opens ways for future research work such as characterization of the surrogated model.
Sessa, S., Marmo, F., Rosati, L., Leonetti, L., Garcea, G., & Casciaro, R. (2018). Evaluation of the capacity surfaces of reinforced concrete sections: Eurocode versus a plasticity-based approach. Meccanica, 53(6), 1493-1512.Go To Meccanica