Capacity of reinforced concrete sections: can limit analysis replace ultimate limit states?

Significance 

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.

Capacity of reinforced concrete sections: can limit analysis replace ultimate limit states? - Advanced Engineering

 

About the author

Dr. Salvatore Sessa graduated in civil engineering in 2005 at the University of Naples Federico II where he was also got a PhD in “Engineering of Materials and Structures” in 2009. In 2007-08 he was Visiting Scholar at the University of California, Berkeley where he studied Structural Reliability and Random Vibrations. He held several postdoc positions researching in inverse identification of cohesive fracture interfaces. In 2014 he returned to his alma mater as postdoc and therefore as Assistant Professor since 2016. In 2018 he obtained the Italian Academic Qualification for the position of Associate Professor of Continuum and Structural Mechanics.

His research activities concern nonlinear analysis of structures with particular focus on seismic analysis of reinforced concrete framed structures and dynamic analysis of masonry structures.

About the author

Dr.Francesco Marmo graduated in Civil Engineering in 2004 at the University of Naples Federico II, where he also obtained a PhD degree in 2008. Since 2013 he is assistant professor at the same University and teaches the MS course of Finite Element Analysis of Structures and the BS course of Continuum and Structural Mechanics. In 2017 he obtained the Italian Academic Qualification for the position of Associate Professor of Continuum and Structural Mechanics. He actively participated to 8 founded research projects regarding the structural safety of heritage buildings and urban areas exposed to seismic risk.

His research in computational mechanics applied to masonry and reinforced concrete structures, contact mechanics and inclusion problems as well as finite elements, form finding problems and analysis of masonry arches and vaults.

About the author

Dr. Leonardo Leonetti was born in 1977 in Italy. He received the master’s degree in Civil Engineering in 2002 and the PhD degree in Computational Mechanics in 2005 from the University of Calabria. From 2010 he is assistant professor of Mechanics of Solids at the University of Calabria where he currently teaches Structural Mechanics.

His research interests include: numerical methods for nonlinear analysis of structures; imperfection sensitivity analysis and optimization of structures undergoing buckling; advanced beam models; solid‐shell finite elements for composite structures undergoing large displacements; hybrid finite elements for material and geometrically nonlinear problems; isogeometric shells.

About the author

Prof. Giovanni Garcea received the master’s degree in Civil Engineering in 1991 and the PhD degree in Computational Mechanics in 1995 from the University of Calabria. Since 2004 he is associate professor of Mechanics of Solids at the University of Calabria where he currently teaches Statics and Nonlinear Structural Analysis.

His research interests include: numerical methods for nonlinear analysis of slender structures; geometrically exact structural models for beams, plates and shells; imperfection sensitivity analysis and optimization of structures undergoing buckling; advanced beam models; solid‐shell finite elements, hybrid and isogeometric formulations. Limit and shakedown analysis. He is on the editorial board of many international journals including Applied Mathematical Modelling.

About the author

Prof. Luciano Rosati graduated with honors in Mechanical Engineering in 1982 and in Civil Engineering in 1984 at the University of Naples Federico II where he got a PhD. In Structural Mechanics in 1989. In 1997 he spent a two-months granted research appointment at the Imperial College in London under the supervision of prof. M. Chrisfield. Since 2001 he is full professor of Structural Mechanics at the University of Naples Federico II where he has been carrying out teaching and research activities about finite elements, nonlinear analysis of structures and continuum mechanics, coordinating 15 research projects as principal investigator and serving as reviewer for several international journals.

He served as member of several committees including the Research Task Committee “Instructions for the Design, Cons of fiber-reinforced composites”, hosted by CNR. (National Research Council) and the Italian branch of the Natural Society of Philosophy.

About the author

Professor Emeritus Raffaele Casciaro graduated in Civil Engineering in 1967 at the University of Rome where he served as postgraduate fellow from 1968 until 1973 when he became assistant professor of Theory of Structures teaching continuum mechanics and structural engineering courses at the University of Calabria where he spent most of his career as associate professor, since 1983, and as full professor, since 1988, until his retirement in 2013.

Professor Casciaro served in various committees and is member of several scientific associations including the International Association of Computational Mechanics – IACM and the Association of Nonlinear Dynamics “Enrico Fermi”.

His research activities are focused on computational analysis of structures by finite elements, nonlinear dynamics, limit and post-critical analysis, adaptive-multilevel algorithms and plasticity.

Reference

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. Meccanica53(6), 1493-1512.

Go To Meccanica

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