Rigid-plastic optimization of solid reinforced concrete structures

Mads Emil Møller Andersen*, Peter Noe Poulsen, John Forbes Olesen, Linh Cao Hoang

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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    Design of solid reinforced concrete structures, e.g., piers and pile caps, is primarily performed using simple hand calculation methods such as the strut-and-tie method. This may lead to designs which are conservative regarding the load-bearing capacity and material consumption, and in turn may result in more expensive designs with an unnecessarily high environmental impact. Finite Element Limit Analysis (FELA), that is, finite element analysis, which employs a rigid-plastic material model, has previously been used for capacity calculations by load optimization of trusses, beams, membranes, plates, shells, and solids. The method utilizes the material of the structure efficiently and is able to show capacities greater than the results of simple plastic hand calculations. FELA has also previously been used in material layout optimization of reinforced concrete membranes, plates, and shells. This paper presents FELA for material optimization of solid reinforced concrete structures. The formulation uses the Modified Mohr-Coulomb material model for concrete, and the reinforcement is modeled using the so-called smeared approach. The optimization procedure seeks to carry the load by varying the amount of smeared reinforcement in each of the three predefined orthogonal directions. The smeared reinforcement variables can either be optimized freely or in distinct zones, for instance, in a zone for bending reinforcement. The material layout is also indirectly optimized by allowing the concrete compressive strength to be a variable. The optimization procedure is applied to the case of a typical four-pile cap.
    Original languageEnglish
    Title of host publicationConcrete Structures: New Trends for Eco-Efficiency and Performance : Proceedings of the fib Symposium 2021
    Publication date2021
    Publication statusPublished - 2021


    • Finite Element Limit Analysis
    • FELA
    • Material layout optimization
    • Solid reinforced concrete
    • Pile cap


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