Rigid-Plastic Modeling of Solid Reinforced Concrete Structure: Using Finite Element Limit Analysis

Mads Emil Møller Andersen

Research output: Book/ReportPh.D. thesis

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Complex triaxial stress states are present in many reinforced concrete structures. These so-called solid structures are often analyzed and validated in the Ultimate Limit State (ULS) using simple hand calculations based on methods designed for plane structures. The hand calculation methods rely on simplifications and can be cumbersome for complicated structures. Consequently, this may result in inefficient designs and excessive material usage.

Numerical programs such as Atena and Diana can model solid structures. The programs are based on Non-Linear Finite Element Analysis (NLFEA), which uses fracture mechanics and complicated non-linear material models. The non-linear material models enable the  methods to accurately predict the structures’ behavior up to collapse. However, the methods require load- or deformation-stepping, and many material parameters are required for the non-linear material models. Consequently, the programs are not suited for general practical design.

Therefore, a numerical method is needed for the practical design of solid reinforced concrete structures in the ULS. It is suggested that Finite Element Limit Analysis (FELA) is such a method. FELA is a combination of the domain discretization of the finite element method with limit analysis using the theorems of rigid-plastic theory. The rigid-plastic material model means that only a few well-defined material parameters are needed.  Furthermore, the problem can be set up as a convex optimization problem, meaning it can be efficiently solved. The results of the FELA calculations are the capacity and the collapse mechanism of the structure. However, FELA does not give information about the level of deformations and cracks in the structure due to the rigid-plastic material model. Furthermore, it is required that the structure is appropriately reinforced, such that it has sufficient ductility, for the method to be valid.

The contributions of this thesis are towards rigid-plastic modeling of solid reinforced structures using Finite Element Limit Analysis. Several research topics related to this main topic are treated. First, an efficient FELA load optimization framework is presented. The framework is based on a new stress-based finite element called the Constant Stress Normal traction (CSNT) element. The capabilities of the framework for analysis of solid reinforced concrete structures are shown in several examples, including a test database with 240 pile caps. The framework is also expanded to be capable of material layout optimization. The material layout optimization can be free or use material groups. Furthermore, the challenge of the effective strength of concrete is treated using two approaches. In the first approach, the influence of the effectiveness factor is included in the yield surface. In the second approach, the effectiveness factor is estimated based on the failure mechanism of the structure 
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages240
ISBN (Electronic)978-87-7475-710-8
Publication statusPublished - 2022
SeriesDCAMM Special Report


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