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Abstract
Complex triaxial stress states are present in many reinforced concrete structures. These socalled 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 NonLinear Finite Element Analysis (NLFEA), which uses fracture mechanics and complicated nonlinear material models. The nonlinear material models enable the methods to accurately predict the structures’ behavior up to collapse. However, the methods require load or deformationstepping, and many material parameters are required for the nonlinear 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 rigidplastic theory. The rigidplastic material model means that only a few welldefined 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 rigidplastic 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 rigidplastic 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 stressbased 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
Numerical programs such as Atena and Diana can model solid structures. The programs are based on NonLinear Finite Element Analysis (NLFEA), which uses fracture mechanics and complicated nonlinear material models. The nonlinear material models enable the methods to accurately predict the structures’ behavior up to collapse. However, the methods require load or deformationstepping, and many material parameters are required for the nonlinear 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 rigidplastic theory. The rigidplastic material model means that only a few welldefined 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 rigidplastic 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 rigidplastic 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 stressbased 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 language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  240 
ISBN (Electronic)  9788774757108 
DOIs  
Publication status  Published  2022 
Series  DCAMM Special Report 

Number  S321 
ISSN  09031685 
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 1 Finished

Rigid Plastic Modelling of Solid Reinforced Concrete Structures
Andersen, M. E. M., Poulsen, P. N., Hoang, L. C., Ravn, U. G., Olesen, J. F. & Ruiz, M. F.
01/06/2019 → 27/04/2023
Project: PhD