Redistribution of bending moments in concrete slabs in the SLS

Abstract: The finite element method (FEM) is commonly used to design the reinforcement in concrete slabs. In order to simplify the analysis and to be able to utilize the superposition principle for evaluating the effect of load combinations, a linear analysis is generally adopted although concrete slabs normally have a pronounced non-linear response. This type of simplification in the modeling procedure will generally lead to unrealistic concentrations of cross-sectional moments and shear forces. Concrete cracks already at service loads, which leads to redistribution of moments and forces. The moment- and force-peaks, obtained through linear finite element analysis, can be redistributed to achieve a distribution more similar to what is seen in reality. The topic of redistribution is however poorly documented and design codes, such as the Eurocode for concrete structures, do not give descriptions of how to perform this in practice. In 2012, guidelines for finite element analysis for the design of reinforced concrete slabs were published in a joint effort between KTH Royal Institute of Technology, Chalmers University of Technology and ELU consulting engineers, which was financially supported by the Swedish Transport Administration. These guidelines aim to include the non-linear response of reinforced concrete into a linear analysis. In this thesis, the guidelines mentioned above are followed to obtain reinforcement plans based on crack control, for a fictitious case study bridge by means of a 3D finite element model. New models were then constructed for non-linear analyses, where the reinforcement plans were implemented into the models by means of both shell elements as well as a mixture of shell and solid elements. The results from the non-linear analyses have been compared to the assumptions given in the guidelines. The results from the non-linear analyses indicate that the recommendations given in the aforementioned guidelines are indeed reasonable when considering crack width control. The shell models yield crack widths equal to approximately half the design value. The solid models, however, yielded cracks widths that were 15 - 20$\%$ lower than the design value. The results show that many factors attribute to the structural behavior during cracking, most noticeably the fracture energy, a parameter not featured in the Eurocode for concrete structures. Some limitations of the models used in this thesis are mentioned as well as areas for further improvement.