Modeling of stress-strain state of reinforced concrete slabs taking into account physical nonlinearity

Reinforced concrete structures have nonlinear properties due to the material and its structure. The onset of cracking leads to additional redistribution of the concrete's stress state. Furthermore, when a concrete slab bends, different layers experience different stresses. The aim of this study was to develop an improved mathematical model of the stress-strain state of reinforced concrete slabs taking into account cracking due to the layer-by-layer description of the physical nonlinearity of concrete. The object of study was a reinforced concrete slab measuring 1395×4500×50 mm, loaded in the middle and simply supported on three sides. In the model, the strength of concrete under complex stress conditions was described using a limit surface in the principal stress space. Additionally, constraints were introduced for rigidity and cracking conditions. The model is implemented using the finite element method in the DIVLOC software package. The modeling results include a picture of the stress-strain state of the slab and a diagram of the formation and development of cracks. Areas with the smallest reserve of bearing capacity are found taking into account the redistribution of stresses. To assess the model's validity, a full-scale experiment was conducted. Using sensor readings, the deformation of various points on the slab was measured. As a result of slab bending, the model showed support separation, which was confirmed experimentally. The discrepancy between the strain sensor readings and the calculated data before cracking was no more than 23%. Under a load of 33 kN, crack initiation was observed. After cracking, the discrepancies decreased to 19−20%. The experimental results confirmed the stress redistribution after cracking and the adequacy of the mathematical model with a layer-by-layer description of concrete nonlinearity.