# Shear cracks in concrete structures subjected to in-plane stresses

Sammanfattning: After only two years of service, extensive cracking was found in the webs of two light-rail commuter line bridges in Stockholm, the Gröndal and Alvik bridges. Due to this incident it was found necessary to study the means available for analysing shear cracking in concrete structures subjected to in-plane stresses. The aim of this PhD project is to study shear cracking with these two bridges as reference. In this thesis, the first part aims to study the possibility of using finite element analysis as a tool for predicting shear cracking for plane state stresses. The second part is concerning how the shear cracks are treated in the concrete design standards.Shear cracking in reinforced beams has been studied with non-linear finite element analyses. In these analyses the shear cracking behaviour was compared to experiments conducted to analyse the shear failure behaviour. Finite element analyses were performed with two different FE programs Abaqus and Atena. The material model used in Atena is a smeared crack model based on damage and fracture theory with either fixed or rotated crack direction. The material model used in Abaqus is based on plasticity and damage theory. The fixed crack model in Atena and the model in Abaqus gave good results for all studied beams. For the two studied deep beams with flanges the results from the rotated crack model were almost the same as obtained with the fixed crack model. The rotated crack model in Atena gave though for some beams a rather poor estimation of the behaviour.The calculation of crack widths of shear cracks has been studied for the long-term load case in the serviceability state for the Gröndal and Alvik bridges, with the means available in the design standards. The methods based on the crack direction corresponding to the principal stress and do not include the effect of aggregate interlocking seems to be too conservative. Two of the studied methods included the effect of aggregate interlocking, it was made either by introducing stresses in the crack plane or implicitly by changing the direction of the crack so that it no longer coincide with the direction of principal stress. For calculations based on probable load conditions, these methods gave estimations of the crack widths that were close to the ones observed at the bridges. Continuous measurements of cracks at the Gröndal and the Alvik bridges have also been included. Monitoring revealed that the strengthening work with post-tensioned tendons has, so far, been successful. It also revealed that the crack width variations after strengthening are mainly temperature dependent where the daily temperature variation creates movements ten times greater than those from a passing light-rail vehicle. Monitoring a crack between the top flange and the webs on the Gröndal Bridge showed that the top flange was moving in a longitudinal direction relative to the web until the strengthening was completed. The crack widths in the sections strengthened solely by carbon fibre laminates seem to increase due to long-term effects.

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