The usage of linear 3D FEA is widespread within the bridge design community, and although this tool provides substantial benefits in the design process, there are certain practical issues related to the application of this analysis tool. A situation in which such an issue prevails is when linear 3D FEA is used to analyze restraint forces due to thermal shrinkage or expansion in concrete slab frame bridges. Effects related to restraint forces in concrete are difficult to model and predict as these forces differ significantly in nature from external loads, and dealing with them in practical design situations is complicated. In this thesis, cracking due to restraint forces in concrete slab frame bridges was investigated using 3D non-linear FE-analyses in the software package ATENA 3D. Using volumetric finite elements, attempts were made to realistically capture the load response and cracking behavior of concrete slab frame bridges subjected to restraint forces induced by temperature differences among members. The initial parts of this thesis aims to find appropriate modelling techniques and material models for the prediction of cracks due to restraint forces in base restrained walls using a previously reported experimental research project as reference. Comparative simulations were performed, using crack widths and crack patterns as comparate. Overall good correspondence was obtained with an exception of deviation in cracks formed at locations near the restrained corners where crack widths were overestimated in the simulations. The technique used to model the restrained boundary proved to be highly influential in the context of obtaining realistic results. Subsequent to the comparative study, a parametric study was performed where the correlation between crack widths and selected attributes was investigated. The parameter which exhibited the most distinct influential effect on the results was the length-to-height (L/H) ratio of the wall. The applicability of a crack control approach intended for crack width estimation in liquid retaining and containment structures made of concrete exposed to thermally induced restraint forces, given in EN 1992-3, was then evaluated for use in design of concrete frame bridges. This approach proved to return conservative results for walls with low L/H-ratios when compared to results produced in the numerical simulations. Finally, a NLFE (non-linear finite element) model of a concrete slab frame bridge designed by the consultancy company Tyréns AB was composed and tested. Different procedures of applying temperature differences between front wall and bridge deck were evaluated. This study indicated that the width of cracks induced by lateral restraint forces decreased when temperature was modelled applying a discrete thermal gradient to members in contact with back filling material compared to using a uniform temperature in these members when temperature differences between bridge deck and wall was simulated. The interacting effects of permanent external load effects and restraint forces were also investigated. Crack widths from NLFE simulations were then compared with corresponding results calculated using linear FEA results as input for design equations given in EN 1992-1-1. The latter resulted in estimated cracks more than 10 times wider than that obtained in the simulations, while crack widths predicted using the EN 1992-3 approach showed better correspondence to the NLFE results.

In Sweden, it is Eurocode 2 which forms the basis for performing a design of concrete structures, in which methods can be found treating the subject of restrained concrete members and cracking in the serviceability limit state. In the code, both detailed hand calculations procedures as well as simplified methods are described. Several proposal of how to treat base restrained structures can be found in other codes and reports. Some state that the procedure given in Eurocode 2 is on the unsafe side as the method relies on stabilized cracking, while some say that the method is over conservative as the restraining actions will prevent the cracks from opening. As these methods are analysed closer and further tested, it is obtained that they all yield different results under the same assumptions. Most of them are within a similar span, and the deviation arises as the various methods takes different aspect into consideration. One method yields a result which is considerably higher than all other, denoted the Chalmers method. As this method is taught at the technical institute of Gothenburg (Chalmers), the large deviation have caused some confusion among Swedish engineers. As the methods are compared to numerical analyses, it is found that the detailed calculation procedure stated in Eurocode 2 yields fairly good prediction of crack widths for lower levels of strain, while for high levels of strain it is over conservative. The Chalmers method seems to underestimate the number of cracks which occur, and thus give rise to the deviating results. It is further found that in relation to more detailed hand calculations, the simplified procedure stated in Eurocode 2 may not always be on the safe side. The procedure is only valid within a certain range which may be exceeded depending on the magnitude of the load and choice of various design parameters. The effect creep have on base restrained structures subjected to long term loads such as shrinkage is further discussed and analysed numerically. Various hand calculation methods suggest that creep have a positive influence on base restrained structures in the sense that the crack width become smaller. The numerical results indicates that this is indeed the case, however, uncertainties of these analyses are considered to be large in relation to the short term analyses. / I Sverige är det Eurokod 2 som används som basis för dimensionering av betongkonstruktioner, i vilken metoder som beskriver sprickkontroll i bruksgränsstadiet för betong utsatt för tvångskrafter återfinns. Både detaljerade handberäkningsmetoder och förenklade metoder beskrivs. I olika koder och rapporter återfinns ett flertal förslag till hur detta problem ska hanteras. Vissa påstår att metoderna som anges i Eurokod 2 är på osäkra sidan då dessa förlitar sig på stabiliserad sprickbildning, medan andra menar att Eurokod 2 är för konservativ då inspänningen kommer förhindra att sprickorna öppnar sig. Då metoderna analyseras noggrannare och testas framgår det att alla genererar olika resultat under samma antaganden. De flesta ligger inom samma spann och skillnaderna uppkommer då de olika metoderna beaktar olika aspekter. En metod genererar dock ett resultat som är högre än alla andra, som i denna rapport benämns som Chalmersmetoden. Då denna metod lärs ut på Göteborgs tekniska universitet (Chalmers) så har de utstickande resultatet skapat en viss förvirring bland konstruktörer i Sverige. Då metoderna jämförs med numeriska analyser framgår det att Eurokod 2 förutspår en rimlig sprickvidd för låga töjningsgrader, medan den verkar vara överkonservativ för höga töjningsgrader. Chalmersmetoden verkar underestimera antalet sprickor som uppkommer i konstruktionen, vilket resulterar i de utstickande resultaten. Fortsättningsvis fastslås det att i relation till en mer detaljerad handberäkning så är den förenklade metoden i Eurokod 2 inte alltid på säkra sidan. Metoden är endast giltig inom ett visst spann, vilket kan överskridas beroende på den egentliga töjningens storlek och valet av dimensioneringsparametrar. Krypningens effekt på fastinspända betongkonstruktioner då de utsätts för långtidslaster så som krympning har också diskuterats och analyserats numeriskt. Olika handberäkningsmetoder antyder att krypningen har en positiv effekt på så sätt att sprickvidden minskar. Även de numeriska resultaten indikeratar att så är fallet, dock anses osäkerheten i dessa analyser vara stor i förhållande till analyser av korttidslaster.