Old bridges in the Netherlands are reassessed to prove their structural safety because of the increased traffic loads. The Eurocode model for the shear capacity of prestressed concrete beams with sufficient shear reinforcement was found to be very conservative for small amounts of transverse reinforcement, which is typical for old bridges. Code provisions based on the modified compression field theory appear to be much more accurate (Bentz, Vecchio, & Collins,2006). On the other hand, these models make no distinction between flexural shear and shear tension failure, while 25% of the bridges consists of T-, I-, or box beams which are sensitive to shear tension failure. The aim of this thesis is to present a more accurate prediction for shear tension failure based on the modified compression field theory (MCFT). The report focuses on both the CSA-model and Response-2000. The CSA-model is a simplification of the MCFT for beams under the assumption that σ_z=0. The CSA-model shear resistance consists of a concrete and steel part. Response-2000 is a cross-sectional analysis program that works as a non-linear finite element analysis and not only takes into account bending but also shear.Response analysis of 32 beams (experiments of Xie (Xie, 2009), Choulli (Choulli, 2005), Hanson (Hanson & Hulbos, 1965) and Leonhardt (Leonhardt, Koch, & Rostasy, 1973)) have been made and compared with the experimental observations. The failure load is predicted with a mean ratio of 1.38 and a COV of 19% compared to the experiments. It was found that for small a/d-ratios predictions are more conservative. Failure mechanisms: rupture of the stirrups, crushing of the web concrete and slipping/major crack opening are found in Response. 87% of the failure mechanisms was predicted correctly compared to the experiments. The critical cross-section compared with the experimentally observed failure zone showed that 60% of the beams was predicted in the failure zone. The shear force in the cross section is resisted by reinforcement steel, aggregate interlock and the uncracked concrete, which were found to take up respectively 1/2, 1/6 and 1/3 of the shear force. The steel part is predicted accurately while the aggregate interlock part is underpredicted due to an over prediction of the crack spacing. The uncracked part is overpredicted for small amounts of reinforcement and underpredicted for larger amounts of reinforcement. The data of the Response analysis have been used to modify the CSA-model to a model solely describing shear tension failure. The comparison showed that the CSA-model underestimates the steel part, overestimates the concrete part, takes a to large cracked height and doesn't take into account the contribution of the uncracked part. From this comparison, modifications for β,θ,V_max,h_crack and ϵ_x are proposed using Response data and proposals from Esfandiari (Esfandiari & Adebar, 2009). The flanges are taken as uncracked and the contribution of the uncracked part is described with a linear elastic shear stress distribution. This has led to a proposal for a model that solely describes shear tension failure, where the most important addition is the contribution of the uncracked height. Calculations show that the model gives conservative predictions compared to the experiments (mean ratio of 1.36 and a COV 22%) and the predictions are almost the same as for Response. The parameters are predicted conservative compared to the Response-2000 predictions.

The bridges built in the 50’s, 60’s and 70’s are reaching the end of their originally service life. Many bridges require reassessment. In 2009 the former ministry of “Volkshuisvesting, Ruimtelijke Ordening en Milieubeheer”(Housing, Spatial Planning and the Environment) carried out a study about the state of the bridges, following several incidents including for example the closure of the Sebastiaansbridge in Delft. The main conclusion from the research was that it is hard to prove that the structural safety of existing bridges and viaducts is sufficient. One of the main topics in the reassessment of the bridges was the shear capacity. The aim of this study is first to investigate the present Eurocode approach to determine the shear tension capacity, secondly if there is a possibility to improve this Eurocode approach or to propose another model. The general main research question is: What model determines the resistance with respect to the formation of shear tension cracks most accurate? Practical experiments of the researchers Choulli[8] and Elzanaty[9] already carried out will serve as a basis to evaluate of differentmodels in this thesis. The experiments consist of single-span prestressed I- and T-beams. The study focusses on two topics. In the first topic attention is paid to the comparison of the analytical stress distribution and the numerical stress distribution of the web of the single span prestressed I- and T-beams. The analytical stress distribution is determined according to the Euler-Bernoulli beam theory, the vertical stress component ¾y is not taken into account. The current Eurocode model is based on the analytical stress distribution. The numerical stress distribution is determined with a linear elastic analysis in the finite element software program DIANA FEA. The following topic is about the choice of a consistent model that predicts the first shear crack in the web and the consideration of a strength criterion. In this study in total there are considered 6 models and 3 strength criterions. Model 1 is the Eurocode model and is considered with the analytical stress distribution. Model 2, the “LE FEA” model is considered with the numerical stress distribution. Model 3, the “midheight” model around the neutral axis, is considered with the analytical stress distribution. Models 4, 5 and 6 respectively the 45°, the 35°and the 30°model, are considered with the analytical stress distribution. Each model consists of a single or a set points in the web of the prestressed beams to consider. For both the textual explanation and the graphical representation of the models, reference is made to sections 5.1.1 and 5.2.1. There are considered 3 strength criterions: the uniaxial tensile strength fctm, the biaxial tensile strength according to “Mohr-Coulomb” and the biaxial tensile strength according to “Huber”. For each model, the set of points or the single point is divided by a value of a strength criterion. This is defined as “model uncertainty”. From the analysis it is found that the analytical stress distribution does not equal the numerical stress distribution at some parts of the prestressed beams. This is the case in the socalled “disturbed areas”. These areas are located near concentrated loads, so around supports and external concentrated loads. After analysis it is found that the analytical stress distribution takes a too high principal tensile stress σ1 into account, in the “disturbed areas”. After analysis of the different stress components σx , σy and τxy , it is found that components σy and τxy are the cause of the deviant stress distribution in the “disturbed areas”. The test set consists of in total 29 experiments: 12 experiments of Choulli and 17 experiments of Elzanaty. First the results per model, per strength criterion of the Choulli and Elzanaty experiments will be combined, from which the mean and the variation coefficient of the “model uncertainties” are determined. The conclusion is based on one important feature: the conclusions are based on both the complete set of experiments and on the set of experiments where no flexural cracks have been observed. In case of the set of experiments where no flexural cracks have been observed, also the experiments where the calculated tensile stress in the ultimate fiber exceeds the uniaxial tensile strength fctm are left out. From the comparison of the analytical and the numerical stress distribution it can be concluded that stress distribution in the socalled “disturbed areas” is overestimated. Based on the complete set of experiments, model 3, the “midheight” around the neutral axis, is preferred. This model offers the best consistency. Concerning the strength criterion: there is a little difference in consistency between the model with uniaxial tensile strength and the model with the biaxial tensile strength(this holds true for both “Mohr-Coulomb” and “Huber”). Based on this it is preferable for practice to reduce the uniaxial tensile strength with 20%. Based on the set without the experiments which showed flexural cracks, it is found that the “means” of the models were lower and that the models are more consistent. Concerning the strength criterion: both the uniaxial tensile strength fctm and the tensile strength according to “Mohr-Coulomb” are overestimated. For future research it is recommended to investigate the influence of present flexural cracks on the stress distribution, what will be the influence on the way of predicting diagonal tension cracking. Fromthe results in this study it can be seen that the presence of flexural cracks can have significant influence on the consistency of the models. Further, it is also important for future research to consider distributed loads in addition to concentrated loads, because in practice there will be always present a significant distributed load.