Nowadays, Rijkswaterstaat reassesses many older concrete bridges to guarantee their structural safety under the influence of increased traffic loads and stricter standards. Many of these concrete bridges contain open straight-legged stirrups, which are not allowed to take into account for the calculations of the shear resistance according to current standards. This often results in theoretical insufficient shear capacity and critical damage to structures, but this is not observed in reality. This indicates that the open straight-legged stirrups probably do contribute to the shear resistance, where an accurate assessment of this contribution could prevent unnecessary and costly structural safety measures. However, very few shear tests with relevant cross-sectional dimensions are performed and documented in literature, especially tests containing open straight-legged stirrups. The application of Nonlinear Finite Element Analysis (NLFEA) is a useful tool to evaluate and understand the behaviour of structures, but provisions for the implementation of open straight-legged stirrups in concrete structures are lacking. Thus, the goal of this research is to provide a finite element modelling strategy that is able to accurately describe the behaviour of concrete beams with open straight-legged stirrups subjected to shear. The research focusses on describing the behaviour of rectangular concrete beams with open and closed straight-legged stirrups with finite element models using DIANA 10.5 [1]. Schramm [2] has performed multiple shear tests on prestressed concrete beams with several no longer permitted stirrups, including open straight-legged stirrups. He found that open straight-legged stirrups can significantly contribute to the transfer of shear forces [2]. The relevance of the rectangular test beams for comparison with box-girders is validated in this thesis, where the stress distributions in a linear elastic rectangular and box-girder cross-section due to axial forces, bending moments, shear forces and torsion are compared. In the interest of providing a suitable solution strategy, Schramm’s test beams with closed and open straight-legged stirrups are reproduced with 3-dimensional nonlinear finite element models based on the recommendations of the RTD1016-1 [3], where the influence of various modelling considerations is investigated. The concrete is modelled with a smeared total strain-based crack model with the Hordijk tensioning and parabolic compression relations, including confinement and lateral cracking effects. Reinforcements are modelled as embedded truss elements with the Von-Mises plasticity model. To describe the accurate anchorage behaviour of the open straight-legged stirrups, the interaction between the surrounding concrete and the stirrups is described with the Shima bond-slip relation. The finite element model is first calibrated with a beam with closed stirrups, where modelling clamped restraints with supports on both sides of the beam result in a too-stiff response. By allowing a little rotational freedom in the form of boundary springs, the stiffness of the beam is manipulated without changing the overall load-bearing behaviour...

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.

Vanuit Rijkswaterstaat is de wens om een snelle, verifieerbare methode te ontwikkelen voor het controleren van de veiligheid voor meerdere T-ligger constructies volgens huidige normen en inzichten. Hierbij dient rekening gehouden te worden met eventuele wijzigingen in de toekomst, welke door de huidige ontwikkelingen op het gebied van dwarskrachtonderzoek te verwachten zijn. Het is de verwachting dat op basis van verfijnde beoordelingen en verder fundamenteel onderzoek de ‘reserves’ middels een quickscan-aanpassing inzichtelijk gemaakt kunnen worden. Hierdoor zou een deel van de onderzochte kunstwerken mogelijk alsnog voldoen aan de veiligheidsnormen. Door diverse berekeningsmethoden met elkaar te vergelijken is getracht een methode te vinden welke simpel toepasbaar is, realistische resultaten voor dwarskracht en moment geeft ten gevolge van de verkeersbelasting en tevens conservatief is. Door deze te vergelijken met diverse Scia-berekeningen is een methode gekozen die het best aan de eerdergenoemde punten voldoet. Tevens zijn de invloeden van meerdere uitgangspunten met elkaar vergeleken. Nadat inzicht is verkregen in de manier waarop de belasting over de liggers is verdeeld, is een generiek systeem gemaakt, een zogenaamde quickscan. De quickscan maakt op een snelle manier duidelijk of de gekozen snede voldoende weerstand kan bieden aan de behorende belastingcombinaties. De quickscan is een generieke, eenvoudig toepasbare, conservatieve methode om ‘het kaf van het koren te scheiden’ voor de dwarskrachttoets, zonder dat daarvoor EEM-software nodig is, welke tevens de Scia-berekeningen zo goed mogelijk benadert. Om deze zo goed mogelijk te ontwikkelen is een beoordelingsprocedure gerealiseerd welke zich vormt tot de quickscan. Om inzicht te verkrijgen in de invloed van de verkeersbelasting op de liggers en om deze conservatief te benaderen, zijn diverse berekeningsmethoden met elkaar vergeleken. Uit deze vergelijking is gebleken dat de beste benadering voor de verkeersbelasting de ‘verspreide methode’ is. Hierbij wordt de belasting gespreid of is deze niet afhankelijk van de locatie van de dwarsdragers. Met deze kennis is de quickscan Boon ontwikkeld. Deze kan worden uitgevoerd door enkele parameters in te vullen, zoals: de lengte van de ligger, het oppervlak van de ligger, het voorspanverloop, de dwarsdragers en door de ‘kritische’ sneden (belangrijke te toetsen sneden) van de ligger te bepalen. Daarna kan snel en slim inzichtelijk worden gemaakt wat de UC op deze sneden van de constructie is, en wat de consequenties van wijziging van uitgangspunten zijn. Uit het onderzoek is gebleken dat het tandemstelsel altijd op een hoek van 30 graden vanaf het gekozen punt tot hart rijstrook moet staan om de maximale dwarskracht in dat punt te vinden. Deze belastingsposities worden automatisch gevonden, waarna direct de dwarskracht en het bijbehorende moment berekend wordt met behulp van de verspreide methode. Hierdoor kan de constructieve beoordeling van de liggers snel inzichtelijk worden gemaakt. De quickscan Boon is een eenvoudig toepasbare, realistische, conservatieve beoordeling voor T-ligger constructies, welke inzicht geeft in de maatgevende belastingcombinatie en gemakkelijk te verifiëren is. De kracht van deze methode is dat door te variëren met diverse parameters (zoals capaciteitsaspecten, te toetsen snede en rijwegindeling) direct de invloed van deze parameters inzichtelijk kan worden gemaakt. Waar de resultaten conservatief en toch reëel zijn.

The growing need for strengthening of concrete structures to improve their structural performance challenges structural engineers to come up with strengthening techniques that is most suitable and effective for a structural system in its deteriorated state. Although there are quite a few techniques in practice for strengthening of concrete structures -reinforced or prestressed, various factors limit their efficiency and performance. Use of novel concrete-based materials such as Ultra High Performance Fibre Reinforced Composite (UHPFRC) can lead to an effective strengthening system due to the exceptional material properties of UHPFRC. In particular, the strain hardening behavior of UHPFRC in tension and its excellent durability. Out of the two main mechanisms of failure in concrete elements namely flexure failure and shear failure, shear failure is the most critical due to the abrupt nature of its mechanisms that leads to complete collapse of the structures with no sign of warning. This makes shear strengthening of prestressed concrete structures, that typically form the supporting elements in large infrastructural units such as bridges, a very essential course of action. To investigate the effectiveness of using UHPFRC in shear strengthening of prestressed concrete elements, the post-tensioned T girders of Helperzoom bridge, Groningen, Netherlands are chosen as reference beams which are strengthened with UHPFRC. The reference beams are subjected to a 3-point bending test to determine their failure mechanism and structural capacity. The reference beam is modelled, and tests are simulated by finite element analysis using ATENA. Since the simulated beam failure in shear compression rather than shear tension by localization of the shear tension crack. In order to understand this behavior and the failure mechanism and to check if the results from the simulations are reasonable, a detailed analysis is performed. The influence of shear reinforcement and prestressing, active in the critical shear region, on the shear capacity and the final failure mode are investigated. The results from the numerical analysis are compared to the results from experimental shear tests performed on existing post-tensioned girders which exhibit a similar mode of failure as observed in the reference T beams. The shear capacity of the reference T beam is also calculated from the Flexural Shear Crack Model proposed by Huber et.al and it is seen that the shear capacity from the numerical analysis from ATENA is in close match to that obtained from the analytical model. The contribution of the arching effect to the shear capacity calculated from the model is between 77% and 87% for the beams tested in this research and the contribution is between 28% and 58% in the beams tested in the experiment. In the last step, the effectiveness of strengthening the reference beam with UHPFRC is determined. The results show that the effect of strengthening with UHPFRC is maximum in the reference beam without stirrups and prestressing both in terms of shear capacity and ductility.

Shear tension failure in thin-webbed prestressed concrete elements is yet to be predicted in an accurate manner. The analytical method uses assumptions to simplify the theory. This makes it less accurate. The calculated resistance to web-shear cracking is based on the principle tensile stress reaching the tensile strength of concrete. Failing in shear tension is more risky than failing in bending, since it often happens abruptly without any warnings. Previous research shows however that shear tension failure often occurs before the principle tensile stress reaches the assumed tensile strength of concrete. This means that the resistance is being overestimated. Comparisons between experimental results and theoretical models have shown that the coefficient of variation for the shear force at web-shear cracking for experiments including flexural cracks is significantly larger than for experiments without flexural cracks. It is assumed that flexural cracks are present when principle tensile stress in the outer fiber is higher than tensile strength in the flange. This indicates that the presence of flexural cracks influence the stress distribution in the areas where web-shear cracking occurs. To find the influence of flexural cracks on web-shear cracking a well documented experiment about continuous prestress concrete members failing in shear tension is used for a case study. Namely the thesis ‘’The Influence of Axial Load and Prestress on The Shear Strength of Web-Shear Critical Reinforced Concrete Elements’’ written by Liping Xie in 2009. Three of the specimen are chosen to be researched, between these three the only changing variable is the amount of prestress. All three fail under shear tension, however one has no observed flexural cracks, one has the flexural cracks and the web-shear cracks occur simultaneously and the last one shows flexural cracks before web-shear cracking. Three analyses are performed per specimen: analytical analysis, linear finite element analysis (LFEA) and a non-linear finite element analysis (NLFEA). These analyses are compared to each other and to the experimental results. An outstanding result is that for every load in every specimen it holds that: σ1_ANA > σ1_LFEA ≥ σ1_NLFEA. The maximum principle tensile stresses calculated with an analytical method are consistently higher than principle tensile stresses that follow from a LFEA and NLFEA. This means that performing a simple analytical analyses gives a lower shear resistance than the LFEA and the NLFEA. All three analyses indicated flexural cracks for the beam in which no flexural cracks were observed. However the NLFEA showed that these were cracks of a maximum crack width of mm at the moment of web-shear cracking. These widths are not visible by eye. All specimen showed web-shear cracks under a shear load lower than predicted, meaning all analyses overestimate the shear tension resistance. A sensitivity analysis is performed to find the influence of shear reinforcement and of the tensile strength of the concrete. Conclusions are that the shear reinforcement has little to no influence up until the moment of web-shear cracking. All analysis overestimate the resistance to web-shear cracking. In this thesis a sensitivity analysis is performed to the influence of the tensile strength of concrete. It is concluded that if the tensile strength of the concrete is reduced by 40% the NLFEA still results in shear forces larger than the shear force at web-shear cracking during the experiments. Another conclusions of this research is that the presence of micro flexural cracks reduce the principle tensile stresses in the adjacent web areas. The specimen in which no flexural cracks were observed during testing shows flexural cracks conform all analyses it is impossible to compare specimen uncracked in bending with specimen cracked in bending. Up until reaching the tensile strength of the concrete the LFEA and the NLFEA are logically equal. When the load is further increased differences between the LFEA and the NLFEA occur. It is assumed that this difference is the result of the presence of the flexural micro cracks. The specimen with the smallest flexural micro cracks showed also the smallest difference between σ1_LFEA and σ1_NLFEA From this it can be concluded that larger cracks result in a larger reduction of σ1. It is expected that if the micro flexural cracks evolve to significant flexural cracks that the principle stresses are reduced even more, resulting in a underestimation of the actual shear tension resistance.

This master thesis investigates the influence of flanges on the shear capacity of reinforced non-rectangular members without shear reinforcement. The study adapts the evaluation procedure developed by Yang (2014) for rectangular cross-sections to analyze plates with holes, I-beams and T-beams.

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.

In the past, many researches on the topic of size effect on concrete structures were mainly focused on the phenomenon of size effect in flexural cracking. The result of those studies can be found today in the concrete structure design specifications of well-known building codes, such as the Eurocode. Nevertheless, the inclusions of the results of those studies into the design specifications are still minimum and therefore, it is necessary to conduct more studies on size effect, especially on other types of cracking. In this thesis, an investigation focused on the size effect in shear tension cracking at prestressed concrete beams was conducted. The model used for investigating the size effect is a prediction that a shear tension crack will occur when the principal tensile stress at a certain location on the web of a beam is equal to the concrete mean uniaxial tensile strength (σ1 = fctm). The investigation was conducted by studying premature shear tension cracking on a group of several I-profile prestressed reinforced concrete beams, called the trusted specimens, which were experimented by Hanson (1964), Choulli (2005), and Elzanaty (1986) under four-point bending tests. These tested beams were numerically investigated using linear elastic finite element analysis (LEFEA) with an aim to find the nearly realistic principal tensile stresses that caused the shear tension crack to initiate below the designated tensile strength of the beams. To study the size effect, the obtained principal tensile stress distributions were analyzed using two new approaches proposed by the author, namely the σ1 area approach and the ratio-of-distances approach. The σ1 area method is a technique for detecting a structural size dependency of the uniaxial tensile strength by comparing rectangles which areas represents a group of σ1 values that have a higher likelihood in achieving the deviated values of fctm and initiate shear tension cracking on the web of the trusted specimens. In contrast, the ratio-of-distances approach investigates the size dependency of the uniaxial tensile strength by observing the locations of σ1max where a shear tension crack initiated in the web of each trusted specimen under an assumption that a shear tension crack is more likely to originate from near the beam neutral axis instead of near the web-flange junction due to the change of thickness at that interface. In conclusion, the result of the investigation was presented. The σ1 area approach confirmed the presence of size effect in shear tension cracking at the trusted specimens by giving a relation that showed a tendency for the smaller specimens to have a higher resistance towards principal tensile stresses compared to the larger specimens. The ratio-of-distances result, on the other hand, implied that the approach has failed to detect the presence of size effect. In that result, the shear cracks from the smaller specimens and the shear cracks from the larger specimens had similar starting points locations, at which the σ1max was located. In addition, several recommendations are provided for future studies on size effect in shear tension cracking. It was recommended to do research this topic on different physical problems and shear tension cracking with the presence of flexural cracks.