Over the last century, over one hundred crack width formulas have been developed to calculate the width and spacing of cracks in reinforced and prestressed concrete elements. It is unclear which formulas are the most accurate. An extensive comparison study is required to determine which formulas accurately describe the crack patterns, consisting of the crack width and spacing. To make such a study possible, this paper proposes categorizing formulas. The categorization of the formulas is based on their applicability, crack pattern representation, and background. The categorization presents an overview of the different assumptions and application areas for describing crack patterns.

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For structures whose structural safety cannot be demonstrated using the applicable code regulations, a nonlinear finite element analysis (NLFEA) can be used to investigate the structural behavior and maximum load capacity. The Dutch Ministry of Infrastructure and Water Management uses a dedicated guideline for NLFEA in such an assessment. This guideline lacks validation on multi-span girder bridges with continuous deck slabs. Particularly, the modeling of the concrete-to-concrete interface between girders and slab deserves attention, since the interface shear transfer can significantly affect the structural behavior. In this paper we investigate the impact of different interface constitutive relations, and validate the selected modeling approach on three experimental shear tests of continuous girders. The finite element models accurately describe the failure processes and predict, on average, a 10% lower shear capacity as observed in the tests. In anticipation of future research, this is an indication that the modeling approach is suitable to be used in engineering practice.

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There are a large number of precast girder bridges in the Netherlands that are made continuous utilizing cast in situ layers and cross beams. When controlled by the Eurocode minimum shear reinforcement requirement, the majority of these bridges that were constructed before the 1970s have insufficient amount of transverse reinforcement, which could make them shear critical. Furthermore, when the continuity is created at intermediate support, the prestressing strands in the precast beams are usually located in the compression zone. This may limit the positive effect of the prestress to the shear capacity of members without transverse reinforcement. The aforementioned concern is not considered by the standard shear design approach of Eurocode. Because of its empirical nature, the shear capacity of these bridges cannot be rationally assessed by the code. Currently, an experimental campaign on full-scale 15m long specimens is underway at Delft University of Technology to investigate the existing challenges. In this paper, the effect of the above-mentioned concerns is illustrated using the predictions of Eurocode and the Dutch Guidelines for the Assessment of Existing Bridges (RBK). Moreover, the difficulties and insights gained from the design and execution of the experiments are discussed.@en

When the shear resistance of prestressed beams with stirrups is determined with the current Eurocode, no distinction is made between regions with and without flexural cracks. This while it may be expected that a region without flexural cracks will have a higher shear resistance. This is due to the lower longitudinal strains and the narrow crack widths, resulting in a higher contribution of aggregate interlock. Also, the Eurocode does not take into account that in regions without flexural cracks, a significant part of the shear force is transferred through the uncracked flanges. This article proposes therefore a shear resistance model, based on Modified Compression Field Theory (MCFT), that does consider the low longitudinal strains and shear transfer through the uncracked flanges. From a comparison it was found that the proposed model can determine shear resistance as accurately as the most comprehensive level III approach of the Model Code 2010. However, the proposed model was found to be much easier to use in engineering practice as no iterations are necessary.

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The Dutch Directorate-General for Public Works and Water Management (Rijkswaterstaat) is assessing its bridges as a part of the major renovation and replacement task of bridge-structures in the Netherlands. For assessments it appears that calculations show that an increasing number of existing bridges no longer comply with current assessment standards or are becoming restricted in their functionality. Complete renovation is costly, results in disruption of traffic, and is not sustainable. The Eurocode permits to demonstrate sufficient safety using a nonlinear finite element analysis (NLFEA). NLFEA offers a possibility to demonstrate additional structural safety of the existing bridge-structures. The challenge is to gain confidence that the approach gives reliable results for the structural safety of the considered bridge. Moreover, experience learns that NLFEA demands many choices to be made by Rijkswaterstaat as a client and will not always lead to unambiguous results. These choices concern modelling aspects, applied safety format, load positions, and the required sensitivity analyses. Another question is what conclusions, based on the obtained results of this analysis, can be drawn for similar structures. This paper shows how Rijkswaterstaat has dealt with these challenges with case 'Peddemors' and what lessons are learned, all from the viewpoint of a client.@en

Diagonal tension cracking is the governing failure mode for bridge girders with a thin web that are highly prestressed and contain little shear reinforcement. When assessing existing bridge girders using the Eurocode 2 [1], it often turns out that it is not possible to demonstrate sufficient resistance to diagonal tension cracking. This paper evaluates the method to determine the maximum principal tensile stresses as used in the Eurocode 2 [1] and investigates how flexural cracks affect the principle tensile stresses in the regions without flexural cracks. This paper also investigates how the tensile strength of the web is affected by the presence of compressive stresses and by the size of the area subjected to high tensile stresses. Based on the results of these investigations, an improved model is proposed to determine the resistance to diagonal tension cracking.

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In the design process of prestressed bridges and viaducts, the required amount of shear reinforcement is determined with a model that assumes the presence of flexural cracks. In order to keep the design process simple, this model is also prescribed to determine the amount of shear reinforcement for the regions of the structure in which, at the ultimate load, no flexural cracks are present. This is a conservative approach, as the conditions for shear transfer are more favourable in the regions without flexural cracks. From structural assessments of existing prestressed bridges and viaducts, it is found that the amount of shear reinforcement is frequently too low in the regions that remain free of flexural cracks. Accordingly, these structures are considered as unqualified, although the actual shear resistance could possibly be sufficient. This is the prime motivation for this research, in which the shear behaviour of prestressed girders in regions without flexural cracks is investigated.Two models are proposed in this dissertation for the determination of the shear resistance in the regions without flexural cracks: –a model for diagonal tension cracking and –a model that considers the contributions of stirrups, aggregate interlock and uncracked flanges after diagonal tension cracking. Depending on the amount of shear reinforcement and the level of prestressing, the governing resistance will be present in either one of these stages. With the proposed models it has become possible to determine the shear that can be resisted in regions without flexural cracks more accurately. The use of the proposed models will therefore prevent that numerous bridges and viaducts are strengthened or replaced while the actual shear resistance is sufficient. @en

In the Netherlands, existing bridges are being assessed to investigate whether they are still capable to resist current and future traffic loads. Bridges that are compiled of single span prestressed girders, appear to have insufficient resistance to diagonal tension cracking. This concerns bridges that do not contain sufficient stirrups. Consequently, diagonal tension cracking could result in an abrupt brittle failure. However, the assessments are performed using the Eurocode model and there is doubt about its accuracy. In this research the accuracy of the Eurocode model is determined by comparing predicted resistances with experimentally found resistances. Moreover the stress distribution according to the Eurocode model is compared with the stress distribution of a linear elastic finite element analysis. Based on the comparison, an alternative model is suggested, that predicts the resistance to diagonal tension cracking more accurately.@en

In the Netherlands, existing bridges are being assessed to investigate whether they are still capable to resist current and future traffic loads. A part of these bridges consists of prestressed I-and T-shaped girders with a low shear reinforcement ratio. This ratio is low because the principle stress criterion was used to verify sufficient shear resistance at the time of engineering. These bridges are now assessed with the present Eurocode. It appears that it is difficult to demonstrate sufficient shear tension resistance. In this paper it is investigated whether existing models can accurately predict shear tension resistance for girders with a low shear reinforcement ratio. The model used in the CSA was found to predict this resistance conservatively and consistent. However, for single span girders with low shear reinforcement ratios, it was also found that it is difficult to demonstrate additional capacity compared to the resistance to diagonal tension cracking.@en

For existing structures, it is of interest to know if codes are conservative. If this is the case, it can be useful to examine if more accurate assessment methods are feasible. This paper addresses this topic for shear tension code requirements. Shear tension failure is of importance for prestressed structures with thin webs such as I- T- and Box girder structures. The studied codes are the fib Model Code (2010) (MC2010), the ACI building codes (ACI) and Eurocode 2 (EC2). These code requirements are based on the concept that the principle tensile stresses are limited to the concrete tensile strength. For that reason the resistance to web shear cracking is studied in this paper. To examine the suitability of the code requirements, 51 single span specimens are gathered. In the associate literature, shear cracks were reported, originating from the web. The experimental found shear capacity is compared with the predicted mean resistance to web shear cracking based on the code requirements. For the specimens uncracked in bending the predictions appear to be accurate and the level of approximation approach suitable. For the specimens cracked in bending, on the other hand, the predictions appear to be conservative. This is caused by the conditions within which the formulas for shear tension are applicable. Not the shear tension formulas but the formulas for flexural shear are applicable for a considerable part of the specimens. This is the case despite the observation that shear cracks in the specimens originated from the web instead of from the flexural cracks in the flange. The application conditions within which the shear tension formulas are applicable appear to be the most relevant topic for future research and offers the best possibility to improve the accuracy of shear tension code requirements.@en