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...

This thesis addresses the topic of ongoing (excessive) deformations observed in balanced cantilever prestressed concrete bridges all over the world. Many authors attribute this behavior to the time-dependent phenomena of creep and shrinkage. Balanced cantilever bridges are classified as creep-sensitive structures, and for that reason, a detailed analysis of the long-term structural behavior, such as deformations and prestress losses, is recommended. However, during the design of these bridges, commonly used code-based models generally tend to underestimate the long-term creep and shrinkage effects. Additionally, various (simplifying) assumptions are made when modeling these bridges, making their actual creep and shrinkage behavior unclear. This work aims to investigate whether the long-term effects of creep and shrinkage are indeed a plausible explanation for the excessive and ongoing deflections detected in a specific balanced cantilever bridge in the Netherlands: the Rooyensteinse Brug. This bridge, inaugurated in 1977 in Zoelen, currently exhibits a deflection at midspan of 0.43 m, more than two times what was anticipated in bridge design. To investigate this behavior, a detailed two-and-a-half-dimensional finite element model was developed, incorporating a time-dependent phased analysis accounting for the construction phases. Creep and shrinkage effects were incorporated into the concrete material model through creep compliance and shrinkage strain curves. A sensitivity study is conducted to analyze the impact of: (i) different code-based models for creep and shrinkage, (ii) accounting for the large creep and shrinkage model uncertainties, (iii) different maturities on the creep compliance curve, and (iv) considering cross-sectional variability in the drying characteristics. The main findings showed that commonly used code-based models, including the current standard Eurocode 2, significantly underestimate the long-term (multi-decade) deflections observed in the Rooyensteinse Brug by 30%. Notably, only the RILEM B4 model (B4), considered the most theoretically grounded creep and shrinkage model, was able to capture the long-term deflection trend reasonably well. Further, acknowledging the inherent uncertainties in B4 significantly widened the range of potential deflections and prestress losses. Using the bounds of the 90% credible interval, the midspan deflections after 60 years range between 0.514 m and 2.91 m, compared to a mean of 0.895 m. The prestress losses range between 18% and 30% in the shear-critical zone, against a mean of 23%. Additionally, accounting for the cross-sectional variability in drying characteristics led to an improvement in both the short-term (first 10 years of service life) and long-term (multi-decade) deflection prediction when comparing the results to in-situ measurements, with differences of 14% and 6.1%, respectively. Based on these predictions, it is expected that the current deflection trend of the Rooyensteinse Brug will continue to decrease linearly (log-scale) for the next two decades. This study demonstrates that a detailed finite element model incorporating time-dependent phased analysis, in combination with the RILEM B4 model and accounting for cross-sectional variability, can explain the observed behavior in the Rooyensteinse Brug. The results support the hypothesis that the long-term effects of creep and shrinkage are the cause of the ongoing trend of excessive deformations in this balanced cantilever prestressed concrete bridge.