Analytical and Numerical Analysis of the Shear Tension Critical Prestressed Beams

Numerous structures constructed in 60’s and 70’s are now reaching their design service life and require reassessment to assure safety of users, reliability and economical exploitation. As a consequence, an adequate structural assessment of existing bridges has recently become a major subject of scientiﬁc work commissioned by the authorities in charge. The bridges designed according to then biding codes are often deemed to be structurally deﬁcient when re-evaluated with more restricting current design provisions. At the same time, it is often in conﬂict with the reality as many of the structures still continue in operation displaying no perceptible deterioration of state nor fatigue. The challenge therefore is to develop more reﬁned models to evaluate the structural behaviour and possible reserves of capacity accounting for the actual condition of the bridge under investigation. One of the potential deﬁciencies is related to the shear tension failure in thin-webbed post- tensioned T-girders which is the item of the this dissertation. The study comprises of two major parts. In the ﬁrst part, the thesis investigates an ability of the shear provisions for reinforced concrete structures as given in the following codes: Canadian Standard Association (CSA), the ﬁb Model Concrete 2010 (MC2010), the Eurocode 2 (EC2) and the RBK 1.1 (Richtlijnen Beoordeling Kunstwerken) to adequately address shear tension critical members. The predictions from codes are calculated for the three selected benchmark continuous I- beams tested in destructive laboratory tests as a part of the research on the inﬂuence of axial load and prestress on the shear strength of web-shear critical reinforced concrete elements at the University of Toronto. Out of three selected beams of interest subjected to approximately the same prestressing force, two contained a varying amount of reinforcement equal to twice and four times the minimum amount shear reinforcement as speciﬁed by the CSA code and one containing no stirrups in the test region. From the comparison of codes it was concluded that shear previsions relating shear resistance to the strain state of the considered section (CSA and MC2010) provide good predictions for members furnished with stirrups but inaccurately evaluate shear resistance for members without shear reinforcement being overly conservative. For this case, the empirical formulation according to the EC2 with mean characteristics applied resulted in the best estimate. In the second part of the study, an attempt to reproduce the tests of the benchmark beams numerically was undertaken. The simulation according to the highest level of approximation as classiﬁed in the MC2010 was performed through a series of nonlinear ﬁnite element analyses. Sensitivity analyses with the diverse variables such as: crack models, shear retention functions, iterative methods and convergence norms were studied to determine their inﬂuence on the ultimate shear strength and competence to recreate the observed in tests performance; i.e. the failure mechanism and crack pattern. From the conducted analyses, it was concluded that satisfactory crack pattern as well as magnitudes of shear resistance can be obtained for all treated specimens. The thesis was completed with considerations regarding the most appropriately performing constitutive model to simulate shear tension failure mechanism for the cases of benchmark tests. For the considered cases of shear tension critical beams, models with the rotating crack, energy convergence norm in combination with force or displacement convergence norm and the modiﬁed Newton-Raphson iterative method are recommended.

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