3D finite element analysis of anchorage zones in post-tensioned concrete girder

The anchorage zone of post-tensioned concrete structures is a discontinuity region, where a redistribution of stress occurs behind the anchor device, as the concentrated prestressing force spreads out over the full concrete section. This disturbed zone is subjected to a very complex three-dimensional state of stress, with transverse tensile forces that cause longitudinal cracks which can extend throughout the beam span, thus causing failure. To prevent excessive cracking, therefore, concrete must be adequately reinforced with supplementary or ‘’bursting'' reinforcement. The problem of the stress distribution in the anchorage zone has been well studied in the past decades using various methods such as linear elastic theory [1-5], experimental investigations [6-7], strut and tie models [7] and finite element analyses [8-10]. Most efforts in the previous analyses have focused on evaluating the ultimate strength of post-tensioned beams tested to anchorage failure and only few works have considered the effects of support reaction. Although ultimate limite states are the most important considerations in the design of prestressed structures, more in depth study is required at serviceability limit states in order to evaluate the effectiveness of bursting reinforcement to control maximum crack width. Prediction of this behavior requires advanced analytical techniques with the ability to simulate the highly nonlinear behaviour of the concrete. To date, most of the nonlinear finite element analyses have consisted of two-dimensional models of the anchorage zones, although it is a three-dimensional one even in a rectangular beam. The main reason for this choice is generally attributed to a lack of a proper description of material properties of concrete. In this study, three-dimensional non-linear finite element analyses have been carried out using the program Atena to simulate the behaviour of end zones of rectangular section post-tensioned girders, with the presence of the support reaction. This program includes an advanced three-dimensional material model which allows employing it as an effective tool for the investigation of reinforced and prestressed concrete elements. The validity of the finite element model has been verified through comparisons with tests reported in literature and it was found good agreement between the experimental and numerical results. The validated model has been used to investigate the influence of the arrangement of bursting reinforcement on stirrups strains and crack development at serviceability and ultimate limit state.