Análise de vigas com protensão não-aderente submetidas a cargas de curta e longa duração via Método dos Elementos Finitos

Abstract

The unbonded prestressed system is an excelent strutural alternative. Its applications are diverse, from beams, slabs, silos and, more recently, composite beams. Prestressed members are able to be designed as slender elements, capable of overcoming large spans while keeping small displacements. In the post-tensioning system, the unbonded tendons are tensioned after the concrete is cast and the stress is transferred to the concrete element at the anchorage points. Therefore, it is necessaryto develop computer models able to simulate those structures considering the particularities of the prestressing system with unbonded tendons. Also, those models must be able to simulate not only the behavior of the structure at the ultimate conditions but also at service situation. In this work, a simple but robust Finite Element based model is proposed for the short-term analysis of unbonded prestressed concrete beams with internal and external tendons. The reinforced concrete beam is discretized using frame elements and the unbonded tendon is considered as a single element with a variable number of straight segments. Material and geometrical nonlinearities are considered where both elements are formulated using the Total Lagrangian approach. The geometrically linear form of both elements is presented to evaluate the effects of the geometric nonlinearity. The structural analysis is performed in two steps. The first step consists of the prestressing force application using Newton-Raphson iterations. The second step consists of the external loading application where the nonlinear equilibrium equations are solved using the Displacement Control Method. Excellent results were obtained for simply supported and continuous beams with different tendon profiles. Also, the effect of nonlinear strain-displacements terms and the use of different models to simulate the concrete behavior are assessed. Additionally, a Finite Element based model for the consideration of long-term loading is presented. This procedure considers that the materials are in a linear range and geometrical nonlinear terms are neglected. Shrinkage and creep of concrete are considered using the Age-Adjusted Effective Modulus and the tendon relaxation is considered using the model avaliable in literature. Very good results were obtained against available data for simply supported and continuous beams under sustained loads.