Análise numérica de vigas de concreto protendido com cabos internos não-aderentes para cargas de curta e longa duração

Abstract

The prestressed concrete structures with internal unbonded tendons, especially beams and slabs, have been widely disseminated and used in construction around the world. The numerical solution of these structures by the finite element method establishes some challenging problems due to the lack of strain compatibility between unbonded tendons and the surrounding concrete and also by the few studies focused on predicting the behavior of flexural structures under long- term service loads. This work presents the application of a finite element formulation for a non- linear numerical analysis for short and long-term loads of unbonded prestressed concrete beams. The finite element formulation consists of unidimensional elements of plane frames with models of 6 and 7 degrees of freedom per element, based on the Euller-Bernoulli beam theory for the reinforced concrete section and a truss element for the simulation of the unbonded tendons. The analysis of short-term loads is carried out in two steps: application of prestressing force and application of external loading. In the prestressing step, the simulation of the immediate losses of elastic shortening of the concrete is carried out by the sequential stretching of multiple prestressing tendons, considering the load control method for the convergence of the non-linear system. For the external loading step, load-displacement curves, load-stress increases, curvatures and deformations along the beam are evaluated, taking into account the displacement control method for iterative solutions. The responses obtained by the implementation of the model were validated for examples availables in the literature of simply supported beams with polygonal tendons, continuous beams with curved tendons and simply supported beams with straight tendons made of Carbon-Fiber-Reinforced Polymer with excellent results for each example. A finite element formulation was developed for the examples of beams under long-term loads with the purpose of evaluating losses due to creep, shrinkage and relaxation of the prestressing steel. The analysis used the Age-Adjusted Effective Modulus Method and normative relationships to obtain long-term effects. The results obtained were excellent compared to the solutions in the literature.