Analytical Models Of Beams Prestressed With External Tendons

External prestressed tendon has been applied widely in repairing or retrofitting aged structures and new composite steel-concrete structures. The analysis methods, however, for such structures were not yet developed enough due to the relative slip between the tendons with the deviators. Namely, the strain compatibility condition of the tendons and host structure, which is the fundamental hypothesis in the conventional analysis method, is no more applicable. Therefore, this work takes into account the slip between the tendons and the deviators as well as the deformation characteristics of the externally prestressed beams and develops some new analytical models for such structures based on Euler-Bernoulli beam theory.Tensioning is one of the most important process as in the constructions of prestressed beams, because the initial tension forces not only determine the stress state of the beams, but also directly affect their performances during service period. This paper thus analyzes the beams prestressed with external tendons in the tensioning stage based on the proposed analytical models. For this purpose, the governing differential equations and corresponding boundary conditions for the tensioning stage are deduced through the vibrational methods, the approximate solutions for the deflection of simply supported beams are then given by the Ritz method.The incremental stress due to the structure deformation is also of great importance in the analysis of external tendons. The most available methods in the literature are only suitable for certain structures with specific types or neglecting the relative slip between the tendons with deviators. This work investigates the kinematical relationship of the elongation of the external tendons and the deformation of the host structures with the slip between the tendons and the deviators. Linearizing the kinematical relationship yields a general formula for the incremental stress of the external tendon due to the deformation of the host structures. Meanwhile, a finite element is developed for the external tendons with the influence of the relative slip, whose stiffness matrix is obtained explicitly. A simplified method to evaluate the incremental stress of the external tendons is also proposed.In order to verify the present models and methods, the analytical deflections of the beams under the test loads which are also studied experimentally in the literature, are deduced with Ritz method. The relationships of load versus displacement and load versus incremental stress increment are also illustrated as well as the effects of the prestressed tendons on the deflection and stress increment.The comparison between the results of the present method with those of the experiments in the literature verifies the feasibility and accuracy of the present models.