| For the past two decades, the use of unbonded tendons in prestressed beams has not been limited to bridges and industrial structures but has also been included in commercial and residential buildings and has been gaining ground for the strengthening and rehabilitation of existing concrete structures. With the emergence of higher concrete strengths, as well as the development of new technologies, the prestressing process can be easily performed at the construction site, thus allowing the utilization of more efficient beam sections and longer spans. This growing use of unbonded tendons for the repair and strengthening of prestressed beams, as well as the emerging combination of bonded and unbonded tendons, has resulted in a need to increase the current knowledge of the behavior of HSC beams prestressed with unbonded tendons.; In comparison to beams with bonded tendons, where the change in strain in a tendon at any section is equal to the change in strain in the adjacent concrete section, there is no compatibility of strains due to the lack of bond at the prestressing steel level. The stress increase in a tendon beyond the effective prestress depends on the deformation of the whole member and the interaction between the concrete beam and the prestressing tendon, which is decoupled over the entire length of the beam. This behavior presents a challenge in developing an analytical model which is based on the equilibrium and mechanics of the beam-tendon system and which can also be implemented at various load levels and limit states. Several equations have been provided from various design codes and many researchers have attempted to provide prediction equations to predict the stress in the tendon at ultimate.; This investigation presents a general approach for the analysis of concrete beams prestressed with unbonded tendons. The proposed methodology considers the beam and tendon as a "trussed--beam" system allowing for the rational use of equilibrium and compatibility equations, as well as law of conservation of energy to predict deflection, load, and stress in the unbonded tendon at various load levels. The methodology is validated using results from tests performed on a total of 13 High Strength Concrete (HSC) beam specimens as well as those from test data available in the literature. The study emphasizes the ultimate stress of the unbonded tendon ( fps) for the purpose of computing the ultimate moment resistance. Two analysis approaches are considered: (1) analysis based on equilibrium, compatibility of deflection, and energy equation and (2) nonlinear finite element analysis (FEA). Various parameters, such as area of reinforcing steel, concrete strength, area of prestressing steel, effective prestress, and span-to-depth ratio, are considered. Results from the experimental study include number of cracks, deflection, and strain in prestressing strand, reinforcing steel, and concrete. Based on the analytical study, a simplified equation for predicting the stress at ultimate is developed. Both the generalized analysis model and the simplified equation predict the behavior of concrete beams with unbonded tendons accurately using rational approximations. |
