Simplified method for failure analysis of concrete beams prestressed with external tendons

The flexural strength of externally prestressed beams depends on the tendon stress at failure. If the tendon is free to slip at the deviators its stress will depend on the global deformation of the whole structure. Thus the tendon stress at failure, and consequently, the flexural strength cannot be evaluated by a local analysis of the critical sections, but a nonlinear analysis of the whole beam-tendon structural system is required. In the past, simplified formulas were proposed to calculate the tendon stress increment at failure avoiding the need for a nonlinear analysis of the entire structure. Some of these formulas have been adopted as code recommendations. Some approaches however do not seem to be consistent with the actual behavior of externally prestressed beams and in some cases excessively high increments of stress are recommended. On the other hand, other approaches appear to be too conservative. In this work a new simplified and rational method of analysis based on shape functions approximating deformations is proposed to study the tendon stress increment and consequently the flexural strength of externally prestressed concrete beams. The proposed simplified method reduces the analysis of externally prestressed structures from a global structure problem to an easier section problem.