Parabolic tendons in prestressed concrete - how accurate are equivalent loads?

The mechanical effects of a parabolic tendon can be modeled replacing the tendon by external loads applied to the concrete. The intensity of these loads depends on the prestressing force P and curvature of the tendons. These two factors are also interrelated because the losses of prestress vary with the curvature. The structural analysis can be simplified by approximating that the line load against the tendon, able to maintain the initial parabolic form of the tendon and called equivalent load, is constant, perpendicular to the centroidal axis of the beam and equal to P/R where R is the radius of curvature of the parabola at its vertex. This approximation is one of the key issues in the textbooks but normally not properly justified. In this paper, the mathematical background for the approximation is formulated. Some typical tendon layouts are analyzed to evaluate the approximation error. The error proved to be insignificant for simple beams. For cantilever and continuous beams more accurate methods in the final design are recommended.