Increase of stress in unbonded tendons in prestressed concrete beams and slabs

Abstract

In the case of prestressed concrete beams with unbonded tendons, in order to design for strength and serviceability, one has to evaluate the effective prestressing force in the tendon, which is beam dependent rather than section dependent, both at ultimate and working loads. The formulae available in the published literature deal only with ultimate load conditions. A simple equation to predict the tendon stress changes for the complete loading range is presented in this paper. The formula was developed using the basic theory of flexure to obtain the equation for the elastic curve, and numerical integration to obtain the curve lengths. Using the computer generated results of the increase in tendon strain for various span lengths, eccentricities, and maximum deflections, a regression equation was developed. This regression equation predicts the increase in tendon strains as a function of the span–eccentricity and eccentricity – maximum deflection ratios. The recently published stress–strain relation which seems to be very accurate is then used to predict the tendon stress. The results are compared with a set of experimental results. The suggested formula is also consistent with some of the available equations for the prediction of the tendon stress at ultimate load.