Stresses in External and Internal Unbonded Tendons: Unified Methodology and Design Equations

A unified methodology is proposed to compute the tendon stresses in externally prestressed beams in elastic and ultimate states, and practical design equations are developed to predict the ultimate tendon stresses. Previous test results have shown that there is an almost linear relationship between the tendon stress increment and the beam midspan deflection in both elastic and inelastic ranges. The key point is to seek this relationship and then the prediction of the tendon stress increment is transferred to the problem of calculating the beam midspan deflection. The second-order effect of external tendons is included in this deformation compatibility based analysis. Moreover, reasonable simplifications are made to establish practical design equations for the prediction of the ultimate tendon stress. The proposed equations are shown to be able to account for most of the important variables and result in good agreement with test data. It is shown that the ultimate stress increment is mainly dependent on the tendon eccentricity and the neutral axis depth, and the second-order effect can be reasonably taken into account using the stress and depth reduction factors.