Creep and shrinkage of concrete and relaxation of prestressing steel cause gradual reduction of compression in concrete and tension in prestressing steel. Inaccurate estimates of long-term prestress losses an cause serviceability problems, including concrete cracking and excessive deflection or camber. In this paper, the authors present an analytical method to predict the long-term prestress losses in precast, pretensioned or post-tensioned concrete members. Design aids are presented for cast-in-place, post-tensioned concrete bridges. The proposed method is based on equilibrium and compatibility principles of solid mechanics and can be used for multistage loading and prestressing. In deriving some of the equations, however, it is assumed that prestressing and dead loads are applied simultaneously and that the long-term effects of concrete creep and shrinkage and relaxation of prestressing steel occur gradually thereafter. Empirical equations in current bridge codes either underestimate or overestimate long-term prestress losses in concrete members, depending on the concrete creep and shrinkage properties and on the non-prestressed steel ratios. Examples show that the presence of non-prestressed steel has significant effects on the long-term deformation and the compressive stress remaining in the concrete after prestress losses.
