Direct Analysis of Prestressed Concrete Members

Expressions for the direct computation of time‐dependent stress and strain in a fully prestressed concrete section with or without nonprestressed reinforcement are given. Linearization of the exponential expression of the relaxation loss reduction factor and the simultaneous use of equilibrium and compatibility equations leads to a compact $2\times 2$ matrix, the solution of which directly gives the time‐dependent stress and strain distribution across the cross section. To directly account for the elastic shortening effect in the posttensioned member, half the transformed area of the prestressing steel is considered while the full transformed area is considered in the case of pretensioned members. The suggested procedure requires neither the prior estimation of loss of prestress due to elastic shortening, concrete creep and shrinkage, and steel relaxation, nor the time‐consuming iterative approach to account for the effect of creep and shrinkage of concrete on steel relaxation. A numerical example of a posttensioned beam is given to demonstrate the method. The method is applicable to pretensioned beams as well.