Relaxation of prestressing steel at varying strain and temperature: Viscoplastic constitutive relation

Recent studies of excessive multidecade deflections of prestressed segmentally erected box girders revealed that more accurate predictions of the prestress loss due to steel relaxation are needed for the design of large-span creep-sensitive structures. In particular, the loss needs to be calculated as part of creep structural analysis, during which the strain of concrete to which the prestressing steel is bonded varies in each time step. The existing empirical formulas used in the European Model Code and American practice, which are valid only for constant strain and constant temperature, are here generalized to arbitrarily variable strain and temperature, heeding obvious asymptotic restrictions and the fact that steel is a viscoplastic material whose constitutive principles are well known. The resulting formula is a memoryless nonlinear equation for the viscoplastic strain rate of steel as a function of the current stress, strain, and temperature. Close fits of all the main test data from the literature, including the available data on the effects of strain and temperature changes, are achieved. The effect of temperature is found to be quite important and is formulated on the basis of the activation energy of viscoplastic flow of metals. Finally, the need for further tests at variable strain and variable temperature is emphasized.