Relaxation of Prestressing Steel at Varying Strain and Temperature: Viscoplastic Constitutive Relation

Recent studiesof excessivemultidecade deflectionsof prestressed segmentally erectedboxgirders revealedthatmore accurate pre- dictionsoftheprestresslossduetosteelrelaxationareneededforthedesignoflarge-spancreep-sensitivestructures.Inparticular,thelossneeds 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 timestep.TheexistingempiricalformulasusedintheEuropeanModelCodeandAmericanpractice,whicharevalidonlyforconstantstrainand 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 theviscoplasticstrainrateofsteelasafunctionofthecurrentstress,strain,andtemperature.Close fitsofallthemaintestdatafromtheliterature, including the available data on the effects of strain and temperature changes, are achieved. The effect of temperature is found to be quite im- portant 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. DOI: 10.1061/(ASCE)EM.1943-7889.0000533. © 2013 American Society of Civil Engineers. CE Database subject headings: Prestressing; Relaxation (mechanical); Viscoplasticity; Steel; Temperature effects. Author keywords: Prestress loss; Relaxation; Viscoplasticity.

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