An Improved Methodology for the Prediction of the Stress at Ultimate in Unbonded Internal and External Steel Tendons

Abstract

This study involves the analysis of the stress increase beyond effective prestress in beams prestressed with unbonded internal or external tendons at their ultimate limit state, Δfps, and is divided into two distinct parts. In the first part, twenty-five equations published between 1962 and 2019 to predict Δfps in unbonded tendons and proposed by various researchers and Codes of Practice are presented. Predicted versus experimental results for Δfps are compared about the 45° perfect correlation line using an updated database comprising 227 laboratory-tested beams obtained from past studies. An extensive statistical analysis is carried out for each equation using the sum of Least Square Deviation Error and Coefficient of Correlation. The percentage of data points representing conservative predictions is also numerically calculated. Statistical analysis confirmed superior performance of the mechanically derived equation developed in the past research (Naaman in ACI Struct J 88:683–692, 1991b, ACI Struct J 99:518–529, 2002; AASHTO in AASHTO LRFD bridge design specifications, AASHTO, Washington, 1994). That equation was rationally derived from a sectional strain compatibility analysis augmented to a member deflection compatibility through the use of a strain reduction coefficient, Ωu. In the second part of the study, and using the updated experimental database, the authors derive a new and improved expression for the strain reduction coefficient, Ωu, that led to the lowest Least Square Deviation Error and highest Coefficient of Correlation. The newly proposed expression for Ωu offers two alternatives, one for precise prediction and the other for code implementation. Based on their findings, the authors strongly recommend the equation of fps (Naaman in ACI Struct J 88:683–692, 1991b, ACI Struct J 99:518–529, 2002; AASHTO in AASHTO LRFD bridge design specifications, AASHTO, Washington, 1994) and the new expression for Ωu for code implementation.