Predictive model for stress at ultimate in internally unbonded steel tendons based on genetic expression programming

Abstract

Predicting the stress increment (Δfps) and in turn, the total stress (fps) in internally unbonded steel tendons at ultimate flexural strength of post-tensioned concrete members is one of the major challenges due to the lack of bond between the steel tendon and surrounding concrete. This article presents the development of a new predictive model to evaluate the stress increment (Δfps) and in turn, the total stress (fps) based on a genetic expression programming (GEP). GEP has the ability to collect all the influential parameters, among all the cross-sectional and the member's geometrical properties, the mechanical properties of materials, and the applied load, in one single closed-form expression for predicting (Δfps). The proposed model was developed based on a comprehensive experimental database of 196 concrete specimens that were collected from literature and the experimental outcomes of 22 beams and one-way post-tensioned concrete slabs which were previously prepared, fabricated, and tested by authors of the present study. A parametric study was conducted to obtain an idea of the relationship between the independent variables and their effect on the stress increment in unbonded tendons at ultimate (i.e., the target parameter (Δfps)). To inspect the potentiality of the proposed (GEP) model against 22 analytical models available in the literature, an extensive comparative study was carried out. The performance of the proposed model was checked according to the values of the coefficient of determination (R2) and different achieved statistical errors. In comparison to the experimental values of (Δfps) and (fps), the proposed model showed the highest coefficient of determination (R2) of 0.78 and 0.93, respectively, compared to the other 22 analytical models. While the values of mean absolute error, relative absolute error, root mean square error, and root-relative square error to determine (Δfps) and (fps) were found to be (60.98, 76.96, 0.45, and 0.47) and (60.98, 76.96, 0.25, and 0.26), respectively.