Contents lists available at ScienceDirect Structures journal homepage: www.elsevier.com/locate/structures Development of applicable design models for concrete columns confined with aramid fiber reinforced polymer using Multi-Expression Programming Alireza Arabshahi a , Nima Gharaei-Moghaddam a , Mohammadreza Tavakkolizadeh b, ⁎ a Graduate Student, Civil Engineering Department, School of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran b Assistant Professor, Civil Engineering Department, School of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran ARTICLE INFO Keywords: Effective confinement threshold Unified Design-oriented model Multi-Expression Programming Stress-Strain curve Partial confinement AFRP ABSTRACT In this paper, a new series of applicable relations, including maximum confined stress and strain as well as the stress–strain relationship, for AFRP confined concrete are proposed based on the design-oriented approach. The main advantages of these new relations are their higher accuracy and unified nature for both circular and square cross sections as well as their ability to predict stress and strain of partially confined columns. For this purpose, a complete database of the available experimental results from the previous studies is collected. In order to achieve higher accuracy and reliability, only part of the collected experimental results that passes a series of deliberately considered criteria are used for derivation of the relations. In addition to the mentioned relations, a threshold for confinement pressure is defined which can be used as a beneficial tool by designers to specify sufficiency of their designed AFRP confinement. Furthermore, a simple relation to predict lateral hoop rupture strain of AFRP wraps is also provided. In order to make the suggested models utilizable for the cases that fibers are not placed per- pendicular to the column axis, simple modification factors are also derived. The proposed models are formulated using an evolutionary algorithm named Multi-Expression Programming (MEP), which is an approach for pre- dicting models in the cases of unknown mathematical structures. Accuracy of the proposed relations is compared with the other available models based on the collected experimental database. The obtained results showed that the suggested relations and especially the stress–strain model are capable to predict behavior of AFRP confined concretes with remarkable accuracy. 1. Introduction Since the introduction of FRP confinement as a method for retro- fitting and rehabilitation of existing and damaged reinforced concrete structures, many researchers and investigators performed extensive experimental and numerical studies on the characteristics of FRP con- finement and its performance [1–6]. Among these countless studies, many are focused on proposition of mathematical models to predict stress and strain of confined concrete columns. The early models were based on the relations developed for steel-confined concrete [7,8]. However, due to the linear stress–strain behavior of FRP and lack of the yield point, the passive pressure provided by FRP wraps differs from the steel pressure and in contrast with the steel confined concrete, there is no softening branch in the stress–strain curve of the FRP confined concrete, provided that full confinement is achieved. As mentioned previously, a large number of constitutive models are available for FRP confined concrete columns with different cross section geometry. These models can be classified in two general categories, namely Analysis- oriented and Design-oriented [9]. The first group is developed by per- forming incremental analysis in order to achieve stress–strain curve [10–12], while in the second category, the models are proposed by calibrating predefined mathematical forms based on numerical regres- sion using databases of existing experimental results [13–16]. Design- oriented models are preferred to the analytic-oriented ones due to their higher simplicity and ease of application, while they are not necessarily more accurate. On the other hand, the consistency of the analysis-or- iented models with mechanical behavior of confined concrete is an advantage. Despite availability of many stress and strain models for FRP con- fined concrete; there are still attempts to propose new more accurate and applicable relations. Moreover, various investigations are per- formed recently to improve the available models or to answer different questions about validity and applicability of the existing models. For instance, many of the available models for concrete confinement are developed based on non-standard cylindrical specimens. This fact rises to the question that does the size of the experimental specimens has any https://doi.org/10.1016/j.istruc.2019.09.019 Received 18 August 2019; Received in revised form 18 September 2019; Accepted 20 September 2019 ⁎ Corresponding author. E-mail addresses: alirezaarabshahi68@gmail.com (A. Arabshahi), Nima.Gharaei@gmail.com (N. Gharaei-Moghaddam), drt@um.ac.ir (M. Tavakkolizadeh). Structures 23 (2020) 225–244 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved. 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