Model for Analysis of Short Columns of Concrete Confined by Fiber-Reinforced Polymer Severino Pereira Cavalcanti Marques 1 ; Dilze Coda ´ dos Santos Cavalcanti Marques 2 ; Jefferson Lins da Silva 3 ; and Ma ´ rcio Andre ´ Arau ´ jo Cavalcante 4 Abstract: This paper presents a numerical model for evaluating the behavior of axially loaded rectangular and cylindrical short columns of concrete confined by fiber-reinforced polymer FRP composites. The proposed formulation considers, for unconfined and confined compressed concrete, a uniaxial constitutive relation that utilizes the area strain as a parameter of measure of the material secant axial stiffness. For unconfined concrete, the model adopts an explicit relationship between axial strain and lateral strain, while for confined concrete, an implicit relation is considered. For this last case, the model employs a simple iterative-incremental approach that describes the entire stress-strain response of the columns. The behavior of the FRP is considered linear elastic until the rupture. To validate the model, a number of columns were analyzed and the numerical results were compared with experimental values published by other authors. This comparison between experimental and numerical results indicates that the model provides satisfactory predictions of the stress-strain response of the columns. DOI: 10.1061/ASCE1090-026820048:4332 CE Database subject headings: Concrete columns; Fiber reinforced polymers; Composite materials; Axial loads; Confinement; Constitutive relations. Introduction The effects of confinement on the behavior of concrete have been studied for many years. Many studies have demonstrated that lat- eral confinement in columns increases the compressive strength, ductility, and energy absorption capacity of the concrete. For practical applications, the confinement has been introduced through conventional reinforcement of steel or by wrapping the concrete with steel jackets and FRP sheets or by filling fiber- reinforced polymer FRP tubes with concrete. The use of FRP as a material for confining columns seems very interesting due to FRP’s mechanical and chemical properties, easiness of applica- tion, and capacity of confinement. Due to renewed interest in the behavior of confined concrete, a number of theoretical and experimental works have been pub- lished in recent years, many of which are concerned with concrete confined by transverse reinforcement, such as in the case of con- ventional reinforced concrete columns. For these cases, several analytical models are available in the literature Mander et al. 1988; Cusson and Paultre 1995; Razvi and Saatcioglu 1999. Such models are frequently used to describe the behavior of con- crete confined by other devices, including steel jackets and fiber composites. However, previous studies have demonstrated that models developed for transverse reinforcement may not be con- servative for specimens confined by composite materials Mirmi- ran and Shahawy 1997. Recently, several models were proposed for describing the behavior of FRP-confined concrete. Most of these models are applicable to the cylindrical specimens Samaan et al. 1998; Saafi et al. 1999; Spoelstra and Monti 1999; Toutanji 1999; Fam and Rizkalla 2001. Few models were formulated for the case of specimens with rectangular cross sections Rochete and Labossie ` re 2000; Wang and Restrepo 2001, for which the confinement effects are smaller than for circular cross sections. This paper presents a numerical model for evaluating the be- havior of axially loaded rectangular and cylindrical short columns of concrete confined by FRP composites. The procedures con- sider, for both unconfined and confined compressed concrete, a uniaxial constitutive relation that utilizes the area strain as a pa- rameter of measure of the material secant axial stiffness. For un- confined concrete, the model adopts an explicit relationship be- tween axial strain and lateral strain, while for confined concrete, an implicit relation is considered. For the last case, the model employs a simple iterative-incremental approach that provides the entire stress-strain response of the columns. The behavior of the FRP is considered linear elastic until the rupture. To validate the model, a number of columns were analyzed and the numerical results were compared with experimental values published by other authors. This comparison between experimental and nu- merical results indicates that the model provides satisfactory pre- dictions of the stress-strain response of the columns. 1 Professor of Civil Engineering, Dept. de Engenharia Estrutural, Uni- versidade Federal de Alagoas, Rod. BR 104, 57072-970, Maceio ´-AL, Brasil. E-mail: smarques@ctec.ufal.br 2 Professor of Civil Engineering, Dept. de Engenharia Estrutural, Uni- versidade Federal de Alagoas, Rod. BR 104, 57072-970, Maceio ´-AL, Brasil. E-mail: dmarques@ctec.ufal.br 3 Student of Civil Engineering, Universidade Federal de Alagoas, Rod. BR 104, 57072-970, Maceio ´-AL, Brasil. E-mail: jeffeng@ctec.ufal.br 4 Student of Civil Engineering, Universidade Federal de Alagoas, Rod. BR 104, 57072-970, Maceio ´-AL, Brasil. E-mail: marciocivil@ ctec.ufal.br Note. Discussion open until January 1, 2005. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and pos- sible publication on September 4, 2002; approved on August 21, 2003. This paper is part of the Journal of Composites for Construction, Vol. 8, No. 4, August 1, 2004. ©ASCE, ISSN 1090-0268/2004/4- 332–340/$18.00. 332 / JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / JULY/AUGUST 2004