This paper presents the development of a resistance model for concrete columns reinforced with Fiber Reinforced Polymer (FRP) reinforcements. The resistance model is used to calculate the probability of failure and reliability index of concrete columns reinforced with FRP reinforcements. The strength limit state functions are developed for reinforced rectangular columns depending on the cross section size, reinforcement ratio, and load eccentricity. For a known eccentricity condition, solutions for the corresponding force-moment strength in the interaction diagram are developed. Sensitivity analysis is performed to determine the design variables that have the highest influence on the reliability index. The First Order Reliability Method (FORM) is employed to calibrate the resistance factor for a broad range of design variables. The study shows that the introduction of FRP reinforcements in place of conventional steel reinforcements improves reliability somewhat because the strength of FRP reinforcements has a lower coefficient of variation than steel or concrete. However, the brittle nature of FRP reinforcements necessitates a reliability index that is greater than that generally implied in flexural structural components. This leads to a resistance factor that is slightly lower than currently accepted for reinforced concrete sections in flexure.

The term `reliability' in structural parlance means the probability of the structure performing its intended function during its expected lifetime under the environmental conditions to which it is exposed. The probability of failure P_f provides an alternative and complementary measure of reliability. The actual capacity of a Reinforced Concrete (RC) structural component differs from the nominal capacity, which is basically the strength of constituent materials and the specified geometrical properties. The main variables in the design of RC columns that are subject to varying degrees of uncertainty and randomness are the loads and material properties. The fundamental case in structural reliability pertains to a component with a resistance R, subjected to some load effect S, which in general accounts for probable under strength and overloading of RC structural members. The variability in load effect S and ultimate strength R is evaluated to determine the probable appropriate resistance factor φ using the ultimate limit state design. In this study, for eccentrically loaded columns with cross-sections subjected to combined bending and thrust, the strength is determined by an interaction relationship between axialforce P and moment M, and thus allowed to iterative procedures typically used in the design practice. This paper presents the derivation of resistance factors for eccentrically loaded columns using reliability analysis. The full range of possible values of load eccentricity, from axial load to pure bending, was investigated in the study. A computer program was written to simulate for each considered design parameter. The reliability analysis was performed for short Glass Fiber Reinforced Polymer (GFRP) reinforced RC columns. The major resistance-related variables investigated in this study include concrete compressive strength of concrete f_c, GFRP reinforcement strength f_f, reinforcement ratio r, aspect ratio of the cross-section d/b, and load eccentricity e, and resistance modelling error c₁. The statistical parameters were based on actual test results. These parameters are used to assess statistically the strength of the eccentrically loaded GFRP reinforced concrete columns.

The availability of the new statistical data for compressive concrete strengths and the strength of GFRP reinforcements help to verify and update the resistance factors for eccentrically loaded concrete columns reinforced with GFRP reinforcements with respect to the existing Indian Standards (IS) for conventionally reinforced concrete columns. Results from the reliability analyses reported herein were employed in the calculation of the strength reduction factors f, covering the full range of possible values of load eccentricity from axial load to pure bending. Sensitivity analysis was performed to identify the most important parameters that influence the reliability of a column. This study provides a rational basis for the selection and recommendation of new resistance factors for RC columns reinforced with GFRP reinforcements and for updating the IS code design procedures.

Structural Engineering Journal, Reliability Analysis, Fiber Reinforced Polymer Reinforcements, Flexural Structural Components, Glass Fiber Reinforced Polymer, GFRP Rreinforcements, Uniaxial Eccentric Compression, Resistance Modelling Errors, Probability Density Functions, Reinforced Concrete Design, Conventional Steel Reinforcements.