Reliability analysis of concrete beams reinforced with carbon fiber-reinforced polymer bars

Abstract

Reinforced concrete structures may have their service life considerably reduced due to steel corrosion. As an alternative to provide durability at low maintenance costs, carbon fiberreinforced polymer (CFRP) bars are used instead of steel. The purpose of this paper is to calculate the CFRP reinforcement of nine residential building beams according to the provisions of ACI 440 1R-06 and subsequently, to perform a reliability analysis with reference to the ultimate and service limit states. The same elements are also designed considering steel reinforcement in order to compare the results for both types of materials. Once designed to fail due to concrete crushing, the reliability analysis of all beams is performed utilizing the program Strand© Structural Risk and Analysis, which, through the First Order Reliability Model (FORM) and Monte Carlo Simulation, computes the reliability indexes, probabilities of failure and sensitivity factors. The material properties, applied loads and dimensions are treated as random variables with different statistical distributions provided by the literature, while the fracture modes are described by two limit state equations, accounting for bending and shear. Similarly, the noncompliance of serviceability requirements is modeled considering the direct method to compute deflections, the Frosch Equation for cracking, as well as the maximum crack width and deflections allowed by the ACI 440 1R-06 guideline. The results showed that the probabilities of failure due to bending and shear are on average higher for the CFRP reinforced beams. They are more likely to exhibit excessive deflections; however, crack widths hardly exceed the permissible limit of 0.7 mm. In general, the variables that most contributed to failure were the concrete compressive strength, CFRP Young Modulus, position of reinforcement and model uncertainty for cracking.