Reliability based design model for RC beams shear strengthened with NSM FRP

Abstract

This paper presents a reliability-based design (RA-based) approach for the shear resistance of reinforced concrete (RC) beams strengthened with near-surface mounted (NSM) carbon fibre–reinforced polymer (CFRP) reinforcement. This approach integrates a semi-empirical model recently developed that couples the truss analogy and the simplified modified com pression field theory within a double-loop iteration scheme. Despite the higher predictive performance of this model over the existing ones, it does not include a reliability framework to allow its use in direct design practice. Therefore, in the present work, this model is adapted to a design-oriented format by introducing characteristic material properties and partial factors in line with Eurocode philosophy and fib recommendations. The statistical variability of material, geometric, and loading parameters is characterised using established probabilistic models, while uncertainties in predicting the effective CFRP strain and the overall shear resistance are quantified through goodness-of-fit testing. Design Assisted by Testing (DAT) is employed to derive characteristic and design values of the effective CFRP strain, leading to a bond-related partial factor γfb for both NSM bars and laminates. The resistance partial factor γR is then calibrated for different target reliability indices using a comprehensive reliability analysis framework employing the First-Order Reliability Method (FORM) with Importance Sampling over an extensively sampled design space and multiple load ratios, enabling assessment across various reliability levels. Both constant and variable forms of γR are derived. The latter is expressed as a function of a combined transverse reinforcement parameter and shown to improve the uniformity of reliability levels across the design domain. The proposed RA-based design model is validated against an experimental database of 114 NSM-CFRP-strengthened beams and illustrated through a detailed design example. A freely available web-based design tool is also provided to facilitate practical application of the model.