Shear Reliability of Reinforced Concrete Beams: A Form-Monte Carlo Framework

Abstract

Shear failure in reinforced concrete (RC) beams is a brittle and often sudden event that poses serious risks to structural safety. While ACI 318-19 and Eurocode 2 provide deterministic shear design provisions, their embedded partial safety factors do not explicitly propagate the statistical variability of resistance and demand variables, resulting in a design space where reliability levels vary substantially from one beam configuration to another. This study develops a fully integrated probabilistic framework that combines the First-Order Reliability Method (FORM) with large-scale Monte Carlo Simulation (MCS, N = 100,000) to quantify shear failure reliability across a parametric space spanning concrete compressive strengths of 20 MPa to 60 MPa, stirrup reinforcement ratios of 0 to 0.004, and shear span-to-depth ratios of 1.5 to 5.0. All basic variables, covering material, geometric, load, and model uncertainty were assigned probability distributions calibrated from experimental databases and the JCSS Probabilistic Model Code. Additionally, Model uncertainty was characterised from 47 beam tests selected from the ACI-DAfStb database. The results show that, for the Compression Chord Capacity Model (CCCM), the calibrated parameters are bias = 1.01 and COV = 0.13. Similarly, the ACI 318-19 model, which is used as the primary design basis in this study, the validation yields bias = 1.28 and COV = 0.29, reflecting its highest scatter. However, the main results used CCCM-calibrated model uncertainty as the more accurate bound. It was observed that the computed reliability indices ranged from 2.04 to 5.12, with beams lacking transverse reinforcement falling below the code target of 3.5 at all shear span-to-depth ratios. In addition, Live load variability was the dominant uncertainty source (32 to 35% of total variance), followed by concrete strength variability (21 to 24%) and model uncertainty (15 to 16%) respectively. A sensitivity analysis confirmed that the results are robust to plausible distribution alternatives, while an elevated concrete coefficient of variation of 0.20, a representative of Nigerian construction site conditions, reduced the reliability index by approximately 0.30 units. Therefore, a reliability-consistent shear partial safety factor of approximately 1.58 is recommended, compared to the ACI equivalent of 1.33. Interestingly, it is clear that the study showed direct implications for code calibration under Nigerian Standards (NIS 369), and the open-source simulation framework is available to support national code revision efforts.