Shear capacity model of RC beams based on MCMC approach and reliability analysis

The research question revolves around accurately predicting the shear capacity of RC beams and enhancing the reliability of such prediction models. This study aims to refine the accuracy of the RC beam shear capacity model. To augment the safety margin, the enhanced model underwent further calibration through a reliability analysis. The shear strength models, rooted in Bayesian theory’s Markov Chain Monte Carlo (MCMC) method and the Modified Compressive Field Theory (MCFT), were introduced. A research database was curated from test data of 782 RC beams sets under shear stress. From this database, six mechanism models were juxtaposed with the MCMC models for comparison. To meet the desired reliability indexes ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>β</mml:mi> <mml:mi mathvariant="normal">T</mml:mi> </mml:msub> </mml:mrow> </mml:math> = 3.2, 3.7, 4.0) in these models, resistance factors ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> </mml:math> ) were incorporated. Both the Monte Carlo and First Order Second Moment (FOSM) methods were employed for the reliability analysis, considering inherent model errors and the probability distribution of primary variables. The effect of different elements on the target reliability index was assessed using a tornado diagram. Findings showed that the refined shear model displayed minimal variance when benchmarked against models from existing literature and national codes, yielding a V test / V cal ratio close to 1.0. The shear components aligned with established mechanical mechanism. Depending on various operational conditions and load combinations, resistance factors fluctuated from 0.377 to 0.516 in the RC beams without stirrup, while resistance factors fluctuated from 0.479 to 0.621 in the RC beams with stirrup. Key determinants, such as the inherent uncertainty in computing model, the live loads, and the cylinder compression strength, significantly influenced the reliability index.