Statistical Analysis of Tubular R/C Sections

Abstract

A statistical analysis of the moment capacity of a tubular reinforced‐concrete (R/C) section is performed. The moment capacity of the cross section is estimated utilizing a second‐order stress‐strain relationship for concrete. This study followed the American Concrete Institute (ACI) code in assuming that the ultimate moment‐capacity limit state is reached when the concrete strain attains a value of 0.003. For the serviceability limit state, it is assumed that the sections fails to perform satisfactorily when the first steel reinforcement bar yields. The capacity of a cross section may vary due to variabilities in section properties, material strengths, and uncertainty associated with the prediction model. A systematic analysis of the propagation of uncertainties associated with these factors and their contribution to the overall uncertainty in the moment capacity is obtained based on the first‐order secondmoment (FOSM) and Monte Carlo simulation techniques. A closed‐form expression is derived for the uncertainty in the moment capacity following the FOSM approach. The FOSM approach provides results that are in good agreement with the Monte Carlo simulation. The results of a parametric study suggest that, for the example chimney, the coefficient of variation of the moment capacity is insensitive to the variation in the steel ratio. The analysis presented in this study would aid in determining resistance factors for probability‐based design of the tubular reinforced‐concrete members.