Probabilistic Assessment of Bending Strength of Statically Indeterminate Reinforced Concrete Beams

The paper presents a reliability analysis of a two-span reinforced concrete beam, taking account of random variations in cross-sectional dimensions, area and position of reinforcement for sagging and hogging bending moments, material strengths, loads and model uncertainties. In addition, the limit state functions for the statically indeterminate beam were derived, considering the static equilibrium requirement after the moments were redistributed as well as the codified allowable limit for the adjusted moment at each beam section. A large number of Monte Carlo simulations were performed in which the basic variables were modeled with normal, lognormal and Gumbel distributions. When the elastic moment distribution was used in evaluating the beam reliability, the two-span beam behaved as a series system with three critical nodes located at the interior support and midspan sections. The probability that the system had at least one overloaded node was greater than the failure probability of an individual node. However, considering moment redistribution made it possible to reduce the amount of reinforcement whilst maintaining the reliability of the beam. When the reinforcement area was reduced by 26% at the support section or 14% at the midspan sections, the failure probability was predicted to be 6.90E-5, which is deemed acceptable for a 50 year reference period.