Structural Reliability Analysis Applied to the Flexural and Shear Design of a Reinforced Concrete Beam

https://doi.org/10.47191/etj/v11i10.15
Reinforced concrete, Structural reliability, Monte Carlo simulation, FOSM, FORM

Authors

  • Milena Nery dos Santos Undergraduate Student in Civil Engineering, Federal University of Alagoas, Campus do Sertão, Technology Division, Delmiro Gouveia, AL 57480-000, Brazil.
  • Vinicius Costa Correia, D.Sc. Professor of Civil Engineering, Federal University of Alagoas, Campus do Sertão, Technology Division, Delmiro Gouveia, AL 57480-000, Brazil (corresponding author).
  • Alverlando Silva Ricardo, D.Sc. Professor of Civil Engineering, Federal University of Alagoas, Campus do Sertão, Technology Division, Delmiro Gouveia, AL 57480-000, Brazil.
Vol. 11 No. 10 (2026): VOLUME 11 ISSUE 10
Articles
October 19, 2026
October 20, 2026

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The design of reinforced concrete structures in Brazil is governed by NBR 6118:2026. However, deterministic design provisions do not explicitly account for uncertainties in structural behavior, which may result in uneconomical designs or inadequate safety levels. Structural reliability analysis provides a probabilistic basis for assessing these uncertainties and quantifying structural safety. This study evaluates the reliability of a reinforced concrete beam with respect to flexural and shear limit states. Failure probabilities were estimated using Monte Carlo simulation, the First-Order Second-Moment method (FOSM), and the First-Order Reliability Method (FORM). Two analyses were conducted. First, the beam was assessed under its original design condition, with fck = 30 MPa. Second, the same beam was analyzed considering concrete strength classes C20, C30, C40, and C50. The three methods provided comparable reliability estimates. The results showed that the probability of failure generally decreased with increasing concrete compressive strength and that the relative importance of the random variables varied according to the failure mode.