Evaluation of steel ratio limits for reinforced concrete beams using reliability analysis and Bayesian methods

Abstract

Structural codes worldwide typically limit the steel reinforcement ratio in elements to mitigate the risk of fragile failure. Notably, standard codes impose such limits; however, constant improvements in material science induce the need for standard codes to be reviewed periodically. This reassessment is important due to advancements in the nominal values of key parameters in structural design and construction, and the uncertainty reduction in material reliability attributed to advancements in manufacturing processes and quality control. This paper addresses the need for a thorough reassessment of the reliability level of steel reinforcement ratio limits in beam elements designed under the provisions of the ACI 318-19 code, given the evolving material properties. Principles of mechanics are used to get an expression of steel reinforcement ratio ($\rho$) limits in terms of the uncertainty in material properties such as concrete and steel. Also, experimental data from multiple resources and available literature are incorporated for model validation. Specifically, compressive strength of concrete ($f_c^{\prime }$), yield stress of steel ($f_y$), modulus of rupture ($f_r$), ultimate deformation of concrete (${\varepsilon }_{cu}$), and the ratio of the transformed area of the concrete section to its gross area (${\beta }_1$) are treated as random variables. The investigation focuses on the compressive strength of concrete values of 28, 35, 42, and 89 MPa alongside with grade 60 and high-strength structural steel. The probability of exceedance of $\rho$ limits is calculated through Bayesian inference programming and Monte Carlo sampling. The results indicate that the minimum steel ratio (${\rho }_{min}$) limit given by ACI 318-19 is considerably higher than the obtained value by code. While the maximum steel ratio (${\rho }_{max}$) is reasonable, taking into account the balanced steel ratio (${\rho }_{balanced}$) value, which gives us a maximum amount of steel that causes a ductile failure. Drawing insights from the results, novel limits may be formulated for these specific $f_c^{\prime }$ values to achieve a reliable and balanced behavior in reinforced concrete members.