Analysis and Design of Reinforced Concrete Beams under Combined Loading Using Numerical Methods in MATLAB Software

Abstract

In this study, a precise numerical analysis of the nonlinear behavior of reinforced concrete (RC) sections under combined axial, flexural, and transverse loading is conducted with the aim of evaluating load-bearing capacity, ductility, and damage propagation patterns. The modeling approach is based on a comprehensive consideration of the nonlinear properties of the constituent materials, including cracked concrete and yielded reinforcement, utilizing strain-geometry compatibility relationships and force equilibrium equations. The interaction between moment and axial force is examined through detailed P−M interaction curves, and moment–curvature (M−ϕ) relationships are derived to assess flexural stiffness throughout various stages of loading. Furthermore, the overall response of the section under transverse loads is modeled through load–displacement (P−Δ) diagrams. Phenomena such as local yielding of reinforcement bars, progressive cracking of concrete, stiffness degradation due to cracking, and geometric instability are incorporated into the model, and the effects of each are analyzed individually. Additionally, graphical representations of strain and stress fields using contour plots illustrate the strain distribution and crack propagation within the section, providing deeper insight into the process of local failure development leading to overall structural collapse. The obtained results indicate a satisfactory correlation between the numerical model and physical trends observed in comparable experimental studies. The proposed model can serve as a reliable tool for predicting the behavior of RC sections under real-world loading conditions and for their performance-based design.