Refined Nonlinear Estimation of Effective Flexural Rigidity in Reinforced Concrete Beams using Curvature Integration

Deflection control in Reinforced Concrete (RC) beams is a fundamental aspect of structural engineering. Most contemporary design codes estimate deflection using the effective moment of inertia formula, which remains largely consistent across various standards. However, an alternative and more precise approach involves computing deflection through the double integration of the moment-curvature relationship along the beam's length, offering superior accuracy but requiring significantly higher computational effort. This study evaluates deflection predictions obtained through experimental testing, conventional code-based calculations, and the moment-curvature double integration method. The findings demonstrate a strong correlation between the experimental data and the results from moment-curvature integration, whereas deflection estimates based on code formulations tend to be overly conservative. Therefore a comprehensive parametric study was performed, considering key parameters such as tensile and compressive reinforcement ratios, and span-to-depth ratio. Based on the study's findings, an empirical model is proposed to determine the effective moment of inertia, offering improved accuracy in deflection predictions while maintaining computational efficiency in RC beam analysis.