Improved Effective Moment of Inertia Equations for RC Beam Deflection Prediction

Accurate deflection calculations are important for ensuring the structural safety and serviceability of Reinforced Concrete (RC) beams. This study uses experimental data from previous research to evaluate the effectiveness of the moment of inertia equations in ACI 318-19 (Bischoff's equation) and SBC 304 (Branson's equation). The results showed that both equations had systematic biases: Bischoff's equation predicted deflections that were 22.8% higher, while Branson's equation predicted deflections that were 14.6% lower, than those measured under service conditions. To address these biases, new equations were developed using nonlinear regression analysis of 78 RC beam specimens from the published literature. The new equations include state-dependent variables related to the concrete strength, reinforcement ratios, and loading state. The proposed state-dependent correction reduced the prediction bias from 16.4% to 4.0% in the service state, from 41.2% to 9.5% in the uncracked state, and from 22.8% to 6.6% in the ultimate state. The statistical validation demonstrated a correlation coefficient greater than 0.95 for all loading states, indicating increased prediction accuracy for structural engineers. The results provide structural design engineers with accurate and realistic deflection prediction capabilities, improving deflection models, which can better support the organizations that adhere to less emphasized design codes. This study addresses a research gap by systematically evaluating the current code-based equations and formulating improved models based on experimental data. These models are then statistically validated. The study follows a structured approach including the background, problem statement, methodology, results, and implications. While the results are promising, the study's scope is limited by the range of the examined beam geometries and loading conditions, suggesting a need for future research to expand the applicability of the models.