Comparative Analysis of Effective Stiffness Models for Immediate Deflection Prediction in Reinforced Concrete Beams

Abstract

Objective: To quantify how effective-stiffness models affect immediate deflection estimates for reinforced concrete beams. Methodology: The Branson, rational Bischoff, and ACI 318-19 formulations were evaluated for rectangular sections with reinforcement ratios of 0.302.00% and applied-to-cracking moment ratios of 1.04.0, totaling 1,098 evaluations. Results: Divergence peaked immediately after cracking and at low reinforcement ratios; ACI 318-19 predicted lower stiffness and larger deflection than Branson over almost the entire domain, the only exception being a negligible reversal (below 0.1%) for the most heavily reinforced section at the highest load ratios. Limitations: No experimental database or long-term effects were considered. Originality: Dimensionless maps identify regions sensitive to model choice. Conclusions: The cracking moment, gross and cracked inertias, and adopted equation should be reported.