Application of Modular Ratio in Predicting the Behavior of Externally Strengthened RE Beams

Abstract

This study presents the development and validation of a theoretical based mathematical expression for predicting the flexural behaviour of externally reinforced concrete (RC) beams using steel plates and carbon fiber-reinforced polymer (CFRP) fabrics. The mathematical expression incorporates the modular ratio as an input variable and was validated against experimental results reported by John et al. (2022, 2022a). Six beam samples, including both control and retrofitted specimens, were analysed. The retrofitting techniques varied in terms of material type, bond thickness, and number of reinforcement layers. Comparative analysis between experimental and theoretical failure loads revealed a strong correlation, with percentage differences ranging from -1.08% to 6.37%. These results demonstrate that the model provides accurate and conservative estimates of load-carrying capacity, which is a desirable characteristic in structural design. Furthermore, Analysis of Variance (ANOVA) was conducted at a 95% confidence level to statistically evaluate the agreement between experimental and theoretical results. The ANOVA yielded a p-value of 0.673, indicating no significant difference between the two datasets. This confirms the model’s predictive reliability and its potential for practical engineering applications. The study concludes that Equation (30) is an effective and efficient tool for assessing the flexural performance of retrofitted RC beams, offering an alternative to exhaustive experimental testing and supporting safer and more cost-effective structural retrofitting strategies.