Enhancing the Goldberg–Richard model with a calibrated influence factor for superior moment–curvature prediction in RC beams

The relationship between moment (M) and curvature (κ) is key to characterising nonlinear flexural behaviour of concrete members. This research develops a new method for enhancing predictive accuracy of the Goldberg and Richard (G-R) Power Law model for predicting the behaviour of concrete under compression using a newly developed calibrated influence factor (CIF). Although the G-R model can provide continuous representations of the nonlinearity of the material, predictive accuracy is limited by the complex nature of design variables for composite members. In order to improve predictive accuracy, dimensional analysis and multivariate nonlinear regression analyses were conducted available experimental database to create a dimension-less CIF based on the Material Interaction Index (MII), which represents the mechanical interaction between steel reinforcement and concrete. Use of the CIF in a closed-form sectional analysis provided a means to enhance the prediction of moment response at ultimate strength. Validation of the CIF was performed against two independent programs and beam test results; results showed the CIF provided significant reductions in mean absolute error (MAE), improvements in root mean square error (RMSE), and R² values greater than 0.99, while maintaining analytical efficiency for performance based design applications.