Statistical Analyses and Parametric Study for Reinforced Concrete Beams Strengthened in Flexure with FRPs

In this paper, statistical analyses and a parametric study are presented for reinforced concrete beams strengthened in flexure using FRP composites. Five variables are considered in this study; namely, the FRP axial stiffness, concrete strength, steel reinforcement ratio, beam depth, and beam span. We aim to develop statistics-based design equations to predict the debonding load, the flexural capacity of the beam cross-section, the maximum deflection at the debonding load, the ductility index, and the debonding strain level in the FRP laminate. Simplifying these statistical models is then carried out to develop robust design equations. These equations hold an advantage over those available in most code specifications because they account for the effect of interactions between various variables on the predicted quantities. The statistical analyses are primarily based on the response surface methodology (RSM) technique. The proposed models are thus referred to as the RSM models. Proposed design equations are then developed by simplifying the RSM models using Monte Carlo simulations and nonlinear regression analysis. Of the five responses considered in the RSM analysis, only the debonding strain level in FRP laminates is considered in the design equations. The data required for the statistical analysis were obtained from finite element models for beams having different combinations of variables. The statistical analyses are followed by a parametric study to investigate the effect of the above five variables and their interactions on the debonding load and the corresponding debonding strain level in the FRP laminate. This involves comparisons in terms of the debonding strain between the predictions of the proposed equation and those of the ACI, fib, Chinese specifications, and Australian standards.