Generalized Nonlinear Moment-Curvature Model for Serviceability-Based Design of Hybrid Reinforced Concrete

Structural applications of hybrid reinforced concrete (HRC) involve a composite system with a fiber-reinforced concrete (FRC) matrix in conjunction with conventional reinforcement. The system offers economic benefits by reducing the number of rebars, minimizing labor costs, and shortening the construction schedule. This paper presents the generalized approach to evaluating closed-form moment-curvature relationships from constitutive models with multilinear equations. The interaction of various moment-curvature solutions is by sequential switching from one mode to the other to form an envelope curve as the minimum moment among all available options. Results lead to explaining the interaction of material and geometrical parameters as well as the interaction of various failure modes. Furthermore, the model can be used for both the ultimate limit state (ULS) and serviceability limit state (SLS) since the strain history is the primary independent variable. These lead to parametric design charts for adjusting material parameters, reinforcement amount and location, and section geometry within the bounds of ρmin and ρbal is applicable for HRC, RC, and FRC sections. Analytical equations show that as the concrete flexural crack extends in a hybrid section, the bridging effect of fibers delays the stress accumulation into the rebar and its subsequent yielding. The efficiency of the volume of concrete that is under tensile loads is significantly improved, extending the serviceability range and increasing the stiffness of cracked concrete. The extension of the serviceability limit range is also associated with potential improvements in durability since the HRC model predicts smaller apparent strains and crack widths at a given load. The proposed solutions are validated by simulating the load-deflection responses of various full-scale flexural tests published in the literature.