Analytical solutions for flexural design of hybrid steel fiber reinforced concrete beams

• A rational procedure for design of hybrid reinforced concrete beams with fibers.
• Analytical solutions for moment, curvature, and deflection to address ductility based design.
• Serviceability based algorithms based on ductility, curvature, or allowable deformation.
• Effect of fibers on the stiffness retention and reduction of curvature for an applied moment.
• Parametric studies of the effect of post crack tensile stiffness, strength, and reinforcement ratio.

Hybrid reinforced concrete (HRC) is referred to as a structural member that combines continuous reinforcement with randomly distributed chopped fibers in the matrix. An analytical model for predicting flexural behavior of HRC which is applicable to conventional and fiber reinforced concrete (FRC) is presented. Equations to determine the moment–curvature relationship, ultimate moment capacity, and minimum flexural reinforcement ratio are explicitly derived. Parametric studies of the effect of residual tensile strength and reinforcement ratio are conducted and results confirm that the use of discrete fibers increases residual tensile strength and enhances moment capacity marginally. However improvements in post-crack stiffness and deformation under load is substantial in comparison to conventional steel reinforcement. Quantitative measures of the effect of fiber reinforcement on the stiffness retention and reduction of curvature at a given applied moment are obtained. The approach can also be presented in a form of a design chart, representing normalized moment capacity as a function of residual tensile strength and reinforcement ratio. Numerical simulations are conducted on the steel fiber reinforced concrete (SFRC) and HRC beam tests from published literature and the analytical solutions predict the experimental flexural responses quite favorably.