Numerical Approach for Residual Strengths of Fiber-Reinforced Concrete Beams with Different Densities

A numerical approach is proposed to predict the flexural stress–crack mouth opening displacement (CMOD) relationship of fiber-reinforced concrete (FRC) beams. The compressive strength and density of concrete as well as various fiber parameters are considered in the compressive and tensile stress–strain relationships of concrete employed in the analysis. The nonlinear hinge model for fictitious crack propagation generalized by Olesen is also utilized to calculate the CMOD from the curvature determined from critical beam sections. The theoretical flexural stress–CMOD curves corresponded well with the measured curves. They indicated that the mean and standard deviation of normalized root mean square error values determined from 136 FRC beams were 0.237 and 0.118, respectively. A comprehensive parametric study is then conducted by numerically analyzing the primary variables influencing the CMOD response of FRC beams at extensive ranges. This enables the formulation of simple closed-form equations to determine the residual flexural strengths straightforwardly. The residual flexural strengths yielded by the derived equations agree better with the test results than with those given by previous empirical equations, yielding fewer scatters in the ratios between the experimental results and predictions is observed. Consequently, the present equations have potential in reliably assessing the residual flexural strengths of FRC with a wide range of variables, such as compressive strength, density, aggregate size, and fiber parameters.