The mechanical properties of concrete vary with the loading rate under dynamic conditions, which can influence the dynamic fracture behavior of structures. The rate effects are believed to arise from the microscopic mechanisms, such as the Stefan effect and inertia effect. In this study, the rigid-body-spring network (RBSN) is employed for the fracture analysis, and the visco-plastic damage model is implemented to represent the rate effect in this macroscopic numerical framework. The parameters in the Perzyna type formulation of the visco-plasticity are calibrated through the direct tensile test with various loading rates as a preliminary simulation. As the loading rate increases, the strength increase is presented in terms of the dynamic increase factor (DIF), and compared with the experimental and empirical results. Next, the flexural beam test is conducted for plain and reinforced concrete beams under impact rates of loading. At the failure stage, different crack patterns are observed depending on the loading rate. The impact loading induces the failure to be more localized on the compressive zone of the beam. In structural aspects, the reinforcement exerts stronger effects on reducing crack width and improving ductility. The ductility is also evaluated through the comparison of load-deformation curves until the final rupture of the beams. This study can provide understandings of the structural rate dependent behavior and the reinforcing effect under dynamic loadings.