This research proposes a method aimed at investigating the detection of bridge damage areas using a rigorous method based on mathematical models of dynamic finite elements. Strengthening of the reinforced concrete (RC) is proposed for increasing the strength of RC structures when they present material degradation. It includes reinforcement with carbon reinforcement composites (CFC) and steel fiber reinforced concrete (SFRC), injection with SikaDur 52 Injection type epoxy resin, and the addition of SikaTop 126 type concrete. Establishment of a set of equations and numerical modeling of the specified method are presented in this study for sparse matrices of a large system of equations. A numerical solver with FEM Ansys software was used to avoid the lack of big-data memory storage on the available hardware. RC material properties have been modeled with the composite material mixture laws as a homogeneous material. Several simulations have been achieved. The results obtained allowed location of stress concentration areas and consequently, detection of important von-Mises equivalent stresses of strength bound in severe load cases as well as graphically visualization of the time history of displacements evolution. The study has also revealed that the reliability design of the probabilistic method with the security margin as a stochastic variable is an effective structural health monitoring approach.