The increasing risk of accidental and/or intentional explosions has highlighted the need for reliable computational tools capable of predicting the damage evolution and collapse behavior of reinforced concrete (RC) structures subjected to blast loading. Although conventional finite element approaches can accurately capture local material response, they often encounter difficulties in representing extensive cracking, fragmentation, member separation, and debris interaction during progressive collapse. This study presents an applied element method (AEM)-based numerical framework for evaluating the blast performance of fiber-reinforced polymer (FRP)-strengthened RC structural systems. The model combines continuum-based material representation with discrete failure mechanisms, enabling automatic simulation of crack initiation, element separation, debris generation, and structural collapse. The numerical model is first compared against a literature blast test on an RC column. It is subsequently employed in a multi-scale investigation comprising FRP-strengthened RC columns subjected to non-uniform blast pressures and a five-story RC frame exposed to the detonation of a 2700-kg TNT charge. The analyses demonstrate that externally bonded FRP confinement substantially reduces damage severity and delays failure progression, while the AEM framework effectively captures local damage evolution and global collapse mechanisms within a unified modeling environment. The study illustrates the potential of AEM as an efficient computational tool for assessing blast resilience and supporting the design of FRP-strengthened RC infrastructure against extreme loading scenarios.