Structural Health Monitoring (SHM) systems estimate damages that affect structural reliability. Modern SHM requires continuous monitoring to detect damage caused by day-to-day loading and usage. SHM analyzes structural integrity and identifies weaknesses leading to potential building collapse. In disaster situations e.g., earthquakes, SHM systems enable early assessment of building safety and therefore ensure evacuation and prevention of human losses. In an urban area, multi-story constructions in congested areas become a hazard if their structural health is not well monitored and maintained properly. A key challenge is the ability to detect damages in an efficient manner for edge computing. In this work, we propose an SNN based low-cost, energy-efficient, and standalone damage classification model for SHM. The proposed classification model is implemented on FPGAs and results show a classification accuracy of 99.46% on a sensory dataset for earthquake damage on a 7-Story concrete building.