Integrated sensing and communication (ISAC) is a key feature of future cellular systems, enabling applications such as intruder detection, monitoring, and tracking using the same infrastructure. However, its potential for structural health monitoring (SHM), which requires the detection of slow and subtle structural changes, remains largely unexplored due to challenges such as multipath interference and the need for ultra-high sensing precision. This study introduces a novel theoretical framework for SHM via ISAC by leveraging reconfigurable intelligent surfaces (RIS) as reference points in collaboration with base stations and users. By dynamically adjusting RIS phases to generate distinct radio signals that suppress background multipath interference, measurement accuracy at these reference points is enhanced. We theoretically analyze RIS-aided collaborative sensing in three-dimensional cellular networks using Fisher information theory, demonstrating how increasing observation time, incorporating additional receivers (even with self-positioning errors), optimizing RIS phases, and refining collaborative node selection can reduce the position error bound to meet SHM's stringent accuracy requirements. Furthermore, we develop a Bayesian inference model to identify structural states and validate damage detection probabilities. Both theoretical and numerical analyses confirm ISAC's capability for millimeter-level deformation detection, highlighting its potential for high-precision SHM applications.