Structural health monitoring (SHM) systems are implemented for structures(e.g., bridges, buildings) to monitor their operations and health status. Wireless sensor networks (WSNs) are becoming an enabling technology for SHM applications that are more prevalent and more easily deployable than traditional wired networks. However, SHM brings new challenges to WSNs: engineering-driven optimal deployment, a large volume of data, sophisticated computing, and so forth. In this paper, we address two important challenges: sensor deployment and decentralized computing. We propose a solution, to deploy wireless sensors at strategic locations to achieve the best estimates of structural health (e.g., damage) by following the widely used wired sensor system deployment approach from civil/structural engineering. We found that faults (caused by communication errors, unstable connectivity, sensor faults, etc.) in such a deployed WSN greatly affect the performance of SHM. To make the WSN resilient to the faults, we present an approach, called FTSHM (fault-tolerance in SHM), to repair the WSN and guarantee a specified degree of fault tolerance. FTSHM searches the repairing points in clusters in a distributed manner, and places a set of backup sensors at those points in such a way that still satisfies the engineering requirements. FTSHM also includes an SHM algorithm suitable for decentralized computing in the energy-constrained WSN, with the objective of guaranteeing that the WSN for SHM remains connected in the event of a fault, thus prolonging the WSN lifetime under connectivity and data delivery constraints. We demonstrate the advantages of FTSHM through extensive simulations and real experimental settings on a physical structure