Structural health monitoring (SHM) refers to the process of implementing a damage detection and characterization strategy for engineering structures. Its objective is to monitor the integrity of structures and detect and pinpoint the locations of possible damages. Although wired network systems still dominate in SHM applications, it is commonly believed that wireless sensor network (WSN) systems will be deployed for SHM in the near future, due to their intrinsic advantages. However, the constraints (e.g., communication, fault tolerance, energy) of WSNs must be considered before their deployment on structures. In this article, we study the methodology of sensor placement optimization for WSN-based SHM. Sensor placement plays a vital role in SHM applications, where sensor nodes are placed on critical locations that are of civil/structural engineering importance. We design a three-phase sensor placement approach, named TPSP, aiming to achieve the following objectives: finding a high-quality placement for a given set of sensors that satisfies the engineering requirements, ensuring communication efficiency and reliability and low placement complexity, and reducing the probability of failures in a WSN. Along with the sensor placement, we enable sensor nodes to develop "connectivity trees" in such a way that maintaining structural health state and network connectivity, for example, in case of a sensor fault, can be done in a distributed manner. The trees are constructed once (unlike dynamic clusters or trees) and do not incur additional communication costs for the WSN. We optimize the performance of TPSP by considering multiple objectives: low communication cost, fault tolerance, and lifetime prolongation. We validate the effectiveness and performance of TPSP through both simulations using real datasets and a proof-of-concept system on a physical structure.