Structural Health Monitoring (SHM) plays a crucial role in maintaining aging and critical infrastructure, supporting applications such as smart cities and digital twinning. These applications demand machine learning models capable of processing large volumes of real-time sensor data at the network edge. However, existing approaches often neglect the challenges of deploying machine learning models at the edge or are constrained by vendor-specific platforms. This paper introduces a scalable and secure edge-computing reference architecture tailored for data-driven SHM. We share practical insights from deploying this architecture at the Memorial Bridge in New Hampshire, US, referred to as the Living Bridge project. Our solution integrates a commercial data acquisition system with off-the-shelf hardware running an open-source edge-computing platform, remotely managed and scaled through cloud services. To support the development of data-driven SHM systems, we propose a resource consumption benchmarking framework called edgeOps to evaluate the performance of machine learning models on edge devices. We study this framework by collecting resource utilization data for machine learning models typically used in SHM applications on two different edge computing hardware platforms. edgeOps was specifically studied on off-the-shelf Linux and ARM-based edge devices. Our findings demonstrate the impact of platform and model selection on system performance, providing actionable guidance for edge-based SHM system design.