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Wireless sensor networks have attracted great attention for applications in structural health monitoring due to their ease of use, flexibility of deployment, and cost-effectiveness. This paper presents a software framework for WiFi-based wireless sensor networks composed of low-cost mass market single-board computers. A number of specific system-level software components were developed to enable robust data acquisition, data processing, sensor network communication, and timing with a focus on structural health monitoring (SHM) applications. The framework was validated on Raspberry Pi computers, and its performance was studied in detail. The paper presents several characteristics of the measurement quality such as sampling accuracy and time synchronization and discusses the specific limitations of the system. The implementation includes a complementary smartphone application that is utilized for data acquisition, visualization, and analysis. A prototypical implementation further demonstrates the feasibility of integrating smartphones as data acquisition nodes into the network, utilizing their internal sensors. The measurement system was employed in several monitoring campaigns, three of which are documented in detail. The suitability of the system is evaluated based on comparisons of target quantities with reference measurements. The results indicate that the presented system can robustly achieve a measurement performance commensurate with that required in many typical SHM tasks such as modal identification. As such, it represents a cost-effective alternative to more traditional monitoring solutions.