This paper takes a first look at the potential consequences of cyberattacks against structural control systems. We design algorithms and implement them in a testbed and on well-known benchmark models for buildings and bridges. Our results show that attacks to structures equipped with semi-active and active vibration control systems can let the attacker oscillate the building or bridge at the resonance frequency, effectively generating threats to the structure and the people using it. We also implement and test the effectiveness of attack-detection systems.