When subjected to lateral excitations, a variety of structures, such as museum artefacts, historical buildings, bridge piers and post-tensioned walled buildings, might uplift and set into rocking motion. Although this mechanism can efficiently limit the internal forces at their base, the possibility of overturning or experiencing increased lateral deformations and accelerations may severely affect the functionality of rocking structures. Nevertheless, suitable seismic control strategies are presently limited and consist mostly in preventing rocking motion altogether, which may induce undesirable stress concentrations and lead to impractical interventions. This thesis examines the alternative of using supplemental rotational inertia devices to control the seismic response of rocking structures. The newly proposed strategy employs inerters, which are mechanical devices that develop resisting forces proportional to the relative acceleration between their terminals and can be combined with a clutch to ensure they act only in opposition to the motion. The fundamental dynamic behaviour of the system is firstly examined considering a free-standing rigid block model. By deriving the corresponding equations of motion, it is demonstrated that the inclusion of the inerter effectively reduces the frequency parameter of the block, resulting in lower seismic demands and enhanced stability due to the well‐known size effects of the rocking behaviour. In subsequent chapters, this simplified single-degree-of-freedom model is gradually extended in order to incorporate the effects of post-tensioned tendons, structural flexibility and higher modes on the response. Overall, the analyses conducted under coherent pulses and real ground motion records show that inerter-equipped structures experience reduced seismic demands and lower probabilities of exceeding limit states usually associated with structural and non-structural damage.
The fundamental knowledge acquired in the first part of this thesis is finally applied to control the seismic response of rocking timber buildings. To this end, a set of three post-tensioned rocking walled buildings, comprising 3, 6 and 9 storeys, is designed following direct-displacement-based design guidelines. Additionally, a set of clutched and non-clutched ball-screw and gear inerters is designed using a newly proposed pre-dimensioning procedure. The performance of bare and protected structures with different levels of apparent mass ratios is then compared in terms of peak inter-storey drifts and floor accelerations. Special attention is paid to the resisting forces developed in the inerters and the mechanism to transfer them to the structural diaphragm. Likewise, the ability of the inerters to control higher-mode effects is closely examined. Finally, a performance-based assessment with particular emphasis on non-structural and contents damage is conducted considering a database of 202 pulse-like ground motion records. Overall, the results of this assessments confirm the trends observed in the analytical examinations of the earlier chapters.