Mean absolute input energy for in-plane vibrations of multiple-support structures subjected to non-stationary horizontal and rocking components

This study proposes a procedure for the estimation of the mean absolute input energy of multiple-support structures subjected to partially correlated, non-stationary, multi-component, seismic actions. The methodology extends the current evaluation of the earthquake input energy of single-support structures to multiple-support ones, and considers the combined action of translational and rotational components. A mean total velocity response spectrum for characterizing the mean absolute input energy of multiple-support structures is derived utilizing their pseudo-static response. The earthquake rotational loading is simulated considering the effects of both time delay and loss of coherency. The main advantage of the proposed method is its simplicity of application to a wide range of bridge systems. In addition, the effects of the geometrical configuration of the structure and the earthquake characteristics on the absolute input energy of straight short-span bridges along their longitudinal direction are parametrically investigated, and recommendations for their safe seismic design are proposed. The numerical results of this study indicate that, if the effect of the spatial variation of strong ground motions is incorporated in seismic analysis of bridges, both the differential and the rotational components of the strong ground motions should be taken into account in their excitation.