A mathematical model for the rocking, overturning and shifting problems in bridges

This work presents a theoretical approach for dealing with the rocking, overturning and shifting problems in bridges subjected to near-source or long-distance earthquake actions. The rocking phenomenon is the “swaying” of a bridge on its supports, which causes local damage at the support positions only, while the overturning phenomenon is associated with the lift-up and, subsequently, the overturning of the whole bridge out of its normal position. Shifting is the horizontal movement of the bridge’s ends away from its supports. In this paper, a simple mathematical model is developed for studying the rocking, overturning and shifting phenomena in bridges as well as the conditions under which these phenomena may occur. Safety indicators for rocking, overturning and shifting of bridges subjected to earthquake actions are derived and presented in graphical form and useful conclusions are drawn.