Analytical modeling of rocking elements

The use of elements connected through compression at their contact surfaces, without tensile capacity, which allow rocking in their transverse direction, was attempted in the construction of bridge piers, masonry walls and frame structures. Columns or bridge piers can be designed to rock or overturn with minimal lateral resistance. However, as shown in this paper, due to the effects of stresses at the contact surfaces, including cracking, yielding and crushing, the lateral resistance varies substantially before rocking and before the columns overturn. Moreover, when the elements are confined between rigid surfaces, or when pre-stressing forces are applied to the connections, the lateral resistance varies substantially. Current models discretized using micro-models, or finite elements, are computationally inefficient for large structural systems, such as bridges or buildings. This paper attempts to model the strength and stiffness variation before rocking, using a macroscopic approach. The stiffness and flexibility formulations developed using virtual work concepts include flexural and shear effects, and can be implemented in many off-the-shelf analytical platforms. The analytical formulations are compared in this paper to the results of multi-purpose finite element models (FEM) for squat and slender columns.