Modeling of Rocking Elastic Flexible Bodies under Static Loading Considering the Nonlinear Stress Distribution at Their Base

Abstract

In recent years, the need for resilient structural systems has led to renewed interest in the use of rocking members instead of conventional ones for the design of earthquake-resistant structures. Due to the usually constrained nature of such members, in addition to the deformability along their height, the nonlinear stress distribution at their base resulting from the partial loading of the rocking interface needs to be taken into account for an accurate estimation of the rocking motion. In this paper, a new approach is proposed for the prediction of the response of elastic rocking bodies under static loading that is able to consider such effects. The nonlinear stress distribution near the contact area results in additional displacements compared to those of the technical theory of bending, and a method to estimate them is presented and incorporated into a macroelement formulation that can be used in the context of a finite-element program. Results for typical examples are presented and compared with those of corresponding commercial software models, showing excellent agreement, while the proposed macroelement requires extremely low runtimes compared to conventional finite-element codes.