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SummaryThis paper presents a macroelement formulation for the prediction of the planar dynamic response of inelastic deformable rocking bodies. The formulation is based on a previous macroelement developed by the authors able to describe the cyclic response of inelastic rocking bodies, which takes into account the deformability both along the height of the member, as well as near the rocking end. Modifications of this formulation to account for other motion modes of rocking members during their dynamic response, namely, sliding and upthrow, as well as modifications to account for damping in a uniform manner during the whole motion, including impacts, are introduced. The dynamic response predicted by the macroelement for free‐standing rigid and deformable rocking bodies is presented and compared with existing theoretical solutions, and the effect of deformability, damping, inelasticity, and friction on the response is discussed.

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Abstract. An increasing interest in the use of rocking members in earthquake resistant structural systems has been observed in recent years. The benefits of such members include the limitation of the damage, re-centering capabilities and reduction of seismic forces transmitted to the rest of the structure due to a yield-like response.Despite the importance of such members, few models able to describe the response of flexible rocking members in structural systems realistically can be found in literature, since most of the research focuses on the response of rigid bodies or ignores the stress nonlinearity near the contact area, which is considered crucial to the accurate determination of the rocking response of deformable rocking bodies. A new macro-element formulation for elastic rocking members has been proposed by the authors in previous papers which is able to take into account this stress nonlinearity, producing results which are very close to the ones produced by conventional finite element programs.Rocking members in structural systems are expected to behave inelastically for large seismic excitations. In this paper, the macroelement presented previously by the authors, which considered the element material to be elastic, is extended to also take material nonlinearity into account. The effect of the nonlinear stress distribution across the rocking interface on the member displacements is determined and approximate formulas for their determination are included in the macro-element formulation. The results produced by the macro-element with the inelastic material are finally compared to the ones of conventional finite element codes, showing very good agreement between the results of the two methods.