A Macro-Element Formulation for Rocking Flexible Bodies With a Deformable Base

Abstract

Abstract. In recent years, an increased interest in the use of rocking members for the design of earthquake resistant structures is observed. As described in the literature, the use of rocking members leads to more resilient structural systems, since, in contrast to conventional members which develop damage and residual deformations, rocking members have the ability to re-center without significant damage, leading to increased structural safety and lower repair costs after a seismic event, while their yield-like response restrains the seismic forces acting on the structure.Although much research has been conducted on the response of rocking members, mainly regarding analytical solutions for free-standing rocking bodies with rigid bases and simplified guidelines for the design of structural rocking members, it is believed that there is a need for simple computational models, which can describe the response of rocking flexible members in structural systems more realistically.In this paper, a new approach that is able to take into account the deformation along the height of the body and along the contact areas, especially required for cases of constrained structural members, is applied for the development of a generalized macro-element, which can be used in the context of a finite element program. The theoretical formulation of the problem is based on the solution of the normalized semi-infinite strip problem with random loads on its free side. The new macro-element is demonstrated using typical example problems and the results are compared with corresponding results obtained with Abaqus, showing excellent agreement. Concerning the required runtimes, the macro-element runs significantly faster compared to conventional finite element codes. 5129