Modeling of Rocking Flexible Bodies Considering the Deformability of Their Base

Abstract eng:
In recent years, the need for resilient structural systems has led to a renewed interest in the use of rocking members, instead of conventional ones, for the design of earthquake resistant structures. This happens because, instead of developing 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 the earthquake event. Furthermore, since rocking members attain their maximum strength just before the onset of rocking, they can reduce the seismic forces acting on the structure similarly to yielding members. Although there has been extensive research on the response of unconstrained bodies allowed to rock and many analytical and experimental results and guidelines have been presented for the design of structural rocking members, it is believed that more research must be conducted on the numerical response of constrained rocking members used in structures. Due to the constrained nature of the rocking motion of these members during an earthquake, either from additional elements such as prestressed tendons or from the surrounding frames, their response differs significantly from the response of freestanding rocking bodies. This happens because significant vertical forces may develop, which continuously alter the rocking response. One effect of these forces is that they cause deformation at the base of the body which can no longer be considered rigid and its deformability has to be taken into account for an accurate estimation of the rocking motion. Up to now, the deformability of rocking bodies was mostly considered only with what concerns their deformation along their height, while their base was considered rigid. In this paper a new approach is proposed, which is able to take into account the deformability of the body along its height, as well as the deformation of its base during rocking. The rotations and the displacements, which originate from the rocking motion and the body’s deformation, are examined for a typical problem of an elastic rocking block and formulas are presented for their calculation. The presented analysis is extended and incorporated into a macroelement, which could be used in the context of a finite element program, such as Opensees. Comparisons of the obtained results with corresponding results obtained with Abaqus show excellent agreement, while the proposed macroelement approach requires extremely low runtimes compared to conventional finite element codes.

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