Seismic response assessment of rocking systems using single degree-of-freedom oscillators

A new modeling for the seismic response assessment of free-standing, rigid or flexible, pure rocking systems is presented. The proposed modeling is based on equivalent single degree-of-freedom (SDOF) oscillators that can be implemented with common engineering software or user-made structural analysis codes. The SDOF models adopted use beam elements that are connected to a nonlinear rotational spring with negative stiffness that describes the self-centering capacity of the rocking member. The loss of energy at impact is treated with an “event-based” approach consistent with Housner's theory. Different variations pertinent to rigid blocks are first presented, and then the concept is extended to the flexible case. The implementation of the method requires some minor programming skills, while thanks to the versatility of the finite element method, it is capable to handle a variety of rocking problems. This is demonstrated with two applications: (a) a vertically restrained block equipped with an elastic tendon and (b) a rigid block coupled with an elastic SDOF oscillator. The accuracy and the efficiency of the proposed modeling is demonstrated using simple wavelets and historical ground motion records.