A rigid-flexible coupled rocking structure with nonlinear stress distribution along its base: Analytical modeling, validation and parametric investigation

Structures allowing their bases to uplift and rock during an earthquake event usually experience less damage; thus, they are more resilient to seismic hazards. Accurate simulation is critical to design and seismic performance evaluation of these flexible rocking structures. Motivated from this, this article presents a new rigid-flexible coupled rocking model for numerical evaluation of flexible rocking structures under both cyclic and dynamic loadings. The key idea in the model formulation is that the total motion of flexible rocking structure can be decomposed into a rigid-body motion and an associated flexible deformation. The flexible deformation of the rocking body is described using displacement field of classical Timoshenko beam. Using this approach and appropriate degrees-of-freedom (DOFs), the governing equations-of-motion for flexible rocking structures are formulated using the variational principle. Multiple springs with appropriate constitutive model are distributed along rocking base to represent the inelastic behavior of rocking body. Potential post-tensioned tendons are also considered in this model. In addition, nonlinear stress distribution along the rocking base, which cannot be considered in existing flexible rocking model, is also incorporated in the developed model. The proposed model is subsequently validated against published experimental data through quasi-static and shake table tests, showing good accuracy when the rocking structure is relatively stockier. Finally, a parametric investigation on the effect of flexibility, nonlinear stress distribution and yield stress of rocking body on the rocking response is performed. This preliminary investigation shows that influence of flexibility and yield stress is significant while impact of nonlinear stress distribution is minor.