Stiffness demand analysis of self-centering rocking wall moment frame structures based on a distributed parameter model

The static and dynamic response equations are derived and solved, respectively, to investigate the stiffness demands of self-centering rocking wall moment frame (SC-RWMF) structures using a proposed self-centering distributed parameter model (SCDPM). The lateral displacements, internal forces, and dynamic response distributions of SC-RWMF structures are theoretically and numerically analyzed, aiming at revealing the relationship between the stiffness demand of SC-RWMF structures and their static and dynamic responses. The ratios of the frame stiffness to rocking wall (RW) stiffness λ and the ones of the RW stiffness to the base rotational restraint stiffness R f are investigated, respectively, to reveal their demands in both static and dynamic performances. The generalized inter-story drift spectra (GIDS), inter-story drift concentricity factor spectra (DCFS), frame shear spectra, and RW shear spectra are explored under seismic excitations. Based on the spectral analysis, a stiffness demand objective function Z ( λ, R f ) is established, considering the structural deformations, deformation concentricity and internal forces. The results show that when (1 ≤ λ ≤ 5) and (1 ≤ R f ≤ 10), the SC-RWMFs can achieve a balance between uniform deformation distribution and reduced structural damage, achieving optimal stiffness demands. The calculated GIDS, DCFS, shear spectrum and the proposed stiffness demand objective function based on the distributed parameter model can serve as useful tools for preliminary elastic design of SC-RWMF structures.