Unreinforced masonry structures, particularly façade walls, are seismically vulnerable due to their weak connections with adjacent walls, floors, and/or roofs. During an earthquake, such walls formulate local mechanisms prone to out-of-plane collapse. This behavior has been largely investigated using classical rocking theory, which assumes the structure responds as a rigid body undergoing rocking motion, with energy dissipation at impact. Due to the complexity of the problem, however, e.g., number of degrees of freedom or boundary conditions, numerical block-based modeling is gaining momentum. However, numerical models lack a consistent and reliable treatment of the energy loss at impact. This paper bridges the gap between the well-established energy loss of classical rocking theory and the treatment of damping in numerical modeling. Specifically, it proposes an equivalent viscous damping model through novel ready-to-use predictive equations that capture the dissipative phenomena during both one-sided and two-sided planar rocking motion. The results reveal a satisfactory performance of the proposed model through comparisons with experimental results from literature and highlight its universality and robustness through applications of the model in fundamentally different block-based numerical modeling software.

This paper investigates, analytically and numerically, the seismic performance of a rocking frame which exhibits flag-shaped hysteretic behavior. The present study establishes the equation of motion for the hybrid rocking frame and examines its seismic behavior under both pulse-type and historic ground motions. Throughout this work, the deformation of the structural members and the sliding between the contacting bodies are ignored. The study introduces the dimensionless design parameters which control the flag-shaped hysteresis loop and reveals their influence on the seismic performance of the hybrid rocking frame. The analysis unveils that prestressing the tendons could be beneficial mostly for small rocking rotations. For large rocking rotations, however, the prestressing force becomes progressively detrimental as the size of the columns increases. The analysis compares hybrid rocking frames with negative, zero, or positive post-uplift lateral stiffness. The results reveal that increasing the stiffness of the frame does not necessarily lead to superior performance. Finally, the seismic performance of the examined rocking frames is sensitive to the characteristics of a ground motion; consequently, the hybrid rocking frame could outperform the freestanding or the opposite.