Dynamic behavior of upgraded rocking wall-moment frames using an extended coupled-two-beam model

Rocking wall-moment frames (RWMFs), which perform well in controlling the soft-story mechanism, can achieve an enhanced performance by substituting their pinned base by a variable base rotational constraint provided by replaceable self-centering and energy dissipation devices. Rather than experiencing damage inside the moment frames, those upgraded RWMFs show a high potential towards seismic resilience by transferring damage to the replaceable base rotational constraint. The effect of this rotational constraint and the stiffness ratio between the moment frame and rocking wall on the dynamic behavior of upgraded RWMFs is investigated with the aid of an extended coupled-two-beam model proposed in this paper. In this model, the rocking wall and moment frame are represented by a linked flexural beam and a shear beam, respectively. The model replaces the fixed base of the flexural beam by a rotational spring to take the variable base rotational constraint into account. Closed-form solutions for modal displacement shapes, modal drifts, modal shear force and modal moment are derived. The model is verified with finite element analysis, and modal contributions to seismic response and drift concentration factor demand under earthquakes are investigated. It is found that within identified ranges of the rotational constraint and the stiffness ratio between the moment frame and rocking wall, a relatively good uniformity of story drift distribution is obtained and the higher modes effect caused by the full releasing of the rocking wall is mitigated. The model, the derived interstory drift spectra and drift concentration factor spectra can serve as useful tools for preliminary resilience oriented design purpose.