Seismic Response of Yielding Structures Coupled to Rocking Walls with Supplemental Damping

Given that the coupling of a framing structure to a strong, rocking wall enforces a first-mode response, this paper investigates the dynamic response of a yielding single-degree-of-freedom oscillator coupled to a rocking wall with supplemental damping (hysteretic or linear viscous) along its sides. The full nonlinear equations of motion are derived, and the study presents an earthquake response analysis in term of inelastic spectra. The study shows that for structures with preyielding period T1<1.0 s the effect of supplemental damping along the sides of the rocking wall is marginal even when large values of damping are used. The study uncovers that occasionally the damped response matches or exceeds the undamped response; however, when this happens, the exceedance is marginal. The paper concludes that for yielding structures with strength less than 10% of their weight the use of supplemental damping along the sides of a rocking wall coupled to a yielding structure is not recommended. The paper shows that supplemental damping along the sides of the rocking wall may have some limited beneficial effects for structures with longer preyielding periods (say T1>1.0 s). Nevertheless, no notable further response reduction is observed when larger values of hysteretic or viscous damping are used.