Effects of Prior Earthquake Damage on Response of Simple Stiffness-Degrading Structures

A systematic study involving over 20,000 single-degree-of-freedom (SDOF) analyses was made to assess the effects of prior earthquake damage on the peak displacement response of simple oscillators. Principal variables were oscillator strength, period of vibration, degree of prior damage, and load-deformation relation. Base input was provided by 18 recorded ground motions, representing different frequency content, duration, and the presence or absence of near-field forward directivity effects. Prior damage was modeled as a reduction in initial stiffness under the assumption that residual displacements are negligible. The study is restricted to cases in which prior demands are less than those that would result if the structure were initially undamaged. For these conditions, prior damage usually has a minor effect on peak displacement response. This was observed for SDOF oscillators having the Takeda load-deformation relation with positive post-yield stiffness and for a modified Takeda relation incorporating pinched hysteresis and strength degradation. Takeda oscillators with negative post-yield stiffness were prone to collapse, whether or not they had experienced prior damage.