Strength reduction factor spectra for SDOF systems with structural fuses

Highly ductile replaceable fuses can greatly improve the performance of structures and mitigate seismic damage. A fused structure refers to a dual system that generally includes the primary structural system and the fuses acting in parallel. Few studies have thoroughly investigated the strength reduction factors of dual systems or their nonlinear response behaviors; instead, a restoring force model was adopted to represent the performance of the whole system while ignoring the interactions between the primary structure and fuses. This paper separates the two components and considers their interaction. The behavior of the primary structure and structural fuses is assumed to be similar to elastic-perfect plastic. Two parameters, the yield displacement ratio (alpha) and the initial stiffness ratio (beta), are introduced to describe the relationship between the fuses and the primary structure. Based on a dual system, the dimensionless governing equation of motion is derived. The strength reduction factor spectra with a known displacement ductility factor (mu) are then calculated under two groups of selected ground motions. The influences of alpha, beta, and mu are investigated statistically. The strength reduction factor spectra of the fused structure can be expressed by the four-stage predictive model developed by Newmark and Hall for traditional structures, but the spectral shape and two plateau values are closely related to alpha, beta, and mu. These two plateaus are crucial for the spectral shape of the four-stage model. Finally, a simplified equation is proposed to estimate the strength reduction factors of dual system considering alpha and beta with equivalent mu.