Displacement Estimation of Structures With Flag-shaped Hysteresis Loops

Time-history analyses were conducted on single-degree-of-freedom (SDOF) systems with flag-shaped hysteresis loops using a far-field ground motion suite to estimate peak displacements, Δₚ, and equivalent deformation cycles, Nc, associated with cumulative displacement demands. The varied parameters included loop dissipation parameters β (0.1 to 1), strength-reduction factors R (2 to 8), positive post-yield stiffness ratios r (0 to 0.9), structural periods T (0.2 s to 3.5 s), period-to-earthquake-record-duration ratios T/D (0.014 to 0.25), and viscous damping models. Empirical equations were proposed for the mean Δₚ and Nc. A comparison was made with responses of a three-storey rocking structure with tension-only friction dissipators (TOFDs). Using T/D instead of T improved displacement predictability for short-period structures and gave similar accuracy for longer-period structures. The greatest Δₚ occurred in low-dissipation structures with β = 0.1, r = 0.0, R = 8, and T/D = 0.014. Conventional displacement estimation methods may underpredict Δₚ. The largest Nc occurred for r = 0.9, β = 0.1, R = 8, and T/D = 0.014. Conservative equations were proposed for Δₚ considering β, R, and T/D with r = 0.0, giving a coefficient of determination R² of 0.89. For Nc, using r = 0.3 as a practical upper-bound representative of common structures, conservative equations were proposed with R² of 0.91. The mean Δₚ and cumulative TOFD displacement of the rocking structure subjected to the ground motion suite were similar to those from SDOF systems with matching β, R, r, and T. The empirical equations provided conservative predictions for the rocking-structure responses.