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, Δ p , and equivalent deformation cycles, N c , 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 Δ p and N c . 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 Δ p 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 Δ p . The largest N c occurred for r = 0.9, β = 0.1, R = 8, and T / D = 0.014. Conservative equations were proposed for Δ p considering β , R , and T / D with r = 0.0, giving a coefficient of determination R 2 of 0.89. For N c , using r = 0.3 as a practical upper‐bound representative of common structures, conservative equations were proposed with R 2 of 0.91. The mean Δ p 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.