What question did this study set out to answer?

To estimate peak displacements and equivalent deformation cycles for structures exhibiting flag-shaped hysteresis loops under seismic ground motions and to establish predictive empirical equations.

September 17, 2026Earthquake Engineering & Structural DynamicsOpen Access

Displacement Estimation of Structures With Flag‐Shaped Hysteresis Loops

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Authors

YZYudi Zhang GMGregory A. MacRae GRGeoffrey W. Rodgers

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Overview

Computational analysis reveals peak and cumulative seismic displacement demands in self-centering structures, suggesting conventional design methods may underestimate peak drift.

Key Points

To estimate peak displacements and equivalent deformation cycles for structures exhibiting flag-shaped hysteresis loops under seismic ground motions and to establish predictive empirical equations.
Conducted nonlinear time-history analyses on single-degree-of-freedom systems under a far-field ground motion suite.
Systematically varied energy dissipation parameters (beta = 0.1 to 1), strength-reduction factors (R = 2 to 8), post-yield stiffness ratios (r = 0 to 0.9), periods (T = 0.2 s to 3.5 s), and period-to-duration ratios (T/D = 0.014 to 0.25).
Validated proposed empirical equations against the numerical dynamic response of a three-story rocking structure fitted with tension-only friction dissipators.
Substituting structural period with the period-to-duration ratio (T/D) improved peak displacement predictability in short-period structures, while low-dissipation, highly non-linear models (beta = 0.1, r = 0.0, R = 8, T/D = 0.014) exhibited the greatest peak demands.
Conservative empirical predictive equations were developed for mean peak displacement with r = 0.0 (R^2 = 0.89) and for equivalent deformation cycles with r = 0.3 (R^2 = 0.91).
Predictions derived from single-degree-of-freedom equations conservatively matched the mean peak and cumulative displacements observed in the three-story rocking structure.

Cite This Study

Zhang et al. (2026) studied this question.

synapsesocial.com/papers/6aabb6c75f706d05830e5682 https://doi.org/10.1002/eqe.70294

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September 17, 2026Earthquake Engineering & Structural DynamicsOpen Access

Displacement Estimation of Structures With Flag‐Shaped Hysteresis Loops

View Full Paper

Ask AI

Bookmark

Authors

YZYudi Zhang GMGregory A. MacRae GRGeoffrey W. Rodgers

Discussion

Member takes

Overview

Computational analysis reveals peak and cumulative seismic displacement demands in self-centering structures, suggesting conventional design methods may underestimate peak drift.

Key Points

To estimate peak displacements and equivalent deformation cycles for structures exhibiting flag-shaped hysteresis loops under seismic ground motions and to establish predictive empirical equations.
Conducted nonlinear time-history analyses on single-degree-of-freedom systems under a far-field ground motion suite.
Systematically varied energy dissipation parameters (beta = 0.1 to 1), strength-reduction factors (R = 2 to 8), post-yield stiffness ratios (r = 0 to 0.9), periods (T = 0.2 s to 3.5 s), and period-to-duration ratios (T/D = 0.014 to 0.25).
Validated proposed empirical equations against the numerical dynamic response of a three-story rocking structure fitted with tension-only friction dissipators.
Substituting structural period with the period-to-duration ratio (T/D) improved peak displacement predictability in short-period structures, while low-dissipation, highly non-linear models (beta = 0.1, r = 0.0, R = 8, T/D = 0.014) exhibited the greatest peak demands.
Conservative empirical predictive equations were developed for mean peak displacement with r = 0.0 (R^2 = 0.89) and for equivalent deformation cycles with r = 0.3 (R^2 = 0.91).
Predictions derived from single-degree-of-freedom equations conservatively matched the mean peak and cumulative displacements observed in the three-story rocking structure.

Cite This Study

Zhang et al. (2026) studied this question.

synapsesocial.com/papers/6aabb6c75f706d05830e5682 https://doi.org/10.1002/eqe.70294

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