Damping-Ductility Relationships for Flag-Shaped Hysteresis
Publication: Journal of Structural Engineering
Volume 147, Issue 7
Abstract
Damping-ductility relationships, as applied in direct displacement-based design (DDBD), are products of equivalent linearization techniques used to estimate the nonlinear response of structures. Currently, suitable relationships are lacking for an increasingly wide range of flag-shaped hysteresis that is possible in practice. This paper seeks to fill that gap. Two commonly used numerical procedures are shown to be equivalent in terms of the equivalent viscous damping ratio (EVDR) produced. From approximately 1 million damping-ductility datapoints, an expression for the EVDR is proposed for flag-shapes defined by four parameters: the fundamental period, loading-to-initial stiffness ratio, unloading-to-loading stiffness ratio, and ductility. Compared to Jacobsen’s curves, the EVDRs obtained are more sensitive to the first two parameters, and this is reflected in the proposed expression. As Jacobsen’s EVDR assumes resonant conditions, the period-dependency is ignored and potentially underestimates the EVDRs for short periods (and vice-versa). A DDBD example demonstrates the design of a flag-shaped hysteresis using the proposed expression. The results of this study offer a flexible damping-ductility formula for the displacement-based design of self-centering seismically resilient structures.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors would like to acknowledge the Centre for eResearch at the University of Auckland which provided the computing resources for this study. This work was also financially supported by the University of Auckland via a doctoral scholarship.
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Journal of Structural Engineering
Volume 147 • Issue 7 • July 2021
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© 2021 American Society of Civil Engineers.
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Received: Sep 1, 2020
Accepted: Feb 22, 2021
Published online: Apr 27, 2021
Published in print: Jul 1, 2021
Discussion open until: Sep 27, 2021
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