The secant stiffness method is applied to the equivalent linearization of nonlinear system. Two types of hysteretic models and a set of 72 ground motions were considered. A new type of flag-shape hysteretic model was introduced which would be compared with the benchmark model.
The two hysteretic models which were used in the analyses were calibrated by the experimental data results to get a set of parameter α, β, and γ. The nonlinear behaviors of the two models were evaluated with Jacobsen’s equivalent damping approach which also adopted the secant stiffness method for the linearization process. The evaluation revealed that Jacobsen’s approach overestimated damping in long period range on other hand underestimated damping in short period range. Two equations to modify the area-based viscous damping by Jacobsen’s approach for each type of hysteretic model were proposed. The two hysteretic models have also been verified by comparing the pseudo-dynamics loading result with the analyses result.

The secant stiffness method is applied to the equivalent linearization of nonlinear system. Two types of hysteretic models and a set of 72 ground motions were considered. A new type of flag-shape hysteretic model was introduced which would be compared with the benchmark model.
The two hysteretic models which were used in the analyses were calibrated by the experimental data results to get a set of parameter α, β, and γ. The nonlinear behaviors of the two models were evaluated with Jacobsen’s equivalent damping approach which also adopted the secant stiffness method for the linearization process. The evaluation revealed that Jacobsen’s approach overestimated damping in long period range on other hand underestimated damping in short period range. Two equations to modify the area-based viscous damping by Jacobsen’s approach for each type of hysteretic model were proposed. The two hysteretic models have also been verified by comparing the pseudo-dynamics loading result with the analyses result.

ABSTRACT
ACKNOWLEDGEMENT
TABLE OF CONTENT
LIST OF FIGURES
LIST OF TABLES
INTRODUCTION AND SCOPE OF RESEARCH
1.1 Introduction
1.2 Research Motivation
1.3 Scope of Research and Limitations
1.4 Thesis Overview
LITERATURE REVIEW
2.1 Concept of Segmental Column
2.2 The Hysteretic Model for Reinforced Concrete
2.3 Concept of Initial Stiffness and Secant Stiffness Based Method
2.3.1 Initial Stiffness Method
2.3.2 Secant Stiffness Method
2.4 Equation of Motion for Single-Degree-of-Freedom-Systems
2.5 Concept of Equivalent Viscous Damping
2.5.1 Hysteretic Damping
2.5.2 Elastic Damping
2.5.3 The Period Dependency
ANALYTICAL STUDY, RESULTS AND DISCUSSIONS
3.1 Modeling Detail
3.1.1 Stiffness-Degrading Self-Centering (SDSC) System and Modified Takeda (MT) System
3.1.2 Model Calibration for Parameter
3.1.3 Post-Yielding Stiffness Coefficient
3.1.4 Stiffness Degradation Coefficient
3.1.5 Energy Dissipation Bar Ratio
3.1.6 The Range of Parameter
3.2 Parametric Study
3.2.1 Parameter Information
3.2.2 Ground Motion Selection
3.2.3 Analyses
3.2.4 Actual Equivalent Viscous Damping
3.2.5 The Equivalent Viscous Damping Based On the Area-Based Viscous Damping
3.2.6 Result and Discussion
CONCLUSION AND SUGGESTION
4.1 Conclusion
4.2 Suggestion
REFERENCES

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