# Low-Cycled Hysteresis Characteristics of Circular Hollow Steel Damper Subjected to Inelastic Behavior

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## Abstract

This study aims to evaluate hysteresis response behavior of circular hollow steel damper (CHSD). Steel dampers are a type of passive dampers and commonly used for seismic dissipation in civil engineering structures. Steel dampers are widely used for seismic energy dissipation because they are easy to install, maintain and they are also inexpensive. CHSD is among steel dampers which dissipates seismic energy through metallic deformation and geometrical elasticity of circular shape and fatigue resistance around welded connection to the end plates. Finite element analysis was conducted in order to evaluate the hysteresis characteristics and low cycle fatigue behavior of CHSD using failure index. To verify the analysis simulation quasi static loading was conducted and the result was compared and satisfactory result was obtained.

## Keywords

Hysteresis characteristics Circular hollow steel damper Aspect ratio Quasi-static loading Large deformation FE analysis## 1 Introduction

## 2 Non-linear Finite Element Analysis

_{tr}: true stress, σ

_{e}: engineering stress, ε

_{tr}: true strain, ε

_{e}: engineering strain. The true yield stress, ultimate stress and strain of a specimen taken from CHSD having thickness 3.2 mm and flattened are 321 MPa, 511 MPa and 22.38% respectively.

## 3 Constraint and Loading Condition

The boundary conditions are controlled at the reference points created at the center both end plates. All the translational and rotational displacement components are fixed at the reference points of the lower end plate. A cyclic load was given at upper end plate reference points in X-direction fixing all the translation and rotation in other direction. The boundary condition and method of loading adopted in the finite element analysis followed to have the specimen shear effect and the same as those used in the tests for verification. A constant strain loading is implemented in which the load is applied by controlling the displacement with the displacement protocol shown in Fig. 8.

## 4 Verification of Finite Element Analysis

### 4.1 Test Set-Up and Process

### 4.2 Comparison of Results

### 4.3 Low Cycle Fatigue Failure

_{p}(t) denote the equivalent plastic strain defined as:

_{p}(t). We use an extended version of the SMCS criterion that was developed for simulating ductile fracture of metals due to void growth. The critical plastic strain ε

_{cr}is first defined as:

_{m}is the mean stress, and σ

_{e}is the von Mises equivalent stress given by Eqs. (7) and (8), respectively. The parameter α is dependent on material. Equation (6) indicates that the critical plastic strain for ductile fracture depends on the stress triaxiality σ

_{m}/σ

_{e}. Then the failure index for monotonic loading is defined as in Eq. (9) (Oh et al. 2011).

_{f}reaches 1.0. The Eqs. (5) and (8) are based on the ductile fracture due to void growth under monotonic tensile deformation. However, we need the effect under cyclic loading, where the void shrinks due to compressive plastic loading. Therefore, the following formulation by Kanvinde and Deierlein is used (Chi et al. 2006; Mackenzie et al. 1977). The equivalent plastic strain ε

_{p}is divided into tensile plastic loading states ε

_{t}(> 0) and compressive plastic loading states ε

_{c}(> 0), which are identified by the sign of σ

_{m}. The significant plastic strain ε*, which represents the amount of void growth, is defined as (Ohsaki and Nakajima 2012):

^{cr}* for ε* is given as:

_{f}*, defined as follows, reaches 1.0:

### 4.4 Effect of Diameter-to-Thickness Ratio

In order to evaluate the effect of diameter-to-thickness ratio on low fatigue failure behavior of circular hollow section damper a using simple approaches called PEEQ Index. The PEEQ Index is given by the ratio of the plastic equivalent strain to the yield strain.

_{y}: yield strain which is given by the ratio of yield strength to young’s modulus (σ

_{y}/E) and the calculated yield strain is approximately 0.002. The equivalent plastic strain was measured around half circumference at middle of the specimen at each node starting from the direction of loading and longitudinally as shown in the section in Fig. 17. The calculated maximum equivalent plastic strain index (PEEQ Index) at each node around the circumference for the parametrical study of analysis specimens (diameter-to-thickness ratio) with the respect to circumference distance is presented in Fig. 18. The circumference distance is measured taking in the loading direction, form extreme compression to extreme tension under cyclic loading. The peak PEEQ Index presented in Fig. 18 are plotted with respect to D/t ratio as shown in Fig. 19. In the way, PEEQ Index measured and calculated at each nodes in longitudinal direction for all analysis specimens is presented in Fig. 20. The peak values PEEQ Index for each analysis specimens also plotted with respect to D/t ratio as shown in Fig. 21. The peak PEEQ Index values calculated in both half circumference and longitudinal direction plotted against D/t ratio forms S-shape curves, Figs. 19 and 21. The lowest PEEQ Indexes can be taken as effective section in CHSD. Thus, from Figs. 19 and 21, D/t ratio between 10 and 20 are the effective cross-section of CHSD.

## 5 Conclusion

The hysteresis and low fatigue failure behavior of circular hollow section steel damper was evaluated through non-linear finite element and the analysis is of course verified by quasi-static loading test and the following conclusion was drawn.

Depending on the diameter-to-thickness ration (D/t) the hysteresis response as well as the buckling mode of circular hollow section steel damper is different. It is found that, thin CHSD, D/t > 27.8, the hysteresis response forms pinching at initial displacement and severe out-of-plane buckling was also observed. As the thickness increase the hysteresis response became stable. The low cycle fatigue behavior is evaluated using failure index and PEEQ index. The failure index for CHS80 × 48.6 × 3.2 reaches 1 at 9.21th cycle where the cyclic load resisting strength started to degrade for both analysis and test results. The diameter-to-thickness parameter considered the PEEQ index in longitudinal and half the circumference. The minimum PEEQ index is found for D/t ratio between 10 and 20. This section can be taken as the effective section for circular hollow section damper.

## Notes

### Acknowledgements

This work was financially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2015-053557) and supported by research fund from Chosun University, 2016.

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