Optimization of seismic response of steel structure using negative stiffness damper
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Abstract
Earthquakes of greater magnitude can cause stark destruction. Seismic protection of structures is one important tool to minimize damages and total collapse of structures. Researchers have made many attempts to achieve this goal with various techniques and one such strategy of seismic response control developed is introducing true negative stiffness in the structure. True negative stiffness is introduced with the help of negative stiffness damper (NSD). The NSD generates force in the direction of the displacement and hence it is called negative stiffness. The present study focuses on modelling NSD device in a commercial software tool (ETABS 2016). Further the device is implemented on 2D steel frame models and seismic parameters such as base shear, storey displacement and top storey acceleration are studied.
Keywords
Negative stiffness damper Seismic response controlIntroduction
During last two to three decades, the reduction of structural response caused by dynamic effects has become a subject of intensive research. Many structural control concepts have been evolved for this purpose, and quite a few of them have been implemented in practice. They include reduction of undesirable vibrational levels of flexible structures due to unexpected large environmental loads, retrofitting existing structures against environmental hazards, protecting seismic equipment and important secondary systems and provision of new concepts of design of structures against environmental loading. These structural control systems can be broadly classified into active control, passive control, semiactive control and hybrid control systems. An alternative approach is to “simulate yielding” by introducing true negative stiffness at prescribed displacement leading to the concept of “apparent weakening”. This is achieved with negative stiffness devices (NSD).
Based on the literature review implementation of NSD device analytically on 2D and 3D models using software tools is ongoing work. Attempts to do the same are on at present. The proposed work will focus on implementing the device on 2D and 3D steel frames using software tools and the same will be studied for different time history loadings. The main aim of the present research is to study the seismic response of steel structure with NSD using ETABS 2016. In the proposed work analytical model of NSD is studied and modeled in ETABS 2016 Software. The NSD is implemented on 2D and 3D steel frames and its effects on the seismic response are studied for three earthquake ground motions viz, Corralit, Holliste and Sylmar. Based upon the reduction in three parameters viz, base shear, storey acceleration and storey displacement the optimal placement of NSD will be decided. However, the same can be used in RCC structures by introducing ANSS but the scope of this work is limited to application on steel structure.
Analytical model of NSD
Analysis of the NSD requires consideration of kinematics and equilibrium of forces in the deformed configuration. Consider the free body diagram of the pivot plate shown in Fig. 2. The forces acting on the pivot plate (FB, FC and Fs) are shown. The figure also shows the GSA force F_{g} which does not act on the pivot plate.
Nominal NSD properties (Pasala et al. 2013)
Quantity  Symbol  Value  Units 

Length BC of pivot plate  l _{1}  25.4  cm 
Length CD of pivot plate  l _{2}  12.7  cm 
NSD spring length  l _{p}  76.2  cm 
NSD spring stiffness  K _{s}  1.4  kN/cm 
NSD spring preload  P _{in}  16.5  kN 
Double hinged column height  h  124.5  cm 
Lever length  l _{lv}  67.3  cm 
NSD engagement displacement  u′_{y}  1.65  cm 
GSA spring S1 stiffness  k _{s1}  4.9  kN/cm 
GSA spring S2 stiffness  k _{s2}  0.3  kN/cm 
GSA spring S2 preload  P _{is2}  8.1  kN 
Negative stiffness device (link element) in ETABS 2016
Properties of NSD used in the force–displacement expression (Gisha et al. 2015)
Parameter  Value 

Distance from spring to fixed pin (l_{1})  0.5842 m 
Distance from lever pin to fixed pin (l_{2})  0.2921 m 
Spring length (l_{s})  1.7526 m 
Gap opening (d_{gap})  0.01651 m 
GSA stiffness for spring 1 k_{g1}  1050.72 kN 
GSA stiffness for spring 2 k_{g2}  28.02 kN 
The initial precompression force in the spring P_{in}  95 kN 
Analytical study
To analyse G + 4 storey 2D steel frame and G + 3 storey 3D steel building under time history analysis in ETABS 2016 for studying the effectiveness of NSD and comparison between seismic response reduction in the form of base shear, storey displacements and top storey acceleration. A G + 4 story 2D steel frame fixed at supports, having a bay width of 5 m (Xdirection) and story height of 3 m is taken up for study. Beam ISMB 200 and column ISMB 225 with steel grade Fe345. The design considerations used are live load5 kN/m, Selfweight is explicitly captured using steel density of value Fe345 grade steel in ETABS 2016, design codeIS1893 (part 1): 2016, special moment resisting frame, importance factor—1 and seismic zone—zoneIII, model considered are as follows.
The study is further extended by converting 2D model in 3D model which is of steel frame having beam ISMB 200 and column ISMB 225 with steel grade Fe345, frames are 5 m in X and Ydirection and storey height is kept same as 3 m in Zaxis, respectively. Slab is modelled as a thin membrane member of thickness 150 mm and a concrete grade of M20. The model is fixed at the base. The selfweight of the frame is explicitly captured using the steel density value for the material in ETABS 2016. Live load of 5 kN/m^{2} is applied directly on slab. Negative stiffness damper is implemented at different positions described below.
Model 7 is the 3D frame of column ISMB 225 and beam ISMB 200 fixed at the base and it is considered as reference model without NSD. Model 8 is the 3D frame of column ISMB 225 and beam ISMB 200 fixed at the base and NSD applied at ground floor level for Bay 1, 2 and 3. Model 9 is the 3D frame of column ISMB 225 and beam ISMB 200 fixed at the base and NSD applied at first floor level for Bay 1, 2 and 3. Model 10 is the 3D frame of column ISMB 225 and beam ISMB 200 fixed at the base and NSD applied at second floor level for Bay 1, 2 and 3. Model 11 is the 3D frame of column ISMB 225 and beam ISMB 200 fixed at the base and NSD applied at third floor level for Bay 1, 2 and 3.
Results and discussions
Conclusions

Negative stiffness damper helps to reduce the base shear and storey acceleration of 2D and 3D frames, respectively, from the results compared with models without NSD for all the three considered earthquake load history.

Optimal position of NSD is decided based upon two seismic parameters namely base shear and storey acceleration.

Based on the present study optimal location obtained of 2D model for Corralit earthquake time history is ground floor of Bay 2, Holliste earthquake time history is first floor of Bay 2 and Sylmar earthquake time history is third floor of Bay 1 or Bay 3, respectively.

Based on the present study optimal location of 3D model for Corralit, Holliste and Sylmar earthquake time history is ground floor of Bay 1 or Bay 3.

Results reveal that different NSD has to be modelled for different structures and for different locations of installation to obtain the best reduction in seismic response.

Overall result shows that NSD increases the displacement at the level of installation of the device due to apparent weakening introduced by NSD. However, it can be controlled by using any passive damper in parallel with NSD.
Notes
References
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