Seismic Analysis of High-Rise Building using Negative Stiffness Device

Abstract

Natural hazard mitigation is one of the most important issues facing civil engineers today. In structural engineering, one of the constant challenges is to find new and better means of protecting existing and new civil structures from the damaging effects of destructive environmental forces, such as wind, waves and earthquakes. Earthquakes are considered the most destructive environmental forces for civil engineering structures. Seismic forces and displacements in existing structures can be effectively reduced in an approach where the structure is intentionally weakened (stiffness and strength are reduced) and damping is added. However, the approach also results in inelastic excursions and permanent deformation of the structural system during a seismic event. A new concept previously proposed by the authors simulates apparent weakening by incorporating a mechanical system that produces true negative stiffness in the structural system. In doing so, inelastic excursions and permanent deformations may be substantially reduced or eliminated. True negative sti?ness means that the force must assist motion, not oppose it as in the case of a positive sti?ness spring. A passive device capable of exhibiting true negative sti?ness, negative sti?ness device (NSD), without external power supply is studied in this project work. A pre-compressed spring is used to generate the force to push the structure and a lever-mechanism is adapted to amplify the generated force. In the present approach an attempt has been made to study an inelastic multistoried RCC building to demonstrate the e?ectiveness of placing NSDs at multiple locations along the height of the building; referred to as “Distributed Isolation” and also by placing NSD’s at base of the building; referred to as “Base Isolation”. By performing nonlinear dynamic analysis, the different parameters which will act as a measure of seismic performance of RCC building such as Base Shear, Top Acceleration, Top Displacement and Column Force are studied.

Introduction

I. INTRODUCTION

A. Negative Stiffness Device

True negative sti?ness means that the force must assist motion, not oppose it as in the case of a positive sti?ness spring. True negative stiffness needs no external power supply. A pre-compressed spring is used to generate the force to push the structure and a lever-mechanism is adapted to amplify the generated force. The reason that this technology has been restricted to small mass applications is the large forces required to develop the necessary negative stiffness. These preload forces are typically on the order of the weight of the isolated structure. The application of negative-stiffness concept to massive structures, such as buildings and bridges, requires modi?cation of the existing mechanisms to reduce the demand for preload force and to package the negative stiffness device in a system that does not impose any additional loads on the structure, other than those needed for achieving the goal of seismic protection.

These requirements lead to the development of the true negative system device (NSD), which has the following components and characteristics:

1) A highly compressed machined spring (CS) that develops the force in the direction of motion (thus, negative stiffness); the magnitude of the force reduces with increasing displacement so that stability of the system is ensured at large displacements;

2) A double chevron self-containing system to resist the preload in the compressed spring and also to prevent the transfer of the vertical component of the preload to the structure;

3) A double negative stiffness magni?cation mechanism that substantially reduces the requirement for preload so that a practical system is achieved;

B. Operation of NSD

The NSD shown in Figure 1.4 is composed of a pre-compressed spring shown in the center of the device as well as the gap spring assemblies on the bottom. A combination of frame elements and plates hold these pieces together. When the device deforms, the pre-compressed spring is the one that creates the force that assists the motion or the negative force and thus the name negative stiffness for the device. The bottom spring assemblies (gap spring assembly mechanism) provide the device inherently with a bilinear elastic positive stiffness in order to make the device engage at larger displacements More specifically, around equilibrium, the positive stiffness caused by the gap spring assembly mechanism, cancels out the negative stiffness caused by the pre-compressed spring so that essentially the force/stiffness generated by the device is close to zero. After a prescribed displacement, the gap spring assembly softens drastically so that the pre-compressed spring acts essentially on its own creating the negative stiffness.

It is noted that the operation of the gap spring assembly is achieved without any yielding so that there is no inherent permanent deformation in the device.

The NSD should be bolted to the bottom of ?oor and the top of NSD is connected to the ceiling of the ?oor using an end-angle assembly that will transfer only the horizontal forces. Any interstory structural deformation will result in the deformation of the top channel, Top chevron (CB2) and the lever-arm. Since the lever-arm is connected to the pivot plate (point-B) and the pivot plate is ?xed at point-C, any deformation of point-B will result in rotation of pivot-plate about point-C. As a result, point-D will displace in the opposite direction to that of point-B. Also, the bottom of CS is connected to Top chevron (CB2), so, point-E will undergo same deformation as point-B. The total lateral deformation of the CS is magni?ed by comparison to the displacement of point A,

(a) by the ratio CD to BC and

(b) due to the movement of point E in the opposite direction to D.

Essentially, any deformation at the top of NSD will result in the horizontal deformation of CS both at the top and bottom; this is the dual ampli?cation.

C. Advantages of NSD

1. The device changes the apparent global lateral stiffness of the structure, without changing the actual stiffness of the structure. The apparent stiffness is reduced to a very low-level simulating global lateral yielding without actual yielding in the main structure.
2. The device produces true horizontal negative stiffness by passively generating a force that assists the imposed displacement. No external power supply is needed since all the elements comprising the device are passive.
3. The device is self-contained and therefore when installed affects only the horizontal stiffness of the system while leaving the vertical stiffness intact. Stability and buckling limits of the structure are not affected. The NSD does not participate in transferring the vertical loads.
4. There is no significant hysteresis in the device. The NSD is essentially elastic.
5. The device provides variable stiffness which becomes positive at large deformations; therefore, its global behavior is “elastic nonlinear”. This is a desired feature as it promotes stability.
6. The device employs a double magnification mechanism that allows for easy adjustment of the negative stiffness value. The gap spring assembly (GSA) mechanism allows for adjustable gap opening.

D. Mathematical Formulation of NSD

In order to derive the force displacement equations of the device, by considering equilibrium of Negative Stiffness Damper following relationships are obtained by Nagarajaiah et al.

II. RESEARCH AIM AND OBJECTIVE

A. Aim

The aim of the research is to study the role of structural control system to enhance the overall structural performance under seismic excitation. The present work is focused to study and find the different parameters viz., Base Shear, Roof Displacement, Roof Acceleration, and Column Force which are acting as a measure of seismic performance of RCC moment resisting framed structure using Negative Stiffness Device as Base Isolation and Distributed Isolation.

B. Objectives

1. To model the NSD in SAP2000.
2. To study and compare the position of NSD as Base Isolation and Distributed Isolation.
3. To study the effect of previous ground acceleration on response of structure.
4. To study the behavior of the building by changing height of structure under different earthquakes.
5. To study and compare the parameters such as Base Shear, Roof Displacement, Roof Acceleration and Column Force.

III. PROBLEM STATEMENT

From the literature survey it is observed that negative stiffness device is very advantageous for control of the structures in the event of an earthquake. But until now NSD has been used for bridge structures and base isolated structures only. In the present study Negative Stiffness Device is used for reducing the effects of an earthquake in High Rise RCC buildings by using at various floors.

The present study has investigated the response of three multi story RCC buildings viz., G+10, G+15 and G+20 storey RCC building. All the Multi Storey RCC structures are analyzed for 5 bays, each in X and Y direction with bay width 3m. All the models are analyzed for a constant storey height of 3.5m. Also, all the models are analyzed for two combinations such as with and without the application of NSD+GSA under the action of four real time histories viz., Imperial Valley (El Centro) (1940), Bhuj (India) (2001), Uttarkashi (India) (1991), Dharmshala (India) (1986). The RCC model in SAP2000 v21 is analyzed for the parameters such as base shear, roof acceleration, roof displacement and column force under all considered earthquakes.

IV. METHODOLOGY

In the first phase of the study a Negative Stiffness Device is first modeled in SAP2000 and G+10 RCC building is analyzed and validated with results available in the considered paper.

In the second phase of the study the RCC multi storey G+10, G+15 and G+20 structures are modeled and analyzed for all the combinations mentioned above under all the considered earthquakes. For all the structures considered in the study Negative stiffness device is applied in the 1st, 3rd and 5th bay along X direction and in all the frames along Y direction at first floor level in base isolated structure as shown in fig. 3.1. and for distributed isolation NSD’s are placed at alternate floors in two ways as Core Isolation and External Isolation as shown in fig. 3.2 and fig. 3.3. The RCC Building is designed as per I.S. 456:2000 and the loads are applied as per IS: 875.

C. Discussion on Summary of Result

1. Base isolation is effective in reducing base shear as compared to distributed isolation in a seismic analysis because base isolation allows the building to move relative to the ground and effectively reducing the amount of seismic energy transmitted to the structure thus reducing the maximum base shear. Base isolation reduces maximum base shear by decoupling the building from the ground motion and absorbing the seismic energy.
2. Roof acceleration in a base isolated structure is reduced because in that, NSD serve to decouple the building's structure from the ground motion. During an earthquake, the isolation devices absorb and dissipate a significant portion of the seismic energy, reducing the amount of energy that is transmitted to the building's structure. This reduction in seismic energy results in a lower roof acceleration.
3. External isolation reduces the maximum displacement as compared to core isolation in a seismic analysis because external isolation provides a larger area for energy dissipation and reducing the displacement of the structure.
4. External isolation reduces the maximum column force as compared to core isolation in a seismic analysis because external isolation provides a larger area for energy dissipation and reduces lateral load due to earthquake and ultimately reducing the forces on the columns. Also, external isolation can reduce the deformations of the structure during seismic events, leading to reduced column forces.

Conclusion

1) The value of base shear for particular height of building depends on earthquakes PGA and period of structure. In case of base isolated structure base shear value decrease because base isolation allows the building to move relative to the ground and effectively reducing the amount of seismic energy transmitted to the structure and reducing the maximum base shear. The value of base shear decreases by maximum 9.85% for G+20 structure subjected to Dharmshala earthquake. In case of distributed isolation value of base shear increases continuously as the height of structure is increased. For Base shear reduction, base isolation has observed to be effective for all three structures. 2) Value of roof acceleration for particular height of building changes with different type of earthquake because the value of peak ground acceleration is different for different earthquake. Roof acceleration is seen maximum (2.63 m/s2) for Dharmshala earthquake for which PGA value is maximum (1.42 m/s2) and roof acceleration is minimum (0.32 m/s2) for Bhuj earthquake for which PGA value is minimum (0.21 m/s2). So, we can say that earthquake having maximum PGA causes higher roof acceleration. 3) Value of roof displacement for particular height of building changes with different type of earthquake. Roof displacement is seen maximum (58.846 mm) for Dharmshala earthquake for which PGA value is maximum and is minimum (4.48 mm) for Bhuj for which PGA value is minimum. So, the earthquake having maximum PGA causes higher roof displacement. With increase in height, value of roof displacement increases for all earthquakes because as we go for higher storey height due to lateral excitation value of roof displacement increases. 4) The value of column force is maximum (1133.057 kN) for Dharmshala earthquake which is having maximum PGA and for Bhuj earthquake is minimum (418.331 kN) for same height of building and for different height it increases as storey height increases because of self-weight, loading on structure and lateral excitation due to earthquake. 5) For Base shear reduction, base isolation has observed to be effective for all three structures. 6) For distributed isolation structure value of roof acceleration continuously increases with increase in storey height for all considered earthquakes. 7) For base isolated structure as height of structure increases % reduction in roof displacement decreases, so it is less effective for reducing roof displacement of high-rise structure. In case of distributed isolation % reduction in roof displacement increases as storey height increases so, as compared to base isolation; distributed isolation is very much effective in reducing top story displacement. 8) For base isolated structure column force on considered column increases as height of structure increases for all considered earthquakes and in case of core isolation for G+10 and G+15 its value increases but thereafter for G+20 it gets decreased. For external isolation, force on column decreases continuously as height of structure is increased because of NSD’s position for that case is around periphery of structure which helps in reducing vibrations effectively and ultimately reduces column force.

References

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Copyright

Copyright © 2023 Shubham Waghchaure, Dr. Manisha Waghmare. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.