Study on the Effect of Geometry and Configuration on the Seismic Performance of Base Isolator

Study on the Effect of Geometry and Configuration on the Seismic Performance of Base Isolator

Rambha K R1

1Student,

Department of Civil Engineering, Mar Athanasius College of Engineering,

Kothamangalam

Alice T V2

2Professor,

Department of Civil Engineering, Mar Athanasius College of Engineering,

Kothamangalam

Abstract – Earthquake results in destructive shaking in most of the cases. The seismic isolation method is generally preferred over traditional methods which rely mainly on strengthening of structural elements. Laminated rubber bearings are most common among the various base isolators. The performance of the base isolator depends on the shear stiffness of the bearing. Geometry of the isolator is studied by choosing three geometries with different shape factors but same base area. The finite element software ANSYS was used to model the circular, square and rectangular models and subjected to non linear static analysis. The results revealed that the circular bearing gives the best performance and it can be sheared to the maximum compared to the other geometries.

Index Terms:- Laminated rubber bearing . Isolator, Shape Factor

1. INTRODUCTION

   Base isolation plays an important role in seismic protection of structures. It is a collection of structural elements which should substantially decouple superstructure from its substructure resting on a shaking ground. The technique was developed to prevent or minimize damage to buildings during an earthquake by reducing seismic stresses in an effective way. Thus the integrity of the structure is protected. Base isolation is widely accepted as one of the most powerful tools of earthquake engineering pertaining to the passive structural vibration control technologies.

   Currently this technique is limited only to large, expensive buildings, sensitive instruments and hospitals. In developing countries like India even it is rare. This is because the isolation increases the overall expense for a structure. In order to make base isolation a viable method for all the cases, it is necessary to reduce the cost of the isolator. Conventionally steel and rubber are used in base isolation. Hence it is important to adopt an optimum configuration and geometry to achieve the required performance using the same materials. The study is required to find the best way to use the available materials for effective seismic isolation. The parametric study of the best geometry gives the effective use of the available materials in a base isolator.

2. GEOMETRY AND SHAPE FACTOR

   Deformation varies with the shape factor and hence the geometry of the rubber bearing. The geometry is defined by the number of layers of rubber and steel and thickness of each layers.The behavior of the rubber bearing is affected by the loaded area and hence the shape factor. A linear elastic theory is the most common method to predict the compression stiffness of a thin elastomeric pad. When the vertical load is applied the height of the rubber decreases and in the meantime the rubber overflows on the lateral part of the isolator.

   In the present study three models square, circular and rectangular bearings are considered with shape factors as follows.

   TABLE1. SHAPE FACTORS OF ISOLATORS

   GEOMETRY	SHAPE FACTOR
   I. Square	3.66
   II. Circular	4.16
   III. Rectangular	3

   Fig.1 Fixed base and isolated base systems

   For the current study the following dimensions are chosen and the single laminate with single steel layer sandwiched between two rubber layers is studied. Then the full thickness is created by repeating the steps. For all the geometries the top area is kept equal but with different shape factors.

   TABLE2. DIMENSIONS OF ISOLATORS

   GEOMETRY	DIMENSION
   Diameter of circular bearing	250mm
   Size of square bearing	220mm
   Size of rectangular bearing	320mm
   Thickness of Rubber layer	2.5mm
   Thickness of Steel layer	1mm
   Number of layers	6

3. ANALYSIS MODEL

   The isolator models are generated using ANSYS 15 finite element software. Three geometries are modeled with fixity at the bottom. The rubber steel interface is modeled using contact and target elements.

   1. Material Property

      Normally 3-D finite element modeling is adopted to analyze the laminated rubber bearing. The hyper elastic material is characterized by the existence of strain energy function W, measured per unit volume of reference state, which is a function of deformation gradient.

      The following form (1)has been adopted :

      W = C10 (I1 3) + C01 (I2 3) + C20 (I1 3)² + C02 (I2 3)²

      + C11 (I1 3)(I2 3) (1)

   2. Modeling

      The rubber and steel volumes are created by extruding the area. The volume is then meshed using hexahedral mapped meshing.SOLID185 is used to model the rubber and steel layer. The nodes in the rubber layer were defined as contact using CONTACT174 and nodes in the steel were defined using TARGET170.

      Fig.2 Circular Isolator model

      Fig.3 Circular model with boundary conditions

      Fig.4 Square Isolator model

      Fig.5 Square model with boundary conditions

      Fig.6 Rectangular Isolator model

      Fig.7 Rectangular model with boundary conditions

4. ANALYSIS

   The behavior of isolators having same base area is studied under the action of both vertical and horizontal forces using non-linear static analysis.

   Each isolator was subjected to a vertical load of 50kN and horizontal shear force. The figures below depict the results obtained from the analysis.

   1. Results for Square bearing

   Fig.8 Deformed shape (Case I)

   Fig.9 Axial stress- sigma y (Case I)

   Fig.8 to Fig.16 shows the results from the analysis. The maximum axial stress is 0.77MPa for the circular bearing. For square model the maximum stress reaches the maximum permissible value which is 4.2 MPa.

   Fig.10 Shear stress- xz (Case I)

   1. Results for Circular bearing

      Fig.11 Deformed shape (Case II)

      Fig.12 Axial stress- sigma y (Case II)

      Fig.13 Shear stress- xz (Case II)

   2. Results for Rectangular bearing

   Fig.14 Displacement vector sum (Case III)

   Axial Stress (N/mm2)

   Fig.16 Horizontal displacement ,Ux (Case III)

   1.2

   1.0

   0.8

   0.6

   0.4

   0.2

   0.0

   0.0

   5.0 10.0 15.0 20.0

   Load (N)

   Fig.18 Stress V/s Displacement for Circular isolator

   0.0

   5.0

   10.0

   Load (N)

   -0.1

   -0.2

   -0.3

   -0.4

   0.1

   0.0

   Axial Stress (N/mm2)

   Fig.19 Axial stress V/s Load in Square isolator

   Fig.20 Axial stress V/s Load in Rectangular isolator

5. OBSERVATIONS

   • Among the three geometries considered in the study circular model takes the maximum shear upto 113% along with 100% vertical load

   • The maximum shear stress in the circular, square and rectangular model is 32 MPa, 1.15 MPa and X MPa respectively

   • Axial stress reaches the maximum permissible value

     4.2 MPa in the square model of isolator

   • Axial stress in the circular model was far below the permissible value and the model can take higher vertical loads until the stress reaches the maximum

   • The circular model gives the best performance among the various geometries considered in the study

   • The results shows that with same base area circular model take the maximum load compared to the square and rectangular bearings

   Rectangular bearing

   Square bearing

   Circular bearing

   0 5 10 15 20

   Circular bearing

   Square bearing

   Rectang ular bearing

   7. FUTURE SCOPE

   The isolators with different shape factors can be modeled in actual dimensions to study the behaviour under various forces.

   A building frame can be modeled along with the isolators and the one which gives best performance can be studied.

   REFFERENCES

   1. Simon Petrovi, David Koren and Vojko Kilar, Applicability of base isolation made ofelastomeric isolators for the protection of cultural heritage , Urbani izziv / Urban Challenge, volume 20, no. 1, 2009

   2. R.G Taylor, Rubber bearings in base-Isolated structures- A summary paper, Bulletin of the New Zealand national society for earthquake engineering, Vol.24,No. 3, September 1991

      Horizontal Displacemnt (mm)

      Axial Stress (N/mm2)

      Fig.17 Comparison of Horizontal displacement among three geometries

      1.2E+0

      1.0E+0

      8.0E-1

      6.0E-1

      4.0E-1

      2.0E-1

      0.0E+0

      0.0 5.0 10.0 15.0 20.0 25.0

      Horizontal displacement (mm)

      Fig.18 Stress V/s Displacement for Circular isolator

      The finite element solution revealed that the circular model of bearing could take maximum displacement compared to other two geometries without failure. Fig.6.18 shows the stress diagram for the circular model plotted against the displacement.

6. CONCLUSIONS

Three geometries were considered in the study with equal base area but different shape factors defining their geometries. The study on the geometry of the isolators revealed the following conclusions.

• The isolators take the load until it meets the limit of stability and thereafter it fails

• The circular isolator can be replaced with the rectangular isolator with same base area

• Among the three geometries considered with equal base area, circular bearings give the best performance

• Higher value of shape factor can be recommended for isolators

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