Estimation of Response of 2-DOF RCC Base Isolated Building to ...

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 7, July 2013)

Estimation of Response of 2- DOF RCC Base Isolated Building to Earthquake Loading Mohd. Zameeruddin Mohd. Saleemuddin1 1

Senior lecturer, MGM’s College of Engineering, Nanded, Maharashtra-India, 2.1 Linear Theory of Base Isolation Linear theory was first proposed by James M. Kelly (1997) [6]. The theory is used to analyze linear as well as non-linear isolation systems. For non-linear systems the analysis by this method is only approximate and such systems the effective stiffness and damping will have to be estimated by equivalent linearization process. The theory is based on the two mass structural models as shown in figure 1

Abstract— The present work focuses on the estimation of response of 2DOF RCC building to earthquake loading as a fixed base structure and base isolated structure, their comparisons. The various parametric studies like frequency, mode of vibrations, modal mass, modal participation factor, base shear using linear theory of base isolation proposed by James Kelly. Keywords—Frequency, Mode of vibration, Modal mass, Modal participation factor, Base shear

m

I. INTRODUCTION

us us

In this era of technological revolution, the world of seismic engineering is in need of creative thinking and advanced technologies beyond conventional solution. Seismic isolation is the best available technology for seismic protection of a variety of structures that have different dynamic characteristics. The ability of the isolation system to dissipate energy makes it consistent with contemporary thinking in seismic engineering. Isolation technology has matured in recent years to a highly dependable and reliable level. Academic research on there is well advanced and its practical application is becoming wide spread throughout the world [1]. The recent earthquakes in various part of the world have again emphasized the fact that the major loss of life in earthquake happens when it is relatively moderate one in areas with poor housing. Many people are killed by the collapse of brittle heavy unreinforced masonry or poorly constructed concrete buildings. Modern structural control technologies such as active control or energy dissipation devices can do little to alleviate this but it is possible that seismic isolation could be adapted to improve the seismic resistance of poor housing and other buildings such as school and hospitals in developing countries.

Ks, cs

mb kb, cb

ub us b

ug Figure1: Parameters of two-degree-of-freedom isolated model [27]

Where, m= Mass of the fixed base structure ks = Stiffness of fixed base structure cs = Damping in fixed base structure mb= Mass of the base slab ks = Stiffness of base isolator cb = Damping in base isolator With reference to the figure 1 Absolute displacement of the two masses are denoted by us and ub, while the displacement of the ground is denoted by ug, In terms of these absolute displacements the equations of motion for the structure and the base are given by

II. MODELING OF A SINGLE STOREYED BASE ISOLATED BUILDING AS 2-DOF SYSTEM: A LINEAR THEORY In this section, the response of a single storeyed fixed base isolated building is estimated. For the systems response spectrum analysis is done. The generalized spectrum as given by I. S. 1893-2002 (Part 1) is used throughout the analysis and hard soil is assumed.

mu  cs (u s  ub )  k s (u s  ub ) mus  mb ub  cb (ub  u g )  k s (ub  u g )

608

(1)

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 7, July 2013) Here in the analysis all the parameters are derived on the basis of relative displacement which are given as,

vs  u s  ub and vs  ub  u g

6. The damping factors for the structure and isolation system  s and  b respectively,  s   c s  and  2m  s  

(2)

 c   s   b  are of same order of magnitude as   2Mb 

Thus in terms of relative displacements the above equations of motion are rewritten as

mvb  mvs  cs vs  k s vs  mug (t )

7. Mass ratio

(m  mb )vb  mvs  cs vs  k s vs  (m  mb )ug (t ) (3) This 2-DOF system of equations, which can be solved directly or through modal decomposition provides insight into the response of isolated system and is applicable to more elaborate models. To develop the modes, frequencies, and participation factors of the system. In the matrix notation the above equation of motion is written as;

M * v * C * v *  K * v*  M * r * ug

 n  {sn , sn }T ; n  1,2 To determine the natural frequency and mode shape assuming,

(4)

vb  b sin b t and vs  s sin s t

k  M m M*   K*   b   m m 0 0 v 1 r*    v*   b  0   0 vs 

0 c C*   b  ks  0

0 c s 

2. Natural frequency of structure

(n2  b2 )bn  (n2 )sn  0

(n2 )bn  (n2   s2 )sn  0

s

Where

is given by,

 n is the frequency of mode.

given by,

b

(1   )n4  (b2   s2 )n2  bn sn  0 is given by,

(8)

The solution of above equation is given by,

12 

4. Natural frequency of structure is greater than that of base,  s >>  b



(7)

For the equation to have non-trivial solution, the determinant of the equation of the above equation should be zero.The characteristic equation for the frequency  n is

b  k b M

1 { s2  b2  (( s2  b2 ) 2  4(1   ) s2b2 )}1 / 2 2(1   )

1 {s2  b2  (( s2  b2 ) 2  4(1   )s2b2 )}1/ 2 2(1   ) (9) The lower of the two roots represents shifted isolation * frequency  b while the higher root represents structural frequency modified by the presence of the isolation system  s* .

22 

 and assume is defined such that     s   b  -2 is order of magnitude 10 .



(6)

and

s  k s m 3. Natural frequency of base

(5)

Substituting equation 5 back into the equation of motion eq. 3 and after some simplification the following equations are obtained,

Where, M= m+ mb The assumptions made in this theory are: 1. Mass of base slab is less than mass of structure i.e. m b  m , but of the same order of magnitude;

that

m less than 1. m  mb

2.2 Determination of Natural Frequencies and Mode Shapes The undamped natural modes of the system are

Where,

5. A ratio

 is defined as  

2

609

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 7, July 2013)

 s >>  b is taken into account and to first order in  , then  b* and  s* are given by, If

12  b*2  b2 (1   ) (1   )  22   s*2   s2 (1   )

(10) 1

(b*2  b2 )b2  (b*2 )s1  0 If we retain terms of order



1

1 mode shape

(n*2 )b1  ( s2  b*2 )s1  0 and set

 b1

 2 mode shape

Figure 2: Mode shapes of two-degree-of-freedom isolated system [27]

the first mode

The matrix equation 4 reduces to

1 

shape is obtained as;  1   





e

The mode shapes are obtained by substituting each of the natural frequencies obtained above in equation 7 thus,

and to the same order of as;

[1  (1   )]



q1  2b*  b*q1  b*2 q1   L1ug

 

(11) second mode shape is obtained

and

q2  2s*  s*q 2  s*2 q2   L2ug

(14)

1     [1  (1   )]    

Where, the damping in the system is implicitly assumed to be low enough to allow retention of the orthogonality of the modes. The participation factors, L1 and L2 for the two modes in these equations are given by,

 1 , whereas  2

 n M *r * Ln  n * n  M 

2

(12) As shown in the figure 2, the structure is nearly rigid in

T

given by  s (1   )

1/ 2

The computation of L1 involves the following matrix multiplications:

M L1 M 1  (1,  )  m M M 1  (1,  )  m

L1  1  

relative displacement,

2

M 1eff 

( L1 M 1 ) 2 M1

is, to same order

are obtained, the

M 1eff  M [1   (1   ) 2 ]

vb and v s can be written as

vb  q1b1  q2b2 and vs  q1s1  q2 s2

(16)

The effective mass in the first mode is given by,

2.3 Determination of Participation Factors and

m  1   M  2m  m 2    m  

Retaining only terms to order 

significance of this result is that high acceleration in the second mode of an isolated structure does not need to be accompanied by a large base shear.

1

m 1  M  m m 0

where,

and is modified 10. The practical

When the two modes,

(15)

T

involves deformation in both the structure and isolation system. The displacement of the top of the structure is of same order as the base displacement, but opposite in direction. The frequency of the first mode as given by equation 10 can be thought of as the modification, owing to the flexibility of the superstructure, of frequency of the isolation system when the structure is rigid, and because the structure is stiff as compared to isolation system, the modification is small. The second mode is very close to a motion where the two masses m, mb, are vibrating completely free in space about the center of mass of the combined system. The frequency of this type of vibration is

or to the order give

(13) 610

 , M1eff = M, the same computation for L2

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 7, July 2013) L2 M2= M + ma where

A base- isolated system aims to reduce the forces experienced by the structure to such a level that no damage will occur to the structure or to nonstructural elements such as partitions, etc thus, a lower value for the structure damping is appropriate. Here in the linear theory of base isolation an approximate from is used where the modal damping factors, 1* and  2* , are given by equation 20 and 21 In complete analysis the damping system is assumed nonclassical, such that the off-diagonal terms of the damping matrix which couple the equations of motion are neglected.

M2 = M + 2ma + a2m and a  1 [1  (1   ) ]



thus

M2  M

(1   )[1  2(1   ) ] and L2 M 2  M (1   )



therefore

L2  

(17)

 n C * n  n M * n T

Together with the shift in frequencies the results reveal why the seismic isolation system is effective. The

2 *n  n* 

participation factor for the second mode  2 which is the mode which involves structural deformation and is of order  is very small if the frequencies b ,  s are well

This is equivalent to neglecting the off diagonal terms of

 C * n which would couple the equations of motion. nT

Utilizing the previous results for M1 and M2

separated. When the frequency of the second mode shifts to a higher value than the original fixed-base frequency, this shift will take the isolated structure out of the range of strong earthquake motion if the input has large spectral accelerations at the original structural frequency. Moreover, since the participation factor for the second mode is very small this mode is almost orthogonal to the

g as earthquake input characterized by r * u differs only by





1

and r

2b*  b*  2b  b (1  2 ) 2 s*  s* 

*

T

 s*   s

 M  0

for n=1 implying that

 Mr  0 nT

(

Because

By orthogonality 1

2 s  s  2b  b 1 

b*  b (1   )1 / 2 we have, (1  2 )  b*   b (1   )1 / 2

*  1  [1  ] and r *  [1 0] thus r  0

nT

and

using

i.e.

T

T

*

(1   )1 / 2 (1   )1 / 2

we have,

b  b  1 / 2    1/ 2 (1   )1 / 2   (1   ) 

 s*  

Therefore, even if the earthquake does have energy at the second mode frequency, the ground motion will not be transmitted into the structure. A seismic isolation system works not by absorbing energy rather it deflects energy through this property of orthogonality.

(21)

The above equation shows that the structural damping is increased by the damping in the bearings  s to the order of

 1/ 2 .

2.4 Determination of Modal Damping Ratio A natural rubber isolation system provides a degree of damping that is in the range of 10-20% of critical damping, while the damping in the structure is generally between 25%. Normally, this large difference in damping between the two components would lead to a coupling of the equations of motion. Hence a complex modal analysis should be used correctly to analyze such system.

2.5 Determination of Modal Coordinates ( q n ), Isolator displacement ( vb max ), Structural displacement ( v s max ) The results of L1, L2,  s ,  b allow to estimate the *

*

response of the system to specific earthquake inputs. If the g (t ) is known, then time history of the ground motion u model components q1(t) and q2(t) are computed by any of the alternative below,by making use of response spectrum; 611

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 7, July 2013) For design purpose 5 % damped acceleration design spectrum is used. In this case,

q1max L2

1

 s*2

=

L1

1



*2 b

S A ( ,  ) * b

* b

and

q2 max

  2 (1   ) 2 S A (b* ,  b* ) [1  (1   ) ]2 S A ( s* ,  s* )  C s   2s    b*4 b*4  

(28) Substituting the value of

=



2 2 s

(24)

3.1 Details of the Building The structural plan of the RCC building used for analysis is given in figure 3. It is perfectly symmetric rectangular building 18 x 12 m in plan.

0.5

max

 (1   ) 2 S A (b* ,  b* )  2 2 S A (s* ,  s* )     b*4 b*4   (25)

max

  2 (1   ) 2 S A (b* ,  b* ) [1  (1   ) ]2 S A ( s* ,  s* )     b*4 b*4   (26)

0.5

2.6 Determination of Base Shear (Vb) The design base shear coefficient is defined by,

K s vs   s2 v s m

(31)

In this section, the response of a single storeyed fixed base isolated building is estimated. For the systems response spectrum analysis is done. The generalized spectrum as given by I.S. 1893-2002 (Part 1) is used throughout the analysis and hard soil is assumed.

After submitting of all the values of quantities from equations 11, 12, 16, and 17 in the equation 19, the base displacement obtained as,

Cs 

(30)

III. PERFORMANCE ANALYSIS

vb max  [( q1 max 11 ) 2  ( q2 max 12 ) 2 ]

vs

0.5

(23)

To estimate various response quantities from peak spectral values the SRSS method is used. Thus the values of the maximum isolation system displacement and structural displacement are given by,

vb max  [( q1 max 21 ) 2  ( q2 max 22 ) 2 ]

0.5

Thus the design base shear is given by; Vb  (m  mb )Cs

vs  q   q  1 1 s



C s  S 2A (b* ,  b* )  (1   ) 2  2 (1  2 )S 2A ( s* ,  s* )

written as,

vb

from equation 26

Thus,

2

vb and v s in modal coordinates can be

vb  q   q  and

 b*

(29)

When the two modes  and  are obtained, the relative 1

2 2 b

and

 (1   ) 2 S A (b* ,  b* ) [1  (1   ) ]2 S A ( s* ,  s* )  Cs       2 (1   ) 2 [(1   ) 2 (1   ) 2 ]  

(22)

Where SA represents the spectral acceleration for the response spectrum considered.

1 1 b

 s*

gives

S A ( s* ,  s* )

displacements

0.5

(27)

for the fixed base structure

C s   s2 S D ( s ,  s )

Figure 3: Plan of Single Storey Building

when the structure is isolated this becomes after substituting the value of v s from equation 26 the following

3.2 Assumed Data of the Building 1. Live load 5 kN/m2 2. Floor finishes 1 kN/m2 3. Seismic zone V 4. Importance factor 1.5

equation is obtained,

612

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 7, July 2013) 7. Max. Displacement,  = mg/K 8. Design of base shear, Vb= AhW

5. Response reduction factor 5 6. Type of soil Hard 7. Grade of concrete M 20 8. Damping in structure (s) 5% 9. Damping in base (b) 10 % 10. Mass of superstructure (m) 335.91 x 103 kgs. 11. Stiffness of super structure (ks) Along the length 676865.72 kN/m Across the length 471572.27 kN/m 12. Mass of base (mb) 102.75 x 103 kgs 13. Stiffness of base (kb) 7700 kN/m 14. Assumed time period of base (T b) 1.5 sec 15. Response spectrum available in I.S code1893 (Part 1) is used for analysis

3.5 Response of Base Isolated Single Storeyed RCC Building In this section, single storeyed RCC building in section 3.1 is considered as base isolated and the response of the same is estimated. In addition to this, a parametric study of base isolated building is carried out for proper understanding of linear theory presented in section 2 from its applications point of view. Elastomeric bearing are used as base isolator. A program in excel is developed for analysis of the above building by linear theory of base isolation. In this study the response quantities of interest are mode shapes, natural frequency, time period, top displacement of structure, displacement of the isolator and base shear. In parametric study, the effect of variation of stiffness, damping and mass ratio of base isolator on mode shape, natural frequency, and base displacement of the superstructure, participation factor and top floor acceleration of the building is evaluated. For this, the time period of base isolator is varied from 1.5 seconds to 4 seconds, at an interval of 0.5 seconds, and the response quantities of interest are determined. For both the systems response spectrum analysis is done. The generalized spectrum as given by I.S. 1893-2002 (Part 2) is used throughout the analysis and hard soil is assumed.

Spectral acceleration

3 2 spectral

1 0 0

2

4

6.987 mm 444.87 kN

6

Time period

Figure4: Design spectral acceleration chart

3.3 Calculations for Fixed Base Building along Length

3.6 Calculations for Base Isolated Building along the Length

1. Total seismic mass M = m+mb 438.67 x 103 kgs 2. Natural frequency of superstructure, s= sqrt(ks/m) 39.28 rad/sec 3. Time Period of superstructure  0.160 sec 4. Natural frequency of base structure,  4.19 rad/sec 5. Time period of base isolator (T b) 1.50 secs 6. Spectral acceleration SA as per figure 4 24.525 7. Max. Displacement,  = mg/K 4.868 mm 8. Design of base shear Vb= AhW 444.87 kN

1. Frequency ratio = 0.011 2. Mass ratio  = m/M = 0.77 3. Natural frequencies as per equation No.10 b* = 4.17 rad/sec; s* = 81.51 rad/sec 4. Modes shapes as per equation No. 11

3.4 Calculations for Fixed Base Building across Length 1. Total seismic mass, M = m+mb 438.67 x 103 kgs 2. Natural frequency of superstructure, s= sqrt(ks/m) 32.78 rad/sec 3. Time Period of superstructure,   0.191 sec 4. Natural frequency of base structure,  4.19 rad/sec 5. Time period of base isolator, (T b) 1.50 secs 6. Spectral acceleration SA as per figure 4 24.525

5. Participation factors, as per equation No.16 & 17 L1 = 0.991; L2 = 0.009 6. Modal damping factors as per equation No. 20 & 21 b*= 9.869; s*= 12.02 7. Spectral acceleration from design spectral acceleration chart given in I.S 1893 Part 1 SA = 4.905; SA  = 9.810 8. Modal coordinates as per equation no. 22 q1max = 0.280; q2max = 12.86

11 12  1 0.011   2  2   1 1.30  2   1

613

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 7, July 2013) 9. Displacements as per equation No.25 vbmax = 0.0016; vsmax= 0.280 9. Design base shear coefficient as per equation No.29 Cs = 0.060 10. Design base shear as per equation No.31 Vb =240.10 kN

3.8 Parametric Study of 2 DOF Isolated Building In this section, the effect of important mechanical properties i.e. stiffness and damping of the isolators on the building response is studied. For that, time period of the base isolator is varied from 1.5 sec to 4 sec, its effect on mode shapes(, natural frequency ( of the combined structure, structural displacements and base shear (Vb) is studied which are explained by following tables.

3.7 Calculations for Base Isolated Building across the Length

TABLE 2 VARIATION OF MODE SHAPE () WITH PERIOD OF BASE ISOLATOR (TB) (as per equation no 11 and 12)

1. Frequency ratio  0.011 2. Mass ratio  = m/M 0.77 3. Natural frequencies as per equation No.10 b* = 17 rad/sec; s* = 81.51 rad/sec 4. Modes shapes as per equation No.11

Tb

11 12  1 0.011   2  2   1 1.30  2   1

1.5 2.0 2.5 3.0 3.5 4.0

5. Participation factors as per equation No.16 & 17 L1 = 0.991; L2= 0.009 6. Modal damping factors as per equation No.20 & 21 b*= 9.869; s* =12.02 7. Spectral acceleration from design spectral acceleration chart given in I.S 1893 Part 1 SA = 4.905 SA   = 9.810 8. Modal coordinatesas per equation No.22 q1max = 0.280; q2max= 12.86 9. Displacements as per equation No. 25 vbmax = 0.0016; vsmax = 0.279 9. Design base shear coefficient as per equation No. 29 Cs = 0.060 10. Design base shear as per equation No.31 Vb = 240.10 kN

Parameter

2

Natural frequency () (rad/sec) Time period (T)(sec)

3

Displacement (v) (mm)

4

Design base shear(Vb)(kN)

1

Fixed Base 39.28 0.160 4.87 444.87

Across the Length First Second mode mode shape shape

11

12

11

12

11

12

11

12

1 1 1 1 1 1

0.011 0.006 0.004 0.003 0.002 0.002

1 1 1 1 1 1

0.011 0.006 0.004 0.003 0.002 0.002

1 1 1 1 1 1

1.30 1.30 1.30 1.31 1.31 1.31

1 1 1 1 1 1

1.302 1.304 1.305 1.305 1.305 1.305

It is seen from the table that if we provide base isolators of longer period of oscillations, the lateral movement of the floor in the structure would be reduced with respect to its undisplaced position TABLE 3 VARIATION OF SHIFTED ISOLATION FREQUENCY STRUCTURAL FREQUENCY



 b*

AND

* s WITH PERIOD OF BASE ISOLATOR (TB)

(As per equation No.10)

Along the Length

TABLE 1 COMPARISON OF TWO SYSTEMS

Sr. No.

Along the Length Second First mode mode shape shape

Tb

Shifted isolation frequency ( b ) *

Base Isolated b* = 4.17 s* = 81.51 T = 1.50 vs= 1.6 vb= 280

1.50 2.00 2.50 3.00 3.50 4.00

Vb = 240.10

614

4.17 3.13 2.51 2.09 1.79 1.57

Structural frequency (s ) *

81.51 81.36 81.29 81.25 81.23 81.21

Across the Length Shifted isolation frequency ( b ) *

4.17 3.13 2.51 2.09 1.79 1.57

Structural frequency (s ) *

81.51 81.36 81.29 81.25 81.23 81.21

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 7, July 2013) TABLE 4 VARIATION OF PARTICIPATION FACTORS WITH PERIOD OF BASE ISOLATOR (TB) (As per equation No.16 and 17)

Tb 1.50 2.00 2.50 3.00 3.50 4.00

Along the Length Participation factor in first mode ( L1) 0.991 0.995 0.997 0.998 0.998 0.999

5. Base isolation lengthens the time period of structure, and thus reduces the pseudo-acceleration for this mode (for design spectrum considered). This results in reduction of earthquake induced forces in the structure. 6. Since the participation factor for the second and higher modes are small, the modal static responses for the second and higher modes are negligible as compared to first mode. Therefore higher modes contribute little to the earthquake response of the structure. 7. The higher mode that produces deformation in the structure is generally not excited by the ground motion, although its pseudo-acceleration is large. Because of rigid body motion which accompanies straining of the base isolated structure the base shear is reduced considerably.

Across the Length Participation factor for second mode ( L2) 0.009 0.005 0.003 0.002 0.002 0.001

TABLE 5 VARIATION OF BASE SHEAR (VB) WITH PERIOD OF BASE ISOLATOR (TB) (As per equation No.31)

Tb

Along the Length Base shear (Vb)

Across the Length Base shear (Vb)

1.50 2.00 2.50 3.00 3.50 4.00

240.10 135.06 86.44 60.02 44.10 33.76

240.10 135.06 86.44 60.02 44.10 33.76

REFERENCES Rajiv Gupta, ―Seismic Base Isolation‖, Birla Institute of Technology and Science Pilani Rajasthan. Lecture material for the national Programme for capacity building of engineers in earthquake risk management (ministry of Home affairs, Government of India New Delhi), 2003, pp. 224-239. [2] Sajal Kanti Deb, ―Seismic Base Isolation-An overview‖, Current Science, Vol.87, No.10, Nov. 2004, pp.25-29. [3] Wang, Yen-po, ―Fundamentals of Seismic Isolation‖, International Training Programs for Seismic Design of Building Structures, Tiawan, 2003, pp.139-149. [4] Kunde M. C. and Jangid R. S., ―Seismic Behavior of Isolated Bridges: A-State-of-the-Art Review‖, Electronic Journal of Structural Engineering, Vol. 3, 2003 pp.140-170. [5] Charles. A. Kircher, ―Seismically Isolated Structures‖, FEMA 451 NEHRP Recommended Provisions, Design examples, 2000, pp.1-48. [6] Kelly J. M., ―Earthquake Resistant Design with Rubber‖, 1997, Springer-Verlag Publications, New York. [7] Li. L, ―Base Isolation Measure for Aseismic Building in China‖, Proceedings of 8th World Conference on Earthquake Engineering, San Francisco, C.A, 1984. [8] Mostaghel, N and Khodaverdian, M, ―Dynamics of ResilientFriction Base Isolators(R-FBI)‖, Earthquake Engineering and Structural Dynamics, Vol. 15, 1987, pp.379-390. [9] Zayas, V. A, Low, S. S, and Mahin, S. A, ―A Simple Pendulum Technique for Achieving Seismic Isolation‖, Earthquake spectra, Vol. 6, 1990, pp.317-334. [10] Mokha, A., Constantinou, M. C and Reinhom, A. M, ―Teflon Bearings in Seismic Base Isolation I: Testing‖, Journal of Structural Engineering, ASCE, Vol.116, 1990, pp.483-454. [11] Lin, T.N and Hone, C. C, ―Base Isolation by Free Rolling Rods under Basement‖, Earthquake Engineering and Structural Dynamics, Vol. 22, 1993, pp.261-273. [1]

IV. CONCLUSIONS The parametric study on 2DOF building helps in determining the effects of variation of stiffness and damping of isolators on the important properties of superstructure, from which the following conclusions are drawn: 1. Due to provision of base isolators, the dynamic response of building changes. It is observed that the shifted isolation frequency of building and that of the base isolator changes significantly with time period of the base isolator. 2. The base shear reduces significantly as the isolation time period increases. 3. For the base isolation to be effective in different modes, the ratio of time period of base and that of fixed system (Tb/Ts) should be as large as practical. 4. The linear theory of base isolation is suitable for estimation of dynamic response of base isolated buildings.

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 7, July 2013) [12] Jangid, R. S. and Londhe, Y. B., ―Effectiveness of Rolling Rods for base Isolation‖, Journal of Structural Engineering, ASCE, Vol.124, 1998, pp.469-472. [13] Su, L., Ahmadi, G. and Tadjbaksh, I. G., ―Performance of Sliding Resilient-Friction Base Isolation System‖, Journal of Structural Engineering, ASCE, Vol.117, 1991, pp.165-181. [14] Dinu Bratosin, ―Non- linear Effects in Seismic Base Isolation‖, Proceedings of Romanian Academy, Series A, Vol. 5, No.03, 2004, pp.1-12. [15] Chopra A. K, ―Dynamics of Structures‖, 1995, Prentice- hall publications, Singapore. [16] I.S.1893 Part1:2002, ―Criteria for Earthquake Resistant Design of Structures: General Provision and Buildings‖, BIS, New Delhi. [17] Datta T. K, ―A State-of-Art-Review on Active Control of Structures‖ ISET Journal of Earthquake Technology, paper No.430, Vol.40 (1), March 2003, pp. 01-17. [18] Ramallo J. C., Johnson E. A., and Spencer B. F., ―Smart Base Isolation Systems‖, Journal of Engineering Mechanics, Vol.128, No.10, 2002, pp.1088-1099. [19] Diptesh Das and C. V. R Murty, ―Brick Masonry In fills in Seismic Design of RC Framed Buildings- Cost Implications‖, Indian Concrete Journal, Vol.138, No. 1, 2004, pp.39-44. [20] Diptesh Das and C. V. R Murty, ―Brick Masonry In fills in Seismic Design of RC Framed Buildings-part 2 Behavior‖, Indian Concrete Journal, Vol. 139, No.1, 2004, pp.31-38.

[21] Elwood K.J. and Eberhard M.O, ―Effective Stiffness of Reinforced Concrete Columns‖, PEER Research Digest 2006-1. [22] J.M Kelly, ―A Seismic Base Isolation: Review and Bibliography‖, Soil Dynamics and Earthquake Engineering, Vol. 5, 1986, pp.202216. [23] Yang, Lee T.Y, and Tsai I.C, ―Response of Multi-degree-of-freedom Structures with Sliding Supports‖, Earthquake Engineering and Structural Dynamics, Vol. 19, 1990, pp.739-752. [24] Lee D.M and Medland I.C, ―Base Isolation System for Earthquake Protection of Multi-storey Shear Structures‖, Earthquake Engineering and Structural Dynamics, Vol. 7, 1979, pp.555-568. [25] Jangid, R. S and Datta, T. K, ― Seismic Behaviour of Base- Isolated Building: A State-of-the-Art- Review’, Structures and Building, Vol. 110, 1995, pp.186-202 [26] N. Chandra Shekar, K. B. S. Sunil Babu, and Pradeep Kumar Ramancharla, ―Equivalent Static Analysis as per IS 1893:2002 – A Simple Software Tool‖, Earthquake Research centre IIIT Hyderabad, India. [27] Kelly J.M, ―Base isolation: Linear Theory and Design‖, Earthquake spectra Vol. 6(2), 1997, pp.223-244. [28] Pankaj Agrawal, Manish Shrikande, ―Earthquake Resistant Design of Structures‖, 2007, Prentice- Hall of India Private Limited, New Delhi. [29] Grewal B. S, ―Higher Engineering Mathematics‖, 2007, Khanna publishers, New Delhi.

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