Seismic Vibration Control of Skew Bridges using Multiple Tuned...

International Journal of Engineering Technology, Management and Applied Sciences

www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476

17 Tappiti Chandrasekhara, Rama Debbarma

Seismic Vibration Control of Skew Bridges using Multiple

Tuned Mass Dampers

Tappiti Chandrasekhara

1

Department of Civil Engineering,

National Institute of Technology Agartala,

Agartala, India

Rama Debbarma2

Department of Civil Engineering,

National Institute of Technology Agartala,

Agartala, India

ABSTRACT

Tuned mass dampers are more effective devices in vibration control of buildings, bridges and other type of sway

structures under earthquake loads as well as wind loads around the world. Because of their efficiency, simple

maintenance have been found in wide range of practical applications. This paper presents an innovative technique for

vibration control of skew bridges using multiple tuned mass dampers (MTMDs) rather than single tuned mass dampers

(STMD). Three real earthquake ground motion records of EL Centro, Kobe and Coalinga, which are known major

earthquakes to be considered in this present study. It is found that MTMDs are more effective in reducing the dynamic

responses of displacement, acceleration and base shear with light structural damping with compare to STMD.

Keywords

skew bridges; vibration control devices; multiple tuned mass dampers; linear time history analysis; seismic responses.

INTRODUCTION

Skew bridges are more vulnerable in case of seismic loads as well as wind induced loads, because presence of

skew angle in their plan orientation. The skew angle can be defined as the angle between the normal to the

centreline of the bridge and centreline of the abutment or pier cap. Skew bridges are common at highways,

river crossing and other extreme grade changes when skewed geometry is necessary due to limitations in

space. Skew bridges are useful when roadway alignment changes are not feasible or economical due to the

topography of the site and also at particular areas where environmental impact is an issue. In skew bridges

seismic responses of displacement, acceleration and base shear are increases as skew angle increases as

compare to that of non-skew bridges. So to reduce these responses vibration control devices are required to

increase their serviceability, structural safety of skew bridges. These responses can be decreased with the

implementation of MTMDs by tune the first mode (fundamental frequency) frequency of primary structure.

Structural control systems increase the energy dissipation capacity of structures during an earthquake by

converting mechanical energy into heat energy. In case of structural control system passive control devices

like tuned mass dampers are more effective control devices without applying external power supply. A TMD

consists of mass mounted on a structure via a spring system and via a viscous damper. In this present study

MTMDs are used for reducing seismic responses of skew bridges and for comparative study non-skew bridges

also considered. It is found that MTMDs playing significant role in mitigation of seismic responses, rather

than STMD. Tuning is the main parameter in vibration control problem. It is defined as the ratio of the natural

frequency of damper to the natural frequency of structure. Daniel et al (2012) used multiple-tuned mass

dampers for control of seismic response of pedestrian bridges due to pedestrian traffic, so that multi tuned

mass dampers effectively reduce acceleration. Debbarma and Hazari (2013) conducted a parametric study to

obtain effectiveness of MTMDs in vibration control of structures under earthquake loads. It is found that as

mass ratio increases, displacements decreases with MTMDs and STMD. But, the effectiveness and robustness

of MTMD is more in comparison with STMD. Patil et al (2012) performed effectiveness of multiple tuned

mass dampers on elevated storage water tanks having capacity of 40m3, in their study displacement decreases

as mass ratio increases and these reductions are up to 91.40% with MTMDs than that of structure without

dampers. MTMDs are playing effective role in seismic vibration control of sway structures compare to

STMD. Adam and Furtuller (2010) studied that TMD performance is assessed by means of response reduction

coefficients, which are generated from the ratio of the structural response with and without TMD attached. It




is found that TMDs are effective in reducing the dynamic response of seismic excited structures with light

structural damping. These responses are decreases with mass ratio between 2% and 8% both for stiff and soft

structures. Sakr (2015) Proposed an innovative technique for using partial floor loads as multiple TMDs at

limited number of floors, for their investigation 5-storey, 25-storey and 50-story buildings are selected to

represent low-, mid-, and high-rise buildings. Wind loads are considered by applying sinusoidal dynamic

loads with different frequencies, whereas earthquake loads are considered by carrying out seismic analysis.

Distribution of the maximum story drift along the building height without MTMDs is 266.8 mm, and for the

controlled building, a peak is 163.2 mm. Umachagi et al (2013) presents an overview on application of

dampers for vibration control of structures and they concludes that controlling devices reduce damage

effectively by increasing the structural safety, serviceability and prevent the building from collapse during the

earthquake. Nagarajaiah and Sonmez (2007) performed a parametric study in frequency domain to investigate

the effectiveness and dynamic characteristics of STMD and MTMDs with variable stiffness. Semi active

MTMDs can also behave as a single semi active TMD in real time by reducing the frequency range to zero.

The redundancy in MTMD makes it more reliable in the sense that if one STMD fails, the rest can be

readjusted instantaneously.

DESCRIPTION OF MTMD SYSTEM

The natural frequencies of the MTMD are uniformly distributed around their average frequency. The natural

frequency, j j ji,e k m of the jth TMD expressed by

j T

nn 1

T j

j 1 T

n 11 j

2 n 1

-n, =

(1)

Where, T is the average frequency of all MTMD and is the non-dimensional frequency bandwidth of the

MTMD system.

The damping co-efficient of the jth TMD is expressed as

j j T jc 2m (2)

Where T damping ratio is kept constant for all TMD.

Total mass of the MTMD system is expressed by the mass ratio defined as,

n

j

j 1 T

s S

m

, =m

(3)

Where, is the mass ratio of the MTMD system and is the tuning frequency ratio of the MTMD

system.

THE EQUATION OF MOTION OF SKEW BRIDGE AND MTMD SYSTEM

The equation of motion of a MDOF system attached with MTMD (as shown in Figure. 1) can be expressed as,

bMY +CY +KY = -Mrz (4)

Where, M,C and K represents mass, damping and stiffness matrix of combined system. bz is the ground

acceleration due to earthquake.




METHODOLOGY AND MODELLING OF BRIDGE

Bridges are modelled using the commercially available finite element software package CSI Bridge 2015 and

tuned mass damper (TMD) parameters are calculated based on the mass of the structure. The following values

are to be taken for analysis and modelling of bridges.

Numerical example

A simply supported bridge with MTMDs as shown in Figure 1.

Length of the Bridge: 60m span having each span of 20m with 2 interior piers, Number of lanes: 2 no having a

width of 14.5m (constant for all skew angles), Bridge type: slab placed on I-section girder with 4 girders

(interior 2 girders and exterior 2 girders), Deck slab thickness: 500mm, Wearing coat thickness: 75mm, Type

of loading: IRC class AA wheeled vehicle load as per IRC: 21-2000, Earthquake data: Real Kobe, EL Centro

and Coalinga ground motion data, Materials: Concrete - M30 grade; Steel – Fe415 grade. The bridge having a

mass of m =5457296.741 Kg-f, the damping ratio of damper is calculated according to Den Hartog’s formula,

stiffness of TMD varies model to model and its depends on the fundamental frequency of primary bridge

structure (first mode frequency). Unless mentioned otherwise, following nominal values are assumed for

various parameters: damping ratio of structures, ξ = 5%, mass ratio, μ = 5% constant values were considered

to all models for clear understanding of problem. The frequencies as mention in table. 1 were tuned to TMD

by fundamental frequency (first mode frequency) of bridges.

Table 1.Fundamental frequency of different type of bridge structures.

Type of bridge Fundamental frequency of primary

structure (rad/sec)

S=0o ( right bridge) 10.30

S=25o 11.18

S=45o 14.89

S=65o 17.40

Fig 1: Bridge with MTMDs

(a) Non- skew bridge (b ) skew bridge

Fig 2: Representation of longitudinal girders for skew bridge and non-skew bridge.




(a ) Right bridge

(a)

(b )Skew bridge with 25o angle

(b)

(c) Skew bridge with 45o angle

(c)

(d) Skew bridge with 65o angle

(d)

Fig 3: Skew bridge models considered for present study.

RESULTS AND DISCUSSION

The variation of displacements of bridges with and without MTMDs considering real Kobe, EL Centro and

Coalinga earthquake time history for different skew angle are shown in Fig.4-6 and Table2. It is observed that

displacement reduces effectively with the application of MTMDs over an STMD. The percentage reduction of

displacement of bridge with MTMDs are 86%, 80.89% and 69.07% (by average of all skew angles) for Kobe,

EL Centro and Coalinga earthquakes respectively. The maximum peak displacement is observed during

earthquake motion when time is 8-12 sec. It can be seen (in Table-2) that maximum percentage reduction for

45o skew angle using MTMD compared to the same skew angle using STMD.

0 5 10 15 20 25 30 35 40 45 50-0.012

-0.008

-0.004

0.000

0.004

0.008

0.012

Dis

pla

cem

en

t (m

)

Time (sec)

w / o T M D

S T M D

M T M D

Skew angle,S=0o

(a)

0 5 10 15 20 25 30 35 40 45 50-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12

Dis

pla

cem

ent

(m)

Time (sec)

w/o TMD

STMD

MTMD

S=25o

(b)




0 5 10 15 20 25 30 35 40 45 50-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

Dis

pla

cem

en

t (m

)

Time (sec)

w/o TMD

STMD

MTMDs

S=45o

(c)

0 5 10 15 20 25 30 35 40 45 50-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Dis

pla

cem

ent

(m)

Time (sec)

w/o TMD

STMD

MTMDs

S=65o

(d)

0 5 10 15 20 25 30-0.012

-0.008

-0.004

0.000

0.004

0.008

0.012

Dis

pla

cem

ent

(m)

Time (sec)

w/o TMD

STMD

MTMDs

S=0o

(e)

0 5 10 15 20 25 30-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12

Dis

pla

cem

ent

(m)

Time (sec)

w/o TMD

STMD

MTMDs

S=25o

(f)

Fig 4: Variation of displacement of bridges against time for different skew angles; (a) – (d) for Kobe

and (e), (f) for EL Centro earthquake.

0 5 10 15 20 25 30-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

Dis

pla

cem

en

t (m

)

Time (sec)

w/o TMD

STMD

MTMDs

S=45o

(g)

0 5 10 15 20 25 30

-0.16

-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12

0.16

Dis

pla

cem

en

t (m

)

Time (sec)

w/o TMD

STMD

MTMDs

S=65o

(h)




0 5 10 15 20 25 30 35 40 45-0.012

-0.008

-0.004

0.000

0.004

0.008

0.012

Dis

plac

emen

t (m

)

Time (sec)

w/o TMD

STMD

MTMDs

S=0o

(i)

(i)

0 5 10 15 20 25 30 35 40 45

-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12

Dis

plac

emen

t (m

)

Time (sec)

w/o TMD

STMD

MTMDs

S=25o

(j)

0 5 10 15 20 25 30 35 40 45-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

Dis

pla

cem

en

t (m

)

Time (sec)

w/o TMD

STMD

MTMDs

S=45o

(k)

0 5 10 15 20 25 30 35 40 45

-0.2

-0.1

0.0

0.1

0.2D

isp

lacem

en

t (m

)

Time (sec)

w/o TMD

STMD

MTMDs

S=65o

(L)

Fig 5:Variation of displacement of bridges against time for different skew angles; (g), (h) for EL Centro

and (i) - (L) for Coalinga earthquake.

Table 2.Displacement of bridge structure with and without MTMDs for Kobe, EL Centro and Coalinga

earthquake having different skew angles.

Type of

Earthquake

Skew angle

Displacement (m) Percentage reduction (%)

w/o TMD STMD MTMD STMD MTMD

Kobe S=0o 0.009 0.002 0.002 71.88 85.62

S=25o 0.109 0.024 0.013 77.98 87.84

S=45o 0.046 0.028 0.007 39.13 83.69

S=65o 0.160 0.059 0.021 63.12 86.87

EL Centro

S=0o 0.010 0.002 0.002 72.9 84.26

S=25o 0.101 0.030 0.023 70.29 76.63

S=45o 0.051 0.028 0.01 45.09 80.39

S=65o 0.147 0.072 0.026 51.02 82.31

Coalinga S=0o 0.009 0.006 0.003 38.50 68.21

S=25o 0.104 0.048 0.012 53.84 88.46

S=45o 0.058 0.03 0.027 48.27 53.53

S=65o 0.171 0.079 0.058 53.80 66.08




Fig 6: Variation of displacement for different skew angles.

The variation of accelerations of bridges considering different skew angles with and without MTMDs are

shown in Fig. 7-9 and Table 3. It is observed that accelerations decreases up to 85.13%, 77.57% and 75.37%

in X-direction; 71.23%, 50% and 68.07% in Y-direction with the application of MTMDs for Kobe, EL Centro

and Coalinga earthquake.

Fig 7:Variation of acceleration for different skew angles.

0 5 10 15 20 25 30 35 40 45 50-10

-8

-6

-4

-2

0

2

4

6

8

10

Acc

eler

atio

n (m

/sec

2 )

Time (sec)

w/o TMD

STMD

MTMD

S=0o

(a)

0 5 10 15 20 25 30 35 40 45 50-10

-8

-6

-4

-2

0

2

4

6

8

10

Acc

eler

atio

n (m

/sec

2 )

Time (sec)

w/o TMD

STMD

MTMD

S=25o

(b)

S=0 S=25 S=45 S=65

Dis

pla

cem

ent

(Ko

be)

Skew angle (degrees)

w/o TMD WSTMD WMTMD

S=0 S=25 S=45 S=65

Acc

eler

atio

n (

Ko

be)


w/o TMD WSTMD WMTMD




0 5 10 15 20 25 30 35 40 45 50-10

-8

-6

-4

-2

0

2

4

6

8

10

Acc

eler

atio

n (m

/sec

2 )

Time (sec)

w/o TMD

STMD

MTMD

S=45o

(c)

0 5 10 15 20 25 30 35 40 45 50-10

-8

-6

-4

-2

0

2

4

6

8

10

Acc

eler

atio

n (m

/sec

2 )

Time (sec)

w/o TMD

STMD

MTMD

S=65o

(d)

0 5 10 15 20 25 30-10

-8

-6

-4

-2

0

2

4

6

8

10

Acc

eler

atio

n (m

/sec

2 )

Time (sec)

w/o TMD

STMD

MTMD

S=0o

(e)

0 5 10 15 20 25 30-10

-8

-6

-4

-2

0

2

4

6

8

10

Acc

eler

atio

n (

m/s

ec2)

Time (sec)

w/o TMD

STMD

MTMD

S=25o

(f)

Fig 8:Variation of Acceleration in X-direction for different skew angles; (a) – (d) for Kobe and (e), (h)

for EL Centro earthquake.

0 5 10 15 20 25 30-10

-8

-6

-4

-2

0

2

4

6

8

10

Acc

eler

atio

n (

m/s

ec2)

Time (sec)

w/o TMD

STMD

MTMD

S=45o

(a)

0 5 10 15 20 25 30-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Acc

eler

atio

n (

m/s

ec2)

Time (sec)

w/o TMD

STMD

MTMD

S=65o

(b)




0 5 10 15 20 25 30 35 40 45-10

-8

-6

-4

-2

0

2

4

6

8

10

Accele

rati

on

(m

/sec

2)

Time (sec)

w/o TMD

STMD

MTMD

S=0o

(c)

0 5 10 15 20 25 30 35 40 45-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Accele

rati

on

(m

/sec

2)

Time (sec)

w/o TMD

STMD

MTMD

S=25o

(d)

0 5 10 15 20 25 30 35 40 45-10

-8

-6

-4

-2

0

2

4

6

8

10

Acc

eler

atio

n (m

/sec

2 )

Time (sec)

w/o TMD

STMD

MTMD

S=45o

(e)

0 5 10 15 20 25 30 35 40 45-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Acc

eler

atio

n (m

/sec

2 )

Time (sec)

w/o TMD

STMD

WMTMD

S=65o

(f)

Fig. 9Variation of Acceleration in X-direction for different skew angles; (a), (b) for EL Centro, (c) - (f)

for Coalinga earthquake.

The Variation of base shear against time of bridges, having different skew angles, with and without MTMDs

are shown in Fig.10-12 and Table 4. From these figures, it can be observed that base shear decreases by

adding MTMDs than that of STMD. The percentage reductions of base shear with MTMDs are 86.8%, 82.91

and 82.26% (by average of all skew angles) in X-direction, 69.92%, 60.10% and 59.56% (by average of skew

angles) in Y-direction respectively.

Fig 10:Variation of base shear for different skew angles.

S=0 S=25 S=45 S=65

Bas

e sh

ear

(Ko

be)


w/o TMD WSTMD WMTMD




Table 3.Acceleration of bridge structure in both the X and y-direction with and without MTMDs for

Kobe, EL Centro and Coalinga earthquake having different skew angles.

Type of

Earthquake

Skew

angle

Acceleration in X-direction

(m/sec2)

Percentage

reduction (%)

Acceleration in Y-direction

(m/sec2)

Percentage

reduction (%)

w/o TMD STMD MTMD STMD MTMD w/o TMD STMD MTMD STMD MTMD

Kobe

S=0o

8.257 2.479 1.257

70.00 84.77

0.015 0.010 0.001

29.57 88.45

S=25o 9.097 2.397 1.286

73.65 85.86 0.012 0.007 0.003

36.58 69.10

S=45o 8.087 2.435 1.205

69.90 85.09 0.011 0.005 0.002

54.46 76.51

S=65o 9.135 2.917 1.385

68.07 84.83 0.031 0.020 0.006

33.72 50.89

EL Centro

S=0o 7.881 2.943 1.453

62.65 81.57 0.004 0.002 0.002

45.70 49.49

S=25o 8.737 3.119 2.608

64.29 70.14 0.049 0.034 0.030

30.00 38.31

S=45o 9.185 3.267 1.621

64.43 82.35 0.024 0.017 0.012

28.47 47.89

S=65o 7.890 3.887 1.875

50.72 76.23 0.098 0.077 0.034

20.78 64.27

Coalinga

S=0o 8.102 3.034 1.864

62.55 76.99 0.005 0.002 0.001

46.76 82.04

S=25o 9.345 3.376 2.217

63.87 76.27 0.056 0.045 0.024

20.00 56.73

S=45o 8.788 2.809 2.089

68.02 76.23 0.032 0.016 0.012

52.04 62.25

S=65o 9.496 4.016 2.659

57.70 71.99 0.114 0.079 0.033

31.16 71.27

Table 4.Base shear of bridge structure in both the X and y-direction with and without MTMDs for

Kobe, EL Centro and Coalinga earthquake having different skew angles.

Type of

Earthquake

Skew

angle

Base shear in X-direction (KN) Percentage

reduction (%)

Base shear in Y-direction (KN) Percentage reduction

(%)

w/o TMD STMD MTMD STMD MTMD w/o TMD STMD MTMD STMD MTMD

Kobe

S=0o 17683.09 4899.79 2514.72 72.29 85.77 0.018 0.008 0.00531 59.61 70.5

S=25o 22782.31 4205.91 2653.72

81.53 88.35 1912.389 610.651 379.415

68.06 80.16

S=45o 18492.7 4983.63 2405.46

73.05 86.99 177.423 74.869 41.667

57.80 76.51

S=65o 22386.82 6724.00 3112.53

69.96 86.09 796.215 605.91 378.072

23.90 52.51

EL Centro

S=0o 20129.21 5192.64 2672.3

74.20 86.72 0.031 0.0098 0.00618

68.38 80.32

S=25o 21398.51 7044.29 4686.24

67.08 78.10 1011.883 852.339 730.913

15.76 27.76

S=45o 20662.44 5656.77 2760.22

72.62 86.64 199.727 87.101 54.011

56.38 72.95

S=65o 19243.22 8322.29 3808.12

56.75 80.21 898.449 595.09 361.192

33.76 59.79

Coalinga

S=0o 17654.01 4449.46 3351.16

74.79 81.01 0.018 0.011 0.0088

38.88 51.81

S=25o 21744.67 5752.03 4333.08

73.54 80.07 1289.047 930.846 609.05

27.78 52.75

S=45o 18777.96 5508.80 2912.24

70.66 84.49 238.812 81.929 55.898

65.69 76.59

S=65o 22945.4 7149.65 3786.20

68.84 83.49 838.511 571.186 359.784

31.88 57.09




0 5 10 15 20 25 30 35 40 45 50-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

Bas

e sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=0o

(a)

0 5 10 15 20 25 30 35 40 45 50-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

Bas

e sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=25o

(b)

0 5 10 15 20 25 30 35 40 45 50-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

Bas

e sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=45o

(c)

0 5 10 15 20 25 30 35 40 45 50-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000B

ase

shea

r (K

N)

Time (sec)

w/o TMD

STMD

MTMDs

S=65o

(d)

0 5 10 15 20 25 30-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

Base

sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=0o

(e)

(e)

0 5 10 15 20 25 30-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

Base

sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=25o

(f)

Fig 11:Variation of base shear in X-direction for different skew angles; (a) - (d) for Kobe; (e) and (f)

for EL Centro earthquake.




0 5 10 15 20 25 30-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

Bas

e sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=45o

(a)

(a)

0 5 10 15 20 25 30-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

Bas

e sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=65o

(b)

0 5 10 15 20 25 30 35 40 45-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

Base

sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=0o

(c)

0 5 10 15 20 25 30 35 40 45-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000B

ase

sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=25o

(d)

0 5 10 15 20 25 30 35 40 45-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

Base

sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=45o

(e)

0 5 10 15 20 25 30 35 40 45-30000

-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

30000

Base

sh

ear

(KN

)

Time (sec)

w/o TMD

STMD

MTMDs

S=65o

(f)

Fig 12:Variation of base shear in X-direction for different skew angles; (a) and (b) for EL Centro; (c)

- (f) for Coalinga earthquake.




CONCLUSION

The Effectiveness of seismic vibration control of skew and non-skew bridges using MTMDs is investigated in

this paper. For comparative study, same thing is also observed using STMD. For analysis and numerical

study, three different real earthquake data’s like, Kobe, EL Centro and Coalinga are considered in this study.

From the results concludes that as skew angle increases responses of displacement, acceleration and base

shear are increases up to certain angle. These increasing seismic responses were decreased by adding MTMDs

to the bridges. MTMDs playing effective role in vibration control of skew bridges rather than STMD.

REFERENCES [1] Adam, C and Furtmuller, T.2010 “Seismic performance of tuned mass dampers”, Mechanics and model-based

control of smart materials and structures, (222).

[2] Daniel, Y, Lavan, O and Levy, R.2012 “Multiple-tuned mass dampers for multimodal control of Pedestrian

bridges”, Journal of Structural Engineering, 138 (9), 1173-1178.

[3] Debbarmma, R and Hazari, S 2013. “Mass distribution of multiple tuned mass dampers for vibration control of

structures under Earthquake load”, International Journal of Emerging Technology and Advanced Engineering,

8(3).

[4] Den-Hartog’s, J.P 1956 Mechanical Vibrations. 4th

ed. McGraw-Hill, New York.

[5] IRC: 21-2000, standard specifications and code of practice for road bridges,cement concrete (plain and

reinforced), third version the Indian roads congress, New Delhi, 2000.

[6] Indian Standard Criteria for Earthquake Resistant Design of Structures Part 1 General Provisions and

Buildings (Fifth Revision) (IS 1893-2002).

[7] Nagarajaiah, S and Sonmez, E. 2007 “Structures with semi active variable stiffness single/multiple tuned

mass dampers”, Journal of Structural Engineering, ASCE, 133(1), 67–77.

[8] Patil, S.S, Javheri, S.B and Konapure, C.G. 2012“Effectiveness of multiple tuned mass dampers”, International

Journal of Engineering and Innovative Technology (IJEIT), 6 (1), 78-83.

[9] Sakr, T.A. 2015 “Vibration control of buildings by using partial floor loads as multiple tuned mass dampers”,

HBRC journal.

[10] Vajreshwari, U, Katta, V, Reddy, G.R and Verma, R. 2013 “Application of dampers for vibration control of

structures”, International Journal of Research in Engineering and Technology, 6-11.

[11] CSI Bridge Manual.

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