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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
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
18 Tappiti Chandrasekhara, Rama Debbarma
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.
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
19 Tappiti Chandrasekhara, Rama Debbarma
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.
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
20 Tappiti Chandrasekhara, Rama Debbarma
(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)
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
21 Tappiti Chandrasekhara, Rama Debbarma
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)
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
22 Tappiti Chandrasekhara, Rama Debbarma
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
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
23 Tappiti Chandrasekhara, Rama Debbarma
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)
Skew angle (degrees)
w/o TMD WSTMD WMTMD
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
24 Tappiti Chandrasekhara, Rama Debbarma
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)
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
25 Tappiti Chandrasekhara, Rama Debbarma
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)
Skew angle (degrees)
w/o TMD WSTMD WMTMD
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
26 Tappiti Chandrasekhara, Rama Debbarma
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
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
27 Tappiti Chandrasekhara, Rama Debbarma
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.
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
28 Tappiti Chandrasekhara, Rama Debbarma
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.
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com October 2016, Volume 4, Issue 10, ISSN 2349-4476
29 Tappiti Chandrasekhara, Rama Debbarma
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.
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