IJR International Journal of Railway

Vol. 3, No. 3 / September 2010, pp. 83-89

Vol. 3, No. 3 / September 2010 − 83 −

The Korean Society for Railway

Dynamic Behaviors of Skewed Bridge with PSC Girders

Wrapped by Steel Plate

Inkyu Rhee†, Lee-Hyeon Kim*, Hyun-Min Kim** and Joo-Beom Lee**

Abstract

This paper attempts to extract the fundamental dynamic properties, i.e. natural frequencies, damping ratios of the 48 m-

long, 20o skewed real bridge with PSC girders wrapped by a steel plate. The forced vibration test is achieved by

mounting 12 Hz-capacity of artificial oscillator on the top of bridge deck. The acceleration histories at the 9 different

locations of deck surface are recorded using accelerometors. From this full-scaled vibration test, the two possible

resonance frequencies are detected at 2.38 Hz and 9.86 Hz of the skewed bridge deck by sweeping a beating frequency

up to 12 Hz. The absolute acceleration/energy exhibits much higher in case of higher-order twist mode, 9.86 Hz due to

the skewness of bridge deck which leads asymmetric situation of vibration. This implies the test bridge is under swinging

vertically in fundamental flexure mode while the bridge is also flickered up and down laterally at 9.86 Hz. This is

probably by asymmetric geometry of skewed deck. A detailed 3D beam-shell bridge models using finite elements are

performed under a series of train loads for modal dynamic analyses. Thereby, the effect of skewness is examined to

clarify the lateral flickering caused by asymmetrical geometry of bridge deck.

Keywords : PSC girder wrapped by steel plate (PCS), Skewed bridge, Forced vibration test, Modal dynamic analysis

1. Introduction

New trends of bridge superstructure have low self-

weighted, long-ranged features while the flexibility of

structure may have increases. This paradox between stiff-

ness and strength of these sorts of new bridge decks can

cause disadvantages especially when it exposed under

moderate/severe dynamic environments such as a high

speed train, gust and seismic motion. One should take a

close look at the dynamic behaviors, e.g. resonance,

damping ratio, maximum vertical displacement, acceleration

and end rotation etc., of new bridge decks beforei-

mplementing to real railroad industry in a practical man-

ner. In this paper, we attempt to examine the bridge with

pre-stressed concretegirders wrapped by steel plates (PCS)

in particular. The PCS girder has its own beneficial

features in that the girder height may have decreased due

to a presence of thin steel plates outside pre-stressed

concrete girder as illustrated in Fig. 1. In addition, the

durability of concrete girder will be much reliable through

a maintenance period after constructiondue to relative

insensitivity against outside atmosphere. A trade-off design

between strength and stiffness of PCS deck allows a long-

spanned bridge.

The skewed deck geometry can cause an additional

stability issue such as track twist since this deck lose the

axis-symmetrical characteristics by reproducing torsional

twist in sectional direction. For extracting an empirical

evidence directly, we simply restrict ourselves to a par-

ticular 48 m-long, 20o skewed and simply supported

PCS girder bridge. This bridge is called Jijang-Gyo

which located in mid-western area of Korea peninsular.

In order to clarify the influence of skewness toward

bridge deck behavior in dynamic situation, the

fundamental dynamic properties such as natural

frequency, damping ratio of the test bridge are essential.

To this ends, a forced vibration test is performed with

inertial oscillator which is mounted directly on the deck

†

*

**

Corresponding author: Research Engineer, Korea Railroad Research Institute

E-mail: rheei@krri.re.kr

Dept. of Structural Eng., Korea Railroad Research Institute

Dept. of Structural Eng., Korea Railroad Research Institute, and Ph.D. candidate

of Civil Eng., Inha University

− 84 −

Inkyu Rhee, Lee-Hyeon Kim, Hyun-Min Kim and Joo-Beom Lee / IJR, 3(3), 83-89, 2010

surface of the test bridge. Finally, a series of linear

dynamic analysis of this bridge in terms of different

skewed angles is analyzed under the train loads with

aids of finite element method.

2. Test Bridge

The test bridge consists of 4 composite girders in which

encompass normal pre-stressed concrete girder with a thin

steel plate as shown in Fig. 2. This surrounding external

steel plate compromises with the internal reinforcing bar

demands in the form of composite action. The bridge has

48 m-long (L) and 10.9 m-wide (H) simply supported bridge

with 20o skewness. This bridge is actually constructed for

local freeway use for automobile.

3. Forced Vibration Test

In an engineering point of view, confined concrete girder

and external steel plates enhances the performance of

girder stiffness so that it allows to control the girder depth.

However, less cross-sectional properties may lead a bridge

to oscillate spuriously and make a meaningful magnifica-

tion at certain frequencies. Thereby, we attempt to extract

experimental dynamic properties, i.e. frequencies at

resonance and damping ratio of the real PCS girder bridge

in order to ensure the fundamental dynamic stability,

especially for a skewed bridge. The maximum 12.0 Hz

capacity of an artificial vibration source with 8-ton unsym-

metrical mass and rotational arms is mounted on the top of

the bridge deck as shown in Fig. 3(a). A total of 9 acceler-

Fig. 1 Conceptual illustration of PCS girder and drawing of its

bridge application (by courtesy of Shinsung Const. Co., Ltd.

Note: Synonym as SCP girder)

Fig. 2 Test bridge: Jijang-Gyo, (a) cross-section, (b) skewed

bridge plan, (c) photo taken before the test (by courtesy of

Shinsung Const. Co., Ltd.)

Fig. 3 Forced vibration test: (a) oscillator, (b) accelerometer,

(c) measuring points on the top of the bridge deck

Dynamic Behaviors of Skewed Bridge with PSC Girders Wrapped by Steel Plate

− 85 −

ometers are used for measuring the vertical accelerations

which attached on the top of deck surface as shown in Fig.

3(b). The locations of accelerometers are at the points of 0,

L/4, 2L/4, 3L/4, L toward longitudinal direction and 0, H/

4, 3H/4, H for transverse direction as depicted in Fig. 3(c).

For acquiring vertical acceleration data, a total of 5 1 g-

accelerometers, a total of 4 5 g-accelerometers and EDX-

1500A, the data acquisition equipment are used. In this

vibration test, we are searching the fundamental modes of

deck by sweeping up rpm (rotation per minute), in other

words, excitation frequencies from 2.0 Hz up to 12.0 Hz.

A total of 35 vibration tests are repeatedly performed and

more refined step size is applied for searching accurate

information near possible resonance points. All 9 acceler-

ometers are wired to send time vs. vertical acceleration

during forced vibration with 50 Hz sampling rate (0.02 sec).

3.1 Natural Frequencies

Vibrations due to periodical wheel loads of a train can

cause the resonance on the bridge deck in conjunction

with similar vibration frequency bands. The resonance

phenomenon of bridge will be initiated as soon as the

exciting frequency reaches the natural one of bridge deck.

This accelerates the amplitude of vibration, in other terms,

vertical acceleration or vertical displacement which is their

second order integrand. This magnification of physical

quantity may affect the unpleasant passenger ride of a train

and could threaten a stability of traction interactions

between a rail and a wheel. Fig. 4 indicates the maximum

absolute acceleration envelop at each frequency sweep

stage from 2.0 Hz to 12.0 Hz. Two distinguishable acceler-

ation peaks are noticeable which means two dominant nat-

ural modes, i.e. fundamental flexural mode, high order

complex mode around 2.48 Hz and 10.0 Hz of excitation

respectively. In parallel, Fig. 5 shows the maximum vertical

accelerations by different exciting frequencies at 0, L/4, L/

2 points. The dominant frequency is mainly coupled at

different modes, 2.37 Hz, 9.86 Hz which are extracted

from frequency domain.

Since we are interested in frequencies near/at resonance

with relatively small deformable energy, two different

dominant frequencies, i.e. 2.37 Hz, 9.86 Hz are compared

in terms of normalized acceleration by peak value of #3

acceleration records in both longitudinal direction of

bridge as shown in Fig. 6(a). It indicates that the relatively

strong vibration is occurred at 9.86 Hz stage rather than

2.38 Hz even though the latter is the fundamental mode

which is 1st order flexural mode. During the forced vibra-

tion test, the authors who are on the bridge deck could feel

the strongest trembles at 9.86 Hz test as comparing other

frequencies. This is quite odd behaviors in normal

orthotropic deck [15] in that higher frequency with relative

lower impact energy reproduces strong vibration. We need

Fig 4.Time-vertical acceleration histories at different stages of

exciting frequencies: 2.48 Hz-(a)(b), 6.0 Hz-(c)(d), 10.0 Hz-

(e)(f), 12.0 Hz-(g)(h)

Fig. 5 Maximum absolute acceleration plot at #1,2 and 3

accelerometer while exciting frequencies sweep up to 12.0 Hz

from 2.0 Hz

− 86 −

Inkyu Rhee, Lee-Hyeon Kim, Hyun-Min Kim and Joo-Beom Lee / IJR, 3(3), 83-89, 2010

to clarify this particular behavior at 9.86 Hz. A similar pat-

tern toward lateral direction of the bridge deck can be

found in Fig. 6(b). However, only difference may arise in

transverse flexure which indicates opposite sign of acceler-

ation at 9.86 Hz of exciting frequency. The important

aspect of Fig. 6(a) is that the lowest prominent frequencies,

2.38 Hz and 9.86 Hz signals have all positive accelerations.

This implies the test bridge is under “swinging” vertically

with limitation of the bridge's gravity itself. However, not

like 2.38 Hz in Fig. 6(b), the normalized acceleration is

“flickered” up and down so that the signs of acceleration

have different at 9.86 Hz. The former is due to fundamental

beam action longitudinally but the latter may be due to

lack of transverse symmetry of the bridge geometry,

20oskewness. This will be discussed in later Section 4.

3.2 Damping Ratio

Once the vibration of a structure is developed, the pas-

sive structure should react to be stabilized a strong vibra-

tion with different sources of resistance such as air-

resistance, kinetic energy absorption due to cohesive fric-

tional materials and geometrical fabrications of superstruc-

ture. Therefore, damping ratio is one of fine index which

can represent the structural vibration absorption ability to

stabilize bridge deck especially under dynamic wheel load

system such as a train load. The bridge deck system suf-

fers from suspended vibrations at every certain minute in

case of train travels repeatedly and periodically. A higher

damping ratio is guaranteed a fast decay of harmful

vibration influence by bridge itself but should be strong

enough to sustain the vertical static loads. The logarithmic

decrement method is most convenient way to quantify the

damping ratio of the test bridge. The determination of log-

arithmic decrement, δ, which is the natural logarithm of

the ratio of any n-th successive amplitudes in the free

vibration of the specimen, and it is given by the following

equation.

Fig. 6 Normalized acceleration plot in longitudinal direction

and transverse direction at 2.48 Hz, 10.0 Hz of exciting

frequencies (2.38 Hz, 9.86 Hz of deck responses)

Fig. 7 Damping ratio calculationsfrom free vibrations at

2.4Hz-excitation frequency

Dynamic Behaviors of Skewed Bridge with PSC Girders Wrapped by Steel Plate

− 87 −

(1)

where, =acceleration at the initial stage of free vibra-

tion, =acceleration at the n-th stage of free vibration.

The amplitudes , can be obtained by using an data

acquisition system to record the decay of free vibrationsat

2.4Hz-excitation frequency after the driving exciter is

turned off. Fig. 7 shows the damping ratios at the different

positions (0, L/4, L/2) at resonance. The average damping

ratio indicates =0.98%.

4. FE Analysis for Skewness Influence

A finite element model of the test bridge is depicted in

Fig 8(a), (b) which is consist of six main parts; pre-

stressed girders, external steel plates, steel diaphragm,

reinforced concrete slab, pre-stressing tendons and rails.

The shell element (S4R) are being adopted for the bridge

deck. PCS girders, rails and pc strands are modeled by

Eulerian beam (B31) and bar (T3D2) element respec-

tively using ABAQUS. A total of 4,119 nodal points and

3,987 elements (S4R:2,880, B31:627, T3D2:479) are dis-

cretized and connected each part with aids of multiple con-

straints method and node sharing method. The material

properties of pre-stressed concrete girder are used for

of static modulus of elasticity under the

confined situation warping by external steel platesand

of Poisson’s ratio. For external steel plates

(SM490B), , are used with thickness

of 11.0 mm. The compressive strengths of concrete are

27.0 MPa and 40.0 MPa for the slab and the girder

respectively. The pre-stressed strand (SWPC7B-15.2 mm)

allows 1.4 MPa and 17.6 MPa for tensile and compressive

stress at the edge fiber each after jacking. The selectiveei-

genmodes for the bridge which are mainly involved in

flexure and twist are shown in Fig. 8(c), (d). The funda-

mental flexural mode and higher order twistmode have

2.36 Hz and 10.01 Hz respectively which are close to

experimental results (2.37 Hz, 9.86 Hz).

Since the test bridge has the 20o skew angle toward

longitudinal direction, the asymmetry of deck surface may

cause a loss of lateral stability in the form of twist across

the bridge width, H. To examine the effect of loss of

geometrical symmetry, Fig. 9 illustrates the three different

δ1

2πn---------

go

gn

-----ln=

go

gn

go

gn

ξ exp

Epsc

33GPa=

υc

0.167=

Es

210GPa= υs

0.3=

Fig. 8 FE models andeigenmodes of the test bridge

(ϕ =skew angle 20o)

Fig. 9 Asymmetric deck (H=10.9 m, L=48 m) skewness simulation with single lane train travel with eccentricity, e=2.87 m with

different level of skew angle ( =0o, 20o, 40o) ϕ

− 88 −

Inkyu Rhee, Lee-Hyeon Kim, Hyun-Min Kim and Joo-Beom Lee / IJR, 3(3), 83-89, 2010

level of skewness, i.e., , and

for FE simulation with eigenmode analysis in order to

compare the difference of deck acceleration, displacement

and most importantly for twist. Fig. 10 illustrates the

natural frequencies and stretching modes variation in terms

of the skew angle. They indicate the deviation of natural

frequencies at each different mode in the amount of

12%~27% ranges as comparing those of orthotrophicbridge.

Twist modes, at 2nd, 5th and 9th modes have relatively

large deviation as comparing other flexural modes. Hence,

one can presume that skewness of bridge deck could affect

to mainly twist behavior of a deck rather than fundamental

/higher-order flexure.

In order to ensure this influence, modal dynamic analy-

ses with singly-laned train loads (KTX) are performed at

the train speed of 190 km/h at resonance as illustrated in

Fig. 11. A modal dynamic analysis is used to analyze tran-

sient linear dynamic problems of the test bridge using

modal superposition. Transient modal dynamic analysis

gives the response of the model as a function of time

based on a given time-dependent loading such as moving

train load as illustrated in Fig. 11(b). The train excitation is

given as a function of time with varying different level of

speed. It is assumed that the magnitude of the excitation

varies linearly within each increment. A total of first 10

modes extracted are beingused to model the dynamic

response of the bridge in terms of fundamental/higher

modes of flexure and twist.

Vertical displacement, acceleration and twist of the

bridge deck are monitored during the singly-laned train

travel at the points of , and as depicted in Fig. 9.

The point is located in the line of loading so that the

vertical displacement variation has relatively small increase

(6%) under an unbalanced train load as comparing that of

no skewness of deck. However, the points and are

ϕ0

00

= ϕ1

20o

= ϕ2

40o

=

A A′ A″

A′

A A″

Fig. 10 Deviation of natural frequencies due to skew angle

increment

Fig. 11 Korea Train eXpress(KTX) loads: (a) Axle loads and

effective beating distance (unit: kN-m), (b) Illustration of

loading scenario with varying train speed

Fig. 12 Deck behaviors in terms of skewness angle at the

points of (a)(b)maximum central displacement and (c)(b)

maximum deck twist variation at train speed of 190 km/h at

point A″

Dynamic Behaviors of Skewed Bridge with PSC Girders Wrapped by Steel Plate

− 89 −

getting more influenced by unsymmetric train load with

asymmetrical deck geometry in the form of increasing

vertical displacement as comparing to that of point . An

amount of 19.3% and 41.1% of vertical displacement have

increased at the point of and as shown in Fig.

12(a)~(b). Fig. 12(c)~(d) shows the deck twist variation

with varying skew angle from 0o to 40o. This indicates the

2~5 times larger twist for point as comparing to that of

orthotropic bridge. As a result of this, one can find that the

increase of skew angle of a deck could worsen the

unsymmetrical displacement vertically especially for the

twist mode. No significant influence to flexural behaviors

is detected. According to [12-14], further increase of a

skew angle over 20o will not be significant effects over

bridge responses. This can also be found in eigen-frequency

deviations of flexures and twists in Fig. 10.

5. Conclusion

The fundamental dynamic properties of real 48m-long

PCS girder bridge with 20o skewness are extracted by

forced vibration test with aids of inertial oscillator. From

this full-scaled vibration test, the two possible resonance

frequencies are detected at 2.38 Hz and 9.86 Hz of the

skewed bridge deck during exciting frequency ranged

from 0.1 Hz to 12 Hz. The absolute acceleration/energy

exhibits much higher in case of higher-order twist mode,

9.86 Hz due to the skewness of bridge deck which leads

asymmetric situation of vibration. This implies the test

bridge is under “swinging” vertically in fundamental

flexure mode. Obviously, the bridge acts like one-

dimensional beam because of its aspect ratio, L/H=4.4.

However, the bridge is also “flickered” up and down

laterally at 9.86 Hz. This is probably by asymmetric

geometry of skewed deck. These observations are

supported by the results from experimental test and a

series of eigenvalue analyses. The dynamic performances

of the test bridge are discussed and compared in form of

quantitative responses from computer simulation. Twist

mode of bridge deck is directly influenced by increasing of

skew angle. This also affects the vertical flexural modes by

increasing the deviation between horizontal displacements,

, and . Similarly, the twist of deck from modal

dynamic analyses supports clearly this phenomenon. In

summary, twist modes and its relevant design limits should

be carefully checked in design process especially in

skewed railway bridges with a long ranged span.

Acknowledgement

The authors wish to acknowledge partial support under

the Grant No. CP04008 of Korea Railroad Research Insti-

tute. The opinions expressed in this paper do not necessar-

ily reflect those of the sponsors.

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A′

A A″

A″

A A′ A″

y′