influence of semirigid joints on fatigue life of steel truss railway bridge
TRANSCRIPT
INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING
Volume 3, No 1, 2012
© Copyright by the authors - Licensee IPA- Under Creative Commons license 3.0
Research article ISSN 0976 – 4399
Received on May, 2012 Published on July 2012 44
Influence of Semirigid joints on fatigue life of steel truss railway bridge Maansingh Patil
1, Pandey. A.D
2
1- Post Graduate Student, Department of Earthquake Engineering, Indian Institute of
Technology, Roorkee, Uttarakhand, India
2- Assistant Professor, Department of Earthquake Engineering, Indian Institute of
Technology, Roorkee, Uttarakhand, India
doi:10.6088/ijcser.201203013005
ABSTRACT
The joints of Riveted Steel Truss Railway Bridge consist of gusset plates which lose their
rigidity due to repeated passages of train loads; therefore the loss of rotational rigidity is to
be taken into account in analysis of Bridge. This joint flexibility tends to alter the vibration
characteristics of the Bridge system and each component of the bridge responds dynamically
to the rapidly varying loads and thus the time history obtained is a function of load variation
and dynamics of the structure, which consequently affects fatigue life of the bridge
components. In past, effect of Semirigid joints has been studied in case of building frames.
So here the knowledge of semirigid joints on building frame has been extended to Steel
Truss Railway Bridge. This present article tries to study the influence of joint flexibility on
the fatigue life of 76.2 m Truss bridge due to moving load at different speeds. The joint
rotational stiffness are reduced by 5%, 10%, 25% and 50%. The result of preliminary studies
conducted on Steel Truss Bridge is presented. It is prime facia that upto 50% reduction in
rotational Stiffness of the joints does not affect the stability of the bridge. However more
detailed studies are required to confirm the findings.
Keywords: Riveted steel bridge, Railway bridge, Bridge analysis.
1. Introduction
In India, Economic progress mainly depends on the railway and is considered as the Life line
of the Nation. India has the second largest rail network in the world, transporting over four
billion people annually and the total figure of existing railway bridges are approx. 1,
20,000.Out of these,731 are long span open girders,19014 are rolled steel joist or plate
girders. So it can be seen that more than 20% are Steel girder bridges. Due to continuous
movement trains, the members and their connections are subjected to repeated loadings due
to which the stiffness of the joint gets reduced, which are more prone to fatigue damage. The
conventional static, dynamic or stability analysis of Steel Trusses bridges assumes that their
members are connected at rigid or hinged joints.
However in reality Steel Trusses are reinforced at their joints by Gusset plates, which possess
rotational flexibility. The presence of this gusset plates has an appreciable effect on the
stiffness of the members of the Bridge and consequently on its behaviour to Static and
Dynamic loading. However, the behaviour of connections is neither rigid nor pinned.
Structures having such flexible Joints in which Joint flexibility becomes important are called
as semirigid frame members. In fatigue assessment of the bridge components the joints are
assumed to be rigid as per RDSO, where joint flexibility is neglected which may affect the
dynamic behaviour of the bridge component, consequently its fatigue life. Therefore it is
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
Volume 3 Issue 1 2012
45
necessary to evaluate the bridge components for semirigid connections.
2. End-fixity factor of Semirigid member
To incorporate the exact stiffness into analysis, experimental results of the various joints of
bridge components is needed. However there are no details available either in textbooks or
online about the exact stiffness of various joints of steel truss bridge, therefore end fixity
factor is used for analysis of the bridge. The concept of Semirigid joints used in case of steel
moment resisting frames using end fixity factor simplifies the analysis of semirigid frame
members. Monforton and Wu, 1963 studied in general way the effect of joint flexibility on
the static analysis of building frames, which is further extended to dynamic analysis by
Ozturk and Catal, 2005.The Semirigid frame member comprising a finite-length beam–
column member with a zero-length rotational spring at each end (the symbol @ represents
the spring) is shown in figure 1. The Joint flexibilities are modelled through linear rotational
springs of stiffness R1 and R2 at the two ends of the beam.
Figure 1: Semirigid beam column elements
The relative stiffness of the beam–column member and the rotational end-spring connection
is measured by an end-fixity factor defined as “rj” by Monforton and Wu, 1963:
( )2,13
1
1=
+
= j
LR
EIr
j
j (1)
Where rj is the end connection Spring stiffness and EI/L is the flexural Stiffness of the
attached member. The Fixity Factors rj defines the rotational stiffness of each end
connection relative to that of that of the attached member. The rotational stiffness of the
pinned connection is idealised as zero and thus the value of the end fixity factor is zero
(rj = 0).For a rigid connection ,rotational stiffness is taken to be infinite and end fixity factor
has a value of unity (rj =1).Therefore, a Semirigid Connection has an end fixity factor
between zero and one (0 <rj < 1).
The rotational stiffness of Ki1 and Ki2 at the ends of the of the ith
semirigid member can be
expressed in terms of end fixity factors (r1 and r2) by equation 2 and 3.
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
Volume 3 Issue 1 2012
46
L
EI
rr
rK i
4
4
3
21
11
−=
(2)
L
EI
rr
rK i
4
4
3
21
22
−=
(3)
3. Fatigue assessment
Fatigue is a critical concern for steel bridge structures. Fatigue behaviour depends largely on
the type of the material used in fabrication, impact factors, number of cycles per passage of
train, types of details etc. To estimate the fatigue life it is required to relate fatigue
performance data for elements to the loads to which the element is subjected in the real
environment. There are two primary groups of information that are required as an input for a
comprehensive fatigue analysis. One group of the information is the data related to the
material behaviour when subjected to cyclic loading, such as laboratory tests for constructing
S N curve and other is the loading history to which the component is subjected. Fatigue test
data is represented in the form of S-N diagrams. The S-N relationship as per BS 5400, 1980
as per equation 4 is used for the fatigue assessment in the present study.
)(log)(log 2 SmkNLog −= (4)
where,
S = Stress range in N/mm2,
N = Total number of allowable cycles for the stress range S,
k2, m are 1.53*1012
and 3 respectively for Class D type of connection.
A railway bridge is subjected to distinct events, every time a particular type of train travels
over it. Once the events are identified, the variation of load or stress versus time (time
history) is to be established. Once the time history is established, by a cycle counting
procedure, each time history is converted to a fatigue spectrum for that event, consisting of
stress range/mean range versus no. of cycles. Typical forms of stress variation that occur in
real structures are almost random in nature and vary in magnitude during its service life.
However, for a railway bridge the random occurrence of loading can be safely neglected as
the traffic model i.e. the frequency and the type of trains are known at the beginning of
fatigue analysis. The variation of stress under real stress environment in a member may
produce a complex waveform which bears little resemblance to that obtain from constant
amplitude loading conditions (used to generate the fatigue performance data) upon which the
design rules are based. Therefore it is necessary to breakdown the complex waveform into
recognizable cycles. To break the complex stress history into constant amplitude, the rain
flow counting method was purposed by Matsuishi and Endo T, 1965.This method identifies
cycles in accordance with the material stress strain response.
Large number of rain flow counting algorithm are available ,Dowing and socie,1982,Nie
Hong,1991 and R ,J Athens, 1997.In the present study, Cycle counting as per ASTM E 1049 -
85 (Reapproved 2011) is used. Firstly, the stress histories are converted for turning points by
in-house Matlab program and then Rain flow function in Matlab (developed by Dr.Adam
Nieslony (1999-2002) is used.
Fatigue damage is a Cumulative phenomenon and the fatigue damage increases with applied
loads in cumulative manner, which may lead to fracture.Large number of cumulative damage
models are available and comprehensive overview of cumulative fatigue damage theories for
metals and alloys have been presented by Fatemi and Yang, 1998.In this study, Linear
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
Volume 3 Issue 1 2012
47
damage rule as per Palmagren, 1924 and Miner, 1945 has been used because of its simplicity
in fatigue assessment. Palmgren –Miner linear damage rule states that the fatigue damage
contributed by each individual stress level is proportional to the number of cycles applied at
that stress level. The fatigue damage at particular stress level is the ratio of the number of the
cycles at stress level to the total number of cycles to failure obtained from S-N diagram at
that level.
4. Open web steel truss railway bridge
4.1 Description of the steel railway bridge.
In the present study, riveted open web Steel Truss Bridge is considered and the data
corresponding to truss bridge configurations and member section details are collected from
Research Design and Standards Organization (RDSO), (Ministry of Railways), Lucknow,
India. The typical description of the various members is given in figure 2.Schmematic
diagram of 76.2 m Long open web Truss girder considered is shown in figure 3(a),(b) ,(c)
and Table 1 gives the general description of the bridge. All sections are built up sections. All
the joints are riveted reinforced at joints with gusset Plates.
Figure 2: General description of steel truss railway bridge
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
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Figure 3 (a):- Elevation of 76.2 m steel truss bridge
Figure 3(b):- Sectional and top plan of 76.2 m steel truss bridge
Figure 3(c): Half end and sectional view of the steel truss bridge
Table 1: Description of 76.2 m Steel Truss Bridge
Type of Truss System Warren Truss
Clear Span (mm) 76200
Centre of Bearings (mm) 78800
No. of Panels 10
Panel length (mm) 7880
Overall length of bridge (mm) 79600
Spacing between two trusses (mm) 6300
Height of Truss (Intersections) (mm) 10500
Assumed Dead Weight of span including track
(ton)
400
Design Life (Years) 100
4.2 Analysis
4.3 General
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
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The 76.2 m Steel truss bridge is modelled in SAP 2000 14.2.4. The joint flexibility is taken
into account in the analysis, by means of modified joint rotational Stiffness. The response of
the Steel Truss Bridge members have been studied by assuming the reduction of joint
Rotational Stiffness by 5%, 10%, 25% and 50%.Based on this reduction, the end fixity factors
and rotational spring constants (Partial Fixity Spring Constants) are calculated. These springs
are modelled in the SAP 2000 14.2.4 in the plane perpendicular to the rivets. To carry out the
analysis, the trains are modelled as a series of concentrated axle loads moving across the
bridge. In this study, Passenger Train (25T P1) is considered as per RDSO as shown in figure
4.
Figure 4: 25T Passenger Train (RDSO)
4.4 Time history analysis
Dynamic analysis is performed by Linear Direct Integration Time history Analysis for
different velocities of train considering 2% damping ratio. The first two vertical modes are
considered for defining mass and stiffness proportional damping. The Main parameters for
dynamic analysis are velocity (v) and time step. Time step is assumed as (lw/8v) where lw is
minimum spacing between axle loads and speeds are assumed as per RDSO and three
different speeds as operating speed(100 kmph) ,rated speed (160 kmph) and future speed
(200kmph) are considered. The train is dicretized at each time step to obtain the stress
histories. The joints of the steel members are considered to be most susceptible for fatigue
damage. Therefore combined stress histories (axial and bending) are obtained for truss
members at joints and at mid span for flexural members (Cross girders and Stringer beams)
because they are built-up sections and the most stressed section is at midspan.
5. Results and discussions
5.1 Influence of joint rotational stiffness on modal analysis.
In the present study, modal analysis is carried out with the help of SAP 2000 software and
modes are considered in the analysis whose cumulative sum of modal mass participation ratio
was up to 90%. The modal analysis helps in determination of natural frequencies and the
corresponding mode shape of the structure, which essentially depends on distribution of
stiffness and mass within the structure .The flexibility of the joints tends to alter the modal
characteristics. In Table 2, the first 12 modes are given which explains the effect of joint
flexibility on modal time periods. It is observed that the rate of change of modal time periods
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
Volume 3 Issue 1 2012
50
increases with the increase in joint flexibility and mode. For the first five modes, the increase
is minimal (max 3%).However 6th
to 11th
mode the increase lay between 8% to 40% at 50%
joint stiffness. Ironically in the 12th
mode, the increase fell to 16% at 50% joint stiffness.
Table 2: First 12 modes of 76.2 m Truss bridges for different joint stiffness
Modal Time Period of 76.2 m w.r.t to Joint Flexibility
Mode Rigid 5% 10% 25% 50%
1 1.675 1.6757 1.6764 1.6791 1.6848
2 0.401 0.4017 0.4023 0.4052 0.4116
3 0.2974 0.2978 0.2981 0.2996 0.3029
4 0.2477 0.2477 0.2478 0.2479 0.2481
5 0.2073 0.2076 0.2079 0.2093 0.2121
6 0.1579 0.1587 0.1596 0.1629 0.1714
7 0.1441 0.1444 0.1447 0.1459 0.1506
8 0.1165 0.1171 0.1179 0.1241 0.1497
9 0.114 0.1141 0.1141 0.1234 0.1497
10 0.1073 0.1093 0.112 0.1234 0.1482
11 0.1022 0.1062 0.1103 0.1227 0.1427
12 0.1022 0.1062 0.1103 0.1145 0.118
Figure 5(a): Bottom chord Figure 5(b): Cross girder 153
Figure 5(c): Diagonal 3 Figure 5(d): Stringer 151
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
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Figure 5(e): Vertical 251
Figure 5(a) to (e): Typical Combined stress history at operating speed of different members
of 76.2 m Truss bridge for rigid joint case
5.2 Influence of joint stiffness on Damage potential of different components of 76.2m
truss bridge.
As we know that, damage potential of any component depends upon combined stress history
(axial +bending) due to moving train loads. Typical stress histories of different components
are shown in Figure 6.1 (a) to (e) for rigid case at operating speed of 100kmph. The leading
loads of that of a locomotive are heavier than the trailing loads of wagons; therefore the
structure is subjected to a greater stress initially as the train traverses the bridge. Once the
locomotive is off the bridge the stress reduce. The peaks in the histories are obtained when
any of the axle loads is at the midspan of the bridge. Bottom chord is subjected to tensile
stress only whereas the Vertical and Diagonals are subjected to both compressive and tensile
stresses in a single passage of train, thus making them more susceptible to fatigue damage.
Cross girders and stringers are flexural members having greater magnitude of stress cycles
therefore they are also prime concern for fatigue damage, whereas Top chords are mainly
compressive in nature,so they are considered to possess infinite life from fatigue point of
view.
5.2.1 Influence on stress range and no of cylces with different joint flexibility.
Typical 9 members are selected to find the effect of joint flexibility on fatigue assessment of
each component with respect due different train speed. Typical stress range histogram is
shown in the Table 3 (a) and (b) for operating speed. Fatigue damage depends upon the stress
range and no of cycles. The stress cycles varies with the joint flexibility, as we can see in case
of bottom chord 11, the 0-1 stress range cycles get reduced with joint flexibility and the
major single cycle changes its bin to higher side. As we know that the fatigue mainly depends
on higher stress range, therefore the fatigue life (Passage to failure) in bottom chord 11
decreases with joint flexibility.Similiarly In case of Stringer 151, the single major single
cycle changes its bin to lower stress range and other important cycles also changes its bin
towards lower side, thus it can be concluded that the fatigue life of stringer 151 decreases
with joint flexibility. Thus finally it can be concluded that joint flexibility alters the stress
histories and consequently stress ranges and cycle counts, which varies due to joint flexibility.
It is also important that damping tends to attenuate high frequency component developed due
to high speed. So presence of 2% realistic damping and joint flexibility tends to alter the
vibration characteristics of bridge component.
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
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Table 3(a): Fatigue spectrum for bottom chord 11 of 76.2 m truss bridge
Fatigue Spectrum for Bottom Chord 11 of 76.2 m Truss Bridge (operating speed)
Stress Interval
Stress Range Rigid 5% 10% 25% 50%
0-1 0.5 204 192 185 176 142
1-2 1.5 0 0 0 0 0
2-3 2.5 0 0 0 0 0
3-4 3.5 0 0 0 0 0
4-5 4.5 0 0 0 0 0
5-6 5.5 0 0 0 0 0
7-8 7.5 1 0 0 0 0
8-9 8.5 0 1 1 1 0
9-10 9.5 0 0 0 0 1
17-18 17.5 0 0 0 0 0
18-19 18.5 0 0 0 0 0
19-20 19.5 0 0 0 0 0
24-25 24.5 0 0 0 0 0
Table 3(b): Fatigue spectrum for stringer 151 of 76.2 m truss bridge
Fatigue spectrum for Stringer 151 of 76.2 m Truss Bridge(operating Speed)
Stress Interval Stress
Range Rigid 5% 10% 25% 50%
0-1 0.5 64 64 63 63 67
1-2 1.5 16 16 16 16 12
7-8 7.5 0 0 0 0 15
8-9 8.5 0 0 0 0 1
9-10 9.5 0 0 0 15 0
10-11 10.5 15 15 15 1 0
11-12 11.5 0 1 1 0 0
12-13 12.5 1 0 0 0 0
17-18 17.5 0 0 0 0 1
22-23 22.5 0 0 0 1 0
23-24 23.5 0 0 0 0 0
24-25 24.5 0 0 1 0 0
25-26 25.5 1 1 0 0 0
26-27 26.5 0 0 0 0 0
27-28 27.5 0 0 0 0 0
28-29 28.5 0 0 0 0 0
29-30 29.5 0 0 0 0 0
5.2.2 Influence of joint flexibility on different members of the bridge with different train
speeds.
Figure 6 (a) to (i) shows the Damage potential (Passage to Failures) with different joint
flexibility with different train speed. It is observed that the life got increased in most of the
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
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cases. Except in case of Bottom Chord 11 and Diagonal 5 where decrease is of about 40%,
Minimal decrease is observed in case of Crossgirder 153 and Vertical 251(less than 5%).With
the change in speed each component responded differently, so it is difficult to find a
particular trend, However the effect of different speed is same at various flexibility( only the
magnitude varies). It is observed that fatigue life of cross girder is the lowest (Minimum 10.7
million cycles to failure at 50% flexibility) as they are subjected to higher magnitude of stress
cycles and then comes the Vertical, Diagonals and Stringers and lastly the bottom chords. It
is also observed that even with the decrease in fatigue life of a member owing to joint
flexibility; the members still have substantial fatigue life.
Figure 6 (a): Bottom chord 11 Figure 6 (b): Bottom chord 12
Figure 6 (c): Cross girder 153 Figure 6 (d): Cross girder 156
Figure 6 (e): Diagonal 3 Figure 6 (f): Stringer 150
Influence of Semirigid joints on fatigue life of steel truss railway bridge
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International Journal of Civil and Structural Engineering
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Figure 6 (g): Stringer 151 Figure 6 (h): Diagonal 5
Figure 6 (i): Vertical 251
Figure 6.3 (a) to (i): Passage to failures (in millions) of various typical members of 76.2 m
Truss bridge with joint flexibility at various speeds.
5.3 Conclusions
1. Bridge components are having substantial fatigue life even after considering the Joint
Flexibility.
2. Joint flexibility tends to alter the vibration characteristics of each component to
loading environment in presence of realistic damping of 2%, thus the damage
potential of each member which depends upon the stress range and cycle counts is
also got affected ,however the change was only 40%(max).
3. In most of members fatigue life got increased, however life of some component got
decreased, the maximum decrease observed is about 40% in one of Bottom Chords
and Verticals.
4. The variation in passage to failure exhibited by each component with the different
speeds makes it difficult to find a particular trend, however the trend is similar at
different flexibilities with change only in magnitudes.
5. It can be concluded that the reduction of joint rotational stiffness up to 50% has less
effect on structural stability of Steel Truss Railway Bridge.
Acknowledgements
The work described in this paper could not be completed without the help of RDSO;
Lucknow.I would like to express my sincere thanks to Mr.S.Singhal, Director of Bridge and
Structure, RDSO – Lucknow and Mr. Atul Verma, ADEN (bridges & Structure), RDSO for
Influence of Semirigid joints on fatigue life of steel truss railway bridge
Maansingh Patil, Pandey. A.D
International Journal of Civil and Structural Engineering
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their valuable guidance during my stay at Lucknow. I express deep regard and sincere
gratitude to Mr.Prabhat Kumar ,Research Scholar , Department of Earthquake Engineering,
Indian Institute of Technology Roorkee, for his kind support in completion of this
project.
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