Influence of Semirigid joints on fatigue life of steel truss railway bridge

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

[email protected]

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.





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





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





48

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





49

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





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





51

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.





52

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





53

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





54

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





55

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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Influence of Semirigid joints on fatigue life of steel truss railway bridge

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