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GOVERNMENT OF INDIA MINISTRY OF RAILWAYS

GUIDELINES FOR

ASSESSMENT OF RESIDUAL FATIGUE LIFE

OF STEEL GIRDER BRIDGES

(REPORT NO.BS-91)

May, 2008

ISSUED BY

RESEARCH DESIGNS & STANDARDS ORGANIZATION LUCKNOW-226011

BS-91 For official use only

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FOREWORD

Indian Railways are having about 1,28,000 bridges out of which about

16,000 are with steel girders. Most of these bridges are sufficiently old and quite often the decisions for their replacement/regirdering are taken on the basis of their age/service life without assessing the residual fatigue life. The available methods for assessment of residual fatigue life require instrumentation of bridges and testing of samples which take very long time to get an assessment of the residual fatigue life. During the last two decades a lot of research has been carried out and the fatigue strength curves for structural steel have been categorized for various type of connections. This has reduced the dependency on actual testing to assess the fatigue strength of connections. Extensive use of computers has enabled the engineers to make detailed computations of actual damage for a given load spectrum. The guidelines for Assessment of Residual Fatigue Life of Steel Girder Bridges have been developed based on traffic studies, keeping in view the difficulties being faced by railways in actual instrumentation and testing of bridge components. Analytical methods have been suggested to get an approximate estimate of residual fatigue life. Such estimates can be compared with the actual field observations and the fatigue strength parameters used in assessment process can be validated.

Shri R.K. Goel, Director/SB-I, Shri A.K. Pandey, ADE/Design , Shri

Dinesh Kumar, SE/Design and Shri Sujeet Nath Gupta, SE/Design have made sincere efforts to understand phenomenon of fatigue as related to steel bridges and suggested a procedure which can be easily understood and applied in practice. Approximate analysis as per BS-5400 Part-10 has been done in respect of IRS standards spans which can be used to get a quick estimate of total design life based on average route GMT.

It is expected that these guidelines shall serve as a useful tool in the

hands of bridge engineers to make an estimate of residual fatigue life of steel girder bridges. Suggestions and feed back for improvement shall be highly appreciated and gratefully acknowledged.

(Piyush Agarwal) Date : 30th May, 2008 Executive Director/B&S

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INDEX

1.0 Introduction 1

2.0 Selection of bridge 2

3.0 Procedure for assessment of residual fatigue life

2

4.0 Simplified approach based on BS:5400 Part-10

10

5.0 Procedure for fatigue life assessment 11

6.0 Conclusion 11

Appendix– A 22

Appendix – B 28

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GUIDELINES FOR ASSESSMENT OF RESIDUAL FATIGUE LIFE OF STEEL GIRDER BRIDGES

1.0 INTRODUCTION

1.1 Fatigue in metals is the process of crack initiation and growth under the action of repetitive loads. Fatigue failure is a progressive failure mode, the final stage of which is unstable crack propagation. Railway bridge members are subjected to ‘fatigue’ because of repeated loading and unloading cycles induced during the passage of a train. Increased locomotive capacities and increasing freight wagon capacities have led to longer and heavier trains known as heavy axle load (HAL) trains. Such trains induce numerous stress cycles of significant magnitude, forcing the fatigue life to be consumed rapidly.

1.2 The residual fatigue life of a steel bridges can play a major role in making

cost-effective decisions regarding rehabilitation versus replacement of exiting bridges, The existing railway bridges have been designed when there was no established method to account for the damaging effects due to fatigue phenomenon. The dynamic effects were taken into design considerations by way of adding up an equivalent static load to estimated loads. It is therefore, important to be aware of the fatigue capacities and residual lives of such bridges. The concept of design life has come up recently. The fatigue life of a bridge is found dependant on the traffic data such as inter-axle spacing, axle load, average annual GMT, influence line diagram of member under consideration, work specifications followed and the fatigue strength of the member details or connections. The actual traffic volume that a bridge is likely to experience during the remaining life of the bridge influences the fatigue life of the bridge components. Therefore, the estimation of residual fatigue life of a bridge, depends on the accuracy achieved in assessment of past traffic data and its future projections as well as the proper estimation of fatigue strength of member detail or connection.

1.3 It should be clearly understood that the estimation of residual fatigue life

gives only an indication of remaining service life from fatigue considerations. There are some other factors such as corrosion, additional stresses due to poor service conditions & stress corrosion, high and low temperature effects, low cycle (high stress) fatigue etc. which also affect the overall service life of steel bridges. The actual residual service life would be dependent on all the above factors for which individual assessment of each factor and an overall engineering judgment

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would be necessary. The contents given here are applicable to assessment of residual life of steel girder bridges from fatigue considerations only, assuming that adequate measures have been taken to keep the structure in sound condition from other considerations.

2.0 SELECTION OF BRIDGE

It can be considered that all the bridges on a section /route are subjected to same type of load sequences or fatigue loads. Therefore, the fatigue damage accumulated on similar type of bridges is almost the same. In case of plate girders, it is observed that the fatigue life is more if the effective span is more. However, in case of open web girders the issue is more complex as the overall fatigue life is determined by the member, having the least fatigue life. Stringers, cross girders, verticals and diagonals are generally found to have lesser fatigue life in comparison to other members. One representative bridge of each type can therefore, be selected for assessing the residual fatigue life of bridges on a particular section.

3.0 PROCEDURE FOR ASSESSMENT OF RESIDUAL FATIGUE LIFE

3.1 The residual fatigue life of an individual member detail or connection is governed by the following parameters:

(a) The stress range spectrum causing fatigue damage. (b) The capacity of the member detail or connection to absorb fatigue

effects. 3.2 The stress range spectrum primarily depends on the loading intensities,

their sequences and the structural configuration in which the member detail or connections are placed. The loading intensities and their sequences can be estimated based on the records available and a representative fatigue load model consisting of various type of trains with their daily frequency of operation can be established. The trains shall be specified with respect to the locomotives, wagons, axle loads, axle spacing, length of trains etc. Care has to be taken to ensure that the overall effects of the actual type of trains running over the bridge are reflected in the representative fatigue load model.

3.3 The fatigue capacity to absorb the fatigue effects primarily depends on the type of connection and represented in the form of stress range verses corresponding number of cycles of constant amplitude stress range that the connection would be able to withstand. Standard curves known as S-

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N curves are available for various types of connections adopted in bridges.

3.4 Past Traffic Studies

The objective of this study is to develop a representative fatigue load model which may truly represent the overall fatigue effects on the bridge due to past traffic. For this purpose, total traffic i.e. train composition, type of locomotives, weight of wagons passed over the bridge during its entire service life is required. From this representative fatigue load model, average number of cycles of various stress ranges experienced by the bridge members in a day can be computed. However, it may not be possible to get all the details of traffic for some reasons. In such cases, a rational approach should be adopted to correctly assess the type of trains and their frequencies in the representative fatigue load model.

3.5. Projected Traffic Studies

As the economy is growing, we may require to consider a heavier traffic pattern for assessment of residual fatigue life. It would be realistic is a futuristic representative fatigue loading pattern is considered. A fatigue load model is again required to represent the fatigue effects of the projected traffic. Studies on projected traffic would take into account any increase in axle loads likely to take place on the route.

3.6 Standard Fatigue Load Models

Standard fatigue load have been developed by RDSO for design of new bridges. These standard load models alongwith train formation diagrams are shown in Table –1 & 2 for MBG & HM loading respectively. These load models may be modified suitably to arrive at the representative fatigue load model for the bridge under consideration. It is again to be understood that accuracy of the assessed fatigue damage due to past or projected traffic would depend on the correctness of the representative fatigue load model chosen.

3.7 Generation of Stress Histories

Once the representative fatigue load models of past and projected traffic are established, the next step is to generate stress histories at critical member details for different types of trains included in load model. It is more reliable and authentic to generate time histories analytically. Relevant set of drawings can be used to know the configuration and develop structural model of the bridge. Standard softwares can be used to generate time histories for different critical locations. The complete set

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of stress histories is thus obtained for each type of train and every critical member detail or connection. The time history can also be obtained through field instrumentation of critical locations of the bridge.

3.8 Decomposition of Stress Histories Stress histories obtained are quite complex and cannot be directly used to

compute fatigue damage. Cycle counting methods) are generally used to convert complex stress histories into stress range histograms of uniformly repeated simple cycles of different stress range. Following two cycles counting methods are commonly used:

i) Reservoir method ii) Rain flow method

Stress range histogram for each identified critical location of bridge is prepared by plotting total no. of cycles obtained from the stress histories against corresponding stress ranges. A complete set of stress range histograms can be obtained for each type of train included in the representative fatigue load model. A typical stress range histogram is shown in Figure-1.

Fig. 1 - A typical stress range histogram

3.9 S-N Curves

3.9.1 These curves represent the relationship between the Stress Range and the corresponding Fatigue Life ‘N’ measured in terms of number of the stress cycles to failure. To develop these curves, fatigue tests are conducted in the laboratory on representative samples. For each stress range different values of number of cycles till failure are obtained. S-N

Num

ber

of

cycl

es

Stress Range

8

curves have been developed based on the data of full size specimen of different type of connections. These S-N curves are found dependent on type of connection and therefore have been categorized accordingly. The standard S-N curves for different types of connection details are available for reference in international codes such as AREMA, BS:5400 Part-10 and EN 1993-1-9 : 2002.

3.9.2 Choosing a S-N curve, appropriate to the type of connection under consideration is very important. Varying assessment of fatigue life are obtained, if the correct category of S-N curve is not selected. It requires deep understanding of the subject and a good sense of engineering judgment to choose an appropriate S-N curve. Primarily following three sources are there to obtain S-N curve.

i) AREMA

For rivetted connections S-N curve for category ‘D’ as given in American Railway Engineering and Maintenance Way Association (AREMA) can be adopted.

Fig. 2 S-N curves for different categories as per AREMA

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General Equation : Cycles to failure, N = A x SR

-3.0 where , SR is in ksi (1 ksi = 7 MPa) Or, log N = log A – 3.0 log SR

Where, N = No. of cycles to failure at stress range SR

A = 2.2 x 109 for Category ‘D’

Table : ‘A’ values for various AREMA Fatigue Categories

Fatigue Category A

A 2.5 x 1010

B 1.2 x 1010

B’ 6.1 x 109

C 4.4 x 109

D 2.2 x 109

E 1.1 x 109

E’ 3.9 x 108

ii) BS:5400 Part-10

BS 5400 Part 10 also specifies category ‘D’ for rivetted type of connection. S-N curves for various categories are given which can be described in the form of the following equation: Log N = log k – m log σr

Where, σr is the constant amplitude stress range at ‘N’ number

of cycles and k & m are constants.

For category ‘D’, k = 1.52 x 1012, σ0= σr at N = 107 which is equal to 53 MPa m = 3.0

The value of ‘k’ corresponds to a probability of failure of 2.3% within the design life.

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Fig.3 S-N curves for different categories as per BS:5400 Part-10

iii) Euro Code EN 1993-1-9 : 2002

Euro code gives detailed fatigue categories of the connections for unwelded, welded and other type of joints. The fatigue category is designated by a number which gives the fatigue strength of the type of connection in MPa corresponding to 2 x 106 number for cycles of constant amplitude. For rivetted type of connections fatigue category 56 may be considered to assess the residual fatigue life.

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Fig. 4 Fatigue strength curves as per Euro Codes.

General equation of the fatigue strength curves is given as under:

Log N = log a – m logR

Where,

R is the fatigue strength

N is the number of cycles to failure of stress range R m is the constant slope of the fatigue strength curve which is

equal to 3 for N < 5 million cycles and 5 for N > 5million cycles.

log a is a constant which depends on the specific segment of the fatigue strength curve. For fatigue category 56 this is equal to 11.546 and 14.777 for N < 5 million and N > 5million cycles respectively.

3.10 Palmgren Miner Damage Summation Hypothesis

This hypothesis is used to assess the accumulated fatigue damage. It

states that if ‘Ni’ cycles of a constant amplitude stress range (i) cause

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failure, than ‘ni’ cycles of ‘i’ will use up a fraction ‘ni/Ni’ of the life. Failure will occur when the sum of used life fractions i.e. Damage Sum (Df) will reach unity, i.e.

Fig. 5 Stress range histogram

Df = Nink

i

i /1

ni = No. of stress cycles actually applied

Ni = No. of stress cycles to failure(To be taken from S-N curve)

k = No. of bins in stress ranges histogram

In case of complex loading, when cycles of different stress range

1, 2, 3 ...... are applied n1, n2, n3, …… times respectively, then the accumulated damage in a period of time, t

D = 3N

3n

2N2n

1N1n

+......................kN

kn

n1

n2

n3

nk

No. of

cycl

es a

ppli

ed

1 2 3

Stress Range

13

Where, N1, N2, N3 are no. of cycles at failure at stress range 1,

2, 3 respectively taken from S-N curve.

The numbers of cycles of a particular stress range are taken from stress histogram of that period of time for which accumulated damage is to be worked out and the number of cycles till failure for the same stress range is taken from S-N Curve.

3.11 Assessment of Residual Fatigue Life

After estimation of fatigue damage, the residual fatigue life of member detail or connection can be computed from the following equation –

0.1eDpD

Where, Dp = Fatigue damage produced by past traffic = PLp1d

De = Fatigue damage due to estimated fatigue life = RLe1d

d1p = Accumulated fatigue damage in one year due to fatigue load model of past traffic.

d1e = Accumulated fatigue damage in one year due to fatigue load model of projected traffic

LR = Residual fatigue life of member detail or connection in years.

LP = Present age of bridge in years.

Thus, the residual fatigue life of all the critical member details or connections can be assessed. The overall residual fatigue life of the bridge is determined by the individual member, having the least residual fatigue life.

4.0 SIMPLIFIED APPROACH BASED ON BS:5400 PART-10

BS:5400 Part-10 suggests a simplified approach for fatigue assessment taking into account the various factors for loading type, design life GMT of the route, effect of multiple cycles etc. The code gives tables for choosing appropriate values of the factors for RU loading which is comparable to MBG loading in terms of EUDL. This approach has been used to give an approximate assessment of total fatigue life of the girders of standard designs. The approach can be used for assessment of fatigue life of non-

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standard girders also. The procedure and results of fatigue life assessment carried out as per simplified approach based on BS 5400 Part-10 for MBG loading are given in Appendix-B.

5.0 PROCEDURE FOR FATIGUE LIFE ASSESSMENT

5.1 Assess average route GMT based on past and projected traffic pattern.

5.2 Use simplified approach as suggested in para 4.0 above to assess residual fatigue life based on route GMT. For standard spans designed for IRS BGML and MBG loadings, the residual life has been assessed and given in Appendix-B.

5.3 Residual life can also be assessed using Palmgren Miner’s detailed summation method as per para 3.0 above.

5.4 If the fatigue life is found inadequate, following options are available:

i) Authenticity of traffic data considered may be reviewed.

ii) Instrumentation of critical members can be carried out to obtain the actual stress ranges and the residual fatigue life can be re-calculated.

iii) Improve track conditions over the bridge to reduce impact. This will help in reducing the stress ranges coming over the bridge and the fatigue life can be extended.

iv) Restrict axle load/volume of traffic over the bridge and institute periodic inspections of those particular details that restricted the fatigue life to ensure adequate safety without other changes.

v) Modify the bridge to improve its fatigue strength by either retrofitting the particular detail that controlled the fatigue life or add extra steel to cross sections to reduce the stresses.

6.0 CONCLUSION

6.1 A fairly good estimate of residual fatigue life can be made using the suggested approach of determining fatigue damage due to past traffic and taking into account the fatigue damage effects of projected traffic. Correct assessment of past and projected traffic is very essential as fatigue life is largely dependent on it.

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6.2 The suggested approach reflects the actual fatigue conditions in railway

bridges and permits the estimate to be updated in future to reflect changes in traffic conditions.

6.3 The suggested approach is analytical in nature and based on traffic data.

Instrumentation may also be carried out to obtain the actual stress ranges and residual fatigue life can be assessed using the approach.

6.4 Re-evaluation of residual fatigue life is to be carried out well before the

estimated residual life is exhausted. 6.5 It is again to be emphasized that it is difficult to make a correct

assessment of the fatigue life as it depends upon many factors. Engineering judgment has to be applied to arrive at a reasonably good estimate. These guidelines are to help the field engineers in making a decision about the remaining fatigue life of the bridge. The estimate can be revised if more sophisticated methods of analysis or actual measured data are employed.

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Table 1 (a) - Standard Fatigue Load Model for MBG Loading

Type of Train

Tra

in N

o.

Train Composition

Weight per Train (t)

GMT per Train

Class of Traffic

Heavy Freight Traffic (100 GMT)

Mixed Traffic Lines with Heavy Traffic (70 GMT)

Subarban Traffic (60 GMT)

Mixed Traffic Lines with Light Traffic (40 GMT)

No. of Trains

GMT No. of Trains

GMT No. of Trains

GMT No. of Trains

GMT

Passenger Trains

1 2 3 4

1+15 2+22 2+26 AC EMU 12

900 1400 1700 700

0.33 0.51 0.62 0.26

3 2 - -

1.0 1.0 - -

6 10 14 -

2.0 5.1 8.7 -

- 5 5 200

- 2.6 3.1 52.0

5 5 - -

1.7 2.6 - -

Freight Trains loaded

5 6 7 8

1+75-4 Wheeler 2+40 BOX 2+55 BOXN 2(2+55 BOXN)

3200 3600 5100 10300

1.17 1.31 1.86 3.76

2 2 10 20

2.3 2.6 18.6 75.2

2 - 4 12

2.3 - 7.4 45.1

- - - -

- - - -

2 5 10 2

2.3 6.5 18.6 7.5

Freight Trains empty

9 10

1+75-4 Wheeler 2+40 BOX

1100 1300

0.40 0.47

- -

- -

- -

- -

- -

- -

2 2

0.8 0.9

Total 39 100.7 48 70.6 210 57.7 33 40.9

17

19

50

29

70

20

50

55

60

19

50

20

50

52

79

28

96

28

96

46

18

23

09

28

96

28

96

1 - 6 x 25 t 15 - 4 x 13.0 t = (900.0 t)TOTAL = 930.0 t(1) PASSENGER TRAIN-1

20

50

(2) PASSENGER TRAIN-2

2 - 6 x 25 t

20

50

29

70

19

50

55

60

19

50

59

40

20

50

22 - 4 x 13.0 t

52

79

TOTAL = 1444.0 t = (1400.0 t)

19

50

55

60

19

50

20

50

28

96

28

96

46

18

28

96

28

96

23

09

19

50

(3) PASSENGER TRAIN (A.C.) -3

29

70

20

50

55

60

19

50

55

60

20

50

2 - 6 x 25 t

19

50

20

50

59

40

2 - 4 x 16.25 t (A.C.)

20

50

19

50

52

79

28

96

46

18

28

96

28

96

28

96

46

18

24 - 4 x 13.0 t

28

96

46

18

28

96

28

96

23

09

TOTAL = 1678.0 t = (1700.0 t)

(4) PASSENGER TRAIN 4 (EMU)

28

96

20

82

1 - 4 x 13.0 tTOTAL = 736.0 t

= (700.0 t)

4 SUCH UNITS FORM ONE TRAIN

28

96

39

95

28

96

28

96

28

96

39

95

28

96

20

82

1 - 4 x 20.0 t 1 - 4 x 13.0 t

Table 1 (b) - Train Formation Diagrams for MBG Loading

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(5) GOODS TRAIN LOADED - 1

2050

2970

1 - 6 x 25.0 tTOTAL = 3195.0 t

= (3200.0 t)75 - 2 x 20.3 T

1950

5560

1950

2050

4931

4900

3922

4900

3922

3922

4900

1961


5940

1950

2 - 6 x 25.0 t

2970

2050

5560

2050

1950

= (3600.0 t)TOTAL = 3551.0 t

2050

1950

5560

1950

2050

2000

6800

2000

2929

2000

2000

40 - 4 x 20.32 t

2 - 6 x 25.0 t


1950

2970

2050

5560

2050

1950

= (5100.0 t)TOTAL = 5140.0 t

55 - 4 x 22.0 t5560

1950

2050

5940

2050

1950

4524

2000

2000

2189

2000

2000


2 - 6 x 25.0 t + 55 - 4 x 22.0 t

1950

2970

2050

5560

1950

2050

TOTAL = 10280.0 t = (10300.0 t)

2000

5560

2050

5940

1950

2050

1950

2000

2000

4524

2189

2000

2 SUCH TRAINS

19

2050

(9) GOODS TRAIN EMPTY - 1

1 - 6 x 25.0 t

2050

2970

5560

1950

1950

TOTAL = 1132.5 t = (1100.0 t)

4931

75 - 2 x 6.55 t

4900

3922

4900

3922

3922

4900

1961

(10) GOODS TRAIN EMPTY = (1300.0 t)

TOTAL = 1308.0 t2050

2050

2970

5560

1950

5560

5940

2050

1950

2050

1950

40 - 4 x 6.3 t

2000

6800

2000

2929

2000

2000

2 - 6 x 25.0 t

1950

Note :-

2. FIGURES IN BRACKETS ARE ROUNDED FIGURES.1. ALL DIMENSIONS IN MILLIMETRES.

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Table 2 (a) - Standard Fatigue Load Model for HM loading

Type of train Train

No. Train Composition

Weight

per

Train

GMT

per

Train

Class of Traffic

Heavy Freight Traffic

(150 GMT)

Mixed Line With Heavy

Traffic

(100 GMT)

Mixed Lines With

Light Traffic

(50 GMT)

No. of

Trains

GMT No. of

Trains

GMT No. of

Trains

GMT

Passenger

Train with

MBG Loco

1 1+15 930 0.339 3 1.018 6 2.037 5 1.697

2 2+22 1444 0.527 2 1.054 10 5.271 5 2.635

3 2+26AC 1678 0.612 0 0.000 14 8.575 0 0.000

Freight Trains

Loaded

Wagons

4 2WA6C+40 (Gondola) 5160 1.883 6 11.300 4 7.534 3 5.650

5 2WDG2+40 (Gondola) 5160 1.883 6 11.300 4 7.534 3 5.650

6 3WDG2+55 (Gondola) 6969 2.544 10 25.437 5 12.718 2 5.087

7 4WDM2+55 (Gondola) 7051 2.574 11 28.310 6 15.442 3 7.721

8 3WAG6A+75 (Gondola) 9369 3.420 7 23.938 4 13.679 2 6.839

9 3WAG6B+75 (Gondola) 9369 3.420 7 23.938 4 13.679 2 6.839

10 3WAG6C+75 (Gondola) 9369 3.420 7 23.938 4 13.679 2 6.839

Freight Trains

Empty

Wagons

11 2WAG6C+40 (Gondola) 1392 0.508 0 0.000 0 0.000 1 0.508

12 3WDG2+55 (Gondola) 1788 0.653 0 0.000 0 0.000 1 0.653

Total 150.233 100 50.120

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Table 2 (b) – Train Formation Diagrams for HM Loading

19

50

29

70

20

50

55

60

19

50

20

50

52

79

28

96

28

96

46

18

23

09

28

96

28

96

= (900.0 t)TOTAL = 930.0 t


20

50


20

50

29

70

19

50

55

60

19

50

59

40

20

50

52

79

TOTAL = 1444.0 t = (1400.0 t)

19

50

55

60

19

50

20

50

28

96

28

96

46

18

28

96

28

96

23

09

19

50

(3) PASSENGER TRAIN (A.C.) -3

29

70

20

50

55

60

19

50

55

60

20

50

19

50

20

50

59

40

20

50

19

50

52

79

28

96

46

18

28

96

28

96

28

96

46

18

28

96

46

18

28

96

28

96

23

09

TOTAL = 1678.0 t = (1700.0 t)

Description of Broad Gauge Trains for H. M. Routes (Fatigue)

(25 t

)

(13 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)

(25 t

)(2

5 t

)

(25 t

)

(16.2

5 t

)

(13 t

)

(16.2

5 t

)

(16.2

5 t

)

(16.2

5 t

)

(16.2

5 t

)

(16.2

5 t

)

(16.2

5 t

)

(16.2

5 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

Sheet 1 of 4

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

(13 t

)

1 MBG LOCO 15 COACHES

2 MBG LOCO 22 COACHES

2 MBG LOCO (2 + 24) COACHES

25

Appendix A Cycle counting Methods A.1 The application of a loading event, in general, produces complex stress histories

that rarely have constant amplitude at most of the structural details. In order to assess the fatigue damage at these details due to the complex stress history, the load history has to be reduced to a sequence of blocks of constant amplitude. The process of identification of the constant amplitude stress ranges and the associated number of cycles present in the stress history is known as ‘cycle counting’. The damage accumulated due to these constant amplitude blocks can be calculated individually and summed using Palmgren-Miner's rule to calculate the total accumulated damage of the structure. The two most commonly employed methods for cycle counting are the ‘Reservoir method’ and the ‘Rainflow method’, both yielding identical results if the rainflow analysis is initiated from the highest peak in the stress history. The reservoir count is employed for short stress histories while the rainflow counting is employed for longer and more complex stress histories.

A.2 Cycle counting by the reservoir method A.2.1. The graphical plot of the stress history, in this method, is imagined as a cross

section of a reservoir filled with water. The water is drained from each of the lowest points successively till the entire reservoir is drained. Each drainage operation represents a cycle of stress range equal in magnitude to the height of the water drained in that particular operation.

A.2.2. The procedure for cycle count by the reservoir method is as follows :-

A.2.2.1. It is assumed that the stress history has been derived taking into consideration such provisions as are applicable with regard to loads, structural details, structural material, methods of analysis and any other modifications necessary.

A.2.2.2. The peaks and valleys are identified in the original stress history (figure A.1) and

joined by straight line segments, if necessary. This modified stress history will be used for the reservoir count as shown in figure A.2.

26

A.2.2.3. A copy of the stress history is appended to the original (figure A.3) and the highest point (A) in the original segment and its counterpart (B) in the appended segment are marked and joined by a straight horizontal line. The portion of the stress history so enclosed will be used to represent the reservoir. In case there are two or more equal peaks in the original segment of the stress history then the first such peak will be considered along with its counterpart from the appended segment.

A.2.2.4. The reservoir is drained successively from the lowest points (E, F, D and C taken in order as shown in figure A.4) which retain water till the entire reservoir is emptied. Each drainage operation corresponds to a cycle of stress range equal in magnitude to the height of the water drained in that particular operation i.e. one cycle of stress range σ A - σ E when drainage is from trough E.

27

A.2.2.5. The stress ranges and their associated number of cycles are sorted according to

the magnitude of the stress ranges for further processing using the Palmgren-Miner criteria.

A.2.3. Consider the following example :-

A stress history consists of the following stress variation

Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Stress 28 -18 8 2 22 -6 20 8 20 -18 22 -4 26 12 A,

O B C D E F G H I J K L M N

In order to conduct a reservoir count appending the first point, as it is the highest, will suffice for the definition of the reservoir. A schematic diagram indicating the extent of drainage from each trough is as shown in figure A.5. The points in the stress history have been labeled from A to O for easy identification.

28

The results from the reservoir count can be tabulated as follows: -

Drainage from Trough

Highest water level at

Stress range

B A 46

J K 40

F G 26

L K 26

D C 6

H G 12

N M 14

The above may be arranged in order for further processing.

A.3 Cycle counting by the rainflow method A.3.1. The rainflow counting technique is based on the visualization of flow of rain over

a sequence of pagoda roofs and essentially counts half cycles. In order to effect the visualization the stress history is rotated such that the time axis is vertical with the origin located towards the top.

Rainflow is assumed to begin from a peak or a trough and the distance it travels determines the magnitude of the stress range, each flow contributing a half cycle.

A.3.2. The procedure for rainflow count is as follows :- A.3.2.1. It is assumed that the stress history conforms to A.2.2.1 and is modified in

accordance with A.2.2.2 so that the stress history is reduced to a sequence of peaks and troughs.

A.3.2.2. The stress history may be modified in accordance with A.2.2.3 so that it begins

and ends with the highest peak (or the deepest trough). A.3.2.3. The stress history is rotated through 90o such that the origin of the time axis is

located towards the top (figure A.6).

29

A.3.2.4. A drop begins to flow (figure A.7) left from a peak (1-2) or right from a trough(1-

3) onto subsequent roofs (3-4-6) unless the surface receiving the drop is formed by a peak which is more positive than the origin of the drop (1-2) for a left flow, or, a trough that is more negative for a right flow(4-5)

A.3.2.5. The path of a drop cannot cross the path of a drop which has fallen from a

higher roof (5-6). A.3.2.6. A drop ceases to flow when it reaches the end of the stress history record (1-3). A.3.2.7. The horizontal displacement of the drop from its origin to its final position

measured in appropriate stress units represents a half cycle of the associated stress range.

A.3.3. Considering the same example as in A.2.3 the rainflow patterns are as shown in

figure A.8.

30

The results from the rainflow count can be tabulated as follows :-

Origin of flow Termination of flow Half cycle stress range

A B 46

B O 46

C D 6

D C 6

E J 40

F G 26

G F 26

H I 12

I H 12

J K 40

K L 26

L K 26

M N 14

N M 14

The half cycles in the above may be combined and subsequently arranged in order for further processing. It may be noted that the results of the rainflow and the reservoir counting are identical in this case.

31

Appendix – B

Assessment without damage calculation

(Simplified Procedure for use on MBG routes only) B.1 Apply MBG standard load in appropriate combination of the dead load, nominal

live load, impact, lurching and centrifugal force. The dead load stress will also have to be considered in determining the effective stress range. The loads shall be applied to the appropriate lengths of the point load influence lines so as to produce maximum and minimum values of stress at the detail under consideration.

B.2 Determine the maximum and minimum values of the principal stresses σp max

and σp min occurring at the location of the detail being assessed.

B.3 Determine the maximum stress range of stress σR max equal to numerical value of σp max - σp min . This should not exceed the limiting value of the stress-range (σT) for the detail under consideration.

B.4 Obtain the limiting stress range σT from the following expression –

σT = k1. k2. k3. k4. k5. σ0

k1 (design life factor) to be worked out by equating σT & σR max k2 (multiple cycle factor) is 1.0 as it is assumed that the loading event

produces only one cycle of stress. k3 (loading factor) is to be taken from Table-B.1. k4 (GMT factor) to be taken from Table –B.2. k5 (lane factor) 1.0 as only single lane bridges are to be analyzed.

σ0 = σr at N = 107,

= 53 MPa

B.5 Equate the limiting stress range, σT with σR max to get, ‘k1’ from the following expression - k1 = σR max/ (k2. k3. k4. k5) σ0

32

Table B.1 Values of k3 for RU loading (considered equivalent to IRS MBG loading)

S.No. Loaded length (L) (m)

Values of k3

1 < 3.4 1.0

2 3.4 to 4 1.09

3 4.0 to 4.6 1.23

4 4.6 to 7.0 1.37

5 7.0 to 10.0 1.53

6 10.0 to 14.0 1.71

7 14.0 to 28.0 1.92

8 > 28.0 2.19

Note : L is the base length of the point load Influence Line

Table B. 2 Values of GMT factor, k4.

Annual GMT

42 - 27 27 - 18 18 - 12 12 - 7 7 - 5 < 5

Values of k4

0.89 1.0 1.13 1.27 1.42 1.6

B.6 Design life in years is the lesser of the following –

i) 120 x k1

-m

ii) 120 x k1-(m+2),

where m = 3 for category ‘D’ Note – For analysis of cross girders and stringers, maximum bending moment is

to be calculated after considering the partial fixity of 33 1/3 % at the supports. This will give maximum bending moment at mid span as 7wl2/72 or say wl2/10. (See figure-B.1)

33

M1 1M

w l

12

2

12

w l 2

W (t/m)

l (m)

24

w l 2

M = i.e. 100% FIXITY AT SUPPORTS1 12

w l 2CASE - I

36

w l 2 w l 2

M2 M2W (t/m)

36

l (m)

2

CASE - II

2M1

3 3

1M = i.e. 33 % FIXITY AT SUPPORTS

Fig. - 1

7 w l

72

Figure B.1 – Fixity at ends of cross girders & stringers

34

Table B.3 Assessed Fatigue life of various members of std. Open Web Girders (Rivetted Type)

(a) 30.5 m span, BGML loading, BA-11122

Member

Stress Range σRmax

(N/mm2)

Loaded Length

‘L' (m)

Loading factor, k3

Design Life (years) for GMT

42 -27 27 -18 18 -12 12 -7 7 -5 <5

L0-L1 68.43 31.926 2.19 413 586 845 1199 1677 2398 L1-L2 69.32 31.926 2.19 397 563 813 1154 1613 2308 L2-L3 81.59 31.926 2.19 244 345 498 708 989 1415 L0-U1 -58.65 31.926 2.19 656 930 1342 1905 2663 3809 U1-L2 113.63 25.54 1.92 39 69 124 177 247 353 L2-U3 85.46 19.16 1.92 143 203 292 415 580 830

U1-U2 -71.73 31.926 2.19 358 508 733 1041 1456 2082 U2-U3 -72.68 31.926 2.19 345 489 705 1001 1400 2002 U1-L1& U3-L3 64.07 10.642 1.71 239 340 490 696 972 1391 Stringer 84.24 5.321 1.37 32 57 105 157 220 315 X-girder 82.94 5.28 1.37 34 62 114 165 231 330

(b) 45.7 m span, BGML loading, BA-11102

Member

Stress Range σRmax

(N/mm2)

Loaded Length

‘L' (m)

Loading factor, k3


42 -27 27 -18 18 -12 12 -7 7 -5 <5

L0-L1 77.12 47.24 2.19 288 409 590 838 1172 1676 L1-L2 67.04 47.24 2.19 439 623 899 1276 1783 2551 L2-L3 84.65 47.24 2.19 218 309 446 634 886 1267 L3-L4 84.96 47.24 2.19 216 306 442 627 876 1253 L0-U1 -92.73 47.24 2.19 166 235 340 482 674 964 U1-L2 96.42 38.38 2.19 148 209 302 429 599 857 L2-U3 -84.27 32.48 2.19 221 314 452 642 898 1284 U3-L4 97.05 26.67 1.92 85 138 200 283 396 567

U1-U2 -73.76 47.24 2.19 330 468 675 958 1339 1915 U2-U3 -98.53 47.24 2.19 138 196 283 402 562 803 U3-U4 -87.82 47.24 2.19 195 277 400 567 793 1135 U1-L1& U3-L3 64.77 11.81 1.71 232 329 474 673 941 1346 Stringer 94.73 5.905 1.37 18 32 58 105 155 221 X-girder 90.64 5.28 1.37 22 40 73 126 177 253

35

(c) 61.0 m span, BGML loading, BA-11172

Member

Stress Range σRmax

(N/mm2)

Loaded Length

‘ L' (m)

Loading factor,

k3


42 -27 27 -18 18 -12 12 -7 7 -5 < 5

L0-L1 73.83 63 2.19 329 466 673 955.12 1335 1910 L1-L2 73.83 63 2.19 329 466 673 955.12 1335 1910 L2-L3 85.86 63 2.19 209 296 428 607.34 849 1214 L3-L4 85.86 63 2.19 209 296 428 607.34 849 1214 L0-U1 -92.83 63 2.19 209 235 338 480.42 672 961 U1-L2 98.51 54 2.19 165 196 283 402.14 562 804 L2-U3 -83.28 45 2.19 138 325 469 665.51 930 1331 U3-L4 57.52 36 2.19 229 986 1423 2019.54 2823 4038

U1-U2 -90.99 63 2.19 176 249 359 510.23 713 1020 U2-U3 -90.99 63 2.19 176 249 359 510.23 713 1020 U3-U4 -91.50 63 2.19 173 245 353 501.71 701 1003 U1-L1 & U3-L3 79.09 15.75 1.92 180 256 369 523.60 732 1047 Stringer 79.17 7.875 1.53 43 78 134 189.60 265 379 X-girder 85.09 5.5 1.37 30 54 100 152.72 213 305

(d) 76.2 m span, BGML loading, BA-11152

Member Stress Range σRmax

(N/mm2)

Loaded Length

‘ L' (m)

Loading factor, k3


42 -27 27 -18 18 -12 12 -7 7 -5 < 5

L0-L1 67.19 78.8 2.19 436 619 892 1267 1771 2533 L1-L2 54.17 78.8 2.19 832 1180 1703 2418 3380 4835 L2-L3 74.41 78.8 2.19 321 455 657 933 1304 1866 L3-L4 72.45 78.8 2.19 348 493 712 1011 1413 2021 L4-L5 74.57 78.8 2.19 319 453 653 927 1296 1854 L0-U1 -58.21 78.8 2.19 671 952 1373 1949 2725 3898 U1-L2 85.92 70.04 2.19 209 296 427 606 847 1212 L2-U3 -86.09 61.29 2.19 207 294 424 602 842 1205 U3-L4 97.26 52.53 2.19 144 204 294 418 584 835 U4-L5 82.91 43.77 2.19 232 329 475 675 943 1349

U1-U2 -74.15 78.8 2.19 325 460 664 943 1318 1886 U2-U3 -74.15 78.8 2.19 325 460 664 943 1318 1886 U3-U4 -84.95 78.8 2.19 216 306 442 627 876 1254 U4-U5 -84.95 78.8 2.19 216 306 442 627 876 1254 U1-L1 & U3-L3 68.43 15.76 1.92 278 395 569 808 1130 1616 Stringer 85.53 7.88 1.37 30 53 97 150 210 301 X-girder 81.36 5.5 1.37 38 68 123 175 244 349

36

Table B.4 Assessed Fatigue life of various members of std. Open Web Girders (welded Type)

(a) 30.5 m span, MBG loading, BA-11462

Member

Stress Range σRmax

(N/mm2)

Loaded Length

‘L' (m)

Loading factor,

k3


42 -27 27 -18 18 -12 12 -7 7 -5 < 5

L0-L1 48.28 31.926 2.19 1175 1667 2406 3415 4774 6830 L1-L2 48.82 31.926 2.19 1137 1613 2327 3303 4617 6605 L2-L3 75.79 31.926 2.19 304 431 622 883 1234 1766 L0-U1 -76.58 31.926 2.19 295 418 603 856 1196 1711 U1-L2 86.43 25.54 1.92 138 196 283 401 561 802 L2-U3 81.96 19.16 1.92 162 230 331 470 658 941 U1-U2 -71.97 31.926 2.19 355 503 726 1031 1441 2062 U2-U3 -72.75 31.926 2.19 344 487 703 998 1395 1996 U1-L1 &U3-L3 73.29 10.642 1.71 160 227 327 465 650 930 Stringer 80.44 5.321 1.37 40 72 127 181 253 362 X-girder 86.27 5.28 1.37 28 51 93 147 205 293

(b) 45.7 m span, MBG loading, BA-11482

Member

Stress Range σRmax

(N/mm2)

Loaded Length

‘L' (m)

Loading factor, k3


42 -27 27 -18 18 -12 12 -7 7 -5 < 5

L0-L1 65.20 47.24 2.19 477 677 977 1387 1938 2773 L1-L2 65.87 47.24 2.19 463 657 947 1345 1880 2690 L2-L3 80.41 47.24 2.19 254 361 521 739 1034 1479 L3-L4 80.64 47.24 2.19 252 358 516 733 1025 1466 L0-U1 -73.18 47.24 2.19 338 479 691 981 1371 1961 U1-L2 104.24 38.38 2.19 115 166 239 339 474 679 L2-U3 -96.83 32.48 2.19 146 207 298 423 592 846 U3-L4 100.45 26.67 1.92 71 125 180 256 357 511 U1-U2 -98.56 47.24 2.19 138 196 283 401 561 803 U2-U3 -99.97 47.24 2.19 132 188 271 385 538 769 U3-U4 -99.92 47.24 2.19 133 188 271 385 539 771 U1-L1& U3-L3 79.48 11.81 1.71 125 178 257 364 509 729 Stringer 85.67 5.905 1.37 29 52 97 150 209 299 X-girder 83.10 5.28 1.37 34 61 113 164 229 328

37

(c) 61.0 m span, MBG loading, BA-11582

Member

Stress Range σRmax

(N/mm2)

Loaded

Length L' (m)

Loading factor, k3


42 -27 27 -18 18 -12 12 -7 7 -5 < 5

L0-L1 56.66 63 2.19 727 1031 1488 2112.76 2953 4225 L1-L2 56.66 63 2.19 727 1031 1488 2112.76 2953 4225 L2-L3 69.51 63 2.19 394 559 806 1144.56 1600 2289 L3-L4 69.51 63 2.19 394 559 806 1144.56 1600 2289 L0-U1 -70.93 63 2.19 394 526 759 1077.06 1506 2154 U1-L2 107.29 54 2.19 371 152 219 311.25 435 622 L2-U3 -91.45 45 2.19 99 245 354 502.58 703 1005 U3-L4 36.79 36 2.19 173 3769 5438 7720.37 10792 15438

U1-U2 -91.87 63 2.19 171 242 349 495.68 693 991 U2-U3 -91.87 63 2.19 171 242 349 495.68 693 991 U3-U4 -91.93 63 2.19 170 242 348 494.71 692 989 U1-L1 & U3-L3 -72.73 15.75 1.92 232 329 474 673.18 941 1346 Stringer 77.69 7.875 1.37 48 86 141 201 281 401 X-girder 73.28 5.5 1.37 64 115 168 239.15 334 478

(d) 76.2 m span, MBG loading, BA-11602

Member Stress

Range σRmax

(N/mm2)

Loaded

Length L'

(m)

Loading factor,

k3


42 -27 27 -18 18 -12 12 -7 7 -5 < 5

Lo--L1 57.484 78.8 2.19 696 988 1425 2024 2829 4046 L1-L2 57.484 78.8 2.19 696 988 1425 2024 2829 4046 L2-L3 75.988 78.8 2.19 301 428 617 876 1225 1752 L3-L4 75.988 78.8 2.19 301 428 617 876 1225 1752 L4-L5 78.975 78.8 2.19 269 381 550 780 1091 1560 L0-U1 -61.070 78.8 2.19 581 824 1189 1688 2359 3375 U1-L2 97.938 70.04 2.19 141 200 288 409 572 818 L2-U3 -84.020 61.29 2.19 223 316 456 648 906 1296 U3-L4 71.950 52.53 2.19 355 504 727 1032 1443 2064 U4-L5 76.689 43.77 2.19 293 416 600 852 1191 1704

U1-U2 -79.639 78.8 2.19 262 372 536 761 1064 1522 U2-U3 -79.639 78.8 2.19 262 372 536 761 1064 1522 U3-U4 -87.985 78.8 2.19 194 275 398 564 789 1128 U4-U5 -87.985 78.8 2.19 194 275 398 564 789 1128 U1-L1 & U3-L3 65.066 15.76 1.92 324 459 662 940 1314 1880 Stringer 84.537 7.88 1.37 60 108 163 231 323 462 X-girder 74.026 5.5 1.37 66 119 172 244 342 489

38

Table B.5 Assessed Fatigue life of std. plate girder bridges for different GMTs (for MBG loading)

Std.

Span RDSO Drg. No.

Stress Range σRmax

(N/mm2)

Loaded Length

L' (m)

Loading factor,

k3


42 -27 27 -18 18 -12 12 -7 7 -5 < 5

12.2 MBG

B-16009 (4 Million)

118.33 13.1 1.71 18 32 58 105 154 221

B-16012 (10 Million)

95.75 13.1 1.71 51 91 147 208 291 417

18.3 MBG

B-16010 (4 Million)

109.35 19.4 1.92 47 84 140 198 277 396

B-16013 (10 Million)

84.22 19.4 1.92 149 212 305 434 606 867

24.4 MBG

B-16011 (4 Million)

93.02 25.6 1.92 105 157 227 322 450 643

BA-16005 (10 Million)

84.15 25.6 1.92 150 212 306 435 608 869

12.2 BGML


112.88 13.1 1.71 22 40 74 127 178 254

18.3 BGML


111.86 19.4 1.92 42 75 130 185 259 370

24.4 BGML


107.20 25.6 1.92 52 92 148 210 294 420

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