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Ministry of Railways Government of India
Assessment of Residual Life of
Ganga Bridge No. 110 UP (Near Kanpur) Lucknow Division Northern Railway
REPORT NO. BS –75
AUGUST – 2005
RESEARCH DESIGNS AND STANDARDS ORGANISATION
MANAK NAGAR LUCKNOW-226011
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PREFACE
After completion of the Codal life of a bridge, field engineers remain in doubt whether the bridge is to be replaced or should be continued. Subject matter assumes further importance when condition of the bridge seems to be good, but from fatigue consideration, it is hard to take any decision. As such, from safety consideration, many such bridges were sanctioned for regirdering.
To overcome the problem arising out of such situations, RDSO asked Zonal Railways that in case of doubt, services of RDSO can be taken in assessment of the residual life estimation of old steel bridges ( not early steel) which have completed its codal life. In response to that, many proposals came to RDSO. Proposal of Ganga Bridge No. 110 on Kanpur – Lucknow section was one of them. Among them, residual life estimation of Bridge No. 110 DN was taken first, since regirdering work of this bridge was a sanctioned work . The report of the testing of this bridge has been published ( Report No. BS-70 ) in Dec.2004. As per conclusion of the report, the estimated residual life of the bridge with present day traffic density was assessed as 32 years and Northern Railway was advised accordingly. By virtue of the test results, the expenditure of about 15 crores Rupees likely to be incurred in regirdering has been saved. It was the good opportunity to test Up line girders also during the Dn line testing, hence for this work, under the guidance of Sh. S.C.Gupta, Director/B&S/Testing, a team of the staffs consisting of S/Shri Ramji lal, K. sukumaran,.V. K. Singh, SRE, Samir Paul and S.K. Awasthi, JRE-1 was constituted. The assessment of residual life of the bridge based on code BS 5400 was done by Sh. R.K. Goel, Director/ B&S/SB-1 and his staff. The instrumentation assistance was provided by the staff of Research Instrumentation Lab, namely S/Shri F.C.Shrivastava,SRE , Harish Kohali and Anand Prakash, JRE-1
Fatigue testing of the samples taken out from the bridge was conducted by the staff of Fatigue Testing Lab., under the guidance of Shri Mohan lal, SRE. All the necessary help / assistance provided in conducting the above tests by the officers and staff of Bridge workshop Northern Railway, Lucknow is sincerely acknowledged. Contribution of all the team members in conducting test under adverse weather conditions specially recording of strain – time history of sectional trains during chilly cold nights and analysis of huge data manually is highly appreciated. Guidance provided by Shri S.C. Gupta, to the team members was worth appreciating, is sincerely acknowledged. Contribution of Sh. R.K.Goel DBS/SB-I and his staff in assessing the residual life using provisions of BS-5400 is also worth appreciating. This report is submitted herewith for further necessary action to N. Rly.
( R. K. Gupta )
Executive Director/ B&S
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INDEX
S.No Contents Page no.
1. Introduction 1
2. Objective 2
3. Details of bridge 2
4. Methodology 3
5. Fatigue 4
6. Instrumentation and recording of data 7
7. Analysis of data 9
8. Observations 9
9 Estimation of residual life 11
10. Fatigue life assessment based on Code BS 5400 approach 13
11. Conclusions 16
TABLES
1 Loading program and test results of fatigue testing of samples
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2 Details of trains passing over the bridge during recording of strains
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3 Observed and modified values of stress ranges and cycles 20
4 Details of traffic density passed during the year 1981 to 2003
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FIGURES
1 Test specimen for fatigue testing 22
2 S-N Curve 23
3 Bar chart of traffic density per year 24
3a Cumulative Increase in traffic density since 1981-2003 24
4 Instrumentation details of strain gauges 25
5 Histogram of observed values of Stress ranges and cycles 26
5a Histogram of modified values of stress ranges and cycles 27
6 Copy of actual record of strains-time history for Pass. train 28
ANNEXURES
I Copy of the letter from CBE/N. Rly. for assessment of Residual life of Bridge No. 110 near Kanpur
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II & IIa Details of strain gauges and its calibration 30
III A sample sheet of stress time history and Rain flow counting method
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IV Assessment of residual fatigue life based on code BS 5400 approach
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Reference 35
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ASSESSMENT OF RESIDUAL FATIGUE LIFE OF BR. NO. 110 UP GANGA BRIDGE NEAR KANPUR , N. RLY.
1.0 INTRODUCTION :
There are large number of bridges constructed after 1905, (The reference year for guessing a bridge whether it is an early steel or not, if metallurgical details are not available) and thus completed its codal life., Field engineers, often find themselves in dilemma to take appropriate decision about such bridges i.e. whether to replace them or to continue them. Main problem comes from fatigue consideration, whether residual life of the bridge is available or not? To solve the field problems, RDSO vide letter no. CBS / Inspection dt. 20.01.2003 offered its assistance to CBE‟s of the Zonal Railways in estimating the residual life of the bridges. In response to that, many railways approached RDSO including N.Rly. with their offer of Ganga bridge no. 110 Dn of Lucknow - Kanpur section ( Annexure-I ). This work was one of the sanctioned work for regirdering under SRSF. As such, among the various options, this work was first taken in hand in the month of Jan.- Feb. 2004 and report No. BS- 70 has been published in the month of Dec. 2004. The report concludes that the bridge is still having life of about 25 to 30 years and hence recommended that regirdering work of the Dn line bridge can be postponed at present saving precious public money.
During the testing of the Dn line bridge girders, Up line girder was also instrumented
to get stress-time history. Some samples were also taken from the instrumented girder for fatigue testing to get residual life of the bridge. This report is prepared after the analysing the test data and estimating the residual life of the up line bridge.
Earlier, RDSO has conducted the study of assessing the residual life of steel girders
fabricated and erected before 1905, designated as “Early Steel Girders”. Laboratory and field trials were conducted on such bridges. S-N Curves were developed by the fatigue testing of the samples taken out from existing / released girders of these bridges. Fatigue damage was assessed using Palmgren Miner‟s Hypothesis. Based on these tests, report no. BS-5 in the name of “Assessment of Residual Life of Early Steel Wrought Iron Girder Bridges” was issued in 1995 to all concerned.
Further more, keeping in view the importance of the subject matter, another report
prepared in the name of “Guidelines for Assessment of Residual Fatigue Life of Early Steel/Wrought Iron Girder Bridges” and issued as BS-39 in september-2001. In this report, in addition to giving some brief details about the subject matter, copy of a sample draft memorandum was also attached for the benefit of Zonal Railways so that, they can do such work in association with some consultants. As a follow up action, Central Railway has got done such work in association with IIT Mumbai for Tapti Bridge.
There are so many approaches to determine the of residual life of steel girder
bridges. Among them, Palmgren Miner‟s theory is more versatile and easy to understand.
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The same principle has been used here, details of which, is given in the subsequent para‟s.
2.0 OBJECTIVE : To assess the residual life of the girders of Bridge no. 110 UP between Lucknow -
Kanpur section , which is a non early steel girder bridge but having life of about 79 years. 3.0 DETAILS OF BRIDGE :
The existing bridge having double BG track consisting of 25x30.48m + 1x12.19 m span was commissioned in the year 1910. Earlier, the bridge was having one BG and one MG track but due to gauge conversion in the year 1993-94, NE Railway survey report found that the girders used for MG traffic are safe to carry BGML loading and since then, the down line traffic of BG are passing through these girders. New girders were erected on down stream side of these girders in the year 1926 and since then the Up line traffic is passing through these new girders. It is worthwhile to point out that the first bridge at this site was constructed for broad gauge line on UP stream side of this bridge in the year 1875. However, the bridge was used for MG line only. The same bridge was then handed over to State Government in the year 1925. The view of the above bridges from the river bed is shown below in photograph-1 and the closeup of Up & Dn line girders from the river bed is shown in photograph-2.
Photograph-1 View of different bridges across river Ganga near Kanpur.
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Photograph-2 View of Up/ DN line bridge girders from the river bed.
4.0 METHODOLOGY : The fatigue life of the above bridges has been assessed by the following two methodologies.
4.1 S-N curve Approach – It is Based on actual field measurements of stress- time history & S-N curve of actual samples of the girders, subjected to Palmgren Miner‟s hypothesis. 4.2 BS- 5400 Approach – It is based on the theoretical calculations of stresses likely experienced by the girders.
The essential information which is required to assess the fatigue life of a structure is the pattern of stresses likely to be observed in it, during the passage of normal traffic and the relationship between the applied stress cycles and the number of times these can be withstood by the material of the structure. This can be achieved by subjecting the representative samples not only to varying constant amplitude cycles or stresses but also to complete stress spectrum. Using test results and curve fitting technique, S-N relationship can be obtained. Under normal service conditions, railway bridge structures are subjected to spectrum of varying stress – amplitude and therefore, a process of damage accumulation continues. The fatigue damage depends on the combined effect of the frequencies of different stress ranges observed by the structure under service loading. Referring to Palm-gren Miner‟s theory of linear damage accumulation , the total damage to the structure is given by D= ∑ ni/Ni.
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Where , ni = Observed number of stress cycles for different stress ranges
Ni = Total number of stress cycles corresponding to observed stress ranges from S-N curve.
i = 1,2,3 …. Upto n stress ranges
When the damage ( D) become equal to 1, the specimen fails and so the failure occurs when D= ∑ ni/Ni. = 1
Many researchers have not been able to find good credence to this hypothesis. The main reason is that a stress cycles causes different extent of damage depending on its application on the material during its life. Research carried out by ORE, under question D-128, has suggested that under assumption of normal distribution of fatigue test data, the probability of failure by fatigue is considerably low when the life is evaluated at two standard deviations below 50 % probability curve. To achieve this, the cumulative damage factor in the above equation is taken as 0.3 by using 50% fatigue failure probability curve, Therefore, in our study the criterion for fatigue failure is taken as D= ∑ ni / Ni = 0.3
5.0 FATIGUE :
The term Fatigue, as it is commonly used, refers to the behavior of materials under the action of repeated stresses or strains as distinguished from the behavior under static stresses or strains. The definition of fatigue as currently stated by the American Society for Testing of Materials (ASTM) is as follows :
“ The process of progressive localized permanent structural change occurring in a material subjected to conditions which produce fluctuating stresses and strain at some point or points and which may culminate in cracks or complete fractures after a sufficient number of fluctuations.”
5.1 Stress range concept in fatigue : The passage of a vehicle over a bridge produces a single major stress cycle with
superimposed vibration stresses. One cycle is the smallest segment of stress versus time variation which is repeated periodically. Under variable amplitude loading the definition of one cycle is not clear, therefore reversal of stresses are considered . In constant amplitude loading, one cycle contains two reversals. For most of the bridges, except the cantilever span bridge, vibration stresses are small enough so as to be safely neglected in fatigue considerations. The difference between maximum stress (S.Max.)and the minimum stress (S. Min.) which corresponds to dead load, is called the stress range (Sr.). The stress range obviously varies with the size of the vehicle, but the minimum stress corresponding to dead load (S. Min.) remains essentially constant throughout the life of the bridge.
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5.2 Equivalent number of cycles : In practice , bridges are always subjected to variable amplitude loading with a compact
load spectrum. For the purpose of analysis, it is convenient to represent a complex load spectrum with an equivalent number of simple load cycles. This is particularly helpful for bridge applications since each vehicle passage produces one complex cycle and this can be represented by equivalent number of simple cycles.
5.3 Counting methods for stress cycles :
The counting methods are used to convert irregular complex load histories into an equivalent number of uniformly repeated simple load cycles. Practically, all counting methods count a cycle with the range from the highest peak to the lowest valley and seek to count other cycles to a manner that maximize the range that are counted. In fatigue, this rule can be justified by assuming that intermediate fluctuations are less important than the overall differences between high and low points. Studies to establish the relationship between numerical probability of structural failure and certain statistical histogram derived from measured load time histories have been done in many fields. Different counting methods for this purpose are available and we must select the most reasonable and practical method for our purpose from amongst the most widely used counting methods, viz. :
a. Rain flow counting method b. Range pair counting method c. Modified range pair counting method d. Peak count method e. Mean crossing peak counting method f. Level crossing count method g. Fatigue meter count method h. Range count method i. Range mean count method j. Modified range count method k. Race track or ordered overall range method
The most widely used counting methods are range pair method, rain flow method and race track method or ordered overall range method. Rain flow counting method has been used in this study because it is most suitable method for condensing load histories.
5.4 Number of cycles :
In design practice two million cycles is considered a suitable maximum life for railway bridges and as a result, it became conventional to limit fatigue determination to two million cycles. This is also influenced to be the fact that the excessive time required for tests to be continued for longer endurance‟s . Moreover, Commission XIII of the International Institute of Welding suggested that all fatigue investigations should include the determination of the fatigue strength at two million cycles and this was defined as the stress at which three
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specimens survived two million cycles unbroken. It is, therefore, accepted conventionally and to reduce test work that the stress that can be withstood for two million applications of loading is the fatigue limits.
5.5 S.N. Curve:
The relationship between constant amplitude stress range (Sre) applied to the specimen and number of cycles upto its failure (N) is called SN Curve. Generally it is plotted on log-log scale with number of cycles in millions on abscissa and stress range in N/mm2 on ordinates. The slopping line represents the finite fatigue life of the material. Mathematically SN curves are defined in log-log form by the following equations:
Log N = Log a –M.Log Sre Where, log a is the intercept on x-axis and M is the reciprocal of the slope of the finite life portion of the SN curve. In normal form N is represented by the following equation:
N = a / (Sre)m 5.6 Fatigue testing:
Out of 12 numbers of specimen selected for fatigue testing from Up line, only 8 specimen ( 4 each from Diagonal and Vertical members ) were fatigue tested in Fatigue testing lab of RDSO. 4 numbers of specimen takenout from bottom chord members could not be tested up till now due to non availability of fatigue testing machine. The specimen of 300mm length without holes were fabricated by welding end plates on either side of the specimen as shown in fig.1. and subjected to fatigue test as per program of loading as shown in table -1. The number of cycles at which the samples tested/failed is also shown in the table.
Sample designated as UD-1did not fail even after completing 2 million cycles at 70 N/mm2 stress range. Other samples have failed below 2 million cycles due to some higher load ranges. Sample designated as UD-4 was kept for testing up to 10 million cycles at 40 N/mm2 stress range but failed prematurely at 1.95 million cycles. The higher values of load ranges are selected , so that the values of stress ranges cover almost all the parts of the anticipated SN curve. The minimum load is taken as 30 KN for all the samples. It has been noticed that generally fatigue crack appears near the weld of end plates and propagates slowly before failure, which shows the ductile nature of the material. The actual values of cycles at failure with their corresponding stress ranges are plotted on log-log scale. The best fit line, representing maximum number of points is drawn. This line represents the SN curve for the material of the girder. The samples designated as UD-2 and UD-3 which failed very early, are not considered for plotting the SN curve as the values are not reliable. The SN relationship so obtained is shown in fig. 2 and is used for calculating the residual life of the girders. The values of constant a and M of the curve, calculated are 321 x 106 and 2.61 respectively. Therefore the equation of the curve is:
N = 321 x 106
(Sre)2.61
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or Log N = Log 321 x 106 - 2.61 log (Sre) 5.7 Traffic Density and Speed:
Since the residual life calculations as per Miner‟s summation rule are based on the damage caused per day by the present day traffic and hence the traffic passed in the past will not effect the residual life calculations. As the traffic density increases in future, the residual life will decrease and will affect the calculations. The details of traffic passed in GMT on the bridge during 1981 to 2003 is shown in table-4, fig.3 & 3a . On perusal of the table and figures , it is seen that the traffic density was 3.64 GMT in the year 1981-82 increases to 16.40 GMT in the year 2000-01. However, it reduces slightly in next 2 years, but expected to rise in the future and will affect the future calculations of residual life. The increase in speed of the rolling stock will also affect the residual life and this will also be considered for future calculations by multiplying the observed stresses by a suitable factor depending upon the Impact Factor. For 30.5 m span, the impact factor is 0.375 at full impact ( Ref. Bridge Rules ) and the observed stresses may be augmented for the higher speed. For calculations of residual life, the likely increase in number of trains in the future should be subtracted from the calculated trains to pass during the remaining life.
6.0 INSTRUMENTATION AND RECORDING OF DATA :
The highly stressed members of span No. 1 from Lucknow end of girder were strain gauged for recording stresses in different members under the passage of normal trains. The view of the girder from river bed and from the top of the pier are shown in the photographs – 3 & 4. The locations of strain gauges are shown in fig. 4. The strains were recorded for the equivalent number of trains passing over the bridge during 24 hours duration. The details of the equivalent number of trains whose recording is done and expected to pass over the bridge during 24 hours are shown in table -2. Electrical resistance strain gauges are used for measuring strains. The details of strain gauges used and their calibrations are given in Annexure - II & II a. Strain gauges were also fixed in one of the rails at Lucknow end for locating the position of wheels of the train passing over the bridge on the recording paper (Wheel marker). The relative distance of the wheels of the particular rolling stock being known, the speed of the trains can be calculated by measuring time interval that elapsed between the passage of particular wheels. The surface of the member is smoothened by emery paper/ grinder and cleaned by acetone before fixing the strain gauges. Strain gauges are fixed with the help of Araldite hardener and kept under pressure for 24 hrs. These are dried by table lamp/heater. A layer of Araldite hardener was applied on strain gauges to protect them from moisture. Three “Brush” oscillogram recorders were used to record the strains for 48 trains passing on the bridge.
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Photograph – 3 View of the tested girder from the river bed
Photograph – 4 View of the girder from top of the pier
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Passenger train can be identified from the dynamic strain signals recorded on the chart paper. This is because there is an initial large strain peak, followed by a substantially lower peak strain level during the passage of the train over the span. The initial large strain peak coincides with the passage of the engine, and the subsequent lower peak strain level corresponds to the passage of the passenger bogies. Similarly, a goods train with fully loaded wagons can be easily identified. This is because the peak strain levels are fairly uniform during the passage of the train, as the axle loads of the engine and the fully loaded goods wagons are roughly similar. The flicks given by strain gauges fixed on the web of the running rail due to passing of wheels on the rail can also be used to identify the type of train alongwith number of coaches/ wagons passing on the tested span.
7.0 ANALYSIS OF DATA : In order to draw the stress histogram i.e. the diagram which represents the number of
times various stress level occurs at a point in a bridge under defined traffic condition, stress- time history records for each type of the train passing over the bridge were analyzed. The analysis of data was done by Rain-flow counting method. This method of counting is preferred for bridges as this method counts all parts of the stress- time history exactly once and is described briefly as under:
In Rain flow counting method, a half cycle is counted from the initial strains to the maximum from whence, it drops to the next slope and to the next maximum and so on. Again a half cycle is counted from the highest maximum reached on the previous half cycle down to the next slope and on the next minimum and so on. The counting started from the minimum strain value and ended at a minimum value when the similarity of the cycle ends. A sample sheet of calculation of stress time history by Rain flow counting method is shown in Annexure-III. The number of cycle were counted separately for each train composition. These half cycles were sum up for all the train recorded and these values are divided by two to make a full cycle. The peak value of these cycles are converted into stresses in N/mm2 as per the conversion factor as shown in Annexure -II & II a. These stresses under dynamic conditions are divided into different groups of stress ranges , like 0-10, 10-20, 20-30, …. N/mm2 and so on, with number of occurrences of these stress ranges .Stress histograms are prepared for different members of the bridge instrumented. With the frequencies of these different stress ranges, stress histograms prepared are shown in table-3 and fig. 5.
8.0 OBSERVATIONS: 8.1 The limited number of samples on which fatigue test were conducted reveals that even
when identical specimens are tested at a single stress range under similar conditions , different fatigue lives have been observed, resulting scatter in SN plot. This scatter can not be eliminated through any extent of refinement in experimental technique and the same appears to be intrinsic as has been observed at all stress ranges. In fact, scatter is an important factor in attaching reliability to determine fatigue life.
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8.2The highest and lowest value of stress level observed are in the bottom chord and vertical members of the truss are 40 & 20 N/mm2 respectively. These values are observed during the entire 48 trains recordings expected to pass over the bridge during 24 hours period. The details of the observed values of stress ranges for different members under dynamic conditions are shown in table no.3 and the corresponding stress histogram for different members of the bridge are shown in fig.5.
8.3 It should be noted that the stresses obtained in the different bridge members during the
test and numerically determined are not indicative of the actual stress levels at the points of stress concentration in the member, which occur at the rivet holes and can be determined by the maximum stress recorded for the members of the girder by multiplying by a stress concentration factor.
8.3.1 As per para. 2.1 of Civil Engineering Report No. C-245 of RDSO, the study conducted
by British Railways on Early Steel / Wrought Iron girders also indicates poor fatigue performance of these type of girders due to cracking of rivet holes due to hole punching and stress concentration factor as such points may be as high as three times the average stresses.
8.3.2 As per Annexure IV of report BS-5 of RDSO, The stress analysis on steel specimen
containing five rivet holes by photo-elastic technique, also suggest that stress concentration factor is approximately 3 near the hole boundary than in between the two holes.
8.3.3 As per para. 3.4 of the report on „ Fatigue life of riveted railway bridges‟ by Bjorn
Akesson of Chalmers university of technology, Sweden, „ The most severe defect ( i.e., stress raiser ) in a riveted connection with respect to fatigue is the rivet hole itself. For an axially loaded infinite plate with a centrally located hole, the nominal stress at the net section is raised by a factor of three at the edges of the hole. The stress concentration factor K is defined as the ratio between the maximum stress at the defect ( in this case the rivet hole ) and the nominal stress at the gross section. Therefore, the stress concentration factor is equal to 3. Even though, there is a substantial rise of the stress near the rivet hole edge, the stress is of the same magnitude as the nominal stress level at a distance of approximately the rivet hole diameter from the rivet hole edge.
8.3.4The observed stress ranges are very low. The fatigue testing of most of the specimen
are conducted for higher ranges as the limit of testing is kept up to 2 million cycles. For lower ranges the test limit is kept up to 10 million cycles. So to save time only one specimen was tested for lower range i.e., at 40 N/mm2, but the specimen fails at 1.95 million cycles and lower segment of the S-N curve could not be drawn. Hence, the life is calculated by extending the upper segment of the curve for observed lower stress ranges. Although the specimen were tested without holes, but due to above reasons the stress concentration factor is taken 2.5 instead of 3.0.
8.3.5 Therefore, considering the above points, the maximum stress obtained in bottom chord
member under the current loading conditions is 100 N/mm2 and for vertical member, the
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value of stress level becomes 50 N/mm2. The modified values of stress level in different members, which may expected to occur at the critical locations after considering the maximum value of stress concentration factor as 2.5 are shown in table no.3 and the corresponding modified stress histograms for different members are shown in fig.5a. The modified stress ranges have been used for estimating the residual life of the girder.
8.4 It is observed that maximum values of strains are obtained when the locomotive of the
train passes over the span in all the members. Records of coaches/ wagons gives lesser values of strains. However, the loaded wagons gives the higher values of the strains and are comparable with the values obtained for the locomotives. The copy of the actual record of a passenger train passing over the bridge is shown in fig. 6.
8.5 Although, there is no speed restriction on the bridge, the observed strains in different
members may be less as actual speed of the trains passing over the bridge was observed below 50 Kmph. The speed of the trains might not be increasing on the bridge due to approaching Station. Hence, correction factor due to Coefficient of Dynamic Effect is not considered in augmentation of observed stresses for calculating the Residual life.
8.6 As the traffic density increases, the residual life decreases. Therefore, for future
calculations of residual life, the increase in number of trains should be subtracted from the calculations of total trains likely to pass during the remaining life of the girders .
9.0 ESTIMATION OF RESIDUAL LIFE:
Considering different safety factors and SN curve developed for limited number of fatigue testing of samples taken out from only vertical and diagonal members of the girders, the calculation of residual life of different members for the present traffic and speed is as follows.
(1) Member : Bottom Chord
Stress Range in N / mm2
No. of observed cycles (n)
No. of theoretical cycles as per SN curve X 106
1.1 2.7
10.5
100 - 75
12
75 - 50 23 50-25 14
Damage per Day (D) =∑ (ni/Ni) = [ (12/1.1) + (23/2.7)+(14/10.5) ] x 1/106 = 20.76 x 10-6 Residual Life = 0 .3/D = 14451 days = 40 years
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(2) Member: End Raker
Stress Range in N / mm2
No. of observed cycles (n)
No. of theoretical cycles as per SN curve X 106
2.7
10.5
75 –50 50-25
32 17
Damage per Day (D) =∑ (ni/Ni) = [ (32/2.7)+(17/10.5) ] x 1/106 = 13.47 x 10-6 Residual Life = 0 .3/D = 22272 days = 61 years (3) Member Vertical
Stress Range in N / mm2
No. of observed cycles (n)
No. of theoretical cycles as per SN curve X 106
10.5
50-25 173
Damage per Day (D) =∑ (ni/Ni) = [ (173/10.5) ] x 1/106 = 16.48 x 10-6 Residual Life = 0 .3/D = 18204 days = 50 years (4) Member: Diagonal
Stress Range in N / mm2
No. of observed cycles (n)
No. of theoretical cycles as per SN curve X 106
2.7 10.5
75-50 21 50-25 20
Damage per Day (D) =∑ (ni/Ni) = [ (21/2.7) + (20/10.5) ] x 1/106 = 9.68 x 10-6 Residual Life = 0 .3/D = 30992 days = 85 years
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(5) Member: Top chord
Stress Range in N / mm2
No. of observed cycles (n)
No. of theoretical cycles as per SN curve X 106
2.7 10.5
75 –50 50 - 25
8 34
Damage per Day (D) =∑ (ni/Ni) = [ (8/2.7) + (34/10.5) ] x 1/106 = 6.20 x 10-6 Residual Life = 0 .3/D = 48387 days = 133 years The total number of trains those can pass during the remaining life of the girders can also be calculated by taking 48 trains passing over the bridge per day, which are responsible for the present rate of fatigue damage. For the bottom chord member for which remaining life estimated is about 40 years, the maximum number of trains those can pass over the bridge estimated are 683280. This figure will be helpful in revised estimation of the residual life in case of increase in traffic density ( increase in number of trains ) in future. The residual life of different members of the bridge calculated is shown below:
Members Residual Life in years
Bottom Chord 40
Vertical 50
End Raker 61
Diagonal 85
Top Chord 133
10.0 FATIGUE LIFE ASSESSMENT BASED ON CODE BS 5400 APPROACH: The residual life of the bridge was also assessed by the procedure given in BS code-540part-10,clause 9.2, assessment without damage calculation.
10.1 General
BS-5400 part 10 is a comprehensive code which is based on the concept of cumulative fatigue damage. The fatigue assessment is based on Palmgren-Miner‟s damage summation model. For fatigue assessment of Railway bridges the methodology for determination of stress range has been described for different type of connections and a simplified procedure has been given for determining the limiting value of the maximum range of stress for the specified design life for two different types of standard loading. The code specifies different factor k1, k2, k3, k4 & k5 for design parameters such as design life, multiple cycle of stress loading, type of standard loading, annual GMT and multiple lane loading
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respectively. The code gives specific methodology and tables to calculate the factors for different design parameters.
10.2 Limiting Stress Range, σT
The constant amplitude non-propagating stress range, σ0 for the constructional detail is chosen appropriately on the basis of Table – 17 & Table 8 of the code. The limiting stress range σT is calculated for RU loading as under: σT = k1. k2. k3. k4. k5. σ0 ……………………………………………………..(1) 10.3 Check for Design Adequacy
The design adequacy of the given detail is checked as per Clause 9.2.2.2 and Clause 9.2.2.3 of the code. Where σRmax (Maximum Stress Range) should not exceed σT, i.e σRmax < σT, the detail may be considered to have a fatigue life in excess of the specified design life.
10.4 RU Loading & IRS-MBG Loading
A comparison of EUDL values of Bending Moment as per RU loading has been made with corresponding values for IRS-MBG loading and it is found that the EUDL values as per RU loading are on higher side as compared to IRS-MBG loading. Therefore, the various factors developed for RU loading as given in BS: 5400 Part 10 have been used for fatigue life analysis of the members of the bridge subjected to MBG loading which is expected to give a fatigue life on a conservative side.
10.5 Fatigue life analysis
The stresses calculated during the analysis and the cross sections provided in the existing design have been used to workout the fatigue life of the truss members. Following assumptions have been made during this study –
a) The maximum axial stresses due to EUDL for IRS loadings have been worked out and the maximum stress range calculated as the difference of dead load stress and the maximum stress likely to come in the member with DL, live load with impact and occasional load.
b) The axial stresses due to load combination with occasional load have been taken into consideration to find out the maximum stress range. This combination rarely occurs in practice, therefore, the analysis is on conservative side.
c) Material properties are assumed to be as per Table-8 of BS-5400 and σ0 value has been taken to be corresponding to detailed classification „E‟ of this table.
d) The fatigue life of standard spans has been assessed by calculating the design life factor k1. This factor has been worked out as σRmax/(σ0 x k3) and fatigue life calculations have been done by inversion, using the equations given in Clause 9.2.3 of BS-5400 Pt.10 by taking fatigue life as minimum of following:
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m
1k
120 Life Fatigue …………………………………………………………..(2)
or
2m
1k
120 Life Fatigue
…………………………………………………………(3)
Where m = 3.0 taken from Table-8 for detailed Class „D‟.
e) Value of RU loading factor k3 has been taken from Table-4 of the code considering the
case of heavy traffic loading, corresponding to the base length (L) of the influence line diagram for the member.
f) Value of GMT factor, k4 is assumed as 1.0 for GMT of 18 to 27 million tonnes. Actual GMT data suggests that this assumption is very much on conservative side.
g) For single lane loading value of lane factor, k5 is taken as 1.0. 10.6 Conclusion
The design calculations for assessment of fatigue life of members of truss girders has been done as given in Annexure-IV for standard annual GMT of 27 to 18. The verticals U1-L1 & U11-L11 are found to have minimum fatigue life of 141 years. As per record the bridge was constructed somewhere around 1926. Therefore, the bridge can be considered to have a remaining fatigue life of about 62 years.
19
11.0 CONCLUSIONS:
i) Based on the field observations, among the different bridge components, bottom chord is having the minimum residual life and that is about 40 years with respect to present day loading intensity. Other members are having more life. As per the procedure given in code BS-5400 Part –10, the minimum life calculated is 62 years for vertical members and other members are having much more life. As such, as a whole, residual life of the bridge with present day loading is taken as 40 years.
ii) The above residual life is for on an average 48 trains per day for UP line. If number of trains increase / decrease in future, residual life can be decrease / increase on prorata basis.
iii) While doing the routine inspection of the bridge girders, a comparatively more attention should be paid on bottom chord members/joints to have fair observations. Based on that RDSO will further review its decision for betterment.
iv) The conclusion is drawn with the understanding that good maintenance and scheduled inspection will be practiced, which is the basic requirement for every bridge.
--------------
20
Table No. 1
Program of loading for fatigue testing of samples of existing bridge girder
Sr.
No
.
Member
Specimen
designation
Stress range
in N/ square
mm
Load range in
KN
Max - Min
Frequency in
cycles/minute
No. of
cycles in
millions
to be
tested
No. of
cycles in
millions
tested upto
1 Vertical UV-1 70 62.00 - 18.60 500 2 or till
failure
which
ever is
earlier
0.71
2 UV-2 100 80.60 – 18.60 ----do---- ----do---- 1.72
3 UV-3 130 99.20 – 18.60 ----do---- ----do---- 0.48
4 UV-4 160 117.80 - 18.60 ----do---- ----do---- 0.23
5 Diagonal UD-1 70 72.00 – 21.60 ----do---- ----do---- 2.00*
6 UD-2 100 93.60 – 21.60 ----do---- ----do---- 0.22
7 UD-3 130 115.20 – 21.60 ----do---- ----do---- 0.14
8 UD-4 40 50.40 – 21.60 ----do---- 10 or till
failure
which
ever is
earlier
1.95
9 Bottom
chord
UB-1 70 61.00 – 18.30 ----do---- 2 or till
failure
which
ever is
earlier
Not tested
due to non
availabilit
y of
fatigue
testing
machine
10 UB-2 100 79.30 – 18.30 ----do---- ----do---- ----do----
11 UB-3 130 97.60 – 18.30 ----do---- ----do---- ----do----
12 UB-4 160 115.90 –18.30 ----do---- ----do---- ----do----
* Sample completed 2 millions cycles but not failed
21
Table No. 2
Details of trains passed during recording of strains
BRIDGE NO. 110 UP
S.No /R.No
Date Train type Time of passing
Engine type
Time ( in sec)
Speed ( in Kmph)
1. 10.12.03 LKM 15.20 - 2.6 24
2. “ GKP- SC exp 15.31 WDM2 2.9 16
3. “ LKM 16.20 - 1.8 35
4. “ Shatabdi Exp 16.32 WAP1 1.0 47
5. 11.12.03 Gomti Exp. 13.00 WAP 1.6 32
6. “ Balamau Pass 13.10 WDM2A 2.2 21
7. “ LKM 14.01 - 3.0 21
8. “ GKP-TVC exp. 14.15 WDM2A 1.6 29
9. “ Shatabdi exp. 16./35 WAP4 1.4 37
10. 12.12.03 Barauni - GWL 11.34 WDM2+ WDM2
1.8 26
11. “ Balamau pass 12.32 WDM2A 4.5 10
12. “ LKM 13.10 - 3.0 21
13. “ LKM 14.05 - 3.2 20
14. “ GKP-TVC exp 14.14 WDM2 1.3 35
15. “ LKM 15.40 - 2.3 28
16. “ Gomti Exp. 15.55 WAP 1.8 29
17. “ Shatabdi exp. 16.27 WAP 1.2 43
18. 13.12.03 Goods 11.45 WDM2 5.6 08
19. “ Balamaui pass 12.30 WDM2 3.8 12
20. 15.12.03 Pushpak Exp 21.35 WDM2 1.6 29
21. “ LKM 22.15 - 2.4 27
22. “ Barauni exp 23.35 WAP 3.0 17
23. “ Vaishali exp 23.57 WAP 1.7 30
24. 16.12.03 Bhopal Exp. 00.07 WDM2A 1.1 42
25. “ Saptkrinti exp 00.30 WAP 3.5 15
26. “ Bandra Exp. 00.55 WAP 3.0 17
27. “ LKM 01.10 - 3.2 19
28. “ Marudhar Exp 01.35 WDM2A 1.1 42
29. “ Farrakka exp 01.55 WAP 1.6 32
30. “ Kushi nagar 02.05 WDM2A 1.3 36
31. “ I AUC pass 02.30 WDM2 4.6 10
32. “ Sabarmati exp. 03.00 WDM2 3.0 15
33. “ Gorakdham 05.40 WAP 2.4 22
34. “ LKM 06.10 - 1.4 37
22
Contd..
S.No /R.No
Date Train type Time of passing
Engine type
Time ( in sec)
Speed ( in Kmph)
35. “ Gomti exp. 06.35 WAP 1.4 37
36. 17.12.03 1 AUC pass 23.15 WDM2 3.2 14
37. 18.12.03 Vaishali exp. 00.05 WAP 1.4 37
38. “ Saptkranti exp 00.15 WAP 1.8 29
39. “ Bandra Exp. 00.35 WAP 1.6 32
40. “ 1 LCM 00.55 - 2.,4 27
41. 18.12.03 Farrakka exp 01.55 WAP 1.6 32
42. “ Kushi nagar 02.30 WDM2 1.2 38
43. “ Marudhar Exp 03.10 WDM2 - -
44. “ Sabarmati exp 04.30 WDM2 1.6 29
45. “ Kaifiyati exp 05.15 WAP 3.2 16
46. 19.12.03 Balamau Pass 12.30 WDM2 1.8 26
47. 22.12.03 Goods 15.20 WDM2 4.1 11
48. 24.12.03 LKM 13.50 - - -
Distance between 1st and last axles of WDM2 = 12.834 Meter Distance between 1st and last axles of WAP1 = 14.390 Meter Distance between 1st and last axles of EMU = 17.679 Meter Distance between 1st and last axles of WAP5 ( 4 wheels) = 13.000 Meter
23
Table No. 3
Observed Value of Stress Range and Cycles during 24 hrs.
Bridge No. 110 UP Recording dt. 10.12.03 to 24.12.03 No. of trains. = 48
S. No. Member Observed Stress Range
(N/mm2)
Modified stress range (N/mm2) Observed X 2.5
No. of Cycles
1. Bottom Chord 0 - 10 0-25 761
“ 10 - 20 25-50 14
“ 20 - 30 50-75 23
“ 30 - 40 75-100 12
2. End Raker 0 - 10 0-25 845
“ 10 - 20 25-50 17
“ 20 - 30 50-75 32
3. Vertical 0 - 10 0-25 1448
“ 10 - 20 25-50 173
4. Diagonal 0 - 10 0-25 845
“ 10 - 20 25-50 20
“ 20 - 30 50-75 21
5. Top Chord 0 - 10 0-25 725
“ 10 - 20 25-50 34
“ 20 - 30 50-75 8
24
Table No. 4
Total traffic density in GMT of bridge No. 110 of UP line, since 1981. (Ref. Letter No. 33W/4/115/W.Br dated 07/10-10-03)
Year Annual Traffic density in GMT in Up Line
GMT / Year
Cumulative GMT
1981-82 3.64 3.64
1982-83 3.90 7.54
1983-84 3.22 10.76
1984-85 3.67 14.43
1985-86 3.59 18.02
1986-87 3.65 21.67
1987-88 5.36 27.03
1988-89 5.93 32.96
1989-90 5.88 38.84
1990-91 6.17 45.01
1991-92 5.29 50.30
1992-93 5.67 56.97
1993-94 6.78 62.75
1994-95 6.58 69.33
1995-96 6.58 75.91
1996-97 6.99 82.90
1997-98 6.56 89.46
1998-99 7.58 97.04
1999-00 8.45 105.49
2000-01 16.40 121.89
2001-02 14.60 136.49
2002-03 10.30 146.79
25
Specimen for fatigue testing
Fig – 1
26
Cycles Vs Stress Range curve
Samples not considered
Fig – 2
SN Curve
1
10
100
0.100 1.000 10.000
No. of cycles in millions
Str
ess R
ange in k
g/s
q.m
m
27
Fig – 3
Fig – 3a
Cummulative increase in traffic density
since 1981 to 2003
0
50
100
150
200
198
1-8
2
198
2-8
3
198
3-8
4
198
4-8
5
198
5-8
6
198
6-8
7
198
7-8
8
198
8-8
9
198
9-9
0
199
0-9
1
199
1-9
2
199
2-9
3
199
3-9
4
199
4-9
5
199
5-9
6
199
6-9
7
199
7-9
8
199
8-9
9
199
9-0
0
200
0-0
1
200
1-0
2
200
2-0
3
Years
Cum
mula
tive
density in G
MT
28
ESTIMATION OF RESIDUAL FATIGUE LIFE OF STEEL GIRDER BRIDGE
SPAN LENGTH - 30.48 M
End Racker Vertical Diagonal Top Chord
( U0 – L1 ) ( U1 – L1 ) ( U2 – L1 ) ( U3 – U4 )
Top Chord Bottom Chord Wheel Marker ( U4 – U5 ) ( L3 – L5 ) (Running Rail)
Circuit for gauge No. 1 to 12 Circuit for gauge No. 13 & 14
SN Member Gauges Channel
1 End Racker (U0-L1) 2 2
2 Vertical (U1-L1) 2 2
3 Diagonal (U2-L1) 2 2
4 Top Chord (U3-U4) 2 2
5 Top Chord (U4-U5) 2 2
6 Bottom Chord (L3-L5) 2 2
7 Wheel Marker 2 1
Total 14 13
Fig. – 4
INSTRUMENTATION DETAILS
Bridge No. 110UP, SPAN – 25 X 30.48 m + 1 X 12.19 m Ganga Bridge Kanpur N. Rly.
29
Bottom Chord761
14 23 12
0
200
400
600
800
0 - 10 10-20 20-30 30-40
Observed Stress Range (N/mm2)
No. of C
ycle
s
Bottom Chord
End Raker
845
17 32
0
200
400
600
800
1000
0 - 10 10-20 20-30
Observed Stress Range (N/mm2)
No. of C
ycle
s
End Raker
Vertical
1448
173
0
500
1000
1500
2000
0 - 10 10-20
Observed Stress Range (N/mm2)
No. of C
ycle
s
Vertical
Diagonal
845
20 21
0
200
400
600
800
1000
0 - 10 10-20 20-30
Observed Stress Range (N/mm2)
No. of C
ycle
s
Diagonal
Top Chord
725
34 8
0
200
400
600
800
0 - 10 10-20 20-30
Observed Stress Range (N/mm2)
No
. o
f C
ycle
s
Top Chord
Fig 5 Histogram of observed values of stress range and No. of cycles
30
Bottom Chord761
14 23 12
0
200
400
600
800
0 - 25 25-50 50-75 75-100
Observed Stress Range (N/mm2)
No. of C
ycle
s
Bottom Chord
End Raker
845
17 32
0
200
400
600
800
1000
0 - 25 25-50 50-75
Observed Stress Range (N/mm2)
No. of C
ycle
s
End Raker
Vertical
1448
173
0
500
1000
1500
2000
0 - 25 25-50
Observed Stress Range (N/mm2)
No. of C
ycle
s
Vertical
Diagonal
845
20 21
0
200
400
600
800
1000
0 - 25 25-50 50-75
Observed Stress Range (N/mm2)
No
. o
f C
ycle
s
Diagonal
Top Chord
725
34 8
0
200
400
600
800
0 - 25 25-50 50-75
Observed Stress Range (N/mm2)
No. of C
ycle
s
Top Chord
Fig 5a Histogram of modified values of stress range and No. of cycles
31
Copy of the actual record of strain – Time history for passenger traiFig – 6
32
Annexure-I
FAX
NORTHERN RAILWAY Headquarters Office
Baroda House,
No. 33- W/4/115IV/W BR New Delhi
Dated: 26.08.03
Executive Director/B&S
RDSO.
Lucknow
Reg:- Ganga Bridge No. 110 between Lucknow- Kanpur Section.
The above bridge consisting of 25x30.48m+1x12.19m span was commissioned in 1910. The
substructure was double line BG track, but the girders were for single line BG track eccentrically
placed. A separate bridge on up-stream side of this bridge (constructed in 1875) (BG) carried the MG
line. In the year 1925, it was decided to hand over the MG bridge to State Govt. and use the BG bridge
both for BG and Mg traffic. So a new set of BG girders were erected on double line BG bridge
substructure. Till 1964, the new girders were carrying BG track and the old girders (also for BG track)
were being utilized for MG track, girder centers were 14’ (4265 mm).
In the year 1993-94 during gauge conversion , the NE Railway survey report found the girder to
be safe to carry BG ML loading. The chemical and physical properties of the steel used in the girders
were also tested and it was reported vide Test Report No. 6352 dated 16/07/1996 by RDSO that the
girder were of mild steel and were retained and substructure was strengthened by jacketing. Therefore,
the MG track on BG girders erected in 1910 was converted to BG , simultaneously the track spacing
was changed from 14’ to 14’ – 9” (by placing track on the down line eccentric to girder center).
However, the girders were checked for the eccentricity and were found safe.
This bridge has now been sanctioned by Railway Board for re-girdering of girder on UP line
(built in 1910) under SRSF.
As the girders were checked for adequacy and design in 1994 and are not early steel, it would
be desirable to assess the residual life of these girders and to save about Rs. 15 Crore required for re-
girdering in case adequate residual life is available.
In the light of these observations, RDSO is required to kindly assess the residual life of the
bridge. Work of re-girdering can be reviewed after this assessment.
Sd / -
(H. K. Jaggi)
for General Manager/ Engg.
33
Annexure – II
Details of strain gauge ( 67 mm ) and its calibration
Make : KYOWA Electronic Instruments Company Ltd. Type : SKF – 22201 Gauge Length : 67 mm Gauge Factor : 2.14+ 1 % Gauge Resistance : 120 + 0.3 Ohms Calibration
Where, R = Gauge Resistance ( 120 Ohms) S = Shunt Resistance (240 K Ohms) GF = Gauge Factor ( 2.14 ) For strain gauge factor 2.14 Therefore,
120 1 Strain = --------------------- X --------
( 120 + 24000 ) 2.14 = 234 X 10-6 Since 240 K ohms shunt resistance was used for calibration and output represents 2 volts (20 division on the chard paper) on the scale. Therefore, 2o Division = 234 X 10-6 strain or 1 Division = 11.7 X 10-6 strain
Stress = Strain X E of steel E of steel Is taken as = 2.11 X 10 6 Kg/cm 2 1 division of chart paper = 11.7X 10-6 X 2.11 X 10 6 = 25 Kg/cm 2 ( approx) = 0.25 kg/mm2
GFX
SR
RStrain
1
34
Annexure – II a
Details of strain gauge ( 10 mm ) and its calibration
Make : KYOWA Electronic Instruments Company Ltd. Type : KFC – 10 – C1 -11 Gauge Length : 10 mm Gauge Factor : 2.11+ 1 % Gauge Resistance : 120 + 0.3 Ohms Calibration
Where, R = Gauge Resistance ( 120 Ohms) S = Shunt Resistance (240 K Ohms) GF = Gauge Factor ( 2.11 ) For strain gauge factor 2.11 Therefore,
120 1 Strain = --------------------- X --------
( 120 + 24000 ) 2.11 = 238 X 10-6 Since 240 K ohms shunt resistance was used for calibration and output represents 2 volts (20 division on the chard paper) on the scale. Therefore, 2o Division = 2384 X 10-6 strain or 1 Division = 11.9 X 10-6 strain
Stress = Strain X E of steel E of steel Is taken as = 2.11 X 10 6 Kg/cm 2 1 division of chart paper = 11.9X 10-6 X 2.11 X 10 6 = 25 Kg/cm 2 ( approx) = 0.25 kg/mm2
GFX
SR
RStrain
1
35
Annexure- III
RAIN FLOW COUNTING DIAGRAMATIC ILLUSTRATION
Diagram not to scale
S No. Half Cycles Peak-1 Peak-2 Difference Stress Range Stress Interval
1. 1,2,2‟,4 -5.0 +18.5 23.5 5.20 >4.5
2. 2,3 +17 +10.0 7.0 1.55 >1.5
3. 3,2‟ +10 +17.0 7.0 1.55 >1.5
4. 4,5 +18.5 -8.5 27.0 5.97 >4.5
5. 5,6,6‟,12,16,16‟,20 -8.5 +22.0 30.5 6.74 >6.0
6. 6,7,7‟,9,9‟,11 +18.5 -7.0 25.5 5.64 >4.5
7. 7,8 +9.5 +18.0 8.5 1.88 >1.5
8. 8,7‟ +18.0 +9.5 8.5 1.88 >1.5
9. 9,10 -3.5 +18.0 21.5 4.75 >4.5
10 10,9‟ +18.0 -3.5 21.5 4.75 >4.5
11 11,6‟ -7.0 +18.5 25.5 5.64 >4.5
12 12,13,13‟,15 +20.0 -6.0 26.0 5.75 >4.5
13 13,14 +1.0 +19.0 18.0 3.98 >3.0
14 14,13‟ +19.0 +1.0 18.0 3.98 >3.0
15 15,16‟ -6.0 +20.0 26.0 5.75 >4.5
16 16,17,17‟,19 +20.0 -5.0 25.0 5.53 >4.5
17 17,18 +20.0 +18.5 16.5 3.65 >3.0
18 18,17‟ +18.5 +2.0 16.5 3.65 >3.0
19 19,16‟ -5.0 +20.0 25.0 5.53 >4.5
Time
Peak Amplitude
36
Annexure - IV
Calculation sheet of fatigue life assessment as per BS5400, Part- 10
ANNEXURE-I (with occasional loads) Calculation Sheet to work out residual fatigue strength of members of Ganga Bridge No. 110 near Kanpur
σ0(N/mm2) = 47 m=3
Number Member dead load (t)
A (cm
2)
Miin. Stress σ min
( t/cm2)
L.L with CDA
(t)
occ. Load
(t)
Max. Load
Dl+LL+ OL (t)
Max. Stress σ max
( t/cm2)
Stress Range σRmax
(t/cm2)
L' (m)
RU loading factor, k3
σRma
x
k1 = Design Life years
N/mm
2 σRmax/σ0*k3
1 2 3 4 5 6 7 8 9 10 11 12 13 13 15
1 U0-U1 -47.45 393.31 -0.12 -93.36 -58.29 -199.1 -0.51 -0.39 32.16 2.19 -39 0.379 2206
2 U1-U2 -48.11 393.31 -0.12 -94.55 -63.16 -205.82 -0.52 -0.4 32.16 2.19 -40 0.389 2045
3 U2-U3 -83.19 393.31 -0.21 -162.81 -63.65 -309.65 -0.79 -0.58 32.16 2.19 -58 0.563 671
4 U3-U4 -83.52 393.31 -0.21 -163.44 -66.64 -313.6 -0.8 -0.59 32.16 2.19 -59 0.573 637
5 U4-U5 -107.06 393.31 -0.27 -209.23 -61.12 -377.41 -0.96 -0.69 32.16 2.19 -69 0.670 398
6 U5-U6 -107.21 393.31 -0.27 -209.54 -57.7 -374.45 -0.95 -0.68 32.16 2.19 -68 0.661 416
7 U6-U7 -107.21 393.31 -0.27 -209.54 -57.7 -374.45 -0.95 -0.68 32.16 2.19 -68 0.661 416
8 U7-U8 -107.06 393.31 -0.27 -209.23 -61.12 -377.41 -0.96 -0.69 32.16 2.19 -69 0.670 398
9 U8-U9 -83.52 393.31 -0.21 -163.44 -66.64 -313.6 -0.8 -0.59 32.16 2.19 -59 0.573 637
10 U9-U10 -83.19 393.31 -0.21 -162.81 -63.65 -309.65 -0.79 -0.58 32.16 2.19 -58 0.563 671
11 U10-U11 -48.11 393.31 -0.12 -94.55 -63.16 -205.82 -0.52 -0.4 32.16 2.19 -40 0.389 2045
12 U11-U12 -47.45 393.31 -0.12 -93.36 -58.29 -199.1 -0.51 -0.39 32.16 2.19 -39 0.379 2206
13 U0-L1 65.3 222.3 0.29 142.29 12.13 219.72 0.99 0.7 32.16 2.19 70 0.680 382
14 U1-L1 -5.99 64.26 -0.09 -37.52 -1.53 -45.04 -0.7 -0.61 5.41 1.37 -61 0.947 141
15 L1-U2 -33.18 116.13 -0.29 -77.88 -9.86 -120.92 -1.04 -0.75 29.17 2.19 -75 0.729 310
16 U2-L3 19.36 99.49 0.19 53.93 6.98 80.27 0.81 0.62 26.26 1.92 62 0.687 370
17 U3-L3 16.1 64.26 0.25 34.37 0 50.47 0.79 0.54 5.334 1.37 54 0.839 203
18 L3-U4 -25.24 116.13 -0.22 -71.22 -5.51 -101.97 -0.88 -0.66 23.35 1.92 -66 0.731 307
19 U4-L5 13.93 99.49 0.14 53.51 4.22 71.66 0.72 0.58 20.44 1.92 58 0.643 452
20 U5-L5 16.1 64.26 0.25 34.37 0 50.47 0.79 0.54 5.334 1.37 54 0.839 203
21 L5-U6 -5.78 116.13 -0.05 -46.36 -3.11 -55.25 -0.48 -0.43 17.53 1.92 -43 0.477 1109
22 U6-L7 -5.78 116.13 -0.05 -46.78 -3.11 -55.67 -0.48 -0.43 17.53 1.92 -43 0.477 1109
23 U7-L7 16.1 64.26 0.25 34.37 0 50.47 0.79 0.54 5.334 1.37 54 0.839 203
24 L7-U8 13.93 99.49 0.14 53.51 4.22 71.66 0.72 0.58 20.44 1.92 58 0.643 452
25 U8-L9 -25.24 116.13 -0.22 -71.22 -5.51 -101.97 -0.88 -0.66 23.35 1.92 -66 0.731 307
26 U9-L9 16.1 64.26 0.25 34.37 0 50.47 0.79 0.54 5.334 1.37 54 0.839 203
27 L9-U10 19.36 99.49 0.19 53.93 6.98 80.27 0.81 0.62 26.26 1.92 62 0.687 370
28 U10-L11 -33.18 116.13 -0.29 -77.88 -9.86 -120.92 -1.04 -0.75 29.17 2.19 -75 0.729 310
29 U11-L11 -5.99 64.26 -0.09 -37.52 -1.53 -45.04 -0.7 -0.61 5.41 1.37 -61 0.947 141
30 L11-U12 65.3 222.3 0.29 142.29 12.13 219.72 0.99 0.7 32.16 2.19 70 0.680 382
31 L1-L3 72.95 241.97 0.3 144.35 26.38 243.68 1.01 0.71 32.16 2.19 71 0.690 366
32 L3-L5 98.58 267.45 0.37 193.74 27.93 320.25 1.2 0.83 32.16 2.19 83 0.806 229
33 L5-L7 110.76 267.45 0.41 217.44 31.92 360.12 1.35 0.94 32.16 2.19 94 0.913 158
34 L7-L9 98.58 267.45 0.37 193.74 27.93 320.25 1.2 0.83 32.16 2.19 83 0.806 229
35 L9-L11 72.95 241.97 0.3 144.35 26.38 243.68 1.01 0.71 32.16 2.19 71 0.690 366
37
Note: (1) L‟ has been taken as the base length of the influence Line Diagram giving max. ordinate value i.e. for stringer and X- girder , L = effective span length for end member, top chord and bottom chord. 2) k3 value has been taken from table-4 of BS-5400 for RU loding for appropriate value of L assuming medium traffic conditions.
3) Design life has been worked out by inversion applying clause 9.2.3 of BS-5400 assuming 'D' detailed class of connnections for which m=3 & σ0=53 N/mm
3
Design life is the minimum of following:
----------
m
1k
120 LifeDesign
2m
1k
120 Life Design
or
38
REFERENCES: 1. Estimation of the residual life of floor system of Ganga Bridge near Balawali ( Civil Engineering Report No. 175 ) 2. Investigations on the assessment of residual life of early steel/wrought iron girder bridges ( Civil Engineering Report No. 245 ) 3. Assessment of fatigue life of early steel/wrought iron girder bridges ( Report No. BS-5 ) 4. Guidelines for assessment of residual life of early steel/wrought iron girder bridges ( Report No. BS-39 ) 5. Statistical distribution of axle loads and stresses in railway bridges ( ORE Report No.1 Question D-128 ) 6. Fatigue life of riveted railway bridges by Bjorn Akesson, Chalmers university of
technology, Sweden . 7. Condition monitoring and life assessment of railway bridge 449/3/34 over river
Tapti near Bhusaval by Department of civil engineering IIT, Mumbai 8. Assessment of residual fatigue life of Ganga bridge near Kanpur, N. Rly. ( Report No. BS- 70 ) 9. Code of practice for fatigue ( BS-5400: Part 10 )
