Remaining fatigue life estimates for riveted railwaybridges

B. IMAM, T. D. RIGHINIOTIS, M. K. CHRYSSANTHOPOULOSSchool of Engineering, University of Surrey, Guildford, Surrey, UK

ABSTRACTA large number of metallic railway bridges currently in use in the UK are of rivetedconstruction and are close to 100 years old. A fatigue assessment methodology is needed forsuch bridges since these may be close to the end of their fatigue lives. Part of such amethodology is the global analysis of the bridge in order to identify the most fatigue criticaldetails. The aim of this paper is to present results, in terms of Miner's damage at the rivetedconnections of a typical riveted UK railway bridge, obtained from a global finite elementanalysis under various train loadings.

KEYWORDS Fatigue Damage, Wrought-Iron Riveted Connections, FE Analysis

INTRODUCTIONA large number of riveted bridges can be found on the railway network in the UK and inother parts of Europe and North America. Continuously increasing loads and the fact thatthese bridges were not explicitly designed against fatigue raise questions regarding theirremaining fatigue life. As is well known, metal fatigue exhibits relatively high levels ofuncertainty and can be influenced by a number of structure- and environment-specific factors.Moreover, the load history, which plays an important role in fatigue life evaluation, is largelyunknown in most cases. In view of the above, there appears to be a need to develop acomprehensive fatigue assessment methodology for riveted railway bridges.

There has been a considerable amount of research in order to study the fatigue behaviour ofriveted bridges. This research has shown that fatigue damage in such bridges is mainlyassociated with secondary, rather than primary, stress effects [1-3]. As a result, rivetedconnections rather than the actual members themselves have been identified as the fatiguecritical locations [1,2,4]. Indeed most of the cracks which have so far been found in rivetedbridges are concentrated in the area of the riveted connections.

A typical riveted connection used in the construction of railway bridges is shown in figure 1.It consists of two angles riveted to the webs of the two connected members. Research hasshown that this type of connection possesses considerable rotational fixity, enabling it todevelop significant bending moment [1, 5]. The restrained out-of-plane deformation of theconnection angle due to the rotational fixity, combined with the stress concentrations at theangle fillet, rivet holes, cope-holes being present and the rivets themselves have beenidentified as possible factors that lead to the fatigue cracking of riveted connections [1-3, 6].

Bridge Management 5, Thomas Telford, London, 2005.

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The majority of the fatigue assessment methodologies for existing riveted bridges that havebeen developed in the past have been based on the S-N approach [7-10]. More elaboratemethodologies based on the study of existing or assumed cracks using Fracture Mechanicshave also been applied [11, 12]. Irrespective of the adopted methodology, selection of thefatigue critical detail(s) in a bridge needs to be addressed.

Here, in order to identify the fatigue-critical connections in a typical riveted UK railwaybridge, a global finite element (FE) analysis of the bridge is carried out. The assumed loadingconsists of both nominal present-day and historical trains and volumes. The rivetedconnections are ranked according to their fatigue criticality which is calculated on an S-Nbasis. The effect of different parameters such as connection fixity, the choice of fatigue detailclassification and dynamic amplification is investigated.

FINITE ELEMENT ANALYSISThe riveted railway bridge under investigation is shown in figure 2.The superstructure ofsuch bridges usually consists of longitudinal rows of railbearers (or stringers) interconnectedwith transverse cross-girders which in turn are connected to longitudinal main girders. Twotypes of connections can be identified in the figure; stringer-to-cross-girder connectionsdenoted by S and cross-girder-to-main-girder connections denoted by C. All the members arebuilt-up using plates, angles and rivets. This wrought-iron bridge has a 9.6 m span, wasconstructed at the beginning of the 20th century and is deemed to be representative of a largenumber of bridges on the UK network. The bridge is assumed to be simply supported on thethree main girders.

main-girder

Fig. 1. Typical riveted connection [4]. Fig. 2. Finite element model of the bridge.

The bridge is modelled using the commercial FE-package ABAQUS 6.3 [13] using 8-nodedshell elements for all members. A Young's modulus of 200 GPa, which is a typical value ofUK-manufactured wrought-iron [14] and a Poisson's ratio of 0.3 are used for the analyses.Particular emphasis is given to the modelling of the riveted connections between themembers which are modelled using axial spring elements with variable stiffness.

The bridge live loading is assumed to consist of two railway traffic models representing twodistinct periods. The loading from 1970 onwards is represented by the BS 5400 mediumtraffic model [15] whereas the loading in the period between 1900 and 1970 is represented by

IMAM ET AL. 419

a historical load model (table 1) which was developed by the authors in collaboration withNetwork Rail. As can be seen, this period is further divided into 3 parts that may be roughlyassociated with historical changes in rail traffic. The BS 5400 traffic model consists of a steeltrain (21.5t max. axle load), two freight trains (25t max. axle load) and a typical passengertrain (20t max. axle load) [15].

Table 1. Historical load model (F=freight, P=passenger, LS=local suburban).

Period

1900-1920

1920-1940

1940-1970

TrafficType

F

P

LS

F

P

LS

F

P

LS

Locomotive Type

0-6-0 SuperheaterFreight Engine4-4-0 Passenger

Engine

0-4-4 Tank Engine

0-6-0 SuperheaterFreight Engine

4-6-0 SuperheatedMixed Traffic Engine

0-4-4 Tank Engine

2-8-0 Freight Engine

4-6-0 SuperheatedMixed Traffic Engine

0-4-4 Tank Engine

WagonType

r̂

r̂

fr~nr̂

AxleWeight

2x8 t

4x8 t

4x81

2xl0t

4x91

4x8 t

2xl0t

4x91

4x8 t

#ofWagons

30

8

4

40

12

4

40

15

6

AnnualFrequency

10,500

11,250

11,250

10,500

18,000

4,500

10,500

18,000

4,500

For the purposes of the analysis, the trains are traversed in static steps of lm over one track ofthe bridge. The axle loads are applied directly on the top flanges of the stringers thusneglecting any load spread due to the rails and sleepers. This assumption has been found toresult in higher stresses in similar bridges [16]. Dynamic effects are accounted for by usingamplification factors from structural codes and field measurements in similar bridges.

The resulting irregular stress histories, obtained at the riveted connections at distances of250mm and 300mm from the stringer-to-cross-girder and cross-girder-to-main-girderinterfaces respectively, are first converted into stress range blocks by using the rainflowcounting method. The damage caused by a single train passage is calculated by applyingMiner's rule to the resulting stress ranges. Three different detail classifications are used forthe riveted connections i.e. Class B, Class D and Class Wrought-Iron (WI). According to BS5400, Class B is used for holes and can be assumed to represent the case of having low or noclamping force in the rivets. A stress concentration factor of 2.4 is used with this class [15].Class D represents riveted lapped or spliced connections with normal or high clamping force.Lastly, Class WI is used to represent riveted wrought-iron connections as proposed by theUK railway assessment code [17] and can be considered as a more realistic case. The BS5400 two-slope design S-N curves [15] are used for the first two classes when calculating thedamage. The WI S-N curve lies between the modified Class B and Class D S-N curves.Consequently, Classes B and D can be regarded as upper and lower bounds for remaining

420 BRIDGE MANAGEMENT 5

fatigue life estimates. Thickness effects, as proposed by BS 7608 [18], are neglected since thethicknesses of the members are in general slightly greater than 16 mm.

RESULTS AND DISCUSSIONIn calculating the total damage of the riveted connections, the bridge is assumed to have beenconstructed in 1900. The connections are numbered as shown in figure 2. The notation, wherethe first symbol refers to the connection in question and the second symbol refers to therelevant direction, is used in the following sections. Previous studies have shown that anincrease in the stiffness of the stringer-to-cross-girder connections results in an increase in thefatigue damage [19]. Consequently, all results presented hereafter are obtained by assumingfully fixed connections since this assumption provides conservative fatigue life estimates

The frequency diagram shown in figure 3 depicts the total number of cycles versus the stressranges experienced by connection S7-S5 under the historical load model and BS 5400medium traffic assuming fixed connections. It can be seen that the maximum stress rangeexperienced by the connection is approximately 45 MPa. All of the stress ranges are belowthe fatigue limit for an assumed Class D, while a very small number is above the fatigue limitfor assumed Classes B and WI.

g 3.0E+07

I•g 2.5E+07

II 2.0E+07z

I

° 1.5E+07

1.0E+07 -

5.0E+06 -0.OE+O0

Class BFatigue

Class DClass WI FatigueFatiaue Limit

0 5 10 15 20 25 30 35 40 45 50 55

Stress Range (MPa)

Fig. 3. Stress range frequency diagram for connection S7-S5 (period 1900-2004).

Effect of detail classification on fatigue damageThe damage of the cross-girder-to-main-girder connections was found to be negligibleirrespective of classification. On the other hand, the damage in the stringer-to-cross-girderconnections, which is the most significant, is found to be axle-dominated with the trainshaving the highest axle loads (Trains No 7 and 8 of BS 5400) producing the highest amountof damage. The most highly damaged connections are found to be the inner stringer-to-cross-girder connections (S7-S5, S8-S6, S3-S5, S4-S6, see figure 2). Figure 4 depicts thecumulative damage as well as the remaining fatigue life of the two most highly-damagedconnections (S7-S5 and S8-S6) for all three detail classifications. It can be seen that a Class B

IMAM ET AL. 421

(no clamping force) leads to the highest damage with remaining fatigue lives of 80 and 85years for the two connections. A Class D (high clamping force) results in remaining lives of289 and 303 years. This comparison makes the effect of clamping force on the fatiguedamage of riveted connections evident. The Class WI results can be seen to lie between theirClass B and Class D counterparts. Damage ranking of the connection is found not to besignificantly affected by the choice of the detail classification.

Figure 4 also depicts a considerable increase in the damage accumulation rate of theconnections after 1970. This fact can be attributed to the introduction of the heavier axle-loadBS 5400 traffic. The rate of damage increase is fairly small over the period 1900-1970 for allthree classes. This increase is larger for Class B after 1970 and can be attributed to the stressrange frequency box (see figure 3) which lies just above the Class B fatigue limit. Thisfrequency box is a result of the BS 5400 heavy axle trains.

It can be seen in figure 4 that about 25 to 35% of the fatigue strength of connections S7-S5and S8-S6 has been expended over the last 34 years for assumed Classes B and WI. Theseaccumulation rates would rise even higher with the introduction of heavier axle trains in thefuture.

0.4 T

| 0.2

23E 0.153u

0.1

0

1900

—=

/

/ /

/ / / ,

' / ^

8Oyrs

A 85 yrs

,x 120 yrs

//* 128 yrs

289 yrs

£ * * 303 yrs

1960

Year

| -*- S7-S5 (Class B) - « - S8-S6 (Class B) - * - S7-S5 (Class D) -*- S8-S6 (Class D) - * - S7-S5 (Class WI) - + - S8-S6 (Class WI)

Fig. 4. Cumulative damage of connections S7-S5 and S8-S6 versus time.

Effect of dynamic amplification on fatigue damageDynamic amplification, especially in short span, unballasted metallic railway bridges, isexpected to have a considerable effect on the stresses experienced by the members andconnections. Due to the sensitivity of fatigue damage on the stress ranges the effect ofdynamic amplification on the damage of the connections is studied here.

Different dynamic amplification factors (DAF), obtained from structural codes and fieldmeasurements in similar bridges, are shown in table 2. These factors are applied to thestatically calculated stress ranges. The factors obtained from Eurocode 1 (EC1) [20] andNetwork Rail [17] are very similar. The D23 factor is based on field measurement as well as

422 BRIDGE MANAGEMENT 5

theoretical studies carried out by the European Rail Research Institute [21]. The remainingdynamic amplification factors were obtained from field measurements on short and mediumspan steel railway bridges [10, 22]. It can be seen in table 2 that there is a good agreementbetween the factors obtained from different sources. However, this is partly because theformulae providing these factors in the European codes are based on more or less the samestudies.

Table 2. Dynamic amplification factors for short-span riveted railway bridge.

EC 1 [201D23 [21]

Byers [22]Tobias & Foutch [10]

Network Rail [17]

Train speedBS 5400 trains

72km/h1.161.161.151.151.14

80km/h1.161.181.191.151.16

160km/h1.271.391.281.221.32

Historical load model trains30

mph1.131.101.141.121.10

40mph1.151.141.111.151.13

50mph1.171.181.191.151.16

60mph1.181.221.231.231.19

70mph1.211.271.301.231.23

The cumulative damage as well as the remaining fatigue lives for the most highly-damagedconnection S7-S5 accounting for the dynamic amplification factors of table 2 and assumingClass WI is shown in figure 5. The case without consideration of any dynamic amplification(no DAF) is also illustrated on the figure. It can be seen that there is a considerable decreasein the remaining fatigue life of the connection due to dynamic amplification. The factorobtained from the D23 report [21] leads to the lowest remaining fatigue life with a decreasefrom 120 years, which is the case without any dynamic amplification, to only 21 years. Theremaining factors result in similar remaining lives ranging between 26 and 31 years.

0.7 -

0.5 -

0.4 -

0.3 -

0.2 -

0.1

n •

^

Y

21 yrs/ ,/26yrs

/ j f 27 yrs^ 0 - 2 8 yrs^ <31 yrs

jft 20 yrs

1960

Year

-No DAF -»-[22] -»-[20] -m-\

Fig. 5. Cumulative damage of connection S7-S5 for different DAFs.

IMAM ET AL. 423

Although the assumption that all stress ranges are multiplied by the same dynamicamplification factor is rather simplistic, it demonstrates that the remaining fatigue lifeestimates are very sensitive to the assumed dynamic amplification. This is due to the shift ofthe entire stress range frequency diagram to the right. This in turn results in the increase ofsome stress ranges that were previously below the fatigue limit to levels above the fatiguelimit.

Other factors influencing fatigue damageThe effect of two trains passing over the bridge simultaneously has also been examined. Itwas found that the simultaneous passage of two trains can lead to an increase in the damageof the stringer-to-cross-girder connections by as much as 400% depending on whether thetrains will enter the bridge at the same time or not. However, since the annual occurrence ofthis phenomenon is rather low, its effect on the total damage of the connections can beregarded as negligible.

Due to the significant variability in the material properties of older steels and wrought-iron[14, 23-25], the effect of Young's modulus on fatigue damage has also been brieflyinvestigated. It was found that a decrease in the value of Young's modulus from 200 GPa to170 GPa, the latter being a low but nevertheless encountered value [25], increases the damageof the stringer-to-cross-girder connections by as much as 510% depending on detailclassification.

CONCLUSIONSIn this paper, a global finite element analysis of a typical riveted UK railway bridge wascarried out in order to identify the most fatigue-critical connections. Total damage in theconnections was calculated under the historical load model and the BS 5400 medium trafficand remaining fatigue life predictions were made. The effect of various parameters such asfatigue detail classification and dynamic amplification were investigated.

The global stress analysis has identified the fully-fixed, inner stringer-to-cross-girderconnections as the most fatigue critical (S7-S5, S8-S6, S3-S5, S4-S6, see figure 2). Thedamage under the historical load model (1900-1970) was found to be small with the damageaccumulation rate increasing due to the introduction of the heavier BS 5400 trains (post-1970). Dynamic amplification was found to result in considerable reduction in the remainingfatigue lives. A more detailed investigation of the most critical connections using FractureMechanics is currently underway.

ACKNOWLEDGEMENTSThe work described in this paper forms part of an ongoing project supported by EPSRC andNetwork Rail. The opinions expressed are those of the authors and do not necessarilyrepresent those of the sponsoring organisations. We would like to thank Mr Brian Bell,Network Rail Project Officer, for valuable discussions and feedback on the methodology andresults reported in this paper.

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424 BRIDGE MANAGEMENT 5

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