Duffield Bridge 1991

DESIGN CONSIDERATIONS FOR LONGITUDINAL FORCES IN RAILWAY BRIDGES

C.F. DUFFIELD, BE, MEngSc, MIEAust Lecturer Department of Civil and Agricultural Engineering, University of Melbourne G.L. HUTCHINSON, MEngSc, DPhil(Oxon.) Professor of Civil Engineering Head of Department of Civil and Agricultural Engineering, University of Melbourne

SUMMARY This paper describes the longitudinal response of railway bridges when subjected to forces generated by the starting or braking of railway vehicles. By comparing experimental results and analytical results with various codes of practice from around the world it has been shown there are significant discrepancies between the codes and conclusions drawn from the analytical and experimental results. Further, the code currently used in Australia ("Australian and New Zealand Rail conferneces - Railway Bridge Design Manual. 1974"), appears to signifiLaudy underestimate the longitudinal force in certain commonly occurring circumstances.

KEYWORDS Railway, Bridges, Longitudinal, Force, Codes ACKNOWLEDGEMENT The Public Transport Corporation (Victoria) provided time release for Mr C.F. Duffield to attend The University of Melbourne. Thiis provision is gratefully acknowledged.

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Colin Duffield graduated in Civil Engineering from Deakin University in 1978 and obtained his MEngSC from the University of Melbourne in 1990. He has held positions with the Shire of Diamond Valley, Golder Associates Pty Ltd and Public Transport Corporation, Victoria. Throughout these appointments he has worked extensively in the areas of structural design and construction, with a particular emphasis on bridges. In 1991 he was appointed Lecturer in Civil Engineering, Department of Civil and Agricultural Engineering, University of Melbourne. His main research interests are in Construction Management and Structural Dynamics Graham Hutchinson is Professor of Civil Engineering and Head of the Department of Civil and Agricultural Engineering at the University of Melbourne. He obtained his MEngSc degree from the University of Melbourne in 1974. He was Lecturer in Civil Engineering at Kings College, Univeristy of London from 1975 until he joined the staff at the University of Melbourne in 1983. He has extensive experience in all aspects of structural engineering systems including dynamic response, stability and susceptability to earthquake loading.

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INTRODUCTION The use of more powerful locomotives capable of pulling heavier, longer trains has increased the longitudinal forces applied to a rail in service. Advanced braking systems are associated with these heavier locomotives and these maximise the adhesion between locomotive and rail. To cope with these increased loads trackwork requires better maintenance and alignment. Also, rails are now continuously welded and this has been shown to distribute live loads away from the point of loading and reduce dynamic effects. Detailed analytical and experimental studies to investigate both the magnitude of applied longitudinal forces and their distribution have been conducted in Europe and America. However, little correlation between this work exists, and the final conclusions of these studies vary substantially. Design of railway bridges in Australia is currently carried out in accordance with the Australian and New Zealand Railway Bridge Design Manual (ANZRC, 1974). Both ANZRC and the American Railway Engineering Association's manual for Railway Engineering (AREA, 1990) permit high reductions in the design value of longitudinal forces to account for their distribution through the rail. This reduction far exceeds the reductions allowed in the European codes such as BS 5400, (refer Fig. 1) and the Office for Research and Experiments of the International Union of Railways (ORE).

Longitudinal force at rail level (kN)

600

BS 5400

500

♦00

300

200-

100-

0 20

40

60

80

100

Span length (m)

Fig. 1 Code recommendations for longitudinal force, continuous rail

This paper presents a brief review of current analytical techniques used to predict longitudinal forces on railway bridges; some typical experimental results and some analytical predictions of longitudinal forces.

CODE APPROACHES CURRENT CODE METHODS ANZRC (1974), is based on AREA guideline's where longitudinal force (LF) transmitted at rail

level is taken to be: LF = 0.15 * vertical live load

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In cases where the rail is continuous over and beyond the bridge the longitudinal force is reduced to: LF = 0.15 * (live load) * bridge length 365

(1)

with the proviso that bridge length/365 does not exceed 0.8. The standard design live load is taken to be the M250 Cooper's load [refer ANZRC (1974)]. The Canadian design code (S29-1978) incorporates Equation 1 except that a heavier Cooper M357 live-load (E80) is recommended The British code (BS5400) uses a stepped limit bound approach, checking for both loadings of vehicles currently running or projected to run in Europe and for rapid transit vehicle systems. For bridges supporting ballasted track the design values for longitudinal force are reduced such that up to one third of the load is assumed to be transmitted beyond the bridge provided there are no rail discontinuities within 18 m of either end of the bridge. ORE (1979) determined various values for the friction coefficient at the bridge bearing level where adhesion values of 0.3 for braking and 0.4 for acceleration (ORE 1971) were adopted. (Adhesion is defined as the ratio of applied horizontal to applied vertical loading). Comparisons have been made (Duffield, 1989), between ANZRC (1974), BS5400 and ORE recommendations for bridges with lengths ranging up to 100 m, (refer Fig 1). BACKGROUND TO EMPIRICAL CODE FORMULAE The longitudinal force provisions of the major codes of practice are based on empirical formulae obtained from field trials.(refer Arya et al 1982). Typically the longitudinal force formulae take the form of the Coulomb force-friction concept, ie LF = µN, where µ is the friction coefficient (adhesion) and N is the vertical live load. Early code values for µ were taken as 0.15 corresponding to values associated with steel to steel friction. AREA later made provision for starting forces to be associated with µ of 0.25 and with µ of 0.15 for braking. Only half this loading was applied if continuous rails were in place. In the current ANZRC provisions the distribution of longitudinal force on continuous rails was revised on the basis of field tests such as AREA (1955, 1961, 1964, 1966, 1967). Neither the ANZRC nor BS5400 account for the• effects of dynamic loads. Moreover the ANZRC does not provide guidance with respect to the distribution of the longitudinal force for: 1. varied restraint conditions of the track beyond the bridge, eg partial fixity due to points or crossings, 2. the condition of the track. (This directly affects the longitudinal stiffness of the track ), 3. the material properties of the bridge, 4. the stiffness of the bridge including bearings and foundations.

EXPERIMENTAL TESTING To further understand the basis of the code formulae and the reasons for the differences between codes a comparison of the test results as presented by AREA (1966) and (1967) along with those of ORE (1969-1985) have been studied. These same experimental results have been used as the basis for comparison with analytical results later in this paper.

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Results from these testing programs for bridges having a continuous rail (ie rail joints welded or fishplated), or non-continuous rail joints (ie joints broken by a moveable span, sliding rail expansion joints or other devices), are summarised is Tables I and II respectively. The ratio of longitudinal bearing reaction to applied vertical load is designated p.B. The percentage ratio of the averaged experimental bearing reactions to the applied longitudinal load are designated X% . Duffield (1989) provides comprehensive details of these structures, the testing programs and interpretation of the results. TABLE I FIELD TEST RESULTS OF BRIDGES WITH CONTINUOUS RAILS Bridge No

Type

Ballast

Bearing

Span

1 2 3 4 5

Steel Steel Steel Steel* Prestressed concrete Prestressed concrete Concrete

No No No Yes Yes Yes Yes

Steel Steel Steel Steel Steel Neoprene Neotopf

Yes Yes

6 7

Concrete 8 * Partially continuous

Max li

Max LLB

16.2 30.0 53.9 30.0 21.5 21.5 15+15

0.366 0.237 0.264 0.350 0.192 0.151 0.387

0.104 0.110 0.118 0.118 0.143 0.054 0.113

Tetron

34.5

0.188

Elastomeric

201.1

0.290 Downhill 0.102

0.05

X% Av 1-111 µ 27.7 43.8 47.7 54.4 81.2 42.1 57.4 64.9 47.8 49.0

TARIN FIELD TEST RESULTS NON-CONTINUOUS JOINTS Bridge Type No Steel 1 2 Steel Steel 3 4 Steel* 5 Prestressed concrete 6 Prestressed concrete 7 Concrete 8 Prestressed Concrete * Partially continuous

Ballast

Bearing

Span

max li

Max µB

X%

No No No Yes Yes

Steel Steel Steel Steel Neoprene

16.2 30.0 53.9 30.0 21.5

0.438 0.246 0.264 0.350 0.161

0.258 0.175 0.256 0.195 0.084

59.7 70.0 97.2 54.4 61.9

Yes

Neotopf

15+15

0.132

0.132

100.

Yes Yes

Tetron Elastomeric

34.5 201.1

0.214 0.094

0.193 0.058

90.3 61.7

Testing of bridge number eight was reported in AREA (1967) and testing of all other bridges in Table I was reported in ORE (1969-85). Note that for bridge number five, in Table I, testing was conducted for two differing bearing type.

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ANALYTICAL TECHNIQUES The problem of estimating the longitudinal forces exerted on railway structures was first considered by Willis (1849) and Stokes (1867). Extensive linear elastic studies have subsequently been undertaken to assist in the prediction of longitudinal forces (eg. Inglis (1951), Siekmeier (1965), Eisses (1975), Fryba (1975), Chu and Lee (1980) and Arya and Agrawal (1982)). In particular, the works of Siekmeier and Fryba have provided well recognised techniques. Much of Fryba's work was conducted under the auspices of an ORE committee set up to investigate braking and acceleration forces on bridges (1966 to 1985). EXISTING ELASTIC THEORETICAL METHODS Siekmeier's linear elastic model Siekmeier (1965) used linear elastic analytical techniques and concluded that track resistance (W), is a function of frictional force (R), and the product of displacement (u) and the elastic restoring force (k). (2) W = R + ku The solution assumes the rail to be a bar of infinite length. If discrete bar lengths are chosen and these bars are fixed to a bridge deck, the longitudinal force transmitted to the bridge, based on Siekmeier's analysis (Duffield, 1989) can be determined from the spring reaction forces. Fryba's Quasi-static distribution Fryba (9174) assumed that longitudinal stresses in bridge beams and rails act separately and independently of corresponding bending stresses. Both the beam and rail were modelled as bars with the connection between them taken as an elastic layer. Fryba's model is presented in Figure 2. A continuous rail is modelled by predetermined discrete lengths of track on either side of the bridge. The longitudinal displacements (ui(x)) of the bar are assumed proportional to the product of the load and the track stiffness coefficient (ki), ie ui(x) = ki * load.

1

2

13

n-1101 14

FIG. 2 QUASI STATIC MODEL (AFTER FRYBA 1974) Analyses were conducted (Duffield 1989) to compare Siekmeier's and Fryba's methods for bridges varying in length up to 150 m. An input live load of M250 Coopers configuration (ANZRC 1974) was adopted with the analysed length of rail each side of the bridge being taken as 20 m. The live load was stepped across the model in 0.1 m increments to determine the peak value responses and the results are presented in Figure 3.

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Bearing read ion (kN)

It should be noted that these results are based on a constant value of EA (5.0 E7 kN) and this value corresponds to the properties of bridge number two (30 m steel bridge, ORE, 1971). The results presented in Figure 3 clearly indicate a large divergence in the predicted results for bearing force reactions for bridges with spans greater than about 20 m in length.

3000

2000

Siekmeier

-a- Fryba 1000 -

0

100

200

Bridge span (m) FIG. 3 PREDICTED BEARING FORCE REACTIONS BASED ON SIEKMEIER (1965) AND FRYBA (1975)

ANALYTICAL MODELS Modelling of bridges where the rail is discontinuous (or free) at the end of the bridge has been undertaken using a simple beam (Case 1) and for a continuous rail a detailed finite element model has been considered (Case 2). These two cases and the input loading are considered in the following sections.

VEHICLE MODEL Train axle loadings have been modelled as either a disc moving across a beam or as a series of moving forces. In the former case, the inertia effects of the loading are included. As the purpose of the model is to study longitudinal forces from vehicle braking and acceleration, adhesion effects are included. The vertical input load P(t) for track fixed to timber sleepers has been be taken as :P(t) = sin 0t,

(3)

where 0 = wavelength of input, t = time For the vertical load non-dynamic inputs P(t) = 1.0 were used and the horizontal force (R(t)) is limited in magnitude by Coulomb's law of friction. IR(01< f(t) P(t)

(4)

where f(t) is usually a function of the speed of the load. If the wheel is sliding (ie R(t) f(t)P(t) : R(t) = ± u0(t) f(t) P(t)

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(5)

697

where f(t) = coefficient of friction Another major factor influencing the horizontal force is the relationship between the braking system of the vehicle, its mass, the wheel diameter and the horizontal velocity of the loading. BEAM MODEL, Case 1 This model is based on the Bernoulli-Euler beam (refer Figure 4) with viscous damping and the solution uses the modal analysis method, where the equations of motion are formed by direct equilibration of all forces acting. A Fourier sine finite integral transformation was used to assist in the simplification of the equations and these were subsequently solved using numerical integration techniques (Duffield 1989).

$(t) u (t) o

071)

/\

u(x,t)

yo(t)

y(x,t)

x 1.4 FIG 4 BERNOULLI-EULER BEAM BEAM MODEL Case 2 To assess the longitudinal dynamic response of bridges, having continuous rail laid on ballast, bridge number two which is a 30 m single span steel structure has been investigated. A finite element model was been developed and a general purpose finite element package was used for the analysis. The loads applied corresponded to measured loads from the testing programs, (eg ORE 1973) and were applied to simulate moving forces decelerating at 3 m/s2. The geometric details of the model are shown in Figure 5. The bridge and rail are modelled as two dimensional beams in a plane and the increment length of these beams has been taken as 1.0 m which involves some 366 degrees of freedom. The rail has been modelled for 30 m each side of the bridge and is connected to the ground by linear springs acting in both the vertical and horizontal directions. Similar springs have been used to connect the rail to the bridge structure. The bridge beams are supported by a pin support and roller bearing. tF

IT17 1.11---30 m

30m

4.

30m-.01

FIG 5 FINITE ELEMENT MODEL

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The model was created with dashpots at every spring location. Initially these were set to zero, and hence the springs representing the track were undamped. The spring stiffness of the track was taken to be 10 kN/m both vertically and horizontally over the full length of the rail. This spring stiffness corresponds with track in good condition (Chu 1980).

RESULTS The experimental results for the bridges having non-continuous rail joints at .cach end of the bridge have -been used for comparison with the simply supported beam model (ie Beam model case 1, refer Figures 6 and 7). Corresponding code results for bridges carrying this type of jointed track are also included. In these analyses the ratio of the applied horizontal to applied vertical loading (adhesion, µ) of 0.3 was applied to both the 30 m and 16 m long bridges and the computed longitudinal forces were found to be greater than those measured (Figures 6 and 7). The measured nondimensional force at the bearing (µB) of the 16 m bridge was 0.258 corresponding to a maximum applied input loading of µ max = 0.438. The results for bridge number two correspond to an applied µmax of 0.246, whilst in the partially non-continuous rail jointed bridge number four µmax = 0.35. For bridge number six (30 m length) µmax equalled 0.132. In bridges two and five the rail to rail joint at the end of the bridges was partially restrained hence the simply supported structure model does not truely represent these bridges. However, the results do confirm that the use of µ = 0.3 for braking situations is quite reasonable, even though the tested bridges were specially prepared with sand to produce maximum adhesion (ie an upper bound condition). The computed results generally ranged up to 0.34 with isolated higher results, indicating they are of reasonable magnitude. 015

0..5

:11

u.. ..y jeko anatyacal moul. o 0.35

...............1) _

ya - 0.10540 ye - 0.175.x.

0.15 00

‘."

ORE racarnmenda•on - &akNg

Z. 0. 0.25

0

Frye

0.2

ad,

es stoo - &

—1

AN2RC A AREA r.0.11110101160111 0.

0

0.25

g •

E 6-

ois

02

ORE n000nwnendaton • &aki - 0250 ..“ BS 5 400 ..,9

—ca

ANZRC I AREA mcannanbione —IL OA

0

Dimensionless position of loading

Dimensionless position of loading

FIG 6 AXIAL FORCE, NON-CONTINUOUS RAIL JOINTS, 30 M SPAN BRIDGE

joinl amly1.41 needle

g

FIG 7 AXIAL FORCE, NONCONTINUOUS RAIL JOINTS, 16 M SPAN BRIDGE

When compared with the code results the value assumed for adhesion becomes critical. In braking the ORE use µ = 0.3, BS5400 use µ = 0.25 and ANZRC use µ = 0.15. The varying initial adhesion values are reflected in the correlation with the computed values. From the limited test results, shown as µ.8 on Figures 6 and 7, it is evident that the ORE recommendations are conservative for the 30 m and 16 m long bridges tested. Also, the ANZRC recommendation appears non-conservative. The recommendations of BS 5400 reflect the test results quite well.

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Analytical results for bridge number 2 are presented in Table III. The results are for a vertical live load of 2064 kN, with adhesion of 0.3 travelling along a corrugated rail having a corrugation wavelength 00 of 48 mm. These analytical results compare well with the experimental results (Figures 8 to 11). This indicates that the analysis of a detailed finite element model such as shown in Figure 5 provides a satisfactory method for predicting the longitudinal forces transmitted. Figures 8 to 11 compare the results using the methods proposed by Siekmeier, Fryba and the various codes with test results.

TABLE III HORIZONTAL REACTION FOR CORRUGATED LOADING, = 0.048 MM, TOTAL VERTICAL LOAD OF 2064 KN Track damping

Response on

(kNs/m)

load stopping (1N) c

RB% Longitudinal response x 100 Vertical load

Nil

-294.5

14.3

50.0

-316.6

15.3

75.0

-320.6

15.5

Figure 10 indicates the analytic technique presented by Siekmeier compares reasonably well with the test results over a limited range, being best for spans of the order of 35 m. The results from Fryba are most consistent where the load is totally on the structure and does not continue to the approach embankments. The code results all appear to be reasonable for bridges of the order of 100 m length however, the small number of tests conducted mean that conclusions should be substantiated by further testing.

30 30

i be 20

•

•

92 ,10

•

.

Stool bov1np Otor bearings Frybs analysts

•

20 • Stool bowing Other boacings • — macron

E:11 U 10

•

0 20

40

60

60

Bridge length (m)

FIG 8 CONTINUOUS RAIL FRYBA VS EXPERIMENTS

700

100

20

40

60

80

100

Bridge length (On)

FIG 9 CONTINUOUS RAIL, LOAD ONLY OVER BRIDGE, FRYBA VS EXPERIMENTS

AUSTROADS Conference Brisbane 1991

• 1 0 • 11.1 wok. • 011.• — 444howler mak.

I. : 2, 4 ,1 100 411.

8

ao 40

s

?r

Bridge at 201.2 rn

40

°

0

10

3 20

-2 74:

•

10 Bridge

40

2C

10

CSC CE •

•

o

•

••••••••1.

—

O

041144 borings

_

-.a NUM

•

•

Stool bowing

•

mx

so

50

100

Bridge length- (m)

Nrpin (m)

FIG 10 CONTINUOUS RAIL SIEKMEIER VS EXPERIMENTS

FIG 11 CONTINUOUS RAIL CODES VS EXPERIMENTS

SUMMARY AND CONCLUSIONS In summary the computed results compare well with the experimental results when the effect of partial fixity of the rail is taken into account. Further the ORE and BS 5400 recommendations match the results well except for the very short span bridges. In the range 30 to 70 m the predictions of BS5400 and ORE seem reasonable except that they are some 25% low for structures of approximately 50 m span. The prediction of the ANZRC is shown to be unsatisfactory in all cases other than for long length structures.

REFERENCES ANZRC (1974). "Australian and New Zealand Railway Bridge Design code", 1974. A.R.E.A. (1955). "Field measurement of forces resulting from rail anchorage", A.R.E.A., proceeding's of the 54th annual convention, vol 56, March 1955, pp 283-321. A.R.E.A. (1966). "Advanced report of Committee 30 - Impact and Bridge Stresses : Field investigation of prestressed concrete beams and piles on the Western Pacific Railroad", A.R.E.A. proceedings, vol 67, bulletin no 594, 1966. A.R.E.A. (1966). "Advanced report of Committee 30 - Field investigation of longitudinal forces in a concrete trestle on the Santa-Fe-Railway", Ekram N.E., A.R.E.A. proceedings, vol 68, bulletin 601, 1966, p 31. A.R.E.A. (1990). Manual for Railway Engineering ARYA A.S. and AGRAWAL S.R. (1982). "Dispersion of tractive and braking forces in railway bridges - Theoretical analysis", Rail International, April 1982, pp 12-25. BRITISH STANDARD (1978). "BS 5400 Part 2 steel, concrete and composite bridges", British Standard, BS 5400, part 2, 1978. CANADIAN STANDARDS ASSOCIATION (1978). "Concrete Railway Bridges", CSA Standard S29 - 1978 CHU K.H. and LEE P.H. (1980). "Effect of longitudinal forces on long welded tracks", Rail International, January 1980, pp 23-34.

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DUFFIELD C.F. (1989). "Longitudinal forces on railway bridges". Master of Engineering Science thesis, University of Melbourne. EISSES J.A. (1975). "Solid-bed track laid for trial service on Netherlands Railways", Rail Engineering International, August 1975, pp 187-194. FRYBA L. (1974). "Quasi-static distribution of braking and starting forces In rail and bridge", Rail International, no 11, November 1974, pp 698-716. FRYBA L. '(1975). "Response of a beam to a rolling mass in the presence of adhesion", Acta Technica C.S.V.A., vol 20, no 1, 1975 pp 673-687. INGLIS C. (1951). "Applied mechanics for Engineers", Cambridge Press, 1951. O.R.E. (1971). "Braking and starting tests on three unballasted steel bridges of about 15, 30 and 60 m spans", O.R.E. Utrecht, report Q D101/RP4/E, April 1971. O.R.E. (1973). "Braking and starting tests on a steel bridge of 30m span with ballast bed", O.R.E. Utrecht, report Q D101/RP5, April 1973. O.R.E. (1974). "Theoretical studies of braking and acceleration forces on bridges", ORE Utrecht report QD 101 RP 6, October 1974. SIEKMEIER E.W. (1965). "The effect of longitudinal forces on continuously welded track and on track ballast", Bulletin of the International Railway Congress Association, July 1965, pp 446-489. STOKES G.G. (1867). "Discussion of a Differential Equation Related to the braking of Railway bridges", Trans Cambridge Phil Soc., Vol 8, Part 5, 1867, pp 707-735. WILLIS R. (1848). Appendix to the report of the Commissioners appointed to inquire into : "Application of Iron to Railway Structures", H.M. Stationary Office, London, 1848.

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