Engineering Structures 31 (2009) 2803–2811

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Engineering Structures

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Dynamic testing of a soil–steel composite railway bridgeEsra Bayoğlu Flener ∗, Raid KaroumiDepartment of Civil and Architectural Engineering, Division of Structural Design and Bridges, The Royal Institute of Technology (KTH), SE-100 44, Stockholm, Sweden

a r t i c l e i n f o

Article history:Received 11 December 2008Received in revised form6 June 2009Accepted 2 July 2009Available online 12 August 2009

Keywords:CulvertsRailway bridgesDynamic loadsField testsDynamic amplification factorsBallast accelerationsMonitoringInstrumentation

a b s t r a c t

Actual dynamic response of a long-span corrugated steel culvert railway bridge is studied. The bridge,which is a type of soil–steel composite structures, has a span of 11 m. Tests were carried out bymeasuring strains and displacements during passages of a locomotive at different speeds. Vertical ballastaccelerations as well as the effects of braking forces were also measured. The tests showed that the speedhas a large influence on the displacements, thrusts and moments. The measured dynamic displacementsand thrusts are as much as 20% larger than the corresponding static response. This is greater than thevalues specified in bridge design codes. Dynamic amplification factors as high as 1.45 were obtained forthe moments at the quarter point which is found to be much larger than the values for the crown point.This type of bridge structure is believed to be less sensitive to resonance from passing trains than othercommon bridge types, due to the high damping values obtained from the forced vibration tests.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Large-span soil–steel composite bridges, also known as corru-gated metal culverts, are generally composed of corrugated steelplates surrounded by compacted granular (sometimes engineered)soil material. These types of composite structures are gettingmorepopular in recent years because they are more economical andhave much shorter construction periods compared to traditionalbridges.The performance of soil–steel structures is governed by

soil–structure interaction. The steel part of the structure has lowflexural stiffness and is prone to deformations. The strength of thecomposite structure comes from the positive effect of the inter-action between soil and metal components. The backfill soil pro-duces earth pressure on the bearing structure and supports muchof the load through confinement and resistance to deformation ofthe flexible metal walls at the same time.Induced dynamic displacements and stresses in this kind of

structures under moving traffic can be higher (or lower) thanthe corresponding static response [1]. Structures have differentresponses to rapid rate of loading. Resonance can also arise undercircumstances due to passage of successive loads. Irregularities anddefects in wheels and track system can also induce large dynamic

∗ Corresponding author. Fax: +46 8 216949.E-mail addresses: Esra.Bayoglu@byv.kth.se (E. Bayoğlu Flener),

Raid.Karoumi@byv.kth.se (R. Karoumi).

0141-0296/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2009.07.028

effects, see [2–4]. The amount of dynamic effects on a structureis usually quantified in design by dynamic amplification factors(DAF), see [5].Full-scale dynamic testing of structures can bring out valuable

information about the performance and prediction of the servicebehaviour that can be utilized for improving current methods ofanalyses. From the dynamic response induced by either ambientor forced excitations, interesting parameters (modal and systemparameters) can be estimated [6]. It is usually much easier andless expensive to measure strains and accelerations than displace-ments. Direct displacement measurements under dynamic loadsare not very oftenperformed as this requires a fixed reference point[7]. If possible, displacements should be measured because ac-cording to design codes, the DAF is evaluated from displacementsobtained from field tests or dynamic simulations.An extensive field testing work was done on a corrugated steel

arch soil–steel composite bridge with 11 m span in 3 stages [8,9].This paper describes and presents the evaluation of results of thethird part (done in May) of these tests. The bridge is located on therailway line between Malmö and Ystad in Sweden. The responseof the bridge during and soon after construction was presented in[10]. The newbridgewas placed on top of an existingmasonry archbridge (see Fig. 1.1) with a gap in between, which leaves the oldbridge structurally functionless. For convenience and simplicitythe structure will be referred as culvert within this paper.There have been many efforts to establish an improved and

more realistic understanding of the interaction and performanceof soil–steel composite structures. Some of this research was

2804 E. Bayoğlu Flener, R. Karoumi / Engineering Structures 31 (2009) 2803–2811

(a) Placement of the culvert over the old bridge. (b) Ongoing backfilling process.

Fig. 1.1. Some of the construction stages of the culvert being installed over the old masonry arch bridge over Skivarp creek.

utilized in updating design procedures. Similar tests have beenconducted on four relatively small-span pipe arch culverts underhighway traffic by Sezen et al. [1]. Static anddynamic loadingunderservice loads was evaluated by measuring deflections and strains.Significance of backfill height was reassured along with dynamicresponse being less critical than the static. Deflections from truckpassages were found by Sezen et al. [1] to be approximately10%–20% less than static deflections. It is questionable if theselow dynamic factors can be applied to bridge with longer spans.Yeau et al. [11] summarizes static and dynamic tests done on39 corrugated steel culverts under highways with spans varyingbetween approximately 3 and 7 m. The maximum deflections dueto dynamic testswere found to be 10%–30% less than themaximumstatic deflections. General trend showed that there is a nonlinearrelationship between strains (and deflections) and backfill height.Manko and Beben [12] presents dynamic load tests on a 6.3m spanbox culvert road bridge. Dynamic coefficients as well as criticalspeeds and vibration velocities were obtained. The variation of thedynamic response, which was consistently higher than the static,was found to be depending onmanydifferent factors such as speed,load scheme, and the location of the point of measurement.

2. Description of the structure and the in situ testing

The culvert is a single radius arch with a radius of 5640 mmdepicted in Fig. 2.1. Maximum span is 10972 mm and the internalheight from the footing level is 4332 mm. The steel plate is 7 mmin thick. The backfill soil is gravel with 0–45 mm particle size andhas a dry density of 2.1 g/cm3. The degree of compaction (RP) ofthe soil is 93%. The section properties and more details about thestructure can be found in [8].Six strain gaugeswere glued on the culvert. All the strain gauges

measured strains in the bridge’s longitudinal direction. They werelocated at the top of the crown on the centreline (sensors 3 &4), 762 mm eccentric from the centreline (sensors 5 & 6), and atthe ‘‘quarter point’’ along the centreline of the bridge (sensors 1& 2) (see Fig. 2.2(a)). The sensors were placed inside the culvertin couples of one at the bottom and the other one at the top ofthe corrugation as seen in Fig. 2.2(b). The vertical displacementof the crown was monitored (using the old bridge as a base) bymeans of a variable differential transformer (LVDT) as seen inFig. 2.3(b). Vertical ballast accelerations were also recorded at twolocations; one in between and one at the side of the rails close tothe quarter point of the bridge. In order to not disturb the ballastthe accelerometers were cautiously placed by removing a fewballast stones and replacing a bag containing the accelerometersurrounded by sand.

Fig. 2.1. Dimensions of the culvert (given in mm) and the axle loads (not to scale).

The tests were carried out using a Swedish RC4 locomotiveengine that has four axles and has a total static service weight of78 tons. The static load tests were also conducted for a total of 11different locomotive positions. Positions of the first axlewere 11m,8.25 m, 5.5 m, and 2.75 m before the crown, on the crown, 1.5 m,2.75 m, 5.5 m, 8.25 m, 11 m and 16 m after the crown.In dynamic tests, the locomotive passed aiming at constant

speeds of 10, 30, 50, 70, 90, and 125 km/h. The tests were repeatedfor the two travel directions (Ystad–Malmö and Malmö–Ystad).Braking tests were also performed with 4 different target speeds(30, 50, 70, and 90 km/h). Locomotive speedsweremeasured usingoptical sensors (see Fig. 2.3(a)) installed at 3 different locations.Measured speeds, which appear in all the figures, were slightlydifferent from the aimed ones.

3. Measurement of random traffic

One convenient way of testing is done under service loadingwithout any control over the input excitation. In the case ofthis culvert, some measurements under random passing trafficwere done shortly after the completion of the structure. BayogluFlener [9] describes and evaluates the construction and backfillingstages of the bridge followed by some measurements of therandom traffic. One example of these is the passage of a cargotrain at approximately 65 km/h, which gave the opportunity totest and calibrate the measuring system. The train configurationand the corresponding vertical displacements can be seen inFig. 3.1(a). The very small difference between the initial and finaldisplacements (before and after the passage of the first train)could be an indication of settlement in the foundations. Thestrain measurements at the crown (upper and lower part of the

E. Bayoğlu Flener, R. Karoumi / Engineering Structures 31 (2009) 2803–2811 2805

a

b

Fig. 2.2. (a) Culvert from the top with locations of strain gauges. (b) The corrugation profile and locations of the strain gauges.

a b

Fig. 2.3. (a) Optical speed sensor. (b) Placement of the LVDT in the gap between the old bridge and the culvert.

corrugation) are given in Fig. 3.1(b) and Fig. 3.1 (c). As clearly seenfrom these figures, the downwards displacement of the top of thecrown comply with the negative strain (compression) pattern atthe top of the section. The high quality of the signals shown inFig. 3.1 enables the evaluation of the train loading. Thus, such asimple instrumentation can convert this bridge into a scale forweighing all passing trains, a so-called Bridge Weigh-in-Motionsystem (B-WIM), see [13].The steel part of the culvert experiences both compression and

moment during the passage of the cargo train. The top sensormeasures only compression (Fig. 3.1(c)) while the bottom sensormeasures both compression and tension (Fig. 3.1(b)). The amountof negative strains shows the extent of the compression in thesection.

4. Test results and calculations

The tests results for only one of the travel directions (namelythe Ystad–Malmö direction) will be presented in this paper due tothe existence of a turn-out very close to the bridge at the Malmöside. The responses, when the locomotive is coming from Malmödirection, could thus have been affected by the existence of thisturn-out. Also, the braking tests were done only in Ystad–Malmödirection.

4.1. Methodology

Data filtering was necessary to achieve values free from noise.The cut off frequency for low-pass filtering the data was chosenas 30 Hz. Comparison made between results filtered at 30 Hz and60 Hz cut off frequency showed negligible differences.

Calculations were carried out according to a certain sign con-vention where; tension, tension at the bottom of the section,elongation and upwards displacements are positive. The strainsmeasured at the top (εtop) and the strains measured at the bottom(εbottom) are used to calculate stresses σtop and σbottom. Section nor-mal forces (Thrusts) (N) per unit width of the structure can then becalculated for every passage of the locomotive as given in Eq. (4.1).Section bending moments (M) are calculated using Eq. (4.2).Extrapolated values were used for the top strains.

N = A ·(σtop + σbottom

)/2 (kN/m) (4.1)

M = W ·(σbottom − σtop

)/2 (kNm/m) (4.2)

where A is the cross-sectional area per meter width (m2/m) andW is the section modulus (m3/m). The curvature of the structurewas not considered when using the basic equations of the theoryof bending since the error would be negligible considering the factthat the ratio of the radius of curvature to the section height is quitehigh.DAF were calculated for each run of the locomotive. The DAF on

vertical displacement of the crown (Φdisp) are calculated accordingto Eq. (4.3). DAFwith respect tomoments and thrusts (Φmoment andΦthrust) are also calculated in the same manner.

Φdisp(i) =δdyn(i)δsta

(4.3)

where Φdisp (i) is the DAF for speed i, while δsta is the maximumstatic displacement, and δdyn (i) is the maximum dynamicdisplacement for speed i.

2806 E. Bayoğlu Flener, R. Karoumi / Engineering Structures 31 (2009) 2803–2811

Stra

in g

auge

rea

ding

(m

icro

stra

in)

Stra

in g

auge

rea

ding

(m

icro

stra

in)

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0 1020304050

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Time (s)

5 22

0.3

0.1

-0.1

-0.3

-0.5

-0.7

-0.9

-1.1

0.5

-1.3

Dis

plac

emen

t of

the

crow

n (m

m)

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 215

Time (s)

22

Loc 1 2 3 4 5 6 7 8 9 10 11 12

76.8t 89t 39t 76t 90t 24t 41t 16t 89t 74t 74t 12t 20t

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Time (s)

5 22

a

b c

Fig. 3.1. (a) Vertical displacement of the crown due to the passage of a cargo train measured using the LVDT sensor. (b) Crown lower strain gauge (sensor 3) measurements.(c) Crown upper strain gauge (sensor 4) measurements, all low-pass filtered at 60 Hz (see [10]).

Fig. 4.1. Measured vertical displacement of the crown for different locomotive speeds (the elapsed time tickmarks are in half seconds (major) and tenth of a second (minor)scales).

4.2. The displacements and strains

Dynamic testswere conductedwith the passage of a locomotivewith speeds up to about 120 km/h. Fig. 4.1 demonstrates thedisplacements measurements taken at different passages of thelocomotive. The highest displacement measured is 0.86 mmfor the highest measured speed 119.5 km/h. The increase indynamic excitations with increasing speeds can clearly be seen.Compressive strains at the top of the corrugation that are plotted

in the same fashion can be seen in Fig. 4.2. The passage of the fouraxles ismore noticeable compared to the displacement plots in thisfigure. The highest strains measured during the passages changebetween−44 and−47 microstrains (µm/m).The maximum vertical displacements of the crown (Max δdyn)

for different speeds are shown in Fig. 4.3. It is possible to comparethe braking test results with the dynamic tests results. Thedifference between braking and dynamic test is quite pronounced.

E. Bayoğlu Flener, R. Karoumi / Engineering Structures 31 (2009) 2803–2811 2807

Fig. 4.2. Measured strains at the crown (solid lines are from the sensor at the top (No: 4) and dashed lines are from the sensor at the bottom (No 3)) for different locomotivespeeds (time scale is same as previous).

Fig. 4.3. Maximum downwards vertical displacements of the crown duringdynamic and braking tests.

This comparison shows that braking gives larger displacements atthe crown than passing at constant speeds.

4.3. The normal forces and the moments

Normal forces (thrusts) during the passage of the locomotivevary depending on the position of the locomotive on the bridge.Fig. 4.4 shows one demonstration of this at the crown centrelinelevel, during passages of the locomotive with different speeds.Maximum thrusts at the crown are observed when the middleof the locomotive is on the crown centreline. The increase in themaximum thrusts with increasing speeds is quite pronounced. Asshown, a steady and consistent increase from approximately −60to−66 kN/m is obtained.

The moments at the crown centreline during the passage of thelocomotive is shown for different speeds in Fig. 4.5. According tothe figure the moments change direction as the locomotive passesover the bridge. The range for moments at the crown is 1.73 to−1.80 kNm/m. Moments are mostly positive during the passagewith peaks as the axles are on the crown centreline. Negativemoments are observed as the middle of the locomotive is over thecrown centreline and they tend to increase with increasing speeds.For speeds 90 km/h and up, the maximum negative moments arelarger in absolute values than the positive moments. Note that thefigure is a collection of 5 individual passages into one plot underthe same time axis and that the moment components created bylive loads are always zero at the beginning and at the end of eachlocomotive run. Braking test results for moments were found to behigher than for the dynamic tests at constant speeds.In Fig. 4.6(b), moments and thrusts at different locations

on the culvert are compared for one selected passage of thelocomotive. The moment values for the crown centreline andcrown eccentric are very close to each other with crown centrelinebeing marginally larger. The moments at the quarter point arerelatively much smaller. The most critical moments are at thecrown. The asynchrony in curves between the crown and thequarter point is due to delay in the loading sequence betweenthem. Quarter point thrusts, shown in Fig. 4.6 (a), indicate howeverthat the compression level due to train passage is more or less thesame within the structure.

4.4. Dynamic amplification factors

Induced static displacements and stresses in this kind ofstructures can be increased under the effect of moving traffic.

Fig. 4.4. Thrusts at the crown centreline for different locomotive speeds (the elapsed time tick marks are in half seconds (major) and tenth of a second (minor) scales).

2808 E. Bayoğlu Flener, R. Karoumi / Engineering Structures 31 (2009) 2803–2811

Fig. 4.5. Moments at the crown centreline for different locomotive speeds (the elapsed time tick marks are in half seconds (major) and tenth of a second (minor) scales).

a b

Fig. 4.6. Thrusts (a) and moments (b) from dynamic tests for approximately 90 km/h locomotive speed at three different locations on the bridge.

There aremany factorswhich can influence the amount of dynamiceffects. Speed of the vehicle, the span and the mass of the bridgestructure are known to be important factors that have largeinfluence on the dynamic response. Number of axles and axle loadsas well as the spacing of the axles can also have large influenceon the dynamic response. The track can have varying dynamiccharacteristics due to differences in ballast, sleepers and othertrack components. Vertical irregularities on the track as well aswheel defects also result in increased dynamic effects [2].The additional dynamic stresses and displacements in the

structure are usually considered in the design by DAF (Φ). Themethod of evaluating the amount of dynamic effects from the fieldmeasurements is explained previously in Section 4.1 by Eq. (4.3).There are various alternatives of determining the DAF. DAF canbe calculated e.g. considering the response for the entire trainpassage or for certain axles, boogies, or wagons of the train. It canbe calculated considering the positive and the negative responseseparately or just by taking the maximum absolute response forthe point under study. Eurocode also suggests that if a dynamicanalysis is required, the dynamic increment should be calculatedaccording to Eq. (4.4).

ϕ′dyn = max |γdyn/γsta| − 1, 0 (4.4)

γdyn is the maximum dynamic response and γsta is the correspond-ing maximum static response at any particular point in the struc-tural element. This approach was followed for the calculation ofthe response of the test results.Fig. 4.7 shows the factor (Φdisp) calculated with respect to

the maximum vertical displacements of the crown. Maximumdynamic displacements during the passages in the oppositedirection (Malmö–Ystad) give higher values. As mentioned before,

Fig. 4.7. DAF for vertical displacement of the crown.

these values are of less interest and are not presented in thispaper as it is believed that the higher values are due to inducedvibrations caused by the turn-out located shortly before the bridge.As seen from Fig. 4.7, the amplification factor for the crowndisplacement reaches 1.2 for the highest speed tested. In addition,the amplification factor is approximately 5 percent largerwhen thelocomotive is braking with full power on the bridge.The DAF formoments and thrusts at different speeds are shown

in Fig. 4.8. Here the moment dynamic factors are calculated usingthe absolute values (regardless of the signs) as tension at thebottom or the top of this kind of symmetrical steel sections wouldplay the same role. Results show that the crown moments (themaximum absolute moment values) are not affected much byincrease in speed. On the contrary, moment at the quarter pointshow very large increases with speed and the DAF reaches up to1.45 for the highest speed. The highest DAF for the thrusts is about1.25 observed at the crown eccentric point.

E. Bayoğlu Flener, R. Karoumi / Engineering Structures 31 (2009) 2803–2811 2809

a b

Fig. 4.8. DAF for (a) thrusts and (b) moments.

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

0 10 20 30 40 50 60 70 80 90 100 110 120 130Speed (km/h)

Dyn

amic

fac

tors

Displacement - Crown centrelineThrust - Crown centrelineMoment - Crown entreline - absolute

Fig. 4.9. The DAF with respect to thrusts, moments and displacements for thecrown centreline of the bridge.

Dynamic factors due to moments were alternatively calculatedby taking the signs of themoments into account by considering thenegative and positive moments individually. The resulting factors(with negative moments) are much higher and almost identicalto the moment amplification at the quarter point given in Fig. 4.8(b). The factors for the positive moments, however, are around 1.0fluctuating between 0.8 and 1.1.A compilation of the dynamic factors for all three measured

response of crown centreline is given in Fig. 4.9. The increase withspeed is quite steady and very similar for the displacements andthrusts. It can be observed that the DAF at the crown centrelinereaches as high as 1.2 which is relatively smaller compared to theother two locations on the bridge.The resulting DAF are compared with the values given in two

bridge design codes which are calculated as follows. Eurocode(2002) [5] suggests the usage of Eq. (4.5) for the dynamic coefficientfor the well maintained tracks.

ΦEurocode =1, 44

√LΦ − 0, 2

+ 0, 82 with 1, 0 ≤ Φ ≤ 1, 67 (4.5)

LΦ is the determinant length in meters. Eurocode does not providedeterminant length specific to steel culverts. In case of arch bridgesand concrete bridges of all types with a depth of cover (hc) morethan 1.0 m, DAF factors may be reduced by subtracting (hc −1.0)/10.According to Swedish bridge design code [14], the DAF is

calculated as

ΦBVBro = 1+4

8+ LΦ. (4.6)

In BV Bro it is suggested that the value of LΦ shall be twice theculvert span. The recommended reduction of the dynamic factor

Table 4.1Recommendations for the dynamic factors (DAF) in two different designregulations.

Eurocode (2002) [5] BV Bro (2006) [14]

Dynamic factor 1.141 1.134Reduced dynamic factor 1.063 1.076

due to increasing soil cover is the same as in Eurocode except thatit is considered for cover height of more than 1.2 m. The resultingdesign values of dynamic factors according to the abovementionedprovisions are given in Table 4.1. Same value for the determinantlength, which is given in BV Bro, is used for all calculations.As noted, the speed of the vehicle is not an ingredient in

calculating these design DAF values. But tests clearly show thathigher DAF can be achieved with higher speeds. The highest testDAF values (given in Figs. 4.7 and 4.8) are much higher than thedesign ones given in Table 4.1. The reduced design values areexceeded after locomotive speed of about 50 km/h. The unreducedare exceeded when speeds are higher than about 90 km/h.

4.5. Bridge dynamic properties and ballast accelerations

Large amplitude vibrations of railway bridges can causedamages such as ballast instability leading to changes in thegeometry of the track and in the worst case scenario, to trainderailment. Thus it is interesting to measure ballast accelerationsto check the bridge safety. To provide safety against ballastinstability, the European bridge design code specifies a limit of3.5 m/s2 for the maximal vertical deck acceleration [5].Consequently, the vertical ballast acceleration was also moni-

tored during the test at two points on the track, about 4 metersfrom the bridge crown point. Fig. 4.10 shows the relation betweenthe maximum vertical ballast acceleration measured in the ballastbetween two sleepers at the middle of the track versus the loco-motive speed. The signals have been filtered at 30 Hz according tothe requirement in the code. The results show very low accelera-tion levels much lower than the code limit of 3.5 m/s2. Thus, noballast instability problems should be expected for this bridge.Fig. 4.11 presents the spectrum of measured strain in sensor 4

at the crown centre line and of the measured crown displacement,for the test at 120 km/h. Fig. 4.12 presents the spectrum ofmeasured crown displacement with no loading (the so-calledambient vibration test). The first two Eigen frequencies of thebridge are clearly seen for both the ambient vibration and forcedvibration tests. The first Eigen frequency is found approximatelyat 4.0 Hz from the ambient vibration test and at 3.5 Hz from theforced vibration test. The lower frequency value is believed to bepartly the result of the additional mass from the locomotive. It isalso interesting to note that vibration modes higher than 15 Hzhave here little contribution to the dynamic response.

2810 E. Bayoğlu Flener, R. Karoumi / Engineering Structures 31 (2009) 2803–2811

Fig. 4.10. Measured maximum vertical ballast acceleration for different speed.

Using the Half Power Bandwidth method, see e.g. [6], thedamping ratio of the first mode of vibration was very roughlyestimated from Fig. 4.11 to about 20% and from Fig. 4.12 to about2%. The reason for this large difference is believed to be the effectof the activation of the soil–structure interaction when the bridgeis loaded, the increased friction damping in the soil when loadedas well as the additional damping from the locomotive, see also[15]. This demonstrates the complexity of the problem as for suchbridge structures, soil–steel composite bridges, the damping isstrongly amplitude dependent. This needs to be considered whencalculating the dynamic response to passing trains, especially atresonance.

5. Conclusions

Soil-steel composite bridges have increased in popularity inrecent years because they are more economical and have muchshorter construction periods compared to traditional bridges. Inthis paper, the actual dynamic response of a long-span corrugatedsteel culvert railway bridge is studied. The performed full-scaledynamic testing brought out valuable information about thedynamic properties and performance of this not well investigatedbridge type.The speed is found to have a great influence on the dynamic

response. The moments at the quarter point are much smallerthan the moment at the crown. However, much greater dynamicamplification factors (DAF) for moments are obtained for thequarter point than for the crown.When the DAF are calculated considering the maximum

absolute moment values, it is found that the crown moment DAF

10 20 30 40 50 60 70

2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

Frequency (Hz)

Spe

ctru

m

1

2

3

4

5

6

7

8

9

Spe

ctru

m

0

10

0 80Frequency (Hz)

Fig. 4.12. Spectrum of measured displacement at the crown, ambient vibrationtest.

values are not as much affected by the speed as the thrust andvertical displacement DAF values. DAF values as high as 1.45 wereobtained for themoments at the quarter point which is found to bemuch larger than the values for the crown point. The DAF for thecrowndisplacement reaches 1.2 for the highest speed tested. Thesevalues are higher than the ones obtained form the bridge designcode (Eurocode) where the simple formula used is only a functionof the span length. The comparisons of braking and dynamic testsat constant speeds showed that braking gives larger displacementsat the crown than passing at constant speeds.Measured ballast accelerations are very low and are much

lower than the specified code limit against ballast instability.The damping ratio was roughly evaluated from the spectrumof the signals to about 20% when the bridge was loaded andabout 2% when unloaded. This demonstrates the complexity of theproblem as for this type of bridge structure the damping is stronglyamplitude dependent. The high damping value obtained need to beverified by additional tests and theoretical analysis.

Acknowledgements

The funding for this project is provided by the Swedish RailwayAdministration (Banverket), ViaCon AB and KTH who are sincerelyacknowledged. The authors of this paper would also like to thankthe KTH laboratory technicians Claes Kullberg and Stefan Trillkottfor their excellent work.

10 20 30 40 50 60 70 80Frequency (Hz)

10 20 30 40 50 60 70 80Frequency (Hz)

10

20

30

40

50

60

70

80

90

Spec

trum

0

100

50

100

150

200

Spec

trum

0

250

Fig. 4.11. Spectrum of measured strain (left) and displacement (right) at the crown, for the test at 120 km/h.

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