Research ArticleEvaluation of Dynamic Load Factors for a High-SpeedRailway Truss Arch Bridge

Ding Youliang and Wang Gaoxin

The Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of EducationSoutheast University Nanjing 210096 China

Correspondence should be addressed to Ding Youliang civilchinahotmailcom

Received 20 May 2016 Revised 18 August 2016 Accepted 21 August 2016

Academic Editor Edoardo Sabbioni

Copyright copy 2016 D Youliang and W Gaoxin This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Studies on dynamic impact of high-speed trains on long-span bridges are important for the design and evaluation of high-speedrailway bridges The use of the dynamic load factor (DLF) to account for the impact effect has been widely accepted in bridgeengineering Although the field monitoring studies are the most dependable way to study the actual DLF of the bridge accordingto previous studies there are few field monitoring data on high-speed railway truss arch bridges This paper presents an evaluationof DLF based on field monitoring and finite element simulation of Nanjing DaShengGuan Bridge which is a high-speed railwaytruss arch bridge with the longest span throughout the worldTheDLFs in different members of steel truss arch are measured usingmonitoring data and simulated using finite element model respectively The effects of lane position number of train carriages andspeed of trains on DLF are further investigated By using the accumulative probability function of the Generalized Extreme ValueDistribution the probability distribution model of DLF is proposed based on which the standard value of DLF within 50-yearreturn period is evaluated and compared with different bridge design codes

1 Introduction

During the bridge design static load effect should multipledynamic load factor (DLF) for consideration of the dynamiceffects Thus accurate evaluation of the DLF will lead to safeand economical designs of new bridges and provide valuableinformation for condition assessment of existing bridgesHowever determining the DLF is a rather complicatedproblem because of the interaction between the bridge andmoving vehicles

Most studies using the analytical approach have beenconducted to investigate the bridge-vehicle interaction andestimate the DLF For example Paultre et al [1] presentedan extensive review of early studies conducted on bridgedynamics and the evaluation of the dynamic amplificationfactor (DAF) McLean and Marsh [2] provided a synthesisthat summarizes the important knowledge and findings withrespect to vehicular dynamic load effects on highway bridgesDeng et al [3] calculated the reliability-based dynamic loadallowance for capacity rating of prestressed concrete girder

bridges Ding et al [4] evaluated the dynamic vehicle axleloads on bridges with different surface conditions Withthe development of field testing technology field tests haveproven to be the best available approach to investigate theactual bridge-vehicle interaction to estimate the DLF Forexample Demeke et al [5] evaluated the dynamic loads ona skew box girder continuous bridge using field test andmodal analysis Nassif andNowak [6] carried out the researchof dynamic load for girder bridges under normal traffic byfield measurement Miyamoto [7] carried out the field testsfor remaining life and load carrying capacity assessment ofconcrete bridges Park et al [8] studied the influence of roadsurface roughness on dynamic impact factor of bridge byfull-scale dynamic testing Furthermore recent years haveseen a growing trend in the application of probabilisticapproaches in the study of DLF using long-term monitoringresults with the aid of structural health monitoring systemFor example Caprani [9] investigated the lifetime highwaybridge traffic load effect from a combination of traffic statesallowing for dynamic amplification using the Generalized

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 5310769 15 pageshttpdxdoiorg10115520165310769

2 Shock and Vibration

(a) View of the Nanjing DaShengGuan Bridge

1

11272

336336 192 108192108

ShanghaiBeijing

➂➁➀ ➃ ➄ ➅ ➆

(b) Elevation drawing of the bridge (unit m)

Figure 1 Nanjing DaShengGuan Bridge

ExtremeValueDistribution Deng andCai [10] developed thedynamic impact factor for performance evaluation of existingmultigirder concrete bridges using the Gumbel distribution

Even though the field tests had been carried out on manytypes of bridge structures according to previous studies thereare few field monitoring data on high-speed railway trussarch bridges In this study a long-term field monitoring wasconducted on the Nanjing DaShengGuan Bridge to collectthe dynamic responses induced by high-speed trains NanjingDaShengGuan Bridge is a steel truss arch bridge with thelongest span throughout the world Its 336m main span and6-track railways rank it the largest bridge with heaviest designloading among the high-speed railway bridges by far Also thedesign speed of 300 kmh of the bridge is on the advancedlevel in the world Thus it is valuable to monitor the actualDLF under normal traffic conditions The DLFs in differentmembers of steel truss arch are measured using monitoringdata and simulated using finite element model respectivelyA parametric study was further carried out to investigate theinfluences of lane position number of train carriages andspeed of trains on DLF To determine the appropriate DLFvalue for design purposes a statistical analysis was finallyconducted

2 Dynamic Strain Responses of the Bridge

21 FieldMonitoring System The subject of this study is Nan-jing DaShengGuan Bridge shown in Figure 1(a) which is asteel truss arch bridge with the span arrangement (108 + 192 +2 times 336 + 192 + 108)mThe elevation drawing of the bridge isshown in Figure 1(b) Due to the remarkable characteristicsof Nanjing DaShengGuan Bridge including long span of themain girder heavy design loading and high speed of trainsa long-term SHM system was designed and installed on theNanjing DaShengGuan Bridge shortly after it was opened

to railway traffic As shown in Figure 1(b) dynamic strainmonitoring of steel truss arch is performed at the 1-1 crosssection in the middle of the first main span of the bridgeThesteel truss arch comprises chord members with box-shapedcross sections (top chord bottom chord and deck chordresp) diagonal web members with I-shaped cross sectionsvertical web members and horizontal and vertical bracingsas shown in Figures 2(a) and 2(b) It can be seen from Figures2(c)ndash2(f) that eight FBG strain sensors are installed on the topchord member the diagonal web member the bottom chordmember and the deck chord member respectively Samplingfrequency of dynamic strain data collection is set to 50Hz

22 Finite Element Modeling of the Bridge and TrainAlthough field monitoring studies remain the most depend-able way to study the dynamic load factors (DLFs) of thebridge the limited monitoring positions have restrictedtheir extensive applications Another method to obtain thedynamic strain responses of the whole bridge is finite element(FE) modeling method Currently with the advances ofcomputer technology FE modeling method has been widelyapplied to obtain results that are in good agreement withthose measured from field tests Figure 3 shows the three-dimensional finite element model of the Nanjing DaSheng-Guan Bridge using ANSYS software A total of 59760 nodesand 112706 elements are built in the model 58370 of whichare beam elements and 54336 of which are shell elementsThetop chords the bottom chords the deck chords the diagonalweb members the vertical web members and the horizontaland vertical bracings of the steel truss arch are simulated byBEAM188 element the diaphragm members and top platesof the steel bridge deck are simulated by SHELL181 elementMoreover the finite element model has 7 bearings Therestraints of 7 bearings are set as follows the middle bearingis constrained with three degrees of translational freedom

Shock and Vibration 3

1500015000

1200

068

007

2

Y1d

Y1u

Y2dY2u

Y3d

Y3u

Y4d Y4u

2

Downstream Upstream

Vertical bracing

Horizontal bracing

Diaphragm memberTop plate

Truss 1 Truss 2 Truss 3

Lane 1 Lane 2 Lane 3 Lane 4

(a) 1-1 cross section of steel truss arch

Shanghai Beijing3

3

4

4

5

5

6

6

Y1dY1u

Y2dY2u

Y3dY3u

Y4dY4u

Top chord member

Diagonal webmember

Vertical web member

Deck chord member

Bottom chord member

(b) 2-2 section of steel truss arch

1000

1000

150

150

850

850

1400Y1d Y1u

(c) 3-3 section of top chord member

Y2dY2u61

0

610

150

150

1398

(d) 4-4 section of diagonal web member

Y3d

Y3u

650

650 80

0

150

150

1400

(e) 5-5 section of bottom chord member

Y4d Y4u

1416

1266

1266

150

150

1400

(f) 6-6 section of deck chord member

Figure 2 Location of strain sensors on the steel truss arch bridge (unit mm)

4 Shock and Vibration

XY

Z

Figure 3 Three-dimensional FE model of Nanjing DaShengGuanBridge

in directions of longitudinal 119883 transverse 119884 and vertical119885 the other bearings are constrained with two degreesof translational freedom in directions of transverse 119884 andvertical 119885 The elastic modulus and poison ratio of the steelare selected as 210GPa and 030 The acceleration of gravityis set to 98ms2 The damping ratio is set to 002

The parameters of the train loads are determined fromthe prototype (CRH3) of trains on the Beijing-Shanghai high-speed railway line The train prototype is an electric multipleunit (EMU) including 8 or 16 carriages The weight of anempty EMU is 380 t and an EMU has a seating capacity of601 people Assuming that the average weight per person is80 kg which is defined from Chinarsquos Ministry of Railways in2001 each carriagersquos weight is 119866 = 53510 kg and the verticalexcitation force generated by awheel is119865 = (1198668)times98Nkg =6554975N Because of the large length of a single carriage(24m) the load model of the carriage is divided into 8 pointloads and the loads of an EMU with 8 or 16 carriages aregrouped as 8times8times119865 or 8times16times119865 Moreover it is supposed thatthe train wheels are always closely touching the surface of thebridge without deviation so the wheels and the surface of thebridge are coupled by the compatibility of displacements andequilibrium of forces at the contact points

23 Results of Dynamic Strain Responses As for dynamicstrain monitoring each chord member or diagonal webmember has two strain sensors on the downstream side andupstream side respectively The average values of two strainsensors are calculated to represent the axial dynamic strain ofthe corresponding member in the truss arch

119860119894=

119878119894d + 119878

119894u

2

(1)

where 119878119894d and 119878

119894u denote the strain data from the 119894thstrain sensors 119884

119894d and 119884119894u respectively 119860 119894 denotes the axial

dynamic strain of the corresponding member Figure 4 showthe typical time histories of dynamic strain data 119860

1sim1198604

when one train passed through the bridge from 92847 pmto 92959 pm on August 7th 2013 Corresponding to thisloading case the simulated dynamic strain responses areobtained using FE model method Its train load for eachcarriage is 535 kN its loading position is lane 2 the number ofits carriages is 8 Figure 4 also shows the results of simulatedstrain responses 119860 s1sim119860 s4 corresponding to 119860 s1sim119860 s4 Itcan be seen that the amplitudes of monitoring strain and

simulated strain are close verifying the effectiveness of theFE modeling method It should be mentioned that althoughpartial trends of monitoring strain and simulated strain arenot consistent such inconsistency will not influence thecalculation results of DLF because the DLF is decided by theamplitude of strain rather than the trend of strain

3 Dynamic Load Factors of the Bridge

31 Definition of the Dynamic Load Factor Bakht and Pin-jarkar [11] suggested the following equation for calculation ofthe dynamic load factor

DLF = 1 + DLA (2)

where DLF denotes the dynamic load factor and DLAdenotes the dynamic load allowance given by

DLA =

119877dyn minus 119877stat

119877stat (3)

where 119877dyn denotes the maximum dynamic strain responseand 119877stat denotes the maximum static strain response

32 Dynamic Load Factors from the Dynamic StrainResponses As for the monitoring strain data the dynamicstrain data can be directly collected by strain sensors (namely119860119894) and the static strain data can be acquired by filtering

the dynamic strain data with a low-pass filter to eliminatethe dynamic components of strain data As for the simulatedstrain data the dynamic and static strain data can be directlyobtained using FE model method Then 119877dyn is calculated by

119877dyn = max (abs (119872)) (4)

where 119872 denotes the monitoring dynamic strain data 119860119894or

the simulated dynamic strain data 119860 s119894 abs(119872) denotes theabsolute value of119872 andmax(abs(119872)) denotes themaximumvalue of abs(119872) And 119877stat is calculated by

119877stat = max (abs (119876)) (5)

where 119876 denotes the monitoring static strain data or thesimulated static strain data abs(119876) denotes the absolute valueof119876 andmax(abs(119876))denotes themaximumvalue of abs(119876)

Therefore the DLF ofmonitoring strain data is calculatedby four steps (i) calculate the maximum amplitude 119877dyn ofmonitoring dynamic strain by using (4) (ii) acquire the staticstrain by using the low-pass filter (iii) calculate themaximumamplitude 119877stat of static strain data by using (5) (iv) calculatethe DLF by using (2) and (3) The DLF of simulated straindata is calculated by three steps (i) calculate the maximumamplitude 119877dyn of simulated dynamic strain by using (4) (ii)calculate the maximum amplitude 119877stat of simulated staticstrain by using (5) (iii) calculate the DLF by using (2) and(3)

It should be noted that an appropriate low-pass filter isimportant to obtain the authentic static strain data In thisstudy the FIR (Finite Impulse Response) filter is used [11]

Shock and Vibration 5

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(a) 1198601 and 119860s1 of top chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(b) 1198602 and 119860s2 of diagonal web member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(c) 1198603 and 119860s3 of bottom chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(d) 1198604 and 119860s4 of deck chord member

Figure 4 Typical dynamic strain responses of field monitoring and FE modeling results

The transfer function of a polynomial of 119899-order FIR filter isdefined by

119867(119911) =

119899

sum

119894=0

119887119894119911minus119894 (6)

and its frequency response is

119867(120596) =

119899

sum

119894=0

119887119894119890minus119895120596119894

= 119887T120593 (120596) (7)

where 119887 = [1198870 1198871 1198872 119887

119899]T is the coefficient vector having

the filter coefficients 120601(120596) = [1 119890minus119895120596

119890minus119895120596119899

]T and T

denotes the transpose of matrix The coefficients of FIR filterare usually symmetric hence they have a spectrum thatexhibits a linear phase and the response to an impulse settlesto zero

Specifically the low-pass FIR filter is decided by fourinput parameters the normalized passband edge frequency120596p the normalized stopband edge frequency 120596s the allowedpassband deviation 120575p and the stopband deviation 120575s [11]Generally the optimal values of four input parameters areobtained by trial-and-error approach [10] In this study theoptimal values of four input parameters are 120596p = 0004 120587Hz120596s = 006 120587Hz 120575p = 1 and 120575s = 60 after trial-and-errorapproach The static strain data are acquired by using thisfilter which show good filtering effect in Figure 5

33 Field Monitoring Results of Dynamic Load Factors Inthis study the dynamic strain responses of the bridge wererecorded for each case having a single train traversing on thebridge 1000 cases (a single train at a time) were selected andthe computed DLFs of 1000 cases are shown in Figure 6 Itis clear from the figures that the DLF is not a deterministic

6 Shock and Vibration

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(a) 1198601 of top chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(b) 1198602 of diagonal web member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(c) 1198603 of bottom chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(d) 1198604 of deck chord member

Figure 5 The dynamic and static strain responses of 1198601sim1198604

quantityThus themeanDLF andmaximumDLF denoted byAV andMVare further computed and also shown in Figure 6The mean DLF and maximum DLF computed from thebottom chord member are the largest of all which are 10862and 11411 respectively And the mean DLF and maximumDLF computed from the top chord member are the smallestof all which are only 10069 and 10106 respectively

34 Dynamic Analysis Results of Dynamic Load FactorsFigure 6 shows the field monitoring results of DLFs for keymembers of the steel truss arch However only DLFs of thetruss 3 as shown in Figure 2(a) have been measured In thissection DLFs for all trusses that is truss 1 truss 2 and truss3 are obtained using the simulated strain responses with theFE modeling methodThe strain data is simulated in 16 casesas shown in Table 1 and the calculation results of DLFs from

truss 3 are shown in Figure 7 Moreover Table 2 shows themonitoring and simulatedAVs of theDLFs and it can be seenthat themonitoring AVs of the DLF are close to the simulatedAVs of the DLFs verifying the effectiveness of the finiteelement modeling method For all 16 cases the maximumDLF of each key member is further obtained Thus Figure 8shows the maximum DLFs for key members of the truss 1truss 2 and truss 3 It can be seen that for each truss themaximum DLFs of the bottom chord member the diagonalweb member the deck chord member and the top chordmember decrease successively which is consistent with themonitoring results Furthermore the maximum DLFs fromtruss 1 and truss 3 is a little higher than those from truss2 Thus for three planes of truss arch the dynamic effectsinduced by high-speed trains for middle truss arch are lessthan those for side truss arch

Shock and Vibration 7

200 400 600 800 10000Segments

0995

1

1005

101

1015

102

DLF

= 10106

= 10069

MV

AV

(a) The top chord member

200 400 600 800 10000Segments

09

1

11

12

13

DLF

= 11318

= 10802

MV

AV

(b) The diagonal web member

200 400 600 800 10000Segments

095

101

107

113

119

125

DLF

MV = 11411

AV = 10862

(c) The bottom chord member

200 400 600 800 10000Segments

095

098

101

104

107

11

DLF

= 10451

= 10197

MV

AV

(d) The deck chord member

Figure 6 Field monitoring results of DLFs

Table 1 16 cases for simulating the strain data

Number of cases Carriage load (kN) Load location Number of carriages Train speed (kmh)1 535 Lane 1 8 2402 535 Lane 2 8 2403 535 Lane 3 8 2404 535 Lane 4 8 2405 535 Lane 1 8 1606 535 Lane 2 8 1607 535 Lane 3 8 1608 535 Lane 4 8 1609 535 Lane 1 16 24010 535 Lane 2 16 24011 535 Lane 3 16 24012 535 Lane 4 16 24013 535 Lane 1 16 16014 535 Lane 2 16 16015 535 Lane 3 16 16016 535 Lane 4 16 160

8 Shock and Vibration

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1004

1006

1008

101D

LF

(a) The top chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

105

107

109

111

DLF

(b) The diagonal web member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

103

105

107

109

111

113

DLF

(c) The bottom chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1

101

102

103

104

105

DLF

(d) The deck chord member

Figure 7 Dynamic load factors for truss 3 using simulated strain responses

Table 2 Monitoring and simulated AVs of the DLFs

DLFs The top chord member The diagonal web member The bottom chord member The deck chord memberMonitoring AV 10069 10802 10862 10197Simulated AV 10068 10768 10781 10215Error () 001 031 075 018

4 Factors Affecting the Dynamic Load Factors

As mentioned in the preceding sections many factors affectthe magnitude of the DLF The influence of lane position oftrains number of train carriages and speed of trains wasstudied and is presented in the following sections

41 Lane Position There are 4 train lanes in the girder ofDaShengGuan Bridge as shown in Figure 2(a) Firstly themeasured DLFs of 1000 trains in Figure 6 are classifiedas 4 groups corresponding to 4 train lanes respectivelyThe total number of the DLFs for each train lane is 250Then for each group the 250 DLFs are divided into 50segments and the mean value of each segment is computedas shown in Figure 9 Furthermore the mean values of thesimulated DLFs in Figure 7 are computed for each train lanerespectively which are also shown in Figure 9 119871 s119894 denotes

the average value of the 119894th train lane 119894 = 1 2 3 4 It can beseen that the influence of lane 1 lane 2 lane 3 and lane 4 onthe DLFs decreases successively for the top chord memberthe diagonal webmember and the bottom chordmember butincreases successively for the deck chord member Thereforewith the train closer to the steel truss arch the dynamic effectis more significant for the deck chord member

42 Number of Train Carriages In China the high-speedelectric multiple unit (EMU) train has 8 carriages or 16carriages respectively In this study an investigation has beencarried out to determine if there is a correlation betweenthe DLF and the number of train carriages Firstly themeasured DLFs of 1000 trains in Figure 6 are classified astwo groups corresponding to the 8 carriages and 16 carriagesrespectively The total number of the DLFs for both 8 and16 carriages is 500 Then for each group the 500 DLFs are

Shock and Vibration 9

Truss 3Truss 2Truss 1

1

105

11

115

DLF

Truss 2 Truss 3Truss 1Location

Deck chordDiagonal chord

Bottom chordTop chord

Figure 8 Maximum dynamic load factors for truss 1 truss 2 andtruss 3

divided into 50 segments and themean value of each segmentis computed as shown in Figure 10 Furthermore the meanvalues 119862s8 and 119862s16 of the simulated DLFs in Figure 7 arecomputed for 8 and 16 carriages respectively which are alsoshown in Figure 10The figures show an increase in the meanDLF for the 8 carriages comparing with the 16 carriagesHowever it can also be noticed that the absolute value of theincrease is very small

43 Speed of Trains According to the field monitoringresults the speed of trains ranges approximately from110 kmh to 250 kmh The results of the DLF (DLF) causedby the speed of trains are plotted in Figure 11 Meanwhile thesimulated DLFs under the speeds of 160 kmh and 240 kmhare shown in Figure 11 which can verify the influenceof train speed on the monitoring DLFs It can be seenthat the speed and DLF are weakly correlated Accordingto the fitting curves shown in Figure 11 even though thecorrelation between speed and DLF is not strong there existsan increasing linear relationship (ie as the speed of trainsincreases the DLF will also increase)

5 Statistical Analysis of theDynamic Load Factors

51 Probability Distribution Model In this study a largeamount of data on DLFs was acquired through field mon-itoring Therefore it is important to introduce a statisticalanalysis to obtain the appropriate design value of DLF Firstlythe accumulative probability function forDLFs is establishedThree types of accumulative probability function are selectedthe normal distribution the Weibull distribution and theGeneralized ExtremeValueDistribution (GEVD) Taking theDLFs in Figure 6(a) for example the accumulative proba-bility and fitting curves using three probability distributionfunctions are shown in Figure 12(a) Their fitting errors areobtained by calculating the variances of residuals between the

monitoring curve and the fitting curve which are 00001120000189 and 0000105 respectively Thus the GEVD is thebest fitting curve which is defined by

119866 (119863) = exp[minus [1 + 119903 (

119863 minus 119887

119886

)]

minus1119903

] (8)

where 119863 denotes the DLFs 119903 119886 and 119887 denote shapeparameter scale parameter and location parameter ofGEVDrespectively which can be estimated by maximum likelihoodmethod In detail Generalized Extreme Value Distribution119866(119863) combines three types of distributions (ie Gumbeldistribution Frechet distribution and Weibull distribution)into a single form The parameters of GEVD in Figure 12(a)are 119903 = minus01279 119886 = 00009 and 119887 = 10066 MoreoverFigures 12(b)ndash12(d) show the fitting curves of GEVD for thediagonal web member the bottom chord member and thedeck chord member It can be seen that the GEVD can welldescribe the probability characteristics of the DLFs

52 Evaluation of Dynamic Load Factors

521 Standard Value of Dynamic Load Factors Eurocode1 [12] specifies that the standard value is the extreme val-ues within 50-year return period The monitoring dynamicstrains are affected by the irregularity of the rail so the calcu-lated DLF of the monitoring dynamic strains has containedthe influence of the irregularity of the rail The irregularityof the rail may be worse later and furthermore influences thecurrent statistics characteristics of the DLFs but whether theirregularity of the rail is really worse or not is hard to decideSo this paper studied the case when the irregularity of therail does not get worse In this case the standard value of themonitored data obtained within a short period of time can beused as the extreme value of the DLF within 50-year returnperiod Specifically the standard value can be calculated by

119875 = 1 minus 119866 (119863p) (9a)

119875 =

1

50119873

(9b)

where119863p denotes the standard value119875denotes the exceedingprobability119873 denotes the number of DLFs in one year OneLDF can be calculated after one train passes the bridge so119873is equal to the total amount of trains passing the bridge in oneyear On consideration that 119863p cannot be directly calculatedby (9a) and (9b) then119863p is numerically calculated byNewtoniteration formula as follows

119863119899+1

p = 119863119899

p +1 minus 119866 (119863

119899

p) minus 119875

1198661015840(119863119899

p) (10)

where 119863119899p is the 119899th iteration of 1198630p and 1198661015840(119863119899

p) is the one-order derivative function of119866(119863119899p) Iteration terminateswhenthe absolute difference between 119863

119899+1

p and 119863119899

p is less than00005 Based on the method above the stand values of DLFsare shown in Table 3 It can be seen that the bottom chord has

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

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Shock and Vibration

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

2 Shock and Vibration

(a) View of the Nanjing DaShengGuan Bridge

1

11272

336336 192 108192108

ShanghaiBeijing

➂➁➀ ➃ ➄ ➅ ➆

(b) Elevation drawing of the bridge (unit m)

Figure 1 Nanjing DaShengGuan Bridge

ExtremeValueDistribution Deng andCai [10] developed thedynamic impact factor for performance evaluation of existingmultigirder concrete bridges using the Gumbel distribution

Even though the field tests had been carried out on manytypes of bridge structures according to previous studies thereare few field monitoring data on high-speed railway trussarch bridges In this study a long-term field monitoring wasconducted on the Nanjing DaShengGuan Bridge to collectthe dynamic responses induced by high-speed trains NanjingDaShengGuan Bridge is a steel truss arch bridge with thelongest span throughout the world Its 336m main span and6-track railways rank it the largest bridge with heaviest designloading among the high-speed railway bridges by far Also thedesign speed of 300 kmh of the bridge is on the advancedlevel in the world Thus it is valuable to monitor the actualDLF under normal traffic conditions The DLFs in differentmembers of steel truss arch are measured using monitoringdata and simulated using finite element model respectivelyA parametric study was further carried out to investigate theinfluences of lane position number of train carriages andspeed of trains on DLF To determine the appropriate DLFvalue for design purposes a statistical analysis was finallyconducted

2 Dynamic Strain Responses of the Bridge

21 FieldMonitoring System The subject of this study is Nan-jing DaShengGuan Bridge shown in Figure 1(a) which is asteel truss arch bridge with the span arrangement (108 + 192 +2 times 336 + 192 + 108)mThe elevation drawing of the bridge isshown in Figure 1(b) Due to the remarkable characteristicsof Nanjing DaShengGuan Bridge including long span of themain girder heavy design loading and high speed of trainsa long-term SHM system was designed and installed on theNanjing DaShengGuan Bridge shortly after it was opened

to railway traffic As shown in Figure 1(b) dynamic strainmonitoring of steel truss arch is performed at the 1-1 crosssection in the middle of the first main span of the bridgeThesteel truss arch comprises chord members with box-shapedcross sections (top chord bottom chord and deck chordresp) diagonal web members with I-shaped cross sectionsvertical web members and horizontal and vertical bracingsas shown in Figures 2(a) and 2(b) It can be seen from Figures2(c)ndash2(f) that eight FBG strain sensors are installed on the topchord member the diagonal web member the bottom chordmember and the deck chord member respectively Samplingfrequency of dynamic strain data collection is set to 50Hz

22 Finite Element Modeling of the Bridge and TrainAlthough field monitoring studies remain the most depend-able way to study the dynamic load factors (DLFs) of thebridge the limited monitoring positions have restrictedtheir extensive applications Another method to obtain thedynamic strain responses of the whole bridge is finite element(FE) modeling method Currently with the advances ofcomputer technology FE modeling method has been widelyapplied to obtain results that are in good agreement withthose measured from field tests Figure 3 shows the three-dimensional finite element model of the Nanjing DaSheng-Guan Bridge using ANSYS software A total of 59760 nodesand 112706 elements are built in the model 58370 of whichare beam elements and 54336 of which are shell elementsThetop chords the bottom chords the deck chords the diagonalweb members the vertical web members and the horizontaland vertical bracings of the steel truss arch are simulated byBEAM188 element the diaphragm members and top platesof the steel bridge deck are simulated by SHELL181 elementMoreover the finite element model has 7 bearings Therestraints of 7 bearings are set as follows the middle bearingis constrained with three degrees of translational freedom

Shock and Vibration 3

1500015000

1200

068

007

2

Y1d

Y1u

Y2dY2u

Y3d

Y3u

Y4d Y4u

2

Downstream Upstream

Vertical bracing

Horizontal bracing

Diaphragm memberTop plate

Truss 1 Truss 2 Truss 3

Lane 1 Lane 2 Lane 3 Lane 4

(a) 1-1 cross section of steel truss arch

Shanghai Beijing3

3

4

4

5

5

6

6

Y1dY1u

Y2dY2u

Y3dY3u

Y4dY4u

Top chord member

Diagonal webmember

Vertical web member

Deck chord member

Bottom chord member

(b) 2-2 section of steel truss arch

1000

1000

150

150

850

850

1400Y1d Y1u

(c) 3-3 section of top chord member

Y2dY2u61

0

610

150

150

1398

(d) 4-4 section of diagonal web member

Y3d

Y3u

650

650 80

0

150

150

1400

(e) 5-5 section of bottom chord member

Y4d Y4u

1416

1266

1266

150

150

1400

(f) 6-6 section of deck chord member

Figure 2 Location of strain sensors on the steel truss arch bridge (unit mm)

4 Shock and Vibration

XY

Z

Figure 3 Three-dimensional FE model of Nanjing DaShengGuanBridge

in directions of longitudinal 119883 transverse 119884 and vertical119885 the other bearings are constrained with two degreesof translational freedom in directions of transverse 119884 andvertical 119885 The elastic modulus and poison ratio of the steelare selected as 210GPa and 030 The acceleration of gravityis set to 98ms2 The damping ratio is set to 002

The parameters of the train loads are determined fromthe prototype (CRH3) of trains on the Beijing-Shanghai high-speed railway line The train prototype is an electric multipleunit (EMU) including 8 or 16 carriages The weight of anempty EMU is 380 t and an EMU has a seating capacity of601 people Assuming that the average weight per person is80 kg which is defined from Chinarsquos Ministry of Railways in2001 each carriagersquos weight is 119866 = 53510 kg and the verticalexcitation force generated by awheel is119865 = (1198668)times98Nkg =6554975N Because of the large length of a single carriage(24m) the load model of the carriage is divided into 8 pointloads and the loads of an EMU with 8 or 16 carriages aregrouped as 8times8times119865 or 8times16times119865 Moreover it is supposed thatthe train wheels are always closely touching the surface of thebridge without deviation so the wheels and the surface of thebridge are coupled by the compatibility of displacements andequilibrium of forces at the contact points

23 Results of Dynamic Strain Responses As for dynamicstrain monitoring each chord member or diagonal webmember has two strain sensors on the downstream side andupstream side respectively The average values of two strainsensors are calculated to represent the axial dynamic strain ofthe corresponding member in the truss arch

119860119894=

119878119894d + 119878

119894u

2

(1)

where 119878119894d and 119878

119894u denote the strain data from the 119894thstrain sensors 119884

119894d and 119884119894u respectively 119860 119894 denotes the axial

dynamic strain of the corresponding member Figure 4 showthe typical time histories of dynamic strain data 119860

1sim1198604

when one train passed through the bridge from 92847 pmto 92959 pm on August 7th 2013 Corresponding to thisloading case the simulated dynamic strain responses areobtained using FE model method Its train load for eachcarriage is 535 kN its loading position is lane 2 the number ofits carriages is 8 Figure 4 also shows the results of simulatedstrain responses 119860 s1sim119860 s4 corresponding to 119860 s1sim119860 s4 Itcan be seen that the amplitudes of monitoring strain and

simulated strain are close verifying the effectiveness of theFE modeling method It should be mentioned that althoughpartial trends of monitoring strain and simulated strain arenot consistent such inconsistency will not influence thecalculation results of DLF because the DLF is decided by theamplitude of strain rather than the trend of strain

3 Dynamic Load Factors of the Bridge

31 Definition of the Dynamic Load Factor Bakht and Pin-jarkar [11] suggested the following equation for calculation ofthe dynamic load factor

DLF = 1 + DLA (2)

where DLF denotes the dynamic load factor and DLAdenotes the dynamic load allowance given by

DLA =

119877dyn minus 119877stat

119877stat (3)

where 119877dyn denotes the maximum dynamic strain responseand 119877stat denotes the maximum static strain response

32 Dynamic Load Factors from the Dynamic StrainResponses As for the monitoring strain data the dynamicstrain data can be directly collected by strain sensors (namely119860119894) and the static strain data can be acquired by filtering

the dynamic strain data with a low-pass filter to eliminatethe dynamic components of strain data As for the simulatedstrain data the dynamic and static strain data can be directlyobtained using FE model method Then 119877dyn is calculated by

119877dyn = max (abs (119872)) (4)

where 119872 denotes the monitoring dynamic strain data 119860119894or

the simulated dynamic strain data 119860 s119894 abs(119872) denotes theabsolute value of119872 andmax(abs(119872)) denotes themaximumvalue of abs(119872) And 119877stat is calculated by

119877stat = max (abs (119876)) (5)

where 119876 denotes the monitoring static strain data or thesimulated static strain data abs(119876) denotes the absolute valueof119876 andmax(abs(119876))denotes themaximumvalue of abs(119876)

Therefore the DLF ofmonitoring strain data is calculatedby four steps (i) calculate the maximum amplitude 119877dyn ofmonitoring dynamic strain by using (4) (ii) acquire the staticstrain by using the low-pass filter (iii) calculate themaximumamplitude 119877stat of static strain data by using (5) (iv) calculatethe DLF by using (2) and (3) The DLF of simulated straindata is calculated by three steps (i) calculate the maximumamplitude 119877dyn of simulated dynamic strain by using (4) (ii)calculate the maximum amplitude 119877stat of simulated staticstrain by using (5) (iii) calculate the DLF by using (2) and(3)

It should be noted that an appropriate low-pass filter isimportant to obtain the authentic static strain data In thisstudy the FIR (Finite Impulse Response) filter is used [11]

Shock and Vibration 5

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(a) 1198601 and 119860s1 of top chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(b) 1198602 and 119860s2 of diagonal web member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(c) 1198603 and 119860s3 of bottom chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(d) 1198604 and 119860s4 of deck chord member

Figure 4 Typical dynamic strain responses of field monitoring and FE modeling results

The transfer function of a polynomial of 119899-order FIR filter isdefined by

119867(119911) =

119899

sum

119894=0

119887119894119911minus119894 (6)

and its frequency response is

119867(120596) =

119899

sum

119894=0

119887119894119890minus119895120596119894

= 119887T120593 (120596) (7)

where 119887 = [1198870 1198871 1198872 119887

119899]T is the coefficient vector having

the filter coefficients 120601(120596) = [1 119890minus119895120596

119890minus119895120596119899

]T and T

denotes the transpose of matrix The coefficients of FIR filterare usually symmetric hence they have a spectrum thatexhibits a linear phase and the response to an impulse settlesto zero

Specifically the low-pass FIR filter is decided by fourinput parameters the normalized passband edge frequency120596p the normalized stopband edge frequency 120596s the allowedpassband deviation 120575p and the stopband deviation 120575s [11]Generally the optimal values of four input parameters areobtained by trial-and-error approach [10] In this study theoptimal values of four input parameters are 120596p = 0004 120587Hz120596s = 006 120587Hz 120575p = 1 and 120575s = 60 after trial-and-errorapproach The static strain data are acquired by using thisfilter which show good filtering effect in Figure 5

33 Field Monitoring Results of Dynamic Load Factors Inthis study the dynamic strain responses of the bridge wererecorded for each case having a single train traversing on thebridge 1000 cases (a single train at a time) were selected andthe computed DLFs of 1000 cases are shown in Figure 6 Itis clear from the figures that the DLF is not a deterministic

6 Shock and Vibration

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(a) 1198601 of top chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(b) 1198602 of diagonal web member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(c) 1198603 of bottom chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(d) 1198604 of deck chord member

Figure 5 The dynamic and static strain responses of 1198601sim1198604

quantityThus themeanDLF andmaximumDLF denoted byAV andMVare further computed and also shown in Figure 6The mean DLF and maximum DLF computed from thebottom chord member are the largest of all which are 10862and 11411 respectively And the mean DLF and maximumDLF computed from the top chord member are the smallestof all which are only 10069 and 10106 respectively

34 Dynamic Analysis Results of Dynamic Load FactorsFigure 6 shows the field monitoring results of DLFs for keymembers of the steel truss arch However only DLFs of thetruss 3 as shown in Figure 2(a) have been measured In thissection DLFs for all trusses that is truss 1 truss 2 and truss3 are obtained using the simulated strain responses with theFE modeling methodThe strain data is simulated in 16 casesas shown in Table 1 and the calculation results of DLFs from

truss 3 are shown in Figure 7 Moreover Table 2 shows themonitoring and simulatedAVs of theDLFs and it can be seenthat themonitoring AVs of the DLF are close to the simulatedAVs of the DLFs verifying the effectiveness of the finiteelement modeling method For all 16 cases the maximumDLF of each key member is further obtained Thus Figure 8shows the maximum DLFs for key members of the truss 1truss 2 and truss 3 It can be seen that for each truss themaximum DLFs of the bottom chord member the diagonalweb member the deck chord member and the top chordmember decrease successively which is consistent with themonitoring results Furthermore the maximum DLFs fromtruss 1 and truss 3 is a little higher than those from truss2 Thus for three planes of truss arch the dynamic effectsinduced by high-speed trains for middle truss arch are lessthan those for side truss arch

Shock and Vibration 7

200 400 600 800 10000Segments

0995

1

1005

101

1015

102

DLF

= 10106

= 10069

MV

AV

(a) The top chord member

200 400 600 800 10000Segments

09

1

11

12

13

DLF

= 11318

= 10802

MV

AV

(b) The diagonal web member

200 400 600 800 10000Segments

095

101

107

113

119

125

DLF

MV = 11411

AV = 10862

(c) The bottom chord member

200 400 600 800 10000Segments

095

098

101

104

107

11

DLF

= 10451

= 10197

MV

AV

(d) The deck chord member

Figure 6 Field monitoring results of DLFs

Table 1 16 cases for simulating the strain data

Number of cases Carriage load (kN) Load location Number of carriages Train speed (kmh)1 535 Lane 1 8 2402 535 Lane 2 8 2403 535 Lane 3 8 2404 535 Lane 4 8 2405 535 Lane 1 8 1606 535 Lane 2 8 1607 535 Lane 3 8 1608 535 Lane 4 8 1609 535 Lane 1 16 24010 535 Lane 2 16 24011 535 Lane 3 16 24012 535 Lane 4 16 24013 535 Lane 1 16 16014 535 Lane 2 16 16015 535 Lane 3 16 16016 535 Lane 4 16 160

8 Shock and Vibration

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1004

1006

1008

101D

LF

(a) The top chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

105

107

109

111

DLF

(b) The diagonal web member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

103

105

107

109

111

113

DLF

(c) The bottom chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1

101

102

103

104

105

DLF

(d) The deck chord member

Figure 7 Dynamic load factors for truss 3 using simulated strain responses

Table 2 Monitoring and simulated AVs of the DLFs

DLFs The top chord member The diagonal web member The bottom chord member The deck chord memberMonitoring AV 10069 10802 10862 10197Simulated AV 10068 10768 10781 10215Error () 001 031 075 018

4 Factors Affecting the Dynamic Load Factors

As mentioned in the preceding sections many factors affectthe magnitude of the DLF The influence of lane position oftrains number of train carriages and speed of trains wasstudied and is presented in the following sections

41 Lane Position There are 4 train lanes in the girder ofDaShengGuan Bridge as shown in Figure 2(a) Firstly themeasured DLFs of 1000 trains in Figure 6 are classifiedas 4 groups corresponding to 4 train lanes respectivelyThe total number of the DLFs for each train lane is 250Then for each group the 250 DLFs are divided into 50segments and the mean value of each segment is computedas shown in Figure 9 Furthermore the mean values of thesimulated DLFs in Figure 7 are computed for each train lanerespectively which are also shown in Figure 9 119871 s119894 denotes

the average value of the 119894th train lane 119894 = 1 2 3 4 It can beseen that the influence of lane 1 lane 2 lane 3 and lane 4 onthe DLFs decreases successively for the top chord memberthe diagonal webmember and the bottom chordmember butincreases successively for the deck chord member Thereforewith the train closer to the steel truss arch the dynamic effectis more significant for the deck chord member

42 Number of Train Carriages In China the high-speedelectric multiple unit (EMU) train has 8 carriages or 16carriages respectively In this study an investigation has beencarried out to determine if there is a correlation betweenthe DLF and the number of train carriages Firstly themeasured DLFs of 1000 trains in Figure 6 are classified astwo groups corresponding to the 8 carriages and 16 carriagesrespectively The total number of the DLFs for both 8 and16 carriages is 500 Then for each group the 500 DLFs are

Shock and Vibration 9

Truss 3Truss 2Truss 1

1

105

11

115

DLF

Truss 2 Truss 3Truss 1Location

Deck chordDiagonal chord

Bottom chordTop chord

Figure 8 Maximum dynamic load factors for truss 1 truss 2 andtruss 3

divided into 50 segments and themean value of each segmentis computed as shown in Figure 10 Furthermore the meanvalues 119862s8 and 119862s16 of the simulated DLFs in Figure 7 arecomputed for 8 and 16 carriages respectively which are alsoshown in Figure 10The figures show an increase in the meanDLF for the 8 carriages comparing with the 16 carriagesHowever it can also be noticed that the absolute value of theincrease is very small

43 Speed of Trains According to the field monitoringresults the speed of trains ranges approximately from110 kmh to 250 kmh The results of the DLF (DLF) causedby the speed of trains are plotted in Figure 11 Meanwhile thesimulated DLFs under the speeds of 160 kmh and 240 kmhare shown in Figure 11 which can verify the influenceof train speed on the monitoring DLFs It can be seenthat the speed and DLF are weakly correlated Accordingto the fitting curves shown in Figure 11 even though thecorrelation between speed and DLF is not strong there existsan increasing linear relationship (ie as the speed of trainsincreases the DLF will also increase)

5 Statistical Analysis of theDynamic Load Factors

51 Probability Distribution Model In this study a largeamount of data on DLFs was acquired through field mon-itoring Therefore it is important to introduce a statisticalanalysis to obtain the appropriate design value of DLF Firstlythe accumulative probability function forDLFs is establishedThree types of accumulative probability function are selectedthe normal distribution the Weibull distribution and theGeneralized ExtremeValueDistribution (GEVD) Taking theDLFs in Figure 6(a) for example the accumulative proba-bility and fitting curves using three probability distributionfunctions are shown in Figure 12(a) Their fitting errors areobtained by calculating the variances of residuals between the

monitoring curve and the fitting curve which are 00001120000189 and 0000105 respectively Thus the GEVD is thebest fitting curve which is defined by

119866 (119863) = exp[minus [1 + 119903 (

119863 minus 119887

119886

)]

minus1119903

] (8)

where 119863 denotes the DLFs 119903 119886 and 119887 denote shapeparameter scale parameter and location parameter ofGEVDrespectively which can be estimated by maximum likelihoodmethod In detail Generalized Extreme Value Distribution119866(119863) combines three types of distributions (ie Gumbeldistribution Frechet distribution and Weibull distribution)into a single form The parameters of GEVD in Figure 12(a)are 119903 = minus01279 119886 = 00009 and 119887 = 10066 MoreoverFigures 12(b)ndash12(d) show the fitting curves of GEVD for thediagonal web member the bottom chord member and thedeck chord member It can be seen that the GEVD can welldescribe the probability characteristics of the DLFs

52 Evaluation of Dynamic Load Factors

521 Standard Value of Dynamic Load Factors Eurocode1 [12] specifies that the standard value is the extreme val-ues within 50-year return period The monitoring dynamicstrains are affected by the irregularity of the rail so the calcu-lated DLF of the monitoring dynamic strains has containedthe influence of the irregularity of the rail The irregularityof the rail may be worse later and furthermore influences thecurrent statistics characteristics of the DLFs but whether theirregularity of the rail is really worse or not is hard to decideSo this paper studied the case when the irregularity of therail does not get worse In this case the standard value of themonitored data obtained within a short period of time can beused as the extreme value of the DLF within 50-year returnperiod Specifically the standard value can be calculated by

119875 = 1 minus 119866 (119863p) (9a)

119875 =

1

50119873

(9b)

where119863p denotes the standard value119875denotes the exceedingprobability119873 denotes the number of DLFs in one year OneLDF can be calculated after one train passes the bridge so119873is equal to the total amount of trains passing the bridge in oneyear On consideration that 119863p cannot be directly calculatedby (9a) and (9b) then119863p is numerically calculated byNewtoniteration formula as follows

119863119899+1

p = 119863119899

p +1 minus 119866 (119863

119899

p) minus 119875

1198661015840(119863119899

p) (10)

where 119863119899p is the 119899th iteration of 1198630p and 1198661015840(119863119899

p) is the one-order derivative function of119866(119863119899p) Iteration terminateswhenthe absolute difference between 119863

119899+1

p and 119863119899

p is less than00005 Based on the method above the stand values of DLFsare shown in Table 3 It can be seen that the bottom chord has

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

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Shock and Vibration

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International Journal of

Shock and Vibration 3

1500015000

1200

068

007

2

Y1d

Y1u

Y2dY2u

Y3d

Y3u

Y4d Y4u

2

Downstream Upstream

Vertical bracing

Horizontal bracing

Diaphragm memberTop plate

Truss 1 Truss 2 Truss 3

Lane 1 Lane 2 Lane 3 Lane 4

(a) 1-1 cross section of steel truss arch

Shanghai Beijing3

3

4

4

5

5

6

6

Y1dY1u

Y2dY2u

Y3dY3u

Y4dY4u

Top chord member

Diagonal webmember

Vertical web member

Deck chord member

Bottom chord member

(b) 2-2 section of steel truss arch

1000

1000

150

150

850

850

1400Y1d Y1u

(c) 3-3 section of top chord member

Y2dY2u61

0

610

150

150

1398

(d) 4-4 section of diagonal web member

Y3d

Y3u

650

650 80

0

150

150

1400

(e) 5-5 section of bottom chord member

Y4d Y4u

1416

1266

1266

150

150

1400

(f) 6-6 section of deck chord member

Figure 2 Location of strain sensors on the steel truss arch bridge (unit mm)

4 Shock and Vibration

XY

Z

Figure 3 Three-dimensional FE model of Nanjing DaShengGuanBridge

in directions of longitudinal 119883 transverse 119884 and vertical119885 the other bearings are constrained with two degreesof translational freedom in directions of transverse 119884 andvertical 119885 The elastic modulus and poison ratio of the steelare selected as 210GPa and 030 The acceleration of gravityis set to 98ms2 The damping ratio is set to 002

The parameters of the train loads are determined fromthe prototype (CRH3) of trains on the Beijing-Shanghai high-speed railway line The train prototype is an electric multipleunit (EMU) including 8 or 16 carriages The weight of anempty EMU is 380 t and an EMU has a seating capacity of601 people Assuming that the average weight per person is80 kg which is defined from Chinarsquos Ministry of Railways in2001 each carriagersquos weight is 119866 = 53510 kg and the verticalexcitation force generated by awheel is119865 = (1198668)times98Nkg =6554975N Because of the large length of a single carriage(24m) the load model of the carriage is divided into 8 pointloads and the loads of an EMU with 8 or 16 carriages aregrouped as 8times8times119865 or 8times16times119865 Moreover it is supposed thatthe train wheels are always closely touching the surface of thebridge without deviation so the wheels and the surface of thebridge are coupled by the compatibility of displacements andequilibrium of forces at the contact points

23 Results of Dynamic Strain Responses As for dynamicstrain monitoring each chord member or diagonal webmember has two strain sensors on the downstream side andupstream side respectively The average values of two strainsensors are calculated to represent the axial dynamic strain ofthe corresponding member in the truss arch

119860119894=

119878119894d + 119878

119894u

2

(1)

where 119878119894d and 119878

119894u denote the strain data from the 119894thstrain sensors 119884

119894d and 119884119894u respectively 119860 119894 denotes the axial

dynamic strain of the corresponding member Figure 4 showthe typical time histories of dynamic strain data 119860

1sim1198604

when one train passed through the bridge from 92847 pmto 92959 pm on August 7th 2013 Corresponding to thisloading case the simulated dynamic strain responses areobtained using FE model method Its train load for eachcarriage is 535 kN its loading position is lane 2 the number ofits carriages is 8 Figure 4 also shows the results of simulatedstrain responses 119860 s1sim119860 s4 corresponding to 119860 s1sim119860 s4 Itcan be seen that the amplitudes of monitoring strain and

simulated strain are close verifying the effectiveness of theFE modeling method It should be mentioned that althoughpartial trends of monitoring strain and simulated strain arenot consistent such inconsistency will not influence thecalculation results of DLF because the DLF is decided by theamplitude of strain rather than the trend of strain

3 Dynamic Load Factors of the Bridge

31 Definition of the Dynamic Load Factor Bakht and Pin-jarkar [11] suggested the following equation for calculation ofthe dynamic load factor

DLF = 1 + DLA (2)

where DLF denotes the dynamic load factor and DLAdenotes the dynamic load allowance given by

DLA =

119877dyn minus 119877stat

119877stat (3)

where 119877dyn denotes the maximum dynamic strain responseand 119877stat denotes the maximum static strain response

32 Dynamic Load Factors from the Dynamic StrainResponses As for the monitoring strain data the dynamicstrain data can be directly collected by strain sensors (namely119860119894) and the static strain data can be acquired by filtering

the dynamic strain data with a low-pass filter to eliminatethe dynamic components of strain data As for the simulatedstrain data the dynamic and static strain data can be directlyobtained using FE model method Then 119877dyn is calculated by

119877dyn = max (abs (119872)) (4)

where 119872 denotes the monitoring dynamic strain data 119860119894or

the simulated dynamic strain data 119860 s119894 abs(119872) denotes theabsolute value of119872 andmax(abs(119872)) denotes themaximumvalue of abs(119872) And 119877stat is calculated by

119877stat = max (abs (119876)) (5)

where 119876 denotes the monitoring static strain data or thesimulated static strain data abs(119876) denotes the absolute valueof119876 andmax(abs(119876))denotes themaximumvalue of abs(119876)

Therefore the DLF ofmonitoring strain data is calculatedby four steps (i) calculate the maximum amplitude 119877dyn ofmonitoring dynamic strain by using (4) (ii) acquire the staticstrain by using the low-pass filter (iii) calculate themaximumamplitude 119877stat of static strain data by using (5) (iv) calculatethe DLF by using (2) and (3) The DLF of simulated straindata is calculated by three steps (i) calculate the maximumamplitude 119877dyn of simulated dynamic strain by using (4) (ii)calculate the maximum amplitude 119877stat of simulated staticstrain by using (5) (iii) calculate the DLF by using (2) and(3)

It should be noted that an appropriate low-pass filter isimportant to obtain the authentic static strain data In thisstudy the FIR (Finite Impulse Response) filter is used [11]

Shock and Vibration 5

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(a) 1198601 and 119860s1 of top chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(b) 1198602 and 119860s2 of diagonal web member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(c) 1198603 and 119860s3 of bottom chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(d) 1198604 and 119860s4 of deck chord member

Figure 4 Typical dynamic strain responses of field monitoring and FE modeling results

The transfer function of a polynomial of 119899-order FIR filter isdefined by

119867(119911) =

119899

sum

119894=0

119887119894119911minus119894 (6)

and its frequency response is

119867(120596) =

119899

sum

119894=0

119887119894119890minus119895120596119894

= 119887T120593 (120596) (7)

where 119887 = [1198870 1198871 1198872 119887

119899]T is the coefficient vector having

the filter coefficients 120601(120596) = [1 119890minus119895120596

119890minus119895120596119899

]T and T

denotes the transpose of matrix The coefficients of FIR filterare usually symmetric hence they have a spectrum thatexhibits a linear phase and the response to an impulse settlesto zero

Specifically the low-pass FIR filter is decided by fourinput parameters the normalized passband edge frequency120596p the normalized stopband edge frequency 120596s the allowedpassband deviation 120575p and the stopband deviation 120575s [11]Generally the optimal values of four input parameters areobtained by trial-and-error approach [10] In this study theoptimal values of four input parameters are 120596p = 0004 120587Hz120596s = 006 120587Hz 120575p = 1 and 120575s = 60 after trial-and-errorapproach The static strain data are acquired by using thisfilter which show good filtering effect in Figure 5

33 Field Monitoring Results of Dynamic Load Factors Inthis study the dynamic strain responses of the bridge wererecorded for each case having a single train traversing on thebridge 1000 cases (a single train at a time) were selected andthe computed DLFs of 1000 cases are shown in Figure 6 Itis clear from the figures that the DLF is not a deterministic

6 Shock and Vibration

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(a) 1198601 of top chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(b) 1198602 of diagonal web member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(c) 1198603 of bottom chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(d) 1198604 of deck chord member

Figure 5 The dynamic and static strain responses of 1198601sim1198604

quantityThus themeanDLF andmaximumDLF denoted byAV andMVare further computed and also shown in Figure 6The mean DLF and maximum DLF computed from thebottom chord member are the largest of all which are 10862and 11411 respectively And the mean DLF and maximumDLF computed from the top chord member are the smallestof all which are only 10069 and 10106 respectively

34 Dynamic Analysis Results of Dynamic Load FactorsFigure 6 shows the field monitoring results of DLFs for keymembers of the steel truss arch However only DLFs of thetruss 3 as shown in Figure 2(a) have been measured In thissection DLFs for all trusses that is truss 1 truss 2 and truss3 are obtained using the simulated strain responses with theFE modeling methodThe strain data is simulated in 16 casesas shown in Table 1 and the calculation results of DLFs from

truss 3 are shown in Figure 7 Moreover Table 2 shows themonitoring and simulatedAVs of theDLFs and it can be seenthat themonitoring AVs of the DLF are close to the simulatedAVs of the DLFs verifying the effectiveness of the finiteelement modeling method For all 16 cases the maximumDLF of each key member is further obtained Thus Figure 8shows the maximum DLFs for key members of the truss 1truss 2 and truss 3 It can be seen that for each truss themaximum DLFs of the bottom chord member the diagonalweb member the deck chord member and the top chordmember decrease successively which is consistent with themonitoring results Furthermore the maximum DLFs fromtruss 1 and truss 3 is a little higher than those from truss2 Thus for three planes of truss arch the dynamic effectsinduced by high-speed trains for middle truss arch are lessthan those for side truss arch

Shock and Vibration 7

200 400 600 800 10000Segments

0995

1

1005

101

1015

102

DLF

= 10106

= 10069

MV

AV

(a) The top chord member

200 400 600 800 10000Segments

09

1

11

12

13

DLF

= 11318

= 10802

MV

AV

(b) The diagonal web member

200 400 600 800 10000Segments

095

101

107

113

119

125

DLF

MV = 11411

AV = 10862

(c) The bottom chord member

200 400 600 800 10000Segments

095

098

101

104

107

11

DLF

= 10451

= 10197

MV

AV

(d) The deck chord member

Figure 6 Field monitoring results of DLFs

Table 1 16 cases for simulating the strain data

Number of cases Carriage load (kN) Load location Number of carriages Train speed (kmh)1 535 Lane 1 8 2402 535 Lane 2 8 2403 535 Lane 3 8 2404 535 Lane 4 8 2405 535 Lane 1 8 1606 535 Lane 2 8 1607 535 Lane 3 8 1608 535 Lane 4 8 1609 535 Lane 1 16 24010 535 Lane 2 16 24011 535 Lane 3 16 24012 535 Lane 4 16 24013 535 Lane 1 16 16014 535 Lane 2 16 16015 535 Lane 3 16 16016 535 Lane 4 16 160

8 Shock and Vibration

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1004

1006

1008

101D

LF

(a) The top chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

105

107

109

111

DLF

(b) The diagonal web member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

103

105

107

109

111

113

DLF

(c) The bottom chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1

101

102

103

104

105

DLF

(d) The deck chord member

Figure 7 Dynamic load factors for truss 3 using simulated strain responses

Table 2 Monitoring and simulated AVs of the DLFs

DLFs The top chord member The diagonal web member The bottom chord member The deck chord memberMonitoring AV 10069 10802 10862 10197Simulated AV 10068 10768 10781 10215Error () 001 031 075 018

4 Factors Affecting the Dynamic Load Factors

As mentioned in the preceding sections many factors affectthe magnitude of the DLF The influence of lane position oftrains number of train carriages and speed of trains wasstudied and is presented in the following sections

41 Lane Position There are 4 train lanes in the girder ofDaShengGuan Bridge as shown in Figure 2(a) Firstly themeasured DLFs of 1000 trains in Figure 6 are classifiedas 4 groups corresponding to 4 train lanes respectivelyThe total number of the DLFs for each train lane is 250Then for each group the 250 DLFs are divided into 50segments and the mean value of each segment is computedas shown in Figure 9 Furthermore the mean values of thesimulated DLFs in Figure 7 are computed for each train lanerespectively which are also shown in Figure 9 119871 s119894 denotes

the average value of the 119894th train lane 119894 = 1 2 3 4 It can beseen that the influence of lane 1 lane 2 lane 3 and lane 4 onthe DLFs decreases successively for the top chord memberthe diagonal webmember and the bottom chordmember butincreases successively for the deck chord member Thereforewith the train closer to the steel truss arch the dynamic effectis more significant for the deck chord member

42 Number of Train Carriages In China the high-speedelectric multiple unit (EMU) train has 8 carriages or 16carriages respectively In this study an investigation has beencarried out to determine if there is a correlation betweenthe DLF and the number of train carriages Firstly themeasured DLFs of 1000 trains in Figure 6 are classified astwo groups corresponding to the 8 carriages and 16 carriagesrespectively The total number of the DLFs for both 8 and16 carriages is 500 Then for each group the 500 DLFs are

Shock and Vibration 9

Truss 3Truss 2Truss 1

1

105

11

115

DLF

Truss 2 Truss 3Truss 1Location

Deck chordDiagonal chord

Bottom chordTop chord

Figure 8 Maximum dynamic load factors for truss 1 truss 2 andtruss 3

divided into 50 segments and themean value of each segmentis computed as shown in Figure 10 Furthermore the meanvalues 119862s8 and 119862s16 of the simulated DLFs in Figure 7 arecomputed for 8 and 16 carriages respectively which are alsoshown in Figure 10The figures show an increase in the meanDLF for the 8 carriages comparing with the 16 carriagesHowever it can also be noticed that the absolute value of theincrease is very small

43 Speed of Trains According to the field monitoringresults the speed of trains ranges approximately from110 kmh to 250 kmh The results of the DLF (DLF) causedby the speed of trains are plotted in Figure 11 Meanwhile thesimulated DLFs under the speeds of 160 kmh and 240 kmhare shown in Figure 11 which can verify the influenceof train speed on the monitoring DLFs It can be seenthat the speed and DLF are weakly correlated Accordingto the fitting curves shown in Figure 11 even though thecorrelation between speed and DLF is not strong there existsan increasing linear relationship (ie as the speed of trainsincreases the DLF will also increase)

5 Statistical Analysis of theDynamic Load Factors

51 Probability Distribution Model In this study a largeamount of data on DLFs was acquired through field mon-itoring Therefore it is important to introduce a statisticalanalysis to obtain the appropriate design value of DLF Firstlythe accumulative probability function forDLFs is establishedThree types of accumulative probability function are selectedthe normal distribution the Weibull distribution and theGeneralized ExtremeValueDistribution (GEVD) Taking theDLFs in Figure 6(a) for example the accumulative proba-bility and fitting curves using three probability distributionfunctions are shown in Figure 12(a) Their fitting errors areobtained by calculating the variances of residuals between the

monitoring curve and the fitting curve which are 00001120000189 and 0000105 respectively Thus the GEVD is thebest fitting curve which is defined by

119866 (119863) = exp[minus [1 + 119903 (

119863 minus 119887

119886

)]

minus1119903

] (8)

where 119863 denotes the DLFs 119903 119886 and 119887 denote shapeparameter scale parameter and location parameter ofGEVDrespectively which can be estimated by maximum likelihoodmethod In detail Generalized Extreme Value Distribution119866(119863) combines three types of distributions (ie Gumbeldistribution Frechet distribution and Weibull distribution)into a single form The parameters of GEVD in Figure 12(a)are 119903 = minus01279 119886 = 00009 and 119887 = 10066 MoreoverFigures 12(b)ndash12(d) show the fitting curves of GEVD for thediagonal web member the bottom chord member and thedeck chord member It can be seen that the GEVD can welldescribe the probability characteristics of the DLFs

52 Evaluation of Dynamic Load Factors

521 Standard Value of Dynamic Load Factors Eurocode1 [12] specifies that the standard value is the extreme val-ues within 50-year return period The monitoring dynamicstrains are affected by the irregularity of the rail so the calcu-lated DLF of the monitoring dynamic strains has containedthe influence of the irregularity of the rail The irregularityof the rail may be worse later and furthermore influences thecurrent statistics characteristics of the DLFs but whether theirregularity of the rail is really worse or not is hard to decideSo this paper studied the case when the irregularity of therail does not get worse In this case the standard value of themonitored data obtained within a short period of time can beused as the extreme value of the DLF within 50-year returnperiod Specifically the standard value can be calculated by

119875 = 1 minus 119866 (119863p) (9a)

119875 =

1

50119873

(9b)

where119863p denotes the standard value119875denotes the exceedingprobability119873 denotes the number of DLFs in one year OneLDF can be calculated after one train passes the bridge so119873is equal to the total amount of trains passing the bridge in oneyear On consideration that 119863p cannot be directly calculatedby (9a) and (9b) then119863p is numerically calculated byNewtoniteration formula as follows

119863119899+1

p = 119863119899

p +1 minus 119866 (119863

119899

p) minus 119875

1198661015840(119863119899

p) (10)

where 119863119899p is the 119899th iteration of 1198630p and 1198661015840(119863119899

p) is the one-order derivative function of119866(119863119899p) Iteration terminateswhenthe absolute difference between 119863

119899+1

p and 119863119899

p is less than00005 Based on the method above the stand values of DLFsare shown in Table 3 It can be seen that the bottom chord has

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

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4 Shock and Vibration

XY

Z

Figure 3 Three-dimensional FE model of Nanjing DaShengGuanBridge

in directions of longitudinal 119883 transverse 119884 and vertical119885 the other bearings are constrained with two degreesof translational freedom in directions of transverse 119884 andvertical 119885 The elastic modulus and poison ratio of the steelare selected as 210GPa and 030 The acceleration of gravityis set to 98ms2 The damping ratio is set to 002

The parameters of the train loads are determined fromthe prototype (CRH3) of trains on the Beijing-Shanghai high-speed railway line The train prototype is an electric multipleunit (EMU) including 8 or 16 carriages The weight of anempty EMU is 380 t and an EMU has a seating capacity of601 people Assuming that the average weight per person is80 kg which is defined from Chinarsquos Ministry of Railways in2001 each carriagersquos weight is 119866 = 53510 kg and the verticalexcitation force generated by awheel is119865 = (1198668)times98Nkg =6554975N Because of the large length of a single carriage(24m) the load model of the carriage is divided into 8 pointloads and the loads of an EMU with 8 or 16 carriages aregrouped as 8times8times119865 or 8times16times119865 Moreover it is supposed thatthe train wheels are always closely touching the surface of thebridge without deviation so the wheels and the surface of thebridge are coupled by the compatibility of displacements andequilibrium of forces at the contact points

23 Results of Dynamic Strain Responses As for dynamicstrain monitoring each chord member or diagonal webmember has two strain sensors on the downstream side andupstream side respectively The average values of two strainsensors are calculated to represent the axial dynamic strain ofthe corresponding member in the truss arch

119860119894=

119878119894d + 119878

119894u

2

(1)

where 119878119894d and 119878

119894u denote the strain data from the 119894thstrain sensors 119884

119894d and 119884119894u respectively 119860 119894 denotes the axial

dynamic strain of the corresponding member Figure 4 showthe typical time histories of dynamic strain data 119860

1sim1198604

when one train passed through the bridge from 92847 pmto 92959 pm on August 7th 2013 Corresponding to thisloading case the simulated dynamic strain responses areobtained using FE model method Its train load for eachcarriage is 535 kN its loading position is lane 2 the number ofits carriages is 8 Figure 4 also shows the results of simulatedstrain responses 119860 s1sim119860 s4 corresponding to 119860 s1sim119860 s4 Itcan be seen that the amplitudes of monitoring strain and

simulated strain are close verifying the effectiveness of theFE modeling method It should be mentioned that althoughpartial trends of monitoring strain and simulated strain arenot consistent such inconsistency will not influence thecalculation results of DLF because the DLF is decided by theamplitude of strain rather than the trend of strain

3 Dynamic Load Factors of the Bridge

31 Definition of the Dynamic Load Factor Bakht and Pin-jarkar [11] suggested the following equation for calculation ofthe dynamic load factor

DLF = 1 + DLA (2)

where DLF denotes the dynamic load factor and DLAdenotes the dynamic load allowance given by

DLA =

119877dyn minus 119877stat

119877stat (3)

where 119877dyn denotes the maximum dynamic strain responseand 119877stat denotes the maximum static strain response

32 Dynamic Load Factors from the Dynamic StrainResponses As for the monitoring strain data the dynamicstrain data can be directly collected by strain sensors (namely119860119894) and the static strain data can be acquired by filtering

the dynamic strain data with a low-pass filter to eliminatethe dynamic components of strain data As for the simulatedstrain data the dynamic and static strain data can be directlyobtained using FE model method Then 119877dyn is calculated by

119877dyn = max (abs (119872)) (4)

where 119872 denotes the monitoring dynamic strain data 119860119894or

the simulated dynamic strain data 119860 s119894 abs(119872) denotes theabsolute value of119872 andmax(abs(119872)) denotes themaximumvalue of abs(119872) And 119877stat is calculated by

119877stat = max (abs (119876)) (5)

where 119876 denotes the monitoring static strain data or thesimulated static strain data abs(119876) denotes the absolute valueof119876 andmax(abs(119876))denotes themaximumvalue of abs(119876)

Therefore the DLF ofmonitoring strain data is calculatedby four steps (i) calculate the maximum amplitude 119877dyn ofmonitoring dynamic strain by using (4) (ii) acquire the staticstrain by using the low-pass filter (iii) calculate themaximumamplitude 119877stat of static strain data by using (5) (iv) calculatethe DLF by using (2) and (3) The DLF of simulated straindata is calculated by three steps (i) calculate the maximumamplitude 119877dyn of simulated dynamic strain by using (4) (ii)calculate the maximum amplitude 119877stat of simulated staticstrain by using (5) (iii) calculate the DLF by using (2) and(3)

It should be noted that an appropriate low-pass filter isimportant to obtain the authentic static strain data In thisstudy the FIR (Finite Impulse Response) filter is used [11]

Shock and Vibration 5

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(a) 1198601 and 119860s1 of top chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(b) 1198602 and 119860s2 of diagonal web member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(c) 1198603 and 119860s3 of bottom chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(d) 1198604 and 119860s4 of deck chord member

Figure 4 Typical dynamic strain responses of field monitoring and FE modeling results

The transfer function of a polynomial of 119899-order FIR filter isdefined by

119867(119911) =

119899

sum

119894=0

119887119894119911minus119894 (6)

and its frequency response is

119867(120596) =

119899

sum

119894=0

119887119894119890minus119895120596119894

= 119887T120593 (120596) (7)

where 119887 = [1198870 1198871 1198872 119887

119899]T is the coefficient vector having

the filter coefficients 120601(120596) = [1 119890minus119895120596

119890minus119895120596119899

]T and T

denotes the transpose of matrix The coefficients of FIR filterare usually symmetric hence they have a spectrum thatexhibits a linear phase and the response to an impulse settlesto zero

Specifically the low-pass FIR filter is decided by fourinput parameters the normalized passband edge frequency120596p the normalized stopband edge frequency 120596s the allowedpassband deviation 120575p and the stopband deviation 120575s [11]Generally the optimal values of four input parameters areobtained by trial-and-error approach [10] In this study theoptimal values of four input parameters are 120596p = 0004 120587Hz120596s = 006 120587Hz 120575p = 1 and 120575s = 60 after trial-and-errorapproach The static strain data are acquired by using thisfilter which show good filtering effect in Figure 5

33 Field Monitoring Results of Dynamic Load Factors Inthis study the dynamic strain responses of the bridge wererecorded for each case having a single train traversing on thebridge 1000 cases (a single train at a time) were selected andthe computed DLFs of 1000 cases are shown in Figure 6 Itis clear from the figures that the DLF is not a deterministic

6 Shock and Vibration

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(a) 1198601 of top chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(b) 1198602 of diagonal web member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(c) 1198603 of bottom chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(d) 1198604 of deck chord member

Figure 5 The dynamic and static strain responses of 1198601sim1198604

quantityThus themeanDLF andmaximumDLF denoted byAV andMVare further computed and also shown in Figure 6The mean DLF and maximum DLF computed from thebottom chord member are the largest of all which are 10862and 11411 respectively And the mean DLF and maximumDLF computed from the top chord member are the smallestof all which are only 10069 and 10106 respectively

34 Dynamic Analysis Results of Dynamic Load FactorsFigure 6 shows the field monitoring results of DLFs for keymembers of the steel truss arch However only DLFs of thetruss 3 as shown in Figure 2(a) have been measured In thissection DLFs for all trusses that is truss 1 truss 2 and truss3 are obtained using the simulated strain responses with theFE modeling methodThe strain data is simulated in 16 casesas shown in Table 1 and the calculation results of DLFs from

truss 3 are shown in Figure 7 Moreover Table 2 shows themonitoring and simulatedAVs of theDLFs and it can be seenthat themonitoring AVs of the DLF are close to the simulatedAVs of the DLFs verifying the effectiveness of the finiteelement modeling method For all 16 cases the maximumDLF of each key member is further obtained Thus Figure 8shows the maximum DLFs for key members of the truss 1truss 2 and truss 3 It can be seen that for each truss themaximum DLFs of the bottom chord member the diagonalweb member the deck chord member and the top chordmember decrease successively which is consistent with themonitoring results Furthermore the maximum DLFs fromtruss 1 and truss 3 is a little higher than those from truss2 Thus for three planes of truss arch the dynamic effectsinduced by high-speed trains for middle truss arch are lessthan those for side truss arch

Shock and Vibration 7

200 400 600 800 10000Segments

0995

1

1005

101

1015

102

DLF

= 10106

= 10069

MV

AV

(a) The top chord member

200 400 600 800 10000Segments

09

1

11

12

13

DLF

= 11318

= 10802

MV

AV

(b) The diagonal web member

200 400 600 800 10000Segments

095

101

107

113

119

125

DLF

MV = 11411

AV = 10862

(c) The bottom chord member

200 400 600 800 10000Segments

095

098

101

104

107

11

DLF

= 10451

= 10197

MV

AV

(d) The deck chord member

Figure 6 Field monitoring results of DLFs

Table 1 16 cases for simulating the strain data

Number of cases Carriage load (kN) Load location Number of carriages Train speed (kmh)1 535 Lane 1 8 2402 535 Lane 2 8 2403 535 Lane 3 8 2404 535 Lane 4 8 2405 535 Lane 1 8 1606 535 Lane 2 8 1607 535 Lane 3 8 1608 535 Lane 4 8 1609 535 Lane 1 16 24010 535 Lane 2 16 24011 535 Lane 3 16 24012 535 Lane 4 16 24013 535 Lane 1 16 16014 535 Lane 2 16 16015 535 Lane 3 16 16016 535 Lane 4 16 160

8 Shock and Vibration

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1004

1006

1008

101D

LF

(a) The top chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

105

107

109

111

DLF

(b) The diagonal web member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

103

105

107

109

111

113

DLF

(c) The bottom chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1

101

102

103

104

105

DLF

(d) The deck chord member

Figure 7 Dynamic load factors for truss 3 using simulated strain responses

Table 2 Monitoring and simulated AVs of the DLFs

DLFs The top chord member The diagonal web member The bottom chord member The deck chord memberMonitoring AV 10069 10802 10862 10197Simulated AV 10068 10768 10781 10215Error () 001 031 075 018

4 Factors Affecting the Dynamic Load Factors

As mentioned in the preceding sections many factors affectthe magnitude of the DLF The influence of lane position oftrains number of train carriages and speed of trains wasstudied and is presented in the following sections

41 Lane Position There are 4 train lanes in the girder ofDaShengGuan Bridge as shown in Figure 2(a) Firstly themeasured DLFs of 1000 trains in Figure 6 are classifiedas 4 groups corresponding to 4 train lanes respectivelyThe total number of the DLFs for each train lane is 250Then for each group the 250 DLFs are divided into 50segments and the mean value of each segment is computedas shown in Figure 9 Furthermore the mean values of thesimulated DLFs in Figure 7 are computed for each train lanerespectively which are also shown in Figure 9 119871 s119894 denotes

the average value of the 119894th train lane 119894 = 1 2 3 4 It can beseen that the influence of lane 1 lane 2 lane 3 and lane 4 onthe DLFs decreases successively for the top chord memberthe diagonal webmember and the bottom chordmember butincreases successively for the deck chord member Thereforewith the train closer to the steel truss arch the dynamic effectis more significant for the deck chord member

42 Number of Train Carriages In China the high-speedelectric multiple unit (EMU) train has 8 carriages or 16carriages respectively In this study an investigation has beencarried out to determine if there is a correlation betweenthe DLF and the number of train carriages Firstly themeasured DLFs of 1000 trains in Figure 6 are classified astwo groups corresponding to the 8 carriages and 16 carriagesrespectively The total number of the DLFs for both 8 and16 carriages is 500 Then for each group the 500 DLFs are

Shock and Vibration 9

Truss 3Truss 2Truss 1

1

105

11

115

DLF

Truss 2 Truss 3Truss 1Location

Deck chordDiagonal chord

Bottom chordTop chord

Figure 8 Maximum dynamic load factors for truss 1 truss 2 andtruss 3

divided into 50 segments and themean value of each segmentis computed as shown in Figure 10 Furthermore the meanvalues 119862s8 and 119862s16 of the simulated DLFs in Figure 7 arecomputed for 8 and 16 carriages respectively which are alsoshown in Figure 10The figures show an increase in the meanDLF for the 8 carriages comparing with the 16 carriagesHowever it can also be noticed that the absolute value of theincrease is very small

43 Speed of Trains According to the field monitoringresults the speed of trains ranges approximately from110 kmh to 250 kmh The results of the DLF (DLF) causedby the speed of trains are plotted in Figure 11 Meanwhile thesimulated DLFs under the speeds of 160 kmh and 240 kmhare shown in Figure 11 which can verify the influenceof train speed on the monitoring DLFs It can be seenthat the speed and DLF are weakly correlated Accordingto the fitting curves shown in Figure 11 even though thecorrelation between speed and DLF is not strong there existsan increasing linear relationship (ie as the speed of trainsincreases the DLF will also increase)

5 Statistical Analysis of theDynamic Load Factors

51 Probability Distribution Model In this study a largeamount of data on DLFs was acquired through field mon-itoring Therefore it is important to introduce a statisticalanalysis to obtain the appropriate design value of DLF Firstlythe accumulative probability function forDLFs is establishedThree types of accumulative probability function are selectedthe normal distribution the Weibull distribution and theGeneralized ExtremeValueDistribution (GEVD) Taking theDLFs in Figure 6(a) for example the accumulative proba-bility and fitting curves using three probability distributionfunctions are shown in Figure 12(a) Their fitting errors areobtained by calculating the variances of residuals between the

monitoring curve and the fitting curve which are 00001120000189 and 0000105 respectively Thus the GEVD is thebest fitting curve which is defined by

119866 (119863) = exp[minus [1 + 119903 (

119863 minus 119887

119886

)]

minus1119903

] (8)

where 119863 denotes the DLFs 119903 119886 and 119887 denote shapeparameter scale parameter and location parameter ofGEVDrespectively which can be estimated by maximum likelihoodmethod In detail Generalized Extreme Value Distribution119866(119863) combines three types of distributions (ie Gumbeldistribution Frechet distribution and Weibull distribution)into a single form The parameters of GEVD in Figure 12(a)are 119903 = minus01279 119886 = 00009 and 119887 = 10066 MoreoverFigures 12(b)ndash12(d) show the fitting curves of GEVD for thediagonal web member the bottom chord member and thedeck chord member It can be seen that the GEVD can welldescribe the probability characteristics of the DLFs

52 Evaluation of Dynamic Load Factors

521 Standard Value of Dynamic Load Factors Eurocode1 [12] specifies that the standard value is the extreme val-ues within 50-year return period The monitoring dynamicstrains are affected by the irregularity of the rail so the calcu-lated DLF of the monitoring dynamic strains has containedthe influence of the irregularity of the rail The irregularityof the rail may be worse later and furthermore influences thecurrent statistics characteristics of the DLFs but whether theirregularity of the rail is really worse or not is hard to decideSo this paper studied the case when the irregularity of therail does not get worse In this case the standard value of themonitored data obtained within a short period of time can beused as the extreme value of the DLF within 50-year returnperiod Specifically the standard value can be calculated by

119875 = 1 minus 119866 (119863p) (9a)

119875 =

1

50119873

(9b)

where119863p denotes the standard value119875denotes the exceedingprobability119873 denotes the number of DLFs in one year OneLDF can be calculated after one train passes the bridge so119873is equal to the total amount of trains passing the bridge in oneyear On consideration that 119863p cannot be directly calculatedby (9a) and (9b) then119863p is numerically calculated byNewtoniteration formula as follows

119863119899+1

p = 119863119899

p +1 minus 119866 (119863

119899

p) minus 119875

1198661015840(119863119899

p) (10)

where 119863119899p is the 119899th iteration of 1198630p and 1198661015840(119863119899

p) is the one-order derivative function of119866(119863119899p) Iteration terminateswhenthe absolute difference between 119863

119899+1

p and 119863119899

p is less than00005 Based on the method above the stand values of DLFsare shown in Table 3 It can be seen that the bottom chord has

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

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Shock and Vibration

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International Journal of

Shock and Vibration 5

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(a) 1198601 and 119860s1 of top chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(b) 1198602 and 119860s2 of diagonal web member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(c) 1198603 and 119860s3 of bottom chord member

Monitoring strainSimulated strain

Stra

in(120583

120576)

minus30

minus15

0

15

30

6 12 18 240Time (s)

(d) 1198604 and 119860s4 of deck chord member

Figure 4 Typical dynamic strain responses of field monitoring and FE modeling results

The transfer function of a polynomial of 119899-order FIR filter isdefined by

119867(119911) =

119899

sum

119894=0

119887119894119911minus119894 (6)

and its frequency response is

119867(120596) =

119899

sum

119894=0

119887119894119890minus119895120596119894

= 119887T120593 (120596) (7)

where 119887 = [1198870 1198871 1198872 119887

119899]T is the coefficient vector having

the filter coefficients 120601(120596) = [1 119890minus119895120596

119890minus119895120596119899

]T and T

denotes the transpose of matrix The coefficients of FIR filterare usually symmetric hence they have a spectrum thatexhibits a linear phase and the response to an impulse settlesto zero

Specifically the low-pass FIR filter is decided by fourinput parameters the normalized passband edge frequency120596p the normalized stopband edge frequency 120596s the allowedpassband deviation 120575p and the stopband deviation 120575s [11]Generally the optimal values of four input parameters areobtained by trial-and-error approach [10] In this study theoptimal values of four input parameters are 120596p = 0004 120587Hz120596s = 006 120587Hz 120575p = 1 and 120575s = 60 after trial-and-errorapproach The static strain data are acquired by using thisfilter which show good filtering effect in Figure 5

33 Field Monitoring Results of Dynamic Load Factors Inthis study the dynamic strain responses of the bridge wererecorded for each case having a single train traversing on thebridge 1000 cases (a single train at a time) were selected andthe computed DLFs of 1000 cases are shown in Figure 6 Itis clear from the figures that the DLF is not a deterministic

6 Shock and Vibration

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(a) 1198601 of top chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(b) 1198602 of diagonal web member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(c) 1198603 of bottom chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(d) 1198604 of deck chord member

Figure 5 The dynamic and static strain responses of 1198601sim1198604

quantityThus themeanDLF andmaximumDLF denoted byAV andMVare further computed and also shown in Figure 6The mean DLF and maximum DLF computed from thebottom chord member are the largest of all which are 10862and 11411 respectively And the mean DLF and maximumDLF computed from the top chord member are the smallestof all which are only 10069 and 10106 respectively

34 Dynamic Analysis Results of Dynamic Load FactorsFigure 6 shows the field monitoring results of DLFs for keymembers of the steel truss arch However only DLFs of thetruss 3 as shown in Figure 2(a) have been measured In thissection DLFs for all trusses that is truss 1 truss 2 and truss3 are obtained using the simulated strain responses with theFE modeling methodThe strain data is simulated in 16 casesas shown in Table 1 and the calculation results of DLFs from

truss 3 are shown in Figure 7 Moreover Table 2 shows themonitoring and simulatedAVs of theDLFs and it can be seenthat themonitoring AVs of the DLF are close to the simulatedAVs of the DLFs verifying the effectiveness of the finiteelement modeling method For all 16 cases the maximumDLF of each key member is further obtained Thus Figure 8shows the maximum DLFs for key members of the truss 1truss 2 and truss 3 It can be seen that for each truss themaximum DLFs of the bottom chord member the diagonalweb member the deck chord member and the top chordmember decrease successively which is consistent with themonitoring results Furthermore the maximum DLFs fromtruss 1 and truss 3 is a little higher than those from truss2 Thus for three planes of truss arch the dynamic effectsinduced by high-speed trains for middle truss arch are lessthan those for side truss arch

Shock and Vibration 7

200 400 600 800 10000Segments

0995

1

1005

101

1015

102

DLF

= 10106

= 10069

MV

AV

(a) The top chord member

200 400 600 800 10000Segments

09

1

11

12

13

DLF

= 11318

= 10802

MV

AV

(b) The diagonal web member

200 400 600 800 10000Segments

095

101

107

113

119

125

DLF

MV = 11411

AV = 10862

(c) The bottom chord member

200 400 600 800 10000Segments

095

098

101

104

107

11

DLF

= 10451

= 10197

MV

AV

(d) The deck chord member

Figure 6 Field monitoring results of DLFs

Table 1 16 cases for simulating the strain data

Number of cases Carriage load (kN) Load location Number of carriages Train speed (kmh)1 535 Lane 1 8 2402 535 Lane 2 8 2403 535 Lane 3 8 2404 535 Lane 4 8 2405 535 Lane 1 8 1606 535 Lane 2 8 1607 535 Lane 3 8 1608 535 Lane 4 8 1609 535 Lane 1 16 24010 535 Lane 2 16 24011 535 Lane 3 16 24012 535 Lane 4 16 24013 535 Lane 1 16 16014 535 Lane 2 16 16015 535 Lane 3 16 16016 535 Lane 4 16 160

8 Shock and Vibration

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1004

1006

1008

101D

LF

(a) The top chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

105

107

109

111

DLF

(b) The diagonal web member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

103

105

107

109

111

113

DLF

(c) The bottom chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1

101

102

103

104

105

DLF

(d) The deck chord member

Figure 7 Dynamic load factors for truss 3 using simulated strain responses

Table 2 Monitoring and simulated AVs of the DLFs

DLFs The top chord member The diagonal web member The bottom chord member The deck chord memberMonitoring AV 10069 10802 10862 10197Simulated AV 10068 10768 10781 10215Error () 001 031 075 018

4 Factors Affecting the Dynamic Load Factors

As mentioned in the preceding sections many factors affectthe magnitude of the DLF The influence of lane position oftrains number of train carriages and speed of trains wasstudied and is presented in the following sections

41 Lane Position There are 4 train lanes in the girder ofDaShengGuan Bridge as shown in Figure 2(a) Firstly themeasured DLFs of 1000 trains in Figure 6 are classifiedas 4 groups corresponding to 4 train lanes respectivelyThe total number of the DLFs for each train lane is 250Then for each group the 250 DLFs are divided into 50segments and the mean value of each segment is computedas shown in Figure 9 Furthermore the mean values of thesimulated DLFs in Figure 7 are computed for each train lanerespectively which are also shown in Figure 9 119871 s119894 denotes

the average value of the 119894th train lane 119894 = 1 2 3 4 It can beseen that the influence of lane 1 lane 2 lane 3 and lane 4 onthe DLFs decreases successively for the top chord memberthe diagonal webmember and the bottom chordmember butincreases successively for the deck chord member Thereforewith the train closer to the steel truss arch the dynamic effectis more significant for the deck chord member

42 Number of Train Carriages In China the high-speedelectric multiple unit (EMU) train has 8 carriages or 16carriages respectively In this study an investigation has beencarried out to determine if there is a correlation betweenthe DLF and the number of train carriages Firstly themeasured DLFs of 1000 trains in Figure 6 are classified astwo groups corresponding to the 8 carriages and 16 carriagesrespectively The total number of the DLFs for both 8 and16 carriages is 500 Then for each group the 500 DLFs are

Shock and Vibration 9

Truss 3Truss 2Truss 1

1

105

11

115

DLF

Truss 2 Truss 3Truss 1Location

Deck chordDiagonal chord

Bottom chordTop chord

Figure 8 Maximum dynamic load factors for truss 1 truss 2 andtruss 3

divided into 50 segments and themean value of each segmentis computed as shown in Figure 10 Furthermore the meanvalues 119862s8 and 119862s16 of the simulated DLFs in Figure 7 arecomputed for 8 and 16 carriages respectively which are alsoshown in Figure 10The figures show an increase in the meanDLF for the 8 carriages comparing with the 16 carriagesHowever it can also be noticed that the absolute value of theincrease is very small

43 Speed of Trains According to the field monitoringresults the speed of trains ranges approximately from110 kmh to 250 kmh The results of the DLF (DLF) causedby the speed of trains are plotted in Figure 11 Meanwhile thesimulated DLFs under the speeds of 160 kmh and 240 kmhare shown in Figure 11 which can verify the influenceof train speed on the monitoring DLFs It can be seenthat the speed and DLF are weakly correlated Accordingto the fitting curves shown in Figure 11 even though thecorrelation between speed and DLF is not strong there existsan increasing linear relationship (ie as the speed of trainsincreases the DLF will also increase)

5 Statistical Analysis of theDynamic Load Factors

51 Probability Distribution Model In this study a largeamount of data on DLFs was acquired through field mon-itoring Therefore it is important to introduce a statisticalanalysis to obtain the appropriate design value of DLF Firstlythe accumulative probability function forDLFs is establishedThree types of accumulative probability function are selectedthe normal distribution the Weibull distribution and theGeneralized ExtremeValueDistribution (GEVD) Taking theDLFs in Figure 6(a) for example the accumulative proba-bility and fitting curves using three probability distributionfunctions are shown in Figure 12(a) Their fitting errors areobtained by calculating the variances of residuals between the

monitoring curve and the fitting curve which are 00001120000189 and 0000105 respectively Thus the GEVD is thebest fitting curve which is defined by

119866 (119863) = exp[minus [1 + 119903 (

119863 minus 119887

119886

)]

minus1119903

] (8)

where 119863 denotes the DLFs 119903 119886 and 119887 denote shapeparameter scale parameter and location parameter ofGEVDrespectively which can be estimated by maximum likelihoodmethod In detail Generalized Extreme Value Distribution119866(119863) combines three types of distributions (ie Gumbeldistribution Frechet distribution and Weibull distribution)into a single form The parameters of GEVD in Figure 12(a)are 119903 = minus01279 119886 = 00009 and 119887 = 10066 MoreoverFigures 12(b)ndash12(d) show the fitting curves of GEVD for thediagonal web member the bottom chord member and thedeck chord member It can be seen that the GEVD can welldescribe the probability characteristics of the DLFs

52 Evaluation of Dynamic Load Factors

521 Standard Value of Dynamic Load Factors Eurocode1 [12] specifies that the standard value is the extreme val-ues within 50-year return period The monitoring dynamicstrains are affected by the irregularity of the rail so the calcu-lated DLF of the monitoring dynamic strains has containedthe influence of the irregularity of the rail The irregularityof the rail may be worse later and furthermore influences thecurrent statistics characteristics of the DLFs but whether theirregularity of the rail is really worse or not is hard to decideSo this paper studied the case when the irregularity of therail does not get worse In this case the standard value of themonitored data obtained within a short period of time can beused as the extreme value of the DLF within 50-year returnperiod Specifically the standard value can be calculated by

119875 = 1 minus 119866 (119863p) (9a)

119875 =

1

50119873

(9b)

where119863p denotes the standard value119875denotes the exceedingprobability119873 denotes the number of DLFs in one year OneLDF can be calculated after one train passes the bridge so119873is equal to the total amount of trains passing the bridge in oneyear On consideration that 119863p cannot be directly calculatedby (9a) and (9b) then119863p is numerically calculated byNewtoniteration formula as follows

119863119899+1

p = 119863119899

p +1 minus 119866 (119863

119899

p) minus 119875

1198661015840(119863119899

p) (10)

where 119863119899p is the 119899th iteration of 1198630p and 1198661015840(119863119899

p) is the one-order derivative function of119866(119863119899p) Iteration terminateswhenthe absolute difference between 119863

119899+1

p and 119863119899

p is less than00005 Based on the method above the stand values of DLFsare shown in Table 3 It can be seen that the bottom chord has

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

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Shock and Vibration

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International Journal of

6 Shock and Vibration

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(a) 1198601 of top chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(b) 1198602 of diagonal web member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(c) 1198603 of bottom chord member

Before filteringAfter filtering

6 12 18 240Time (s)

Stra

in(120583

120576)

minus30

minus15

0

15

30

(d) 1198604 of deck chord member

Figure 5 The dynamic and static strain responses of 1198601sim1198604

quantityThus themeanDLF andmaximumDLF denoted byAV andMVare further computed and also shown in Figure 6The mean DLF and maximum DLF computed from thebottom chord member are the largest of all which are 10862and 11411 respectively And the mean DLF and maximumDLF computed from the top chord member are the smallestof all which are only 10069 and 10106 respectively

34 Dynamic Analysis Results of Dynamic Load FactorsFigure 6 shows the field monitoring results of DLFs for keymembers of the steel truss arch However only DLFs of thetruss 3 as shown in Figure 2(a) have been measured In thissection DLFs for all trusses that is truss 1 truss 2 and truss3 are obtained using the simulated strain responses with theFE modeling methodThe strain data is simulated in 16 casesas shown in Table 1 and the calculation results of DLFs from

truss 3 are shown in Figure 7 Moreover Table 2 shows themonitoring and simulatedAVs of theDLFs and it can be seenthat themonitoring AVs of the DLF are close to the simulatedAVs of the DLFs verifying the effectiveness of the finiteelement modeling method For all 16 cases the maximumDLF of each key member is further obtained Thus Figure 8shows the maximum DLFs for key members of the truss 1truss 2 and truss 3 It can be seen that for each truss themaximum DLFs of the bottom chord member the diagonalweb member the deck chord member and the top chordmember decrease successively which is consistent with themonitoring results Furthermore the maximum DLFs fromtruss 1 and truss 3 is a little higher than those from truss2 Thus for three planes of truss arch the dynamic effectsinduced by high-speed trains for middle truss arch are lessthan those for side truss arch

Shock and Vibration 7

200 400 600 800 10000Segments

0995

1

1005

101

1015

102

DLF

= 10106

= 10069

MV

AV

(a) The top chord member

200 400 600 800 10000Segments

09

1

11

12

13

DLF

= 11318

= 10802

MV

AV

(b) The diagonal web member

200 400 600 800 10000Segments

095

101

107

113

119

125

DLF

MV = 11411

AV = 10862

(c) The bottom chord member

200 400 600 800 10000Segments

095

098

101

104

107

11

DLF

= 10451

= 10197

MV

AV

(d) The deck chord member

Figure 6 Field monitoring results of DLFs

Table 1 16 cases for simulating the strain data

Number of cases Carriage load (kN) Load location Number of carriages Train speed (kmh)1 535 Lane 1 8 2402 535 Lane 2 8 2403 535 Lane 3 8 2404 535 Lane 4 8 2405 535 Lane 1 8 1606 535 Lane 2 8 1607 535 Lane 3 8 1608 535 Lane 4 8 1609 535 Lane 1 16 24010 535 Lane 2 16 24011 535 Lane 3 16 24012 535 Lane 4 16 24013 535 Lane 1 16 16014 535 Lane 2 16 16015 535 Lane 3 16 16016 535 Lane 4 16 160

8 Shock and Vibration

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1004

1006

1008

101D

LF

(a) The top chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

105

107

109

111

DLF

(b) The diagonal web member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

103

105

107

109

111

113

DLF

(c) The bottom chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1

101

102

103

104

105

DLF

(d) The deck chord member

Figure 7 Dynamic load factors for truss 3 using simulated strain responses

Table 2 Monitoring and simulated AVs of the DLFs

DLFs The top chord member The diagonal web member The bottom chord member The deck chord memberMonitoring AV 10069 10802 10862 10197Simulated AV 10068 10768 10781 10215Error () 001 031 075 018

4 Factors Affecting the Dynamic Load Factors

As mentioned in the preceding sections many factors affectthe magnitude of the DLF The influence of lane position oftrains number of train carriages and speed of trains wasstudied and is presented in the following sections

41 Lane Position There are 4 train lanes in the girder ofDaShengGuan Bridge as shown in Figure 2(a) Firstly themeasured DLFs of 1000 trains in Figure 6 are classifiedas 4 groups corresponding to 4 train lanes respectivelyThe total number of the DLFs for each train lane is 250Then for each group the 250 DLFs are divided into 50segments and the mean value of each segment is computedas shown in Figure 9 Furthermore the mean values of thesimulated DLFs in Figure 7 are computed for each train lanerespectively which are also shown in Figure 9 119871 s119894 denotes

the average value of the 119894th train lane 119894 = 1 2 3 4 It can beseen that the influence of lane 1 lane 2 lane 3 and lane 4 onthe DLFs decreases successively for the top chord memberthe diagonal webmember and the bottom chordmember butincreases successively for the deck chord member Thereforewith the train closer to the steel truss arch the dynamic effectis more significant for the deck chord member

42 Number of Train Carriages In China the high-speedelectric multiple unit (EMU) train has 8 carriages or 16carriages respectively In this study an investigation has beencarried out to determine if there is a correlation betweenthe DLF and the number of train carriages Firstly themeasured DLFs of 1000 trains in Figure 6 are classified astwo groups corresponding to the 8 carriages and 16 carriagesrespectively The total number of the DLFs for both 8 and16 carriages is 500 Then for each group the 500 DLFs are

Shock and Vibration 9

Truss 3Truss 2Truss 1

1

105

11

115

DLF

Truss 2 Truss 3Truss 1Location

Deck chordDiagonal chord

Bottom chordTop chord

Figure 8 Maximum dynamic load factors for truss 1 truss 2 andtruss 3

divided into 50 segments and themean value of each segmentis computed as shown in Figure 10 Furthermore the meanvalues 119862s8 and 119862s16 of the simulated DLFs in Figure 7 arecomputed for 8 and 16 carriages respectively which are alsoshown in Figure 10The figures show an increase in the meanDLF for the 8 carriages comparing with the 16 carriagesHowever it can also be noticed that the absolute value of theincrease is very small

43 Speed of Trains According to the field monitoringresults the speed of trains ranges approximately from110 kmh to 250 kmh The results of the DLF (DLF) causedby the speed of trains are plotted in Figure 11 Meanwhile thesimulated DLFs under the speeds of 160 kmh and 240 kmhare shown in Figure 11 which can verify the influenceof train speed on the monitoring DLFs It can be seenthat the speed and DLF are weakly correlated Accordingto the fitting curves shown in Figure 11 even though thecorrelation between speed and DLF is not strong there existsan increasing linear relationship (ie as the speed of trainsincreases the DLF will also increase)

5 Statistical Analysis of theDynamic Load Factors

51 Probability Distribution Model In this study a largeamount of data on DLFs was acquired through field mon-itoring Therefore it is important to introduce a statisticalanalysis to obtain the appropriate design value of DLF Firstlythe accumulative probability function forDLFs is establishedThree types of accumulative probability function are selectedthe normal distribution the Weibull distribution and theGeneralized ExtremeValueDistribution (GEVD) Taking theDLFs in Figure 6(a) for example the accumulative proba-bility and fitting curves using three probability distributionfunctions are shown in Figure 12(a) Their fitting errors areobtained by calculating the variances of residuals between the

monitoring curve and the fitting curve which are 00001120000189 and 0000105 respectively Thus the GEVD is thebest fitting curve which is defined by

119866 (119863) = exp[minus [1 + 119903 (

119863 minus 119887

119886

)]

minus1119903

] (8)

where 119863 denotes the DLFs 119903 119886 and 119887 denote shapeparameter scale parameter and location parameter ofGEVDrespectively which can be estimated by maximum likelihoodmethod In detail Generalized Extreme Value Distribution119866(119863) combines three types of distributions (ie Gumbeldistribution Frechet distribution and Weibull distribution)into a single form The parameters of GEVD in Figure 12(a)are 119903 = minus01279 119886 = 00009 and 119887 = 10066 MoreoverFigures 12(b)ndash12(d) show the fitting curves of GEVD for thediagonal web member the bottom chord member and thedeck chord member It can be seen that the GEVD can welldescribe the probability characteristics of the DLFs

52 Evaluation of Dynamic Load Factors

521 Standard Value of Dynamic Load Factors Eurocode1 [12] specifies that the standard value is the extreme val-ues within 50-year return period The monitoring dynamicstrains are affected by the irregularity of the rail so the calcu-lated DLF of the monitoring dynamic strains has containedthe influence of the irregularity of the rail The irregularityof the rail may be worse later and furthermore influences thecurrent statistics characteristics of the DLFs but whether theirregularity of the rail is really worse or not is hard to decideSo this paper studied the case when the irregularity of therail does not get worse In this case the standard value of themonitored data obtained within a short period of time can beused as the extreme value of the DLF within 50-year returnperiod Specifically the standard value can be calculated by

119875 = 1 minus 119866 (119863p) (9a)

119875 =

1

50119873

(9b)

where119863p denotes the standard value119875denotes the exceedingprobability119873 denotes the number of DLFs in one year OneLDF can be calculated after one train passes the bridge so119873is equal to the total amount of trains passing the bridge in oneyear On consideration that 119863p cannot be directly calculatedby (9a) and (9b) then119863p is numerically calculated byNewtoniteration formula as follows

119863119899+1

p = 119863119899

p +1 minus 119866 (119863

119899

p) minus 119875

1198661015840(119863119899

p) (10)

where 119863119899p is the 119899th iteration of 1198630p and 1198661015840(119863119899

p) is the one-order derivative function of119866(119863119899p) Iteration terminateswhenthe absolute difference between 119863

119899+1

p and 119863119899

p is less than00005 Based on the method above the stand values of DLFsare shown in Table 3 It can be seen that the bottom chord has

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 7

200 400 600 800 10000Segments

0995

1

1005

101

1015

102

DLF

= 10106

= 10069

MV

AV

(a) The top chord member

200 400 600 800 10000Segments

09

1

11

12

13

DLF

= 11318

= 10802

MV

AV

(b) The diagonal web member

200 400 600 800 10000Segments

095

101

107

113

119

125

DLF

MV = 11411

AV = 10862

(c) The bottom chord member

200 400 600 800 10000Segments

095

098

101

104

107

11

DLF

= 10451

= 10197

MV

AV

(d) The deck chord member

Figure 6 Field monitoring results of DLFs

Table 1 16 cases for simulating the strain data

Number of cases Carriage load (kN) Load location Number of carriages Train speed (kmh)1 535 Lane 1 8 2402 535 Lane 2 8 2403 535 Lane 3 8 2404 535 Lane 4 8 2405 535 Lane 1 8 1606 535 Lane 2 8 1607 535 Lane 3 8 1608 535 Lane 4 8 1609 535 Lane 1 16 24010 535 Lane 2 16 24011 535 Lane 3 16 24012 535 Lane 4 16 24013 535 Lane 1 16 16014 535 Lane 2 16 16015 535 Lane 3 16 16016 535 Lane 4 16 160

8 Shock and Vibration

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1004

1006

1008

101D

LF

(a) The top chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

105

107

109

111

DLF

(b) The diagonal web member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

103

105

107

109

111

113

DLF

(c) The bottom chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1

101

102

103

104

105

DLF

(d) The deck chord member

Figure 7 Dynamic load factors for truss 3 using simulated strain responses

Table 2 Monitoring and simulated AVs of the DLFs

DLFs The top chord member The diagonal web member The bottom chord member The deck chord memberMonitoring AV 10069 10802 10862 10197Simulated AV 10068 10768 10781 10215Error () 001 031 075 018

4 Factors Affecting the Dynamic Load Factors

As mentioned in the preceding sections many factors affectthe magnitude of the DLF The influence of lane position oftrains number of train carriages and speed of trains wasstudied and is presented in the following sections

41 Lane Position There are 4 train lanes in the girder ofDaShengGuan Bridge as shown in Figure 2(a) Firstly themeasured DLFs of 1000 trains in Figure 6 are classifiedas 4 groups corresponding to 4 train lanes respectivelyThe total number of the DLFs for each train lane is 250Then for each group the 250 DLFs are divided into 50segments and the mean value of each segment is computedas shown in Figure 9 Furthermore the mean values of thesimulated DLFs in Figure 7 are computed for each train lanerespectively which are also shown in Figure 9 119871 s119894 denotes

the average value of the 119894th train lane 119894 = 1 2 3 4 It can beseen that the influence of lane 1 lane 2 lane 3 and lane 4 onthe DLFs decreases successively for the top chord memberthe diagonal webmember and the bottom chordmember butincreases successively for the deck chord member Thereforewith the train closer to the steel truss arch the dynamic effectis more significant for the deck chord member

42 Number of Train Carriages In China the high-speedelectric multiple unit (EMU) train has 8 carriages or 16carriages respectively In this study an investigation has beencarried out to determine if there is a correlation betweenthe DLF and the number of train carriages Firstly themeasured DLFs of 1000 trains in Figure 6 are classified astwo groups corresponding to the 8 carriages and 16 carriagesrespectively The total number of the DLFs for both 8 and16 carriages is 500 Then for each group the 500 DLFs are

Shock and Vibration 9

Truss 3Truss 2Truss 1

1

105

11

115

DLF

Truss 2 Truss 3Truss 1Location

Deck chordDiagonal chord

Bottom chordTop chord

Figure 8 Maximum dynamic load factors for truss 1 truss 2 andtruss 3

divided into 50 segments and themean value of each segmentis computed as shown in Figure 10 Furthermore the meanvalues 119862s8 and 119862s16 of the simulated DLFs in Figure 7 arecomputed for 8 and 16 carriages respectively which are alsoshown in Figure 10The figures show an increase in the meanDLF for the 8 carriages comparing with the 16 carriagesHowever it can also be noticed that the absolute value of theincrease is very small

43 Speed of Trains According to the field monitoringresults the speed of trains ranges approximately from110 kmh to 250 kmh The results of the DLF (DLF) causedby the speed of trains are plotted in Figure 11 Meanwhile thesimulated DLFs under the speeds of 160 kmh and 240 kmhare shown in Figure 11 which can verify the influenceof train speed on the monitoring DLFs It can be seenthat the speed and DLF are weakly correlated Accordingto the fitting curves shown in Figure 11 even though thecorrelation between speed and DLF is not strong there existsan increasing linear relationship (ie as the speed of trainsincreases the DLF will also increase)

5 Statistical Analysis of theDynamic Load Factors

51 Probability Distribution Model In this study a largeamount of data on DLFs was acquired through field mon-itoring Therefore it is important to introduce a statisticalanalysis to obtain the appropriate design value of DLF Firstlythe accumulative probability function forDLFs is establishedThree types of accumulative probability function are selectedthe normal distribution the Weibull distribution and theGeneralized ExtremeValueDistribution (GEVD) Taking theDLFs in Figure 6(a) for example the accumulative proba-bility and fitting curves using three probability distributionfunctions are shown in Figure 12(a) Their fitting errors areobtained by calculating the variances of residuals between the

monitoring curve and the fitting curve which are 00001120000189 and 0000105 respectively Thus the GEVD is thebest fitting curve which is defined by

119866 (119863) = exp[minus [1 + 119903 (

119863 minus 119887

119886

)]

minus1119903

] (8)

where 119863 denotes the DLFs 119903 119886 and 119887 denote shapeparameter scale parameter and location parameter ofGEVDrespectively which can be estimated by maximum likelihoodmethod In detail Generalized Extreme Value Distribution119866(119863) combines three types of distributions (ie Gumbeldistribution Frechet distribution and Weibull distribution)into a single form The parameters of GEVD in Figure 12(a)are 119903 = minus01279 119886 = 00009 and 119887 = 10066 MoreoverFigures 12(b)ndash12(d) show the fitting curves of GEVD for thediagonal web member the bottom chord member and thedeck chord member It can be seen that the GEVD can welldescribe the probability characteristics of the DLFs

52 Evaluation of Dynamic Load Factors

521 Standard Value of Dynamic Load Factors Eurocode1 [12] specifies that the standard value is the extreme val-ues within 50-year return period The monitoring dynamicstrains are affected by the irregularity of the rail so the calcu-lated DLF of the monitoring dynamic strains has containedthe influence of the irregularity of the rail The irregularityof the rail may be worse later and furthermore influences thecurrent statistics characteristics of the DLFs but whether theirregularity of the rail is really worse or not is hard to decideSo this paper studied the case when the irregularity of therail does not get worse In this case the standard value of themonitored data obtained within a short period of time can beused as the extreme value of the DLF within 50-year returnperiod Specifically the standard value can be calculated by

119875 = 1 minus 119866 (119863p) (9a)

119875 =

1

50119873

(9b)

where119863p denotes the standard value119875denotes the exceedingprobability119873 denotes the number of DLFs in one year OneLDF can be calculated after one train passes the bridge so119873is equal to the total amount of trains passing the bridge in oneyear On consideration that 119863p cannot be directly calculatedby (9a) and (9b) then119863p is numerically calculated byNewtoniteration formula as follows

119863119899+1

p = 119863119899

p +1 minus 119866 (119863

119899

p) minus 119875

1198661015840(119863119899

p) (10)

where 119863119899p is the 119899th iteration of 1198630p and 1198661015840(119863119899

p) is the one-order derivative function of119866(119863119899p) Iteration terminateswhenthe absolute difference between 119863

119899+1

p and 119863119899

p is less than00005 Based on the method above the stand values of DLFsare shown in Table 3 It can be seen that the bottom chord has

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Shock and Vibration

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1004

1006

1008

101D

LF

(a) The top chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

105

107

109

111

DLF

(b) The diagonal web member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

103

105

107

109

111

113

DLF

(c) The bottom chord member

2 3 4 5 6 7 8 9 10 11 12 13 14 15 161Number of cases

1

101

102

103

104

105

DLF

(d) The deck chord member

Figure 7 Dynamic load factors for truss 3 using simulated strain responses

Table 2 Monitoring and simulated AVs of the DLFs

DLFs The top chord member The diagonal web member The bottom chord member The deck chord memberMonitoring AV 10069 10802 10862 10197Simulated AV 10068 10768 10781 10215Error () 001 031 075 018

4 Factors Affecting the Dynamic Load Factors

As mentioned in the preceding sections many factors affectthe magnitude of the DLF The influence of lane position oftrains number of train carriages and speed of trains wasstudied and is presented in the following sections

41 Lane Position There are 4 train lanes in the girder ofDaShengGuan Bridge as shown in Figure 2(a) Firstly themeasured DLFs of 1000 trains in Figure 6 are classifiedas 4 groups corresponding to 4 train lanes respectivelyThe total number of the DLFs for each train lane is 250Then for each group the 250 DLFs are divided into 50segments and the mean value of each segment is computedas shown in Figure 9 Furthermore the mean values of thesimulated DLFs in Figure 7 are computed for each train lanerespectively which are also shown in Figure 9 119871 s119894 denotes

the average value of the 119894th train lane 119894 = 1 2 3 4 It can beseen that the influence of lane 1 lane 2 lane 3 and lane 4 onthe DLFs decreases successively for the top chord memberthe diagonal webmember and the bottom chordmember butincreases successively for the deck chord member Thereforewith the train closer to the steel truss arch the dynamic effectis more significant for the deck chord member

42 Number of Train Carriages In China the high-speedelectric multiple unit (EMU) train has 8 carriages or 16carriages respectively In this study an investigation has beencarried out to determine if there is a correlation betweenthe DLF and the number of train carriages Firstly themeasured DLFs of 1000 trains in Figure 6 are classified astwo groups corresponding to the 8 carriages and 16 carriagesrespectively The total number of the DLFs for both 8 and16 carriages is 500 Then for each group the 500 DLFs are

Shock and Vibration 9

Truss 3Truss 2Truss 1

1

105

11

115

DLF

Truss 2 Truss 3Truss 1Location

Deck chordDiagonal chord

Bottom chordTop chord

Figure 8 Maximum dynamic load factors for truss 1 truss 2 andtruss 3

divided into 50 segments and themean value of each segmentis computed as shown in Figure 10 Furthermore the meanvalues 119862s8 and 119862s16 of the simulated DLFs in Figure 7 arecomputed for 8 and 16 carriages respectively which are alsoshown in Figure 10The figures show an increase in the meanDLF for the 8 carriages comparing with the 16 carriagesHowever it can also be noticed that the absolute value of theincrease is very small

43 Speed of Trains According to the field monitoringresults the speed of trains ranges approximately from110 kmh to 250 kmh The results of the DLF (DLF) causedby the speed of trains are plotted in Figure 11 Meanwhile thesimulated DLFs under the speeds of 160 kmh and 240 kmhare shown in Figure 11 which can verify the influenceof train speed on the monitoring DLFs It can be seenthat the speed and DLF are weakly correlated Accordingto the fitting curves shown in Figure 11 even though thecorrelation between speed and DLF is not strong there existsan increasing linear relationship (ie as the speed of trainsincreases the DLF will also increase)

5 Statistical Analysis of theDynamic Load Factors

51 Probability Distribution Model In this study a largeamount of data on DLFs was acquired through field mon-itoring Therefore it is important to introduce a statisticalanalysis to obtain the appropriate design value of DLF Firstlythe accumulative probability function forDLFs is establishedThree types of accumulative probability function are selectedthe normal distribution the Weibull distribution and theGeneralized ExtremeValueDistribution (GEVD) Taking theDLFs in Figure 6(a) for example the accumulative proba-bility and fitting curves using three probability distributionfunctions are shown in Figure 12(a) Their fitting errors areobtained by calculating the variances of residuals between the

monitoring curve and the fitting curve which are 00001120000189 and 0000105 respectively Thus the GEVD is thebest fitting curve which is defined by

119866 (119863) = exp[minus [1 + 119903 (

119863 minus 119887

119886

)]

minus1119903

] (8)

where 119863 denotes the DLFs 119903 119886 and 119887 denote shapeparameter scale parameter and location parameter ofGEVDrespectively which can be estimated by maximum likelihoodmethod In detail Generalized Extreme Value Distribution119866(119863) combines three types of distributions (ie Gumbeldistribution Frechet distribution and Weibull distribution)into a single form The parameters of GEVD in Figure 12(a)are 119903 = minus01279 119886 = 00009 and 119887 = 10066 MoreoverFigures 12(b)ndash12(d) show the fitting curves of GEVD for thediagonal web member the bottom chord member and thedeck chord member It can be seen that the GEVD can welldescribe the probability characteristics of the DLFs

52 Evaluation of Dynamic Load Factors

521 Standard Value of Dynamic Load Factors Eurocode1 [12] specifies that the standard value is the extreme val-ues within 50-year return period The monitoring dynamicstrains are affected by the irregularity of the rail so the calcu-lated DLF of the monitoring dynamic strains has containedthe influence of the irregularity of the rail The irregularityof the rail may be worse later and furthermore influences thecurrent statistics characteristics of the DLFs but whether theirregularity of the rail is really worse or not is hard to decideSo this paper studied the case when the irregularity of therail does not get worse In this case the standard value of themonitored data obtained within a short period of time can beused as the extreme value of the DLF within 50-year returnperiod Specifically the standard value can be calculated by

119875 = 1 minus 119866 (119863p) (9a)

119875 =

1

50119873

(9b)

where119863p denotes the standard value119875denotes the exceedingprobability119873 denotes the number of DLFs in one year OneLDF can be calculated after one train passes the bridge so119873is equal to the total amount of trains passing the bridge in oneyear On consideration that 119863p cannot be directly calculatedby (9a) and (9b) then119863p is numerically calculated byNewtoniteration formula as follows

119863119899+1

p = 119863119899

p +1 minus 119866 (119863

119899

p) minus 119875

1198661015840(119863119899

p) (10)

where 119863119899p is the 119899th iteration of 1198630p and 1198661015840(119863119899

p) is the one-order derivative function of119866(119863119899p) Iteration terminateswhenthe absolute difference between 119863

119899+1

p and 119863119899

p is less than00005 Based on the method above the stand values of DLFsare shown in Table 3 It can be seen that the bottom chord has

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

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Shock and Vibration

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 9

Truss 3Truss 2Truss 1

1

105

11

115

DLF

Truss 2 Truss 3Truss 1Location

Deck chordDiagonal chord

Bottom chordTop chord

Figure 8 Maximum dynamic load factors for truss 1 truss 2 andtruss 3

divided into 50 segments and themean value of each segmentis computed as shown in Figure 10 Furthermore the meanvalues 119862s8 and 119862s16 of the simulated DLFs in Figure 7 arecomputed for 8 and 16 carriages respectively which are alsoshown in Figure 10The figures show an increase in the meanDLF for the 8 carriages comparing with the 16 carriagesHowever it can also be noticed that the absolute value of theincrease is very small

43 Speed of Trains According to the field monitoringresults the speed of trains ranges approximately from110 kmh to 250 kmh The results of the DLF (DLF) causedby the speed of trains are plotted in Figure 11 Meanwhile thesimulated DLFs under the speeds of 160 kmh and 240 kmhare shown in Figure 11 which can verify the influenceof train speed on the monitoring DLFs It can be seenthat the speed and DLF are weakly correlated Accordingto the fitting curves shown in Figure 11 even though thecorrelation between speed and DLF is not strong there existsan increasing linear relationship (ie as the speed of trainsincreases the DLF will also increase)

5 Statistical Analysis of theDynamic Load Factors

51 Probability Distribution Model In this study a largeamount of data on DLFs was acquired through field mon-itoring Therefore it is important to introduce a statisticalanalysis to obtain the appropriate design value of DLF Firstlythe accumulative probability function forDLFs is establishedThree types of accumulative probability function are selectedthe normal distribution the Weibull distribution and theGeneralized ExtremeValueDistribution (GEVD) Taking theDLFs in Figure 6(a) for example the accumulative proba-bility and fitting curves using three probability distributionfunctions are shown in Figure 12(a) Their fitting errors areobtained by calculating the variances of residuals between the

monitoring curve and the fitting curve which are 00001120000189 and 0000105 respectively Thus the GEVD is thebest fitting curve which is defined by

119866 (119863) = exp[minus [1 + 119903 (

119863 minus 119887

119886

)]

minus1119903

] (8)

where 119863 denotes the DLFs 119903 119886 and 119887 denote shapeparameter scale parameter and location parameter ofGEVDrespectively which can be estimated by maximum likelihoodmethod In detail Generalized Extreme Value Distribution119866(119863) combines three types of distributions (ie Gumbeldistribution Frechet distribution and Weibull distribution)into a single form The parameters of GEVD in Figure 12(a)are 119903 = minus01279 119886 = 00009 and 119887 = 10066 MoreoverFigures 12(b)ndash12(d) show the fitting curves of GEVD for thediagonal web member the bottom chord member and thedeck chord member It can be seen that the GEVD can welldescribe the probability characteristics of the DLFs

52 Evaluation of Dynamic Load Factors

521 Standard Value of Dynamic Load Factors Eurocode1 [12] specifies that the standard value is the extreme val-ues within 50-year return period The monitoring dynamicstrains are affected by the irregularity of the rail so the calcu-lated DLF of the monitoring dynamic strains has containedthe influence of the irregularity of the rail The irregularityof the rail may be worse later and furthermore influences thecurrent statistics characteristics of the DLFs but whether theirregularity of the rail is really worse or not is hard to decideSo this paper studied the case when the irregularity of therail does not get worse In this case the standard value of themonitored data obtained within a short period of time can beused as the extreme value of the DLF within 50-year returnperiod Specifically the standard value can be calculated by

119875 = 1 minus 119866 (119863p) (9a)

119875 =

1

50119873

(9b)

where119863p denotes the standard value119875denotes the exceedingprobability119873 denotes the number of DLFs in one year OneLDF can be calculated after one train passes the bridge so119873is equal to the total amount of trains passing the bridge in oneyear On consideration that 119863p cannot be directly calculatedby (9a) and (9b) then119863p is numerically calculated byNewtoniteration formula as follows

119863119899+1

p = 119863119899

p +1 minus 119866 (119863

119899

p) minus 119875

1198661015840(119863119899

p) (10)

where 119863119899p is the 119899th iteration of 1198630p and 1198661015840(119863119899

p) is the one-order derivative function of119866(119863119899p) Iteration terminateswhenthe absolute difference between 119863

119899+1

p and 119863119899

p is less than00005 Based on the method above the stand values of DLFsare shown in Table 3 It can be seen that the bottom chord has

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

International Journal of

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Active and Passive Electronic Components

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Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Shock and Vibration

10 20 30 40 500Segments

1006

1007

1008

1009

101D

LF

Lane 4 Ls4 = 10065

Lane 3 Ls3 = 10067

Lane 2 Ls2 = 10069

Lane 1 Ls1 = 10073

(a) The top chord member

10 20 30 40 500Segments

107

108

109

11

DLF

Lane 4 Ls4 = 10736

Lane 3 Ls3 = 10758

Lane 2 Ls2 = 10777

Lane 1 Ls1 = 10802

(b) The diagonal web member

10 20 30 40 500Segments

106

108

11

112

DLF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(c) The bottom chord member

10 20 30 40 500Segments

1012

1019

1026

1033

104D

LF

Lane 4 Ls4 = 10671

Lane 3 Ls3 = 10760

Lane 2 Ls2 = 10818

Lane 1 Ls1 = 10877

(d) The deck chord member

Figure 9 The influence of train lanes on the mean DLF

Table 3 Stand values of dynamic load factors

Member type The top chord member The diagonal web member The bottom chord member The deck chord memberStandard value 10115 11376 11613 10549

the maximum stand value 11613 Moreover the maximumvalue of the DLFs in Figure 6 for each structural member iscomputed and the correlation between standard values andmaximum values is shown in Figure 13 The fitting curvesand the corresponding parameters of linear correlations areshown in Figure 13 using the least square method where 119896denotes slope term and denotes the constant term It can beseen that the correlation shows obvious linear correlation

522 Comparison with Different Bridge Design Codes

(1) The Manual for Railway Engineering (USA) According tothe Manual for Railway Engineering [13] the DLF for steelbridges can be defined as follows

DLF = 1 + 120583 (11a)

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

8 carriages16 carriages

1

1005

101

1015

102D

LF

10 20 30 40 500Segments

Cs8 = 10078

Cs16 = 10059

(a) The top chord member

8 carriages16 carriages

10 20 30 40 500Segments

1

105

11

115

12

125

DLF

Cs8 = 10843

Cs16 = 10693

(b) The diagonal web member

8 carriages16 carriages

1

105

11

115

12

125

DLF

10 20 30 40 500Segments

Cs8 = 10923

Cs16 = 10640

(c) The bottom chord member

8 carriages16 carriages

1

102

104

106

108

DLF

10 20 30 40 500Segments

Cs8 = 10278

Cs16 = 10152

(d) The deck chord member

Figure 10 Number of train carriages versus mean DLF

and if 119871 lt 244m

120583 =

03

119878

+ 04 minus

1198712

500

(11b)

and if 119871 ⩾ 244m

120583 =

03

119878

+ 016 +

183

119871 minus 094

(11c)

where 119871 denotes the span length and 119878 denotes the bridgewidth

(2) The UIC Code 776-IR According to the UIC Code 776-IR [14] if the railway bridges are designed by the UIC loaddiagram then the DLF can be defined as follows

DLF1=

096

radic119871120579minus 02

+ 088 (12a)

DLF2=

144

radic119871120579minus 02

+ 082 (12b)

DLF3=

216

radic119871120579minus 02

+ 076 (12c)

where DLF1 DLF

2 and DLF

3denote three kinds of DLFs

and 119871120579denotes the loading length If DLF

1 DLF

2 and DLF

3

are less than 10 then DLF1 DLF

2 and DLF

3take the value

10 The code specifies that for railway lanes under goodmaintenance DLF

1is used to calculate the DLF of shearing

force and DLF2is used to calculate the DLF of bending

movement for other railway lanes DLF2is used to calculate

the DLF of shearing force and DLF3is used to calculate the

DLF of bending movement

(3) BSI-BS5400 According to the BSI-BS5400 [15] the DLFof the high-speed railway coaches is 12 when it is used to

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

1002

1004

1006

1008

101

1012

1014D

LF

(a) The top chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

104

106

108

11

112

114

116

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(b) The diagonal web member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

102

105

108

111

114

117

12

DLF

130 150 170 190 210 230 250110Train speed (kmh)

(c) The bottom chord member

Monitoring DLFSimulated DLF at 160kmhSimulated DLF at 240kmh

130 150 170 190 210 230 250110Train speed (kmh)

DLF

1

102

104

106

(d) The deck chord member

Figure 11 Speed of trains versus DLF

calculate the bending movement and the shearing force Butfor railways without ballast groove the longitudinal girder fordirectly bearing the railway load and the transverse girder ofsingle-track railway the DLF should be 14

(4) Fundamental Code for Design on Railway Bridge andCulvert (China) According to the fundamental code fordesign on railway bridge and culvert in China [16] the DLFfor continuous steel bridges is defined as follows

DLF = 1 +

28

40 + 119871

(13)

But if the train speed exceeds 200 kmh according to thetemporary regulation on the latest design of 200 kmsim250 km

special railway for passengers [17] the DLF for continuoussteel bridges is defined as follows

DLF4=

0996

radic119871120593minus 02

+ 0913 (14a)

DLF5=

1494

radic119871120593minus 02

+ 0851 (14b)

where DLF4and DLF

5denote the DLFs for shearing force

and bending movement respectively and if DLF4and DLF

5

are less than 10 then DLF4and DLF

5take the value 10 119871

120593

denotes the loading length Specifically 119871120593is calculated by

119871120593= 120582

1

119873

119873

sum

119899=1

119882119899 (15a)

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 13

The monitoring curveThe normal distribution

The Weibull distributionThe GEVD

0

02

04

06

08

1Ac

cum

ulat

ive p

roba

bilit

y

1006 1008 101 1012 10141004DLF

(a) The top chord member

Monitoring curveFitting GEVD

108 111 114105DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

b = 10763

a = 00132

r = minus01708

(b) The diagonal web member

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

106 109 112 115103DLF

Monitoring curveFitting GEVD

b = 10814

a = 00241

r = minus02787

(c) The bottom chord member

101 102 103 104 1051DLF

0

02

04

06

08

1

Cum

ulat

ive p

roba

bilit

y

Monitoring curveFitting GEVD

b = 10169

a = 00045

r = minus00191

(d) The deck chord memberFigure 12 The accumulative probability and its fitting curves

where 120582 is the reduction factor and

if 119873 = 1

120582 = 10

(15b)

if 119873 = 2

120582 = 12

(15c)

if 119873 = 3

120582 = 13

(15d)

if 119873 = 4

120582 = 14

(15e)

if 119873 ⩾ 5

120582 = 15

(15f)

119873 denotes the number of spans119882119899denotes the length of the

119894th span Moreover if 119871120593lt 361m 119871

120593= 361m if 119871

120593is less

than the maximum span 119871120593takes the value of the maximum

span

(5) DS804 (Germany) According to the DS804 code inGermany [18] the UIC load diagram is used to be the designload and the DLF is defined by the following

if 119871 ⩽ 361m

DLF = 167 (16a)

and if 361m lt 119871 lt 65m

DLF = 082 +

144

radic119871 minus 02

(16b)

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Shock and Vibration

Table 4 Summary of dynamic load factors according to different bridge design codes

Code USA code UIC code BSI-BS5400 China code DS804 code JNR code

DLF 11755DLF1= 10

DLF2= 10

DLF3= 10

12 DLF4= 10

DLF5= 10

10 11124

1

105

11

115

12

The s

tand

ard

valu

e

105 11 1151The maximum value

c = minus0082

k = 1085

Fitting curveTop chordDiagonal chord

Bottom chordDeck chord

Figure 13 Correlation between standard values and maximumvalues of DLF

and if 119871 ⩾ 65m

DLF = 10 (16c)

(6) JNR (Japan) According to the JNR code in Japan [19] theDLF of steel bridge is defined by

DLF = 1 + 120583 (17a)

120583 =

10

65 + 119871

+

052

11987102

(17b)

120583max = 07 (17c)

for the double track railway the DLF should multiply thereduction factor 120572

if 119871 ⩽ 80m

120572 = 1 minus

119871

200

(18a)

and if 119871 gt 80m

120572 = 06 (18b)

Table 3 summarizes the dynamic load factors accordingto different bridge design codes By comparing the DLFs inTables 2 and 4 it can be noticed that the maximum DLF

obtained from the present study which is 11613 is close tothe specified values in the USA code and BSI-BS5400 codeAnd UIC Code China code and DS804 code are found to bethe most unsafe in deriving the value of the DLF for designpurposes

6 Conclusions

In this study an evaluation of dynamic load factors for ahigh-speed railway truss arch bridge was carried out usingthe monitoring strain data and finite element simulation Onthe basis of the results obtained from this particular studythe following conclusions which can provide reference forsimilar kinds of bridges can be drawn

(1) For each plane of steel truss arch the dynamic loadfactors (DLFs) decrease in turn in the bottom chordmember diagonal web member deck chord memberand top chordmember Furthermore for three planesof truss arch the dynamic effects induced by high-speed trains for middle truss arch are less than thosefor side truss arch

(2) Strong correlations were found between the trainlane and the DLF With the train lane closer tothe side truss arch the DLF is larger for the deckchordmember and smaller for the top chordmemberdiagonal web member and bottom chord member

(3) The mean DLF obtained from trains with 8 carriagesin a given sensor location was found to be larger thanthe mean DLF obtained from trains with 16 carriagesHowever it can also be noticed that the absolute valueof the increase is very small

(4) Even though weak correlations were found betweenthe speed of trains and the DLFs there exists anincreasing linear relationship (ie as the speed oftrains increases the DLF will also increase)

(5) The Generalized Extreme Value Distribution can welldescribe the probability characteristics of the DLFsbased on which the standard values of DLFs within50-year return period are evaluated and are close tothe specified values in the USA code and BSI-BS5400code

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 15

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Natural Science Foundationof China (no 51438002 and no 51578138) the FundamentalResearch Funds for the Central Universities (no2242016K41066) the Innovation Plan Program for OrdinaryUniversity Graduates of Jiangsu Province in 2014 (noKYLX 0156) and the Scientific Research Foundation ofGraduate School of Southeast University (no YBJJ1441)

References

[1] P Paultre O Chaallal and J Proulx ldquoBridge dynamics anddynamic amplification factorsmdasha review of analytical andexperimental findingsrdquo Canadian Journal of Civil Engineeringvol 19 no 2 pp 260ndash278 1992

[2] D L McLean and M L Marsh ldquoDynamic impact factorsfor bridgesrdquo NCHRP Synthesis 266 Transportation ResearchBoard Washington DC USA 1998

[3] L Deng C S Cai and M Barbato ldquoReliability-based dynamicload allowance for capacity rating of prestressed concrete girderbridgesrdquo Journal of Bridge Engineering vol 16 no 6 pp 872ndash880 2011

[4] L Ding H Hao and X Zhu ldquoEvaluation of dynamic vehicleaxle loads on bridges with different surface conditionsrdquo Journalof Sound and Vibration vol 323 no 3ndash5 pp 826ndash848 2009

[5] B A Demeke H T C Tommy and Y Ling ldquoEvaluation ofdynamic loads on a skew box girder continuous bridge Part Ifield test andmodal analysisrdquo Engineering Structures vol 29 no6 pp 1064ndash1073 2007

[6] H H Nassif and A S Nowak ldquoDynamic load for girder bridgesunder normal trafficrdquo Archives of Civil Engineering vol 42 no4 pp 381ndash400 1997

[7] A Miyamoto ldquoField tests for remaining life and load carryingcapacity assessment of concrete bridgesrdquo inBridgeMaintenanceSafety Management Resilience and Sustainability Proceedingsof the Sixth International IABMAS Conference Stresa LakeMaggiore Italy 8ndash12 July 2012 pp 157ndash164 CRC Press NewYork NY USA 2012

[8] Y S Park D K Shin and T J Chung ldquoInfluence of road surfaceroughness on dynamic impact factor of bridge by full-scaledynamic testingrdquo Canadian Journal of Civil Engineering vol 32no 5 pp 825ndash829 2005

[9] C C Caprani ldquoLifetime highway bridge traffic load effectfrom a combination of traffic states allowing for dynamicamplificationrdquo Journal of Bridge Engineering vol 18 no 9 pp901ndash909 2013

[10] L Deng and C S Cai ldquoDevelopment of dynamic impact factorfor performance evaluation of existing multi-girder concretebridgesrdquo Engineering Structures vol 32 no 1 pp 21ndash31 2010

[11] B Bakht and S G Pinjarkar ldquoDynamic testing of highwaybridgesmdasha reviewrdquo Transportation Research Record vol 1223pp 93ndash100 1989

[12] Eurocode ldquoThe European standard en Eurocode 1 action onstructuresrdquo 1991

[13] The American Railway Engineering and Maintenance of WayAssociationManual for Railway Engineering 2003

[14] UIC Loads to Be Considered in Railway Bridge Design UICCode 776-IR UIC Paris France 4th edition 1994

[15] BSI ldquoSteel concrete and composite bridgerdquo Tech Rep BSI-BS5400 1978

[16] TB100021-2005 ldquoFundamental code for design on railwaybridge and culvertrdquo 2005

[17] The Ministry of Railways The Temporary Regulation on theLatest Design of 200 kmsim250 km Special Railway for PassengersThe Ministry of Railways 2007 (Chinese)

[18] DS804 Vorschrift fur Eisenbahn Brucken and Sontige IngenieurBauwerke 1993 (German)

[19] Japan Road Association (JNR) Specifications for HighwayBridges 1978 (Japanese)

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of