TCIE_A_839603

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Author(s): Sudathip Tangwongchai

Article title: Suitable effective strip width of continuous bridge deck slabs system over flexible steel I-girders

Article no: 839603

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SudathipChartreeSomchai

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Chucheepsakul

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AQ1 Please provide an institutional e-mail address for corresponding author.

AQ2 The reference citation SAP2000 (2002) has been changed to Wilson et al. (2000) to match theauthor name and date in the reference list. Please check and confirm.

AQ3 The reference AASHTO (2004) is cited in the text but is not listed in the references list. Pleaseeither delete in-text citation or provide full reference details following journal style[http://www.tandf.co.uk/journals/authors/style/reference/tf_ChicagoAD.pdf].

AQ4 Please provide the name of the city of publication for reference American Concrete Institute [ACI](2008).

AQ5 The reference Barker and Puckett (1997) is listed in the references list but is not cited in the text.Please either cite the reference or remove it from the references list.

AQ6 The authors name in the following reference Fang et al. (1990) has been modified to match theCrossRef system. Kindly check and approve the edit.

AQ7 Please provide remaining authors name instead of et al. for reference Wilson et al. (2000).

AQ8 The reference WSD (2002) is cited in the table but is not listed in the references list. Please eitherdelete in-table citation or provide full reference details following journal style[http://www.tandf.co.uk/journals/authors/style/reference/tf_ChicagoAD.pdf].

Suitable effective strip width of continuous bridge deck slabs system over flexible steelI-girders

Sudathip Tangwongchai*, Chartree Lertsima and Somchai Chucheepsakul

Department of Civil Engineering, King Mongkuts University of Technology Thonburi, Bangkok 10140, Thailand

5 (Received 28 September 2010; accepted 30 August 2012)

Applying existing design standard provisions or analytical solutions is typically acceptable for the evaluation of slabnegative moments subjected to moving traffic loads. As a breakthrough in computer technology, the finite element-basedapproach has become a notably versatile tool used for bridge deck analysis. In this study, a reliable finite elementmodeling technique is employed to discretize the models of a continuous bridge deck slab over steel I-girder system.

10 The continuity between the girders and bridge slab has been carefully treated to ensure the overall structural action ofthe bridge deck. The key parameters affecting the deck slab moment such as slab system rigidity, girder spacing, patternsof moving loads and number of loaded traffic lanes are carefully considered in this study. The effective strip widthconcept has been used so as to take into account the evaluation of the slab negative moment. Based on the presentnumerical results, a set of reliable empirical formulas is proposed to determine the effective strip widths used for the

15 direct assessment of the negative moment in a bridge deck slab. The application of these formulas is then compared withother provisions. Based on the suggested formulas, the slab reinforcement can be moderated for a common range ofbridge deck proportions.

Keywords: effective strip width; slab-over-girder bridge; finite element model; negative slab moment

20 1. Introduction to the bridge deck analysis

Determination of the transverse bending moment in acomposite bridge deck has been a major concern ofdesign engineers for many years. In general, it is difficultto predict realistic behavior of a deck slab system using

25 hand calculations. The concrete deck on steel girderswith shear stud connection providing composite actionsis the most popular type of bridge in service nowadays.In bridge deck analysis, a major change in the positiveand negative transverse moments in the slab takes place

30 along the span due to moving trucks. A more realisticestimation of the slab deck moment can be obtainedwhen the longitudinal and transverse effects of the trucklocation are considered at the same time. To take intoaccount bridge deck analysis, current American

35 Association of State Highway and Transportation Offi-cials (AASHTO) design methods (Standard 2002; LRFD2007) have been widely used by engineers for their easeof use. AASHTO slab moment formulas seem to inade-quately reflect the actual moments due to the ignorance

40 of moving truck loads, girder deflection, and othersignificant characteristics of the composite deck system.In particular, more flexible girders will result in largerdifferential deflections among the girders leading to asmaller negative bending moment in the deck and a

45considerable reduction in the top reinforcing steel inbridge decks. A number of load patterns may increasethe bending moment in a deck slab, and therefore, arefined analysis may be required for this purpose.

Before the invention of digital computers, various50methods based on stiffness approach and specific assump-

tions such as the grillage analogy and orthotropic platehad been developed leading these classical approaches tobe excessively simplified. In recent times, it has beenwell recognized that three-dimensional (3D) finite

55element analysis (FEA) can closely approximate flexuralresponses in the deck slab of such configurations. UsingFEA, the limitation in analysis calculation has beenovercome. As a result, all parameters that influence thestructural behavior of composite deck systems can be

60incorporated in the analysis model at the same time.In the literature, although the negative slab moment

has been studied by several researchers (Bakht andJaeger 1985; Fang et al. 1990; Cao 1996), some discrep-ancies can be recognized among the different

65approaches. In general, the effective strip width concept(Standard 2002; LRFD 2007) has been widely used totake into account the evaluation of such negative slabmoments. The present study performs several casestudies on bridge geometries so as to investigate the

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*Corresponding author. Email: [email protected]

Journal of the Chinese Institute of Engineers, 2013http://dx.doi.org/10.1080/02533839.2013.839603

2013 The Chinese Institute of Engineers

TCIE 839603 CE: VK QA: SN7 September 2013 Coll: QC:Initial
Original text:Inserted TextPlease provide an institutional e-mail address for corresponding author.

5 parameters influencing the maximum negative momentsin the deck slab by means of the effective strip widthconcept. Extensive parametric studies on bridge geome-tries and the locations along the bridge span where thenegative slab moment is of interest are conducted based

10 on the refined 3D FEA. The effect of elastic supports aswell as a number of lane loads, which have never beenmentioned together in the literature, is also taken intoconsideration in this study. A general design guideline ofthe deck slab moment is then proposed based on the

15 effective strip width concept. In relation to the deck slabdesign viewpoint, the reinforcement requirementevaluated from the present study is also investigated bycomparing with AASHTO design codes.

2. Effective strip width approach

20 A slab on girders is a hybrid structure made up ofconcrete slab and steel girders so that this unit respondsas a composite body. Figure 1(b) shows the primarydeflection of the bridge deck induced by truck wheelloads as the slab is supported by rigid girders. The effect

25 of secondary deflection of the bridge deck due to truckwheel loads is demonstrated in Figure 1(c). Therefore,the overall deflection in Figure 1(a) can be accomplishedby separated analyses of primary deflection in Figure 1(b)and secondary deflection in Figure 1(c). As a rule,

30 primary deflection appears to induce a significant influ-ence on the live load negative moment in deck slab (MLL)at the location where the girders are rigidly restrainedwhile the secondary deflection tends to produce thecontrary effect. As a result, great reduction in the nega-

35 tive moment but increase in the positive moment in theslab can be clearly observed in the vicinity of midspanwhere the secondary deflection is predominant.

The effective strip width (BE) concept has been stud-ied for a long time to use as a simplified method for the

40 evaluation of MLL. The early well-known study on thistopic was conducted by Westergaard (1930). To be ableto determine MLL, a so-called effective strip widthapproach has been proposed by several researchers anddesign provisions (AASHTO 2002, 2007; Tangwongchai

45 2003) and adopted as a useful formula to compute the

maximum MLL per unit width of slab. The effective stripwidth BE was developed by assuming that the momentwas distributed uniformly over a certain width of asimple span slab in the direction perpendicular to the

50span of the slabs S as defined below:

BE PS4MLL 1

A modification of Westergaards original proposalwas performed so that BE for a two-edge simply

55supported slab can be determined as 1.90S+ 6.56c, whereS is the center-to-center spacing of the girders in metersand c is the diameter of the equivalent area of a wheelload in meters as demonstrated in Figure 2. It should benoted that BE was adopted to determine the maximum

60moment per unit width in a simply supported slab in thelast edition of AASHTO Standard Specifications (2002).According to AASHTO Specifications (2002) oncontinuous slabs over three or more supported girders, acontinuity factor of 0.8 shall be applied to the simple

65span live load moment for both positive and negativemoments. In AASHTO LRFD Specifications (2007), BEused to compute MLL as recommended in Table 4.6.2.1.3-1 is equal to 1220 + 0.25Smm (48 + 3S in.) for cast-in-place decks where S is the center-to-center spacing of

70the girders in mm.Instead using either Specifications (2002, 2007) or

Westergaard (1930), the approximate elastic method ofanalysis simulates the behavior of the bridge deck withtransverse strips of deck provided to compute the

75moment, MLL. The strip width for negative bending BEis recommended in this study. The strips based on FEAmodeling are run from edge-to-edge of the bridge deckand are modeled as continuous beams supported at thecenterlines of the girders. When using the recommended

80strips, the slab moments MLL can be computed with anequivalent one-way bending strip BE.

3. FEA modeling of bridge deck

In this study, a refined FEA modeling technique isemployed to predict an MLL closer to the reality.

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Figure 1. Typical deformations of bridge deck under truck loading: (a) total deflection; (b) primary deflection; (c) secondarydeflection.

2 S. Tangwongchai et al.


5 The analytical models are developed using a well-knowncomputer program SAP2000 (Wilson et al. 2000).Several concerns of the bridge deck configurations, i.e.the diaphragm connection with girders, loading patternswhich produce the most adverse effects due to combined

10 global and local loading, the eccentricity between thedeck slab and the centroid of girder, the eccentricitybetween the centroid of girder and the bearing supports,the effect of longitudinal compressive force in the slabon its flexural behavior through effect of Poissons ratio,

15 and the shear connection between the slab and girder areexplicitly considered in the present study.

To simulate an FEA model of a bridge deck moreaccurately, many databases of bridges (Lee and Yau2002; CAN/CSA-S6-06 2006; Tangwongchai and

20 Chucheepsakul 2006) are reviewed to select the appro-priate geometric parameters on the basis of applicableranges for bridge design practice. Based mostly onconstruction frequencies, all possible combinations ofparameters that characterize the geometry of a composite

25 steel-concrete bridge are considered in FEA modeling soas to reveal those influences on BE under various loadingpatterns of design trucks at the different span locations(y). In particular, the following parameters are consideredas follows: S = 1.50m (5 ft), 1.80m (6 ft), 2.30m

30 (7.50 ft), 3m (10 ft); y/L= 0 (at support), 0.25 (at quarterspan), 0.50 (at midspan); L/H = 18 where L and H standfor span length and height of I-girders, respectively; fourflexible stiffnesses Dy/Dx (Cao 1996) = 74.71, 65.29,55.15, 44.09. It should be noted that Dy and Dx are

35 based on an orthotropic plate theory to account for thedifferent bending stiffnesses of a deck in the longitudinal(Dy parallel to the traffic) and transverse directions (Dx).For the finite element modeling, the authors use fixedvalues of slab thickness (t), L, and H constantly 0.20m

40 (8 in.), 15.24m (50 ft), and 0.86m (33.93 in.), respec-tively, while the others are varied to obtain all values ofthe parameters. The considered bridge deck configura-tions are demonstrated in Figure 3.

In this study, the bridge deck composite-action45 behavior is also taken into consideration in the FEA

model. The interaction between the deck slab discretizedby shell elements and the girder discretized by beam

elements is simulated into the Eccentric Shell-BeamModel (ESBM). Figure 4(a) and (b) show the physical

50configurations and ESBM in FEA for a Slab-on-girderbridge used in this study, where e2 is a distance betweenthe neutral axis of the composite section (T-shape inFigure 4(a)) and the midplane of the slab, and e1 isdistance between the neutral axis of the T-section and

55that of the girder.To take into account the eccentricity between the

deck slab and the centroid of girder (e1 + e2), the shellelements are connected to beam elements by a so-calledrigid link element to resist shear and bending. The rigid

60link element is short in length, and it connects themidplane of the slab with the centroid of girder-frame.The supports of girders are simulated by using dimen-sionless beam elements to account for the eccentricitybetween the centroid of girders and the bearing supports.

65In practice, ESBM (see Figure 4(b)) has been selectedherein since it is usually reliable while retaining simplic-ity for the surface structure in transverse analysis as well

S/2 S/2

BE

P

c

y

x

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Figure 2. BE and infinitesimal region (c) of a design load P.

Figure 3. Typical bridge deck configurations.

Figure 4. Physical configuration and FEA modeling of a slab-on-girder bridge: (a) 3-D physical T-section; (b) 3-D physicalT-section.

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Journal of the Chinese Institute of Engineers 3

Original text:Inserted TextThe reference citation SAP2000 (2002) has been changed to Wilson et al. (2000) to match the author name and date in the reference list. Please check and confirm.

as in longitudinal direction (Chan and Chan 1999; Bapat2009). Throughout this study, pinned-roller restraints are

5 used for the sake of simply supported and continuoussupported conditions for 1-span truck loading and 2-spantruck loading, respectively. Based on the customarydesign practice of bridge decks, Poissons ratios of aconcrete slab and steel girders are designated as 0.20

10 and 0.30, respectively. The concrete slab has a 28-daycompressive strength fc of 35.58MPa (5.16 ksi) resultingin the concrete elastic modulus Ec of 28,270MPa(4100 ksi) according to recommendation of ACI 318-08

(2008). For steel girders, the magnitude of steel elastic15modulus Eg is selected as 199,950MPa (29,000 ksi). The

integer number of the Modula ratio n (Eg/Ec) of 7 isused.

4. Loading conditions

The bridge deck is loaded in different vehicle patterns20which may occur during a real traffic situation, single

trucks and groups of trucks are placed at specific loca-tions along the longitudinal span of the bridge and the

Figure 5. Possible patterns of trucks in transverse direction for MLL evaluation: (a) NL= 1; (b) NL= 2; (c) NL= 3.



trucks are then placed at different transverse locationsfor trial and error. It is considered that a design truck

5 (HS-20 design truck) can be placed anywhere within aclear width w of a roadway for extreme effect due todifferent number of traffic lanes NL. It is assumed thatthe wheels of a single axle are spaced at 1.83m (6 ft),and the minimum distance between the wheels of two

10 side-by-side truck is 1.22m (4 ft). Figure 5 demonstratesthe schematic of possible patterns of truck moving later-ally on a typical bridge roadway width for the evaluationof MLL.

In the loading analysis, the bridge is divided into15 four sections for the purpose of result processing and

comparison. The maximum moment M usually occurs ateither the middle or rear wheel location. Near the abut-ment, as shown in Figure 6(a), the critical negativemoments usually occur under the rear wheel (Y2). At the

20 midspan as shown in Figure 6(b), the maximum momentM usually occurs under the middle wheel (Yc) and whenthe spacing between the middle and rear axles (V) isequal to 9.14m (30 ft). The variations of V are variedbetween 4.27m (14 ft) and 9.14m (30 ft) to produce

25 extreme force effects (AASHTO 2004).A wheel load is modeled as a patch load distributed

over a finite area in FEA models. The tire contact areafor an HS20-44 truck is assumed as a rectangle, with alength of 0.51m (20 in.) and a width of 0.25m (10 in.)

30 (AASHTO 2007). To attain a more accurate estimationof critical moments M, the tire print loads are enlargedby spreading outwards through the midplane of the slab

at critical sections. The contact area of a wheel load isenlarged by projecting on the midplane of the slab with

35a distribution angle of 45 (AASHTO 2007) as illus-trated in the Figure 7.

5. Numerical results

The characteristic results of the present parameters influ-encing MLL in deck slab are scrutinized. Figure 8 shows

40the typical effect of S on the proportion expressed by theratio between MLL and an HS20-44 truck wheel load Pof 72.5 kN (16 kips) (MLL/P) for three different locationsalong bridge span (y/L= 0, 0.25 and 0.50). In this study,impact factor IM of 1.33 and multiple presence factors m

45of 1.20, 1.00, and 0.85 for 1-lane, 2-lane, and 3-laneloadings, respectively, are presented to MLL/P inaccordance with recommendation of AASHTO LRFD

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Figure 6. Longitudinal locations of centers of governing gravity axes: (a) under Y2 at rigid zones (V= 4.27m); (b) under Yc atflexible zones (V= 4.279.14m).

Figure 7. Dispersion of truck wheel loads on deck slab.

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Original text:Inserted TextThe reference AASHTO (2004) is cited in the text but is not listed in the references list. Please either delete in-text citation or provide full reference details following journal style

(2007). In particular, MLL/P starts decreasing with theincrease of y/L. That is to say the magnitude of MLL/P

5 appears to be larger near the support (y/L= 0) and smal-ler in the region of midspan (y/L= 0.50). Likewise, S hasconsiderable influence on MLL/P: as S becomes larger,MLL/P increases in general especially at the supportregion (y/L= 0). Moreover, NL seems to produce influ-

10 ence on MLL/P to a certain extent. However, the effect of

NL appears to be identical when NL is equal to two andthree as illustrated in Figure 8(b) and (c).

Based on the present numerical results, BE can becalculated according to Equation (1) for each S, y/L, and

15NL. Table 1 shows the comparison between BE calculatedfrom the present FEA with respect to spacing S and loca-tion designated y/L and those obtained from AASHTOSpecifications (Standard 2002; LRFD 2007).

With respect to the present FEA results, it can be seen20that y/L is influential on BE to the greatest extent in

accordance with the assumptions used by Cao and Shing(1999). The maximum NL of three gives the maximumMLL by implying the minimum value of BE. In addition,it is apparent that BE is usually maximum at the midspan

25section (y/L= 0.50), where the structural flexibility ofbridge deck is largest. On the other hand, the minimumBE can be observed, where the bridge deck is rigidlyrestrained at the support (y/L= 0). However, someinconsistencies can be observed between BE at the quarter

30span and midspan. In some circumstances, BE at thequarter span is larger than the midspan. This is becauseof the accompanying effects of girder spacing S andnumber of lane loaded NL. Those parameters also producea significant influence on BE. Therefore, the present BE

35includes not only the effect of structural flexibility ofbridge deck (y/L and S) but also loading characteristics(NL).

6. Proposed effective strip widths BEInstead of using Table 1, the following empirical formu-

40las have been proposed to directly compute BE in theevaluation of MLL. In addition, it is apparent that BE isusually maximum at the midspan section when the struc-tural flexibility of bridge deck is largest. On the otherhand, the minimum BE can be observed when the bridge

45deck is rigidly restrained at the support. Based on regres-sion analyses, the general relationship of BE is thendeveloped. The formulations of BE are proposed in termsof S and y/L as follows:

For support region:

BE 0:12S2 0:87S 2:24 250

For other regions:

BE 0:01S2 0:19S 1:55 3

55It is noted that this formula is applicable for1.5m6 S6 3m, S/L6 0.02, S/t6 18.

7. Required reinforcement area in bridge deck slab

In general, several provisions have recommended theminimum amount of reinforcement area (Asmin) or

0.00 .25 .50

100

mM

LL

- /P

0

3

6

9

12

15

18

21

24

27

30

33

S = 1.5 m

S = 1.8 m

S = 2.3 m

S = 3 m

0.00 .25 .500

3

6

9

12

15

18

21

24

27

30

33

S = 1.5 m

S = 1.8 m

S = 2.3 m

S = 3 m

Locations Along Bridge Span, y/L



0.00 .25 .50

100M

LL

- /P10

0ML

L- /P

0

3

6

9

12

15

18

21

24

27

30

33

S = 1.5 m S = 1.8 m S = 2.3 m S = 3 m

(a)

(b)

(c)

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Figure 8. Variation of MLL/P with respect to locationdesignated y/L: (a) one lane loaded (NL= 1); (b) two laneloaded (NL= 2); (c) three lane loaded (NL= 3).



5 percentage of reinforcement area in gross concretesection for each top layer provided in the deck slab ineach direction. For instance, Asmin of 0.380mm

2/mm(about 0.20% reinforcement steel) has been providedaccording to AASHTO (2007) by means of the empirical

10 design method while Asmin of 0.30% has been suggestedby BD 81/02 (2002) and CHBDC (2006). To deal withMLL, the required reinforcement areas in transversedirection of deck slab (AsT) calculated by differentapproaches are shown in Figure 9. It is apparent that AsT

15 computed by the present proposed formula of BE givesmoderate results of AsT compared with those obtainedfrom AASHTO Specifications. When compared withCHBDC (2006) and BD 81/02 (2002), which have thebasic concept of arching action (compression membrane

20 action), the present study tends to give underestimatedresults of BE to a certain extent.

According to the present study, it has been suggestedthat current AASHTO design procedures should benoticeably conservative as they usually give considerably

25 larger MLL than the present FEA. The potential

advantage of the present FEA is that the amounts of slabreinforcements can be lower compared with theAASHTO counterpart. It should be noted that AASHTOor empirical method is based mainly on the consideration

30of punching shear failure. However, flexure is theprimary failure mode when a deck is subjected tomoving loads (Cao 1996). In the utilization of thisdesign concept, it is important to note that the design ofa bridge deck is expected to be more economical than

35traditional designs.

8. Concluding remarks

The present study performs a parametric study on bridgegeometries and patterns of truck loading base on aso-called ESBM technique. Among the parameters that

40have influence on the negative slab moment MLL, thepresent analysis reveals that the location designated bythe ratio between distance along the bridge span awayfrom the support y and bridge span L (y/L) can producea significant effect on MLL. Moreover, girder spacing S

45is also influential on MLL to a great extent. Based on thepresent numerical results, empirical formulas have beenproposed to determine the effective strip width BE.Compared with other existing methods in evaluation ofMLL, the proposed BE formulas appear to provide

50moderate results for required reinforcement areas inbridge deck slabs. The present study has also impliedthat bridge slab reinforcement may be minimized whena bridge with small girder spacing has been selected.This should result in more realistic and economical

55designs of bridge deck slabs for the common ranges ofdeck slab proportions under various numbers of truckloadings.

AcknowledgementsThe present research was partially supported by the Thailand

60Research Fund through the Royal Golden Jubilee PhD Program[grant no. PHD/0167/2546]. The first author also owes verygreat supports to her co-advisor (P. Benson Shing).

Table 1. Obtaining widths BE in meter using FEA, AASHTO LRFD, and standards method.

Girder spacing S, m (ft)

FEA (including m factors (LRFD 2007) AASHTO

Ratios between distance along girder y and girder span L, y/L

LRFD (2007) WSD (2002)

Support, 0 Quarter span, 0.25 Middle span, 0.50

Number of loaded traffic lanes, NL

1 2 3 1 2 3 1 2 3

1.5 (5) 1.26 1.23 1.22 1.93 1.63 1.35 1.78 1.30 1.28 0.78 0.661.8 (6) 1.07 1.03 1.00 1.55 1.39 1.27 1.67 1.38 1.21 0.69 0.702.3 (7.5) 1.03 0.91 0.90 1.59 1.40 1.16 1.59 1.41 1.22 0.67 0.733 (10) 0.93 0.73 0.68 1.65 1.20 1.04 1.79 1.33 1.15 0.72 0.77

Figure 9. Percentages of reinforcement area AsT/Asmin due todifferent methods vs. S.

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Original text:Inserted TextThe reference WSD (2002) is cited in the table but is not listed in the references list. Please either delete in-table citation or provide full reference details following journal style

Nomenclature

Asmin Minimum amount of reinforcement area in transversedirection of deck slab

AsT10 Required amount of reinforcement area in transversedirection of deck slab

BE Effective strip widthc15 Diameter of the equivalent area of a wheel loadDx Flexible stiffness of a deck in transverse directionDy Flexible stiffness of a deck in longitudinal direction

20 Ec Modulus of elasticity of the concrete deckEg Modulus of elasticity of the girdere125 Distance between neutral axis of composite section

(T-shape) and that of the girdere2 Distance between neutral axis of T-section and

mid-plane of the slab30 L Span length of I-girder

MLL Live load moment in deck slabMLL35 Critical negative moment in deck slab due to live loadNL Number of traffic lanesP Design wheel load

40 S Center-to-center spacing of I-girderst Slab thicknessV45 Spacing between the middle and rear axlesy Parameter of longitudinal loading locationsY1 Longitudinal location of front wheel

50 Y2 Longitudinal location of rear wheelYc Longitudinal location of middle wheel

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Original text:Inserted TextPlease provide the name of the city of publication for reference American Concrete Institute [ACI] (2008).Original text:Inserted TextThe reference Barker and Puckett (1997) is listed in the references list but is not cited in the text. Please either cite the reference or remove it from the references list.Original text:Inserted TextThe authors name in the following reference Fang et al. (1990) has been modified to match the CrossRef system. Kindly check and approve the edit.Original text:Inserted TextPlease provide remaining authors name instead of et al. for reference Wilson et al. (2000).

TCIE_A_839603

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Transcript of TCIE_A_839603