Research ArticleFlexural Behavior of Slab-Rib Integrated Bridge Decks with GFRPSkin and Polyurethane Foam Core

Jing Li1 Jun Wang 1 Bishnu Prasad Yadav1 Jiye Chen2 Qiang Jin3 and Weiqing Liu 1

1College of Civil Engineering Nanjing Tech University Nanjing China2School of Civil Engineering and Surveying University of Portsmouth Portsmouth UK3College of Civil and Hydraulic Engineering Xinjiang Agricultural University Urumqi China

Correspondence should be addressed to Jun Wang wangjun3312njtecheducn

Received 26 June 2019 Accepted 11 August 2020 Published 3 December 2020

Academic Editor Ivan Giorgio

Copyright copy 2020 Jing Li et al is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

is paper presents experimental and analytical studies on flexural behavior of slab-rib integrated Sandwich composite deckseinfluences of layers of glass fiber-reinforced polymer (GFRP) facesheets foam densities and the existence of webs and cross beamsare discussed herein e test results showed that the existence of vertical webs remarkably improved the debonding of thefacesheets from the foam core thus increasing the ultimate load by 59 compared with the specimens without webs However theexistence of horizontal webs has insignificant effect on the failure mode and ultimate load Increasing the number of layers ofGFRP facesheets from 2 to 4 and 6 results in 100 and 214 increments in ultimate loads respectively while the specimen withlower density of foam had a higher ultimate load than the specimen with higher density of foam due to deformation compatibilitybetween GFRP skins and foam core with low density e analysis software Abaqus Explicit was used to simulate the flexuralbehavior of test specimens and the numerical results agreed well with the test datae verified finite element model was extendedto analyze the influences of the number of GFRP layers on the top of decks and the height of vertical webs Based on equivalentmethod and compatibility of shear deformation the flexural and shear rigidities were estimated en analytical solution fordisplacement of the slab-rib integrated Sandwich composite decks subjected to four-point load was derived out Comparison ofanalytical and experimental results shows that the displacements can be precisely predicted by the present theoretical model

1 Introduction

Fiber-reinforced polymer (FRP) sandwich compositesconsisted of two thin facesheets and low-density cores andhave been successfully applied as bridge decks bumps foranti-collision of piers structural walls and roofs etc in civilinfrastructure [1ndash4] due to their advantageous properties oflight weight high flexural strength and rigidity and sub-stantial resistance to corrosion Compared with pultrudedhollow FRP modules foam-filled sandwich composites ex-hibit improvement on local buckling of the lamina andcontribute to decreasing the stress concentration at the web-flange joint [5] Among their applications in bridges FRPsandwiches used as decks in deck-girder bridges or as slabsare beneficial for maintenance purposes and convenience ofthe replacement of the bridge to accommodate traffic

increment In the case of reinforced concrete (RC) deckreplacement FRP sandwich slabs usually have high thick-ness to provide the required flexural rigiditye behavior ofFRP Sandwich decks is greatly influenced by the choice ofcross section and materials

e performance of constructed bridges with FRPSandwich decks is of interest to the researchers and trans-portation agencies Sharaf et al [6] investigated the flexuralbehavior of GFRP-polyurethane foam sandwich panels withdifferent foam densities It was shown that the ultimate loadand stiffness increased by 165 and 113 as the coredensity was doubled However significant relative hori-zontal slip occurred between the upper and lower skins dueto the shear deformation of foam core [6] Chen and Davalos[7] studied the strength properties of the facesheet ofsandwich composite panels with honeycomb core and

HindawiAdvances in Materials Science and EngineeringVolume 2020 Article ID 3597056 14 pageshttpsdoiorg10115520203597056

developed an optimized facesheet configuration eysuggested that the compressive strength of the facesheet wasmore critical and controlled the design e design and fieldtesting of a GFRP corrugated-core sandwich bridge indi-cated that the dynamic effects were insignificant and thisstructure is a competitive short-span bridge alternative [8]In order to improve the structural efficiency and decrease thedeck weight Osei-Antw et al [9] designed a novel GFRPsandwich slab-bridge in which the core consisted of high-density and low-density balsa and a FRP arch Although theperformance of this bridge structure is much better thanstructures with uniform core the complex configuration andfabrication obstruct its extensive application

One of the most severe defects associated with sandwichcomposite decks is the face-core delamination Many studieshave been carried out to improve the debonding resistanceMohamed et al [10] compared the mechanical behaviors ofGFRP sandwich structures with web-core trapezoid andpolyurethane rigid foam eir test results showed thatspecimens with trapezoid foam core had highest load carryingcapacity under flexural loads and compression due to thepresence of shear layer A similar approach of trapezoidal-shaped polyurethane foam core was considered by Tuwairet al [11] who found that the shear webs contributed sig-nificantly to delaying the delamination of the skins from thecoree numerical analysis of Mostafa et al [12] showed thatinserting shear keys between the GFRP facesheets and thePVC foam core would improve the shear resistance of thesandwich panels and the panels with uniaxial shear keys hadhigher shear strength than the panels with bi-axial shear keysis is because the shear keys cause the loss of the solidarity ofthe bulk materials at the foam surface Reis and Rizkalla [13]investigated the mechanical behavior of 3-dimensional (3D)GFRP sandwich panels and found that increasing the densityof through-thickness fibers resulted in decreasing the tensilestrength of the facesheets significantly due to the wavinessamong the fibers in the perpendicular direction

Although significant advancements have been made onFRP sandwich composites over the last two decades biggertolerance occurs in the hand layup sandwiches than inpultruded profiles Furthermore the intricate connectingdetails in deck-girder bridges are more challenging than theintegrated structures [14 15] To decrease the number ofconnections and improve the overall performance ofcomposite decks this work aims to develop a slab-rib in-tegrated composite sandwich deck e mechanical prop-erties of both the composite and foam materials areoptimally designed for flexural loads Flexural tests havebeen conducted on nine slab-rib integrated sandwich deckswith GFRP skins and polyurethane foam core FRP layersfoam densities horizontal and vertical webs and crossbeams were varied to study the deck behavior A 3D finiteelement (FE) model is constructed and the results arecompared with the experimental data e FE model wasfurther used to investigate the influence of height of verticalwebs and thickness of FRP skin in the compression regionMoreover based on equivalent method and compatibility ofshear deformation the flexural and shear rigidities of in-tegrated sandwich decks were obtained en Timoshenko

Beam eory (TBT) was applied to calculate the deforma-tions of sandwich decks under flexural loads Comparisonsof analytical and experimental results are presented anddiscussed

2 Slab-Rib Integrated Bridge Deck Systems

21 Description of the System Geometry e bridge decksystem consists of a slab and two ribs (Figure 1) e ribscontribute to improving the longitudinal stiffness of the slab intraffic direction e study of Fettahoglu [16] showed thatlocalized high stress concentrations occurred in the slab withthickness less than 10mm under wheel loads MoreoverEurocode 3 part 2 [17] suggests the ratio of distance betweenribs to slab thickness et is no more than 25 and the rib spacinge is no more than 300mm under wheel loads us the heightof the foam core of slab is taken as 55mm and the distance offoam core between the ribs is taken as 260mm Because theheight of ribs has more significant influence on the defor-mation the deck than the width of ribs the width-to-heightratio of the foam core of the ribs is taken as 067 e overalllength andwidth of the slab foam are 2m and 06me lengthof the rib foams is the same as that of slabs

Five types of slab-rib integrated deck systems with thesame overall dimension are designed to evaluate the effectsof webs and cross beams as shown in Figure 1 (1) withoutwebs and cross beams (2) with vertical webs (3) withhorizontal webs (4) with vertical and horizontal webs (5)with cross webs For deck systems with cross beams twodifferent arrangements of cross beams are investigated (1)located in the mid-span and supports and (2) located in thesupports merely Figure 1 shows the cross section and 3Dsketches of the different types of deck systems

e test specimens differed in terms of the number ofglass fabric layers of the FRP facesheets (ie fiber volumepercent) the vertical and horizontal webs the cross beamsand the density of polyurethane foams e thickness of allGFRP webs is 16mme cross beams are of the same widthand height of foam cores as ribs

22 Material Properties e face skins and vertical andhorizontal webs were fabricated using E-glass fabrics andvinyl ester resin e fiber volume in both the longitudinaland circumferential portions is 1 1 Five tension couponswere tested according to ASTM D 638 [18] Table 1 lists thetension properties of GFRP laminates Two types of closed-cell polyurethane foams with density of 100 kgm3 and150 kgm3 were used in this study For each density fivecubic coupons with side length of 50mm were tested inaccordance with ASTM D C 365C 365 [19] to obtain thecompressive properties Table 2 presents the measuredproperties of polyurethane foams

3 Experimental Program

31 Specimen for Test Nine specimens were prepared tostudy the flexural behavior of slab-rib integrated bridgedecks with GFRP composite skins and polyurethane foamcore Table 3 lists the details of the test specimens To make

2 Advances in Materials Science and Engineering

the slab-rib structures (Figure 2) the foam panels were cutinto separations for slabs ribs and diaphragms Orthogonalgrids (25mmtimes 25mmtimes 2mm) were grooved and holes withdiameter of 5mm and depth of 2mm were drilled on thesurface of the foam panels to enhance the bonding strengthbetween the GFRP skin and foam core Before wrappingwith bidirectional glass fabric layers the foam separationswere assembled into slab-rib structures en vacuum-assisted resin infusion process was used to fabricate thespecimens

32 Experimental Setup e specimens were tested underfour-point flexural loads acted at about one-third in-tervals of the span e experimental setup consists of a500 kN load cell which transfers the load to two loadheads using a spreader steel beame deflections at mid-span and supports were measured using linear variabledisplacement transducers (LVDTs) e typical test setupof four-point simply supported decks is shown in

Figure 3 In order to monitor stress state of the mid-spancross section 12 strain gages (gauge length 10 mm) werebonded to the top side and bottom surfaces of the testspecimens as shown in Figure 4 Static loads were ap-plied at a rate of 2 mmmin All the specimens were testedto a point where the loading could not be increasedanymore

4 Experimental Results and Discussion

41 Failure Modes Figure 5 provides a summary of thetypical failure modes e failures of specimens withoutwebs and cross beams (ie S2D S4D and S6D) weregoverned by debonding of GFRP facesheets from the foamcore outward facing wrinkled tearing of facesheets in thecorner of slabs near the loading points and shear cracksthat propagated from the narrow side of slabs to ribsMoreover transverse cracks appeared on the back of slabsdue to the shear failure of GFRP facesheets under theloading points e specimens with different layers ofGFRP facesheets exhibited similar failure modes Con-trary to expectations the specimen with lower foamdensity has much smaller debonding area on the topfacesheets than the specimens with higher foam densityis may be attributed to the lower rigidity of foams withsmaller density which allows compatible deformationunder debonding loads

1

2

t

t

6010

5100 70 260

(a)

2

3 1

(b)

2

4 1

(c)

4 3 1

2

(d)

Slab

RibCross beam

(e)

Figure 1 Configuration of slab-rib integrated bridge deck systems (a) cross section of sandwich decks without webs (b) cross section ofsandwich decks with vertical webs (c) cross section of sandwich decks with horizontal webs (d) cross section of sandwich decks with verticaland horizontal webs and (e) 3D view of decks with cross beams (1 foam core 2 FRP skin 3 vertical webs 4 horizontal webs)

Table 1 Tensile properties of GFRP

Property Value e ()Tensile strength (MPa) 304 831Tensile modulus (GPa) 26 647Poissonrsquos ratio 022 657e coefficient of variation

Advances in Materials Science and Engineering 3

e specimen with horizontal webs has similar failurepattern with the specimen without webs while the specimenwith vertical webs showed full bond between skins and thecores under vertical loads Crushing of the top skin and foamat the loading points dominated the failure modes ofspecimens with vertical webs is suggests that addingvertical webs is a reliable method to prevent the debondingof facesheets and foam core

e specimen with cross beams at the supports exhibitedshear failure of foam and crushing of skins at the loadingpoint and no obvious debonding of the skins was observedFor specimen with 3 cross beams at the supports and mid-span the top face was multi-waved wrinkled due to thedebonding of facesheets e additional cross beam in themid-span is unable to play a positive role in this structure

42 Load-Displacement Curves Load versus mid-span dis-placement measured from the test specimens is presented inFigure 6 along with a discussion on the effect of variousparameters on the structural behavior of the slab-rib decksAll the test specimens exhibited similar load-displacementprofiles e load increased almost linearly up to themaximum and then suddenly decreased when the GFRPfacesheets on the top of slabs were crushed near the loadingpoints After that the load increased until a new crackformed in the inner foams

It is obvious that the rigidity of slab-rib decks was ac-cordingly increased as the layer number of GFRP skinsincreased Very thin woven fabric layers may result inpremature failure of the facesheets in the loading pointIndeed the ultimate loads of specimens with 4 and 6 layersof GFRP skins are two and three times as much as that of

specimens with 2 layers of GFRP skins respectively and theultimate deformation increased by about 25 On thecontrary the ultimate load of specimen with foam density of100 kgm3 was 33 higher than that of specimen with foamdensity of 150 kgm3 is is because debonding of the topfacesheets and local buckling of GFRP dominate the failuremodes of specimens with higher foam density while thedebonding of facesheets does not extensively occur in thespecimens with lower foam density

e specimen with horizontal webs has similar ultimateload and slope of linear phase of load-displacement curve asspecimens without webs while the ultimate load of thespecimen with vertical webs is 59 higher than the specimenwithout webs e specimen with horizontal and verticalwebs has a little higher ultimate load (6) than the specimenwith vertical webs is suggests that adding vertical webs inslab-rib sandwich decks is a more reliable method to im-prove the debonding of facesheets and enhance the loadcarry capacity than adding horizontal webs

By comparing the responses of specimens with andwithout cross beams it can be concluded that adding 2 crossbeams at the supports contributes to increasing the ultimateloads by 27 while adding 3 cross beams at the supports andmid-span is not useful to enhance the ultimate loads andrigidity e additional cross beam in the mid-span tends toprevent the transverse deformation of the ribs and then theincompatible deformation occurred between the foam coreand skins resulting in large area debonding of facesheets

43 Strain Distributions Figure 7 shows the typical mid-span strain distribution through the depth of slab-ribsandwich decks For specimen without webs and crossbeams the longitudinal strain distributions remained flat upto 80 of ultimate load and the strains increased almostlinearly with increasing load e specimens with additionalhorizontal webs and cross beams at supports have similarstrain distribution to specimens without webs and crossbeams However the specimens with vertical webs or twocross beams behaved nonlinearly during loadinge strainsof the bottom facesheets of specimen with three cross beamsexhibited a bias to large value is is the reason that thespecimen with three cross beams is more prone to failurethan others

5 FE Model Construction

e finite element software ABAQUS has been successfullyused to simulate the performance of steel bridge deckpavement with fiber-reinforced epoxy resin-modified as-phalt [20] In this paper a 3D FE model has been developedusing Abaqus Explicit to analyze the flexural properties of

Table 3 Summary of test matrix and results

Specimen P (kN) P1(kN) P1P δ1 (mm) δ2 (mm) δ2δ1S2D 3435 3164 092 2655 2495 094S4D 6866 7284 106 3327 3108 083S6D 10770 10901 101 3379 2973 088S4d 9115 8767 096 3895 3526 091S4DV 10925 11718 107 3889 3453 089S4DH 6873 7123 104 3146 2715 086S4DVH 11561 12105 105 4568 3996 088S4DT2 8719 9223 106 3852 mdash mdashS4DT3 6556 7064 108 2980 mdash mdashIn the first column the letters d andDmean the densities of synthetic foamsare 100 kgm3 and 150 kgm3 respectively the letters V and H mean thespecimens have vertical and horizontal webs the letter T means thespecimens have cross beams the first number means the number of FRPlayers of the GFRP skins and the numbers 2 and 3 mean the number ofcross beams respectively In the first row P is the tested ultimate load andP1 is the ultimate load obtained from FE model δ1 is the tested maximumdeformation and δ2 is the calculated deformation from equation (17)

Table 2 Compressive properties of PU foams

Foam density (kgm3) Compressive strength (MPa) e () Compressive modulus (MPa) e ()100 0767 657 15527 527150 1566 357 3764 608e coefficient of variation

4 Advances in Materials Science and Engineering

(a) (b) (c)

(d) (e) (f )

Figure 2 Fabrication procedure of test specimens (a) the separation foams which have been grooved and drilled on the surface (b)assembling foams of slab and ribs (c) assembling diaphragms (d) wrapping the assembled foams with GFRP and (e f ) vacuum-assistedresin infusion process

1700

720

S4D

Figure 3 Test setup (units mm)

21

3

(a)

4~9

LVDT 2

LVDT 1

LVDT 3

(b)

1000 1000

101112

(c)

Figure 4 Locations of LVDTs and strain gauges (a) plane view from the top (b) side view and (c) plane view from the bottom (units mm)

Advances in Materials Science and Engineering 5

slab-rib integrated decks e material properties of bothGFRP and polyurethane foam were obtained from coupontest results e GFRP facesheets and webs are assumed tobehave in a linear elastic manner and the Hashin criterion isused to predict the failure of GFRP Hashin failure criteriahas been successfully applied to predict failure and post-failure of anisotropic fiber-reinforced materials [21] ematerial property of polyurethane foam is specified in the

elastic-plastic model in which the plasticity modulus istaken as 50 of elastic modulus

GFRP facesheets and webs are modeled by S4R shellelement while polyurethane foam is modeled by C3D8Rbrick element e test specimens are simply supportedSurface-to-surface contact elements are used to simulate theinterface between GFRP and foam core is type of contactconsiders slip and separation Hence slipdebonding is

(a) (b) (c)

(d) (e) (f )

(g) (h) (i)

(j) (k) (l)

Figure 5 Failure modes (a) S2D (b) S4D (c) S4D (d) S6D (e) S4DH (f ) S4DV (g) S4DVH (h) S4DV (i) S4d (j) S4d (k) S4DT2(l) S4DT3

6 Advances in Materials Science and Engineering

displayed if either occurs between the GFRP surface andfoam surface e friction coefficient is taken as 03 for thecontact surface of GFRP and foam core

51 Comparison of Numerical and Experimental Resultse simulated failure modes of typical specimens are shownin Figure 8 e FE model successfully captures the localbuckling of the top facesheets of the test specimens eMises stress of S4DV at the loading points was smaller thanthose of specimens S4D and S4DH and the debonding areaof GFRP skin of S4DV was much smaller than those ofspecimens S4D and S4DH For specimen S4DT3 stressconcentration occurred in the intersection of ribs and thecross beam in the mid-span under flexural loads resulting inincompatibility deformation of the cross beam in the mid-span

e comparison of numerical and experimental load-displacement curves of the test specimens is shown inFigure 9 e numerical curves in Figure 9 show that themodel offered reasonable trend with the test data ie FE

analysis is capable of capturing the overall shapes of thetested load-displacement histories Table 3 reveals thatthe numerical ultimate loads are in good agreement withthe experimental values

e finite element analysis is extended to study the ef-fects of the height of vertical webs and the thickness of GFRPskins on the compressive region which are not tested in theexperimental program

52 Influence of theHeight ofVerticalWebs eexperimentalresults indicated that the existing vertical webs contribute toimproving the debonding of facesheets from foam core Toinvestigate the influence of geometry of vertical webs threedifferent heights of vertical webs (ie 80mm 105mm and125mm) are tried on S4D specimens respectively Figure 10(a)shows load-displacement curves of S4D specimens with dif-ferent height of vertical webs under flexural loads Increasingthe heights of vertical webs from 80mm to 105mm and125mm resulted in 9 and 27 enhancement of ultimateloads and 17 and 35 enhancement of rigidities

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Figure 6 Load-displacement responses

Advances in Materials Science and Engineering 7

53 Influence of GFRP Layers on the Compressive Regione experimental results indicated that local bucklingtends to occur in the thin facesheets on the compressiveregion of sandwich decks To investigate the influence ofGFRP layers on the top of decks three different layers(ie 4 6 and 8) are tried on the top of S4D specimens

respectively Figure 10(b) shows load-displacementcurves of S4D specimens with different GFRP layers onthe top under flexural loads Increasing layers of GFRP onthe top from 4 to 6 and 8 resulted in 15 and 32 en-hancement of ultimate loads and 7 and 16 en-hancement of rigidities

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

0

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(a)

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ndash02 0 02 04 06 08 1ndash04Strain ()

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ght f

rom

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m)

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ndash02 0 02 04 06 08 1ndash04Strain ()

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ectio

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Figure 7 Typical strain distribution curves across the depth at mid-span (a) S4D (b) S4DH (c) S4DV (d) S4DT2 and (e) S4DT3

8 Advances in Materials Science and Engineering

e simulated results indicated that the height of verticalwebs had significant effect on the rigidity while the layernumber of GFRP on the compressive region had significanteffect on the load carrying capacities

6 Theoretical Calculations

61 Prediction of Flexural Rigidity To simplify the calcula-tion the equivalent method is used to predict the flexuralrigidity of slab-rib integrated sandwich decks in which thedeck rigidity (EI)eff is directly computed based on thetransformed section technique e transformed section isobtained by replacing core material with an equivalentamount of FRP e cross section of the integrated com-posite decks is shown in Figure 11(a) e transformationfactor α is determined by the elastic modulus ratio of foamcore to FRP facesheets

λ Ec

Ef

(1)

where Ec and Ef are Youngrsquos moduli of foam core and FRPrespectively

e distances of centroids of foam core and integrateddecks to the bottom of decks yc0 and yc are given as

yc0 bh1 h2 + 05h1( 1113857 + ah

22

bh1 + 2ah2

(2)

yc a + 2tf1113872 1113873h

22 + b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 h2 + 05h1 + tf1113872 1113873

b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 + 2 a + 2tf1113872 1113873h2

(3)

where a and b are the width of core of slabs and ribs re-spectively h1 and h2 are the height of core of slabs and ribsrespectively and tf is the thickness of facesheets

e equivalent core height heq is

heq λ bh1 + 2ah2( 1113857

b (4)

+ 2849e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1987e + 00

s Mises(Avg 75)

xyz

(a)

+ 2238e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1214e + 00

s Mises(Avg 75)

xyz

(b)

+ 3285e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 2794e + 00

s Mises(Avg 75)

xyz

(c)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(d)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(e)

Figure 8 Simulated Mises stress contour at failure (unit MPa) (a) S4D (b) S4DV (c) S4DT3 (top surface) (d) S4DT3 (bottom surface)

Advances in Materials Science and Engineering 9

0

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(kN

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FEM curveExperimental curve

(a)

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(b)

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(c)

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(d)

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(e)

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FEM curveExperimental curve

(f )

020406080

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(kN

)

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FEM curveExperimental curve

(g)

0

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(kN

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FEM curveExperimental curve

(h)

Figure 9 Continued

10 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

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(kN

)

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FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

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S4D-80S4D-105S4D-125

(a)

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(kN

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Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

the slab-rib structures (Figure 2) the foam panels were cutinto separations for slabs ribs and diaphragms Orthogonalgrids (25mmtimes 25mmtimes 2mm) were grooved and holes withdiameter of 5mm and depth of 2mm were drilled on thesurface of the foam panels to enhance the bonding strengthbetween the GFRP skin and foam core Before wrappingwith bidirectional glass fabric layers the foam separationswere assembled into slab-rib structures en vacuum-assisted resin infusion process was used to fabricate thespecimens

32 Experimental Setup e specimens were tested underfour-point flexural loads acted at about one-third in-tervals of the span e experimental setup consists of a500 kN load cell which transfers the load to two loadheads using a spreader steel beame deflections at mid-span and supports were measured using linear variabledisplacement transducers (LVDTs) e typical test setupof four-point simply supported decks is shown in

Figure 3 In order to monitor stress state of the mid-spancross section 12 strain gages (gauge length 10 mm) werebonded to the top side and bottom surfaces of the testspecimens as shown in Figure 4 Static loads were ap-plied at a rate of 2 mmmin All the specimens were testedto a point where the loading could not be increasedanymore

4 Experimental Results and Discussion

41 Failure Modes Figure 5 provides a summary of thetypical failure modes e failures of specimens withoutwebs and cross beams (ie S2D S4D and S6D) weregoverned by debonding of GFRP facesheets from the foamcore outward facing wrinkled tearing of facesheets in thecorner of slabs near the loading points and shear cracksthat propagated from the narrow side of slabs to ribsMoreover transverse cracks appeared on the back of slabsdue to the shear failure of GFRP facesheets under theloading points e specimens with different layers ofGFRP facesheets exhibited similar failure modes Con-trary to expectations the specimen with lower foamdensity has much smaller debonding area on the topfacesheets than the specimens with higher foam densityis may be attributed to the lower rigidity of foams withsmaller density which allows compatible deformationunder debonding loads

1

2

t

t

6010

5100 70 260

(a)

2

3 1

(b)

2

4 1

(c)

4 3 1

2

(d)

Slab

RibCross beam

(e)

Figure 1 Configuration of slab-rib integrated bridge deck systems (a) cross section of sandwich decks without webs (b) cross section ofsandwich decks with vertical webs (c) cross section of sandwich decks with horizontal webs (d) cross section of sandwich decks with verticaland horizontal webs and (e) 3D view of decks with cross beams (1 foam core 2 FRP skin 3 vertical webs 4 horizontal webs)

Table 1 Tensile properties of GFRP

Property Value e ()Tensile strength (MPa) 304 831Tensile modulus (GPa) 26 647Poissonrsquos ratio 022 657e coefficient of variation

Advances in Materials Science and Engineering 3

e specimen with horizontal webs has similar failurepattern with the specimen without webs while the specimenwith vertical webs showed full bond between skins and thecores under vertical loads Crushing of the top skin and foamat the loading points dominated the failure modes ofspecimens with vertical webs is suggests that addingvertical webs is a reliable method to prevent the debondingof facesheets and foam core

e specimen with cross beams at the supports exhibitedshear failure of foam and crushing of skins at the loadingpoint and no obvious debonding of the skins was observedFor specimen with 3 cross beams at the supports and mid-span the top face was multi-waved wrinkled due to thedebonding of facesheets e additional cross beam in themid-span is unable to play a positive role in this structure

42 Load-Displacement Curves Load versus mid-span dis-placement measured from the test specimens is presented inFigure 6 along with a discussion on the effect of variousparameters on the structural behavior of the slab-rib decksAll the test specimens exhibited similar load-displacementprofiles e load increased almost linearly up to themaximum and then suddenly decreased when the GFRPfacesheets on the top of slabs were crushed near the loadingpoints After that the load increased until a new crackformed in the inner foams

It is obvious that the rigidity of slab-rib decks was ac-cordingly increased as the layer number of GFRP skinsincreased Very thin woven fabric layers may result inpremature failure of the facesheets in the loading pointIndeed the ultimate loads of specimens with 4 and 6 layersof GFRP skins are two and three times as much as that of

specimens with 2 layers of GFRP skins respectively and theultimate deformation increased by about 25 On thecontrary the ultimate load of specimen with foam density of100 kgm3 was 33 higher than that of specimen with foamdensity of 150 kgm3 is is because debonding of the topfacesheets and local buckling of GFRP dominate the failuremodes of specimens with higher foam density while thedebonding of facesheets does not extensively occur in thespecimens with lower foam density

e specimen with horizontal webs has similar ultimateload and slope of linear phase of load-displacement curve asspecimens without webs while the ultimate load of thespecimen with vertical webs is 59 higher than the specimenwithout webs e specimen with horizontal and verticalwebs has a little higher ultimate load (6) than the specimenwith vertical webs is suggests that adding vertical webs inslab-rib sandwich decks is a more reliable method to im-prove the debonding of facesheets and enhance the loadcarry capacity than adding horizontal webs

By comparing the responses of specimens with andwithout cross beams it can be concluded that adding 2 crossbeams at the supports contributes to increasing the ultimateloads by 27 while adding 3 cross beams at the supports andmid-span is not useful to enhance the ultimate loads andrigidity e additional cross beam in the mid-span tends toprevent the transverse deformation of the ribs and then theincompatible deformation occurred between the foam coreand skins resulting in large area debonding of facesheets

43 Strain Distributions Figure 7 shows the typical mid-span strain distribution through the depth of slab-ribsandwich decks For specimen without webs and crossbeams the longitudinal strain distributions remained flat upto 80 of ultimate load and the strains increased almostlinearly with increasing load e specimens with additionalhorizontal webs and cross beams at supports have similarstrain distribution to specimens without webs and crossbeams However the specimens with vertical webs or twocross beams behaved nonlinearly during loadinge strainsof the bottom facesheets of specimen with three cross beamsexhibited a bias to large value is is the reason that thespecimen with three cross beams is more prone to failurethan others

5 FE Model Construction

e finite element software ABAQUS has been successfullyused to simulate the performance of steel bridge deckpavement with fiber-reinforced epoxy resin-modified as-phalt [20] In this paper a 3D FE model has been developedusing Abaqus Explicit to analyze the flexural properties of

Table 3 Summary of test matrix and results

Specimen P (kN) P1(kN) P1P δ1 (mm) δ2 (mm) δ2δ1S2D 3435 3164 092 2655 2495 094S4D 6866 7284 106 3327 3108 083S6D 10770 10901 101 3379 2973 088S4d 9115 8767 096 3895 3526 091S4DV 10925 11718 107 3889 3453 089S4DH 6873 7123 104 3146 2715 086S4DVH 11561 12105 105 4568 3996 088S4DT2 8719 9223 106 3852 mdash mdashS4DT3 6556 7064 108 2980 mdash mdashIn the first column the letters d andDmean the densities of synthetic foamsare 100 kgm3 and 150 kgm3 respectively the letters V and H mean thespecimens have vertical and horizontal webs the letter T means thespecimens have cross beams the first number means the number of FRPlayers of the GFRP skins and the numbers 2 and 3 mean the number ofcross beams respectively In the first row P is the tested ultimate load andP1 is the ultimate load obtained from FE model δ1 is the tested maximumdeformation and δ2 is the calculated deformation from equation (17)

Table 2 Compressive properties of PU foams

Foam density (kgm3) Compressive strength (MPa) e () Compressive modulus (MPa) e ()100 0767 657 15527 527150 1566 357 3764 608e coefficient of variation

4 Advances in Materials Science and Engineering

(a) (b) (c)

(d) (e) (f )

Figure 2 Fabrication procedure of test specimens (a) the separation foams which have been grooved and drilled on the surface (b)assembling foams of slab and ribs (c) assembling diaphragms (d) wrapping the assembled foams with GFRP and (e f ) vacuum-assistedresin infusion process

1700

720

S4D

Figure 3 Test setup (units mm)

21

3

(a)

4~9

LVDT 2

LVDT 1

LVDT 3

(b)

1000 1000

101112

(c)

Figure 4 Locations of LVDTs and strain gauges (a) plane view from the top (b) side view and (c) plane view from the bottom (units mm)

Advances in Materials Science and Engineering 5

slab-rib integrated decks e material properties of bothGFRP and polyurethane foam were obtained from coupontest results e GFRP facesheets and webs are assumed tobehave in a linear elastic manner and the Hashin criterion isused to predict the failure of GFRP Hashin failure criteriahas been successfully applied to predict failure and post-failure of anisotropic fiber-reinforced materials [21] ematerial property of polyurethane foam is specified in the

elastic-plastic model in which the plasticity modulus istaken as 50 of elastic modulus

GFRP facesheets and webs are modeled by S4R shellelement while polyurethane foam is modeled by C3D8Rbrick element e test specimens are simply supportedSurface-to-surface contact elements are used to simulate theinterface between GFRP and foam core is type of contactconsiders slip and separation Hence slipdebonding is

(a) (b) (c)

(d) (e) (f )

(g) (h) (i)

(j) (k) (l)

Figure 5 Failure modes (a) S2D (b) S4D (c) S4D (d) S6D (e) S4DH (f ) S4DV (g) S4DVH (h) S4DV (i) S4d (j) S4d (k) S4DT2(l) S4DT3

6 Advances in Materials Science and Engineering

displayed if either occurs between the GFRP surface andfoam surface e friction coefficient is taken as 03 for thecontact surface of GFRP and foam core

51 Comparison of Numerical and Experimental Resultse simulated failure modes of typical specimens are shownin Figure 8 e FE model successfully captures the localbuckling of the top facesheets of the test specimens eMises stress of S4DV at the loading points was smaller thanthose of specimens S4D and S4DH and the debonding areaof GFRP skin of S4DV was much smaller than those ofspecimens S4D and S4DH For specimen S4DT3 stressconcentration occurred in the intersection of ribs and thecross beam in the mid-span under flexural loads resulting inincompatibility deformation of the cross beam in the mid-span

e comparison of numerical and experimental load-displacement curves of the test specimens is shown inFigure 9 e numerical curves in Figure 9 show that themodel offered reasonable trend with the test data ie FE

analysis is capable of capturing the overall shapes of thetested load-displacement histories Table 3 reveals thatthe numerical ultimate loads are in good agreement withthe experimental values

e finite element analysis is extended to study the ef-fects of the height of vertical webs and the thickness of GFRPskins on the compressive region which are not tested in theexperimental program

52 Influence of theHeight ofVerticalWebs eexperimentalresults indicated that the existing vertical webs contribute toimproving the debonding of facesheets from foam core Toinvestigate the influence of geometry of vertical webs threedifferent heights of vertical webs (ie 80mm 105mm and125mm) are tried on S4D specimens respectively Figure 10(a)shows load-displacement curves of S4D specimens with dif-ferent height of vertical webs under flexural loads Increasingthe heights of vertical webs from 80mm to 105mm and125mm resulted in 9 and 27 enhancement of ultimateloads and 17 and 35 enhancement of rigidities

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S6DS4DS2D

(a)

0

20

40

60

80

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

S4DS4d

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DVHS4DV

S4DHS4

(c)

0

20

40

60

80

100

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DT3S4DT2S4D

(d)

Figure 6 Load-displacement responses

Advances in Materials Science and Engineering 7

53 Influence of GFRP Layers on the Compressive Regione experimental results indicated that local bucklingtends to occur in the thin facesheets on the compressiveregion of sandwich decks To investigate the influence ofGFRP layers on the top of decks three different layers(ie 4 6 and 8) are tried on the top of S4D specimens

respectively Figure 10(b) shows load-displacementcurves of S4D specimens with different GFRP layers onthe top under flexural loads Increasing layers of GFRP onthe top from 4 to 6 and 8 resulted in 15 and 32 en-hancement of ultimate loads and 7 and 16 en-hancement of rigidities

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

0

40

80

120

160

(a)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(b)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(c)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(d)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(e)

Figure 7 Typical strain distribution curves across the depth at mid-span (a) S4D (b) S4DH (c) S4DV (d) S4DT2 and (e) S4DT3

8 Advances in Materials Science and Engineering

e simulated results indicated that the height of verticalwebs had significant effect on the rigidity while the layernumber of GFRP on the compressive region had significanteffect on the load carrying capacities

6 Theoretical Calculations

61 Prediction of Flexural Rigidity To simplify the calcula-tion the equivalent method is used to predict the flexuralrigidity of slab-rib integrated sandwich decks in which thedeck rigidity (EI)eff is directly computed based on thetransformed section technique e transformed section isobtained by replacing core material with an equivalentamount of FRP e cross section of the integrated com-posite decks is shown in Figure 11(a) e transformationfactor α is determined by the elastic modulus ratio of foamcore to FRP facesheets

λ Ec

Ef

(1)

where Ec and Ef are Youngrsquos moduli of foam core and FRPrespectively

e distances of centroids of foam core and integrateddecks to the bottom of decks yc0 and yc are given as

yc0 bh1 h2 + 05h1( 1113857 + ah

22

bh1 + 2ah2

(2)

yc a + 2tf1113872 1113873h

22 + b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 h2 + 05h1 + tf1113872 1113873

b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 + 2 a + 2tf1113872 1113873h2

(3)

where a and b are the width of core of slabs and ribs re-spectively h1 and h2 are the height of core of slabs and ribsrespectively and tf is the thickness of facesheets

e equivalent core height heq is

heq λ bh1 + 2ah2( 1113857

b (4)

+ 2849e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1987e + 00

s Mises(Avg 75)

xyz

(a)

+ 2238e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1214e + 00

s Mises(Avg 75)

xyz

(b)

+ 3285e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 2794e + 00

s Mises(Avg 75)

xyz

(c)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(d)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(e)

Figure 8 Simulated Mises stress contour at failure (unit MPa) (a) S4D (b) S4DV (c) S4DT3 (top surface) (d) S4DT3 (bottom surface)

Advances in Materials Science and Engineering 9

0

20

40

0 10 20 30 40

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(a)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(c)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(d)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(e)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(f )

020406080

100120140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(g)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(h)

Figure 9 Continued

10 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

S4D-80S4D-105S4D-125

(a)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

e specimen with horizontal webs has similar failurepattern with the specimen without webs while the specimenwith vertical webs showed full bond between skins and thecores under vertical loads Crushing of the top skin and foamat the loading points dominated the failure modes ofspecimens with vertical webs is suggests that addingvertical webs is a reliable method to prevent the debondingof facesheets and foam core

e specimen with cross beams at the supports exhibitedshear failure of foam and crushing of skins at the loadingpoint and no obvious debonding of the skins was observedFor specimen with 3 cross beams at the supports and mid-span the top face was multi-waved wrinkled due to thedebonding of facesheets e additional cross beam in themid-span is unable to play a positive role in this structure

42 Load-Displacement Curves Load versus mid-span dis-placement measured from the test specimens is presented inFigure 6 along with a discussion on the effect of variousparameters on the structural behavior of the slab-rib decksAll the test specimens exhibited similar load-displacementprofiles e load increased almost linearly up to themaximum and then suddenly decreased when the GFRPfacesheets on the top of slabs were crushed near the loadingpoints After that the load increased until a new crackformed in the inner foams

It is obvious that the rigidity of slab-rib decks was ac-cordingly increased as the layer number of GFRP skinsincreased Very thin woven fabric layers may result inpremature failure of the facesheets in the loading pointIndeed the ultimate loads of specimens with 4 and 6 layersof GFRP skins are two and three times as much as that of

specimens with 2 layers of GFRP skins respectively and theultimate deformation increased by about 25 On thecontrary the ultimate load of specimen with foam density of100 kgm3 was 33 higher than that of specimen with foamdensity of 150 kgm3 is is because debonding of the topfacesheets and local buckling of GFRP dominate the failuremodes of specimens with higher foam density while thedebonding of facesheets does not extensively occur in thespecimens with lower foam density

e specimen with horizontal webs has similar ultimateload and slope of linear phase of load-displacement curve asspecimens without webs while the ultimate load of thespecimen with vertical webs is 59 higher than the specimenwithout webs e specimen with horizontal and verticalwebs has a little higher ultimate load (6) than the specimenwith vertical webs is suggests that adding vertical webs inslab-rib sandwich decks is a more reliable method to im-prove the debonding of facesheets and enhance the loadcarry capacity than adding horizontal webs

By comparing the responses of specimens with andwithout cross beams it can be concluded that adding 2 crossbeams at the supports contributes to increasing the ultimateloads by 27 while adding 3 cross beams at the supports andmid-span is not useful to enhance the ultimate loads andrigidity e additional cross beam in the mid-span tends toprevent the transverse deformation of the ribs and then theincompatible deformation occurred between the foam coreand skins resulting in large area debonding of facesheets

43 Strain Distributions Figure 7 shows the typical mid-span strain distribution through the depth of slab-ribsandwich decks For specimen without webs and crossbeams the longitudinal strain distributions remained flat upto 80 of ultimate load and the strains increased almostlinearly with increasing load e specimens with additionalhorizontal webs and cross beams at supports have similarstrain distribution to specimens without webs and crossbeams However the specimens with vertical webs or twocross beams behaved nonlinearly during loadinge strainsof the bottom facesheets of specimen with three cross beamsexhibited a bias to large value is is the reason that thespecimen with three cross beams is more prone to failurethan others

5 FE Model Construction

e finite element software ABAQUS has been successfullyused to simulate the performance of steel bridge deckpavement with fiber-reinforced epoxy resin-modified as-phalt [20] In this paper a 3D FE model has been developedusing Abaqus Explicit to analyze the flexural properties of

Table 3 Summary of test matrix and results

Specimen P (kN) P1(kN) P1P δ1 (mm) δ2 (mm) δ2δ1S2D 3435 3164 092 2655 2495 094S4D 6866 7284 106 3327 3108 083S6D 10770 10901 101 3379 2973 088S4d 9115 8767 096 3895 3526 091S4DV 10925 11718 107 3889 3453 089S4DH 6873 7123 104 3146 2715 086S4DVH 11561 12105 105 4568 3996 088S4DT2 8719 9223 106 3852 mdash mdashS4DT3 6556 7064 108 2980 mdash mdashIn the first column the letters d andDmean the densities of synthetic foamsare 100 kgm3 and 150 kgm3 respectively the letters V and H mean thespecimens have vertical and horizontal webs the letter T means thespecimens have cross beams the first number means the number of FRPlayers of the GFRP skins and the numbers 2 and 3 mean the number ofcross beams respectively In the first row P is the tested ultimate load andP1 is the ultimate load obtained from FE model δ1 is the tested maximumdeformation and δ2 is the calculated deformation from equation (17)

Table 2 Compressive properties of PU foams

Foam density (kgm3) Compressive strength (MPa) e () Compressive modulus (MPa) e ()100 0767 657 15527 527150 1566 357 3764 608e coefficient of variation

4 Advances in Materials Science and Engineering

(a) (b) (c)

(d) (e) (f )

Figure 2 Fabrication procedure of test specimens (a) the separation foams which have been grooved and drilled on the surface (b)assembling foams of slab and ribs (c) assembling diaphragms (d) wrapping the assembled foams with GFRP and (e f ) vacuum-assistedresin infusion process

1700

720

S4D

Figure 3 Test setup (units mm)

21

3

(a)

4~9

LVDT 2

LVDT 1

LVDT 3

(b)

1000 1000

101112

(c)

Figure 4 Locations of LVDTs and strain gauges (a) plane view from the top (b) side view and (c) plane view from the bottom (units mm)

Advances in Materials Science and Engineering 5

slab-rib integrated decks e material properties of bothGFRP and polyurethane foam were obtained from coupontest results e GFRP facesheets and webs are assumed tobehave in a linear elastic manner and the Hashin criterion isused to predict the failure of GFRP Hashin failure criteriahas been successfully applied to predict failure and post-failure of anisotropic fiber-reinforced materials [21] ematerial property of polyurethane foam is specified in the

elastic-plastic model in which the plasticity modulus istaken as 50 of elastic modulus

GFRP facesheets and webs are modeled by S4R shellelement while polyurethane foam is modeled by C3D8Rbrick element e test specimens are simply supportedSurface-to-surface contact elements are used to simulate theinterface between GFRP and foam core is type of contactconsiders slip and separation Hence slipdebonding is

(a) (b) (c)

(d) (e) (f )

(g) (h) (i)

(j) (k) (l)

Figure 5 Failure modes (a) S2D (b) S4D (c) S4D (d) S6D (e) S4DH (f ) S4DV (g) S4DVH (h) S4DV (i) S4d (j) S4d (k) S4DT2(l) S4DT3

6 Advances in Materials Science and Engineering

displayed if either occurs between the GFRP surface andfoam surface e friction coefficient is taken as 03 for thecontact surface of GFRP and foam core

51 Comparison of Numerical and Experimental Resultse simulated failure modes of typical specimens are shownin Figure 8 e FE model successfully captures the localbuckling of the top facesheets of the test specimens eMises stress of S4DV at the loading points was smaller thanthose of specimens S4D and S4DH and the debonding areaof GFRP skin of S4DV was much smaller than those ofspecimens S4D and S4DH For specimen S4DT3 stressconcentration occurred in the intersection of ribs and thecross beam in the mid-span under flexural loads resulting inincompatibility deformation of the cross beam in the mid-span

e comparison of numerical and experimental load-displacement curves of the test specimens is shown inFigure 9 e numerical curves in Figure 9 show that themodel offered reasonable trend with the test data ie FE

analysis is capable of capturing the overall shapes of thetested load-displacement histories Table 3 reveals thatthe numerical ultimate loads are in good agreement withthe experimental values

e finite element analysis is extended to study the ef-fects of the height of vertical webs and the thickness of GFRPskins on the compressive region which are not tested in theexperimental program

52 Influence of theHeight ofVerticalWebs eexperimentalresults indicated that the existing vertical webs contribute toimproving the debonding of facesheets from foam core Toinvestigate the influence of geometry of vertical webs threedifferent heights of vertical webs (ie 80mm 105mm and125mm) are tried on S4D specimens respectively Figure 10(a)shows load-displacement curves of S4D specimens with dif-ferent height of vertical webs under flexural loads Increasingthe heights of vertical webs from 80mm to 105mm and125mm resulted in 9 and 27 enhancement of ultimateloads and 17 and 35 enhancement of rigidities

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S6DS4DS2D

(a)

0

20

40

60

80

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

S4DS4d

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DVHS4DV

S4DHS4

(c)

0

20

40

60

80

100

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DT3S4DT2S4D

(d)

Figure 6 Load-displacement responses

Advances in Materials Science and Engineering 7

53 Influence of GFRP Layers on the Compressive Regione experimental results indicated that local bucklingtends to occur in the thin facesheets on the compressiveregion of sandwich decks To investigate the influence ofGFRP layers on the top of decks three different layers(ie 4 6 and 8) are tried on the top of S4D specimens

respectively Figure 10(b) shows load-displacementcurves of S4D specimens with different GFRP layers onthe top under flexural loads Increasing layers of GFRP onthe top from 4 to 6 and 8 resulted in 15 and 32 en-hancement of ultimate loads and 7 and 16 en-hancement of rigidities

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

0

40

80

120

160

(a)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(b)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(c)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(d)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(e)

Figure 7 Typical strain distribution curves across the depth at mid-span (a) S4D (b) S4DH (c) S4DV (d) S4DT2 and (e) S4DT3

8 Advances in Materials Science and Engineering

e simulated results indicated that the height of verticalwebs had significant effect on the rigidity while the layernumber of GFRP on the compressive region had significanteffect on the load carrying capacities

6 Theoretical Calculations

61 Prediction of Flexural Rigidity To simplify the calcula-tion the equivalent method is used to predict the flexuralrigidity of slab-rib integrated sandwich decks in which thedeck rigidity (EI)eff is directly computed based on thetransformed section technique e transformed section isobtained by replacing core material with an equivalentamount of FRP e cross section of the integrated com-posite decks is shown in Figure 11(a) e transformationfactor α is determined by the elastic modulus ratio of foamcore to FRP facesheets

λ Ec

Ef

(1)

where Ec and Ef are Youngrsquos moduli of foam core and FRPrespectively

e distances of centroids of foam core and integrateddecks to the bottom of decks yc0 and yc are given as

yc0 bh1 h2 + 05h1( 1113857 + ah

22

bh1 + 2ah2

(2)

yc a + 2tf1113872 1113873h

22 + b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 h2 + 05h1 + tf1113872 1113873

b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 + 2 a + 2tf1113872 1113873h2

(3)

where a and b are the width of core of slabs and ribs re-spectively h1 and h2 are the height of core of slabs and ribsrespectively and tf is the thickness of facesheets

e equivalent core height heq is

heq λ bh1 + 2ah2( 1113857

b (4)

+ 2849e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1987e + 00

s Mises(Avg 75)

xyz

(a)

+ 2238e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1214e + 00

s Mises(Avg 75)

xyz

(b)

+ 3285e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 2794e + 00

s Mises(Avg 75)

xyz

(c)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(d)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(e)

Figure 8 Simulated Mises stress contour at failure (unit MPa) (a) S4D (b) S4DV (c) S4DT3 (top surface) (d) S4DT3 (bottom surface)

Advances in Materials Science and Engineering 9

0

20

40

0 10 20 30 40

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(a)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(c)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(d)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(e)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(f )

020406080

100120140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(g)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(h)

Figure 9 Continued

10 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

S4D-80S4D-105S4D-125

(a)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

(a) (b) (c)

(d) (e) (f )

Figure 2 Fabrication procedure of test specimens (a) the separation foams which have been grooved and drilled on the surface (b)assembling foams of slab and ribs (c) assembling diaphragms (d) wrapping the assembled foams with GFRP and (e f ) vacuum-assistedresin infusion process

1700

720

S4D

Figure 3 Test setup (units mm)

21

3

(a)

4~9

LVDT 2

LVDT 1

LVDT 3

(b)

1000 1000

101112

(c)

Figure 4 Locations of LVDTs and strain gauges (a) plane view from the top (b) side view and (c) plane view from the bottom (units mm)

Advances in Materials Science and Engineering 5

slab-rib integrated decks e material properties of bothGFRP and polyurethane foam were obtained from coupontest results e GFRP facesheets and webs are assumed tobehave in a linear elastic manner and the Hashin criterion isused to predict the failure of GFRP Hashin failure criteriahas been successfully applied to predict failure and post-failure of anisotropic fiber-reinforced materials [21] ematerial property of polyurethane foam is specified in the

elastic-plastic model in which the plasticity modulus istaken as 50 of elastic modulus

GFRP facesheets and webs are modeled by S4R shellelement while polyurethane foam is modeled by C3D8Rbrick element e test specimens are simply supportedSurface-to-surface contact elements are used to simulate theinterface between GFRP and foam core is type of contactconsiders slip and separation Hence slipdebonding is

(a) (b) (c)

(d) (e) (f )

(g) (h) (i)

(j) (k) (l)

Figure 5 Failure modes (a) S2D (b) S4D (c) S4D (d) S6D (e) S4DH (f ) S4DV (g) S4DVH (h) S4DV (i) S4d (j) S4d (k) S4DT2(l) S4DT3

6 Advances in Materials Science and Engineering

displayed if either occurs between the GFRP surface andfoam surface e friction coefficient is taken as 03 for thecontact surface of GFRP and foam core

51 Comparison of Numerical and Experimental Resultse simulated failure modes of typical specimens are shownin Figure 8 e FE model successfully captures the localbuckling of the top facesheets of the test specimens eMises stress of S4DV at the loading points was smaller thanthose of specimens S4D and S4DH and the debonding areaof GFRP skin of S4DV was much smaller than those ofspecimens S4D and S4DH For specimen S4DT3 stressconcentration occurred in the intersection of ribs and thecross beam in the mid-span under flexural loads resulting inincompatibility deformation of the cross beam in the mid-span

e comparison of numerical and experimental load-displacement curves of the test specimens is shown inFigure 9 e numerical curves in Figure 9 show that themodel offered reasonable trend with the test data ie FE

analysis is capable of capturing the overall shapes of thetested load-displacement histories Table 3 reveals thatthe numerical ultimate loads are in good agreement withthe experimental values

e finite element analysis is extended to study the ef-fects of the height of vertical webs and the thickness of GFRPskins on the compressive region which are not tested in theexperimental program

52 Influence of theHeight ofVerticalWebs eexperimentalresults indicated that the existing vertical webs contribute toimproving the debonding of facesheets from foam core Toinvestigate the influence of geometry of vertical webs threedifferent heights of vertical webs (ie 80mm 105mm and125mm) are tried on S4D specimens respectively Figure 10(a)shows load-displacement curves of S4D specimens with dif-ferent height of vertical webs under flexural loads Increasingthe heights of vertical webs from 80mm to 105mm and125mm resulted in 9 and 27 enhancement of ultimateloads and 17 and 35 enhancement of rigidities

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S6DS4DS2D

(a)

0

20

40

60

80

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

S4DS4d

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DVHS4DV

S4DHS4

(c)

0

20

40

60

80

100

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DT3S4DT2S4D

(d)

Figure 6 Load-displacement responses

Advances in Materials Science and Engineering 7

53 Influence of GFRP Layers on the Compressive Regione experimental results indicated that local bucklingtends to occur in the thin facesheets on the compressiveregion of sandwich decks To investigate the influence ofGFRP layers on the top of decks three different layers(ie 4 6 and 8) are tried on the top of S4D specimens

respectively Figure 10(b) shows load-displacementcurves of S4D specimens with different GFRP layers onthe top under flexural loads Increasing layers of GFRP onthe top from 4 to 6 and 8 resulted in 15 and 32 en-hancement of ultimate loads and 7 and 16 en-hancement of rigidities

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

0

40

80

120

160

(a)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(b)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(c)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(d)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(e)

Figure 7 Typical strain distribution curves across the depth at mid-span (a) S4D (b) S4DH (c) S4DV (d) S4DT2 and (e) S4DT3

8 Advances in Materials Science and Engineering

e simulated results indicated that the height of verticalwebs had significant effect on the rigidity while the layernumber of GFRP on the compressive region had significanteffect on the load carrying capacities

6 Theoretical Calculations

61 Prediction of Flexural Rigidity To simplify the calcula-tion the equivalent method is used to predict the flexuralrigidity of slab-rib integrated sandwich decks in which thedeck rigidity (EI)eff is directly computed based on thetransformed section technique e transformed section isobtained by replacing core material with an equivalentamount of FRP e cross section of the integrated com-posite decks is shown in Figure 11(a) e transformationfactor α is determined by the elastic modulus ratio of foamcore to FRP facesheets

λ Ec

Ef

(1)

where Ec and Ef are Youngrsquos moduli of foam core and FRPrespectively

e distances of centroids of foam core and integrateddecks to the bottom of decks yc0 and yc are given as

yc0 bh1 h2 + 05h1( 1113857 + ah

22

bh1 + 2ah2

(2)

yc a + 2tf1113872 1113873h

22 + b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 h2 + 05h1 + tf1113872 1113873

b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 + 2 a + 2tf1113872 1113873h2

(3)

where a and b are the width of core of slabs and ribs re-spectively h1 and h2 are the height of core of slabs and ribsrespectively and tf is the thickness of facesheets

e equivalent core height heq is

heq λ bh1 + 2ah2( 1113857

b (4)

+ 2849e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1987e + 00

s Mises(Avg 75)

xyz

(a)

+ 2238e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1214e + 00

s Mises(Avg 75)

xyz

(b)

+ 3285e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 2794e + 00

s Mises(Avg 75)

xyz

(c)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(d)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(e)

Figure 8 Simulated Mises stress contour at failure (unit MPa) (a) S4D (b) S4DV (c) S4DT3 (top surface) (d) S4DT3 (bottom surface)

Advances in Materials Science and Engineering 9

0

20

40

0 10 20 30 40

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(a)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(c)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(d)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(e)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(f )

020406080

100120140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(g)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(h)

Figure 9 Continued

10 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

S4D-80S4D-105S4D-125

(a)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

slab-rib integrated decks e material properties of bothGFRP and polyurethane foam were obtained from coupontest results e GFRP facesheets and webs are assumed tobehave in a linear elastic manner and the Hashin criterion isused to predict the failure of GFRP Hashin failure criteriahas been successfully applied to predict failure and post-failure of anisotropic fiber-reinforced materials [21] ematerial property of polyurethane foam is specified in the

elastic-plastic model in which the plasticity modulus istaken as 50 of elastic modulus

GFRP facesheets and webs are modeled by S4R shellelement while polyurethane foam is modeled by C3D8Rbrick element e test specimens are simply supportedSurface-to-surface contact elements are used to simulate theinterface between GFRP and foam core is type of contactconsiders slip and separation Hence slipdebonding is

(a) (b) (c)

(d) (e) (f )

(g) (h) (i)

(j) (k) (l)

Figure 5 Failure modes (a) S2D (b) S4D (c) S4D (d) S6D (e) S4DH (f ) S4DV (g) S4DVH (h) S4DV (i) S4d (j) S4d (k) S4DT2(l) S4DT3

6 Advances in Materials Science and Engineering

displayed if either occurs between the GFRP surface andfoam surface e friction coefficient is taken as 03 for thecontact surface of GFRP and foam core

51 Comparison of Numerical and Experimental Resultse simulated failure modes of typical specimens are shownin Figure 8 e FE model successfully captures the localbuckling of the top facesheets of the test specimens eMises stress of S4DV at the loading points was smaller thanthose of specimens S4D and S4DH and the debonding areaof GFRP skin of S4DV was much smaller than those ofspecimens S4D and S4DH For specimen S4DT3 stressconcentration occurred in the intersection of ribs and thecross beam in the mid-span under flexural loads resulting inincompatibility deformation of the cross beam in the mid-span

e comparison of numerical and experimental load-displacement curves of the test specimens is shown inFigure 9 e numerical curves in Figure 9 show that themodel offered reasonable trend with the test data ie FE

analysis is capable of capturing the overall shapes of thetested load-displacement histories Table 3 reveals thatthe numerical ultimate loads are in good agreement withthe experimental values

e finite element analysis is extended to study the ef-fects of the height of vertical webs and the thickness of GFRPskins on the compressive region which are not tested in theexperimental program

52 Influence of theHeight ofVerticalWebs eexperimentalresults indicated that the existing vertical webs contribute toimproving the debonding of facesheets from foam core Toinvestigate the influence of geometry of vertical webs threedifferent heights of vertical webs (ie 80mm 105mm and125mm) are tried on S4D specimens respectively Figure 10(a)shows load-displacement curves of S4D specimens with dif-ferent height of vertical webs under flexural loads Increasingthe heights of vertical webs from 80mm to 105mm and125mm resulted in 9 and 27 enhancement of ultimateloads and 17 and 35 enhancement of rigidities

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S6DS4DS2D

(a)

0

20

40

60

80

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

S4DS4d

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DVHS4DV

S4DHS4

(c)

0

20

40

60

80

100

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DT3S4DT2S4D

(d)

Figure 6 Load-displacement responses

Advances in Materials Science and Engineering 7

53 Influence of GFRP Layers on the Compressive Regione experimental results indicated that local bucklingtends to occur in the thin facesheets on the compressiveregion of sandwich decks To investigate the influence ofGFRP layers on the top of decks three different layers(ie 4 6 and 8) are tried on the top of S4D specimens

respectively Figure 10(b) shows load-displacementcurves of S4D specimens with different GFRP layers onthe top under flexural loads Increasing layers of GFRP onthe top from 4 to 6 and 8 resulted in 15 and 32 en-hancement of ultimate loads and 7 and 16 en-hancement of rigidities

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

0

40

80

120

160

(a)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(b)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(c)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(d)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(e)

Figure 7 Typical strain distribution curves across the depth at mid-span (a) S4D (b) S4DH (c) S4DV (d) S4DT2 and (e) S4DT3

8 Advances in Materials Science and Engineering

e simulated results indicated that the height of verticalwebs had significant effect on the rigidity while the layernumber of GFRP on the compressive region had significanteffect on the load carrying capacities

6 Theoretical Calculations

61 Prediction of Flexural Rigidity To simplify the calcula-tion the equivalent method is used to predict the flexuralrigidity of slab-rib integrated sandwich decks in which thedeck rigidity (EI)eff is directly computed based on thetransformed section technique e transformed section isobtained by replacing core material with an equivalentamount of FRP e cross section of the integrated com-posite decks is shown in Figure 11(a) e transformationfactor α is determined by the elastic modulus ratio of foamcore to FRP facesheets

λ Ec

Ef

(1)

where Ec and Ef are Youngrsquos moduli of foam core and FRPrespectively

e distances of centroids of foam core and integrateddecks to the bottom of decks yc0 and yc are given as

yc0 bh1 h2 + 05h1( 1113857 + ah

22

bh1 + 2ah2

(2)

yc a + 2tf1113872 1113873h

22 + b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 h2 + 05h1 + tf1113872 1113873

b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 + 2 a + 2tf1113872 1113873h2

(3)

where a and b are the width of core of slabs and ribs re-spectively h1 and h2 are the height of core of slabs and ribsrespectively and tf is the thickness of facesheets

e equivalent core height heq is

heq λ bh1 + 2ah2( 1113857

b (4)

+ 2849e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1987e + 00

s Mises(Avg 75)

xyz

(a)

+ 2238e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1214e + 00

s Mises(Avg 75)

xyz

(b)

+ 3285e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 2794e + 00

s Mises(Avg 75)

xyz

(c)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(d)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(e)

Figure 8 Simulated Mises stress contour at failure (unit MPa) (a) S4D (b) S4DV (c) S4DT3 (top surface) (d) S4DT3 (bottom surface)

Advances in Materials Science and Engineering 9

0

20

40

0 10 20 30 40

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(a)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(c)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(d)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(e)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(f )

020406080

100120140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(g)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(h)

Figure 9 Continued

10 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

S4D-80S4D-105S4D-125

(a)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

displayed if either occurs between the GFRP surface andfoam surface e friction coefficient is taken as 03 for thecontact surface of GFRP and foam core

51 Comparison of Numerical and Experimental Resultse simulated failure modes of typical specimens are shownin Figure 8 e FE model successfully captures the localbuckling of the top facesheets of the test specimens eMises stress of S4DV at the loading points was smaller thanthose of specimens S4D and S4DH and the debonding areaof GFRP skin of S4DV was much smaller than those ofspecimens S4D and S4DH For specimen S4DT3 stressconcentration occurred in the intersection of ribs and thecross beam in the mid-span under flexural loads resulting inincompatibility deformation of the cross beam in the mid-span

e comparison of numerical and experimental load-displacement curves of the test specimens is shown inFigure 9 e numerical curves in Figure 9 show that themodel offered reasonable trend with the test data ie FE

analysis is capable of capturing the overall shapes of thetested load-displacement histories Table 3 reveals thatthe numerical ultimate loads are in good agreement withthe experimental values

e finite element analysis is extended to study the ef-fects of the height of vertical webs and the thickness of GFRPskins on the compressive region which are not tested in theexperimental program

52 Influence of theHeight ofVerticalWebs eexperimentalresults indicated that the existing vertical webs contribute toimproving the debonding of facesheets from foam core Toinvestigate the influence of geometry of vertical webs threedifferent heights of vertical webs (ie 80mm 105mm and125mm) are tried on S4D specimens respectively Figure 10(a)shows load-displacement curves of S4D specimens with dif-ferent height of vertical webs under flexural loads Increasingthe heights of vertical webs from 80mm to 105mm and125mm resulted in 9 and 27 enhancement of ultimateloads and 17 and 35 enhancement of rigidities

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S6DS4DS2D

(a)

0

20

40

60

80

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

S4DS4d

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DVHS4DV

S4DHS4

(c)

0

20

40

60

80

100

0 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

S4DT3S4DT2S4D

(d)

Figure 6 Load-displacement responses

Advances in Materials Science and Engineering 7

53 Influence of GFRP Layers on the Compressive Regione experimental results indicated that local bucklingtends to occur in the thin facesheets on the compressiveregion of sandwich decks To investigate the influence ofGFRP layers on the top of decks three different layers(ie 4 6 and 8) are tried on the top of S4D specimens

respectively Figure 10(b) shows load-displacementcurves of S4D specimens with different GFRP layers onthe top under flexural loads Increasing layers of GFRP onthe top from 4 to 6 and 8 resulted in 15 and 32 en-hancement of ultimate loads and 7 and 16 en-hancement of rigidities

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

0

40

80

120

160

(a)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(b)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(c)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(d)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(e)

Figure 7 Typical strain distribution curves across the depth at mid-span (a) S4D (b) S4DH (c) S4DV (d) S4DT2 and (e) S4DT3

8 Advances in Materials Science and Engineering

e simulated results indicated that the height of verticalwebs had significant effect on the rigidity while the layernumber of GFRP on the compressive region had significanteffect on the load carrying capacities

6 Theoretical Calculations

61 Prediction of Flexural Rigidity To simplify the calcula-tion the equivalent method is used to predict the flexuralrigidity of slab-rib integrated sandwich decks in which thedeck rigidity (EI)eff is directly computed based on thetransformed section technique e transformed section isobtained by replacing core material with an equivalentamount of FRP e cross section of the integrated com-posite decks is shown in Figure 11(a) e transformationfactor α is determined by the elastic modulus ratio of foamcore to FRP facesheets

λ Ec

Ef

(1)

where Ec and Ef are Youngrsquos moduli of foam core and FRPrespectively

e distances of centroids of foam core and integrateddecks to the bottom of decks yc0 and yc are given as

yc0 bh1 h2 + 05h1( 1113857 + ah

22

bh1 + 2ah2

(2)

yc a + 2tf1113872 1113873h

22 + b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 h2 + 05h1 + tf1113872 1113873

b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 + 2 a + 2tf1113872 1113873h2

(3)

where a and b are the width of core of slabs and ribs re-spectively h1 and h2 are the height of core of slabs and ribsrespectively and tf is the thickness of facesheets

e equivalent core height heq is

heq λ bh1 + 2ah2( 1113857

b (4)

+ 2849e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1987e + 00

s Mises(Avg 75)

xyz

(a)

+ 2238e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1214e + 00

s Mises(Avg 75)

xyz

(b)

+ 3285e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 2794e + 00

s Mises(Avg 75)

xyz

(c)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(d)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(e)

Figure 8 Simulated Mises stress contour at failure (unit MPa) (a) S4D (b) S4DV (c) S4DT3 (top surface) (d) S4DT3 (bottom surface)

Advances in Materials Science and Engineering 9

0

20

40

0 10 20 30 40

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(a)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(c)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(d)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(e)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(f )

020406080

100120140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(g)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(h)

Figure 9 Continued

10 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

S4D-80S4D-105S4D-125

(a)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

53 Influence of GFRP Layers on the Compressive Regione experimental results indicated that local bucklingtends to occur in the thin facesheets on the compressiveregion of sandwich decks To investigate the influence ofGFRP layers on the top of decks three different layers(ie 4 6 and 8) are tried on the top of S4D specimens

respectively Figure 10(b) shows load-displacementcurves of S4D specimens with different GFRP layers onthe top under flexural loads Increasing layers of GFRP onthe top from 4 to 6 and 8 resulted in 15 and 32 en-hancement of ultimate loads and 7 and 16 en-hancement of rigidities

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

0

40

80

120

160

(a)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(b)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(c)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(d)

10 P20 P40 P

60 P80 P

ndash02 0 02 04 06 08 1ndash04Strain ()

Hei

ght f

rom

bot

tom

of s

ectio

n (m

m)

0

40

80

120

160

(e)

Figure 7 Typical strain distribution curves across the depth at mid-span (a) S4D (b) S4DH (c) S4DV (d) S4DT2 and (e) S4DT3

8 Advances in Materials Science and Engineering

e simulated results indicated that the height of verticalwebs had significant effect on the rigidity while the layernumber of GFRP on the compressive region had significanteffect on the load carrying capacities

6 Theoretical Calculations

61 Prediction of Flexural Rigidity To simplify the calcula-tion the equivalent method is used to predict the flexuralrigidity of slab-rib integrated sandwich decks in which thedeck rigidity (EI)eff is directly computed based on thetransformed section technique e transformed section isobtained by replacing core material with an equivalentamount of FRP e cross section of the integrated com-posite decks is shown in Figure 11(a) e transformationfactor α is determined by the elastic modulus ratio of foamcore to FRP facesheets

λ Ec

Ef

(1)

where Ec and Ef are Youngrsquos moduli of foam core and FRPrespectively

e distances of centroids of foam core and integrateddecks to the bottom of decks yc0 and yc are given as

yc0 bh1 h2 + 05h1( 1113857 + ah

22

bh1 + 2ah2

(2)

yc a + 2tf1113872 1113873h

22 + b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 h2 + 05h1 + tf1113872 1113873

b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 + 2 a + 2tf1113872 1113873h2

(3)

where a and b are the width of core of slabs and ribs re-spectively h1 and h2 are the height of core of slabs and ribsrespectively and tf is the thickness of facesheets

e equivalent core height heq is

heq λ bh1 + 2ah2( 1113857

b (4)

+ 2849e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1987e + 00

s Mises(Avg 75)

xyz

(a)

+ 2238e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1214e + 00

s Mises(Avg 75)

xyz

(b)

+ 3285e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 2794e + 00

s Mises(Avg 75)

xyz

(c)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(d)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(e)

Figure 8 Simulated Mises stress contour at failure (unit MPa) (a) S4D (b) S4DV (c) S4DT3 (top surface) (d) S4DT3 (bottom surface)

Advances in Materials Science and Engineering 9

0

20

40

0 10 20 30 40

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(a)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(c)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(d)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(e)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(f )

020406080

100120140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(g)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(h)

Figure 9 Continued

10 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

S4D-80S4D-105S4D-125

(a)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

e simulated results indicated that the height of verticalwebs had significant effect on the rigidity while the layernumber of GFRP on the compressive region had significanteffect on the load carrying capacities

6 Theoretical Calculations

61 Prediction of Flexural Rigidity To simplify the calcula-tion the equivalent method is used to predict the flexuralrigidity of slab-rib integrated sandwich decks in which thedeck rigidity (EI)eff is directly computed based on thetransformed section technique e transformed section isobtained by replacing core material with an equivalentamount of FRP e cross section of the integrated com-posite decks is shown in Figure 11(a) e transformationfactor α is determined by the elastic modulus ratio of foamcore to FRP facesheets

λ Ec

Ef

(1)

where Ec and Ef are Youngrsquos moduli of foam core and FRPrespectively

e distances of centroids of foam core and integrateddecks to the bottom of decks yc0 and yc are given as

yc0 bh1 h2 + 05h1( 1113857 + ah

22

bh1 + 2ah2

(2)

yc a + 2tf1113872 1113873h

22 + b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 h2 + 05h1 + tf1113872 1113873

b + 2tf1113872 1113873 h1 + 2tf1113872 1113873 + 2 a + 2tf1113872 1113873h2

(3)

where a and b are the width of core of slabs and ribs re-spectively h1 and h2 are the height of core of slabs and ribsrespectively and tf is the thickness of facesheets

e equivalent core height heq is

heq λ bh1 + 2ah2( 1113857

b (4)

+ 2849e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1987e + 00

s Mises(Avg 75)

xyz

(a)

+ 2238e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 1214e + 00

s Mises(Avg 75)

xyz

(b)

+ 3285e + 02+ 1115e + 02+ 1023e + 02+ 9304e + 01+ 8381e + 01+ 7458e + 01+ 6535e + 01+ 5611e + 01+ 4688e + 01+ 3765e + 01+ 2842e + 01+ 1918e + 01+ 9952e + 00+ 7194e + 00+ 2794e + 00

s Mises(Avg 75)

xyz

(c)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(d)

+ 3489e + 02+ 8151e + 01+ 7477e + 01+ 6804e + 01+ 6131e + 01+ 5458e + 01+ 4785e + 01+ 4111e + 01+ 3438e + 01+ 2765e + 01+ 2092e + 01+ 1418e + 01+ 7452e + 00+ 7194e + 00

s Mises(Avg 75)

xyz

(e)

Figure 8 Simulated Mises stress contour at failure (unit MPa) (a) S4D (b) S4DV (c) S4DT3 (top surface) (d) S4DT3 (bottom surface)

Advances in Materials Science and Engineering 9

0

20

40

0 10 20 30 40

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(a)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(c)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(d)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(e)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(f )

020406080

100120140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(g)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(h)

Figure 9 Continued

10 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

S4D-80S4D-105S4D-125

(a)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

0

20

40

0 10 20 30 40

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(a)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(b)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(c)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(d)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(e)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(f )

020406080

100120140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(g)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(h)

Figure 9 Continued

10 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

S4D-80S4D-105S4D-125

(a)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

e inertia of FRP facesheets webs and the equivalentmoment of inertia of foam core are given as

If b1t

3f

12+ b1tfd

21

⎛⎝ ⎞⎠ + 2b2t

3f

12+ b2tfd

22

⎛⎝ ⎞⎠ +b3t

3f

12+ b3tfd

23

⎛⎝ ⎞⎠ + 2tfh

31

12+ h1tfd

24

⎛⎝ ⎞⎠ + 4tfh

32

12+ h2tfd

25

⎛⎝ ⎞⎠ (5)

Iwv ntwh

31

12+ twh1 h2 + 05h1 + tf minus yc1113872 1113873

21113890 1113891 (6)

Iwh bt

3w

12+ btw yc minus tf minus h2 minus 05tw1113872 1113873

2 (7)

Ic bh

3eq

12+ bheq yc0 minus yc( 1113857

2 (8)

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

FEM curveExperimental curve

(i)

Figure 9 Comparison of numerical and experimental load-displacement curves for (a) S2D (b) S4D (c) S6D (d) S4d (e) S4DV (f ) S4DH(g) S4DVH (h) S4DT2 and (i) S4DT3

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)

S4D-80S4D-105S4D-125

(a)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Load

(kN

)

Displacement (mm)S4D-2S4D-4S4D-6

(b)

Figure 10 Simulated load-displacement curves of S4D (a) with different height of vertical webs and (b) with different GFRP layers on thecompressive region

Advances in Materials Science and Engineering 11

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

where d1 h1+h2+15tf minus yc d2 h2+05tf minus yc d4

05h1+h2+05tf minus yc d5 05h2+05tf minus yc If Iwv and Iwh are themoment of inertia about the neutral axis of the facesheetsvertical and horizontal webs respectively Ic is the equivalentmoment of inertia of the core and n is the number of verticalwebs

With the transformed section the equivalent moment ofinertia (I)eq for the integrated decks can be calculated asfollows

Ieq If + Iwv + Iwh + Ic (9)

62 Prediction of Shear Rigidity Based on the compatibilityof shear deformation of foam core and webs under verticalloads as shown in Figure 11(b) the deformation of core ofslab strengthened by webs and facesheets Δ is given by

Δ 2Δf + nΔw + 1113944n+1

i1Δci (10)

where Δf Δw and Δci are the shear deformations of face-sheets webs and foam cores under vertical loadsrespectively

From equation (10) the shear strain of cores strength-ened by webs and facesheets c is given by

cb1 2cftf + ncwtw + 1113944n+1

i1ccLi (11)

where cf cw and cc are the shear strain of facesheets websand cores respectively tw is the thickness of the webs and Liis the width of cores separated by webs

According to the shear stress constitutive law the shearstress of cores strengthened by webs and facesheets τ can beexpressed as

τG0

b1 2τftf

Gf

+nτwtw

Gw

+1113936

n+1i1 τcLi

Gc

(12)

where τf τw and τc are the shear stress of facesheets websand cores respectively and G0 Gf Gw and Gc are the shear

tw

a

h1

h2tf

b

b1

b2 b3

(a)

q2q2

L1 L2 L3 L4

f

w

w

f

C1

C2

C4

C3

twtf tf

w

b1

(b)

Figure 11 Section of the sandwich deck and the slab configuration under vertical load (a) Cross section of the deck (b) Shear deformationof the slab strengthened by webs

12 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

modulus of core of slab strengthened by webs and facesheetsfacesheets webs and bare cores respectively

It is assumed that no debonding occurred among the coresfacesheets and webs under vertical loads us according tothe principle of complementary shear stress the shear stressesof facesheets webs and cores have following relationship

τ τf τw τc (13)

Substituting equation (13) into equation (12) we obtainthe shear modulus of foam of slab strengthened by webs andfacesheets

1G0

2tf

Gfb1+

ntw

Gwb1+

1113936n+1i1 Li

Gcb1 (14)

In the case of foam of ribs G1 is given by

1G1

4tf

Gf 2a + 4tf1113872 1113873+

2a

Gc 2a + 4tf1113872 1113873 (15)

e equivalent shear rigidity (GA)eq(GA)eq G0A0 + G1A1 (16)

where A0 and A1 are the areas of slab and ribs

63 Prediction of Deformations FRP composites display ingeneral a much higher longitudinal-to-shear modulus ratiothan isotropicmaterials and this ratio tends to increase as theanisotropy degree of the material increases us sheardeformation in the composite structures will increase as theanisotropy degree of the material increases [22] To accountfor shear deformation the deformation in the mid-span ofcomposite decks is obtained based on Timoshenko Beameory (TBT)

wL

21113874 1113875

Pa 3L2

minus 4e2

1113872 1113873

48EfIeq+

Pe2k(GA)eq

(17)

where P is applied load L is span length e is the distancefrom the support to loading point and k is shear correctionfactor k is taken as 1 which is the same as the value in boxsections [23]

Because the effects of the cross beams were not con-sidered in analyzing flexural and shear rigidities of thesandwich decks equation (17) was used to calculate the mid-span displacement of the slab-rib integrated sandwich deckswithout cross beams Comparisons of the analytical and themeasured displacements at the mid-span under the maxi-mum loads showed good agreement as given in Table 3

7 Conclusions

e flexural behaviors of slab-rib integrated sandwichcomposite decks were investigated e results obtainedfrom this study are summarized as follows

(1) Debonding of the facesheets to the foam core and thelocal buckling of facesheets on the compressive re-gion governed the failure modes of specimens

without webs e specimens with horizontal webshave similar failure modes to those without webse existence of the vertical webs contributes toimproving the debonding of the facesheets from thefoam core Moreover the specimens with lower foamdensity have smaller debonding area than thespecimens with higher foam density because thelower rigidity of foams allows compatible defor-mation under debonding loads e cross beam inthe mid-span is not helpful to improve thedebonding of facesheets

(2) Increasing the number of layers of GFRP skins from2 to 4 and 6 results in 100 and 214 increments inload carrying capacities respectively while higherdensity of foam core results in decrease of the ul-timate load due to deformation compatibility be-tween GFRP skins and foam core with low densitye existence of horizontal webs has an insignificanteffect on both load carrying capacity and rigiditywhile the existence of vertical webs contributes tosignificantly enhancing the load carry capacity ofslab-rib sandwich decks Adding 2 cross beams at thesupports is helpful to increase the load carryingcapacity to some extent while adding 3 cross beamsat the supports and mid-span is not useful to en-hance the load carrying capacity and rigidity

(3) e analysis program Abaqus Explicit was used tosimulate the flexural behaviors of tested specimense models provide reasonable simulations of thetested results e verified model was extended toanalyze the influences of the height of vertical websand GFRP layers on the compressive region

(4) Based on equivalent method and compatibility ofshear deformation the flexural and shear rigiditieswere estimated including the mid-span deflectioncomputations with TBT under 4-point loading epredicted deflections corresponding to maximumload agree well with the experimental data

Data Availability

e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e financial support from the National Natural ScienceFoundation of China (Grant No51578283) Modern Scienceand Technology Support Program of Jiangsu ConstructionIndustry of China (Grant No 2016-13) and Top Six TalentProjects in Jiangsu Province China (Grant No JZ-024) isgreatly appreciated Professor Weiqing Liu unfortunatelypassed away on June 3 2020 e authors would like toexpress their gratitude to Professor Liu for his contributionto the paper

Advances in Materials Science and Engineering 13

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering

References

[1] G Zi B M Kim Y K Hwang and Y H Lee ldquoAn experi-mental study on static behavior of a GFRP bridge deck filledwith a polyurethane foamrdquo Composite Structures vol 82no 2 pp 257ndash268 2008

[2] J Wang H GangaRao M Li M Liang and W Liu ldquoAxialbehavior of columns with glass fiber reinforced polymercomposite shells and syntactic foam corerdquo Journal of Com-posites for Construction vol 23 no 2 Article ID 040180832019

[3] A Manalo S Surendar G van Erp and B BenmokraneldquoFlexural behavior of an FRP sandwich system with glass-fiberskins and a phenolic core at elevated in-service temperaturerdquoComposite Structures vol 152 pp 96ndash105 2016

[4] S Satasivam and Y Bai ldquoMechanical performance of boltedmodular GFRP composite sandwich structures using standardand blind boltsrdquo Composite Structures vol 117 pp 59ndash702014

[5] D Y Moon G Zi D H Lee B M Kim and Y K HwangldquoFatigue behavior of the foam-filled GFRP bridge deckrdquoComposites Part B Engineering vol 40 no 2 pp 141ndash1482009

[6] T Sharaf W Shawkat and A Fam ldquoStructural performanceof sandwich wall panels with different foam core densities inone-way bendingrdquo Journal of Composite Materials vol 44no 19 pp 2249ndash2263 2010

[7] A Chen and J F Davalos ldquoDevelopment of facesheet forhoneycomb FRP sandwich panelsrdquo Journal of CompositeMaterials vol 46 no 26 pp 3277ndash3295 2012

[8] H S Ji W Song and Z J Ma ldquoDesign test and field ap-plication of a GFRP corrugated-core sandwich bridgerdquo En-gineering Structures vol 32 no 9 pp 2814ndash2824 2010

[9] M Osei-Antw J Castro AP Vassilopoulos and T KellerldquoFRP-balsa composite sandwich bridge deck with complexcore assemblyrdquo Journal of Composites for Constructionvol 17 no 6 Article ID 04013011 2013

[10] M Mohamed S Anandan Z Huo V Birman J Volz andK Chandrashekhara ldquoManufacturing and characterization ofpolyurethane based sandwich composite structuresrdquo Com-posite Structures vol 123 pp 169ndash179 2015

[11] H Tuwair H J Volz MA ElGawady M MohamedK Chandrashekhara and V Birman ldquoTesting and evaluationof polyurethane-based GFRP sandwich bridge deck panelswith polyurethane foam corerdquo Journal of Bridge Engineeringvol 21 no 1 Article ID 04015033 2016

[12] A Mostafa K Shankar and E V Morozov ldquoInfluence ofshear keys orientation on the shear performance of compositesandwich panel with PVC foam core numerical studyrdquoMaterials amp Design vol 51 pp 1008ndash1017 2013

[13] E M Reis and S H Rizkalla ldquoMaterial characteristics of 3-DFRP sandwich panelsrdquo Construction and Building Materialsvol 22 no 6 pp 1009ndash1018 2008

[14] J Knippers E Pelke M Gabler and D Berger ldquoBridges withglass fibre-reinforced polymer decks the road bridge infriedberg Germanyrdquo Structural Engineering Internationalvol 20 no 4 pp 400ndash404 2010

[15] V Mara M Al-Emrani and R Haghani ldquoA novel connectionfor fibre reinforced polymer bridge decks conceptual designand experimental investigationrdquo Composite Structuresvol 117 no 1 pp 83ndash97 2014

[16] A Fettahoglu ldquoOptimizing rib width to height and rib spacingto deck plate thickness ratios in orthotropic decksrdquo CogentEngineering vol 3 no 1 p 1154703 2016

[17] B Standards ldquoDesign of steel structures-steel bridges brusselEuropean committee for standardization Eurocode 3-designof steel structures-part 2 steel bridgesrdquo 2006

[18] ASTM D638 Standard Test Method for Tensile Properties ofPlastics ASTM International West Conshohocken PA USA2014

[19] ASTM C365C365-16 Standard test method for flatwisecompressive properties of sandwich cores ASTM InternationalConshohocken PA USA 2016

[20] H Zhang C Zhou K Li P Gao Y Pan and Z ZhangldquoMaterial and structural properties of fiber-reinforced resincomposites as thin overlay for steel bridge deck pavementrdquoAdvances in Materials Science and Engineering vol 2019Article ID 9840502 13 pages 2019

[21] I Lapczyk and J A Hurtado ldquoProgressive damage modelingin fiber-reinforced materialsrdquo Composites Part A AppliedScience and Manufacturing vol 38 no 11 pp 2333ndash23412007

[22] A B SS Neto and H LL Rovere ldquoFlexural stiffness char-acterization of fiber reinforced plastic (FRP) pultrudedbeamsrdquo Composite Structures vol 81 pp 274ndash282 2007

[23] M D Hayes and J J Lesko ldquoMeasurement of the timoshenkoshear stiffness I effect of warpingrdquo Journal of Composites forConstruction vol 11 no 3 pp 336ndash342 2007

14 Advances in Materials Science and Engineering