Modeling and Analysis of GFRP Bridge Deck Panels Filledwith Polyurethane Foam

Hesham Tuwair1; Jeffery Volz2; Mohamed A. ElGawady, M.ASCE3; K. Chandrashekhara4; and Victor Birman5

Abstract: This paper presents finite-element analyses and analytical models of innovative, small-scale, prototype deck panels examinedunder monotonic bending. The deck panels consisted of two glass fiber–reinforced polymer (GFRP) facesheets separated by webs formedfrom E-glass–woven fabric placed around trapezoidal-shaped, low-density, polyurethane foam segments. The proposed panel exhibited ahigher structural performance in terms of flexural stiffness, strength, and shear stiffness than those of conventional sandwich panels.Analytical models were used to predict critical facesheet wrinkling in the sandwich panel. Furthermore, a three-dimensional model using sim-ulation software was developed for analysis of the proposed panel system under monotonic four-point loading. The finite-element results interms of strength, stiffness, and deflection were found to be in good agreement with those from the experimental results. A parametric studywas also conducted to further evaluate the effects of the stiffness of the top facesheet fiber layers, the mass density of the polyurethane foam,the existence of web layers, and the introduction of an overlay above the top facesheet. A flexural beam theory approach was used to predictthe flexural strength of the sandwich panel.DOI: 10.1061/(ASCE)BE.1943-5592.0000849.© 2016 American Society of Civil Engineers.

Author keywords: Sandwich panels; Glass fiber–reinforced polymer (GFRP); Polyurethane foam;Wrinkling; Finite-element analysis.

Introduction

Fiber-reinforced polymer (FRP) composites have become a popularconstruction material for infrastructures, such as columns andbridge decks (Dawood and ElGawady 2013; Abdelkarim andElGawady 2015). FRP sandwich panels are typically used forbridge decks. These panels are typically composed of two stiff FRPfacesheets separated by a core material. The cores can be solid, flex-ible, or cellular, which can include honeycombs, corrugated struc-tures, truss webs, C-shaped cores, I-shaped cores, and Z-shapedcores. Balsa was the first core material considered for use in applica-tions in which the weight was not critical (Stanley and Adams2001). Honeycomb cores represent one of the best options availablefor providing high shear strength and transverse stiffness-to-weightratios. It is unfortunate that they also require special care to guaran-tee sufficient bonding, which increases the production costs.Facesheets typically provide the bending strength, whereas thecore provides the shear strength (Allen 1969). The core delayslocal buckling of the compressed facesheets.

FRP sandwich bridge decks represent an alternative to conven-tional concrete bridge decks. These panels offer a number of addi-tional benefits, including high corrosion resistance, environmentalresistance, and higher strength-to-weight ratios. They can also beused to accelerate bridge construction while incurring minimumtraffic interruptions. Using lightweight FRP decks significantlyreduces the seismic demand on bridges (Russo and Zuccarello2007; Alagusundaramoorthy and Reddy 2008).

Skinwrinklingmaybea criticalmodeof failure for sandwichpan-els, because the facesheets have a relatively small thickness.Wrinkling is defined as a form of local instability in a compressionfacesheet, inwhich thewavelength of thewrinkledpart is of the sameorder as the thickness of the core (Carlsson and Kardomateas 2011).It can also be producedbynonlinear displacement patternswithin thesoft core (Sokolinsky and Frostig 1999).Wrinkling leads to stiffnesslosses andmaycontrol theultimate strengthof the sandwich panel.

Wrinkling forms can be classified into three types: single sided,symmetric, and antisymmetric. Single-sided wrinkling typicallyoccurs in the compression facesheet of the sandwich panel duringbending. Both symmetric and antisymmetric wrinkling generallyoccur in sandwich elements that have faces that are subjected toconcentric axial compressive loads (Allen 1969). Wrinkling mayoccur either toward the core or outward, depending on the compres-sion stiffness and adhesive strength of the core. Wrinkling is a localphenomenon that is affected by the material properties of the face-sheet and core.

The critical wrinkling load is a function of the stiffness of core,the stiffness of the facesheet, the loading configurations, and thesystem geometry. Gdoutos et al. (2003) studied facesheet wrinklingin sandwich columns and beams containing foam cores and honey-comb cores. They found that wrinkling occurred in sandwich panelsthat had foam cores. However, it did not occur in those with honey-comb cores. Birman and Bert (2004) analytically examined thewrinkling of composite-facesheet sandwich panels that were testedunder biaxial loading, where different models were used. Theauthors concluded that the models used are appropriate for wrin-kling analysis depending on the size of the buckling, the effect ofthe core stiffness, and the shearing stresses in the core.

1Graduate Research Assistant, Dept. of Civil, Architectural, andEnvironmental Engineering, Missouri Univ. of Science and Technology,Rolla, MO 65401. E-mail: hrthw2@mst.edu

2Associate Professor, School of Civil Engineering and EnvironmentalScience, Univ. of Oklahoma, Norman, OK 73019. E-mail: volz@ou.edu

3Benavides Associate Professor, Dept. of Civil, Architectural, andEnvironmental Engineering, Missouri Univ. of Science and Technology,Rolla, MO 65401 (corresponding author). E-mail: elgawadym@mst.edu

4Curators’ Professor, Dept. of Mechanical and Aerospace Engineering,Missouri Univ. of Science and Technology, Rolla, MO 65401. E-mail:chandra@mst.edu

5Professor, Engineering Education Center, Missouri Univ. of Scienceand Technology, St. Louis, MO 63131. E-mail: vbirman@mst.edu

Note. This manuscript was submitted on November 23, 2014;approved on August 31, 2015; published online on January 22, 2016.Discussion period open until June 22, 2016; separate discussions must besubmitted for individual papers. This paper is part of the Journal ofBridge Engineering, © ASCE, ISSN 1084-0702.

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Using analytical approaches to find an exact solution for wrin-kling problems may be limited by assumptions adopted for thesemethods. Thus, in the last two decades, researchers have begun toimplement finite-element (FE) analysis to investigate wrinklingbehavior (e.g., Aref and Alampalli 2001). Wan et al. (2005) usedANSYS to develop a three-dimensional (3D) model that could beused to investigate the structural behavior of a glass FRP (GFRP)bridge deck system. They also conducted a parametric study andfound that a good balance is required between the rigidity of thesupporting girders and the GFRP deck to meet the design strengthand serviceability demands.

Many approaches were used to model the sandwich panels,replacing the sandwich structure with an equivalent plate or shellelement that had approximately the same properties. Anotherapproach is called the discrete layer model, in which the sandwichpanel is divided into discrete layers, and each layer is defined sepa-rately (Noor et al. 1996). Morcous et al. (2010) used four FE model-ing approaches, including one-layer modeling, three-layer modeling,actual configuration modeling, and simplified I-beam modeling, toassess the structural behavior of honeycomb sandwich panels. Theyfound that the simplified I-beam modeling approach was the mostcomputationally efficient method for studying the overall perform-ance of honeycomb sandwich panels.

Tuwair et al. (2015b) recently developed a new multicellularFRP bridge panel (Fig. 1) in which the initial production costs andmanufacturing difficulties were reduced while the system perform-ance was improved. This proposed system was designed so that thepanel would behave as a flexural system in the perpendicular direc-tion to traffic and as a truss system in the parallel direction. Thepanel consisted of GFRP facesheets that were separated by a trape-zoidal-shaped, polyurethane foam core. Because the most commonproblem in sandwich panels arises when the facesheets debondfrom the core, the web layers were introduced in this system to

further connect the top and bottom facesheets. In addition, theseweb layers increased both the shear stiffness of the core and the flex-ural stiffness of the panel. The corrugated shape was chosen toreduce the span length within a compressed facesheet so that theeffects of localized deformations could be mitigated. To take theresearch out of the laboratory, a full-scale deck panel was recentlymanufactured by Structural Composites, Inc., to serve as a proof ofconcept (Volz et al. 2014). On the basis of the manufacturing find-ings, the costs of this panel system were less than the costs of com-parable honeycomb FRP decks, and the initial costs of this systemcould compete with those of reinforced concrete decks.

In this study, classic mechanics-based models, including thoseof Heath (1960), Allen (1969), the Winkler Elastic Foundation(WEF) (Carlsson and Kardomateas 2011), and Hoff and Mautner(1945), were used to predict critical facesheet wrinkling in thedeveloped sandwich panel. In addition, Abaqus 6.11 FE code wasused to conduct numerical simulations of the developed panels. Theresults were verified and compared with the experimental resultsgathered from four-point bending tests conducted on the sandwichpanels (Tuwair et al. 2015b; Tuwair et al. 2016). The verified FEmodel was then used to conduct a parametric study to investigatethe effects of the stiffness of the top facesheet fiber layers, the massdensity of the polyurethane foam, and the existence of an overlayon top of the deck on the deflection, initial stiffness, and strength ofthe GFRP panels. In addition, a simple theoretical approach basedon load equilibrium and strain compatibility was developed to pre-dict the flexural strength of the sandwich panel.

Calculating the CriticalWrinkling Stress

Several approaches were used in this study to predict the criticalwrinkling stress in the facesheet of the sandwich panel (s cr). Heath

Fig. 1. Test setup: (a) cross section of the developed panel (all dimensions are in inches, 1 in. = 25.4 mm); (b) schematic of static flexural test setup

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(1960) developed a model that takes into consideration the thick-ness of the facesheet and core in addition to the material propertiesto calculate the wrinkling load of a sandwich panel. The modelassumes that both the facesheet and the core are isotropic materials.The wrinkling stress, according to the model of Heath (1960), canbe calculated as

s cr; Heath ¼ 2 hf Ec Ef

3 hc ð1� y 2f Þ

" #12

(1)

where Ec and Ef are Young’s modulus of the foam and facesheetmaterial, respectively; hf and hc are the facesheet and core thick-nesses, respectively; and vf is Poisson’s ratio of the facesheetmaterial.

Allen (1969) modeled the facesheet as an infinitely long plateon an elastic core of infinite thickness. The wrinkling stress ofthe top facesheet was derived by assuming that the facesheet wasattached to the surface of the core and allowed to deform in anout-of-plane direction only. Thus, no axial strains occurred at thefacesheet-core interface in the course of wrinkling. FollowingAllen (1969)

s cr;Allen ¼ 3½12 3� vcð Þ2 1þ vcð Þ2��1=3 E1=3f E2=3

c (2)

where vc is Poisson’s ratio of the core.The WEF model (Carlsson and Kardomateas 2011) was used to

predict critical wrinkling stress. This approach assumes that thecore consists of linear elastic springs acting as an elastic foundationthat supports the facesheet; the core shear modulus is neglected.The WEF becomes more realistic in the case of symmetry, becausethe mode of deformation in the core is both tension and compres-sion. The wrinkling stress by theWEFmodel is given by

s cr;WEF ¼ 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiEf Echf6hc

s(3)

The effect of the shear modulus of the core is ignored in all threeapproaches. Thus, they provide reasonable results for sandwichpanels that have either a very low shear modulus or a relatively longwrinkling wavelength.

Hoff and Mautner (1945) used an energy & approach to predictthe critical wrinkling stress that considered the shear modulus of thecore. The following are the main two assumptions of Hoff andMautner (1945): (1) the facesheet undergoes a symmetric sinusoidaldisplacement; and (2) the wave damps out linearly through thethickness of the core. The following equation was developed to cal-culate the critical compressive stress:

s cr;Hoff & Mautner ¼ 0:91ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEf EcGc

3p

(4)

where Gc is the transverse shear modulus of the core. It should benoted that the web layers in the core were not included in theseequations because the wrinkling is a local phenomenon that occursat the top facesheet of themidspan between the web layers.

Experimental Work

Panel Description

Two sandwich panels were manufactured and tested during thisstudy. Each panel was composed of GFRP/polyurethane facesheets

separated by low-density trapezoidal-shaped polyurethane foam.The top and bottom facesheets were connected by corrugated weblayers (Fig. 1). Each of the top and bottom facesheets were con-structed of three layers of 0/90° woven E-glass roving fabric(WR18/3010; Owens Corning, Toledo, Ohio). Three plies of645° double-bias E-glass fabric (E-BXM1715; Vectorply, PhenixCity, AL) were oriented relative to the longitudinal axis of thepanel. Three plies were used to form each of the corrugated websthat were integrated into the facesheets. Each of the facesheet andweb layers contained 330 g/m2 (9.73 oz/sq yd) and 304 g/m2

(8.96 oz/sq yd) E-glass fibers in the longitudinal and transversedirections, respectively. The fabric was infused with a new ther-moset polyurethane resin system. This resin was modifiedrecently by Bayer MaterialScience (Pittsburgh) and features a lon-ger pot life, which enabled it to be used with the vacuum-assistedresin transfer molding (VARTM) process. The average thicknessof each laminate (after resin infusion) is shown in Fig. 1(a). Moredetailed information on this new panel system can be found inTuwair et al. (2015a, b). In the case of a full-scale panel, which willbe presented in a different study, vertical web layers may be addedat the ends of the panel so that the extended bottom flange wouldnot exist as seen in these tested small-scale panels [Fig. 1(a)].

Test Setup for Four-Point Loading

Each specimen was tested under four-point loading. Each panelhad a span length of 1,092.20 mm (43.0 in.) and total depth of105.41 mm (4.15 in.). This representation is approximately one-half scale. However, it should be noted that the thickness andcharacteristics of the different layers need to be tailored for thefull-scale panel on the basis of the required design loads. Eachpanel was tested under two equal point loads that were applied at393.70 mm (15.5 in.) from each support. This setup provided asection of constant moment within the panel and a shear span-to-depth ratio of 3.74 [considering a shear span of 393.70 mm (15.5in.) and a depth of 105.41 mm (4.15 in.)].

The specimen was simply supported using two steel plates, eachwith a width of 50.80 mm (2.0 in.), that could freely rotate around asteel rod that was 25.40 mm (1.0 in.) in diameter, as illustrated inFig. 1(b). The loading was applied through 50.80-mm (2.0-in.) steelplates. Rubber pads with a shore A hardness of 60 were placedbetween the specimen and the contact points to avoid potential localcrushing. Each specimen was loaded in a displacement controlat a loading rate of 1.27 mm/min (0.05 in./min) in an MTS880Universal Testing Machine (MTS, Eden Prairie, Minnesota) untilfailure occurred.

FEAnalysis of the Sandwich Panel

A FE commercial code, Abaqus 6.11, was used to construct theprototype deck panel that is discussed in the experimental worksection. The FE model (depicted in Fig. 2) was used to betterunderstand the behavior of the proposed configuration and to ver-ify the model against the experimental results under monotonicloading. Once the model was validated, it was also used to manu-facture a full-scale panel that will be presented in a differentstudy.

Three-dimensional FE modeling can be approached by using ei-ther detailed or reduced models. In both models, the core is modeledusing solid elements. However, in the detailed models, the face-sheets are modeled by solid elements, whereas in the reduced mod-els, the facesheets aremodeled by shell elements. A 3D fully detailedmodel is computationally expensive, because the facesheets are

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typicallymuch thinner than the core, dictating a very refinedmesh inthe fully detailed model. However, 3D fully detailed models typi-cally yield more accurate results. A 3D fully detailed approach wasused in this study.

Element Type and Assumptions

The elements of the core, the facesheets, and the web layers(Fig. 3) were defined by solid 3D continuum elements that hadeight-node, integration-reduced, linear brick elements (C3D8R,hourglass control). These elements had three translational degreesof freedom at each node. The use of these elements helped preventmesh instability, commonly referred to as hourglassing, whichmay occur in reduced-integration elements (Dassault SystèmesSIMULIA 2013).

A perfect bond was assumed to exist between the sandwichpanel components used in the model because delamination did notoccur during the experimental tests. After each experimental test,the panels were examined carefully for delamination. Furthermore,several cross sections were taken from each tested panel, and nodelamination was observed. The different panel components weremeshed so that the interface between any two panel componentsshared the same nodes.

Loading and Boundary Conditions

The sandwich panel was modeled as a simply supported beam.Similar to the experimental work, the applied loads were simulatedin the model as line loads applied by steel plates that were 50.80 mm(2 in.) wide. Rigid 3D elements were used to model the steel plates.Rigid steel plates were placed at the support location. The boundaryconditions [Fig. 2(b)] were defined as a pin support at one end and aroller support at the other end. A perfect contact was assumed toexist between the loading steel plates and the surface of the sandwichpanel. The panel was monotonically loaded at the loading pads in adisplacement control mode until failure occurred. The Abaqusimplicit solver was used to analyze the sandwich panels.

Material Properties

FRP CompositesThe FRPmaterials were assumed to be linear elastic isotropic mate-rials on the macroscale level because the interwoven fibers were or-thogonal to each other, and the glass fiber content in the longitudinal(wrap) and transverse (fill) directions are approximately the same.Moreover, the thickness of these layers is small compared withother dimensions.

On the basis of material characterization tests (Tuwair et al.2015a), the elastic moduli of the facesheet in tension (Ef,þ) andcompression (Ef,−) were 13.97 GPa (2,027 ksi) and 13.23 GPa(1,919 ksi), respectively. The elastic moduli of the web layers were11.80 GPa (1,712 ksi) and 7.26 GPa (1,053 ksi) in tension and com-pression, respectively. The ultimate tensile stresses (s fþ) of thefacesheet and the web layers were 264.80 MPa (38.4 ksi) and176.50 MPa (25.6 ksi), respectively, whereas the ultimate compres-sive stresses (s f−) of the facesheet and the web layers were 102.70MPa (14.9 ksi) and 128.7 MPa (18.6 ksi). Poison’s ratios (y ) were0.27 and 0.30 for the facesheets and the shear layers, respectively. TheFE model was assumed to have failed when the stresses in the FRPmaterials reached the ultimate tensile or compressive stress value.

Polyurethane FoamA low-density closed-cell polyurethane foam with trapezoidal-shaped segments was used as the core material. The material prop-erties were determined experimentally. The foam had a mass den-sity of 32 kg/m3 (2.0 lb/cu ft) (low-density foam) and was 1,219.20mm (48 in.) long. A crushable foam model (available in the Abaquslibrary) was used to model the foammaterial. An elastic modulus of2.1 MPa (301.8 psi) and a yield stress of 0.056 MPa (8.1 psi) (Fig.4), used to model the low-density foam, were determined from ear-lier experimental work (Tuwair 2015a). A high-density polyur-ethane foam of 96 kg/m3 (6.0 lb/cu ft) was also used for the para-metric study.

Fig. 2. FEmodel: (a) 3D view of simulated FEmodel; (b) centerline boundary condition of the support

Fig. 3. FE model components: (a) GFRP facesheets; (b) GFRP weblayers; (c) low-density polyurethane foam

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Results and Discussion

Experimental Results

The average load-deflection curve measured at the midspan for twopanels is illustrated in Fig. 5. Both panels exhibited an essentiallylinear response throughout the ascending loading-deflectionresponse. A slight reduction in the stiffness was observed justbefore the panel failure. This reduction resulted from outward skinwrinkling that occurred at the top facesheet between the loadingpoints. This observation was also verified by strain gauge readings.The average maximum deflection recorded at the midspan was25.65 mm (1.01 in.) at an average failure load of 79.31 kN (17.83kips).

Both specimens produced a loud popping sound at the load ofapproximately 56.94 kN (12.80 kips) and the deflection of 19.05mm (0.75 in.). Closer examination revealed that a portion of thetop facesheet (at the midspan) experienced outward wrinkling[Fig. 6(a)]. Fig. 6(b) reflects a sudden softening that occurred inthe compression facesheet as a result of wrinkling. Both specimensproduced a second loud popping sound at failure. This sound wasaccompanied by compression failure of the top facesheet beneathone of the loading points.

Bridge deck elements are stiffness driven and typically con-trolled by deflection to ensure the element functions properly anddoes not cause discomfort to individuals using the structure. In addi-tion, limiting the deflection is done in an attempt to minimize crack-ing of the wearing surface. It is unfortunate that there are no deflec-tion limits suggested for FRP decks, but a limit ranging from L/300to L/800 is adopted in the design of various FRP bridge decks (Kinget al. 2012; Alampalli and Kunin 2002; Alampalli et al. 2002). Thelimit state is typically kept at L/800, as proposed in the AASHTOcode (AASHTO 2013), and is also proposed in the current practicesin FRP composites technology by Federal Highway Administration(FHWA 2011). A typical range of L/300–L/800 applied to the1,092.20-mm (43-in.) tested panel span results in a deflection limitrange of 1.27–3.56 mm (0.05–0.14 in.). The investigated panelreached its initial failure mode, in the form of wrinkling, at a deflec-tion of approximately 10.16 mm (0.40 in.) or 2.9 times the upperserviceability deflection limit. As expected, serviceability is thecontrolling limit state in these sandwich panels. This result indicatesthat the design of these panels will likely always be controlled byflexural stiffness and serviceability rather than strength. This result

Fig. 5. Experimental load-deflection results

Fig. 4. Compression stress versus strain curves of low-density andhigh-density polyurethane foam

Fig. 6. Experimental test results: (a) outward facesheet wrinkling failure; (b) load versus strain at midspan

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was also expected, considering that the FRP panels that wereexplored in previous research were almost always controlled byserviceability in experiments and design. Thus, a larger cross sec-tion, with reasonable facesheet and web layer thicknesses, is neededto achieve the serviceability limit state.

Analytical Results

The measured applied load from the experimental work was used tocalculate the stress at both the top and the bottom facesheets. The

calculations predicted the maximum compressive bending stressesof 77.50 MPa (11.24 ksi) and the wrinkling stress of 34.82 MPa(5.05 ksi), which corresponds to the load of 35.58 kN (8.0 kips)[Fig. 6(b)]. Technical beam theory (Allen 1969) was used to esti-mate the global stresses.

Eqs. (1)–(4) were used to predict the critical wrinkling stressesof the top facesheet. Both the polyurethane foam and the facesheetswere modeled as isotropic materials. The data used for the calcula-tions are summarized in Table 1. The Heath (1960), Allen (1969),WEF (Carlsson and Kardomateas 2011), and Hoff and Mautner(1945) models yielded the values 21.17 MPa (3.07 ksi), 21.86 MPa(3.17 ksi), 20.41 MPa (2.96 ksi), and 25.51 MPa (3.70 ksi), respec-tively. A comparison between these analytical formulas and the ex-perimental results is presented in Fig. 7. As seen in Fig. 7, all mod-els except for the Hoff and Mautner (1945) model underestimatedthe facesheet wrinkling by approximately 39%. The Hoff andMautner (1945) model also underestimated the facing wrinkling by27% and was the most accurate model because it accounts for theinfluence of the transverse shear modulus of the core. It was alsonoted that the wrinkling wavelength was relatively short [Fig. 6(a)],which represents the situation in which the Hoff and Mautner(1945) model, which accounts for the shear stiffness of the core, isquite reasonable.

The two strain gauges used in the experimental work weremounted to the middle top surface of the facesheet. Each gauge wasattached at a distance of 50.80 mm (2 in.) from the longitudinal cen-terline of the panel. As is explained in the FE results section, anasymmetry issue was observed during the experimental work thatcaused the recorded wrinkling observed in the experimental work tobe relatively higher than that at which the actual wrinkling began.As a consequence, the values predicted by these models will alwaysprovide more conservative (lower) results than those recordedthrough the experimental work.

FE Results

The deformed shapes of both the experimental test panel and the FEmodel are illustrated in Fig. 8. It should be noted that because theexperimental results for the two specimens were almost identical,one FEmodel was discussed in this section to avoid potential confu-sion. The deflection measured at the midspan of the panel in theexperiment is compared with that obtained from the FE model inFig. 9. The FEmodel, in general, captured the tested sandwich panelbehavior. The average maximum deflection recorded at midspan inthe test was 25.65 mm (1.01 in.) at the average failure load of 79.31kN (17.83 kips). The FE model predicted an ultimate load of 94.75kN (21.3 kips), which was 19.4% higher than that measured duringthe experiment. The FE models also predicted deflection of 32.51mm (1.28 in.) at the peak load, which was 26.7% higher than thatmeasured during the experiment (Fig. 9). The flexural rigidity

Table 1. Summary of Data Used for Wrinkling Calculations

Parameter Value

Facesheet thickness, hf [mm (in.)] 2.29 (0.09)Core thickness, hc [mm (in.)] 100.84 (3.97)Compressive modulus of low-density foam,Ec [MPa (psi)]

2.1 (301.8)

Compressive modulus of high-density foam,Ect [MPa (psi)]

37.1 (5,380)

Compressive modulus of facesheet, Ef [GPa (ksi)] 13.23 (1,919)Poisson’s ratios of the facesheet material, y f 0.27Poisson’s ratio of the foam, y c 0.3Transverse shear modulus of low-density foam,Gc [MPa (psi)]

0.8 (116.1)

Transverse shear modulus of high-density foam,Gc [MPa (psi)]

14.3 (2,069)

5.05

3.07 3.17 2.96

3.7

0

5

10

15

20

25

30

35

40

0

1

2

3

4

5

6

Wri

nklin

g St

ress

(MPa

))isk(ssertSgnilknir

W

Analytical Models

Experiment

Heath (1960)

Allen (1969)

WEFA (Carlsson andKardomateas 2011)

Hoff and Mautner (1945)

Fig. 7. Comparison of different analytical formulas with the experi-mental results

Fig. 8. Deformed shape for experimental and FE results

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predicted by the FE model was 6.6% lower than that exhibited bythe panel during the test. The maximum tensile strain on the bottomfacesheet of the midspan recorded during the experiment was0.0091 mm/mm, whereas the value obtained for the FE model was0.0097 mm/mm. Thus, the difference between the two strain valueswas 6.2%.

The FE model tended to overestimate the predicted deflection atmidspan and the strength. The difference in the deflection betweenthe FE model and the experiment was attributed to several reasons.One reason was the asymmetry that appeared during the experi-ment. Although every effort wasmade to ensure symmetric loading,the wrinkling at the top facesheet that occurred during the test was

closer to one of the loading points, not exactly in the middle of thespecimen, which indicates slight asymmetry in either the test fixtureor the test specimen. The area underneath the loading points wasnot perfectly leveled, which produced asymmetric loading condi-tions during the experiment. These conditions caused one of the50.80-mm (2-in.) loading steel plates to apply more load than theother, which resulted in an earlier compression failure than thatobserved in the FEmodel. This explanation was verified by runningtwo FE models in which the loading was asymmetric. One loadingpoint was assumed to be subjected to loads higher than those of theother by 5% and 10% for the first and second models, respectively.The results collected from this portion of the study are illustrated inFig. 9. Including asymmetry reduced both the ultimate strength ofthe panel and its maximum deflection.

Another potential reason for the difference in the resultsobtained from the experiment and the FE model was the manufac-turing process, which produced some variability in the differentlayers. This slight variability also affected the FE model predic-tions. Last, inherent and simplified assumptions used in the FEmodel, such as assuming that the FRP material is isotropic, resultedin additional differences between the experimental and analyticalresults.

The FE model correctly predicted the deformed shape and modeof failure (Figs. 8 and 10, respectively). The contours of the totalequivalent plastic strain (which is a scalar quantity) are illustrated inFig. 10(c); a value greater than 0 indicates that plastic deformationoccurred. The top FRP facesheet exhibited outward wrinklingbetween the two applied loads during the experiment, which subse-quently displayed local compression failure at the loading line. Thisfailure was induced by a high stress concentration [Fig. 10(a)]. TheFE model exhibited a similar behavior [Figs. 10(b and c)]; it pre-dicted a high stress concentration at the top facesheet between thetwo loading points, which indicates outward wrinkling. Ultimate

Fig. 9. Comparison of experimental versus numerical results (Note:FEA = finite-element analysis; PEEQ = effective plastic strain-scalar;Sym = symmetric; Unsym = unsymmetric)

Fig. 10. Compression failure under the loading pads: (a) for the experimental specimen; (b) for the FEmodel; (c) contours of plastic strains show ini-tial failure at the top facesheet caused by wrinkling and ultimate failure caused by excessive compressive stresses at the loading points

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failure occurred due to high stress concentration at the contact sur-face under the loading pads that led to crushing of the top facesheet.Overall, these results validated the modeling assumptions and sim-plifications that were used in the analysis to predict the sandwichpanel behavior. Accordingly, this model can reasonably predict thebehavior of such sandwich panels under monotonic loading.

Parametric Study

The benefit of FE modeling is the ability to alter a wide variety ofparameters to investigate a range of behavior of the prototype panel.As a result, the FE model that was previously verified experimen-tally was used for the parametric study to better understand thebehavior and potential of the panels. The parameters investigatedincluded the following:• Effect of the stiffness of the FRP layers in the top facesheet;• Effect of the mass density of the polyurethane foam;• Effect of the web layers; and• Effect of an overlay.

The FE model of the actual panel that was validated in the pre-ceding section was used as the sandwich panel-reference (SP-R)model in the following simulation studies.

Effects of Stiffness of the Top FRP Facesheet

This section of the study was conducted to investigate the effect ofthe top facesheet stiffness on outward skin wrinkling and overall

performance. The top facesheet stiffness was increased by addingGFRP layers. The modified cross section was identical to the refer-ence model, SP-R, except for the number of layers in the top face-sheet, which were increased to five, seven, and nine layers for mod-els SP-5L, SP-7L, and SP-9L, respectively. The load versus themidspan deflection responses for these panels are illustrated in Fig.11(a). Fig. 11(b) shows a plot of the top facesheet longitudinal straindistributions between the two loading points normalized by themaximum longitudinal strain of the SP-R. The relative out-of-planedeflection that occurred along the clear distance between the load-ing points is illustrated in Fig. 11(c).

As shown in Fig. 11(a), increasing the top facesheet stiffnessincreased the ultimate load and initial stiffness and slightlyincreased the midspan deflection at peak loads. The increased stiff-ness compensated for the increased strength and limited the increasein the deflection. Increasing the number of layers of the top face-sheet resulted in an increase in the moment of inertia for models SP-5L, SP-7L, and SP-9L by 15.4%, 28.9%, and 41%, respectively. Inaddition, increasing the number of top facesheet layers increasedthe panel initial stiffnesses by 17.3%, 31.5%, and 43.2% for modelsSP-5L, SP-7L, and SP-9L, respectively. In general, the strength wasincreased from 94.75 kN (21.3 kips) at a deflection of 32.51 mm(1.28 in.) for the SP-R panel to 153.02 kN (34.4 kips) at a deflectionof 40.39 mm (1.59 in.) for the SP-9L panel, which corresponds toincreases of 61% and 24%, respectively, in strength and deflectionat peak load.

Increasing the FRP top facesheet stiffness also changed themode of failure. Panels with fewer FRP layers (SP-R and SP-5L)

Fig. 11. Effects of FRP in the top facesheet: (a) applied load versus midspan deflection; (b) longitudinal compressive strains in the top facesheetbetween the loading points; (c) relative out-of-plane deflection in the top facesheet between the loading points

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experienced outward skin wrinkling at midspan, as shown in Fig.11(b), whereas panels with a large number of FRP layers (SP-7Land SP-9L) had smaller local compressive strains and did not dis-play wrinkling deformation [Figs. 11(b and c)]. Note that thechange from seven to nine layers resulted in very little change in thenormalized compressive strain and outward deflection in the topfacesheet. The SP-R model displayed the largest variation in com-pression strain distribution with a ratio of 10 between a maximumand a minimum strain. The SP-5L, SP-7L, and SP-9L models dis-played ratios of variation of 2.5, 1.0, and 1.0, respectively. Localcrushing under loading points caused ultimate failure in all panels.

Effects of Polyurethane Foam

The influence of the density of polyurethane foam on the structuralperformance of the sandwich panel was also investigated. Threepanel models were examined, namely, SP-1F, SP-R, and SP-2F,which corresponded to panels with no foam, a low-density foam [32kg/m3 (2 lb/cu ft)], and a high-density foam [96 kg/m3 (6 lb/cu ft)],respectively. The compressive stress-strain behavior of both typesof foam is illustrated in Fig. 4.

The load versus the midspan deflection response of the threepanels was compared. As shown in Fig. 12(a), the existence andabsence of the foam core did not affect the stiffness of the panel,which confirms the findings of Allen (1969) that low-density coresdo not noticeably contribute to the overall bending stiffness ofsandwich panels. In contrast, the ultimate strength increased by7.5% when the high-density foam was used in the case of a SP-2F

panel. It should be noted also that the top facesheet compressivestrain value was approximately 0.003 [Fig. 6(b)], which corre-sponds to compressive stresses of approximately 10 and 60 psi forthe low- and high-density foams (Fig. 4), respectively. These lowvalues also support the previous finding that the foam did notnoticeably contribute to the overall bending stiffness.

It was unexpected that the local compressive strain concentra-tion was reduced by 40% in the SP-1F panel compared with thatof the SP-R panel [Fig. 12(b)]. This reduction was explained bythe absence of foam, which triggered the external webs to buckleoutward (Fig. 13). As a result, the interior webs moved apart fromeach other, which brought the top facesheet downward (i.e., out-ward wrinkling was reduced as a result of the buckling of theexternal webs).

Local compressive strains at the top facesheet were reduced by72% when the low-density foam was replaced with a high-densityfoam in the SP-2F panel [Figs. 12(b and c)]. This reduction wascaused by the high transverse shear modulus of the high-densityfoam, which significantly increased the stress at wrinkling from25.51 MPa (3.70 ksi) in the SP-R panel to 174.44 MPa (25.3 ksi) inthe SP-2F panel. As a result, SP-2F failed as a result of the compres-sive stresses under the loading pads at stresses lower than the wrin-kling stresses.

Thus, if it is required to prevent wrinkling, high-density foamshould be used. Considering that the downside of this foam is itsweight, which results in a heavier deck panel, the optimal sandwichpanel could use a low-density polyurethane foam, combined withadditional layers of FRP in the top facesheet, to prevent wrinkling.

Fig. 12. Effects of polyurethane foam: (a) applied load versus midspan deflection; (b) longitudinal compressive strains in the top facesheet betweenthe loading points; (c) relative out-of-plane deflection in the top facesheet between the loading points

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Effects of Web Layers

The core of a sandwich panel has to be stiff and rigid enough toresist the shear forces and prevent sliding of the facesheets relativeto each other. The rigidity of the core also alleviates local stress con-centration and wrinkling.

Three panel models were investigated to better understand theeffects of the web layers on the response of the FRP panels. Onemodel (SP-R) represented the reference panel. The SP-1W panelhad no web layers (i.e., the top and bottom facesheets were con-nected only by the low-density polyurethane foam). The SP-2Wpanel had two external webs only, without foam. The external webswere used to maintain a composite action between the facesheetsand the foam core.

All panels were loaded in the same manner as that used for theexperimental specimens. The load-versus-midspan deflection ofthe three sandwich models is illustrated in Fig. 14(a). Removing theweb layers significantly changed the response of the specimen. TheSP-1W curve had an initially linear region, followed by a nonlinearregion. The panel behavior was affected by the polyurethane foamcore behavior (i.e., the panel supported a higher load without signif-icant damage). The top and bottom facesheets did not reach theirultimate stresses, because they behaved as two independent platesas a result of the very low stiffness [2.1 MPa (301.8 psi)] of thepolyurethane foam core. Both the ultimate strength and initial stiff-ness were significantly reduced by 96% and 95%, respectively. Asillustrated in Figs. 14(b and c), local wrinkling did not occur in theSP-1W panel. However, local indentation was the major concern

Fig. 13. Deformed shapes for (a) SP-R panel and (b) SP-1F panel

Fig. 14. Effects of web layers: (a) applied load versus midspan deflection; (b) longitudinal compressive strains in the top facesheet between the load-ing points; (c) relative out-of-plane deflection in the top facesheet between the loading points

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about the use of flexible foam, as clearly demonstrated in Fig. 14(c),which caused the facesheet to buckle on the compression side.

For the SP-2W panel model, both the ultimate strength and ini-tial stiffness were reduced by 56.6% and 27.0%, respectively [Fig.14(a)]. The SP-2W panel behaved linearly until it failed due to ex-cessive local compression failure at the loading points. Wrinklingdid not occur [Figs. 14(b and c)] because the external webs faileddue to buckling before the top facesheet reached critical wrinkling.

Effects of an Overlay Applied Over the Top Facesheet

Bridge decks require a surface texture to provide skid resistance andwear resistance to traffic. In addition, the overlay helps to distributethe applied load on the bridge deck and hence prevents highly local-ized concentrated forces on the FRP panels. Many different wearingsurfaces, such as steel, asphalt, and polymer concrete, have beenused on bridge decks (Aboutaha 2001). Polymer concrete overlayswere not considered in this study, because several studies conductedfor the U.S. Department of Transportation showed that polymerconcrete will likely crack due to differential movement between thedeck panels (Robert et al. 2002).

Three panels, SP-R, SP-C, and SP-A, were used to investigatethe effects of no overlay, a concrete overlay, and an asphalt overlay,respectively, on the performance of the panels. The SP-R panel wasused as the reference model. A 12.7-mm (0.5-in.) concrete layerwas used in the SP-C panel as the overlay on the top of the sandwichpanel (Fig. 15). It should be noted that the overlay thickness of afull-scale bridge deck would be higher than what was used in thisanalysis. However, the goal here was to understand the effect of theoverlay on the system. Three-dimensional brick solid elements(C3D8R) were used to model the concrete layer. The concrete dam-age plasticity model was used to model the overlay with a concretecompressive strength of 49.98 MPa (7.25 ksi). The material proper-ties used for the concrete and model parameters were obtained fromTyau (2009) and Dawood et al. (2014). The tension and compres-sion stress-strain curves, and their corresponding damage curves,were defined using the Abaqus software. The general parameters ofthe concrete damage plasticity were as follows• Dilation angle (c ) = 31;• Flow potential eccentric = 0.1 m;• Initial biaxial/uniaxial ratio (sc0/sb0) = 1.16;• Ratio of the second stress invariant on the tensilemeridian (kc) =

0.666; and• Viscosity parameter (m ) = 0.

Full composite action was assumed between the FRP sandwichpanel and the overlay. The full composite action can be achievedpractically by either adhesives and/or mechanical connectors(Deskovic et al. 1995; Jain and Lee 2012).

In the SP-A panel, a 12.7-mm (0.5-in.) asphalt overlay (Fig. 15)was used over the sandwich panel. The asphalt was expected to

perform better than the concrete in terms of durability and con-structability. Asphalt is a flexible material, so any differential move-ments between the FRP panels would not affect it significantly com-pared with concrete. Another advantage of using asphalt is themuch shorter installation time (i.e., it does not require a long curetime compared with both regular concrete and polymer concrete).Three-dimensional brick solid elements (C3D8R) were used tomodel the asphalt layer. The asphalt material was modeled inAbaqus using the Prony series to model the viscoelasticity of theasphalt material. The asphalt had a Young’s modulus of 3,500 MPa(507.63 ksi) and a Poisson ratio of 0.35 (Koohmishi 2013).

The explicit solver was used to analyze the SP-C model becausethe implicit solver (used for all other models) was not able to solvethis problem due to convergence problems. The explicit analysisusing the Newton-Raphson iteration to enforce the equilibrium con-dition at each step can be used to solve highly nonlinear systems.

The concrete layer weighed approximately 109 N (24.5 lb)[assuming a normal-weight concrete with a mass density of 23.6kN/m3 (150 lb/cu ft)], whereas the sandwich panel itself weighed105 N (23.6 lb) and had a mass density of approximately2.36 kN/m3 (15 lb/cu ft). The flexural moment demand thatresulted from the self-weight of the concrete layer was 16.3 N/m(144 lb/in.), which was only approximately 0.1% of the flexuralmoment capacity of the reference panel SP-R.

The load-versus-midspan deflection responses for the three pan-els are shown in Fig. 16(a). The SP-C panel with concrete overlaybehaved linearly until it reached the load of approximately104.09 kN (23.4 kips) at a midspan deflection of 14.98 mm (0.59in.). A sudden drop then occurred in the load, which was producedby compression failure in the concrete layer, close to the loadingpoints. This failure can be explained by the recorded von Misesstresses at the concrete and FRP surfaces. The recorded von Misesstresses in the midspan top facesheet are shown in Fig. 17. Thestresses in the concrete layer displayed a linear behavior until theconcrete reached its ultimate compressive stress of 49.98MPa (7.25ksi). The FRP panel contribution to the composite panel strengthwas quite small until this stage. High compressive stress concentra-tions at the loading points led to sudden failure. The load was thencarried by the FRP panel itself (Fig. 17). The SP-C panel, however,displayed initial stiffness that was 124% higher than that of the ref-erence FRP panel SP-R, which was attributed to the beneficial con-tribution of the concrete overlay, which delayed local FRP ruptureunder the loading points. High stress concentration under the load-ing points led to failure of the FRP after the top facesheet reachedits ultimate strength [97.56MPa (14.15 ksi)].

The normalized longitudinal strain distributions and the relativeout-of-plane deflection that occurred along the clear distancebetween the top facesheet loading points are illustrated in Figs.16(b and c). As shown in Fig. 16(b), the SP-C panel experi-enced a small, nearly uniform compressive strain compared with

Fig. 15. 3D view of the simulated FEmodel with an overlay

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the highly concentrated strains in the case of the SP-R panel. Thepeak compressive strain in the top facesheet of SP-C was onlyapproximately 4% of that in the SP-R panel. Wrinkling, wasrecorded for the SP-C panel at the maximum load just before thefirst failure occurred in the concrete layer.

The SP-A panel behaved linearly until it reached a load ofapproximately 187.71 MPa (42.2 kips) at a midspan deflection of1.23 [Fig. 16(a)]. Then, the panel started to fail due to buckling inthe webs. The SP-A panel displayed initial stiffness that was

approximately 94% higher than that of the reference FRP panel SP-R as a result of the beneficial contribution of the asphalt overlay. Itshould be noted that the viscoelasticity of the asphalt prevented fail-ure in the facesheet until the stresses reached 86% of its ultimatetensile strength, whereas failure occurred in the SP-R panels whenthe stress reached only 53% of its ultimate tensile strength.

Figs. 16(b and c) illustrate the normalized longitudinal strain dis-tribution and the relative out-of-plane deflection between the topfacesheet loading points. The SP-C and SP-A panels did not experi-ence excessive compressive strain concentrations. Therefore, it wasobserved that both overlays significantly decreased the compressionstrains and prevented wrinkling.

Simplified Flexural AnalysisMethod

This section discusses a simplified analysis method that may beapplied to the prototype panel analyzed in this study. The sandwichpanel (Fig. 1) was analyzed by assuming one-way bending. Theanalysis was based on the principles of strain compatibility andforce equilibrium. The main assumptions used in the analysis wereas follows: (1) the plane section remains in plane; (2) a perfect bondexists between the panel components; and (3) the materials are lin-ear elastic. The analysis based on these assumptions providesdesign engineers with a tool for calculating the nominal flexuralstrength of the proposed sandwich panel.

The sandwich panel compressed facesheet experiences localinstability (wrinkling) if the compressive stress induced in the top

Fig. 16. Effects of an overlay: (a) applied load versus midspan deflection; (b) longitudinal compressive strains in the top facesheet between the load-ing points; (c) relative out-of-plane deflection in the top facesheet between the loading points

Fig. 17. Longitudinal stresses at the midspan top facesheet for the con-crete and FRP surfaces

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facesheet exceeds the wrinkling stress. The panel strength, there-fore, will be limited by the strains that cause wrinkling.

Because the wrinkling stress (swr) estimated using the Hoff andMautner (1945) model was the closest to the experimental result, itwas used in this calculation as the limiting stress for the top face-sheet. The wrinkling strain (0.0027 mm/mm)was found by dividingthe wrinkling stress by the facesheet compressive modulus of elas-ticity. The wrinkling strain was assumed to be uniform along thetop facesheet. Because of the change in strain through the thickness(in addition to the trapezoidal geometry of the panel), the sectionproperties were calculated in small segments at 1/20th along thecross-section height (Fig. 18). Using strain compatibility for thestudied section, the strains in each segment were estimated by usingsimilar triangles [see Eq. (5)]. Consequently, Eq. (6) was used tocalculate the forces in each segment level. Here, the strain was mul-tiplied by both its modulus of elasticity (whether in tension or incompression) and the area of the segment. The foam was neglectedin the strength calculations because it has a low modulus of elastic-ity. Then, the neutral axis location (c) was calculated by using aniterative procedure using Eqs. (7) and (8) and superimposing therequirement of equilibrium between tensile and compressive forcesin the cross section. The section capacity was then computed usingEq. (9)

ɛi ¼ dic

� �ɛwr (5)

Fi ¼ Ei ɛi Ai (6)

Ft;total ¼Xn¼ðd�cÞ=20

i¼1

Fi (7)

Fc;total ¼Xn¼c=20

i¼1

Fi (8)

Mcap ¼Xn¼d=20

i¼1

Fi di (9)

where « i is the strain in segment i; di is the distance from the cen-ter of segment i to the neutral axis; c is the distance from theextreme upper fiber of the panel to the neutral axis; d is the panelthickness; «wr is the wrinkling strain for the compressed facesheet;Fi is the compressive or tensile force; Ei is the modulus of elastic-ity (either of the facesheet or of the web layer) when the segment iis in either compression or tension; Ai is the cross-sectional area ofsegment i; Ft,total is the total of all of the tensile forces in the ten-sion side; Fc,total is the total of all of the compressive forces in thecompression side; andMcap is the capacity flexural moment for thesandwich panel.

The analytical results indicate that reasonable accuracy can beachieved with the assumptions used in this approach. The analyticalprocedure underestimated the flexural capacity by 16.2% (com-pared with the experimental results). This difference could be aresult of the assumptions used in estimating the wrinkling strain andin the flexural analysis. Furthermore, the experimental panel sectionthickness varied with a coefficient of variation of 7.2%, whereas theanalytical model used only one thickness value. Another reason forthe difference between the experimental and analytical results couldbe the variability (12.9% coefficient of variation) in the resultsobtained from the experimental calculations for the compressivemodulus of elasticity of the top facesheet, which directly affects thewrinkling stress.

Summary and Conclusions

Two specimens were tested in one-way bending under four-pointbending. Both the FE model and the analytical methods were used toanalyze the behavior in each panel. A parametric study was con-ducted using FEM by considering the effect of the number of FRPlayers in the top facesheet, the mass density of the polyurethanefoam, the effect of web layers, and the effect of an overlay of concreteor asphalt above the top facesheet. An analytical model based on flex-ural beam theory was used to estimate the sandwich panel flexuralcapacity. The following conclusions were drawn from this study:1. The behavior of the developed sandwich panel can be treated as

linear-elastic up to failure.2. The proposed FE model can reasonably predict the bending

behavior of the sandwich panel under monotonic loading.3. The ultimate strength obtained from the FE model was 19.4%

higher than that obtained from the experiment. This differencewas a result of the asymmetry encountered in the experimentalsetup. However, the flexural rigidity predicted by modelingwas 6.6% lower than that obtained in the experiment.

4. Different analytical models were used to estimate outwardskin wrinkling, which triggered failure in the experiment. Allthe models underestimated the facesheet wrinkling stress by26.7%–39%. The Hoff and Mautner (1945) model was themost accurate because it accounts for the influence of thetransverse shear modulus of the core.

5. The following can be concluded from the results of the FE para-metric study:a. The outward skin-wrinkling tendency decreased as the

number of layers in the top facesheet increased.b. The foam core characteristics affect the local stress concen-

tration in the compression facesheet. However, the occur-rence of wrinkling was local and did not affect the bendingstiffness of the different specimens. Last, because all panelsdisplayed an ultimate limit state of local FRP rupture at theapplied load, the existence of the core foam had an insignif-icant effect on strength.

c. The panel behavior was significantly dependent on theproperties of the web layers. Using a low-density

Fig. 18. Compression and tension couple at the nominal moment

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polyurethane foam as a core without webs proved to beinsufficient for providing the necessary rigidity, which ledto a local indentation phenomenon under loading points.Both the ultimate strength and the flexural rigidity werereduced by approximately 95%. However, adding the exter-nal webs to the core, in addition to foam, significantlyimproved panel behavior.

d. The concrete and asphalt overlay significantly improvedthe behavior of the panels. The flexural stiffness increasedby 125% and 94% for concrete and asphalt, respectively.The overlay layers significantly reduced outward wrinklingof the top facesheet.

6. The simplified flexural analysis method reasonably predictedthe panel flexural capacity with an error of approximately 16%.Therefore, this method can be used for estimating the proposedpanel capacity at the preliminary design stage.

Acknowledgments

The authors acknowledge the financial support provided by theMissouri Department of Transportation and theNational UniversityTransportation Center at Missouri University of Science andTechnology.

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