Research Article Structural Performance of a Hybrid FRP...

Research ArticleStructural Performance of a HybridFRP-Aluminum Modular Triangular Truss SystemSubjected to Various Loading Conditions

Dongdong Zhang1 Yaxin Huang1 Qilin Zhao1 Fei Li2 Feng Li1 and Yifeng Gao1

1 College of Field Engineering PLA University of Science and Technology Nanjing 210007 China2 Institute of Logistics Engineering of PLA Chongqing 400000 China

Correspondence should be addressed to Qilin Zhao zhaohsql919163com

Received 7 May 2014 Revised 23 July 2014 Accepted 28 July 2014 Published 28 August 2014

Academic Editor Antonio Boccaccio

Copyright copy 2014 Dongdong Zhang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A novel hybrid FRP-aluminum truss system has been employed in a two-rut modular bridge superstructure composed of twininverted triangular trussesThe actual flexural behavior of a one-rut truss has been previously investigated under the on-axis loadingtest however the structural performance of the one-rut truss subjected to an off-axis load is still not fully understood In this papera geometrical linear finite element model is introduced and validated by the on-axis loading test the structural performance of theone-rut truss subjected to off-axis load was numerically obtained the dissimilarities of the structural performance between the twodifferent loading cases are investigated in detail The results indicated that (1) the structural behavior of the off-axis load differsfrom that of the on-axis load and the off-axis load is the critical loading condition controlling the structural performance of thetriangular truss (2) under the off-axis load the FRP trussed members and connectors bear certain out-of-plane bending momentsand are subjected to a complicated stress state and (3) the stress state of these members does not match that of the initial designand optimization for the redesign of these members is needed especially for the pretightened teeth connectors

1 Introduction

Truss is an efficient structural form According to the type ofcross section and the number of chord members trusses canbe classified as plane trusses triangular trusses rectangulartrusses and other polygon trusses Among these variouscross section trusses the triangular truss shows remarkablestructural advantages over the conventional plane and rectan-gular trusses such as the evident weight and material savingscompared to the rectangular truss [1] the excellent torsionalproperties compared to the plane truss [2] and the lowernumber of joints compared to the rectangular truss [3] Thestructural advantages and aesthetics of the triangular trusshave long been recognized by structural engineers [2] andit has been widely used in civil infrastructures and aerospaceengineering

In civil infrastructures the triangular truss has beenemployed on a limited basis for a number of structures such as

roof truss girders transmission towers highway overheadsign structures crane booms portal frames and offshore oilrig platform legs [2] Common practices for the joint designof these structures are tubular welding joints and weldedor bolted connections using gusset plates The constructionmaterials of these triangular trusses are mainly wood steelor aluminum materials In addition to these applicationsthe triangular-truss configuration is popularly applied inaerospace engineering such as the supporting structure ofantenna array [4] solar array [5] space station [6] and airship[7ndash10] and the antennas of satellite [11 12] However dueto the critical weight control in aerospace engineering theirmaterials are mainly lightweight alloys or advance compositematerials with high stiffnessstrength-to-weight ratios Thejoints are mainly welded or bolted connections fusion jointsor all-composite connectors [13 14] It is noteworthy thatall of the triangular trusses mentioned are subjected mainlyto continuously distributed loads or eccentric concentrated

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 615927 13 pageshttpdxdoiorg1011552014615927

2 The Scientific World Journal

loads normal to the chord members or concentrated loadsalong the chord members and the values of these loads areoften nonheavy loads

However in bridge engineering especially for heavy traf-fic loading the instances in which a bridge truss of this naturehas been designed and constructed are fewer than thosein civil infrastructures and aerospace engineering Actuallythe first triangular-truss bridge was completed in 1930 andit was a through-type truss supporting two railway linesand constructed of lattice-box girders with diagonal bracingforming a triangular pattern [2] A five-span triangular-trussbridge was built to carry monorail traffic It was made upof two independent truss bridges the single top chord ofwhich supports the monorail [2] It should be noted thatthe cross sections of these trusses are upright trianglesand the joints are mainly welded or bolted connectionsWith regard to the inverted triangular cross section trussthere are also some applications in bridges For examplea deck-truss bridge has been built in Canada and its twocompression top chords support the floor beams and stringerfor the deck and a single lower chord is in tension [2] Atriangular cross section truss of modest span was designedas a deck-type bridge which was composed of two lanescarrying a highway vehicle traffic loading [1] In addition anemergency truss bridge named FB48 has been employed bythe Swedish army This emergency bridge was a deck-typebridge with twin triangular trusses and has a span of 48mAdditionally the analogous truss bridges FB56 and FB88have been developed based on FB48 [15] Today the invertedtriangular-truss continuation is more commonly applied asthe truss girders that support the concrete deck in highwayand railway bridges [16 17] These truss-girder bridges areoften composed of twin inverted triangular trusses whichare fabricated entirely from unstiffened circular tubes theconnectors of which are welded tubular nodes It is notedthat the construction materials of these triangular trussesare mainly isotropic steel materials and the instances inwhich composite materials with anisotropy have been usedin these triangular-truss bridges are limited A hybrid FRP-aluminummodular bridge has been designed by the authorswhich was composed of twin inverted triangular trusses andthe modular structural units are connected by male jugs orfemale jaws based on a novel jointing system named thepretightened teeth connection (PTTC) [18] It is noteworthythat the upper and lower chords are not integral due to itsmodular characteristic unlike in the case of the existingcontinuous composite triangular trusses

For the above-mentioned triangular-truss bridges exceptfor their dead weight the loads directly subjected to thetrusses are mainly the vehicle traffic load normal to the chordmembers The chord members mainly bear compressionand tension loads or are simultaneously combined with thebending moment For the two-lane or multilane bridgesbesides on-axis traffic load these triangular trusses may alsobear off-axis bending load which has been recognized as themost critical load case and will lead to a certain torsionalmoment in the structure In response to this problem theliterature [2] has mentioned that these trusses behave asexcellent torsional properties because of their triangular cross

Male jug and Lower chord memberDiagonal web memberVertical web member

female jaw

12m12m

085

m

Figure 1 3D view of the one-rut triangular-truss system

sections however detailed studies have not been conductedin the literature At present according to the publishedliterature studies on the subject of the mechanical propertiesof these steel triangular-truss bridges subjected to off-axisloads are limited With regard to the proposed modularcomposite triangular truss [18] the actual flexural behavior ofa one-rut truss has been previously investigated under the on-axis bending loading test in the already published paper [18]However the structural performance of the truss under anoff-axis loading case has still not been investigated and thisis the gap that this paper seeks to cover Indeed triangulartrusses with differing structural configurations will exhibitrespective torsional performances and thus the proposedmodular composite triangular truss will show extraordinarystructural behavior controlling the design of the FRP trussedmembers and connectors when subjected to an off-axis load

In comparison with the paper that already published themain attention in this work is to investigate the structuralperformance of the one-rut triangular truss subjected to off-axis load In this paper a simple description of the modularhybrid truss is presented A geometrical linear finite elementmodel is introduced and validated by the previous on-axis loading test The structural performance of the one-ruttriangular truss subjected to off-axis load was numericallyobtained using the finite elementmodelThedissimilarities ofthe structural performance between the two different loadingcases were then studied in detail

2 Description of the ModularTriangular-Truss System

A hybrid FRP-aluminum space truss system was applied toa two-rut bridge superstructure which enables a modularstructural form to be erected and dismantled manually withindividual structural units It has a span length of 12m anda total width of 32m The two-rut bridge is composed oftwin triangular trusses which are linked by transverse bracesEach truss was designed as an inverted triangular crosssection with a 12m width and 085m depth (see Figure 1)Additionally each rut is a deck-truss-type bridge structureand consists of an aluminum deck supported by FRP andaluminum trussed members The four modular standardstructural units are connected by male jugs and female jawsbased on the pretightened teeth connection (PTTC)The totalweight is approximately 6 kN for one rut and only 15 kN per

The Scientific World Journal 3

(a) (b)

Figure 2 3D view of the composite tubular connection for (a) HFRP trussed members and (b) GFRP trussed members [18]

unit A 3D view of a one-rut triangular truss as designed isshown in Figure 1

In the proposed triangular-truss system pultruded FRPprofiles and aluminum profiles for structural applicationswere selected for the trussed members (see Figure 1) ApultrudedHFRP tube andGFRP tube were used for the lowerchord members and diagonal web members respectivelyHere the HFRP material consists of an admixture of E-glass fiber carbon fiber and basalt fiber embedded in anisophthalic vinyl ester resin The wrought aluminum alloy7A05 was selected for the vertical webmembers bridge deckand connectors The mechanical properties of the compositematerials used are listed in [18]

For the FRP trussed members it is worth noting that allof these members were designed initially as pure tension-compression members and were only subjected to the axialdirect forces in the preliminary design phase in which thetriangular truss was simplified as a plane truss model In thisanalyticalmodel the triangular trusswas simplified as a planetrussThe vertical and upper chordmemberswere substitutedfor the two aluminum vertical web members and bridgedeck respectively Then the axial direct forces in the trussedmembers were calculated according to structural mechanics

A novel joint system named the pretightened teethconnection (PTTC) is employed in the proposed modulartriangular truss Compared to the low connection efficiencyattained using conventional composite-material connectiontechniques for FRP tubes the pretightened teeth connec-tion (PTTC) has higher connection efficiency [19] Thepretightened teeth connection involves a ring- or stripe-shaped tooth structure grooved at the connection end ofthe composite components and well-matched teeth on thealuminumpiece connectedwith the composite (see Figure 2)After the composite tube is screwed into the inside of theexternal aluminum tube manually the internal aluminumtube is compressed into the composite tube and the latter willbe expanded because the external diameter of the internalaluminum tube is larger than the internal diameter of thecomposite tube In this way certain positive radial stresses(normal stresses) are exerted onto the composite teeth Thecapacity to transfer a large external load is obtained because

an interlaminar shear stress of the extrusion-type unidirec-tional fiber-reinforced composite material is higher than thatof pure resin [20] and the radial compressive stress enhancesthe interlaminar shear strength

It is worth stressing that this pretightened teeth connectorwas preliminarily designed as a pure tension-compressionmember it was only subjected to the axial direct forces andthe bending moment was not considered or included Moreinformation regarding the pretightened teeth connectionincluding its load-transfer mechanism can be found in [19]Based on the pretightened teeth connection the junction ofthe aluminum constructional elements with the FRP trussedprofiles can be easily realized Welding technology was usedfor the junctions of aluminum profiles and HFRPGFRPtubes for which the stresses are relatively small whereas aflange joint was used for HFRP tubes with male jugs orfemale jaws for which the stresses are much larger Thedetailed design of the pretightened teeth connection andvarious junctions for the proposed triangular-truss systemwere presented in [18]

Until now four structural units of the prototypetriangular-truss system have been fabricated by the factoryTo understand the actual flexural behavior of the structurethese four prefabricated structural units were mounted asa simply supported structure and subjected to the on-axisfour-point bending loading test as shown in Figure 3 Theexperimental results showed the feasibility of the proposedhybrid triangular truss which displayed a linear behaviorunder the ultimate limit of the loading level Both the stiffnessand strength were well within the design requirements andthe bridge features a sound structural flexural behavior inthe on-axis loading condition

However because one of the connectors of the specimenwas damaged at a large loading level over the service loadin the on-axis loading condition the relevant experimentalstudy was not conducted under an off-axis load in [18] Therupture of the connector was mainly due to the insufficientstrength of the aluminum welding line in one of the GFRPdiagonal web members At present all of the aluminumwelding lines of the structural units are retreated in thefactory


Figure 3 Single-span simply supported triangular truss and its on-axis four-point bending loading test setup

XY

Z

ConstrainsPin joint by ldquoCPrdquo command

Figure 4 Finite element model of the one-rut triangular-trussstructure

3 Finite Element Model

In order to understand the structural performance of thespecimen subjected to off-axis load a geometrical linear finiteelement model was used The finite element model (FEM) ofthemodular composite triangular truss was established usingthe general purpose finite element analysis software ANSYS100The finite elementmodel is simply introduced as follows

31 Modeling Process To accurately simulate the proposedtriangular-truss system two types of elements (SHELL andBEAM elements) were employed to model the various struc-tural members The SHELL63 element was selected for themodeling of aluminum thin plate of the bridge deck while theBEAM188 element was employed to simulate the crisscross-ing ldquoIrdquo beams and trussed members respectively Howeverbecause it is difficult to precisely simulate the regions ofthe connectors located at both sides of the structural unitsthe connector and its conterminous chord members were allmodeled using beam elements other than the solid elementsIn the finite elementmodel the connectors were simplified asa segment of the corresponding chord members

The coordinate system was defined with the 119909-axis paral-lel to the lower chords the 119910-axis parallel to the cross beamsand the 119911-axis parallel to the structure height The origin ofthe coordinate system was at the node located at one side ofthe lower chordmember as shown in Figure 4 In this definedcoordinate system the displacement boundary conditionswere set as follows the nodes at 119909 = 0 119910 = 0 and 119911 = 0 wererestrained in the x- y- and z-directions (pinned condition)

and the nodes at 119909 = 12m 119910 = 0 and 119911 = 0 were restrainedin the y- and z-directions (roller condition) In addition thenodes at 119909 = 0 119910 = plusmn06m and 119911 = 085m and at 119909 = 12m119910 = plusmn06m and 119911 = 085mwere restrained in the y-directionto avoid lateral deflection In addition the pin joints wereeffectively realized by defining a set of coupled degrees offreedom using the command ldquoCPrdquo

In this linear anisotropic material model the bucklingissue of the compressive members was not considered Theelasticity modulus and Poissonrsquos ratio used in the finiteelement model were provided by the manufacturer andare summarized in Table 1 In addition the geometricalnonlinearity was also not considered in the finite elementmodel The finite element model of the entire specimen isshown in Figure 4 The detailed finite element model wasestablished in [18]

32 Loading Cases Differ from [18] in the finite elementmodel (FEM) two loading cases were simulated according tothe practical traffic loading conditions referred to as the on-axis loading condition and the off-axis loading condition asshown in Figure 5

During the loading process for each case the correspond-ing uniformly distributed wheel load was transformed intopoint loads acting on each node in the loading area of the thinplate The numerical simulations were performed with eightloading levels (2P = 10 20 32 40 52 60 70 and 75 kN) Thedeadweightwas not considered in this finite element analysis

The stress state in certain FRP trussed members and thedisplacement at the midspan of the lower chord memberwere abstracted respectivelyThe numerical results of the on-axis loading model are presented in Section 4 and are com-pared with experimental results to further validate the finiteelement model the comparison of the on-axis loading modeland the off-axis loading model is presented in Section 5 toobtain the dissimilarity of the structural performances of thetriangular truss under the two different loading conditions

4 Verification of the Finite Element Modelby Experiment

In this section based on the on-axis four-point loading testthat was conducted in previous work [18] the validationof the established finite element model (FEM) was furtherperformed by comparing the numerical solutions with theexperimental results including the vertical displacement atthemidspan of the lower chordmember and the internal axialdirect forces in some FRP trussed members

41 Displacement at the Midspan For this hybrid triangular-truss system the deflection is an important factor affectingthe normal use of the structure considering the requirementof the guidelines In the validation the vertical displacementwas compared for the numerical values and the experimentalresults Indeed in the on-axis four-point bending loading test[18] two loading steps were applied to the specimen from0 kN to 56 kN with an interval of 40 kN in the first step andthen from 56 kN to 75 kN with an interval of 20 kN in the


Table 1 Mechanical properties of all materials used in the finite element model

Materials amp members Modulus of elasticity (GPa) Poissonrsquos ratioHFRP members 119864

1= 616 119864

2= 1198643= 83 119866

12= 11986613= 51 119866

23= 46 ]

12= ]13= 031 ]

23= 034

GFRP members 1198641= 315 119864

2= 1198643= 72 119866

12= 11986613= 44 119866

23= 41 ]

12= ]13= 028 ]

23= 033

Al alloy members 119864 = 60 ] = 033

P P

(a)

350

500

350

700

500

3000 45004500

On-axis loading

Off-axis loading

(b)

Figure 5 Two different loading configurations in the finite element model (a) Side view and (b) top view (dimensions in mm)

0 10 20 30 40 500

10

20

30

40

50

60

70

80

Load

(kN

)

Vertical displacement at midspan (mm)

Numerical values Experimental results

Figure 6 Comparison of the vertical displacement between thenumerical values and the experimental results

second step However in this paper only eight loading levelswere selected and compared with the numerical results andthey are 0 10 20 32 40 52 60 70 and 75 kN

Figure 6 shows the comparison of two load-displacementcurves obtained from the finite element model and exper-iments subjected to an on-axis load It can be found thatthe two curves are linear and notably close to each other

The maximum difference between the two curves is less than15Thus the finite elementmodel can be used to predict thedisplacement of the proposed triangular-truss system withsatisfactory accuracy

42 Internal Axial Direct Forces in the FRP Trussed MembersFor the internal axial direct forces only two representativeFRP trussed members (N2 and N5) were compared betweenthe numerical solutions and the experimental results (seeFigure 7) It is noted that in [18] only the internal axialdirect forces of the maximum load level were comparedhowever in this work about seven load levels were calculatedand compared to obtain a more reliable verification resultAs shown in Figure 7 the internal axial direct forces inthe compared trussed members are very similar to the twocurves especially for the N2 trussed member In memberN5 the discrepancy of the two curves is very small andthe maximum difference is approximately 61 Thus thefinite element model is also an available model in terms ofcalculating the internal forces in the FRP trussed members ofthe hybrid triangular-truss system

In general the finite element model (FEM) can accu-rately predict mechanical behaviors such as the deflectionsand internal forces of the proposed hybrid triangular-trusssystem The modeling techniques can be used to analyzethe structural performance of the specimen under the twodifferent loading conditions


0 20 40 60 80 100 120 140 160 180 200 2200

10

20

30

40

50

60

70

80Lo

ad (k

N)

Internal axial forces (kN)

N5

N2

P P


(a)

0

10

20

30

40

50

60

70

80

Load

(kN

)

minus90 minus80 minus70 minus60 minus50 minus40 minus30 minus20 minus10 0Internal axial forces (kN)

N2

N5


PP

(b)

Figure 7 Comparison of the internal axial forces in the trussed members between FEA and test (a) N2 and (b) N5

5 Numerical Results of the Two DifferentLoading Conditions and Their Comparison

In this section the numerical results under the two differentloading conditions are presented and compared to obtain thedissimilarities of the structural performance including thevertical and horizontal displacement at the midspan of thelower chord member the deformation of the HFRP lowerchord member and the stress state of FRP trussed membersand the connectors

51 Displacement and Deformation Figure 8 shows the com-parison of the displacement at the midspan of the lowerchord member of the structure between the two differentloading cases In Figure 8 the vertical displacement andthe horizontal displacement were compared respectively Itcan be found that for the vertical displacement the twoloading-displacement curves are both linear and notablyclose to each other (see Figure 8(a))Themaximumdifferencebetween the two curves is less than 19 That is the off-axisloading condition will not alter the vertical displacement ofthe proposed triangular-truss system for the on-axis loadingcase The obtained load-displacement curves have a slopeof 1546 times 106Nm which is an indication of the integralstructural stiffness (flexural stiffness) of the proposed hybridtriangular-truss system In addition the maximum verticaldisplacement under the on-axis load and the off-axis loadis 453mm and 462mm respectively and both are belowthe admissible deflection limit with a value of 80mm (L150)recommended by themilitary bridge design codeGJB 1162-91[21] The structure is still in the elastic regime at the ultimatelimit of the loading level

However for the horizontal displacement it clearlyshows that the values vary dramatically between the on-axis loading and the off-axis loading curves (Figure 8(b))

The horizontal displacement under each on-axis loading levelis approximately 0mm however the maximum horizontaldisplacement can reach as high as 296mm at a loading levelof 75 kN (about 14 of the width of structure) In the off-axis loading condition the large horizontal displacements aremainly caused by the torsional moment For the horizontaldisplacement the admissible limit is not recommended bythe military bridge design code GJB 1162-91 [1]

Figure 9 shows the horizontal deformed shape of theHFRP lower chord members at various off-axis loadinglevels It is noted that the measured deformed shape appearsuniformly with an increasing applied load and the shapeis symmetrical about the span center The displacement isgreatest at the midspan among the virtual gauging pointsat each loading level The horizontal deformed shape of thelower chord members under various on-axis loading levelsis not plotted because the values are all 0mm Thereforethe horizontal displacement is the main dissimilarity of theproposed triangular truss under the two different loadingcases

52 Stress State in the FRP Trussed Members and the Con-nectors In this section the stress states in the FRP trussedmembers and the connectors were compared between theon-axis loading and the off-axis loading respectively Thestress states include the axial direct stress bending stress andsuperimposed stress in the 119883-119885 plane and the 119883-119884 planeHere the superimposed stress is the sum of the axial directstress and the bending stress The coordinate system wasdefined with the 119909-axis parallel to the lower chords the 119910-axis parallel to the cross beams and the 119911-axis parallel tothe structure height Namely the stresses in the 119883-119885 planeand the 119883-119884 plane are referred to as the in-plane (verticalplane along the truss) and the out-of-plane (horizontal planealong the truss) stresses respectively It is noted that all


0 10 20 30 40 50Vertical displacement at midspan (mm)

On-axis loading Off-axis loading

0

10

20

30

40

50

60

70

80Lo

ad (k

N)

(a)

0 40 80 120 160 200 240 280 320 Horizontal displacement at midspan (mm)

0

10

20

30

40

50

60

70

80

Load

(kN

)


(b)

Figure 8 Comparison of the displacement at the midspan of the lower chord member between the on-axis load and the off-axis load (a)Vertical displacement and (b) horizontal displacement

00 15 30 45 60 75 90 105 120minus100

minus50

0

50

100

150

200

250

300

350

Hor

izon

tal d

ispla

cem

ent (

mm

)

Location of virtual displacement meter (m)

12 kN20 kN32 kN40 kN


The virtual displacement meter

Figure 9 Variation in the overall horizontal displacement of theHFRP lower chord member with increasing applied off-axis load P

the numerical stress states in this section were calculated atthe maximum load level of 75 kN

Figures 11ndash15 show the comparison of the stress contoursin the HFRP lower chord members of the two differentloading models at the maximum loading level All of thestress contours were directly extracted from the finite elementmodels Due to space confinements the stress contours ofthe GFRP diagonal web members are not presented in thispaper because the regularity of the comparison results is

the same as that of theHFRP lower chordmembers describedin the following paragraphs As displayed in Figure 11 thelower chord members are subjected to certain axial directstresses and the maximum value is approximately 79MPawhich is less than the material strength The distribution andvalues of the axial direct stress in the lower chordmember aresimilar to the two different loading models

Figure 12 shows the bending stress contours in the 119883-119885plane of the HFRP lower chord members It can be foundthat there were certain bending stresses in the lower chordmembers Additionally the maximum stresses are mainlydistributed at the two sides of the lower chord member foreach structural unit (the two sides are marked as box ldquoArdquo inFigure 10(a)) and themaximum value along the overall lowerchord member is approximately minus828MPa for both loadingcases It is noteworthy that this stress state does not matchthat of the initial design in which the lower chord memberswere only subjected to axial direct forces and were all puretension-compression members This is mainly attributed tothe dissimilarities of the joints between the actual truss andthe ideal simplified plane truss as shown in Figure 10 Inthe ideal simplified plane truss used in the initial designthe nodes A1015840 and B1015840 are all hinge-jointed nodes however inthe actual space truss the nodes 119860 and 119861 are rigid-jointednodes In addition the ldquotrdquo values are 0mm and 185mm in thesimplified plane truss model and the actual space triangulartruss respectively (see Figure 10) That is the three verticalweb members are directly and rigidly joined to the lowerchord member other than the connectors When the trussis subjected to an off-axis load part of the external loadsare transferred to the vertical web members and the verticalcomponent of the forces in these vertical web members arethen subjected to the lower chord members Thus the lowerchord member bears a certain bending moment in the 119883-119885plane


AA B A

t

(a)

B998400

A998400

A998400

(b)

Figure 10 Comparison of the jointing nodes (a) The actual triangular truss and (b) the ideal simplified plane truss

XY

Z

2681132634

3845844281

5010555928

6175267575

7339979222

(a)

XY

Z

2681432558

3830244046

497955534

6127867022

727667851

(b)

Figure 11 Contours of the internal direct axial stress in the HFRP lower chord members (a) On-axis loading case and (b) off-axis loadingcase (units in MPa)

minus82814

minus69928

minus57043

minus44157

minus31271

minus18386

minus55

7386

20271

33157

XY

Z

(a)

minus82798

minus69929

minus5706

minus44191

minus31322

minus18453

minus5584

7285

20154

33023

XY

Z

(b)

Figure 12 Contours of the 119883-119885 plane bending stress of the HFRP lower chord members (a) On-axis loading case and (b) off-axis loadingcase (units in MPa)


minus0278E minus 08minus0237E minus 08



minus0288E minus 090128E minus 09

0544E minus 090960E minus 09

X

Y

Z

(a)

minus4693

minus29474

minus12018

5438

22894

4035

57806

75262

92718

110174

X

Y

Z

(b)


minus55818

minus40879

minus2594

minus11001

3938

18877

33816

48755

63694

78633

XY

Z

(a)

minus558

minus40541

minus25281

minus10021

5239

20498

35758

51018

66278

81537

XY

Z

(b)

Figure 14 Contours of the 119883-119885 plane superimposed stress of the HFRP lower chord members (a) On-axis loading case and (b) off-axisloading case (units in MPa)

In regard to the comparison of the two different loadingmodels the distributions of the bending stresses in the 119883-119885plane are nearly identical and the difference of themaximumvalue is only 063 Namely the off-axis loading conditionwill not change the119883-119885 plane bending stress of the proposedtriangular truss under an on-axis loading condition This ismainly because the vertical components of the applied loadin the119883-119885 plane are equal to each other for the two differentloading cases and thus the bending moments in the 119883-119885plane are identical

However for the bending stress in the119883-119884 plane there isa large dissimilarity between the two different loading mod-els as shown in Figure 13 In the on-axis loading conditionthe bending stresses along the lower chord members are allequal to approximately 0MPa (Figure 13(a)) in contrast inthe off-axis loading condition themaximum value is approx-imately 1102MPa (Figure 13(b)) The maximum stresses aremainly distributed at the two sides of the lower chordmemberfor each structural unit (the two sides are marked as boxldquoArdquo in Figure 10(a)) as shown in Figure 13(b) The HFRP


26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)


lower chord members are subjected to bending momentsboth in the 119883-119884 plane and in the 119883-119885 plane under theoff-axis loading and the maximum stress in the 119883-119884 plane(Figure 13(b)) was approximately 3336 times that in the 119883-119885 plane (Figure 12(b)) Therefore compared to the on-axisloading the off-axis loading has a greater influence on the119883-119884 plane bendingmoment in theHFRP lower chordmembersThis is mainly because under an off-axis load part of theexternal load is transferred to the vertical web members andthe horizontal components of the forces in these vertical webmembers are then subjected to the lower chord member Inaddition the truss bears a torsionalmoment under an off-axisload and the truss exhibits a torsionally deformed shape thatenlarges the horizontal component of the forces Thereforethe lower chord members bear certain bending moments inthe119883-119884 plane From another point of view under an off-axistraffic load part of the torsional moment of the triangulartruss is resisted by the horizontal bending deformation of thelower chord members

In addition to the aforementioned individual axial directstress and the bending stress contours the superimposedstress contours were also extracted and analyzed Figures 14and 15 show the superimposed stress contours of the HFRPlower chord members in the 119883-119885 and 119883-119884 planes respec-tively In Figure 14 the distributions of the superimposedstress in the119883-119885 plane are nearly identical and the values areequal to each other between the two finite element modelsHowever in the 119883-119884 plane there is a large dissimilarity foreither the distribution or the values between the two differentloading models additionally the maximum119883-119884 plane stressin the off-axis loading case is approximately 2134 times thatin the on-axis loading case as shown in Figure 15 In additionunder the off-axis loading the maximum superimposedstress in the 119883-119884 plane (Figure 15(b)) is approximately 2073times that in the119883-119885 plane (Figure 14(b)) in contrast underon-axial loading the maximum superimposed stress in the119883-119884 plane (Figure 15(a)) is equal to that in the 119883-119885 plane

(Figure 14(a)) That is for the HFRP lower chord membersthe off-axis load only influences the superimposed stress inthe119883-119884 plane other than in the119883-119885 plane

Indeed the aforementioned superimposed stress is a sumof the axial direct stress and the bending stress That is thesuperimposed stress in the 119883-119885 plane is the sum of the axialdirect stress and the bending stress in the119883-119885 plane and thesuperimposed stress in the 119883-119884 plane is the sum of the axialdirect stress and the bending stress in the 119883-119884 plane Thusthe distribution of the axial direct stress and the bendingstress determine the distribution of the superimposed stressAdditionally the regularity of the comparison results of thebending stress is identical to that of the superimposed stress

Combining Figures 14 and 15 with Figures 11ndash13 theproportion of the axial direct stress and the bending stressaccounting for the maximum superimposed stress in thelower chord members respectively can be obtained Theresults are summarized in Table 2 the data of which wereobtained at the maximum load level of 75 kN As shown inTable 2 in the 119883-119885 plane the bending stress possesses asmall part in the superimposed stress and the axial directstress accounts for almost the entire part of either the on-axis loadingmodel or the off-axis loadingmodel In additionthe same stress results exist in the 119883-119884 plane under the on-axis loading Indeed because the lower chord members weredesigned according to the maximum superimposed stressand the axial direct stress accounts for almost the entiremaximum superimposed stress this stress state does matchthat of the initial design in which the lower chord membersare only subjected to pure axial direct stress

However for the bending stress in the 119883-119884 plane underoff-axis loading the result is significantly different the ratiosof the axial direct stress and the bending stress are 4644and 5356 respectively The bending stress and the axialdirect stress play nearly equivalent roles in the maximumsuperimposed stress This stress state does not match that ofthe initial design in which the lower chordmembers are only


Table 2 Comparison of the maximum superimposed stress with the corresponding individual stresses in the lower chord members at themaximum load level of 75 kN

Comparison of the maximum superimposedstress in the lower chord members

In119883-119885 plane In X-Y planeSuperimposed

stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

On-axis loadValue (MPa) 7863 7922 minus059 7922 7922 0Ratio () 10075 minus075 100 0

Off-axis loadValue (MPa) 8154 7851 303 16906 7851 9055Ratio () 9628 372 4644 5356

Off-axis value to on-axis value ratio 1037 0991 2134 0991

Table 3 Comparison of the maximum superimposed stress in the connectors at the maximum load level of 75 kN

Comparison of the maximumsuperimposed stress in the connectors

In119883-119885 plane In119883-119884 planeSuperimposed

stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

On-axis loadValue (MPa) 11415 5950 5465 8235 8235 0Ratio () 5212 4788 100 0



subjected to the axial direct forces and were pure tension-compression members In general this shows that the off-axis loading condition also plays a great role in the119883-119884 planesuperimposed stress

For the connectors joining the lower chord members thevalue and proportion of the axial direct stress and the bendingstress accounting for themaximum superimposed stress werealso extractedThe results are summarized in Table 3 the dataof which were also obtained at the maximum load level of75 kN The superimposed stress contours are not presentedhere due to the limitation of coverage As shown in Table 3in the 119883-119884 plane the axial direct stress possesses 100 ofthe superimposed stress in the on-axis loading case howeverunder an off-axis load the bending stress and the axialdirect stress play nearly equivalent roles in the maximumsuperimposed stress The connectors bear certain bendingstresses in the 119883-119884 plane mainly because of the torsionmoment of the truss subjected to an off-axis load In the119883-119885plane the bending stress and the axial direct stress also playnearly equivalent roles in the maximum superimposed stressunder either an on-axis load or an off-axis load The certainbending moment in the 119883-119885 plane is mainly attributed tothe dissimilarities of the joints between the actual truss andthe ideal simplified plane truss (see Figure 10) as analyzed inparagraph three of Section 52 Generally both the axial directforces and the local bending moment exist in the connectors

under an off-axis loading and this stress state does notmatchthat of the initial design in which the connectors are onlysubjected to tension or compression forces

In addition in the 119883-119885 plane it shows that the super-imposed stress in the off-axis loading case is equal tothat in the on-axis loading case in contrast in the 119883-119884plane the superimposed stress in the off-axis loading case isapproximately 1944 times that in the on-axis loading caseNamely the off-axis loading condition plays a critical role onthe superimposed stress of the connectors

In summary the off-axis loading case plays a critical rolein controlling the bending stress and the superimposed stressout of the plane in the lower chord members and connectorsrespectively When subjected to an off-axis load there arecertain out-of-plane bending moments in the lower chordmembers and the connectors which is mainly due to thetorsional moment of the truss along with the specific nodeconfigurationWhen subjected to both an off-axis load and anoff-axis load the lower chordmembers and connectors bear acertain in-plane bendingmoment which is mainly attributedto the specific node configuration of the trussThe stress statein these members does not match that of the initial designin which the lower chord members and connectors are onlysubjected to the axial direct forces and were pure tension-compression members In addition the superimposed stress


under an off-axis load is much larger than that under an on-axis load The triangular truss should be designed criticallyaccording to the off-axis loading condition other than the on-axis loading condition

53 Discussion For the HFRP lower chord members theoff-axis load is the critical loading condition controllingthe 119883-119884 plane stress In the 119883-119884 plane the bending stressand the axial direct stress account for nearly equivalentparts of the maximum superimposed stress under the off-axis load and this stress state does not match that of theinitial design in which the lower chord members are onlysubjected to pure axial direct forces Thus these HFRP lowerchord members cannot simply be designed according to thepure tension-compressionmember and the bendingmomentshould be included in the initial design Moreover the resultsshow that the maximum bending stress in the 119883-119884 plane isapproximately 3336 times that in the119883-119885 plane under an off-axis load and the included bendingmoment should select themaximum value in the119883-119884 plane under an off-axis load

Indeed if the isotropic aluminum material is used forthese lower chord members the bending problem cannotbe highlighted However it should be given significant con-sideration for anisotropic composite materials because theinterlaminar shear stress of the extrusion-type unidirectionalfiber-reinforced composite materials is low When subjectedto certain bending and shear stresses the HFRP lower chordmembers will bear a complicated and harmful stress state thatmay cause the cracks of the FRP composite tube Thus theHFRP lower chord members should be designed criticallyaccording to the structural properties of the proposed trian-gular truss subjected to an off-axis load

For the connectors the bending stress and the axialdirect stress also account for a nearly equivalent portionof the maximum superimposed stress in both the 119883-119884 and119883-119885 planes under an off-axis load and the same resultsapply to the stress state in the 119883-119885 plane under an on-axis load Namely in addition to the axial direct force theconnectors bear a certain local bending moment in all of thevarious loading conditions (see Figure 16)The connectors aresubjected to a complicated stress state which does not matchthe pure tension-compression state in the initial design Inaddition the 119883-119884 plane superimposed stress in the off-axisloading case is approximately 1944 times that in the on-axisloading case Namely the off-axis loading condition playsa critical role in controlling the superimposed stress of theconnectors

When subjected to a local bending moment the connec-tor will bear certain additional longitudinal stresses along theconnector Indeed in the connector there are also certainshear forces that will cause local shear stress at the local area(the change position) of the cross section (see Figure 16)Because of the low interlaminar shear stress of the extrusion-type unidirectional fiber-reinforced composite materials thecomposite tube of the connector may cause longitudinalcracks under the additional longitudinal stress along withlocal shear damage under local shear stress Thus these con-nectors based on the pretightened teeth connection cannot

Longitudinal stress Local area

Bending momentShear stress

Axial direct force

Figure 16 Diagram of the loading state in the pretightened teethconnector

simply be designed as pure tension-compression membersOnly if the axial direct force the local bending moment andthe shear forces are all included in the initial design theconnectors enable a larger bearing capacity and exhibit betterstructural properties The pretightened teeth connector willbe redesigned for thismodular truss to obtain a larger bearingcapacity and the structural properties under a complicatedstress statewill be investigated in detail in forthcomingworks

6 Conclusions

A hybrid FRP-aluminum modular truss system was intro-duced which is composed of twin triangular trusses andis connected by male jugs and female jaws based on thepretightened teeth connection technique The structural per-formance of its one-rut triangular truss subjected to an off-axis load was obtained numerically using the finite elementmodel which has been validated by the on-axis loading testThe dissimilarities of the structural performance betweenthe two different loading cases were studied in detail Thefollowing conclusions were drawn

(1) The structural behavior of the off-axis load differsmuch from that of the on-axis load and the off-axis loading case plays a critical role in controllingthe structural performance of the triangular trussThe triangular truss should be designed criticallyaccording to the off-axis loading condition other thanthe on-axis loading condition

(2) For the vertical displacement two loading-displace-ment curves are both linear and notably close toeach other under two different loading cases and themaximum difference between the two curves is lessthan 19 However for the horizontal displacementthe values vary dramatically between the on-axisloading and the off-axis loading curves The largehorizontal displacements are mainly caused by thetorsional moment of the truss subjected to an off-axisload

(3) For the internal force in the FRP trussed members(or the pretightened teeth connector) the only dis-similarity between the two different loading cases isthe out-of-plane bending stress The off-axis loadingcondition plays a critical role in controlling the out-of-plane bending stress and the superimposed stress


In addition under an off-axis load themaximumout-of-plane bending stress and superimposed stress ismuch larger than the corresponding in-plane stresses

(4) For the FRP trussed members the in-plane bendingstress possesses a small part of the superimposedstress and the axial direct stress accounts for almostthe entire part in either the on-axis loading caseor the off-axis loading case However due to thetorsionalmoment alongwith specific node configura-tion these members bear certain out-of-plane bend-ing stresses under off-axial loads The out-of-planebending stresses and the axial direct stresses accountfor a nearly equivalent portion of the maximumsuperimposed stress This stress state does not matchthat of the initial design in which the lower chordmember was designed as a pure tension-compressionmember Therefore these HFRP lower chord mem-bers should be redesigned critically according to thestructural properties under off-axis loads

(5) Due to the specific node configuration the pretight-ened teeth connectors bear a certain in-plane bend-ing moment under both loading cases in additiondue to the torsional moment along with specificnode configuration they also bear a certain out-of-plane bending moment under an off-axis loadThese bending stress and axial direct stress accountfor a nearly equivalent proportion of the maximumsuperimposed stress Namely both axial direct forcesand the local bendingmoment exist in the connectorsand the connectors are subjected to a complicatedstress state The stress state does not match up to thatof the initial design using a simplified plane trussmodel in which they were only subjected to puretension-compression forces Thus these connectorsshould also be redesigned and optimized for this typeof modular triangular truss

Conflict of Interests

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

Acknowledgments

The research work reported in this paper was supported bythe Major State Basic Research Development Program ofChina (973 Program) under Grant no 2012CB026202 and theNational Science and Foundation Program of China underGrant no 11372355

References

[1] R H Durfee ldquoDesign of a triangular cross section bridge trussrdquoJournal of Structural Engineering vol 113 no 5 pp 2399ndash24141987

[2] R H Durfee ldquoReview of triangular cross section truss systemsrdquoJournal of Structural Engineering vol 112 no 5 pp 1088ndash10961986

[3] Z S Makowski Steel Space Structures Michael Joseph LondonUK 1963

[4] S Y Du ldquoAdvanced composite materials and aerospace engi-neeringrdquo Acta Materiae Compositae Sinica vol 24 no 1 pp 1ndash12 2007

[5] S Ju D Z Jiang R A Shenoi and J Y Xiao ldquoFlexural prop-erties of lightweight FRP composite truss structuresrdquo Journal ofComposite Materials vol 45 no 19 pp 1921ndash1930 2011

[6] BHu J-X Xue andD-Q Yan ldquoStructuralmaterials and designstudy for space stationrdquo Fiber composites no 2 pp 60ndash64 2004

[7] R Schutze ldquoLightweight carbon fibre rods and truss structuresrdquoMaterials and Design vol 18 no 4ndash6 pp 231ndash238 1997

[8] T Brandt ldquoZeppelin NT the utility airship zeppelin NT as aplatform for remote sensing for enwironmental and industrialapplicationsrdquo in Proceedings of the 7th AIAA Aviation Tech-nology Integration and Operations Conference pp 1833ndash1836Belfast North Ireland September 2007

[9] L Jamison G S Sommer and I R Porche High-AltitudeAirship for the Future Force Army RAND Corporation SantaMonica Calif USA 2005

[10] httpwwwsolarimpulsecom[11] NG Stephen andY Zhang ldquoCoupled tension-torsion vibration

of repetitive beam-like structuresrdquo Journal of Sound and Vibra-tion vol 293 no 1-2 pp 253ndash265 2006

[12] T Uozumi and A Kito ldquoCarbon fibre-reinforced plastic trussstructures for satellite using braidingresin transfer mouldingprocessrdquo Journal of Materials Design and Applications vol 221no 2 pp 93ndash101 2007

[13] S Ju Flexural performance and design optimization with nonlin-ear constraints of a composite truss structure [PhD thesis] ChinaNational University of Defense Technology 2011

[14] X-L Luo Design and loading capacity analysis in integratedjoints of composite truss [MS thesis] Harbin Institute ofTechnology 2013

[15] C F Foss and T J Gander Janersquos Military Vehicles and LogisticsJanersquos Information Group Surrey Canada 1991

[16] H G Dauner A Oribasi and D Wery ldquoThe Lully viaduct acomposite bridge with steel tube trussrdquo Journal of Construc-tional Steel Research vol 46 no 1ndash3 pp 67ndash68 1998

[17] A Reis and J J O Pedro ldquoComposite truss bridges new trendsdesign and researchrdquo Steel Construction vol 4 no 3 pp 176ndash182 2011

[18] D-D Zhang Q-L Zhao Y-X Huang F Li H-S Chenand D-S Miao ldquoFlexural properties of a lightweight hybridFRP-aluminum modular space truss bridge systemrdquo CompositeStructures vol 108 pp 600ndash615 2014

[19] A-Z Deng Q-L Zhao F Li and H S Chen ldquoResearch onbearing capacity of single tooth to composite pre-tightenedteeth connectionrdquo Journal of Reinforced and Plastic Compositevol 32 no 21 pp 1603ndash1613 2013

[20] X-B Chen Handbook of Polymer Matrix Composite ChemicalIndustry Press Beijing China 2004

[21] ldquoChina national military standard general code for militarybridge designrdquo Tech Rep GJB 1162-91 1992

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



loads normal to the chord members or concentrated loadsalong the chord members and the values of these loads areoften nonheavy loads

However in bridge engineering especially for heavy traf-fic loading the instances in which a bridge truss of this naturehas been designed and constructed are fewer than thosein civil infrastructures and aerospace engineering Actuallythe first triangular-truss bridge was completed in 1930 andit was a through-type truss supporting two railway linesand constructed of lattice-box girders with diagonal bracingforming a triangular pattern [2] A five-span triangular-trussbridge was built to carry monorail traffic It was made upof two independent truss bridges the single top chord ofwhich supports the monorail [2] It should be noted thatthe cross sections of these trusses are upright trianglesand the joints are mainly welded or bolted connectionsWith regard to the inverted triangular cross section trussthere are also some applications in bridges For examplea deck-truss bridge has been built in Canada and its twocompression top chords support the floor beams and stringerfor the deck and a single lower chord is in tension [2] Atriangular cross section truss of modest span was designedas a deck-type bridge which was composed of two lanescarrying a highway vehicle traffic loading [1] In addition anemergency truss bridge named FB48 has been employed bythe Swedish army This emergency bridge was a deck-typebridge with twin triangular trusses and has a span of 48mAdditionally the analogous truss bridges FB56 and FB88have been developed based on FB48 [15] Today the invertedtriangular-truss continuation is more commonly applied asthe truss girders that support the concrete deck in highwayand railway bridges [16 17] These truss-girder bridges areoften composed of twin inverted triangular trusses whichare fabricated entirely from unstiffened circular tubes theconnectors of which are welded tubular nodes It is notedthat the construction materials of these triangular trussesare mainly isotropic steel materials and the instances inwhich composite materials with anisotropy have been usedin these triangular-truss bridges are limited A hybrid FRP-aluminummodular bridge has been designed by the authorswhich was composed of twin inverted triangular trusses andthe modular structural units are connected by male jugs orfemale jaws based on a novel jointing system named thepretightened teeth connection (PTTC) [18] It is noteworthythat the upper and lower chords are not integral due to itsmodular characteristic unlike in the case of the existingcontinuous composite triangular trusses

For the above-mentioned triangular-truss bridges exceptfor their dead weight the loads directly subjected to thetrusses are mainly the vehicle traffic load normal to the chordmembers The chord members mainly bear compressionand tension loads or are simultaneously combined with thebending moment For the two-lane or multilane bridgesbesides on-axis traffic load these triangular trusses may alsobear off-axis bending load which has been recognized as themost critical load case and will lead to a certain torsionalmoment in the structure In response to this problem theliterature [2] has mentioned that these trusses behave asexcellent torsional properties because of their triangular cross

Male jug and Lower chord memberDiagonal web memberVertical web member

female jaw

12m12m

085

m

Figure 1 3D view of the one-rut triangular-truss system

sections however detailed studies have not been conductedin the literature At present according to the publishedliterature studies on the subject of the mechanical propertiesof these steel triangular-truss bridges subjected to off-axisloads are limited With regard to the proposed modularcomposite triangular truss [18] the actual flexural behavior ofa one-rut truss has been previously investigated under the on-axis bending loading test in the already published paper [18]However the structural performance of the truss under anoff-axis loading case has still not been investigated and thisis the gap that this paper seeks to cover Indeed triangulartrusses with differing structural configurations will exhibitrespective torsional performances and thus the proposedmodular composite triangular truss will show extraordinarystructural behavior controlling the design of the FRP trussedmembers and connectors when subjected to an off-axis load

In comparison with the paper that already published themain attention in this work is to investigate the structuralperformance of the one-rut triangular truss subjected to off-axis load In this paper a simple description of the modularhybrid truss is presented A geometrical linear finite elementmodel is introduced and validated by the previous on-axis loading test The structural performance of the one-ruttriangular truss subjected to off-axis load was numericallyobtained using the finite elementmodelThedissimilarities ofthe structural performance between the two different loadingcases were then studied in detail

2 Description of the ModularTriangular-Truss System

A hybrid FRP-aluminum space truss system was applied toa two-rut bridge superstructure which enables a modularstructural form to be erected and dismantled manually withindividual structural units It has a span length of 12m anda total width of 32m The two-rut bridge is composed oftwin triangular trusses which are linked by transverse bracesEach truss was designed as an inverted triangular crosssection with a 12m width and 085m depth (see Figure 1)Additionally each rut is a deck-truss-type bridge structureand consists of an aluminum deck supported by FRP andaluminum trussed members The four modular standardstructural units are connected by male jugs and female jawsbased on the pretightened teeth connection (PTTC)The totalweight is approximately 6 kN for one rut and only 15 kN per


(a) (b)












XY

Z


















1= 616 119864

2= 1198643= 83 119866

12= 11986613= 51 119866

23= 46 ]

12= ]13= 031 ]

23= 034

GFRP members 1198641= 315 119864

2= 1198643= 72 119866

12= 11986613= 44 119866

23= 41 ]

12= ]13= 028 ]

23= 033

Al alloy members 119864 = 60 ] = 033

P P

(a)

350

500

350

700

500

3000 45004500

On-axis loading

Off-axis loading

(b)


0 10 20 30 40 500

10

20

30

40

50

60

70

80

Load

(kN

)










0 20 40 60 80 100 120 140 160 180 200 2200

10

20

30

40

50

60

70

80Lo

ad (k

N)


N5

N2

P P


(a)

0

10

20

30

40

50

60

70

80

Load

(kN

)


N2

N5


PP

(b)












0

10

20

30

40

50

60

70

80Lo

ad (k

N)

(a)


0

10

20

30

40

50

60

70

80

Load

(kN

)


(b)


00 15 30 45 60 75 90 105 120minus100

minus50

0

50

100

150

200

250

300

350

Hor

izon

tal d

ispla

cem

ent (

mm

)











AA B A

t

(a)

B998400

A998400

A998400

(b)


XY

Z

2681132634

3845844281

5010555928

6175267575

7339979222

(a)

XY

Z

2681432558

3830244046

497955534

6127867022

727667851

(b)


minus82814

minus69928

minus57043

minus44157

minus31271

minus18386

minus55

7386

20271

33157

XY

Z

(a)

minus82798

minus69929

minus5706

minus44191

minus31322

minus18453

minus5584

7285

20154

33023

XY

Z

(b)








X

Y

Z

(a)

minus4693

minus29474

minus12018

5438

22894

4035

57806

75262

92718

110174

X

Y

Z

(b)


minus55818

minus40879

minus2594

minus11001

3938

18877

33816

48755

63694

78633

XY

Z

(a)

minus558

minus40541

minus25281

minus10021

5239

20498

35758

51018

66278

81537

XY

Z

(b)





26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)












stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)












XY

Z


















1= 616 119864

2= 1198643= 83 119866

12= 11986613= 51 119866

23= 46 ]

12= ]13= 031 ]

23= 034

GFRP members 1198641= 315 119864

2= 1198643= 72 119866

12= 11986613= 44 119866

23= 41 ]

12= ]13= 028 ]

23= 033

Al alloy members 119864 = 60 ] = 033

P P

(a)

350

500

350

700

500

3000 45004500

On-axis loading

Off-axis loading

(b)


0 10 20 30 40 500

10

20

30

40

50

60

70

80

Load

(kN

)










0 20 40 60 80 100 120 140 160 180 200 2200

10

20

30

40

50

60

70

80Lo

ad (k

N)


N5

N2

P P


(a)

0

10

20

30

40

50

60

70

80

Load

(kN

)


N2

N5


PP

(b)












0

10

20

30

40

50

60

70

80Lo

ad (k

N)

(a)


0

10

20

30

40

50

60

70

80

Load

(kN

)


(b)


00 15 30 45 60 75 90 105 120minus100

minus50

0

50

100

150

200

250

300

350

Hor

izon

tal d

ispla

cem

ent (

mm

)











AA B A

t

(a)

B998400

A998400

A998400

(b)


XY

Z

2681132634

3845844281

5010555928

6175267575

7339979222

(a)

XY

Z

2681432558

3830244046

497955534

6127867022

727667851

(b)


minus82814

minus69928

minus57043

minus44157

minus31271

minus18386

minus55

7386

20271

33157

XY

Z

(a)

minus82798

minus69929

minus5706

minus44191

minus31322

minus18453

minus5584

7285

20154

33023

XY

Z

(b)








X

Y

Z

(a)

minus4693

minus29474

minus12018

5438

22894

4035

57806

75262

92718

110174

X

Y

Z

(b)


minus55818

minus40879

minus2594

minus11001

3938

18877

33816

48755

63694

78633

XY

Z

(a)

minus558

minus40541

minus25281

minus10021

5239

20498

35758

51018

66278

81537

XY

Z

(b)





26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)












stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











XY

Z


















1= 616 119864

2= 1198643= 83 119866

12= 11986613= 51 119866

23= 46 ]

12= ]13= 031 ]

23= 034

GFRP members 1198641= 315 119864

2= 1198643= 72 119866

12= 11986613= 44 119866

23= 41 ]

12= ]13= 028 ]

23= 033

Al alloy members 119864 = 60 ] = 033

P P

(a)

350

500

350

700

500

3000 45004500

On-axis loading

Off-axis loading

(b)


0 10 20 30 40 500

10

20

30

40

50

60

70

80

Load

(kN

)










0 20 40 60 80 100 120 140 160 180 200 2200

10

20

30

40

50

60

70

80Lo

ad (k

N)


N5

N2

P P


(a)

0

10

20

30

40

50

60

70

80

Load

(kN

)


N2

N5


PP

(b)












0

10

20

30

40

50

60

70

80Lo

ad (k

N)

(a)


0

10

20

30

40

50

60

70

80

Load

(kN

)


(b)


00 15 30 45 60 75 90 105 120minus100

minus50

0

50

100

150

200

250

300

350

Hor

izon

tal d

ispla

cem

ent (

mm

)











AA B A

t

(a)

B998400

A998400

A998400

(b)


XY

Z

2681132634

3845844281

5010555928

6175267575

7339979222

(a)

XY

Z

2681432558

3830244046

497955534

6127867022

727667851

(b)


minus82814

minus69928

minus57043

minus44157

minus31271

minus18386

minus55

7386

20271

33157

XY

Z

(a)

minus82798

minus69929

minus5706

minus44191

minus31322

minus18453

minus5584

7285

20154

33023

XY

Z

(b)








X

Y

Z

(a)

minus4693

minus29474

minus12018

5438

22894

4035

57806

75262

92718

110174

X

Y

Z

(b)


minus55818

minus40879

minus2594

minus11001

3938

18877

33816

48755

63694

78633

XY

Z

(a)

minus558

minus40541

minus25281

minus10021

5239

20498

35758

51018

66278

81537

XY

Z

(b)





26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)












stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1= 616 119864

2= 1198643= 83 119866

12= 11986613= 51 119866

23= 46 ]

12= ]13= 031 ]

23= 034

GFRP members 1198641= 315 119864

2= 1198643= 72 119866

12= 11986613= 44 119866

23= 41 ]

12= ]13= 028 ]

23= 033

Al alloy members 119864 = 60 ] = 033

P P

(a)

350

500

350

700

500

3000 45004500

On-axis loading

Off-axis loading

(b)


0 10 20 30 40 500

10

20

30

40

50

60

70

80

Load

(kN

)










0 20 40 60 80 100 120 140 160 180 200 2200

10

20

30

40

50

60

70

80Lo

ad (k

N)


N5

N2

P P


(a)

0

10

20

30

40

50

60

70

80

Load

(kN

)


N2

N5


PP

(b)












0

10

20

30

40

50

60

70

80Lo

ad (k

N)

(a)


0

10

20

30

40

50

60

70

80

Load

(kN

)


(b)


00 15 30 45 60 75 90 105 120minus100

minus50

0

50

100

150

200

250

300

350

Hor

izon

tal d

ispla

cem

ent (

mm

)











AA B A

t

(a)

B998400

A998400

A998400

(b)


XY

Z

2681132634

3845844281

5010555928

6175267575

7339979222

(a)

XY

Z

2681432558

3830244046

497955534

6127867022

727667851

(b)


minus82814

minus69928

minus57043

minus44157

minus31271

minus18386

minus55

7386

20271

33157

XY

Z

(a)

minus82798

minus69929

minus5706

minus44191

minus31322

minus18453

minus5584

7285

20154

33023

XY

Z

(b)








X

Y

Z

(a)

minus4693

minus29474

minus12018

5438

22894

4035

57806

75262

92718

110174

X

Y

Z

(b)


minus55818

minus40879

minus2594

minus11001

3938

18877

33816

48755

63694

78633

XY

Z

(a)

minus558

minus40541

minus25281

minus10021

5239

20498

35758

51018

66278

81537

XY

Z

(b)





26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)












stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 20 40 60 80 100 120 140 160 180 200 2200

10

20

30

40

50

60

70

80Lo

ad (k

N)


N5

N2

P P


(a)

0

10

20

30

40

50

60

70

80

Load

(kN

)


N2

N5


PP

(b)












0

10

20

30

40

50

60

70

80Lo

ad (k

N)

(a)


0

10

20

30

40

50

60

70

80

Load

(kN

)


(b)


00 15 30 45 60 75 90 105 120minus100

minus50

0

50

100

150

200

250

300

350

Hor

izon

tal d

ispla

cem

ent (

mm

)











AA B A

t

(a)

B998400

A998400

A998400

(b)


XY

Z

2681132634

3845844281

5010555928

6175267575

7339979222

(a)

XY

Z

2681432558

3830244046

497955534

6127867022

727667851

(b)


minus82814

minus69928

minus57043

minus44157

minus31271

minus18386

minus55

7386

20271

33157

XY

Z

(a)

minus82798

minus69929

minus5706

minus44191

minus31322

minus18453

minus5584

7285

20154

33023

XY

Z

(b)








X

Y

Z

(a)

minus4693

minus29474

minus12018

5438

22894

4035

57806

75262

92718

110174

X

Y

Z

(b)


minus55818

minus40879

minus2594

minus11001

3938

18877

33816

48755

63694

78633

XY

Z

(a)

minus558

minus40541

minus25281

minus10021

5239

20498

35758

51018

66278

81537

XY

Z

(b)





26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)












stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0

10

20

30

40

50

60

70

80Lo

ad (k

N)

(a)


0

10

20

30

40

50

60

70

80

Load

(kN

)


(b)


00 15 30 45 60 75 90 105 120minus100

minus50

0

50

100

150

200

250

300

350

Hor

izon

tal d

ispla

cem

ent (

mm

)











AA B A

t

(a)

B998400

A998400

A998400

(b)


XY

Z

2681132634

3845844281

5010555928

6175267575

7339979222

(a)

XY

Z

2681432558

3830244046

497955534

6127867022

727667851

(b)


minus82814

minus69928

minus57043

minus44157

minus31271

minus18386

minus55

7386

20271

33157

XY

Z

(a)

minus82798

minus69929

minus5706

minus44191

minus31322

minus18453

minus5584

7285

20154

33023

XY

Z

(b)








X

Y

Z

(a)

minus4693

minus29474

minus12018

5438

22894

4035

57806

75262

92718

110174

X

Y

Z

(b)


minus55818

minus40879

minus2594

minus11001

3938

18877

33816

48755

63694

78633

XY

Z

(a)

minus558

minus40541

minus25281

minus10021

5239

20498

35758

51018

66278

81537

XY

Z

(b)





26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)












stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










AA B A

t

(a)

B998400

A998400

A998400

(b)


XY

Z

2681132634

3845844281

5010555928

6175267575

7339979222

(a)

XY

Z

2681432558

3830244046

497955534

6127867022

727667851

(b)


minus82814

minus69928

minus57043

minus44157

minus31271

minus18386

minus55

7386

20271

33157

XY

Z

(a)

minus82798

minus69929

minus5706

minus44191

minus31322

minus18453

minus5584

7285

20154

33023

XY

Z

(b)








X

Y

Z

(a)

minus4693

minus29474

minus12018

5438

22894

4035

57806

75262

92718

110174

X

Y

Z

(b)


minus55818

minus40879

minus2594

minus11001

3938

18877

33816

48755

63694

78633

XY

Z

(a)

minus558

minus40541

minus25281

minus10021

5239

20498

35758

51018

66278

81537

XY

Z

(b)





26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)












stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















X

Y

Z

(a)

minus4693

minus29474

minus12018

5438

22894

4035

57806

75262

92718

110174

X

Y

Z

(b)


minus55818

minus40879

minus2594

minus11001

3938

18877

33816

48755

63694

78633

XY

Z

(a)

minus558

minus40541

minus25281

minus10021

5239

20498

35758

51018

66278

81537

XY

Z

(b)





26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)












stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










26811

32634

38458

44281

50105

55928

61752

67575

73399

79222

X

Y

Z

(a)

minus19933

1066

22065

43064

64064

85063

106062

127061

14806

16906

X

Y

Z

(b)












stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress







stressAxial direct

stressBendingstress

Superimposedstress

Axial directstress

Bendingstress

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















Axial direct force



6 Conclusions











Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Structural Performance of a Hybrid FRP...

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Transcript of Research Article Structural Performance of a Hybrid FRP...