Research ArticleAnalysis on Flexural Capacity of Square Steel Tube TrussConcrete Beams with Grouted Chords

Kun Wang 123 Zhiyu Zhu 1 Huihui Luo 4 and Ahmed Ahmad Omar 1

1College of Civil Science and Engineering Yangzhou University Yangzhou 225127 China2Hunan Province Engineering Laboratory of Bridge Structure (CSUST) Changsha 410015 China3Jiangsu Hanjian Group Company Limited Yangzhou 225000 China4College of Guangling Yangzhou University Yangzhou 225127 China

Correspondence should be addressed to Huihui Luo 060137yzueducn

Received 28 October 2020 Revised 29 December 2020 Accepted 8 January 2021 Published 12 February 2021

Academic Editor Shazim A Memon

Copyright copy 2021 Kun Wang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this research paper simulations on five specimens of square steel tube truss concrete beams with grouted chords wereconducted by finite element analysis (FEA) software ABAQUS Comparison of failure modes vertical load-deflection curves andsteel tube strain variation with tests was done e rationality and validity of the FEA models were also verified On this basisparameter analysis was carried out and the influence of concrete strength steel ratio of upper and lower chords and spacing ofsteel tube truss joints on the vertical load-deflection curves were obtained From the results of tests and parameter analysis designformulae of flexural bearing capacity for composite beams were proposed based on the assumption that steel tubes are equivalentto ordinary longitudinal steel bars Accordingly the results indicated that the steel tubes of the upper chords in the compositebeams cannot get yield for full sections due to the structural requirements the steel tube of the lower chords will be the first toreach fully yielding and the upper concrete crushed subsequently showing a failure mode analogous to that of the under-reinforced concrete beam the steel ratio of lower chords is the primary factor affecting the flexural capacity of the normal sectionamong the parameters the calculation from the proposed design formulae for the flexural capacity of normal section is inagreement with the tests and simulations is research could provide reference for the design of this kind of composite beam

1 Introduction

Square steel tube truss concrete beams belong to a kind ofsteel-concrete composite component which is fabricated byreplacing longitudinal steel bars with upper and lowerchords and replacing stirrups with vertical and oblique webmembers of square steel tube truss In order to avoid cave-infailure the upper and lower chords of steel tube trusses areusually grouted with cement paste [1 2] Compared toordinary reinforced concrete beams square steel tube trussconcrete beams have the advantages of higher load-carryingcapacity larger stiffness and better integrity performanceConsequently making them suitable for long-span heavy-load and prefabricated building structures Steel tube trussescan be prefabricated in the factory transported to theconstruction site and placed in the framework before

pouring concrete It is not necessary to tie up steel bars thisshortens the construction period and improves efficiencyFor structures that are not suitable for supporting formworkthe formwork can be suspended on the steel trusses and theconstruction loads can be borne by the steel trusses so as toindicate self-bearing during the construction stage Due tothe fact that the square steel tube truss concrete compositebeam have higher rigidity and bearing capacity if they areused as precast members they can minimize the section sizeand reduce transport and lifting costs Recent researches onthis kind of composite beams have not covered patternfailures and the main factors affecting the flexural capacity ofnormal sections erefore it is of great engineering sig-nificance to investigate the flexural performance of thesquare steel tube truss concrete beams and propose calcu-lation methods of the flexural capacity of this kind of beam

HindawiAdvances in Materials Science and EngineeringVolume 2021 Article ID 6694291 13 pageshttpsdoiorg10115520216694291

Recently steel trusses are widely utilized in long-spanbuildings and bridge structures due to their light self-weightand high bearing capacity [3ndash5] On the other hand if steeltrusses are directly used as frame beams the followingdrawbacks can be encountered low section stiffness largeappearance size poor durability and lower fire resistanceperformance Moreover in cast-in-place concrete structuresthe connection details of steel trusses with floor slab andconcrete columns are also complex erefore steel trussesare often buried into concrete beams to form flexuralcomposite members which can overcome the aboveproblems To this point reports on concrete beams withembedded steel trusses mainly focus on bearing capacitystiffness and crack width Zheng et al [6 7] and Zhang et al[8] studied the flexural and seismic behaviour of prestressedsteel tube truss concrete composite beams with groutedchords and the calculation formulae for bearing capacityand crack width of normal sections were put forwardFurthermore Deng et al [9] investigated the flexural be-haviour of steel truss reinforced concrete beams withrectangular and T-shaped sections Wang and Mu [10] alsostudied the cross-sectional strain distribution deformationstress increment of prestressed tendons and crack distri-bution for unbonded prestressed lattice-type steel-rein-forced concrete beams by tests Arafa et al [11] thenanalyzed the shear performance of concrete beams withembedded angle steel truss under different shear span ratiosby the finite element model Nevertheless Colajanni et al[12] investigated the failure modes and stress transfermechanism of steel-concrete trussed beams In additionChen et al [13] proposed a theoretical calculating model forcomposite box girders with corrugated steel webs and steeltrusses Relevant researches indicate that the load-carryingcapacity and stiffness of concrete beams could be improvedby substituting ordinary steel bars skeleton with steel trussesHowever the above-mentioned research studies do notinclude test and numerical studies of the square steel tubetruss concrete beams with grouted chords proposed in thispaper e finite element analysis (FEA) method was used tocurb issues of high cost few parameter variables and in-sufficient stress state investigation

erefore to study the flexural behaviour of square steeltube truss concrete beams with grouted chords the FEAmodels for this type of composite beams were established bysoft ABAQUS e predicted vertical load-deflection curvesfailure patterns and steel tube strain distribution werecompared with the test results e parameter analysis wasalso carried out Finally the calculation approach of flexuralcapacity for square steel tubular truss beams with groutedchords was established based on the tested and simulatedresults is provided a basis for the design of such com-posite beams

2 Establishment of Finite ElementAnalysis Models

21ConstitutiveRelationofMaterials Due to the monotonicloading in tests concrete is often simulated without con-sidering the influence of damage thus the plastic aspect ofthe damage plastic (DP) model provided by ABAQUS isadopted [14] e stress-strain (σminusε) relationship of concretesubjected to uniaxial tension and compression assumes thetwo-parameter model [15] recommended in code for designof concrete structures (GB20010-2010) as shown inFigure 1(a) and expressed by equation (1) where fc ε0 ft andεt0 are the axial compressive strength peak compressivestrain axial tensile strength and corresponding strain ofconcrete respectively αa and αd are the coefficients pa-rameters of ascending and descending stages for the com-pressive curve αt is the factor of descending segment fortensile curve In FEA models the shear expansion angle ψ ofconcrete takes 30deg the eccentricity e is equal to 01 theultimate strength ratio σb0σc0 between biaxial and uniaxialcompression for the concrete assumes 116 and the strengthratio of concrete under equal biaxial compression to triaxialcompression Kc takes 23 For the purpose of convergencythe viscosity coefficient μ 0001 is adopted in the calcula-tion e steel tube stress-strain (σaminusεa) curve for the upperand lower chords web members and connecting rods of thetrusses adopt the ideal elastic-plastic model as shown inFigure 1(b) where fa εya and Ea are the yield strength yieldstrain and modulus of elasticity for steel tubes

σ

fc middot αa

εε0

1113888 1113889 + 3 minus 2αa( 1113857 middotεε0

1113888 1113889

2

+ αa minus 2( 1113857 middotεε0

1113888 1113889

3⎡⎣ ⎤⎦ 0le εle ε0

fc middotεε0( 1113857

αd εε0( 11138572

+ εε0( 1113857 εgt ε0

ft middot 12εε0

1113888 1113889 minus 02εε0

1113888 1113889

6⎡⎣ ⎤⎦ εt0 lt εlt 0

ft middotεεt( 1113857

αt εεt0 minus 1( 111385717

+ εεt0( 1113857σ εlt εt0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

2 Advances in Materials Science and Engineering

In order to prevent the chords of steel tube trusses fromcave-in failure cement paste used as grouting material waspoured into both the upper and lower chords Due to thelack of coarse aggregate the peak compressive strain ofhardened grouting material is larger than that of ordinaryconcrete which is in the range of 0003 to 0004 [16] Atpresent there is almost no research on the constitutiverelation of hardened cement paste so the uniaxial com-pression two-parameter model for concrete offered inGB20010-2010 is used as a reference us the stress-strain(σg minus εg) relation of grouting material subjected to uniaxial

compression is proposed in this paper as shown inequation (2) in which fg and εg0 are the axial compressivestrength and corresponding strain for the hardened cementpaste and value of εg0 takes 00035 e comparison be-tween the compressive stress-strain (σg minus εg) relation andthe test results of grouting material is illustrated inFigure 1(c) which reveals that the proposed model isessentially identical with tests and it can be used for FEAmodels e constitutive relationship of grouting materialsubjected to tension is the same as that of ordinary concretewith the same strength

σg

fg middot αa

εg

εg01113888 1113889 + 3 minus 2αa( 1113857 middot

εg

εg01113888 1113889

2

+ αa minus 2( 1113857 middotεg

εg01113888 1113889

3⎡⎣ ⎤⎦ 0le εg le εg0

fg middotεgεg01113872 1113873

αd εgεg01113872 11138732

+ εgεg01113872 1113873 εg gt εg0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)

22 Finite Element Model and Boundary Conditions etypical FEA model of square steel tube truss concrete beamestablished by soft ABAQUS is illustrated in Figure 2During modelling three kinds of parts square steel tubetrusses shown in Figure 2(a) concrete beam shown inFigure 2(b) which involves grouting materials and rigidplates for loading and support were established respectivelySince the web members and linking rods of the square steeltube truss were not grouted the corresponding solid in theconcrete beam part was hollowed out by cutting commandsfor the grouting material of the upper and lower chord thecorresponding solids in the concrete beam part were cut offand retained Tetrahedral element C3D10 with highergeometric adaptability is used for concrete and groutingmaterials the shell element S4R is used for square steel tubesand solid element C3D8R is used for rigid plates ereasonable sizes of the element division can improve thecomputational efficiency and precision of the FEA models

roughout the analysis the FEA results are more consistentwith the experimental results when the overall grid size is15mm and 50mm for trusses and concrete surface re-spectively and adaptive grid technique is applied for con-crete internal grids To simplify the analysis in FEAmodelling the slip between the steel trusses part and theconcrete beam part is neglected and the embed technique isadopted to carry out coupling

e two ends of the FEA model of the composite beamare simply supported and four-point loading is adopted Inorder to prevent stress concentration the four rigid platesare separately set at two supports and two loading points onthe composite beam and tie technology is applied to bindthe rigid plates and concrete surfaces as shown inFigure 2(c) Here the value of symmetrical vertical con-centrated load takes P2 and Ux Uy and Uz are the dis-placements of the supports in the direction of globalcoordinates X Y and Z respectively For the simply

o ε0

εt0ε

ft

fc

σ

(a)

εaεya

oEa

ndashεya

fa

ndashfa

σa

(b)

0000 0002 0004 00060

7

14

21

28

35

σ g (M

Pa)

εg

Proposed modelTest

(c)

Figure 1 Constitutive relationship of materials (a) Concrete (b) Steel tube (c) Grouting material

Advances in Materials Science and Engineering 3

supported beam fixed hinge support is set at the left end(Ux Uy Uz 0) and sliding hinge support is set at the rightend (Ux Uy 0) and the vertical loads are placed by dis-placement control method

3 Verification of the Numerical Model

31 e Experiments Figure 3 gives the layout of reinforce-ment and strain gauges for square steel tube truss concretebeamswith grouted chords and the specimens were numberedas B-1simB-5 e length of beam specimens is 2700mm thecalculated span is 2500mm the cross-sectional size is200mmtimes 300mm and the concrete strength grade is C40emeasured average compressive strength of concrete cube fcu is448MPa axial compressive strength fc is 3405MPa axialtensile strength ft is 32MPa and modulus of elasticity Ec is336times104MPa [17] Grouting material was made by PO 425ordinary silicate cement UEA expansive agent FDN super-plasticizer and tap-water e measured mean axial com-pressive strength fg of grouting material cube after 28-daysstandard curing is 363MPa e cross-sectional sizes ofconnecting rods and web members for all embedded steeltrusses take 25mmtimes 25mmtimes 2mm and the yield strength fais 360MPa e yield strength fa for chord tubes with cross-sectional sizes of 30mmtimes30mmtimes 2mm 30times 30mm

times 3mm 40mmtimes 40mmtimes2mm and 40mmtimes 40mmtimes 3mm is 297MPa 345MPa 355MPa and 312MParespectively

In the tests four-point symmetrical loading was adopted bydistributive girder as shown in Figure 4e total vertical loadPis measured by a load sensor and the deflectionΔ atmidspan iscalculated according to the data of dial indicators at midspanand supports Strain gauges are fixed on the upper and lowerchords of steel tube trusses and concrete in the pure bendingsegment e test results showed that all the five beam spec-imens showed flexural failure with the concrete in compres-sion zone crushing after the lower chords reaching full tensileyielding while the upper chords not yielding completely

32 Load-Deflection Curves Figure 5 shows the comparisonof load-deflection (PminusΔ) curves obtained from beam spec-imens and FEA models Table 1 lists the simulated and testcrack stiffnesses (Escr and Etcr) and ultimate loads (Psu and Ptu)It was found that the crack loads calculated by the FEAmodels are close to the test results but the crack dis-placement calculated was smaller than that of the measuredvalues which caused crack stiffnesses for FEA models whichwere greater than that of tests With the increase of verticalloads the predicted stiffnesses after cracking were also largerthan measured results since the yield of steel tubes of lower

Hollowed out solids for web members

Retained solids for grouting materials in steel tube

(a)

Upper chords

Upper chords

Web membersConnecting rod

(b)

Steel trusses

P2P2

Ux = 0 Uy = 0 Uz = 0 Uy = 0 Uz = 0 Concretey

zx

(c)

Figure 2 Finite element analysis model (a) Part of concrete beam (b) Part of steel tube truss (c) Loading and constraints

4 Advances in Materials Science and Engineering

chords is a gradual process and there is no obvious yieldpoint on the calculated and test curves which is obviouslydifferent from the yield case of the ordinary reinforcedconcrete beam when the failure is achieved the predictedultimate loadsrsquo Psu are close to the test values Ptu with about5

Generally the calculated curves and ultimate bearingcapacities are similar to the tested ones e reason for the

increase of initial stiffness and post-cracking stiffnessmentioned above could be explained as follows (1) theconcrete elements in the FEA models are continuous andthere is no crack development thus the impact of crackingcannot be accurately considered in the whole loading pro-cess (2) DP model is adopted for concrete without con-sidering the impact of the damage (3) e slip between steeltrusses and concrete are considered in the FEA models

5020

20

50

250 250 250 250 250 250 250 250 250 2502700

300

Upper chords Vertical web member

Diagonal web memberUpper chords

(a)

200200200200200200200200200200 2502502700

50 20

50

300 20

Upper chords Vertical web member

Diagonal web memberUpper chords

(b)

240

B-1130

Steel tube30 times 30 times 2

Steel tube40 times 40 times 2Steel tube

40 times 40 times 2

240

B-2130

Steel tube30 times 30 times 2

Steel tube30 times 30 times 3

240

B-3130

Steel tube30 times 30 times 2

Steel tube40 times 40 times 3

240

B-4130

Steel tube30 times 30 times 3

Steel tube40 times 40 times 3

240

B-5130

Steel tube30 times 30 times 2

Steel tube30 times 30 times 3

(c)

15

5555

5512

0

(d)

S9

S12

S1S2(3)

S4

S10(11)

S6(7)S5

S8

S13S14(15)

S16

S17S18

S19S20

(e)

Figure 3 Detailed configurations of embedded square steel tube trusses and gauges distribution (unit mm) (a) Elevation view for beamspecimens B-1 B-2 B-3 and B-4 (b) Elevation view of beam specimen B-5 (c) Cross-section details (d) Strain gauges on concrete (e) Straingauges on steel truss

Advances in Materials Science and Engineering 5

0 5 10 15 20 25 30 350

50

100

150

200

250

Δ (mm)TestedSimulated

P (k

N)

(a)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(b)

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(c)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(d)

Figure 5 Continued

Hinge support

Hydraulic jack

Load cell

Beam specimen

Distribution girder

Dial indicator

Figure 4 Loading apparatus

6 Advances in Materials Science and Engineering

33 Comparison of FailureModes e ultimate compressivestrain εcu of concrete is often taken as 00033 When thecompressive strain (denoted by E11) in the length directionof concrete exceeds εcu it indicates that concrete is crushede yield of steel tube trusses could be observed by theplastic strains (represented as PE11) When the plastic strainPE11 of the upper and lower chords of the steel tube trussesin the axial direction of members is greater than zero itindicated that the chords reached yielding Taking typicalbeam specimen B-1 as example the strain of concrete andplastic strain of steel tube trusses for the FEAmodel at failurewere obtained as shown in Figures 6(a) and 6(b) As shownin Figure 6(a) the compressive strain E11 of concrete in theupper part of the pure bending segment of the FEA beammodel was far from the ultimate compressive strain of 00033up to 001 and the depth of the compression zone was about30mm which indicates that the concrete had been crushedand the simulated failure was basically consistent with theexperimental observation shown in Figure 6(c) It can beconcluded from Figure 6(b) that the lower chords of steeltube trusses have yielded in the whole pure bending seg-ment with a maximum yield strain of 00359 which indi-cates that the FEA results can clearly reflect the observationof failure

34 Strain Variation of Steel Tubes e test and calculatedcurves of vertical load (P) and steel tube strain (ε) arecompared in Figure 7 where strain gauges S1 and S9 werefixed on the upper and lower chords From initial loading tofailure the vertical load-strain (Pminusε) curves correspondingto the measuring point S1 calculated by the FEA method arematching with the measured results in which the steel tubestrains of S1 vary linearly with the increase of vertical loadsand the strains yield slightly at the peak load for somespecimens For the measuring point S2 there is a certain gapbetween the simulated and tested load-strain curves whichis mainly reflected by the fact that the slope of the calculatedcurves is larger than that of the tested ones before yielding ofthe steel tubes but when the loads reached the peak valuesthe calculated strains of S1 are greater than the yield straine reason for the above distinction could be explained bythe DP model of the concrete which was adopted wherebythe elements were continuous without considering cracks

4 Parameter Analysis

Studies on flexural capacity and parameter analysis onvertical load-deflection curves by FEA models were con-ducted e primary analysis parameters involved theconcrete strength grade fcuk steel ratio of upper and lowerchords (ρa

prime and ρa) and the spacing (s) between adjacenttruss joints Table 2 gives basic information In the parameteranalysis the FEA models were taken as a simply supportedbeam with the length of 2700mm the calculated span of2500mm and the cross-section size of 200mmtimes 300mme dimensions of the web member and connecting rods forencased steel trusses were both 25mmtimes 25mmtimes 2mmesteel tube yield strength is fy 235Nmm2 and the concretestrength is taken as the standard value In addition no shearfailure occurred in these FEA models

Table 1 Comparison of crack and ultimate loads between sim-ulation and tests

Beamnumber

Ecrs

(kNmm)Ecrt

(kNmm) Pus (kN) Put (kN) PutPus

B-1 673 210 1854 1850 100B-2 680 250 1987 1940 098B-3 708 270 2289 2180 095B-4 734 281 2333 2200 094B-5 678 214 1986 1960 099

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(e)

Figure 5 Load-deflection curves of tests and FEA models (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Advances in Materials Science and Engineering 7

Crushing of concrete+4794e ndash 02

E E11

+4367e ndash 02+3940e ndash 02+3513e ndash 02+3086e ndash 02+2659e ndash 02+2232e ndash 02+1805e ndash 02+1378e ndash 02+9510e ndash 03+5240e ndash 03+9699e ndash 04ndash3300e ndash 03ndash1007e ndash 02

(a)

Yielding of steel tube

+3590e ndash 02

PE PE11SNEG (fraction = ndash10)

+3251e ndash 02+2912e ndash 02+2573e ndash 02+2235e ndash 02+1896e ndash 02+1557e ndash 02+1218e ndash 02+8791e ndash 03+5403e ndash 03+2014e ndash 03ndash1375e ndash 03ndash4763e ndash 03

(b)

Crushing of concrete

(c)

Figure 6 Comparison of failure modes (a) Crushing of concrete for FEA model (b) Yielding of steel trusses for FEA model (c) Failuremode of beam specimens

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(a)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(b)

Figure 7 Continued

8 Advances in Materials Science and Engineering

41 Concrete Strength Figure 8(a) gives the vertical load-deflection (PminusΔ) curve of square steel tube truss concrete beamswith grouted chords under different concrete strength gradesWhen the concrete strength grades are C30 C40 and C50respectively the initial stiffnesses for PminusΔ curves are basicallythe same and the stiffnesses after cracking and yielding in-creased slightly e peak values of vertical loads at failure are1350 kN 1376 kN and 1398 kN respectively with an incre-ment of 19 and 36 is indicates that improving theconcrete strength could enhance the vertical load ofmembers toa certain extent however the increments were very small

42 Steel Ratio of Upper Chords e vertical load-deflection(PminusΔ) curves for square steel tube truss concrete beams withdifferent steel ratio of upper chords are compared inFigure 8(b) With an increment of steel ratio the cross-sectional area Aa

prime is in the order of 232mm2 342mm2 and448mm2 and an increment of 474 and 931 e curveshapes are essentially similar and the stiffnesses increasedslightly after cracking e vertical load peak at failurecorresponding to the cross-sectional area of the differentupper chord steel tubes is 1334 kN 1344 kN and 1350 kNrespectively and the vertical peak loads increase by 07 and

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(c)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(d)

ndash2000 0 2000 4000 6000 8000 100000

50

100

150

200

250

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(e)

Figure 7 Vertical load-strain curve of steel tube (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Table 2 Parameters of FEA models

Analytical parameters Range of parameters DescriptionConcrete strength grade C30 C45 C50 fcuk 30Nmm2 40Nmm2 and 50Nmm2

Steel ratio of upper chords (ρaprime) 043 063 083 Area 232mm2 342mm2 and 448mm2

Steel ratio of lower chords (ρa) 164 213 256 Area 888mm2 1152mm2 1400mm2

Spacing of truss joint (s) 200mm 250mm 500mm mdash

Advances in Materials Science and Engineering 9

12 respectively It can be seen that increasing the sectionalarea of the upper chords has little influence on enhancing thevertical bearing capacity Due to the structural requirementsof upper chords of steel trusses the sectional area is generallylarge and they cannot reach full yielding at peak loads

43 Steel Ratio of Lower Chords Figure 8(c) shows the in-fluence of the steel ratio of the lower chords on the verticalload-deflection (PminusΔ) for the composite beams It indicates

that the vertical peak load and yield stiffness of the com-posite beam raised with an increase of steel ratio of the lowerchordsWhen the steel ratio is 164 213 and 256 withcross-sectional areas of 888mm2 1152mm2 and 1400mm2the corresponding vertical peak loads are 1842 kN2304 kN and 2726 kN respectively and the increase rate isabout 25 and 48 e analytical results show that thevertical bearing capacity of the composite beam can be ef-fectively improved by increasing the cross-sectional area ofthe lower chords

0

40

80

120

160P

(kN

)

0 5 10 15 20 25 30 35Δ (mm)

C30 (fcuk = 30MPa)C40 (fcuk = 40MPa)C50 (fcuk = 50MPa)

(a)

0

50

100

150

P (k

N)

Δ (mm)0 5 10 15 20 25 30 35

ρprimea = 043 (Aprimea = 232mm2)ρprimea = 063 (Aprimea = 342mm2)ρprimea = 083 (Aprimea = 448mm2)

(b)

0 5 10 15 20 25 30 35Δ (mm)

0

50

100

150

200

250

300

P (k

N)

ρa = 164 (Aa = 888mm2)ρa = 213 (Aa = 1152mm2)ρa = 256 (Aa = 1400mm2)

(c)

Δ (mm)0 5 10 15 20 25 30 35

P (k

N)

0

50

100

150

200

s = 200mms = 250mms = 500mm

(d)

Figure 8 Influence of different parameters on load-deflection curves (a) Concrete strength grade (b) Steel ratio of steel tube of upperchords (c) Steel ratio of steel tube of lower chords (d) Truss joint spacing

10 Advances in Materials Science and Engineering

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

In order to prevent the chords of steel tube trusses fromcave-in failure cement paste used as grouting material waspoured into both the upper and lower chords Due to thelack of coarse aggregate the peak compressive strain ofhardened grouting material is larger than that of ordinaryconcrete which is in the range of 0003 to 0004 [16] Atpresent there is almost no research on the constitutiverelation of hardened cement paste so the uniaxial com-pression two-parameter model for concrete offered inGB20010-2010 is used as a reference us the stress-strain(σg minus εg) relation of grouting material subjected to uniaxial

compression is proposed in this paper as shown inequation (2) in which fg and εg0 are the axial compressivestrength and corresponding strain for the hardened cementpaste and value of εg0 takes 00035 e comparison be-tween the compressive stress-strain (σg minus εg) relation andthe test results of grouting material is illustrated inFigure 1(c) which reveals that the proposed model isessentially identical with tests and it can be used for FEAmodels e constitutive relationship of grouting materialsubjected to tension is the same as that of ordinary concretewith the same strength

σg

fg middot αa

εg

εg01113888 1113889 + 3 minus 2αa( 1113857 middot

εg

εg01113888 1113889

2

+ αa minus 2( 1113857 middotεg

εg01113888 1113889

3⎡⎣ ⎤⎦ 0le εg le εg0

fg middotεgεg01113872 1113873

αd εgεg01113872 11138732

+ εgεg01113872 1113873 εg gt εg0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)

22 Finite Element Model and Boundary Conditions etypical FEA model of square steel tube truss concrete beamestablished by soft ABAQUS is illustrated in Figure 2During modelling three kinds of parts square steel tubetrusses shown in Figure 2(a) concrete beam shown inFigure 2(b) which involves grouting materials and rigidplates for loading and support were established respectivelySince the web members and linking rods of the square steeltube truss were not grouted the corresponding solid in theconcrete beam part was hollowed out by cutting commandsfor the grouting material of the upper and lower chord thecorresponding solids in the concrete beam part were cut offand retained Tetrahedral element C3D10 with highergeometric adaptability is used for concrete and groutingmaterials the shell element S4R is used for square steel tubesand solid element C3D8R is used for rigid plates ereasonable sizes of the element division can improve thecomputational efficiency and precision of the FEA models

roughout the analysis the FEA results are more consistentwith the experimental results when the overall grid size is15mm and 50mm for trusses and concrete surface re-spectively and adaptive grid technique is applied for con-crete internal grids To simplify the analysis in FEAmodelling the slip between the steel trusses part and theconcrete beam part is neglected and the embed technique isadopted to carry out coupling

e two ends of the FEA model of the composite beamare simply supported and four-point loading is adopted Inorder to prevent stress concentration the four rigid platesare separately set at two supports and two loading points onthe composite beam and tie technology is applied to bindthe rigid plates and concrete surfaces as shown inFigure 2(c) Here the value of symmetrical vertical con-centrated load takes P2 and Ux Uy and Uz are the dis-placements of the supports in the direction of globalcoordinates X Y and Z respectively For the simply

o ε0

εt0ε

ft

fc

σ

(a)

εaεya

oEa

ndashεya

fa

ndashfa

σa

(b)

0000 0002 0004 00060

7

14

21

28

35

σ g (M

Pa)

εg

Proposed modelTest

(c)

Figure 1 Constitutive relationship of materials (a) Concrete (b) Steel tube (c) Grouting material

Advances in Materials Science and Engineering 3

supported beam fixed hinge support is set at the left end(Ux Uy Uz 0) and sliding hinge support is set at the rightend (Ux Uy 0) and the vertical loads are placed by dis-placement control method

3 Verification of the Numerical Model

31 e Experiments Figure 3 gives the layout of reinforce-ment and strain gauges for square steel tube truss concretebeamswith grouted chords and the specimens were numberedas B-1simB-5 e length of beam specimens is 2700mm thecalculated span is 2500mm the cross-sectional size is200mmtimes 300mm and the concrete strength grade is C40emeasured average compressive strength of concrete cube fcu is448MPa axial compressive strength fc is 3405MPa axialtensile strength ft is 32MPa and modulus of elasticity Ec is336times104MPa [17] Grouting material was made by PO 425ordinary silicate cement UEA expansive agent FDN super-plasticizer and tap-water e measured mean axial com-pressive strength fg of grouting material cube after 28-daysstandard curing is 363MPa e cross-sectional sizes ofconnecting rods and web members for all embedded steeltrusses take 25mmtimes 25mmtimes 2mm and the yield strength fais 360MPa e yield strength fa for chord tubes with cross-sectional sizes of 30mmtimes30mmtimes 2mm 30times 30mm

times 3mm 40mmtimes 40mmtimes2mm and 40mmtimes 40mmtimes 3mm is 297MPa 345MPa 355MPa and 312MParespectively

In the tests four-point symmetrical loading was adopted bydistributive girder as shown in Figure 4e total vertical loadPis measured by a load sensor and the deflectionΔ atmidspan iscalculated according to the data of dial indicators at midspanand supports Strain gauges are fixed on the upper and lowerchords of steel tube trusses and concrete in the pure bendingsegment e test results showed that all the five beam spec-imens showed flexural failure with the concrete in compres-sion zone crushing after the lower chords reaching full tensileyielding while the upper chords not yielding completely

32 Load-Deflection Curves Figure 5 shows the comparisonof load-deflection (PminusΔ) curves obtained from beam spec-imens and FEA models Table 1 lists the simulated and testcrack stiffnesses (Escr and Etcr) and ultimate loads (Psu and Ptu)It was found that the crack loads calculated by the FEAmodels are close to the test results but the crack dis-placement calculated was smaller than that of the measuredvalues which caused crack stiffnesses for FEA models whichwere greater than that of tests With the increase of verticalloads the predicted stiffnesses after cracking were also largerthan measured results since the yield of steel tubes of lower

Hollowed out solids for web members

Retained solids for grouting materials in steel tube

(a)

Upper chords

Upper chords

Web membersConnecting rod

(b)

Steel trusses

P2P2

Ux = 0 Uy = 0 Uz = 0 Uy = 0 Uz = 0 Concretey

zx

(c)

Figure 2 Finite element analysis model (a) Part of concrete beam (b) Part of steel tube truss (c) Loading and constraints

4 Advances in Materials Science and Engineering

chords is a gradual process and there is no obvious yieldpoint on the calculated and test curves which is obviouslydifferent from the yield case of the ordinary reinforcedconcrete beam when the failure is achieved the predictedultimate loadsrsquo Psu are close to the test values Ptu with about5

Generally the calculated curves and ultimate bearingcapacities are similar to the tested ones e reason for the

increase of initial stiffness and post-cracking stiffnessmentioned above could be explained as follows (1) theconcrete elements in the FEA models are continuous andthere is no crack development thus the impact of crackingcannot be accurately considered in the whole loading pro-cess (2) DP model is adopted for concrete without con-sidering the impact of the damage (3) e slip between steeltrusses and concrete are considered in the FEA models

5020

20

50

250 250 250 250 250 250 250 250 250 2502700

300

Upper chords Vertical web member

Diagonal web memberUpper chords

(a)

200200200200200200200200200200 2502502700

50 20

50

300 20

Upper chords Vertical web member

Diagonal web memberUpper chords

(b)

240

B-1130

Steel tube30 times 30 times 2

Steel tube40 times 40 times 2Steel tube

40 times 40 times 2

240

B-2130

Steel tube30 times 30 times 2

Steel tube30 times 30 times 3

240

B-3130

Steel tube30 times 30 times 2

Steel tube40 times 40 times 3

240

B-4130

Steel tube30 times 30 times 3

Steel tube40 times 40 times 3

240

B-5130

Steel tube30 times 30 times 2

Steel tube30 times 30 times 3

(c)

15

5555

5512

0

(d)

S9

S12

S1S2(3)

S4

S10(11)

S6(7)S5

S8

S13S14(15)

S16

S17S18

S19S20

(e)

Figure 3 Detailed configurations of embedded square steel tube trusses and gauges distribution (unit mm) (a) Elevation view for beamspecimens B-1 B-2 B-3 and B-4 (b) Elevation view of beam specimen B-5 (c) Cross-section details (d) Strain gauges on concrete (e) Straingauges on steel truss

Advances in Materials Science and Engineering 5

0 5 10 15 20 25 30 350

50

100

150

200

250

Δ (mm)TestedSimulated

P (k

N)

(a)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(b)

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(c)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(d)

Figure 5 Continued

Hinge support

Hydraulic jack

Load cell

Beam specimen

Distribution girder

Dial indicator

Figure 4 Loading apparatus

6 Advances in Materials Science and Engineering

33 Comparison of FailureModes e ultimate compressivestrain εcu of concrete is often taken as 00033 When thecompressive strain (denoted by E11) in the length directionof concrete exceeds εcu it indicates that concrete is crushede yield of steel tube trusses could be observed by theplastic strains (represented as PE11) When the plastic strainPE11 of the upper and lower chords of the steel tube trussesin the axial direction of members is greater than zero itindicated that the chords reached yielding Taking typicalbeam specimen B-1 as example the strain of concrete andplastic strain of steel tube trusses for the FEAmodel at failurewere obtained as shown in Figures 6(a) and 6(b) As shownin Figure 6(a) the compressive strain E11 of concrete in theupper part of the pure bending segment of the FEA beammodel was far from the ultimate compressive strain of 00033up to 001 and the depth of the compression zone was about30mm which indicates that the concrete had been crushedand the simulated failure was basically consistent with theexperimental observation shown in Figure 6(c) It can beconcluded from Figure 6(b) that the lower chords of steeltube trusses have yielded in the whole pure bending seg-ment with a maximum yield strain of 00359 which indi-cates that the FEA results can clearly reflect the observationof failure

34 Strain Variation of Steel Tubes e test and calculatedcurves of vertical load (P) and steel tube strain (ε) arecompared in Figure 7 where strain gauges S1 and S9 werefixed on the upper and lower chords From initial loading tofailure the vertical load-strain (Pminusε) curves correspondingto the measuring point S1 calculated by the FEA method arematching with the measured results in which the steel tubestrains of S1 vary linearly with the increase of vertical loadsand the strains yield slightly at the peak load for somespecimens For the measuring point S2 there is a certain gapbetween the simulated and tested load-strain curves whichis mainly reflected by the fact that the slope of the calculatedcurves is larger than that of the tested ones before yielding ofthe steel tubes but when the loads reached the peak valuesthe calculated strains of S1 are greater than the yield straine reason for the above distinction could be explained bythe DP model of the concrete which was adopted wherebythe elements were continuous without considering cracks

4 Parameter Analysis

Studies on flexural capacity and parameter analysis onvertical load-deflection curves by FEA models were con-ducted e primary analysis parameters involved theconcrete strength grade fcuk steel ratio of upper and lowerchords (ρa

prime and ρa) and the spacing (s) between adjacenttruss joints Table 2 gives basic information In the parameteranalysis the FEA models were taken as a simply supportedbeam with the length of 2700mm the calculated span of2500mm and the cross-section size of 200mmtimes 300mme dimensions of the web member and connecting rods forencased steel trusses were both 25mmtimes 25mmtimes 2mmesteel tube yield strength is fy 235Nmm2 and the concretestrength is taken as the standard value In addition no shearfailure occurred in these FEA models

Table 1 Comparison of crack and ultimate loads between sim-ulation and tests

Beamnumber

Ecrs

(kNmm)Ecrt

(kNmm) Pus (kN) Put (kN) PutPus

B-1 673 210 1854 1850 100B-2 680 250 1987 1940 098B-3 708 270 2289 2180 095B-4 734 281 2333 2200 094B-5 678 214 1986 1960 099

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(e)

Figure 5 Load-deflection curves of tests and FEA models (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Advances in Materials Science and Engineering 7

Crushing of concrete+4794e ndash 02

E E11

+4367e ndash 02+3940e ndash 02+3513e ndash 02+3086e ndash 02+2659e ndash 02+2232e ndash 02+1805e ndash 02+1378e ndash 02+9510e ndash 03+5240e ndash 03+9699e ndash 04ndash3300e ndash 03ndash1007e ndash 02

(a)

Yielding of steel tube

+3590e ndash 02

PE PE11SNEG (fraction = ndash10)

+3251e ndash 02+2912e ndash 02+2573e ndash 02+2235e ndash 02+1896e ndash 02+1557e ndash 02+1218e ndash 02+8791e ndash 03+5403e ndash 03+2014e ndash 03ndash1375e ndash 03ndash4763e ndash 03

(b)

Crushing of concrete

(c)

Figure 6 Comparison of failure modes (a) Crushing of concrete for FEA model (b) Yielding of steel trusses for FEA model (c) Failuremode of beam specimens

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(a)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(b)

Figure 7 Continued

8 Advances in Materials Science and Engineering

41 Concrete Strength Figure 8(a) gives the vertical load-deflection (PminusΔ) curve of square steel tube truss concrete beamswith grouted chords under different concrete strength gradesWhen the concrete strength grades are C30 C40 and C50respectively the initial stiffnesses for PminusΔ curves are basicallythe same and the stiffnesses after cracking and yielding in-creased slightly e peak values of vertical loads at failure are1350 kN 1376 kN and 1398 kN respectively with an incre-ment of 19 and 36 is indicates that improving theconcrete strength could enhance the vertical load ofmembers toa certain extent however the increments were very small

42 Steel Ratio of Upper Chords e vertical load-deflection(PminusΔ) curves for square steel tube truss concrete beams withdifferent steel ratio of upper chords are compared inFigure 8(b) With an increment of steel ratio the cross-sectional area Aa

prime is in the order of 232mm2 342mm2 and448mm2 and an increment of 474 and 931 e curveshapes are essentially similar and the stiffnesses increasedslightly after cracking e vertical load peak at failurecorresponding to the cross-sectional area of the differentupper chord steel tubes is 1334 kN 1344 kN and 1350 kNrespectively and the vertical peak loads increase by 07 and

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(c)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(d)

ndash2000 0 2000 4000 6000 8000 100000

50

100

150

200

250

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(e)

Figure 7 Vertical load-strain curve of steel tube (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Table 2 Parameters of FEA models

Analytical parameters Range of parameters DescriptionConcrete strength grade C30 C45 C50 fcuk 30Nmm2 40Nmm2 and 50Nmm2

Steel ratio of upper chords (ρaprime) 043 063 083 Area 232mm2 342mm2 and 448mm2

Steel ratio of lower chords (ρa) 164 213 256 Area 888mm2 1152mm2 1400mm2

Spacing of truss joint (s) 200mm 250mm 500mm mdash

Advances in Materials Science and Engineering 9

12 respectively It can be seen that increasing the sectionalarea of the upper chords has little influence on enhancing thevertical bearing capacity Due to the structural requirementsof upper chords of steel trusses the sectional area is generallylarge and they cannot reach full yielding at peak loads

43 Steel Ratio of Lower Chords Figure 8(c) shows the in-fluence of the steel ratio of the lower chords on the verticalload-deflection (PminusΔ) for the composite beams It indicates

that the vertical peak load and yield stiffness of the com-posite beam raised with an increase of steel ratio of the lowerchordsWhen the steel ratio is 164 213 and 256 withcross-sectional areas of 888mm2 1152mm2 and 1400mm2the corresponding vertical peak loads are 1842 kN2304 kN and 2726 kN respectively and the increase rate isabout 25 and 48 e analytical results show that thevertical bearing capacity of the composite beam can be ef-fectively improved by increasing the cross-sectional area ofthe lower chords

0

40

80

120

160P

(kN

)

0 5 10 15 20 25 30 35Δ (mm)

C30 (fcuk = 30MPa)C40 (fcuk = 40MPa)C50 (fcuk = 50MPa)

(a)

0

50

100

150

P (k

N)

Δ (mm)0 5 10 15 20 25 30 35

ρprimea = 043 (Aprimea = 232mm2)ρprimea = 063 (Aprimea = 342mm2)ρprimea = 083 (Aprimea = 448mm2)

(b)

0 5 10 15 20 25 30 35Δ (mm)

0

50

100

150

200

250

300

P (k

N)

ρa = 164 (Aa = 888mm2)ρa = 213 (Aa = 1152mm2)ρa = 256 (Aa = 1400mm2)

(c)

Δ (mm)0 5 10 15 20 25 30 35

P (k

N)

0

50

100

150

200

s = 200mms = 250mms = 500mm

(d)

Figure 8 Influence of different parameters on load-deflection curves (a) Concrete strength grade (b) Steel ratio of steel tube of upperchords (c) Steel ratio of steel tube of lower chords (d) Truss joint spacing

10 Advances in Materials Science and Engineering

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

supported beam fixed hinge support is set at the left end(Ux Uy Uz 0) and sliding hinge support is set at the rightend (Ux Uy 0) and the vertical loads are placed by dis-placement control method

3 Verification of the Numerical Model

31 e Experiments Figure 3 gives the layout of reinforce-ment and strain gauges for square steel tube truss concretebeamswith grouted chords and the specimens were numberedas B-1simB-5 e length of beam specimens is 2700mm thecalculated span is 2500mm the cross-sectional size is200mmtimes 300mm and the concrete strength grade is C40emeasured average compressive strength of concrete cube fcu is448MPa axial compressive strength fc is 3405MPa axialtensile strength ft is 32MPa and modulus of elasticity Ec is336times104MPa [17] Grouting material was made by PO 425ordinary silicate cement UEA expansive agent FDN super-plasticizer and tap-water e measured mean axial com-pressive strength fg of grouting material cube after 28-daysstandard curing is 363MPa e cross-sectional sizes ofconnecting rods and web members for all embedded steeltrusses take 25mmtimes 25mmtimes 2mm and the yield strength fais 360MPa e yield strength fa for chord tubes with cross-sectional sizes of 30mmtimes30mmtimes 2mm 30times 30mm

times 3mm 40mmtimes 40mmtimes2mm and 40mmtimes 40mmtimes 3mm is 297MPa 345MPa 355MPa and 312MParespectively

In the tests four-point symmetrical loading was adopted bydistributive girder as shown in Figure 4e total vertical loadPis measured by a load sensor and the deflectionΔ atmidspan iscalculated according to the data of dial indicators at midspanand supports Strain gauges are fixed on the upper and lowerchords of steel tube trusses and concrete in the pure bendingsegment e test results showed that all the five beam spec-imens showed flexural failure with the concrete in compres-sion zone crushing after the lower chords reaching full tensileyielding while the upper chords not yielding completely

32 Load-Deflection Curves Figure 5 shows the comparisonof load-deflection (PminusΔ) curves obtained from beam spec-imens and FEA models Table 1 lists the simulated and testcrack stiffnesses (Escr and Etcr) and ultimate loads (Psu and Ptu)It was found that the crack loads calculated by the FEAmodels are close to the test results but the crack dis-placement calculated was smaller than that of the measuredvalues which caused crack stiffnesses for FEA models whichwere greater than that of tests With the increase of verticalloads the predicted stiffnesses after cracking were also largerthan measured results since the yield of steel tubes of lower

Hollowed out solids for web members

Retained solids for grouting materials in steel tube

(a)

Upper chords

Upper chords

Web membersConnecting rod

(b)

Steel trusses

P2P2

Ux = 0 Uy = 0 Uz = 0 Uy = 0 Uz = 0 Concretey

zx

(c)

Figure 2 Finite element analysis model (a) Part of concrete beam (b) Part of steel tube truss (c) Loading and constraints

4 Advances in Materials Science and Engineering

chords is a gradual process and there is no obvious yieldpoint on the calculated and test curves which is obviouslydifferent from the yield case of the ordinary reinforcedconcrete beam when the failure is achieved the predictedultimate loadsrsquo Psu are close to the test values Ptu with about5

Generally the calculated curves and ultimate bearingcapacities are similar to the tested ones e reason for the

increase of initial stiffness and post-cracking stiffnessmentioned above could be explained as follows (1) theconcrete elements in the FEA models are continuous andthere is no crack development thus the impact of crackingcannot be accurately considered in the whole loading pro-cess (2) DP model is adopted for concrete without con-sidering the impact of the damage (3) e slip between steeltrusses and concrete are considered in the FEA models

5020

20

50

250 250 250 250 250 250 250 250 250 2502700

300

Upper chords Vertical web member

Diagonal web memberUpper chords

(a)

200200200200200200200200200200 2502502700

50 20

50

300 20

Upper chords Vertical web member

Diagonal web memberUpper chords

(b)

240

B-1130

Steel tube30 times 30 times 2

Steel tube40 times 40 times 2Steel tube

40 times 40 times 2

240

B-2130

Steel tube30 times 30 times 2

Steel tube30 times 30 times 3

240

B-3130

Steel tube30 times 30 times 2

Steel tube40 times 40 times 3

240

B-4130

Steel tube30 times 30 times 3

Steel tube40 times 40 times 3

240

B-5130

Steel tube30 times 30 times 2

Steel tube30 times 30 times 3

(c)

15

5555

5512

0

(d)

S9

S12

S1S2(3)

S4

S10(11)

S6(7)S5

S8

S13S14(15)

S16

S17S18

S19S20

(e)

Figure 3 Detailed configurations of embedded square steel tube trusses and gauges distribution (unit mm) (a) Elevation view for beamspecimens B-1 B-2 B-3 and B-4 (b) Elevation view of beam specimen B-5 (c) Cross-section details (d) Strain gauges on concrete (e) Straingauges on steel truss

Advances in Materials Science and Engineering 5

0 5 10 15 20 25 30 350

50

100

150

200

250

Δ (mm)TestedSimulated

P (k

N)

(a)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(b)

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(c)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(d)

Figure 5 Continued

Hinge support

Hydraulic jack

Load cell

Beam specimen

Distribution girder

Dial indicator

Figure 4 Loading apparatus

6 Advances in Materials Science and Engineering

33 Comparison of FailureModes e ultimate compressivestrain εcu of concrete is often taken as 00033 When thecompressive strain (denoted by E11) in the length directionof concrete exceeds εcu it indicates that concrete is crushede yield of steel tube trusses could be observed by theplastic strains (represented as PE11) When the plastic strainPE11 of the upper and lower chords of the steel tube trussesin the axial direction of members is greater than zero itindicated that the chords reached yielding Taking typicalbeam specimen B-1 as example the strain of concrete andplastic strain of steel tube trusses for the FEAmodel at failurewere obtained as shown in Figures 6(a) and 6(b) As shownin Figure 6(a) the compressive strain E11 of concrete in theupper part of the pure bending segment of the FEA beammodel was far from the ultimate compressive strain of 00033up to 001 and the depth of the compression zone was about30mm which indicates that the concrete had been crushedand the simulated failure was basically consistent with theexperimental observation shown in Figure 6(c) It can beconcluded from Figure 6(b) that the lower chords of steeltube trusses have yielded in the whole pure bending seg-ment with a maximum yield strain of 00359 which indi-cates that the FEA results can clearly reflect the observationof failure

34 Strain Variation of Steel Tubes e test and calculatedcurves of vertical load (P) and steel tube strain (ε) arecompared in Figure 7 where strain gauges S1 and S9 werefixed on the upper and lower chords From initial loading tofailure the vertical load-strain (Pminusε) curves correspondingto the measuring point S1 calculated by the FEA method arematching with the measured results in which the steel tubestrains of S1 vary linearly with the increase of vertical loadsand the strains yield slightly at the peak load for somespecimens For the measuring point S2 there is a certain gapbetween the simulated and tested load-strain curves whichis mainly reflected by the fact that the slope of the calculatedcurves is larger than that of the tested ones before yielding ofthe steel tubes but when the loads reached the peak valuesthe calculated strains of S1 are greater than the yield straine reason for the above distinction could be explained bythe DP model of the concrete which was adopted wherebythe elements were continuous without considering cracks

4 Parameter Analysis

Studies on flexural capacity and parameter analysis onvertical load-deflection curves by FEA models were con-ducted e primary analysis parameters involved theconcrete strength grade fcuk steel ratio of upper and lowerchords (ρa

prime and ρa) and the spacing (s) between adjacenttruss joints Table 2 gives basic information In the parameteranalysis the FEA models were taken as a simply supportedbeam with the length of 2700mm the calculated span of2500mm and the cross-section size of 200mmtimes 300mme dimensions of the web member and connecting rods forencased steel trusses were both 25mmtimes 25mmtimes 2mmesteel tube yield strength is fy 235Nmm2 and the concretestrength is taken as the standard value In addition no shearfailure occurred in these FEA models

Table 1 Comparison of crack and ultimate loads between sim-ulation and tests

Beamnumber

Ecrs

(kNmm)Ecrt

(kNmm) Pus (kN) Put (kN) PutPus

B-1 673 210 1854 1850 100B-2 680 250 1987 1940 098B-3 708 270 2289 2180 095B-4 734 281 2333 2200 094B-5 678 214 1986 1960 099

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(e)

Figure 5 Load-deflection curves of tests and FEA models (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Advances in Materials Science and Engineering 7

Crushing of concrete+4794e ndash 02

E E11

+4367e ndash 02+3940e ndash 02+3513e ndash 02+3086e ndash 02+2659e ndash 02+2232e ndash 02+1805e ndash 02+1378e ndash 02+9510e ndash 03+5240e ndash 03+9699e ndash 04ndash3300e ndash 03ndash1007e ndash 02

(a)

Yielding of steel tube

+3590e ndash 02

PE PE11SNEG (fraction = ndash10)

+3251e ndash 02+2912e ndash 02+2573e ndash 02+2235e ndash 02+1896e ndash 02+1557e ndash 02+1218e ndash 02+8791e ndash 03+5403e ndash 03+2014e ndash 03ndash1375e ndash 03ndash4763e ndash 03

(b)

Crushing of concrete

(c)

Figure 6 Comparison of failure modes (a) Crushing of concrete for FEA model (b) Yielding of steel trusses for FEA model (c) Failuremode of beam specimens

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(a)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(b)

Figure 7 Continued

8 Advances in Materials Science and Engineering

41 Concrete Strength Figure 8(a) gives the vertical load-deflection (PminusΔ) curve of square steel tube truss concrete beamswith grouted chords under different concrete strength gradesWhen the concrete strength grades are C30 C40 and C50respectively the initial stiffnesses for PminusΔ curves are basicallythe same and the stiffnesses after cracking and yielding in-creased slightly e peak values of vertical loads at failure are1350 kN 1376 kN and 1398 kN respectively with an incre-ment of 19 and 36 is indicates that improving theconcrete strength could enhance the vertical load ofmembers toa certain extent however the increments were very small

42 Steel Ratio of Upper Chords e vertical load-deflection(PminusΔ) curves for square steel tube truss concrete beams withdifferent steel ratio of upper chords are compared inFigure 8(b) With an increment of steel ratio the cross-sectional area Aa

prime is in the order of 232mm2 342mm2 and448mm2 and an increment of 474 and 931 e curveshapes are essentially similar and the stiffnesses increasedslightly after cracking e vertical load peak at failurecorresponding to the cross-sectional area of the differentupper chord steel tubes is 1334 kN 1344 kN and 1350 kNrespectively and the vertical peak loads increase by 07 and

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(c)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(d)

ndash2000 0 2000 4000 6000 8000 100000

50

100

150

200

250

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(e)

Figure 7 Vertical load-strain curve of steel tube (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Table 2 Parameters of FEA models

Analytical parameters Range of parameters DescriptionConcrete strength grade C30 C45 C50 fcuk 30Nmm2 40Nmm2 and 50Nmm2

Steel ratio of upper chords (ρaprime) 043 063 083 Area 232mm2 342mm2 and 448mm2

Steel ratio of lower chords (ρa) 164 213 256 Area 888mm2 1152mm2 1400mm2

Spacing of truss joint (s) 200mm 250mm 500mm mdash

Advances in Materials Science and Engineering 9

12 respectively It can be seen that increasing the sectionalarea of the upper chords has little influence on enhancing thevertical bearing capacity Due to the structural requirementsof upper chords of steel trusses the sectional area is generallylarge and they cannot reach full yielding at peak loads

43 Steel Ratio of Lower Chords Figure 8(c) shows the in-fluence of the steel ratio of the lower chords on the verticalload-deflection (PminusΔ) for the composite beams It indicates

that the vertical peak load and yield stiffness of the com-posite beam raised with an increase of steel ratio of the lowerchordsWhen the steel ratio is 164 213 and 256 withcross-sectional areas of 888mm2 1152mm2 and 1400mm2the corresponding vertical peak loads are 1842 kN2304 kN and 2726 kN respectively and the increase rate isabout 25 and 48 e analytical results show that thevertical bearing capacity of the composite beam can be ef-fectively improved by increasing the cross-sectional area ofthe lower chords

0

40

80

120

160P

(kN

)

0 5 10 15 20 25 30 35Δ (mm)

C30 (fcuk = 30MPa)C40 (fcuk = 40MPa)C50 (fcuk = 50MPa)

(a)

0

50

100

150

P (k

N)

Δ (mm)0 5 10 15 20 25 30 35

ρprimea = 043 (Aprimea = 232mm2)ρprimea = 063 (Aprimea = 342mm2)ρprimea = 083 (Aprimea = 448mm2)

(b)

0 5 10 15 20 25 30 35Δ (mm)

0

50

100

150

200

250

300

P (k

N)

ρa = 164 (Aa = 888mm2)ρa = 213 (Aa = 1152mm2)ρa = 256 (Aa = 1400mm2)

(c)

Δ (mm)0 5 10 15 20 25 30 35

P (k

N)

0

50

100

150

200

s = 200mms = 250mms = 500mm

(d)

Figure 8 Influence of different parameters on load-deflection curves (a) Concrete strength grade (b) Steel ratio of steel tube of upperchords (c) Steel ratio of steel tube of lower chords (d) Truss joint spacing

10 Advances in Materials Science and Engineering

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

chords is a gradual process and there is no obvious yieldpoint on the calculated and test curves which is obviouslydifferent from the yield case of the ordinary reinforcedconcrete beam when the failure is achieved the predictedultimate loadsrsquo Psu are close to the test values Ptu with about5

Generally the calculated curves and ultimate bearingcapacities are similar to the tested ones e reason for the

increase of initial stiffness and post-cracking stiffnessmentioned above could be explained as follows (1) theconcrete elements in the FEA models are continuous andthere is no crack development thus the impact of crackingcannot be accurately considered in the whole loading pro-cess (2) DP model is adopted for concrete without con-sidering the impact of the damage (3) e slip between steeltrusses and concrete are considered in the FEA models

5020

20

50

250 250 250 250 250 250 250 250 250 2502700

300

Upper chords Vertical web member

Diagonal web memberUpper chords

(a)

200200200200200200200200200200 2502502700

50 20

50

300 20

Upper chords Vertical web member

Diagonal web memberUpper chords

(b)

240

B-1130

Steel tube30 times 30 times 2

Steel tube40 times 40 times 2Steel tube

40 times 40 times 2

240

B-2130

Steel tube30 times 30 times 2

Steel tube30 times 30 times 3

240

B-3130

Steel tube30 times 30 times 2

Steel tube40 times 40 times 3

240

B-4130

Steel tube30 times 30 times 3

Steel tube40 times 40 times 3

240

B-5130

Steel tube30 times 30 times 2

Steel tube30 times 30 times 3

(c)

15

5555

5512

0

(d)

S9

S12

S1S2(3)

S4

S10(11)

S6(7)S5

S8

S13S14(15)

S16

S17S18

S19S20

(e)

Figure 3 Detailed configurations of embedded square steel tube trusses and gauges distribution (unit mm) (a) Elevation view for beamspecimens B-1 B-2 B-3 and B-4 (b) Elevation view of beam specimen B-5 (c) Cross-section details (d) Strain gauges on concrete (e) Straingauges on steel truss

Advances in Materials Science and Engineering 5

0 5 10 15 20 25 30 350

50

100

150

200

250

Δ (mm)TestedSimulated

P (k

N)

(a)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(b)

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(c)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(d)

Figure 5 Continued

Hinge support

Hydraulic jack

Load cell

Beam specimen

Distribution girder

Dial indicator

Figure 4 Loading apparatus

6 Advances in Materials Science and Engineering

33 Comparison of FailureModes e ultimate compressivestrain εcu of concrete is often taken as 00033 When thecompressive strain (denoted by E11) in the length directionof concrete exceeds εcu it indicates that concrete is crushede yield of steel tube trusses could be observed by theplastic strains (represented as PE11) When the plastic strainPE11 of the upper and lower chords of the steel tube trussesin the axial direction of members is greater than zero itindicated that the chords reached yielding Taking typicalbeam specimen B-1 as example the strain of concrete andplastic strain of steel tube trusses for the FEAmodel at failurewere obtained as shown in Figures 6(a) and 6(b) As shownin Figure 6(a) the compressive strain E11 of concrete in theupper part of the pure bending segment of the FEA beammodel was far from the ultimate compressive strain of 00033up to 001 and the depth of the compression zone was about30mm which indicates that the concrete had been crushedand the simulated failure was basically consistent with theexperimental observation shown in Figure 6(c) It can beconcluded from Figure 6(b) that the lower chords of steeltube trusses have yielded in the whole pure bending seg-ment with a maximum yield strain of 00359 which indi-cates that the FEA results can clearly reflect the observationof failure

34 Strain Variation of Steel Tubes e test and calculatedcurves of vertical load (P) and steel tube strain (ε) arecompared in Figure 7 where strain gauges S1 and S9 werefixed on the upper and lower chords From initial loading tofailure the vertical load-strain (Pminusε) curves correspondingto the measuring point S1 calculated by the FEA method arematching with the measured results in which the steel tubestrains of S1 vary linearly with the increase of vertical loadsand the strains yield slightly at the peak load for somespecimens For the measuring point S2 there is a certain gapbetween the simulated and tested load-strain curves whichis mainly reflected by the fact that the slope of the calculatedcurves is larger than that of the tested ones before yielding ofthe steel tubes but when the loads reached the peak valuesthe calculated strains of S1 are greater than the yield straine reason for the above distinction could be explained bythe DP model of the concrete which was adopted wherebythe elements were continuous without considering cracks

4 Parameter Analysis

Studies on flexural capacity and parameter analysis onvertical load-deflection curves by FEA models were con-ducted e primary analysis parameters involved theconcrete strength grade fcuk steel ratio of upper and lowerchords (ρa

prime and ρa) and the spacing (s) between adjacenttruss joints Table 2 gives basic information In the parameteranalysis the FEA models were taken as a simply supportedbeam with the length of 2700mm the calculated span of2500mm and the cross-section size of 200mmtimes 300mme dimensions of the web member and connecting rods forencased steel trusses were both 25mmtimes 25mmtimes 2mmesteel tube yield strength is fy 235Nmm2 and the concretestrength is taken as the standard value In addition no shearfailure occurred in these FEA models

Table 1 Comparison of crack and ultimate loads between sim-ulation and tests

Beamnumber

Ecrs

(kNmm)Ecrt

(kNmm) Pus (kN) Put (kN) PutPus

B-1 673 210 1854 1850 100B-2 680 250 1987 1940 098B-3 708 270 2289 2180 095B-4 734 281 2333 2200 094B-5 678 214 1986 1960 099

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(e)

Figure 5 Load-deflection curves of tests and FEA models (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Advances in Materials Science and Engineering 7

Crushing of concrete+4794e ndash 02

E E11

+4367e ndash 02+3940e ndash 02+3513e ndash 02+3086e ndash 02+2659e ndash 02+2232e ndash 02+1805e ndash 02+1378e ndash 02+9510e ndash 03+5240e ndash 03+9699e ndash 04ndash3300e ndash 03ndash1007e ndash 02

(a)

Yielding of steel tube

+3590e ndash 02

PE PE11SNEG (fraction = ndash10)

+3251e ndash 02+2912e ndash 02+2573e ndash 02+2235e ndash 02+1896e ndash 02+1557e ndash 02+1218e ndash 02+8791e ndash 03+5403e ndash 03+2014e ndash 03ndash1375e ndash 03ndash4763e ndash 03

(b)

Crushing of concrete

(c)

Figure 6 Comparison of failure modes (a) Crushing of concrete for FEA model (b) Yielding of steel trusses for FEA model (c) Failuremode of beam specimens

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(a)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(b)

Figure 7 Continued

8 Advances in Materials Science and Engineering

41 Concrete Strength Figure 8(a) gives the vertical load-deflection (PminusΔ) curve of square steel tube truss concrete beamswith grouted chords under different concrete strength gradesWhen the concrete strength grades are C30 C40 and C50respectively the initial stiffnesses for PminusΔ curves are basicallythe same and the stiffnesses after cracking and yielding in-creased slightly e peak values of vertical loads at failure are1350 kN 1376 kN and 1398 kN respectively with an incre-ment of 19 and 36 is indicates that improving theconcrete strength could enhance the vertical load ofmembers toa certain extent however the increments were very small

42 Steel Ratio of Upper Chords e vertical load-deflection(PminusΔ) curves for square steel tube truss concrete beams withdifferent steel ratio of upper chords are compared inFigure 8(b) With an increment of steel ratio the cross-sectional area Aa

prime is in the order of 232mm2 342mm2 and448mm2 and an increment of 474 and 931 e curveshapes are essentially similar and the stiffnesses increasedslightly after cracking e vertical load peak at failurecorresponding to the cross-sectional area of the differentupper chord steel tubes is 1334 kN 1344 kN and 1350 kNrespectively and the vertical peak loads increase by 07 and

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(c)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(d)

ndash2000 0 2000 4000 6000 8000 100000

50

100

150

200

250

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(e)

Figure 7 Vertical load-strain curve of steel tube (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Table 2 Parameters of FEA models

Analytical parameters Range of parameters DescriptionConcrete strength grade C30 C45 C50 fcuk 30Nmm2 40Nmm2 and 50Nmm2

Steel ratio of upper chords (ρaprime) 043 063 083 Area 232mm2 342mm2 and 448mm2

Steel ratio of lower chords (ρa) 164 213 256 Area 888mm2 1152mm2 1400mm2

Spacing of truss joint (s) 200mm 250mm 500mm mdash

Advances in Materials Science and Engineering 9

12 respectively It can be seen that increasing the sectionalarea of the upper chords has little influence on enhancing thevertical bearing capacity Due to the structural requirementsof upper chords of steel trusses the sectional area is generallylarge and they cannot reach full yielding at peak loads

43 Steel Ratio of Lower Chords Figure 8(c) shows the in-fluence of the steel ratio of the lower chords on the verticalload-deflection (PminusΔ) for the composite beams It indicates

that the vertical peak load and yield stiffness of the com-posite beam raised with an increase of steel ratio of the lowerchordsWhen the steel ratio is 164 213 and 256 withcross-sectional areas of 888mm2 1152mm2 and 1400mm2the corresponding vertical peak loads are 1842 kN2304 kN and 2726 kN respectively and the increase rate isabout 25 and 48 e analytical results show that thevertical bearing capacity of the composite beam can be ef-fectively improved by increasing the cross-sectional area ofthe lower chords

0

40

80

120

160P

(kN

)

0 5 10 15 20 25 30 35Δ (mm)

C30 (fcuk = 30MPa)C40 (fcuk = 40MPa)C50 (fcuk = 50MPa)

(a)

0

50

100

150

P (k

N)

Δ (mm)0 5 10 15 20 25 30 35

ρprimea = 043 (Aprimea = 232mm2)ρprimea = 063 (Aprimea = 342mm2)ρprimea = 083 (Aprimea = 448mm2)

(b)

0 5 10 15 20 25 30 35Δ (mm)

0

50

100

150

200

250

300

P (k

N)

ρa = 164 (Aa = 888mm2)ρa = 213 (Aa = 1152mm2)ρa = 256 (Aa = 1400mm2)

(c)

Δ (mm)0 5 10 15 20 25 30 35

P (k

N)

0

50

100

150

200

s = 200mms = 250mms = 500mm

(d)

Figure 8 Influence of different parameters on load-deflection curves (a) Concrete strength grade (b) Steel ratio of steel tube of upperchords (c) Steel ratio of steel tube of lower chords (d) Truss joint spacing

10 Advances in Materials Science and Engineering

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

0 5 10 15 20 25 30 350

50

100

150

200

250

Δ (mm)TestedSimulated

P (k

N)

(a)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(b)

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(c)

Δ (mm)TestedSimulated

0 5 10 15 20 25 30 350

50

100

150

200

250

P (k

N)

(d)

Figure 5 Continued

Hinge support

Hydraulic jack

Load cell

Beam specimen

Distribution girder

Dial indicator

Figure 4 Loading apparatus

6 Advances in Materials Science and Engineering

33 Comparison of FailureModes e ultimate compressivestrain εcu of concrete is often taken as 00033 When thecompressive strain (denoted by E11) in the length directionof concrete exceeds εcu it indicates that concrete is crushede yield of steel tube trusses could be observed by theplastic strains (represented as PE11) When the plastic strainPE11 of the upper and lower chords of the steel tube trussesin the axial direction of members is greater than zero itindicated that the chords reached yielding Taking typicalbeam specimen B-1 as example the strain of concrete andplastic strain of steel tube trusses for the FEAmodel at failurewere obtained as shown in Figures 6(a) and 6(b) As shownin Figure 6(a) the compressive strain E11 of concrete in theupper part of the pure bending segment of the FEA beammodel was far from the ultimate compressive strain of 00033up to 001 and the depth of the compression zone was about30mm which indicates that the concrete had been crushedand the simulated failure was basically consistent with theexperimental observation shown in Figure 6(c) It can beconcluded from Figure 6(b) that the lower chords of steeltube trusses have yielded in the whole pure bending seg-ment with a maximum yield strain of 00359 which indi-cates that the FEA results can clearly reflect the observationof failure

34 Strain Variation of Steel Tubes e test and calculatedcurves of vertical load (P) and steel tube strain (ε) arecompared in Figure 7 where strain gauges S1 and S9 werefixed on the upper and lower chords From initial loading tofailure the vertical load-strain (Pminusε) curves correspondingto the measuring point S1 calculated by the FEA method arematching with the measured results in which the steel tubestrains of S1 vary linearly with the increase of vertical loadsand the strains yield slightly at the peak load for somespecimens For the measuring point S2 there is a certain gapbetween the simulated and tested load-strain curves whichis mainly reflected by the fact that the slope of the calculatedcurves is larger than that of the tested ones before yielding ofthe steel tubes but when the loads reached the peak valuesthe calculated strains of S1 are greater than the yield straine reason for the above distinction could be explained bythe DP model of the concrete which was adopted wherebythe elements were continuous without considering cracks

4 Parameter Analysis

Studies on flexural capacity and parameter analysis onvertical load-deflection curves by FEA models were con-ducted e primary analysis parameters involved theconcrete strength grade fcuk steel ratio of upper and lowerchords (ρa

prime and ρa) and the spacing (s) between adjacenttruss joints Table 2 gives basic information In the parameteranalysis the FEA models were taken as a simply supportedbeam with the length of 2700mm the calculated span of2500mm and the cross-section size of 200mmtimes 300mme dimensions of the web member and connecting rods forencased steel trusses were both 25mmtimes 25mmtimes 2mmesteel tube yield strength is fy 235Nmm2 and the concretestrength is taken as the standard value In addition no shearfailure occurred in these FEA models

Table 1 Comparison of crack and ultimate loads between sim-ulation and tests

Beamnumber

Ecrs

(kNmm)Ecrt

(kNmm) Pus (kN) Put (kN) PutPus

B-1 673 210 1854 1850 100B-2 680 250 1987 1940 098B-3 708 270 2289 2180 095B-4 734 281 2333 2200 094B-5 678 214 1986 1960 099

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(e)

Figure 5 Load-deflection curves of tests and FEA models (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Advances in Materials Science and Engineering 7

Crushing of concrete+4794e ndash 02

E E11

+4367e ndash 02+3940e ndash 02+3513e ndash 02+3086e ndash 02+2659e ndash 02+2232e ndash 02+1805e ndash 02+1378e ndash 02+9510e ndash 03+5240e ndash 03+9699e ndash 04ndash3300e ndash 03ndash1007e ndash 02

(a)

Yielding of steel tube

+3590e ndash 02

PE PE11SNEG (fraction = ndash10)

+3251e ndash 02+2912e ndash 02+2573e ndash 02+2235e ndash 02+1896e ndash 02+1557e ndash 02+1218e ndash 02+8791e ndash 03+5403e ndash 03+2014e ndash 03ndash1375e ndash 03ndash4763e ndash 03

(b)

Crushing of concrete

(c)

Figure 6 Comparison of failure modes (a) Crushing of concrete for FEA model (b) Yielding of steel trusses for FEA model (c) Failuremode of beam specimens

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(a)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(b)

Figure 7 Continued

8 Advances in Materials Science and Engineering

41 Concrete Strength Figure 8(a) gives the vertical load-deflection (PminusΔ) curve of square steel tube truss concrete beamswith grouted chords under different concrete strength gradesWhen the concrete strength grades are C30 C40 and C50respectively the initial stiffnesses for PminusΔ curves are basicallythe same and the stiffnesses after cracking and yielding in-creased slightly e peak values of vertical loads at failure are1350 kN 1376 kN and 1398 kN respectively with an incre-ment of 19 and 36 is indicates that improving theconcrete strength could enhance the vertical load ofmembers toa certain extent however the increments were very small

42 Steel Ratio of Upper Chords e vertical load-deflection(PminusΔ) curves for square steel tube truss concrete beams withdifferent steel ratio of upper chords are compared inFigure 8(b) With an increment of steel ratio the cross-sectional area Aa

prime is in the order of 232mm2 342mm2 and448mm2 and an increment of 474 and 931 e curveshapes are essentially similar and the stiffnesses increasedslightly after cracking e vertical load peak at failurecorresponding to the cross-sectional area of the differentupper chord steel tubes is 1334 kN 1344 kN and 1350 kNrespectively and the vertical peak loads increase by 07 and

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(c)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(d)

ndash2000 0 2000 4000 6000 8000 100000

50

100

150

200

250

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(e)

Figure 7 Vertical load-strain curve of steel tube (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Table 2 Parameters of FEA models

Analytical parameters Range of parameters DescriptionConcrete strength grade C30 C45 C50 fcuk 30Nmm2 40Nmm2 and 50Nmm2

Steel ratio of upper chords (ρaprime) 043 063 083 Area 232mm2 342mm2 and 448mm2

Steel ratio of lower chords (ρa) 164 213 256 Area 888mm2 1152mm2 1400mm2

Spacing of truss joint (s) 200mm 250mm 500mm mdash

Advances in Materials Science and Engineering 9

12 respectively It can be seen that increasing the sectionalarea of the upper chords has little influence on enhancing thevertical bearing capacity Due to the structural requirementsof upper chords of steel trusses the sectional area is generallylarge and they cannot reach full yielding at peak loads

43 Steel Ratio of Lower Chords Figure 8(c) shows the in-fluence of the steel ratio of the lower chords on the verticalload-deflection (PminusΔ) for the composite beams It indicates

that the vertical peak load and yield stiffness of the com-posite beam raised with an increase of steel ratio of the lowerchordsWhen the steel ratio is 164 213 and 256 withcross-sectional areas of 888mm2 1152mm2 and 1400mm2the corresponding vertical peak loads are 1842 kN2304 kN and 2726 kN respectively and the increase rate isabout 25 and 48 e analytical results show that thevertical bearing capacity of the composite beam can be ef-fectively improved by increasing the cross-sectional area ofthe lower chords

0

40

80

120

160P

(kN

)

0 5 10 15 20 25 30 35Δ (mm)

C30 (fcuk = 30MPa)C40 (fcuk = 40MPa)C50 (fcuk = 50MPa)

(a)

0

50

100

150

P (k

N)

Δ (mm)0 5 10 15 20 25 30 35

ρprimea = 043 (Aprimea = 232mm2)ρprimea = 063 (Aprimea = 342mm2)ρprimea = 083 (Aprimea = 448mm2)

(b)

0 5 10 15 20 25 30 35Δ (mm)

0

50

100

150

200

250

300

P (k

N)

ρa = 164 (Aa = 888mm2)ρa = 213 (Aa = 1152mm2)ρa = 256 (Aa = 1400mm2)

(c)

Δ (mm)0 5 10 15 20 25 30 35

P (k

N)

0

50

100

150

200

s = 200mms = 250mms = 500mm

(d)

Figure 8 Influence of different parameters on load-deflection curves (a) Concrete strength grade (b) Steel ratio of steel tube of upperchords (c) Steel ratio of steel tube of lower chords (d) Truss joint spacing

10 Advances in Materials Science and Engineering

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

33 Comparison of FailureModes e ultimate compressivestrain εcu of concrete is often taken as 00033 When thecompressive strain (denoted by E11) in the length directionof concrete exceeds εcu it indicates that concrete is crushede yield of steel tube trusses could be observed by theplastic strains (represented as PE11) When the plastic strainPE11 of the upper and lower chords of the steel tube trussesin the axial direction of members is greater than zero itindicated that the chords reached yielding Taking typicalbeam specimen B-1 as example the strain of concrete andplastic strain of steel tube trusses for the FEAmodel at failurewere obtained as shown in Figures 6(a) and 6(b) As shownin Figure 6(a) the compressive strain E11 of concrete in theupper part of the pure bending segment of the FEA beammodel was far from the ultimate compressive strain of 00033up to 001 and the depth of the compression zone was about30mm which indicates that the concrete had been crushedand the simulated failure was basically consistent with theexperimental observation shown in Figure 6(c) It can beconcluded from Figure 6(b) that the lower chords of steeltube trusses have yielded in the whole pure bending seg-ment with a maximum yield strain of 00359 which indi-cates that the FEA results can clearly reflect the observationof failure

34 Strain Variation of Steel Tubes e test and calculatedcurves of vertical load (P) and steel tube strain (ε) arecompared in Figure 7 where strain gauges S1 and S9 werefixed on the upper and lower chords From initial loading tofailure the vertical load-strain (Pminusε) curves correspondingto the measuring point S1 calculated by the FEA method arematching with the measured results in which the steel tubestrains of S1 vary linearly with the increase of vertical loadsand the strains yield slightly at the peak load for somespecimens For the measuring point S2 there is a certain gapbetween the simulated and tested load-strain curves whichis mainly reflected by the fact that the slope of the calculatedcurves is larger than that of the tested ones before yielding ofthe steel tubes but when the loads reached the peak valuesthe calculated strains of S1 are greater than the yield straine reason for the above distinction could be explained bythe DP model of the concrete which was adopted wherebythe elements were continuous without considering cracks

4 Parameter Analysis

Studies on flexural capacity and parameter analysis onvertical load-deflection curves by FEA models were con-ducted e primary analysis parameters involved theconcrete strength grade fcuk steel ratio of upper and lowerchords (ρa

prime and ρa) and the spacing (s) between adjacenttruss joints Table 2 gives basic information In the parameteranalysis the FEA models were taken as a simply supportedbeam with the length of 2700mm the calculated span of2500mm and the cross-section size of 200mmtimes 300mme dimensions of the web member and connecting rods forencased steel trusses were both 25mmtimes 25mmtimes 2mmesteel tube yield strength is fy 235Nmm2 and the concretestrength is taken as the standard value In addition no shearfailure occurred in these FEA models

Table 1 Comparison of crack and ultimate loads between sim-ulation and tests

Beamnumber

Ecrs

(kNmm)Ecrt

(kNmm) Pus (kN) Put (kN) PutPus

B-1 673 210 1854 1850 100B-2 680 250 1987 1940 098B-3 708 270 2289 2180 095B-4 734 281 2333 2200 094B-5 678 214 1986 1960 099

0 5 10 15 20 25 30 35Δ (mm)

TestedSimulated

0

50

100

150

200

250

P (k

N)

(e)

Figure 5 Load-deflection curves of tests and FEA models (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Advances in Materials Science and Engineering 7

Crushing of concrete+4794e ndash 02

E E11

+4367e ndash 02+3940e ndash 02+3513e ndash 02+3086e ndash 02+2659e ndash 02+2232e ndash 02+1805e ndash 02+1378e ndash 02+9510e ndash 03+5240e ndash 03+9699e ndash 04ndash3300e ndash 03ndash1007e ndash 02

(a)

Yielding of steel tube

+3590e ndash 02

PE PE11SNEG (fraction = ndash10)

+3251e ndash 02+2912e ndash 02+2573e ndash 02+2235e ndash 02+1896e ndash 02+1557e ndash 02+1218e ndash 02+8791e ndash 03+5403e ndash 03+2014e ndash 03ndash1375e ndash 03ndash4763e ndash 03

(b)

Crushing of concrete

(c)

Figure 6 Comparison of failure modes (a) Crushing of concrete for FEA model (b) Yielding of steel trusses for FEA model (c) Failuremode of beam specimens

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(a)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(b)

Figure 7 Continued

8 Advances in Materials Science and Engineering

41 Concrete Strength Figure 8(a) gives the vertical load-deflection (PminusΔ) curve of square steel tube truss concrete beamswith grouted chords under different concrete strength gradesWhen the concrete strength grades are C30 C40 and C50respectively the initial stiffnesses for PminusΔ curves are basicallythe same and the stiffnesses after cracking and yielding in-creased slightly e peak values of vertical loads at failure are1350 kN 1376 kN and 1398 kN respectively with an incre-ment of 19 and 36 is indicates that improving theconcrete strength could enhance the vertical load ofmembers toa certain extent however the increments were very small

42 Steel Ratio of Upper Chords e vertical load-deflection(PminusΔ) curves for square steel tube truss concrete beams withdifferent steel ratio of upper chords are compared inFigure 8(b) With an increment of steel ratio the cross-sectional area Aa

prime is in the order of 232mm2 342mm2 and448mm2 and an increment of 474 and 931 e curveshapes are essentially similar and the stiffnesses increasedslightly after cracking e vertical load peak at failurecorresponding to the cross-sectional area of the differentupper chord steel tubes is 1334 kN 1344 kN and 1350 kNrespectively and the vertical peak loads increase by 07 and

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(c)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(d)

ndash2000 0 2000 4000 6000 8000 100000

50

100

150

200

250

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(e)

Figure 7 Vertical load-strain curve of steel tube (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Table 2 Parameters of FEA models

Analytical parameters Range of parameters DescriptionConcrete strength grade C30 C45 C50 fcuk 30Nmm2 40Nmm2 and 50Nmm2

Steel ratio of upper chords (ρaprime) 043 063 083 Area 232mm2 342mm2 and 448mm2

Steel ratio of lower chords (ρa) 164 213 256 Area 888mm2 1152mm2 1400mm2

Spacing of truss joint (s) 200mm 250mm 500mm mdash

Advances in Materials Science and Engineering 9

12 respectively It can be seen that increasing the sectionalarea of the upper chords has little influence on enhancing thevertical bearing capacity Due to the structural requirementsof upper chords of steel trusses the sectional area is generallylarge and they cannot reach full yielding at peak loads

43 Steel Ratio of Lower Chords Figure 8(c) shows the in-fluence of the steel ratio of the lower chords on the verticalload-deflection (PminusΔ) for the composite beams It indicates

that the vertical peak load and yield stiffness of the com-posite beam raised with an increase of steel ratio of the lowerchordsWhen the steel ratio is 164 213 and 256 withcross-sectional areas of 888mm2 1152mm2 and 1400mm2the corresponding vertical peak loads are 1842 kN2304 kN and 2726 kN respectively and the increase rate isabout 25 and 48 e analytical results show that thevertical bearing capacity of the composite beam can be ef-fectively improved by increasing the cross-sectional area ofthe lower chords

0

40

80

120

160P

(kN

)

0 5 10 15 20 25 30 35Δ (mm)

C30 (fcuk = 30MPa)C40 (fcuk = 40MPa)C50 (fcuk = 50MPa)

(a)

0

50

100

150

P (k

N)

Δ (mm)0 5 10 15 20 25 30 35

ρprimea = 043 (Aprimea = 232mm2)ρprimea = 063 (Aprimea = 342mm2)ρprimea = 083 (Aprimea = 448mm2)

(b)

0 5 10 15 20 25 30 35Δ (mm)

0

50

100

150

200

250

300

P (k

N)

ρa = 164 (Aa = 888mm2)ρa = 213 (Aa = 1152mm2)ρa = 256 (Aa = 1400mm2)

(c)

Δ (mm)0 5 10 15 20 25 30 35

P (k

N)

0

50

100

150

200

s = 200mms = 250mms = 500mm

(d)

Figure 8 Influence of different parameters on load-deflection curves (a) Concrete strength grade (b) Steel ratio of steel tube of upperchords (c) Steel ratio of steel tube of lower chords (d) Truss joint spacing

10 Advances in Materials Science and Engineering

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

Crushing of concrete+4794e ndash 02

E E11

+4367e ndash 02+3940e ndash 02+3513e ndash 02+3086e ndash 02+2659e ndash 02+2232e ndash 02+1805e ndash 02+1378e ndash 02+9510e ndash 03+5240e ndash 03+9699e ndash 04ndash3300e ndash 03ndash1007e ndash 02

(a)

Yielding of steel tube

+3590e ndash 02

PE PE11SNEG (fraction = ndash10)

+3251e ndash 02+2912e ndash 02+2573e ndash 02+2235e ndash 02+1896e ndash 02+1557e ndash 02+1218e ndash 02+8791e ndash 03+5403e ndash 03+2014e ndash 03ndash1375e ndash 03ndash4763e ndash 03

(b)

Crushing of concrete

(c)

Figure 6 Comparison of failure modes (a) Crushing of concrete for FEA model (b) Yielding of steel trusses for FEA model (c) Failuremode of beam specimens

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(a)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(b)

Figure 7 Continued

8 Advances in Materials Science and Engineering

41 Concrete Strength Figure 8(a) gives the vertical load-deflection (PminusΔ) curve of square steel tube truss concrete beamswith grouted chords under different concrete strength gradesWhen the concrete strength grades are C30 C40 and C50respectively the initial stiffnesses for PminusΔ curves are basicallythe same and the stiffnesses after cracking and yielding in-creased slightly e peak values of vertical loads at failure are1350 kN 1376 kN and 1398 kN respectively with an incre-ment of 19 and 36 is indicates that improving theconcrete strength could enhance the vertical load ofmembers toa certain extent however the increments were very small

42 Steel Ratio of Upper Chords e vertical load-deflection(PminusΔ) curves for square steel tube truss concrete beams withdifferent steel ratio of upper chords are compared inFigure 8(b) With an increment of steel ratio the cross-sectional area Aa

prime is in the order of 232mm2 342mm2 and448mm2 and an increment of 474 and 931 e curveshapes are essentially similar and the stiffnesses increasedslightly after cracking e vertical load peak at failurecorresponding to the cross-sectional area of the differentupper chord steel tubes is 1334 kN 1344 kN and 1350 kNrespectively and the vertical peak loads increase by 07 and

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(c)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(d)

ndash2000 0 2000 4000 6000 8000 100000

50

100

150

200

250

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(e)

Figure 7 Vertical load-strain curve of steel tube (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Table 2 Parameters of FEA models

Analytical parameters Range of parameters DescriptionConcrete strength grade C30 C45 C50 fcuk 30Nmm2 40Nmm2 and 50Nmm2

Steel ratio of upper chords (ρaprime) 043 063 083 Area 232mm2 342mm2 and 448mm2

Steel ratio of lower chords (ρa) 164 213 256 Area 888mm2 1152mm2 1400mm2

Spacing of truss joint (s) 200mm 250mm 500mm mdash

Advances in Materials Science and Engineering 9

12 respectively It can be seen that increasing the sectionalarea of the upper chords has little influence on enhancing thevertical bearing capacity Due to the structural requirementsof upper chords of steel trusses the sectional area is generallylarge and they cannot reach full yielding at peak loads

43 Steel Ratio of Lower Chords Figure 8(c) shows the in-fluence of the steel ratio of the lower chords on the verticalload-deflection (PminusΔ) for the composite beams It indicates

that the vertical peak load and yield stiffness of the com-posite beam raised with an increase of steel ratio of the lowerchordsWhen the steel ratio is 164 213 and 256 withcross-sectional areas of 888mm2 1152mm2 and 1400mm2the corresponding vertical peak loads are 1842 kN2304 kN and 2726 kN respectively and the increase rate isabout 25 and 48 e analytical results show that thevertical bearing capacity of the composite beam can be ef-fectively improved by increasing the cross-sectional area ofthe lower chords

0

40

80

120

160P

(kN

)

0 5 10 15 20 25 30 35Δ (mm)

C30 (fcuk = 30MPa)C40 (fcuk = 40MPa)C50 (fcuk = 50MPa)

(a)

0

50

100

150

P (k

N)

Δ (mm)0 5 10 15 20 25 30 35

ρprimea = 043 (Aprimea = 232mm2)ρprimea = 063 (Aprimea = 342mm2)ρprimea = 083 (Aprimea = 448mm2)

(b)

0 5 10 15 20 25 30 35Δ (mm)

0

50

100

150

200

250

300

P (k

N)

ρa = 164 (Aa = 888mm2)ρa = 213 (Aa = 1152mm2)ρa = 256 (Aa = 1400mm2)

(c)

Δ (mm)0 5 10 15 20 25 30 35

P (k

N)

0

50

100

150

200

s = 200mms = 250mms = 500mm

(d)

Figure 8 Influence of different parameters on load-deflection curves (a) Concrete strength grade (b) Steel ratio of steel tube of upperchords (c) Steel ratio of steel tube of lower chords (d) Truss joint spacing

10 Advances in Materials Science and Engineering

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

41 Concrete Strength Figure 8(a) gives the vertical load-deflection (PminusΔ) curve of square steel tube truss concrete beamswith grouted chords under different concrete strength gradesWhen the concrete strength grades are C30 C40 and C50respectively the initial stiffnesses for PminusΔ curves are basicallythe same and the stiffnesses after cracking and yielding in-creased slightly e peak values of vertical loads at failure are1350 kN 1376 kN and 1398 kN respectively with an incre-ment of 19 and 36 is indicates that improving theconcrete strength could enhance the vertical load ofmembers toa certain extent however the increments were very small

42 Steel Ratio of Upper Chords e vertical load-deflection(PminusΔ) curves for square steel tube truss concrete beams withdifferent steel ratio of upper chords are compared inFigure 8(b) With an increment of steel ratio the cross-sectional area Aa

prime is in the order of 232mm2 342mm2 and448mm2 and an increment of 474 and 931 e curveshapes are essentially similar and the stiffnesses increasedslightly after cracking e vertical load peak at failurecorresponding to the cross-sectional area of the differentupper chord steel tubes is 1334 kN 1344 kN and 1350 kNrespectively and the vertical peak loads increase by 07 and

0

50

100

150

200

250

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(c)

ndash2000 0 2000 4000 6000 8000 10000

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

0

50

100

150

200

250

P (k

N)

(d)

ndash2000 0 2000 4000 6000 8000 100000

50

100

150

200

250

S1 (Simulated)S1 (Tested)

S9 (Simulated)S9 (Tested)

ε (με)

P (k

N)

(e)

Figure 7 Vertical load-strain curve of steel tube (a) B-1 (b) B-2 (c) B-3 (d) B-4 (e) B-5

Table 2 Parameters of FEA models

Analytical parameters Range of parameters DescriptionConcrete strength grade C30 C45 C50 fcuk 30Nmm2 40Nmm2 and 50Nmm2

Steel ratio of upper chords (ρaprime) 043 063 083 Area 232mm2 342mm2 and 448mm2

Steel ratio of lower chords (ρa) 164 213 256 Area 888mm2 1152mm2 1400mm2

Spacing of truss joint (s) 200mm 250mm 500mm mdash

Advances in Materials Science and Engineering 9

12 respectively It can be seen that increasing the sectionalarea of the upper chords has little influence on enhancing thevertical bearing capacity Due to the structural requirementsof upper chords of steel trusses the sectional area is generallylarge and they cannot reach full yielding at peak loads

43 Steel Ratio of Lower Chords Figure 8(c) shows the in-fluence of the steel ratio of the lower chords on the verticalload-deflection (PminusΔ) for the composite beams It indicates

that the vertical peak load and yield stiffness of the com-posite beam raised with an increase of steel ratio of the lowerchordsWhen the steel ratio is 164 213 and 256 withcross-sectional areas of 888mm2 1152mm2 and 1400mm2the corresponding vertical peak loads are 1842 kN2304 kN and 2726 kN respectively and the increase rate isabout 25 and 48 e analytical results show that thevertical bearing capacity of the composite beam can be ef-fectively improved by increasing the cross-sectional area ofthe lower chords

0

40

80

120

160P

(kN

)

0 5 10 15 20 25 30 35Δ (mm)

C30 (fcuk = 30MPa)C40 (fcuk = 40MPa)C50 (fcuk = 50MPa)

(a)

0

50

100

150

P (k

N)

Δ (mm)0 5 10 15 20 25 30 35

ρprimea = 043 (Aprimea = 232mm2)ρprimea = 063 (Aprimea = 342mm2)ρprimea = 083 (Aprimea = 448mm2)

(b)

0 5 10 15 20 25 30 35Δ (mm)

0

50

100

150

200

250

300

P (k

N)

ρa = 164 (Aa = 888mm2)ρa = 213 (Aa = 1152mm2)ρa = 256 (Aa = 1400mm2)

(c)

Δ (mm)0 5 10 15 20 25 30 35

P (k

N)

0

50

100

150

200

s = 200mms = 250mms = 500mm

(d)

Figure 8 Influence of different parameters on load-deflection curves (a) Concrete strength grade (b) Steel ratio of steel tube of upperchords (c) Steel ratio of steel tube of lower chords (d) Truss joint spacing

10 Advances in Materials Science and Engineering

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

12 respectively It can be seen that increasing the sectionalarea of the upper chords has little influence on enhancing thevertical bearing capacity Due to the structural requirementsof upper chords of steel trusses the sectional area is generallylarge and they cannot reach full yielding at peak loads

43 Steel Ratio of Lower Chords Figure 8(c) shows the in-fluence of the steel ratio of the lower chords on the verticalload-deflection (PminusΔ) for the composite beams It indicates

that the vertical peak load and yield stiffness of the com-posite beam raised with an increase of steel ratio of the lowerchordsWhen the steel ratio is 164 213 and 256 withcross-sectional areas of 888mm2 1152mm2 and 1400mm2the corresponding vertical peak loads are 1842 kN2304 kN and 2726 kN respectively and the increase rate isabout 25 and 48 e analytical results show that thevertical bearing capacity of the composite beam can be ef-fectively improved by increasing the cross-sectional area ofthe lower chords

0

40

80

120

160P

(kN

)

0 5 10 15 20 25 30 35Δ (mm)

C30 (fcuk = 30MPa)C40 (fcuk = 40MPa)C50 (fcuk = 50MPa)

(a)

0

50

100

150

P (k

N)

Δ (mm)0 5 10 15 20 25 30 35

ρprimea = 043 (Aprimea = 232mm2)ρprimea = 063 (Aprimea = 342mm2)ρprimea = 083 (Aprimea = 448mm2)

(b)

0 5 10 15 20 25 30 35Δ (mm)

0

50

100

150

200

250

300

P (k

N)

ρa = 164 (Aa = 888mm2)ρa = 213 (Aa = 1152mm2)ρa = 256 (Aa = 1400mm2)

(c)

Δ (mm)0 5 10 15 20 25 30 35

P (k

N)

0

50

100

150

200

s = 200mms = 250mms = 500mm

(d)

Figure 8 Influence of different parameters on load-deflection curves (a) Concrete strength grade (b) Steel ratio of steel tube of upperchords (c) Steel ratio of steel tube of lower chords (d) Truss joint spacing

10 Advances in Materials Science and Engineering

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

44 SpacingofTruss Joint e influence of different truss jointspacing (s) on the load-deflection (PminusΔ) curves for square steeltube truss concrete beams is given in Figure 8(d) When thespacing is 200mm 250mm and 500mm the calculated PminusΔcurves are similar in the shape with almost no difference epeak values of vertical loads reach 1473 kN 1472 kN and1452 kN respectively with a slight decrease It can be statedthat the variation of truss joint spacing had almost no impacton the vertical load-carrying capacity

5 Flexural Capacity of Normal Section

51 Basic Assumptions To simplify analysis and facilitateengineering applications the following assumptions aremade (1) a section remains a plane before and after bending(2) e grouting material is equivalent to concrete (3) etensile strength of concrete is neglected (4) e constitutiverelation of concrete is the same as that used in GB50010-2010for the flexural capacity of reinforced concrete beams (5)For steel tubes of upper and lower chords the average stressis the product of the average strain and modulus of elasticitywhich cannot exceed its yield strength

52 Calculation Sketch and Formula rough experimentand calculation it can be seen that the steel tubes of lowerchords for composite beams reached the yield strength firstand the concrete in the compression zone was crushedsubsequently Due to the structural requirements the upperchords generally cannot completely yield thus the corre-sponding average stress can be expressed by σa

prime Figure 9gives the sketch for calculating flexural capacity Mu of thenormal section Here the stress pattern of concrete in thecompression zone can be equivalent to a rectangle with astress of α1fc α1 is the ratio of equivalent concrete com-pressive strength to concrete axial compressive strength fa isthe yield strength of lower chords b and h are the width anddepth of the cross-section respectively h0 is the effectivedepth of the cross-section that is the distance from thecentroid of the lower chords to the compression edge aa

prime isthe distance from the centroid of the upper chords to thecompression edge x is the depth of compression zone

faAa minus σaprimeAaprime minus α1fcbx 0 (3)

Mu

λ σaprimeAaprime h0 minus aa

prime( 1113857 + a1fcbx h0 minus 05x( 1113857 (4)

σaprime Eaεcu 1 minus

βaaprime

x1113888 1113889lefa (5)

xle ξbh0 (6)

e previous tests indicated that by using the samereinforcement areas and strength the flexural capacity ofcomposite beams which are reinforced with steel truss willbe greater than that of ordinary reinforced concrete beamsand thus an amplifying factor λ is usually introduced topredict the flexural capacity [18] erefore force andbending moment equilibrium equation (3) and (4) can beestablished according to Figure 9 in which σa

prime is calculatedaccording to formula (5) where β is the ratio of the depth ofcompression zone to the actual one and εcu is the concreteultimate compressive strain In order to prevent over-re-inforcement failure the depth x of the compression zoneshould meet the requirements of expression (6) where ξb isthe relative balanced depth of the compression zone

On the basis of FEA calculations and tests the relation ofamplifying factor λ of flexural capacity and steel ratio ρa oflower chords is illustrated in Figure 10 By regressionanalysis the coefficient λ can be calculated as follows

λ 0766ρminus0136a (7)

53 Comparison of Flexural Capacity of Normal Sectione comparison of the tested value Mu

t simulated value Mus

by FEA models and calculated value Muc by equation (4) for

the flexural capacity of composite beams is shown in Table 3e ratios Mu

cMut and Mu

cMus are in the range of 094 to

109 which indicates that the formula for predicting theflexural capacity of normal sections proposed in this paper arecorresponding with the tested and simulated results

6 Discussion

e test and FEA methods in this paper mainly focused onthe flexural performance of square steel tube truss concretebeams with grouted chords subjected to under-reinforcedfailure Based on the calculation method of the flexuralcapacity of normal sections for this kind of composite beamwas established and the relation between the amplifyingfactor λ of bending bearing capacity and the steel ratio ρa oflower chords was put forward However due to the limitednumber of tests and FEAmodels the steel ratio of the lowerchords in this study was only within the range of 113ndash259 and the influence of the yield of the upper chords onthe amplifying factor λ of bending capacity was also notconsidered In addition the design formula of crack widthand short-term stiffness of this type of composite beam hasnot been proposed due to unsatisfactory crack simulationand predicted load-deflection curves erefore an in-depth study should be carried out in combination with testresults

Advances in Materials Science and Engineering 11

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

0010 0015 0020 0025 00300005ρa

03

08

λ

13

18

Beam specimensFEA modelsFitting

Figure 10 Relation of amplifying factor λ and steel ratio ρa

Table 3 Comparison of flexural capacities for tests simulation and formula

Serial number ρa () Mut (kNmiddotm) Mu

s (kNmiddotm) Muc (kNmiddotm) Mu

c Mut Mu

c Mus

B-1 113 694 695 742 107 107B-2 120 728 745 761 105 102B-3 164 818 858 895 109 104B-4 164 825 875 895 108 102B-5 120 735 745 761 104 102CB-1 113 mdash 506 491 mdash 097CB-2 113 mdash 516 500 mdash 097CB-3 113 mdash 524 508 mdash 097CB-4 113 mdash 500 491 mdash 098CB-5 113 mdash 504 491 mdash 098CB-6 113 mdash 506 491 mdash 097CB-7 164 mdash 691 670 mdash 097CB-8 213 mdash 864 830 mdash 096CB-9 259 mdash 1022 974 mdash 095CB-10 120 mdash 552 518 mdash 094CB-11 120 mdash 552 518 mdash 094CB-12 120 mdash 545 518 mdash 095

b

Aa

faAa

Aprimea

σ primeaAprimeax = βx0

α1 fcεcu

h0

x0

Muλ

aa

aprimea

h

Figure 9 Calculation of flexural capacity of normal section

12 Advances in Materials Science and Engineering

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13

7 Conclusions

(1) e established FEA models could well reflect thevertical load-carrying capacities and failure modesfor steel tube truss concrete beams with groutedchords e under-reinforced failure was observedwhere the lower chords reached tensile yield andsubsequently the upper concrete was crushed

(2) With an increase of the steel ratio of the lowerchord steel tubes the vertical load-carrying ca-pacity of the square steel tube truss concrete beamincreased whereas the concrete strength steelratio of the upper chord steel tubes and truss jointspacing had little effect on the vertical load-car-rying capacity

(3) e predicting flexural capacity of composite beamsby proposed formulae is in agreement with the testedand FEA results which could be applied in engi-neering design

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors appreciate the support of the National ScienceFoundation of China (51878589) China Postdoctoral Sci-ence Foundation (2019M651762) Six Talent Peaks Project ofJiangsu Province (2017-JZ-038) Science and TechnologyPlanning Project of Yangzhou City (YZ2018068) andProject of Innovation and Entrepreneurship Plan of JiangsuProvince (2019)

References

[1] W Z Zheng G M Zhang X D Liu and B Y ZhangldquoExperimental research on ultimate bearing capacity of N-joints of grouted square steel tube trussesrdquo Journal ofSoutheast University (English Edition vol 23 no 4pp 566ndash570 2007

[2] W Z Zheng X D Liu B Y Zhang and G M ZhangldquoExperimental research on cave-in ultimate bearing capacityof grouted-round-steel tuberdquo Journal of Architectural Struc-ture vol 29 no 2 pp 85ndash91 2008 in Chinese

[3] W Huang Z Lai B Chen and P Yao ldquoExperimental be-havior and analysis of prestressed concrete-filled steel tube(CFT) truss girdersrdquo Engineering Structures vol 152pp 607ndash618 2017

[4] Y-H Huang A-R Liu J-Y Fu and Y-L Pi ldquoExperimentalinvestigation of the flexural behavior of CFST trusses withinterfacial imperfectionrdquo Journal of Constructional Steel Re-search vol 137 pp 52ndash65 2017

[5] Z-q Fu B-h Ji W Zhu andH-b Ge ldquoBending behaviour oflightweight aggregate concrete-filled steel tube spatial truss

beamrdquo Journal of Central South University vol 23 no 8pp 2110ndash2117 2016

[6] W Z Zheng X D Liu and B Y Zhang ldquoExperimental study oncomposite beam of grouting round steel tube truss-concreterdquoJournal of Architectural Structure vol 20 no 1 pp 15ndash22 2009

[7] W Zheng K Wang and G Zhang ldquoExperimental study onhysteretic behavior of prestressed truss concrete compositebeamsrdquo Earthquake Engineering and Engineering Vibrationvol 9 no 1 pp 65ndash74 2010

[8] B Y Zhang W Z Zheng and Z G Yuan ldquoMechanicalproperties of truss concrete composite beam prestressedencased with circular steel tubesrdquo Journal of Jilin University(Engineering and Technology Edition) vol 38 no 3pp 636ndash641 2008 in Chinese

[9] Z H Deng K Chen and C Feng ldquoExperimental study onbending resistance of truss steel reinforced concrete beamsrdquoIndustrial Construction vol 45 no 12 pp 178ndash182 2015 inChinese

[10] L G Wang and G B Mu ldquoResearch on bending performanceof prestressed lattice Type steel reinforced concrete beamrdquoEngineering Mechanics vol 28 no 8 pp 113ndash118 2011 inChinese

[11] M Arafa M A Alqedra and R Salim ldquoPerformance of RCbeams with embedded steel trusses using nonlinear FEManalysisrdquo Advances in Civil Engineering vol 2018 Article ID9079818 8 pages 2018

[12] P Colajanni L La Mendola and A Monaco ldquoStress transferand failure mechanisms in steel-concrete trussed beamsexperimental investigation on slab-thick and full-thickbeamsrdquo Construction and Building Materials vol 161pp 267ndash281 2018

[13] Y Y Chen J C Dong Z J Tong et al ldquoFlexural behavior ofcomposite box girders with corrugated steel webs and trussesrdquoEngineering Structures vol 209 Article ID 110275 2020

[14] K Hibbitt and Sorensen Inc ABAQUSstandard UserrsquosManual Version 641 Hibbitt Karlsson and Sorensen IncPawtucket RI USA 2003

[15] GB50010-2010 Code for Concrete Structure Design ChinaBuilding Industry Press Beijing China 2010 in Chinese

[16] G M Zhang Study on the Basic Problems of PrestressedConcrete Composite Beams with Built-In Grouting Square SteelTube Truss Harbin Institute of Technology Harbin China2008 in Chinese

[17] GBT 50152-2012 Standard Test Methods for ConcreteStructures China Building Industry Press Beijing China2012 in Chinese

[18] H T Zhao Steel amp Concrete Composite Structure Sciencepress Beijing China 2001 in Chinese

Advances in Materials Science and Engineering 13