Research ArticleAnalysis of Concrete-Filled Square Steel Tube ShortColumns under Eccentric Loading

Qifeng Shan1 Jingming Cai 23 Xiaopeng Li4 and Jiawei Tan3

1Zhejiang Industry Polytechnic College Shaoxing China2Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education Southeast University Nanjing China3Department of Civil Engineering KU Leuven Belgium4Department of Civil and Environmental Engineering University of California Irvine USA

Correspondence should be addressed to Jingming Cai jingmingcaikuleuvenbe

Received 4 April 2019 Revised 11 May 2019 Accepted 28 May 2019 Published 20 June 2019

Academic Editor Giovanni Minafo

Copyright copy 2019 Qifeng Shan et al This 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

The concrete-filled square steel tube (CFSST) columns have been widely applied in structural engineering Although manyconstitutivemodels have been proposed to describe CFSST short columns under concentric loading the applicability of the existingconcentric model in the analysis of CFSST short columns under eccentric loading has not been properly verified In this paper theeccentric behaviors of CFSST short columnswere investigatedwith the software of ABAQUSstandard It was found that the contactstress between steel tube and inner concrete was seriously affected by eccentric ratios indicating that the confinement effect of steeltube on inner concrete was different under concentric and eccentric loading In this paper a new stress-strain model of innerconcrete which considered the influence of eccentricity was developed and verified with existing experimental results It was foundthat the proposed stress-strain model was more accurate in simulating the eccentric behaviors of CFSST short columns

1 Introduction

Concrete-filled steel tube (CFST) columns are typical com-posite members consisting of outer steel tube infilled withinner concrete The outer steel tube confines the inner con-crete which increases the compressive strength and ductilityof CFST columns The inner concrete forms an ideal coreto withstand the compressive loading and it prevents localbuckling of the outer steel tube particularly in square CFSTcolumns Numerous tests have illustrated that CFST columnshave both higher strength and ductility under compressiveloading when compared with traditional steel reinforcedconcrete columns [1] In current international practicesCFST columns have been widely applied as vertical load-bearing components in high-rise structures bridges andocean infrastructures [2ndash5]

In engineering practice however it was noticed thatCFST columns are inevitably subjected to eccentric com-pressive loading although the columns are designed tosustain concentric loadingThis may be due to geometric andmaterial imperfections during the manufacturing process

minor misalignment during the construction process oraccidental lateral drift in the service and so on Extensiveexperimental researches have been conducted to investigatethe mechanical behaviors of CFST columns under eccentricloading [6ndash8] concluding that CFST columns exhibited goodductile behavior with a bending failure mode under eccentricloading Numerical analyses based on finite element methodwere also performed to simulate the mechanical behavior ofCFST short columns under eccentrical compression loadingWang and Liu [9] investigated the behavior of slender squaretubed reinforced concrete short columns subjected to eccen-tric compressionwith FEAmodel Li andChen [10] simulatedand studied the mechanical behavior of eccentrically loadedhigh strength concrete-filled high strength square steel tubestub columns Han et al [11] established an FEA modelto simulate the eccentrical behavior of the CFST columnswith gaps Sheehan et al [12] developed an FEA modelto investigate the mechanical behaviors of concrete-filledelliptical steel hollow sections under eccentric compressionAlthoughmany FEAmodels have been developed to describeCFST columns under concentric loading the applicability

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 8420181 12 pageshttpsdoiorg10115520198420181

2 Mathematical Problems in Engineering

Loading line

Rigid plate

Concrete

Steel tube

Loading line900 m

m

H

B

300 mm

Z

YX

el

＞x=＞y = 0

rx=rz = 0

rx=rz = 0

＞x=＞y = ＞z = 0

Figure 1 FEA model of CFSST columns under eccentric loading

and accuracy of these FEA models have not been properlyverified

In order to increase the accuracy of FEA models theconstitutive model of inner concrete needs to be carefullyconsidered and established In above-mentioned studies theconstitutive model proposed by Han et al [13] was normallyadopted to simulate the eccentric behavior of inner concreteThis model considers the confinement effect of steel on innerconcrete and the quasi-brittle behavior of inner concreteAlthough reasonable predictions have been obtained by someresearchers the applicability and accuracy of this model tosimulate the eccentric behavior of inner concrete have notbeen carefully investigated In fact it should be noted that thestress distribution for inner concrete is closely related withthe degree of eccentricity suggesting that the constitutivemodel needs to consider eccentricity change as a criticalparameter Similar investigations have been conducted forfiber-reinforced polymer- (FRP-) confined concrete columnsunder eccentric loading by both experimental and analyticalmethods [14ndash17] It has been concluded that eccentricallyloaded columns exhibit different mechanical behavior inaccordance with different eccentricities Therefore the con-stitutive models for FRP-confined concrete under concentricloading cannot be directly applied and thus new constitutivemodels have been proposed and verified [18 19] Cai et alinvestigated the circular concrete-filled steel tube columnsunder eccentric loading it was found that the steel tubeprovided nonuniform confinement stress to inner concreteunder eccentric loading [20] For concrete-filled square steeltube however the stress concentration phenomenon wasmuch more evident than circular steel tube which increasedthe nonlinearity and complexity for concrete-filled squaresteel tube columns under eccentric loading

Set against this background this paper aimed to investi-gate the eccentric behavior of concrete-filled square steel tubeshort columns with different eccentricities A new constitu-tive model that considers the influences of eccentricities was

proposed The accuracy of the new constitutive model wasverified via comparing with published experimental results

2 FEA Modeling

In order to analyze the influence of eccentricities on theeccentric behavior of the CFSST columns the FEA modelwas established as shown in Figure 1 The ratio of length tocross-sectional width for the specimen is three which canbe classified as a typical short column Two rigid plates withinfinite stiffness were attached on the two ends of CFSSTcolumn The interaction between the rigid plate and steeltube was defined as Tie contact thus the stress could beeffectively transferred under eccentric loading The interac-tions between rigid palate and inner concrete were definedas hard contact in order to prevent the penetration of theinner concrete into the rigid plate at the constraint locationsThe concentric and eccentric loading was applied on the toprigid plate along the loading line As has been depicted inFigure 1 all the freedom degrees for the loading line wereconstrained except the displacement along the Z axis and therotation around the Y axis so that the eccentric load could beapplied on the CFSST column An identical loading line wasalso attached on the bottom rigid plate to provide the reactionforce in which all the freedom degrees were constrainedexcept the rotation around Y axis The interaction betweeninner concrete and steel tube was defined as contact surfaceswhere the Mohr-Coulomb friction model and hard contactmodel were used to define the contact behaviors in bothtangential and normal directions respectively [21] All thecomponents including inner concrete steel tube and rigidplate were modeled using eight-node solid elements withreduced integration (C3D8R)

The five-stage stress-strain model proposed by Han etal [13] was applied to describe the isotropic elastic-plasticbehavior of steel as shown in (1) and Figure 2

Mathematical Problems in Engineering 3

stres

s

0

Strain

fy

1 2 3

Figure 2 Stress-strain model for steel

(a) (b) (c)

e=1e=05e=0

P1

P2P3 P4

P5

S1-1

S2-1

S3-1

S4-1

S1-05

S2-05

S3-05

S4-05

S1-0

S2-0

S3-0

S4-0

Figure 3 Failure modes for CFSST columns with eccentricity ratios of (a) e = 0 (b) e = 05 (c) e = 1

120590119904 =

E119904120576119904 120576119904 lt 120576119890minus1198601205762119904 + 119861120576119904 + 119862 120576119890 lt 120576119904 le 1205761198901119891119905119910 1205761198901 lt 120576119904 le 1205761198902119891119905119910 [1 + 06 120576119904 minus 1205761198902

1205761198903 minus 1205761198902 ] 1205761198902 lt 120576119904 le 120576119890316119891119905119910 120576119904120576119904 gt 1205761198903

(1)

where 120576119890=08119891119905119910119864119878 1205761198901=15120576119890 1205761198902=101205761198901 1205761198903=1001205761198901 A=02119891119905119910(1205761198901 minus 120576119890)2 B=2A1205761198901 and C=08119891119910+A1205761198902-B120576119890

The stress-strain model proposed by Han [13] was alsoapplied to simulate the quasibrittle behavior of inner con-crete which is shown in (2)

119910 =

2119909 minus 1199092 (119909 le 1)119909

1205730 (119909 minus 1)16+15119909 + 119909 (119909 gt 1) (2)

where 119909 = 1205761205760 119910 = 1205901205900 1205900 = 1198911015840119888 1205760 = 120576119888 +8001205760210minus6120576119888 = (1300 + 1251198911015840119888 )10minus6 1205730 = 1198911015840119888 0112radic1 + 120585 and 120585 =119860 119904119891119905119910119860119888119891119888119896

The concrete damaged plasticity (CDP) model inABAQUS was applied to illustrate the plastic behaviorof concrete [22 23] In above equations 119860 119904 and 119860119888 arethe cross-sectional area of square steel tube and innerconcrete which were set as 11400 mm2 and 78400 mm2in this modelling respectively The parameters 119891119905119910 and 1198911015840119888and are the yield strength of steel and cylinder strengthof inner concrete which were set as 340 MPa and 40MPain this modelling respectively The fracture energy modelproposed was used to simulate the tensile softening behaviorof concrete [23] Poissonrsquos ratio and elastic modulus for innerconcrete are taken as 02 and 4730radic1198911015840119888 according to ACI318-11 [24] respectively

The typical failure modes for CFSST columns with dif-ferent eccentric ratios are shown in Figure 3 The eccentricratio (e) was defined as 119890 = 119890119897119861 where 119890119897 is the distancefrom loading line to symmetry axis and B is defined as thehalf of outsidewidth of square steel tube as shown in Figure 1For CFSST column under concentric loading (e=0) as shownin Figure 3(a) an obvious outward local-buckling behaviorcan be observed in the midsection of steel tube It should be

4 Mathematical Problems in Engineering

(a) (b) (c)

S Mises+4800e+02+5000e+01+4621e+01+4242e+01+3863e+01+3484e+01+3105e+01+2726e+01+2347e+01+1968e+01+1589e+01+1209e+01+8304e+00+4513e+00

Figure 4 Failure modes for typical sections (a) S4-0 (b) S4-05 (c) S4-1

(a) (b) (c)

S S33+5000e+00+4583e+00+4167e+00+3750e+00+3333e+00+2917e+00+2500e+00+2083e+00+1667e+00+1250e+00+8333e-01+4167e-01+0000e+00-1550e+02

Figure 5 The tensile stress distribution of inner concrete with different eccentrical ratios (a) e = 0 (b) e = 05 (c) e = 1

noted that the outward local-buckling behavior appeared onall the four sides of the square steel tube thus the specimenshowed a drum-like failure mode For CFSST column withthe eccentric ratio of 05 the outward local-buckling behaviorcan be observed on the compressive side With the furtherincrease of eccentric ratio as can be seen in Figure 3(c) thelocal-buckling behavior wasmore evident on the compressiveside and flank either side while no buckling behavior wasobserved on the tensile side It can be concluded that theCFSST columns have quite different composite behaviorbetween steel tube and inner concrete with different eccentricratios Four sections of each column ie S1 S2 S3 and S4were selected for further analysis as shown in Figure 3 Thesuffix number for each section ie 0 05 and 1 representsthe eccentric ratio of the columnThemidsections for typicalCFSST columns ie S4-0 S4-05 and S4-1 are shown inFigure 4 For section S4-0 as shown in Figure 4(a) the innerconcrete was separated from steel tube except for the cornerarea and an obvious stress concentration phenomenon canbe observed in the corner area from the stress nephogramFor sections S4-05 and S4-1 the inner concrete was separated

from steel tube mainly in compressive side and flank eitherside while the steel tube was well contacted with innerconcrete in the tensile side Also the stress concentrationphenomenon for sections S4-05 and S4-1was not as severe assection S4-0 indicating the stress distribution was differentwhen the eccentric ratio changed The stress distributionof inner concrete with different eccentricity ratios is shownin Figure 5 where negative stress represents tension whilepositive stress represents compression For CFSST columnunder concentric loading all the inner concrete was undercompression stress as shown in Figure 5(a) For CFSST col-umn with the eccentric ratio of 05 as shown in Figure 5(b)an apparent tensile region appeared in the tensile side Withthe increase of eccentric ratio as shown in Figure 5(c) thetensile region expanded as well The maximum tensile stressin Figure 5(c) was about 4 MPa indicating that some tensilefractures and cracks may appear on the tensile side of theconcrete part

In order to find the relationship between confinementeffect and eccentric ratios five typical points ie P1 P2P3 P4 and P5 for each section were selected which is

Mathematical Problems in Engineering 5

S1-0-P1S1-0-P2S1-0-P3S1-0-P4S1-0-P5S1-0-AV

5 10 15 20 250Axial shortening (mm)

0

10

20

30

40

Con

tact

Stre

ss (M

Pa)

(a) S1-0

S2-0-P1S2-0-P2S2-0-P3S2-0-P4S2-0-P5S2-0-AV

0

10

20

30

40

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-0

S3-0-P1S3-0-P2S3-0-P3S3-0-P4S3-0-P5S3-0-AV

5 10 15 20 250Axial shortening (mm)

05

101520253035404550556065

Con

tact

Stre

ss (M

Pa)

(c) S3-0

S4-0-P1S4-0-P2S4-0-P3S4-0-P4S4-0-P5S4-0-AV

05

10152025303540455055606570758085

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-0

Figure 6 Contact stress for CFSST columns under axial loading

shown in Figure 3 The contact stress between steel tubeand inner concrete at each point can be obtained withABAQUSstandard software The contact stress for CFSSTcolumns with typical eccentric ratios ie 0 05 and 1 isdiscussed as follows

21 Concentric Loading (119890 = 0) The contact stress betweensteel tube and inner concrete for CFSST columns under con-centric loading are shown in Figure 6 As the nomenclature

for each curve the first parameter denotes the section thesecond parameter denotes the eccentrical ratio and the thirdparameter denotes the location of the detected points It canbe seen that the contact stresses are very similar for eachsection at P1 P3 and P5 By contrast the contact stress atP2 and P4 is much higher than other detected points Thisis reasonable because P2 and P4 were located in the corner-angle area thus the inner concrete was well confined due tostress concentration phenomenon which is quite different

6 Mathematical Problems in Engineering

S1-0-AVS2-0-AVS3-0-AVS4-0-AVE0-AV

0

5

10

15

20

25

30

35

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 7 Average contact stress for CFSST columns (e=0)

from concrete-filled circular steel tube [20] It can also befound that the contact stress was fluctuated around zero at theinitial stage for P1 P3 and P5 while contact stress increasedlinearly during the initial stage for P2 and P4

It can be concluded that the contact stress can be quitedifferent at different regions In order to simplify the stressdistribution the average curve was also plotted in Figure 6Considering the symmetry of each section the contact stressfor each section can be represented by the average curveTheaverage curves for each section are shown in Figure 7 it canbe seen that the distribution of stress was also nonuniformalong the axial direction of the CFSST column Thus anaverage curve for each section curve E0-AV was also plottedin Figure 7

22 Eccentric Loading (119890 = 05 and 1) The contact stressfor CFSST columns under eccentric loading is shown inFigure 8 With the increase of eccentrical ratio the contactstress decreased significantly indicating that the confinementeffect was weakened as well It can be found that the contactstress at P2 and P4 is much higher than P1 P3 and P5 whichis due to the stress concentration phenomenon in the corner-angle area as well Also it can be seen that the contact stressdistributed nonuniformly in P1 P3 and P5 indicating theeccentric loading has a great impact on the distribution ofstress on the sections Taking curve S4-05-P5 as an examplethe contact stress fluctuated around zero during the initialstage suggesting that the inner concrete was separated fromthe steel tube due to the different Poissonrsquos ratios of theconcrete and the steel With increasing axial displacementthe contact stress in S4-05-P5 increased slowly because theinner concrete was crushed and contacted with steel tube inthis stage With the further increase of eccentric loading thecontact stress in S4-05-P5 decreased rapidly and fluctuatedaround zero again during the last stage This is attributed to

the outward local buckling in the compressive side of steeltube leading to the gradual separation between the innerconcrete and the steel tube in this stage

The average contact stresses for CFSST columns undereccentric loading are shown in Figure 9 The contact stressfor CFSST columns with the eccentrical ratios of 05 and 1was represented by curves E05-AV and E1-AV respectively Itcan be seen that the contact stress decreased with the increaseof eccentric ratios

23 New Stress-Strain Model for Core Concrete The averagecontact stress for columns with different eccentric ratios ie0 05 and 1 is shown in Figure 10 It is evident that the contactstress decreased rapidly with the increase of eccentric ratiosthus the influence of eccentric ratios should be considered inthe stress-strain model A new parameter k which representsthe influence of eccentric loading was proposed as follows

119878119894 = int1198891199060

120590 (120576119894) d120576 (3)

119896 = 1198781198941198780 (4)

where 119878119894 represents the area under the contact stress curvesfor CFSST columns with different eccentrical ratios Theconfinement coefficient (k) at different eccentric ratios rcould be obtained according to (3) and (4) which is shownin Figure 10

As shown in Figure 11 the confinement coefficientdecreased with the increase of eccentric ratios which isconsistent with the previous discussions With the nonlinearfitting approach the confinement coefficient (k) can beexpressed as follows

119896 = 059 exp(minus 119890044) + 042 (5)

where 119896 is confinement coefficient and 119890 is the eccentric ratioof CFSST columns

Based on the stress-strain model proposed by Tao et al[24] a new three-stage constitutive model which consideredthe influence of eccentric loading was proposed During theinitial stage steel tube has negligible confinement for innerconcreteTherefore the stress-strain relationship for confinedconcrete during the initial stage is linear and no confinementeffect or eccentric ratios were considered in this stage whichwas given by

1205901198911015840119888 =

119860119883 + 11986111988321 + (119860 minus 2)119883 + (119861 minus 1)1198832 0 lt 120576 le 1205761198880 (6)

where X = 1205761205761198880 A=11986411988812057611988801198911015840119888 B=(119860 minus 12)055 minus 1 1205761198880=000076+radic(06261198911015840119888 minus 433) times 10minus7

With the increase of axial deformation the concrete wasgradually cursed and contacted with the steel tube thusthe confinement effect should be considered in this stageHowever the eccentricity also has an important influence onthe stress distribution of CFSST columns the confinementeffect was weakened with the increase of eccentrical ratios

Mathematical Problems in Engineering 7

S1-05-P1S1-05-P2S1-05-P3S1-05-P4S1-05-P5S1-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50C

onta

ct S

tress

(MPa

)

(a) S1-05

S2-05-P1S2-05-P2S2-05-P3S2-05-P4S2-05-P5S2-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-05

S3-05-P1S3-05-P2S3-05-P3S3-05-P4S3-05-P5S3-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

(c) S3-05

S4-05-P1S4-05-P2S4-05-P3S4-05-P4S4-05-P5S4-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-05

Figure 8 Contact stress for CFSST columns under eccentric loading (e = 05)

During the second stage a plateau was proposed which isshown as follows 120576119888119888

1205761198880 = 119890119898 1205761198880 lt 120576 le 120576119888119888 (7)

where m= (29224-0003671198911015840119888 )(1198911198611198911015840119888 )03124+00021198911015840

119888 119891B =025119896(1 + 0027119891119910) expminus0028Bt(1 + 16 lowast 10minus10(1198911015840119888 )48) 119896 =059 exp(minuse044) + 042

During the third stage both the confinement effect andeccentrical ratios should be considered in the stress-strainmodel which is shown as follows

120590 = 119891119903 + (1198911015840119888 minus 119891119903) exp [minus(120576 minus 120576119888119888120572 )12] 120576 ge 120576119888119888 (8)

where 119891119903 = 011198961198911015840119888 120572 = 0005 + 120585119888 120585119888 = 119860 119904119891119910119860119888119891119888119896 119896 =059 exp(minuse044) + 042

8 Mathematical Problems in Engineering

S1-05-AVS2-05-AVS3-05-AVS4-05-AVE05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25C

onta

ct S

tress

(MPa

)

(a) e=05

S1-1-AVS2-1-AVS3-1-AVS4-1-AVE1-AV

0

5

10

15

20

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) e=1

Figure 9 Average contact stress for CFSST columns under eccentric loading

S1

S0

E0-AVE05-AVE1-AV

S05

0

5

10

15

20

25

30

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 10 Area enclosed by the stress-strain curves and the horizontal axis

3 Validation of the ProposedConstitutive Model

In order to validate the stress-strain model for CFSSTcolumns under eccentric loading the simulation resultswere compared with the experimental results from differ-ent references as shown in Figure 12 Both Hanrsquos modeland the current proposed model were used to model themechanical behavior of inner concrete During the initialstage both Hanrsquos model and the current model gave an

accurate prediction With the increase of axial deformationthe current model was more accurate especially during thestrain-softening stage

The carrying capacities for CFSST columns are shownin Table 1 in which 119875119905119890119904119905 and 119875119865119864 are the peak load derivedfrom experiment and FEA model with current proposedstress-strain model respectively It can be seen that a goodprediction could be achieved and the average variationbetween predicted and experimental results is below 5Thus it can be concluded that the model proposed in this

Mathematical Problems in Engineering 9

(1 048)(09 049)

(08 051)(07 054)

(06 056)

(05 061)(04 065)

(03 071)

(02 079)

(01 089)

Data point Fitted curve

(1 1)

04

05

06

07

08

09

10

Con

finem

ent c

oeffi

cien

t

01 02 03 04 05 06 07 08 09 1000Eccentric ratio

Figure 11 The confinement coefficient (k) for CFSST columns under eccentric loading

Table 1 Comparisons between experimental and simulational results

Ref Specimen t (mm) 119891119905119910(MPa) 119891119888(MPa) 119863119890(mm) 119875119905119890119904119905(kN) 119875119865119864(kN) 119875119865119864119875119905119890119904119905HS1C40SA-02 57 5145 432 1050 1440 1397 097HS1C40SB-02 57 5145 432 2200 2085 1793 086HS1C40SB-02 57 5145 432 2325 2550 2499 098HS1C50SA-02 57 5145 553 1300 1380 1408 102HS1C50SB-02 57 5145 553 1900 2140 2012 094HS1C50SE-02 57 5145 553 3450 2470 2346 095HS1C40SA-04 57 5145 432 2650 1190 1083 091

[25] HS1C40SB-04 57 5145 432 3800 1620 1669 103HS1C40SE-04 57 5145 432 4975 2150 2171 101HS1C50SA-04 57 5145 553 2450 1220 1159 095HS1C50SE-04 57 5145 553 4775 2250 2295 102HS1C40SA-06 57 5145 432 3500 1110 988 089HS1C40SB-06 57 5145 432 5550 1500 1530 102HS1C40SE-06 57 5145 432 7400 1700 1632 096HS1C50SA-06 57 5145 553 5500 1020 1081 106

Mean 0971Standard Deviation 0054EC1-2 4 43456 1105 20 21297 1980 093EC2-2 4 43456 1105 35 17172 1528 089

[10] EC3-2 4 43456 1105 50 14549 1484 102EC4-2 4 43456 1105 65 12441 1169 094EC5-2 5 43310 1105 50 16301 1597 098EC6-2 6 43690 1105 50 17972 1707 095Mean 0951Standard deviation 0041

10 Mathematical Problems in Engineering

(1)HS1C50SB-02[25] (2)HS1C50SA-04[25]

(3)EC1-2[10] (4)EC4-2[10]

Test Hans model Current model

5 10 15 20 25 30 35 400Axial shortening (mm)

0

500

1000

1500

2000

2500A

xial

load

(kN

)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=02

Test Hans model Current model

0

200

400

600

800

1000

1200

1400

Axi

al lo

ad (k

N)

10 20 30 40 500Axial shortening (mm)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=04

Test Hans model Current model

1 2 3 4 5 6 7 80Axial shortening (mm)

0

500

1000

1500

2000

2500

Axi

al lo

ad (k

N)

t=4 mm fＳ=43456 MPaf＝=1105 MPa e=0133

Test Hans model Current model

0

500

1000

1500

2000A

xial

load

(kN

)

2 4 6 8 100Axial shortening (mm)

t=4mm fＳ=43456 MPaf＝=1105 MPa e=0433

Figure 12 Comparisons between experimental and simulational result

paper is accurate in simulating the eccentric behavior ofCFSST columns

4 Conclusions

This paper numerically investigated the eccentric behavior ofCFSST columns The finite element analysis found that theconfinement effect of steel tube on concrete was seriouslyweakened with the increasing of eccentricities Thereforeexisting models tended to overestimate the mechanicalbehavior of CFSST columns and were not applicable whenthe CFSST columns were under eccentric loadingThis paperproposed a new stress-strain model of CFSST introducinga new parameter to consider the influence of eccentricity

on the confinement effect Comparisons between simula-tional results and experimental results from different sourcesvalidated the accuracy the proposed model has a higherapplicability to simulate the eccentric behavior of CFSSTcolumns especially during the strain-softening stage

Nomenclature

119860119888 Cross-sectional area of concrete119860 119904 Cross-sectional area of the steel tubeD119890 Eccentric distance119864119862 Elastic modulus of concrete119864119878 Elastic modulus of steel119890 Eccentrical ratio1198911015840119888 Cylinder strength of the concrete

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

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Mathematical Problems in Engineering 3

stres

s

0

Strain

fy

1 2 3

Figure 2 Stress-strain model for steel

(a) (b) (c)

e=1e=05e=0

P1

P2P3 P4

P5

S1-1

S2-1

S3-1

S4-1

S1-05

S2-05

S3-05

S4-05

S1-0

S2-0

S3-0

S4-0

Figure 3 Failure modes for CFSST columns with eccentricity ratios of (a) e = 0 (b) e = 05 (c) e = 1

120590119904 =

E119904120576119904 120576119904 lt 120576119890minus1198601205762119904 + 119861120576119904 + 119862 120576119890 lt 120576119904 le 1205761198901119891119905119910 1205761198901 lt 120576119904 le 1205761198902119891119905119910 [1 + 06 120576119904 minus 1205761198902

1205761198903 minus 1205761198902 ] 1205761198902 lt 120576119904 le 120576119890316119891119905119910 120576119904120576119904 gt 1205761198903

(1)

where 120576119890=08119891119905119910119864119878 1205761198901=15120576119890 1205761198902=101205761198901 1205761198903=1001205761198901 A=02119891119905119910(1205761198901 minus 120576119890)2 B=2A1205761198901 and C=08119891119910+A1205761198902-B120576119890

The stress-strain model proposed by Han [13] was alsoapplied to simulate the quasibrittle behavior of inner con-crete which is shown in (2)

119910 =

2119909 minus 1199092 (119909 le 1)119909

1205730 (119909 minus 1)16+15119909 + 119909 (119909 gt 1) (2)

where 119909 = 1205761205760 119910 = 1205901205900 1205900 = 1198911015840119888 1205760 = 120576119888 +8001205760210minus6120576119888 = (1300 + 1251198911015840119888 )10minus6 1205730 = 1198911015840119888 0112radic1 + 120585 and 120585 =119860 119904119891119905119910119860119888119891119888119896

The concrete damaged plasticity (CDP) model inABAQUS was applied to illustrate the plastic behaviorof concrete [22 23] In above equations 119860 119904 and 119860119888 arethe cross-sectional area of square steel tube and innerconcrete which were set as 11400 mm2 and 78400 mm2in this modelling respectively The parameters 119891119905119910 and 1198911015840119888and are the yield strength of steel and cylinder strengthof inner concrete which were set as 340 MPa and 40MPain this modelling respectively The fracture energy modelproposed was used to simulate the tensile softening behaviorof concrete [23] Poissonrsquos ratio and elastic modulus for innerconcrete are taken as 02 and 4730radic1198911015840119888 according to ACI318-11 [24] respectively

The typical failure modes for CFSST columns with dif-ferent eccentric ratios are shown in Figure 3 The eccentricratio (e) was defined as 119890 = 119890119897119861 where 119890119897 is the distancefrom loading line to symmetry axis and B is defined as thehalf of outsidewidth of square steel tube as shown in Figure 1For CFSST column under concentric loading (e=0) as shownin Figure 3(a) an obvious outward local-buckling behaviorcan be observed in the midsection of steel tube It should be

4 Mathematical Problems in Engineering

(a) (b) (c)

S Mises+4800e+02+5000e+01+4621e+01+4242e+01+3863e+01+3484e+01+3105e+01+2726e+01+2347e+01+1968e+01+1589e+01+1209e+01+8304e+00+4513e+00

Figure 4 Failure modes for typical sections (a) S4-0 (b) S4-05 (c) S4-1

(a) (b) (c)

S S33+5000e+00+4583e+00+4167e+00+3750e+00+3333e+00+2917e+00+2500e+00+2083e+00+1667e+00+1250e+00+8333e-01+4167e-01+0000e+00-1550e+02

Figure 5 The tensile stress distribution of inner concrete with different eccentrical ratios (a) e = 0 (b) e = 05 (c) e = 1

noted that the outward local-buckling behavior appeared onall the four sides of the square steel tube thus the specimenshowed a drum-like failure mode For CFSST column withthe eccentric ratio of 05 the outward local-buckling behaviorcan be observed on the compressive side With the furtherincrease of eccentric ratio as can be seen in Figure 3(c) thelocal-buckling behavior wasmore evident on the compressiveside and flank either side while no buckling behavior wasobserved on the tensile side It can be concluded that theCFSST columns have quite different composite behaviorbetween steel tube and inner concrete with different eccentricratios Four sections of each column ie S1 S2 S3 and S4were selected for further analysis as shown in Figure 3 Thesuffix number for each section ie 0 05 and 1 representsthe eccentric ratio of the columnThemidsections for typicalCFSST columns ie S4-0 S4-05 and S4-1 are shown inFigure 4 For section S4-0 as shown in Figure 4(a) the innerconcrete was separated from steel tube except for the cornerarea and an obvious stress concentration phenomenon canbe observed in the corner area from the stress nephogramFor sections S4-05 and S4-1 the inner concrete was separated

from steel tube mainly in compressive side and flank eitherside while the steel tube was well contacted with innerconcrete in the tensile side Also the stress concentrationphenomenon for sections S4-05 and S4-1was not as severe assection S4-0 indicating the stress distribution was differentwhen the eccentric ratio changed The stress distributionof inner concrete with different eccentricity ratios is shownin Figure 5 where negative stress represents tension whilepositive stress represents compression For CFSST columnunder concentric loading all the inner concrete was undercompression stress as shown in Figure 5(a) For CFSST col-umn with the eccentric ratio of 05 as shown in Figure 5(b)an apparent tensile region appeared in the tensile side Withthe increase of eccentric ratio as shown in Figure 5(c) thetensile region expanded as well The maximum tensile stressin Figure 5(c) was about 4 MPa indicating that some tensilefractures and cracks may appear on the tensile side of theconcrete part

In order to find the relationship between confinementeffect and eccentric ratios five typical points ie P1 P2P3 P4 and P5 for each section were selected which is

Mathematical Problems in Engineering 5

S1-0-P1S1-0-P2S1-0-P3S1-0-P4S1-0-P5S1-0-AV

5 10 15 20 250Axial shortening (mm)

0

10

20

30

40

Con

tact

Stre

ss (M

Pa)

(a) S1-0

S2-0-P1S2-0-P2S2-0-P3S2-0-P4S2-0-P5S2-0-AV

0

10

20

30

40

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-0

S3-0-P1S3-0-P2S3-0-P3S3-0-P4S3-0-P5S3-0-AV

5 10 15 20 250Axial shortening (mm)

05

101520253035404550556065

Con

tact

Stre

ss (M

Pa)

(c) S3-0

S4-0-P1S4-0-P2S4-0-P3S4-0-P4S4-0-P5S4-0-AV

05

10152025303540455055606570758085

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-0

Figure 6 Contact stress for CFSST columns under axial loading

shown in Figure 3 The contact stress between steel tubeand inner concrete at each point can be obtained withABAQUSstandard software The contact stress for CFSSTcolumns with typical eccentric ratios ie 0 05 and 1 isdiscussed as follows

21 Concentric Loading (119890 = 0) The contact stress betweensteel tube and inner concrete for CFSST columns under con-centric loading are shown in Figure 6 As the nomenclature

for each curve the first parameter denotes the section thesecond parameter denotes the eccentrical ratio and the thirdparameter denotes the location of the detected points It canbe seen that the contact stresses are very similar for eachsection at P1 P3 and P5 By contrast the contact stress atP2 and P4 is much higher than other detected points Thisis reasonable because P2 and P4 were located in the corner-angle area thus the inner concrete was well confined due tostress concentration phenomenon which is quite different

6 Mathematical Problems in Engineering

S1-0-AVS2-0-AVS3-0-AVS4-0-AVE0-AV

0

5

10

15

20

25

30

35

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 7 Average contact stress for CFSST columns (e=0)

from concrete-filled circular steel tube [20] It can also befound that the contact stress was fluctuated around zero at theinitial stage for P1 P3 and P5 while contact stress increasedlinearly during the initial stage for P2 and P4

It can be concluded that the contact stress can be quitedifferent at different regions In order to simplify the stressdistribution the average curve was also plotted in Figure 6Considering the symmetry of each section the contact stressfor each section can be represented by the average curveTheaverage curves for each section are shown in Figure 7 it canbe seen that the distribution of stress was also nonuniformalong the axial direction of the CFSST column Thus anaverage curve for each section curve E0-AV was also plottedin Figure 7

22 Eccentric Loading (119890 = 05 and 1) The contact stressfor CFSST columns under eccentric loading is shown inFigure 8 With the increase of eccentrical ratio the contactstress decreased significantly indicating that the confinementeffect was weakened as well It can be found that the contactstress at P2 and P4 is much higher than P1 P3 and P5 whichis due to the stress concentration phenomenon in the corner-angle area as well Also it can be seen that the contact stressdistributed nonuniformly in P1 P3 and P5 indicating theeccentric loading has a great impact on the distribution ofstress on the sections Taking curve S4-05-P5 as an examplethe contact stress fluctuated around zero during the initialstage suggesting that the inner concrete was separated fromthe steel tube due to the different Poissonrsquos ratios of theconcrete and the steel With increasing axial displacementthe contact stress in S4-05-P5 increased slowly because theinner concrete was crushed and contacted with steel tube inthis stage With the further increase of eccentric loading thecontact stress in S4-05-P5 decreased rapidly and fluctuatedaround zero again during the last stage This is attributed to

the outward local buckling in the compressive side of steeltube leading to the gradual separation between the innerconcrete and the steel tube in this stage

The average contact stresses for CFSST columns undereccentric loading are shown in Figure 9 The contact stressfor CFSST columns with the eccentrical ratios of 05 and 1was represented by curves E05-AV and E1-AV respectively Itcan be seen that the contact stress decreased with the increaseof eccentric ratios

23 New Stress-Strain Model for Core Concrete The averagecontact stress for columns with different eccentric ratios ie0 05 and 1 is shown in Figure 10 It is evident that the contactstress decreased rapidly with the increase of eccentric ratiosthus the influence of eccentric ratios should be considered inthe stress-strain model A new parameter k which representsthe influence of eccentric loading was proposed as follows

119878119894 = int1198891199060

120590 (120576119894) d120576 (3)

119896 = 1198781198941198780 (4)

where 119878119894 represents the area under the contact stress curvesfor CFSST columns with different eccentrical ratios Theconfinement coefficient (k) at different eccentric ratios rcould be obtained according to (3) and (4) which is shownin Figure 10

As shown in Figure 11 the confinement coefficientdecreased with the increase of eccentric ratios which isconsistent with the previous discussions With the nonlinearfitting approach the confinement coefficient (k) can beexpressed as follows

119896 = 059 exp(minus 119890044) + 042 (5)

where 119896 is confinement coefficient and 119890 is the eccentric ratioof CFSST columns

Based on the stress-strain model proposed by Tao et al[24] a new three-stage constitutive model which consideredthe influence of eccentric loading was proposed During theinitial stage steel tube has negligible confinement for innerconcreteTherefore the stress-strain relationship for confinedconcrete during the initial stage is linear and no confinementeffect or eccentric ratios were considered in this stage whichwas given by

1205901198911015840119888 =

119860119883 + 11986111988321 + (119860 minus 2)119883 + (119861 minus 1)1198832 0 lt 120576 le 1205761198880 (6)

where X = 1205761205761198880 A=11986411988812057611988801198911015840119888 B=(119860 minus 12)055 minus 1 1205761198880=000076+radic(06261198911015840119888 minus 433) times 10minus7

With the increase of axial deformation the concrete wasgradually cursed and contacted with the steel tube thusthe confinement effect should be considered in this stageHowever the eccentricity also has an important influence onthe stress distribution of CFSST columns the confinementeffect was weakened with the increase of eccentrical ratios

Mathematical Problems in Engineering 7

S1-05-P1S1-05-P2S1-05-P3S1-05-P4S1-05-P5S1-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50C

onta

ct S

tress

(MPa

)

(a) S1-05

S2-05-P1S2-05-P2S2-05-P3S2-05-P4S2-05-P5S2-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-05

S3-05-P1S3-05-P2S3-05-P3S3-05-P4S3-05-P5S3-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

(c) S3-05

S4-05-P1S4-05-P2S4-05-P3S4-05-P4S4-05-P5S4-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-05

Figure 8 Contact stress for CFSST columns under eccentric loading (e = 05)

During the second stage a plateau was proposed which isshown as follows 120576119888119888

1205761198880 = 119890119898 1205761198880 lt 120576 le 120576119888119888 (7)

where m= (29224-0003671198911015840119888 )(1198911198611198911015840119888 )03124+00021198911015840

119888 119891B =025119896(1 + 0027119891119910) expminus0028Bt(1 + 16 lowast 10minus10(1198911015840119888 )48) 119896 =059 exp(minuse044) + 042

During the third stage both the confinement effect andeccentrical ratios should be considered in the stress-strainmodel which is shown as follows

120590 = 119891119903 + (1198911015840119888 minus 119891119903) exp [minus(120576 minus 120576119888119888120572 )12] 120576 ge 120576119888119888 (8)

where 119891119903 = 011198961198911015840119888 120572 = 0005 + 120585119888 120585119888 = 119860 119904119891119910119860119888119891119888119896 119896 =059 exp(minuse044) + 042

8 Mathematical Problems in Engineering

S1-05-AVS2-05-AVS3-05-AVS4-05-AVE05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25C

onta

ct S

tress

(MPa

)

(a) e=05

S1-1-AVS2-1-AVS3-1-AVS4-1-AVE1-AV

0

5

10

15

20

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) e=1

Figure 9 Average contact stress for CFSST columns under eccentric loading

S1

S0

E0-AVE05-AVE1-AV

S05

0

5

10

15

20

25

30

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 10 Area enclosed by the stress-strain curves and the horizontal axis

3 Validation of the ProposedConstitutive Model

In order to validate the stress-strain model for CFSSTcolumns under eccentric loading the simulation resultswere compared with the experimental results from differ-ent references as shown in Figure 12 Both Hanrsquos modeland the current proposed model were used to model themechanical behavior of inner concrete During the initialstage both Hanrsquos model and the current model gave an

accurate prediction With the increase of axial deformationthe current model was more accurate especially during thestrain-softening stage

The carrying capacities for CFSST columns are shownin Table 1 in which 119875119905119890119904119905 and 119875119865119864 are the peak load derivedfrom experiment and FEA model with current proposedstress-strain model respectively It can be seen that a goodprediction could be achieved and the average variationbetween predicted and experimental results is below 5Thus it can be concluded that the model proposed in this

Mathematical Problems in Engineering 9

(1 048)(09 049)

(08 051)(07 054)

(06 056)

(05 061)(04 065)

(03 071)

(02 079)

(01 089)

Data point Fitted curve

(1 1)

04

05

06

07

08

09

10

Con

finem

ent c

oeffi

cien

t

01 02 03 04 05 06 07 08 09 1000Eccentric ratio

Figure 11 The confinement coefficient (k) for CFSST columns under eccentric loading

Table 1 Comparisons between experimental and simulational results

Ref Specimen t (mm) 119891119905119910(MPa) 119891119888(MPa) 119863119890(mm) 119875119905119890119904119905(kN) 119875119865119864(kN) 119875119865119864119875119905119890119904119905HS1C40SA-02 57 5145 432 1050 1440 1397 097HS1C40SB-02 57 5145 432 2200 2085 1793 086HS1C40SB-02 57 5145 432 2325 2550 2499 098HS1C50SA-02 57 5145 553 1300 1380 1408 102HS1C50SB-02 57 5145 553 1900 2140 2012 094HS1C50SE-02 57 5145 553 3450 2470 2346 095HS1C40SA-04 57 5145 432 2650 1190 1083 091

[25] HS1C40SB-04 57 5145 432 3800 1620 1669 103HS1C40SE-04 57 5145 432 4975 2150 2171 101HS1C50SA-04 57 5145 553 2450 1220 1159 095HS1C50SE-04 57 5145 553 4775 2250 2295 102HS1C40SA-06 57 5145 432 3500 1110 988 089HS1C40SB-06 57 5145 432 5550 1500 1530 102HS1C40SE-06 57 5145 432 7400 1700 1632 096HS1C50SA-06 57 5145 553 5500 1020 1081 106

Mean 0971Standard Deviation 0054EC1-2 4 43456 1105 20 21297 1980 093EC2-2 4 43456 1105 35 17172 1528 089

[10] EC3-2 4 43456 1105 50 14549 1484 102EC4-2 4 43456 1105 65 12441 1169 094EC5-2 5 43310 1105 50 16301 1597 098EC6-2 6 43690 1105 50 17972 1707 095Mean 0951Standard deviation 0041

10 Mathematical Problems in Engineering

(1)HS1C50SB-02[25] (2)HS1C50SA-04[25]

(3)EC1-2[10] (4)EC4-2[10]

Test Hans model Current model

5 10 15 20 25 30 35 400Axial shortening (mm)

0

500

1000

1500

2000

2500A

xial

load

(kN

)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=02

Test Hans model Current model

0

200

400

600

800

1000

1200

1400

Axi

al lo

ad (k

N)

10 20 30 40 500Axial shortening (mm)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=04

Test Hans model Current model

1 2 3 4 5 6 7 80Axial shortening (mm)

0

500

1000

1500

2000

2500

Axi

al lo

ad (k

N)

t=4 mm fＳ=43456 MPaf＝=1105 MPa e=0133

Test Hans model Current model

0

500

1000

1500

2000A

xial

load

(kN

)

2 4 6 8 100Axial shortening (mm)

t=4mm fＳ=43456 MPaf＝=1105 MPa e=0433

Figure 12 Comparisons between experimental and simulational result

paper is accurate in simulating the eccentric behavior ofCFSST columns

4 Conclusions

This paper numerically investigated the eccentric behavior ofCFSST columns The finite element analysis found that theconfinement effect of steel tube on concrete was seriouslyweakened with the increasing of eccentricities Thereforeexisting models tended to overestimate the mechanicalbehavior of CFSST columns and were not applicable whenthe CFSST columns were under eccentric loadingThis paperproposed a new stress-strain model of CFSST introducinga new parameter to consider the influence of eccentricity

on the confinement effect Comparisons between simula-tional results and experimental results from different sourcesvalidated the accuracy the proposed model has a higherapplicability to simulate the eccentric behavior of CFSSTcolumns especially during the strain-softening stage

Nomenclature

119860119888 Cross-sectional area of concrete119860 119904 Cross-sectional area of the steel tubeD119890 Eccentric distance119864119862 Elastic modulus of concrete119864119878 Elastic modulus of steel119890 Eccentrical ratio1198911015840119888 Cylinder strength of the concrete

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

4 Mathematical Problems in Engineering

(a) (b) (c)

S Mises+4800e+02+5000e+01+4621e+01+4242e+01+3863e+01+3484e+01+3105e+01+2726e+01+2347e+01+1968e+01+1589e+01+1209e+01+8304e+00+4513e+00

Figure 4 Failure modes for typical sections (a) S4-0 (b) S4-05 (c) S4-1

(a) (b) (c)

S S33+5000e+00+4583e+00+4167e+00+3750e+00+3333e+00+2917e+00+2500e+00+2083e+00+1667e+00+1250e+00+8333e-01+4167e-01+0000e+00-1550e+02

Figure 5 The tensile stress distribution of inner concrete with different eccentrical ratios (a) e = 0 (b) e = 05 (c) e = 1

noted that the outward local-buckling behavior appeared onall the four sides of the square steel tube thus the specimenshowed a drum-like failure mode For CFSST column withthe eccentric ratio of 05 the outward local-buckling behaviorcan be observed on the compressive side With the furtherincrease of eccentric ratio as can be seen in Figure 3(c) thelocal-buckling behavior wasmore evident on the compressiveside and flank either side while no buckling behavior wasobserved on the tensile side It can be concluded that theCFSST columns have quite different composite behaviorbetween steel tube and inner concrete with different eccentricratios Four sections of each column ie S1 S2 S3 and S4were selected for further analysis as shown in Figure 3 Thesuffix number for each section ie 0 05 and 1 representsthe eccentric ratio of the columnThemidsections for typicalCFSST columns ie S4-0 S4-05 and S4-1 are shown inFigure 4 For section S4-0 as shown in Figure 4(a) the innerconcrete was separated from steel tube except for the cornerarea and an obvious stress concentration phenomenon canbe observed in the corner area from the stress nephogramFor sections S4-05 and S4-1 the inner concrete was separated

from steel tube mainly in compressive side and flank eitherside while the steel tube was well contacted with innerconcrete in the tensile side Also the stress concentrationphenomenon for sections S4-05 and S4-1was not as severe assection S4-0 indicating the stress distribution was differentwhen the eccentric ratio changed The stress distributionof inner concrete with different eccentricity ratios is shownin Figure 5 where negative stress represents tension whilepositive stress represents compression For CFSST columnunder concentric loading all the inner concrete was undercompression stress as shown in Figure 5(a) For CFSST col-umn with the eccentric ratio of 05 as shown in Figure 5(b)an apparent tensile region appeared in the tensile side Withthe increase of eccentric ratio as shown in Figure 5(c) thetensile region expanded as well The maximum tensile stressin Figure 5(c) was about 4 MPa indicating that some tensilefractures and cracks may appear on the tensile side of theconcrete part

In order to find the relationship between confinementeffect and eccentric ratios five typical points ie P1 P2P3 P4 and P5 for each section were selected which is

Mathematical Problems in Engineering 5

S1-0-P1S1-0-P2S1-0-P3S1-0-P4S1-0-P5S1-0-AV

5 10 15 20 250Axial shortening (mm)

0

10

20

30

40

Con

tact

Stre

ss (M

Pa)

(a) S1-0

S2-0-P1S2-0-P2S2-0-P3S2-0-P4S2-0-P5S2-0-AV

0

10

20

30

40

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-0

S3-0-P1S3-0-P2S3-0-P3S3-0-P4S3-0-P5S3-0-AV

5 10 15 20 250Axial shortening (mm)

05

101520253035404550556065

Con

tact

Stre

ss (M

Pa)

(c) S3-0

S4-0-P1S4-0-P2S4-0-P3S4-0-P4S4-0-P5S4-0-AV

05

10152025303540455055606570758085

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-0

Figure 6 Contact stress for CFSST columns under axial loading

shown in Figure 3 The contact stress between steel tubeand inner concrete at each point can be obtained withABAQUSstandard software The contact stress for CFSSTcolumns with typical eccentric ratios ie 0 05 and 1 isdiscussed as follows

21 Concentric Loading (119890 = 0) The contact stress betweensteel tube and inner concrete for CFSST columns under con-centric loading are shown in Figure 6 As the nomenclature

for each curve the first parameter denotes the section thesecond parameter denotes the eccentrical ratio and the thirdparameter denotes the location of the detected points It canbe seen that the contact stresses are very similar for eachsection at P1 P3 and P5 By contrast the contact stress atP2 and P4 is much higher than other detected points Thisis reasonable because P2 and P4 were located in the corner-angle area thus the inner concrete was well confined due tostress concentration phenomenon which is quite different

6 Mathematical Problems in Engineering

S1-0-AVS2-0-AVS3-0-AVS4-0-AVE0-AV

0

5

10

15

20

25

30

35

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 7 Average contact stress for CFSST columns (e=0)

from concrete-filled circular steel tube [20] It can also befound that the contact stress was fluctuated around zero at theinitial stage for P1 P3 and P5 while contact stress increasedlinearly during the initial stage for P2 and P4

It can be concluded that the contact stress can be quitedifferent at different regions In order to simplify the stressdistribution the average curve was also plotted in Figure 6Considering the symmetry of each section the contact stressfor each section can be represented by the average curveTheaverage curves for each section are shown in Figure 7 it canbe seen that the distribution of stress was also nonuniformalong the axial direction of the CFSST column Thus anaverage curve for each section curve E0-AV was also plottedin Figure 7

22 Eccentric Loading (119890 = 05 and 1) The contact stressfor CFSST columns under eccentric loading is shown inFigure 8 With the increase of eccentrical ratio the contactstress decreased significantly indicating that the confinementeffect was weakened as well It can be found that the contactstress at P2 and P4 is much higher than P1 P3 and P5 whichis due to the stress concentration phenomenon in the corner-angle area as well Also it can be seen that the contact stressdistributed nonuniformly in P1 P3 and P5 indicating theeccentric loading has a great impact on the distribution ofstress on the sections Taking curve S4-05-P5 as an examplethe contact stress fluctuated around zero during the initialstage suggesting that the inner concrete was separated fromthe steel tube due to the different Poissonrsquos ratios of theconcrete and the steel With increasing axial displacementthe contact stress in S4-05-P5 increased slowly because theinner concrete was crushed and contacted with steel tube inthis stage With the further increase of eccentric loading thecontact stress in S4-05-P5 decreased rapidly and fluctuatedaround zero again during the last stage This is attributed to

the outward local buckling in the compressive side of steeltube leading to the gradual separation between the innerconcrete and the steel tube in this stage

The average contact stresses for CFSST columns undereccentric loading are shown in Figure 9 The contact stressfor CFSST columns with the eccentrical ratios of 05 and 1was represented by curves E05-AV and E1-AV respectively Itcan be seen that the contact stress decreased with the increaseof eccentric ratios

23 New Stress-Strain Model for Core Concrete The averagecontact stress for columns with different eccentric ratios ie0 05 and 1 is shown in Figure 10 It is evident that the contactstress decreased rapidly with the increase of eccentric ratiosthus the influence of eccentric ratios should be considered inthe stress-strain model A new parameter k which representsthe influence of eccentric loading was proposed as follows

119878119894 = int1198891199060

120590 (120576119894) d120576 (3)

119896 = 1198781198941198780 (4)

where 119878119894 represents the area under the contact stress curvesfor CFSST columns with different eccentrical ratios Theconfinement coefficient (k) at different eccentric ratios rcould be obtained according to (3) and (4) which is shownin Figure 10

As shown in Figure 11 the confinement coefficientdecreased with the increase of eccentric ratios which isconsistent with the previous discussions With the nonlinearfitting approach the confinement coefficient (k) can beexpressed as follows

119896 = 059 exp(minus 119890044) + 042 (5)

where 119896 is confinement coefficient and 119890 is the eccentric ratioof CFSST columns

Based on the stress-strain model proposed by Tao et al[24] a new three-stage constitutive model which consideredthe influence of eccentric loading was proposed During theinitial stage steel tube has negligible confinement for innerconcreteTherefore the stress-strain relationship for confinedconcrete during the initial stage is linear and no confinementeffect or eccentric ratios were considered in this stage whichwas given by

1205901198911015840119888 =

119860119883 + 11986111988321 + (119860 minus 2)119883 + (119861 minus 1)1198832 0 lt 120576 le 1205761198880 (6)

where X = 1205761205761198880 A=11986411988812057611988801198911015840119888 B=(119860 minus 12)055 minus 1 1205761198880=000076+radic(06261198911015840119888 minus 433) times 10minus7

With the increase of axial deformation the concrete wasgradually cursed and contacted with the steel tube thusthe confinement effect should be considered in this stageHowever the eccentricity also has an important influence onthe stress distribution of CFSST columns the confinementeffect was weakened with the increase of eccentrical ratios

Mathematical Problems in Engineering 7

S1-05-P1S1-05-P2S1-05-P3S1-05-P4S1-05-P5S1-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50C

onta

ct S

tress

(MPa

)

(a) S1-05

S2-05-P1S2-05-P2S2-05-P3S2-05-P4S2-05-P5S2-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-05

S3-05-P1S3-05-P2S3-05-P3S3-05-P4S3-05-P5S3-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

(c) S3-05

S4-05-P1S4-05-P2S4-05-P3S4-05-P4S4-05-P5S4-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-05

Figure 8 Contact stress for CFSST columns under eccentric loading (e = 05)

During the second stage a plateau was proposed which isshown as follows 120576119888119888

1205761198880 = 119890119898 1205761198880 lt 120576 le 120576119888119888 (7)

where m= (29224-0003671198911015840119888 )(1198911198611198911015840119888 )03124+00021198911015840

119888 119891B =025119896(1 + 0027119891119910) expminus0028Bt(1 + 16 lowast 10minus10(1198911015840119888 )48) 119896 =059 exp(minuse044) + 042

During the third stage both the confinement effect andeccentrical ratios should be considered in the stress-strainmodel which is shown as follows

120590 = 119891119903 + (1198911015840119888 minus 119891119903) exp [minus(120576 minus 120576119888119888120572 )12] 120576 ge 120576119888119888 (8)

where 119891119903 = 011198961198911015840119888 120572 = 0005 + 120585119888 120585119888 = 119860 119904119891119910119860119888119891119888119896 119896 =059 exp(minuse044) + 042

8 Mathematical Problems in Engineering

S1-05-AVS2-05-AVS3-05-AVS4-05-AVE05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25C

onta

ct S

tress

(MPa

)

(a) e=05

S1-1-AVS2-1-AVS3-1-AVS4-1-AVE1-AV

0

5

10

15

20

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) e=1

Figure 9 Average contact stress for CFSST columns under eccentric loading

S1

S0

E0-AVE05-AVE1-AV

S05

0

5

10

15

20

25

30

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 10 Area enclosed by the stress-strain curves and the horizontal axis

3 Validation of the ProposedConstitutive Model

In order to validate the stress-strain model for CFSSTcolumns under eccentric loading the simulation resultswere compared with the experimental results from differ-ent references as shown in Figure 12 Both Hanrsquos modeland the current proposed model were used to model themechanical behavior of inner concrete During the initialstage both Hanrsquos model and the current model gave an

accurate prediction With the increase of axial deformationthe current model was more accurate especially during thestrain-softening stage

The carrying capacities for CFSST columns are shownin Table 1 in which 119875119905119890119904119905 and 119875119865119864 are the peak load derivedfrom experiment and FEA model with current proposedstress-strain model respectively It can be seen that a goodprediction could be achieved and the average variationbetween predicted and experimental results is below 5Thus it can be concluded that the model proposed in this

Mathematical Problems in Engineering 9

(1 048)(09 049)

(08 051)(07 054)

(06 056)

(05 061)(04 065)

(03 071)

(02 079)

(01 089)

Data point Fitted curve

(1 1)

04

05

06

07

08

09

10

Con

finem

ent c

oeffi

cien

t

01 02 03 04 05 06 07 08 09 1000Eccentric ratio

Figure 11 The confinement coefficient (k) for CFSST columns under eccentric loading

Table 1 Comparisons between experimental and simulational results

Ref Specimen t (mm) 119891119905119910(MPa) 119891119888(MPa) 119863119890(mm) 119875119905119890119904119905(kN) 119875119865119864(kN) 119875119865119864119875119905119890119904119905HS1C40SA-02 57 5145 432 1050 1440 1397 097HS1C40SB-02 57 5145 432 2200 2085 1793 086HS1C40SB-02 57 5145 432 2325 2550 2499 098HS1C50SA-02 57 5145 553 1300 1380 1408 102HS1C50SB-02 57 5145 553 1900 2140 2012 094HS1C50SE-02 57 5145 553 3450 2470 2346 095HS1C40SA-04 57 5145 432 2650 1190 1083 091

[25] HS1C40SB-04 57 5145 432 3800 1620 1669 103HS1C40SE-04 57 5145 432 4975 2150 2171 101HS1C50SA-04 57 5145 553 2450 1220 1159 095HS1C50SE-04 57 5145 553 4775 2250 2295 102HS1C40SA-06 57 5145 432 3500 1110 988 089HS1C40SB-06 57 5145 432 5550 1500 1530 102HS1C40SE-06 57 5145 432 7400 1700 1632 096HS1C50SA-06 57 5145 553 5500 1020 1081 106

Mean 0971Standard Deviation 0054EC1-2 4 43456 1105 20 21297 1980 093EC2-2 4 43456 1105 35 17172 1528 089

[10] EC3-2 4 43456 1105 50 14549 1484 102EC4-2 4 43456 1105 65 12441 1169 094EC5-2 5 43310 1105 50 16301 1597 098EC6-2 6 43690 1105 50 17972 1707 095Mean 0951Standard deviation 0041

10 Mathematical Problems in Engineering

(1)HS1C50SB-02[25] (2)HS1C50SA-04[25]

(3)EC1-2[10] (4)EC4-2[10]

Test Hans model Current model

5 10 15 20 25 30 35 400Axial shortening (mm)

0

500

1000

1500

2000

2500A

xial

load

(kN

)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=02

Test Hans model Current model

0

200

400

600

800

1000

1200

1400

Axi

al lo

ad (k

N)

10 20 30 40 500Axial shortening (mm)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=04

Test Hans model Current model

1 2 3 4 5 6 7 80Axial shortening (mm)

0

500

1000

1500

2000

2500

Axi

al lo

ad (k

N)

t=4 mm fＳ=43456 MPaf＝=1105 MPa e=0133

Test Hans model Current model

0

500

1000

1500

2000A

xial

load

(kN

)

2 4 6 8 100Axial shortening (mm)

t=4mm fＳ=43456 MPaf＝=1105 MPa e=0433

Figure 12 Comparisons between experimental and simulational result

paper is accurate in simulating the eccentric behavior ofCFSST columns

4 Conclusions

This paper numerically investigated the eccentric behavior ofCFSST columns The finite element analysis found that theconfinement effect of steel tube on concrete was seriouslyweakened with the increasing of eccentricities Thereforeexisting models tended to overestimate the mechanicalbehavior of CFSST columns and were not applicable whenthe CFSST columns were under eccentric loadingThis paperproposed a new stress-strain model of CFSST introducinga new parameter to consider the influence of eccentricity

on the confinement effect Comparisons between simula-tional results and experimental results from different sourcesvalidated the accuracy the proposed model has a higherapplicability to simulate the eccentric behavior of CFSSTcolumns especially during the strain-softening stage

Nomenclature

119860119888 Cross-sectional area of concrete119860 119904 Cross-sectional area of the steel tubeD119890 Eccentric distance119864119862 Elastic modulus of concrete119864119878 Elastic modulus of steel119890 Eccentrical ratio1198911015840119888 Cylinder strength of the concrete

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 5

S1-0-P1S1-0-P2S1-0-P3S1-0-P4S1-0-P5S1-0-AV

5 10 15 20 250Axial shortening (mm)

0

10

20

30

40

Con

tact

Stre

ss (M

Pa)

(a) S1-0

S2-0-P1S2-0-P2S2-0-P3S2-0-P4S2-0-P5S2-0-AV

0

10

20

30

40

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-0

S3-0-P1S3-0-P2S3-0-P3S3-0-P4S3-0-P5S3-0-AV

5 10 15 20 250Axial shortening (mm)

05

101520253035404550556065

Con

tact

Stre

ss (M

Pa)

(c) S3-0

S4-0-P1S4-0-P2S4-0-P3S4-0-P4S4-0-P5S4-0-AV

05

10152025303540455055606570758085

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-0

Figure 6 Contact stress for CFSST columns under axial loading

shown in Figure 3 The contact stress between steel tubeand inner concrete at each point can be obtained withABAQUSstandard software The contact stress for CFSSTcolumns with typical eccentric ratios ie 0 05 and 1 isdiscussed as follows

21 Concentric Loading (119890 = 0) The contact stress betweensteel tube and inner concrete for CFSST columns under con-centric loading are shown in Figure 6 As the nomenclature

for each curve the first parameter denotes the section thesecond parameter denotes the eccentrical ratio and the thirdparameter denotes the location of the detected points It canbe seen that the contact stresses are very similar for eachsection at P1 P3 and P5 By contrast the contact stress atP2 and P4 is much higher than other detected points Thisis reasonable because P2 and P4 were located in the corner-angle area thus the inner concrete was well confined due tostress concentration phenomenon which is quite different

6 Mathematical Problems in Engineering

S1-0-AVS2-0-AVS3-0-AVS4-0-AVE0-AV

0

5

10

15

20

25

30

35

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 7 Average contact stress for CFSST columns (e=0)

from concrete-filled circular steel tube [20] It can also befound that the contact stress was fluctuated around zero at theinitial stage for P1 P3 and P5 while contact stress increasedlinearly during the initial stage for P2 and P4

It can be concluded that the contact stress can be quitedifferent at different regions In order to simplify the stressdistribution the average curve was also plotted in Figure 6Considering the symmetry of each section the contact stressfor each section can be represented by the average curveTheaverage curves for each section are shown in Figure 7 it canbe seen that the distribution of stress was also nonuniformalong the axial direction of the CFSST column Thus anaverage curve for each section curve E0-AV was also plottedin Figure 7

22 Eccentric Loading (119890 = 05 and 1) The contact stressfor CFSST columns under eccentric loading is shown inFigure 8 With the increase of eccentrical ratio the contactstress decreased significantly indicating that the confinementeffect was weakened as well It can be found that the contactstress at P2 and P4 is much higher than P1 P3 and P5 whichis due to the stress concentration phenomenon in the corner-angle area as well Also it can be seen that the contact stressdistributed nonuniformly in P1 P3 and P5 indicating theeccentric loading has a great impact on the distribution ofstress on the sections Taking curve S4-05-P5 as an examplethe contact stress fluctuated around zero during the initialstage suggesting that the inner concrete was separated fromthe steel tube due to the different Poissonrsquos ratios of theconcrete and the steel With increasing axial displacementthe contact stress in S4-05-P5 increased slowly because theinner concrete was crushed and contacted with steel tube inthis stage With the further increase of eccentric loading thecontact stress in S4-05-P5 decreased rapidly and fluctuatedaround zero again during the last stage This is attributed to

the outward local buckling in the compressive side of steeltube leading to the gradual separation between the innerconcrete and the steel tube in this stage

The average contact stresses for CFSST columns undereccentric loading are shown in Figure 9 The contact stressfor CFSST columns with the eccentrical ratios of 05 and 1was represented by curves E05-AV and E1-AV respectively Itcan be seen that the contact stress decreased with the increaseof eccentric ratios

23 New Stress-Strain Model for Core Concrete The averagecontact stress for columns with different eccentric ratios ie0 05 and 1 is shown in Figure 10 It is evident that the contactstress decreased rapidly with the increase of eccentric ratiosthus the influence of eccentric ratios should be considered inthe stress-strain model A new parameter k which representsthe influence of eccentric loading was proposed as follows

119878119894 = int1198891199060

120590 (120576119894) d120576 (3)

119896 = 1198781198941198780 (4)

where 119878119894 represents the area under the contact stress curvesfor CFSST columns with different eccentrical ratios Theconfinement coefficient (k) at different eccentric ratios rcould be obtained according to (3) and (4) which is shownin Figure 10

As shown in Figure 11 the confinement coefficientdecreased with the increase of eccentric ratios which isconsistent with the previous discussions With the nonlinearfitting approach the confinement coefficient (k) can beexpressed as follows

119896 = 059 exp(minus 119890044) + 042 (5)

where 119896 is confinement coefficient and 119890 is the eccentric ratioof CFSST columns

Based on the stress-strain model proposed by Tao et al[24] a new three-stage constitutive model which consideredthe influence of eccentric loading was proposed During theinitial stage steel tube has negligible confinement for innerconcreteTherefore the stress-strain relationship for confinedconcrete during the initial stage is linear and no confinementeffect or eccentric ratios were considered in this stage whichwas given by

1205901198911015840119888 =

119860119883 + 11986111988321 + (119860 minus 2)119883 + (119861 minus 1)1198832 0 lt 120576 le 1205761198880 (6)

where X = 1205761205761198880 A=11986411988812057611988801198911015840119888 B=(119860 minus 12)055 minus 1 1205761198880=000076+radic(06261198911015840119888 minus 433) times 10minus7

With the increase of axial deformation the concrete wasgradually cursed and contacted with the steel tube thusthe confinement effect should be considered in this stageHowever the eccentricity also has an important influence onthe stress distribution of CFSST columns the confinementeffect was weakened with the increase of eccentrical ratios

Mathematical Problems in Engineering 7

S1-05-P1S1-05-P2S1-05-P3S1-05-P4S1-05-P5S1-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50C

onta

ct S

tress

(MPa

)

(a) S1-05

S2-05-P1S2-05-P2S2-05-P3S2-05-P4S2-05-P5S2-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-05

S3-05-P1S3-05-P2S3-05-P3S3-05-P4S3-05-P5S3-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

(c) S3-05

S4-05-P1S4-05-P2S4-05-P3S4-05-P4S4-05-P5S4-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-05

Figure 8 Contact stress for CFSST columns under eccentric loading (e = 05)

During the second stage a plateau was proposed which isshown as follows 120576119888119888

1205761198880 = 119890119898 1205761198880 lt 120576 le 120576119888119888 (7)

where m= (29224-0003671198911015840119888 )(1198911198611198911015840119888 )03124+00021198911015840

119888 119891B =025119896(1 + 0027119891119910) expminus0028Bt(1 + 16 lowast 10minus10(1198911015840119888 )48) 119896 =059 exp(minuse044) + 042

During the third stage both the confinement effect andeccentrical ratios should be considered in the stress-strainmodel which is shown as follows

120590 = 119891119903 + (1198911015840119888 minus 119891119903) exp [minus(120576 minus 120576119888119888120572 )12] 120576 ge 120576119888119888 (8)

where 119891119903 = 011198961198911015840119888 120572 = 0005 + 120585119888 120585119888 = 119860 119904119891119910119860119888119891119888119896 119896 =059 exp(minuse044) + 042

8 Mathematical Problems in Engineering

S1-05-AVS2-05-AVS3-05-AVS4-05-AVE05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25C

onta

ct S

tress

(MPa

)

(a) e=05

S1-1-AVS2-1-AVS3-1-AVS4-1-AVE1-AV

0

5

10

15

20

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) e=1

Figure 9 Average contact stress for CFSST columns under eccentric loading

S1

S0

E0-AVE05-AVE1-AV

S05

0

5

10

15

20

25

30

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 10 Area enclosed by the stress-strain curves and the horizontal axis

3 Validation of the ProposedConstitutive Model

In order to validate the stress-strain model for CFSSTcolumns under eccentric loading the simulation resultswere compared with the experimental results from differ-ent references as shown in Figure 12 Both Hanrsquos modeland the current proposed model were used to model themechanical behavior of inner concrete During the initialstage both Hanrsquos model and the current model gave an

accurate prediction With the increase of axial deformationthe current model was more accurate especially during thestrain-softening stage

The carrying capacities for CFSST columns are shownin Table 1 in which 119875119905119890119904119905 and 119875119865119864 are the peak load derivedfrom experiment and FEA model with current proposedstress-strain model respectively It can be seen that a goodprediction could be achieved and the average variationbetween predicted and experimental results is below 5Thus it can be concluded that the model proposed in this

Mathematical Problems in Engineering 9

(1 048)(09 049)

(08 051)(07 054)

(06 056)

(05 061)(04 065)

(03 071)

(02 079)

(01 089)

Data point Fitted curve

(1 1)

04

05

06

07

08

09

10

Con

finem

ent c

oeffi

cien

t

01 02 03 04 05 06 07 08 09 1000Eccentric ratio

Figure 11 The confinement coefficient (k) for CFSST columns under eccentric loading

Table 1 Comparisons between experimental and simulational results

Ref Specimen t (mm) 119891119905119910(MPa) 119891119888(MPa) 119863119890(mm) 119875119905119890119904119905(kN) 119875119865119864(kN) 119875119865119864119875119905119890119904119905HS1C40SA-02 57 5145 432 1050 1440 1397 097HS1C40SB-02 57 5145 432 2200 2085 1793 086HS1C40SB-02 57 5145 432 2325 2550 2499 098HS1C50SA-02 57 5145 553 1300 1380 1408 102HS1C50SB-02 57 5145 553 1900 2140 2012 094HS1C50SE-02 57 5145 553 3450 2470 2346 095HS1C40SA-04 57 5145 432 2650 1190 1083 091

[25] HS1C40SB-04 57 5145 432 3800 1620 1669 103HS1C40SE-04 57 5145 432 4975 2150 2171 101HS1C50SA-04 57 5145 553 2450 1220 1159 095HS1C50SE-04 57 5145 553 4775 2250 2295 102HS1C40SA-06 57 5145 432 3500 1110 988 089HS1C40SB-06 57 5145 432 5550 1500 1530 102HS1C40SE-06 57 5145 432 7400 1700 1632 096HS1C50SA-06 57 5145 553 5500 1020 1081 106

Mean 0971Standard Deviation 0054EC1-2 4 43456 1105 20 21297 1980 093EC2-2 4 43456 1105 35 17172 1528 089

[10] EC3-2 4 43456 1105 50 14549 1484 102EC4-2 4 43456 1105 65 12441 1169 094EC5-2 5 43310 1105 50 16301 1597 098EC6-2 6 43690 1105 50 17972 1707 095Mean 0951Standard deviation 0041

10 Mathematical Problems in Engineering

(1)HS1C50SB-02[25] (2)HS1C50SA-04[25]

(3)EC1-2[10] (4)EC4-2[10]

Test Hans model Current model

5 10 15 20 25 30 35 400Axial shortening (mm)

0

500

1000

1500

2000

2500A

xial

load

(kN

)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=02

Test Hans model Current model

0

200

400

600

800

1000

1200

1400

Axi

al lo

ad (k

N)

10 20 30 40 500Axial shortening (mm)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=04

Test Hans model Current model

1 2 3 4 5 6 7 80Axial shortening (mm)

0

500

1000

1500

2000

2500

Axi

al lo

ad (k

N)

t=4 mm fＳ=43456 MPaf＝=1105 MPa e=0133

Test Hans model Current model

0

500

1000

1500

2000A

xial

load

(kN

)

2 4 6 8 100Axial shortening (mm)

t=4mm fＳ=43456 MPaf＝=1105 MPa e=0433

Figure 12 Comparisons between experimental and simulational result

paper is accurate in simulating the eccentric behavior ofCFSST columns

4 Conclusions

This paper numerically investigated the eccentric behavior ofCFSST columns The finite element analysis found that theconfinement effect of steel tube on concrete was seriouslyweakened with the increasing of eccentricities Thereforeexisting models tended to overestimate the mechanicalbehavior of CFSST columns and were not applicable whenthe CFSST columns were under eccentric loadingThis paperproposed a new stress-strain model of CFSST introducinga new parameter to consider the influence of eccentricity

on the confinement effect Comparisons between simula-tional results and experimental results from different sourcesvalidated the accuracy the proposed model has a higherapplicability to simulate the eccentric behavior of CFSSTcolumns especially during the strain-softening stage

Nomenclature

119860119888 Cross-sectional area of concrete119860 119904 Cross-sectional area of the steel tubeD119890 Eccentric distance119864119862 Elastic modulus of concrete119864119878 Elastic modulus of steel119890 Eccentrical ratio1198911015840119888 Cylinder strength of the concrete

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

6 Mathematical Problems in Engineering

S1-0-AVS2-0-AVS3-0-AVS4-0-AVE0-AV

0

5

10

15

20

25

30

35

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 7 Average contact stress for CFSST columns (e=0)

from concrete-filled circular steel tube [20] It can also befound that the contact stress was fluctuated around zero at theinitial stage for P1 P3 and P5 while contact stress increasedlinearly during the initial stage for P2 and P4

It can be concluded that the contact stress can be quitedifferent at different regions In order to simplify the stressdistribution the average curve was also plotted in Figure 6Considering the symmetry of each section the contact stressfor each section can be represented by the average curveTheaverage curves for each section are shown in Figure 7 it canbe seen that the distribution of stress was also nonuniformalong the axial direction of the CFSST column Thus anaverage curve for each section curve E0-AV was also plottedin Figure 7

22 Eccentric Loading (119890 = 05 and 1) The contact stressfor CFSST columns under eccentric loading is shown inFigure 8 With the increase of eccentrical ratio the contactstress decreased significantly indicating that the confinementeffect was weakened as well It can be found that the contactstress at P2 and P4 is much higher than P1 P3 and P5 whichis due to the stress concentration phenomenon in the corner-angle area as well Also it can be seen that the contact stressdistributed nonuniformly in P1 P3 and P5 indicating theeccentric loading has a great impact on the distribution ofstress on the sections Taking curve S4-05-P5 as an examplethe contact stress fluctuated around zero during the initialstage suggesting that the inner concrete was separated fromthe steel tube due to the different Poissonrsquos ratios of theconcrete and the steel With increasing axial displacementthe contact stress in S4-05-P5 increased slowly because theinner concrete was crushed and contacted with steel tube inthis stage With the further increase of eccentric loading thecontact stress in S4-05-P5 decreased rapidly and fluctuatedaround zero again during the last stage This is attributed to

the outward local buckling in the compressive side of steeltube leading to the gradual separation between the innerconcrete and the steel tube in this stage

The average contact stresses for CFSST columns undereccentric loading are shown in Figure 9 The contact stressfor CFSST columns with the eccentrical ratios of 05 and 1was represented by curves E05-AV and E1-AV respectively Itcan be seen that the contact stress decreased with the increaseof eccentric ratios

23 New Stress-Strain Model for Core Concrete The averagecontact stress for columns with different eccentric ratios ie0 05 and 1 is shown in Figure 10 It is evident that the contactstress decreased rapidly with the increase of eccentric ratiosthus the influence of eccentric ratios should be considered inthe stress-strain model A new parameter k which representsthe influence of eccentric loading was proposed as follows

119878119894 = int1198891199060

120590 (120576119894) d120576 (3)

119896 = 1198781198941198780 (4)

where 119878119894 represents the area under the contact stress curvesfor CFSST columns with different eccentrical ratios Theconfinement coefficient (k) at different eccentric ratios rcould be obtained according to (3) and (4) which is shownin Figure 10

As shown in Figure 11 the confinement coefficientdecreased with the increase of eccentric ratios which isconsistent with the previous discussions With the nonlinearfitting approach the confinement coefficient (k) can beexpressed as follows

119896 = 059 exp(minus 119890044) + 042 (5)

where 119896 is confinement coefficient and 119890 is the eccentric ratioof CFSST columns

Based on the stress-strain model proposed by Tao et al[24] a new three-stage constitutive model which consideredthe influence of eccentric loading was proposed During theinitial stage steel tube has negligible confinement for innerconcreteTherefore the stress-strain relationship for confinedconcrete during the initial stage is linear and no confinementeffect or eccentric ratios were considered in this stage whichwas given by

1205901198911015840119888 =

119860119883 + 11986111988321 + (119860 minus 2)119883 + (119861 minus 1)1198832 0 lt 120576 le 1205761198880 (6)

where X = 1205761205761198880 A=11986411988812057611988801198911015840119888 B=(119860 minus 12)055 minus 1 1205761198880=000076+radic(06261198911015840119888 minus 433) times 10minus7

With the increase of axial deformation the concrete wasgradually cursed and contacted with the steel tube thusthe confinement effect should be considered in this stageHowever the eccentricity also has an important influence onthe stress distribution of CFSST columns the confinementeffect was weakened with the increase of eccentrical ratios

Mathematical Problems in Engineering 7

S1-05-P1S1-05-P2S1-05-P3S1-05-P4S1-05-P5S1-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50C

onta

ct S

tress

(MPa

)

(a) S1-05

S2-05-P1S2-05-P2S2-05-P3S2-05-P4S2-05-P5S2-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-05

S3-05-P1S3-05-P2S3-05-P3S3-05-P4S3-05-P5S3-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

(c) S3-05

S4-05-P1S4-05-P2S4-05-P3S4-05-P4S4-05-P5S4-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-05

Figure 8 Contact stress for CFSST columns under eccentric loading (e = 05)

During the second stage a plateau was proposed which isshown as follows 120576119888119888

1205761198880 = 119890119898 1205761198880 lt 120576 le 120576119888119888 (7)

where m= (29224-0003671198911015840119888 )(1198911198611198911015840119888 )03124+00021198911015840

119888 119891B =025119896(1 + 0027119891119910) expminus0028Bt(1 + 16 lowast 10minus10(1198911015840119888 )48) 119896 =059 exp(minuse044) + 042

During the third stage both the confinement effect andeccentrical ratios should be considered in the stress-strainmodel which is shown as follows

120590 = 119891119903 + (1198911015840119888 minus 119891119903) exp [minus(120576 minus 120576119888119888120572 )12] 120576 ge 120576119888119888 (8)

where 119891119903 = 011198961198911015840119888 120572 = 0005 + 120585119888 120585119888 = 119860 119904119891119910119860119888119891119888119896 119896 =059 exp(minuse044) + 042

8 Mathematical Problems in Engineering

S1-05-AVS2-05-AVS3-05-AVS4-05-AVE05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25C

onta

ct S

tress

(MPa

)

(a) e=05

S1-1-AVS2-1-AVS3-1-AVS4-1-AVE1-AV

0

5

10

15

20

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) e=1

Figure 9 Average contact stress for CFSST columns under eccentric loading

S1

S0

E0-AVE05-AVE1-AV

S05

0

5

10

15

20

25

30

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 10 Area enclosed by the stress-strain curves and the horizontal axis

3 Validation of the ProposedConstitutive Model

In order to validate the stress-strain model for CFSSTcolumns under eccentric loading the simulation resultswere compared with the experimental results from differ-ent references as shown in Figure 12 Both Hanrsquos modeland the current proposed model were used to model themechanical behavior of inner concrete During the initialstage both Hanrsquos model and the current model gave an

accurate prediction With the increase of axial deformationthe current model was more accurate especially during thestrain-softening stage

The carrying capacities for CFSST columns are shownin Table 1 in which 119875119905119890119904119905 and 119875119865119864 are the peak load derivedfrom experiment and FEA model with current proposedstress-strain model respectively It can be seen that a goodprediction could be achieved and the average variationbetween predicted and experimental results is below 5Thus it can be concluded that the model proposed in this

Mathematical Problems in Engineering 9

(1 048)(09 049)

(08 051)(07 054)

(06 056)

(05 061)(04 065)

(03 071)

(02 079)

(01 089)

Data point Fitted curve

(1 1)

04

05

06

07

08

09

10

Con

finem

ent c

oeffi

cien

t

01 02 03 04 05 06 07 08 09 1000Eccentric ratio

Figure 11 The confinement coefficient (k) for CFSST columns under eccentric loading

Table 1 Comparisons between experimental and simulational results

Ref Specimen t (mm) 119891119905119910(MPa) 119891119888(MPa) 119863119890(mm) 119875119905119890119904119905(kN) 119875119865119864(kN) 119875119865119864119875119905119890119904119905HS1C40SA-02 57 5145 432 1050 1440 1397 097HS1C40SB-02 57 5145 432 2200 2085 1793 086HS1C40SB-02 57 5145 432 2325 2550 2499 098HS1C50SA-02 57 5145 553 1300 1380 1408 102HS1C50SB-02 57 5145 553 1900 2140 2012 094HS1C50SE-02 57 5145 553 3450 2470 2346 095HS1C40SA-04 57 5145 432 2650 1190 1083 091

[25] HS1C40SB-04 57 5145 432 3800 1620 1669 103HS1C40SE-04 57 5145 432 4975 2150 2171 101HS1C50SA-04 57 5145 553 2450 1220 1159 095HS1C50SE-04 57 5145 553 4775 2250 2295 102HS1C40SA-06 57 5145 432 3500 1110 988 089HS1C40SB-06 57 5145 432 5550 1500 1530 102HS1C40SE-06 57 5145 432 7400 1700 1632 096HS1C50SA-06 57 5145 553 5500 1020 1081 106

Mean 0971Standard Deviation 0054EC1-2 4 43456 1105 20 21297 1980 093EC2-2 4 43456 1105 35 17172 1528 089

[10] EC3-2 4 43456 1105 50 14549 1484 102EC4-2 4 43456 1105 65 12441 1169 094EC5-2 5 43310 1105 50 16301 1597 098EC6-2 6 43690 1105 50 17972 1707 095Mean 0951Standard deviation 0041

10 Mathematical Problems in Engineering

(1)HS1C50SB-02[25] (2)HS1C50SA-04[25]

(3)EC1-2[10] (4)EC4-2[10]

Test Hans model Current model

5 10 15 20 25 30 35 400Axial shortening (mm)

0

500

1000

1500

2000

2500A

xial

load

(kN

)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=02

Test Hans model Current model

0

200

400

600

800

1000

1200

1400

Axi

al lo

ad (k

N)

10 20 30 40 500Axial shortening (mm)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=04

Test Hans model Current model

1 2 3 4 5 6 7 80Axial shortening (mm)

0

500

1000

1500

2000

2500

Axi

al lo

ad (k

N)

t=4 mm fＳ=43456 MPaf＝=1105 MPa e=0133

Test Hans model Current model

0

500

1000

1500

2000A

xial

load

(kN

)

2 4 6 8 100Axial shortening (mm)

t=4mm fＳ=43456 MPaf＝=1105 MPa e=0433

Figure 12 Comparisons between experimental and simulational result

paper is accurate in simulating the eccentric behavior ofCFSST columns

4 Conclusions

This paper numerically investigated the eccentric behavior ofCFSST columns The finite element analysis found that theconfinement effect of steel tube on concrete was seriouslyweakened with the increasing of eccentricities Thereforeexisting models tended to overestimate the mechanicalbehavior of CFSST columns and were not applicable whenthe CFSST columns were under eccentric loadingThis paperproposed a new stress-strain model of CFSST introducinga new parameter to consider the influence of eccentricity

on the confinement effect Comparisons between simula-tional results and experimental results from different sourcesvalidated the accuracy the proposed model has a higherapplicability to simulate the eccentric behavior of CFSSTcolumns especially during the strain-softening stage

Nomenclature

119860119888 Cross-sectional area of concrete119860 119904 Cross-sectional area of the steel tubeD119890 Eccentric distance119864119862 Elastic modulus of concrete119864119878 Elastic modulus of steel119890 Eccentrical ratio1198911015840119888 Cylinder strength of the concrete

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018

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Dierential EquationsInternational Journal of

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AnalysisInternational Journal of

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Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 7

S1-05-P1S1-05-P2S1-05-P3S1-05-P4S1-05-P5S1-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50C

onta

ct S

tress

(MPa

)

(a) S1-05

S2-05-P1S2-05-P2S2-05-P3S2-05-P4S2-05-P5S2-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) S2-05

S3-05-P1S3-05-P2S3-05-P3S3-05-P4S3-05-P5S3-05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

(c) S3-05

S4-05-P1S4-05-P2S4-05-P3S4-05-P4S4-05-P5S4-05-AV

0

5

10

15

20

25

30

35

40

45

50

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(d) S4-05

Figure 8 Contact stress for CFSST columns under eccentric loading (e = 05)

During the second stage a plateau was proposed which isshown as follows 120576119888119888

1205761198880 = 119890119898 1205761198880 lt 120576 le 120576119888119888 (7)

where m= (29224-0003671198911015840119888 )(1198911198611198911015840119888 )03124+00021198911015840

119888 119891B =025119896(1 + 0027119891119910) expminus0028Bt(1 + 16 lowast 10minus10(1198911015840119888 )48) 119896 =059 exp(minuse044) + 042

During the third stage both the confinement effect andeccentrical ratios should be considered in the stress-strainmodel which is shown as follows

120590 = 119891119903 + (1198911015840119888 minus 119891119903) exp [minus(120576 minus 120576119888119888120572 )12] 120576 ge 120576119888119888 (8)

where 119891119903 = 011198961198911015840119888 120572 = 0005 + 120585119888 120585119888 = 119860 119904119891119910119860119888119891119888119896 119896 =059 exp(minuse044) + 042

8 Mathematical Problems in Engineering

S1-05-AVS2-05-AVS3-05-AVS4-05-AVE05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25C

onta

ct S

tress

(MPa

)

(a) e=05

S1-1-AVS2-1-AVS3-1-AVS4-1-AVE1-AV

0

5

10

15

20

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) e=1

Figure 9 Average contact stress for CFSST columns under eccentric loading

S1

S0

E0-AVE05-AVE1-AV

S05

0

5

10

15

20

25

30

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 10 Area enclosed by the stress-strain curves and the horizontal axis

3 Validation of the ProposedConstitutive Model

In order to validate the stress-strain model for CFSSTcolumns under eccentric loading the simulation resultswere compared with the experimental results from differ-ent references as shown in Figure 12 Both Hanrsquos modeland the current proposed model were used to model themechanical behavior of inner concrete During the initialstage both Hanrsquos model and the current model gave an

accurate prediction With the increase of axial deformationthe current model was more accurate especially during thestrain-softening stage

The carrying capacities for CFSST columns are shownin Table 1 in which 119875119905119890119904119905 and 119875119865119864 are the peak load derivedfrom experiment and FEA model with current proposedstress-strain model respectively It can be seen that a goodprediction could be achieved and the average variationbetween predicted and experimental results is below 5Thus it can be concluded that the model proposed in this

Mathematical Problems in Engineering 9

(1 048)(09 049)

(08 051)(07 054)

(06 056)

(05 061)(04 065)

(03 071)

(02 079)

(01 089)

Data point Fitted curve

(1 1)

04

05

06

07

08

09

10

Con

finem

ent c

oeffi

cien

t

01 02 03 04 05 06 07 08 09 1000Eccentric ratio

Figure 11 The confinement coefficient (k) for CFSST columns under eccentric loading

Table 1 Comparisons between experimental and simulational results

Ref Specimen t (mm) 119891119905119910(MPa) 119891119888(MPa) 119863119890(mm) 119875119905119890119904119905(kN) 119875119865119864(kN) 119875119865119864119875119905119890119904119905HS1C40SA-02 57 5145 432 1050 1440 1397 097HS1C40SB-02 57 5145 432 2200 2085 1793 086HS1C40SB-02 57 5145 432 2325 2550 2499 098HS1C50SA-02 57 5145 553 1300 1380 1408 102HS1C50SB-02 57 5145 553 1900 2140 2012 094HS1C50SE-02 57 5145 553 3450 2470 2346 095HS1C40SA-04 57 5145 432 2650 1190 1083 091

[25] HS1C40SB-04 57 5145 432 3800 1620 1669 103HS1C40SE-04 57 5145 432 4975 2150 2171 101HS1C50SA-04 57 5145 553 2450 1220 1159 095HS1C50SE-04 57 5145 553 4775 2250 2295 102HS1C40SA-06 57 5145 432 3500 1110 988 089HS1C40SB-06 57 5145 432 5550 1500 1530 102HS1C40SE-06 57 5145 432 7400 1700 1632 096HS1C50SA-06 57 5145 553 5500 1020 1081 106

Mean 0971Standard Deviation 0054EC1-2 4 43456 1105 20 21297 1980 093EC2-2 4 43456 1105 35 17172 1528 089

[10] EC3-2 4 43456 1105 50 14549 1484 102EC4-2 4 43456 1105 65 12441 1169 094EC5-2 5 43310 1105 50 16301 1597 098EC6-2 6 43690 1105 50 17972 1707 095Mean 0951Standard deviation 0041

10 Mathematical Problems in Engineering

(1)HS1C50SB-02[25] (2)HS1C50SA-04[25]

(3)EC1-2[10] (4)EC4-2[10]

Test Hans model Current model

5 10 15 20 25 30 35 400Axial shortening (mm)

0

500

1000

1500

2000

2500A

xial

load

(kN

)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=02

Test Hans model Current model

0

200

400

600

800

1000

1200

1400

Axi

al lo

ad (k

N)

10 20 30 40 500Axial shortening (mm)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=04

Test Hans model Current model

1 2 3 4 5 6 7 80Axial shortening (mm)

0

500

1000

1500

2000

2500

Axi

al lo

ad (k

N)

t=4 mm fＳ=43456 MPaf＝=1105 MPa e=0133

Test Hans model Current model

0

500

1000

1500

2000A

xial

load

(kN

)

2 4 6 8 100Axial shortening (mm)

t=4mm fＳ=43456 MPaf＝=1105 MPa e=0433

Figure 12 Comparisons between experimental and simulational result

paper is accurate in simulating the eccentric behavior ofCFSST columns

4 Conclusions

This paper numerically investigated the eccentric behavior ofCFSST columns The finite element analysis found that theconfinement effect of steel tube on concrete was seriouslyweakened with the increasing of eccentricities Thereforeexisting models tended to overestimate the mechanicalbehavior of CFSST columns and were not applicable whenthe CFSST columns were under eccentric loadingThis paperproposed a new stress-strain model of CFSST introducinga new parameter to consider the influence of eccentricity

on the confinement effect Comparisons between simula-tional results and experimental results from different sourcesvalidated the accuracy the proposed model has a higherapplicability to simulate the eccentric behavior of CFSSTcolumns especially during the strain-softening stage

Nomenclature

119860119888 Cross-sectional area of concrete119860 119904 Cross-sectional area of the steel tubeD119890 Eccentric distance119864119862 Elastic modulus of concrete119864119878 Elastic modulus of steel119890 Eccentrical ratio1198911015840119888 Cylinder strength of the concrete

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

8 Mathematical Problems in Engineering

S1-05-AVS2-05-AVS3-05-AVS4-05-AVE05-AV

5 10 15 20 250Axial shortening (mm)

0

5

10

15

20

25C

onta

ct S

tress

(MPa

)

(a) e=05

S1-1-AVS2-1-AVS3-1-AVS4-1-AVE1-AV

0

5

10

15

20

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

(b) e=1

Figure 9 Average contact stress for CFSST columns under eccentric loading

S1

S0

E0-AVE05-AVE1-AV

S05

0

5

10

15

20

25

30

Con

tact

Stre

ss (M

Pa)

5 10 15 20 250Axial shortening (mm)

Figure 10 Area enclosed by the stress-strain curves and the horizontal axis

3 Validation of the ProposedConstitutive Model

In order to validate the stress-strain model for CFSSTcolumns under eccentric loading the simulation resultswere compared with the experimental results from differ-ent references as shown in Figure 12 Both Hanrsquos modeland the current proposed model were used to model themechanical behavior of inner concrete During the initialstage both Hanrsquos model and the current model gave an

accurate prediction With the increase of axial deformationthe current model was more accurate especially during thestrain-softening stage

The carrying capacities for CFSST columns are shownin Table 1 in which 119875119905119890119904119905 and 119875119865119864 are the peak load derivedfrom experiment and FEA model with current proposedstress-strain model respectively It can be seen that a goodprediction could be achieved and the average variationbetween predicted and experimental results is below 5Thus it can be concluded that the model proposed in this

Mathematical Problems in Engineering 9

(1 048)(09 049)

(08 051)(07 054)

(06 056)

(05 061)(04 065)

(03 071)

(02 079)

(01 089)

Data point Fitted curve

(1 1)

04

05

06

07

08

09

10

Con

finem

ent c

oeffi

cien

t

01 02 03 04 05 06 07 08 09 1000Eccentric ratio

Figure 11 The confinement coefficient (k) for CFSST columns under eccentric loading

Table 1 Comparisons between experimental and simulational results

Ref Specimen t (mm) 119891119905119910(MPa) 119891119888(MPa) 119863119890(mm) 119875119905119890119904119905(kN) 119875119865119864(kN) 119875119865119864119875119905119890119904119905HS1C40SA-02 57 5145 432 1050 1440 1397 097HS1C40SB-02 57 5145 432 2200 2085 1793 086HS1C40SB-02 57 5145 432 2325 2550 2499 098HS1C50SA-02 57 5145 553 1300 1380 1408 102HS1C50SB-02 57 5145 553 1900 2140 2012 094HS1C50SE-02 57 5145 553 3450 2470 2346 095HS1C40SA-04 57 5145 432 2650 1190 1083 091

[25] HS1C40SB-04 57 5145 432 3800 1620 1669 103HS1C40SE-04 57 5145 432 4975 2150 2171 101HS1C50SA-04 57 5145 553 2450 1220 1159 095HS1C50SE-04 57 5145 553 4775 2250 2295 102HS1C40SA-06 57 5145 432 3500 1110 988 089HS1C40SB-06 57 5145 432 5550 1500 1530 102HS1C40SE-06 57 5145 432 7400 1700 1632 096HS1C50SA-06 57 5145 553 5500 1020 1081 106

Mean 0971Standard Deviation 0054EC1-2 4 43456 1105 20 21297 1980 093EC2-2 4 43456 1105 35 17172 1528 089

[10] EC3-2 4 43456 1105 50 14549 1484 102EC4-2 4 43456 1105 65 12441 1169 094EC5-2 5 43310 1105 50 16301 1597 098EC6-2 6 43690 1105 50 17972 1707 095Mean 0951Standard deviation 0041

10 Mathematical Problems in Engineering

(1)HS1C50SB-02[25] (2)HS1C50SA-04[25]

(3)EC1-2[10] (4)EC4-2[10]

Test Hans model Current model

5 10 15 20 25 30 35 400Axial shortening (mm)

0

500

1000

1500

2000

2500A

xial

load

(kN

)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=02

Test Hans model Current model

0

200

400

600

800

1000

1200

1400

Axi

al lo

ad (k

N)

10 20 30 40 500Axial shortening (mm)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=04

Test Hans model Current model

1 2 3 4 5 6 7 80Axial shortening (mm)

0

500

1000

1500

2000

2500

Axi

al lo

ad (k

N)

t=4 mm fＳ=43456 MPaf＝=1105 MPa e=0133

Test Hans model Current model

0

500

1000

1500

2000A

xial

load

(kN

)

2 4 6 8 100Axial shortening (mm)

t=4mm fＳ=43456 MPaf＝=1105 MPa e=0433

Figure 12 Comparisons between experimental and simulational result

paper is accurate in simulating the eccentric behavior ofCFSST columns

4 Conclusions

This paper numerically investigated the eccentric behavior ofCFSST columns The finite element analysis found that theconfinement effect of steel tube on concrete was seriouslyweakened with the increasing of eccentricities Thereforeexisting models tended to overestimate the mechanicalbehavior of CFSST columns and were not applicable whenthe CFSST columns were under eccentric loadingThis paperproposed a new stress-strain model of CFSST introducinga new parameter to consider the influence of eccentricity

on the confinement effect Comparisons between simula-tional results and experimental results from different sourcesvalidated the accuracy the proposed model has a higherapplicability to simulate the eccentric behavior of CFSSTcolumns especially during the strain-softening stage

Nomenclature

119860119888 Cross-sectional area of concrete119860 119904 Cross-sectional area of the steel tubeD119890 Eccentric distance119864119862 Elastic modulus of concrete119864119878 Elastic modulus of steel119890 Eccentrical ratio1198911015840119888 Cylinder strength of the concrete

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 9

(1 048)(09 049)

(08 051)(07 054)

(06 056)

(05 061)(04 065)

(03 071)

(02 079)

(01 089)

Data point Fitted curve

(1 1)

04

05

06

07

08

09

10

Con

finem

ent c

oeffi

cien

t

01 02 03 04 05 06 07 08 09 1000Eccentric ratio

Figure 11 The confinement coefficient (k) for CFSST columns under eccentric loading

Table 1 Comparisons between experimental and simulational results

Ref Specimen t (mm) 119891119905119910(MPa) 119891119888(MPa) 119863119890(mm) 119875119905119890119904119905(kN) 119875119865119864(kN) 119875119865119864119875119905119890119904119905HS1C40SA-02 57 5145 432 1050 1440 1397 097HS1C40SB-02 57 5145 432 2200 2085 1793 086HS1C40SB-02 57 5145 432 2325 2550 2499 098HS1C50SA-02 57 5145 553 1300 1380 1408 102HS1C50SB-02 57 5145 553 1900 2140 2012 094HS1C50SE-02 57 5145 553 3450 2470 2346 095HS1C40SA-04 57 5145 432 2650 1190 1083 091

[25] HS1C40SB-04 57 5145 432 3800 1620 1669 103HS1C40SE-04 57 5145 432 4975 2150 2171 101HS1C50SA-04 57 5145 553 2450 1220 1159 095HS1C50SE-04 57 5145 553 4775 2250 2295 102HS1C40SA-06 57 5145 432 3500 1110 988 089HS1C40SB-06 57 5145 432 5550 1500 1530 102HS1C40SE-06 57 5145 432 7400 1700 1632 096HS1C50SA-06 57 5145 553 5500 1020 1081 106

Mean 0971Standard Deviation 0054EC1-2 4 43456 1105 20 21297 1980 093EC2-2 4 43456 1105 35 17172 1528 089

[10] EC3-2 4 43456 1105 50 14549 1484 102EC4-2 4 43456 1105 65 12441 1169 094EC5-2 5 43310 1105 50 16301 1597 098EC6-2 6 43690 1105 50 17972 1707 095Mean 0951Standard deviation 0041

10 Mathematical Problems in Engineering

(1)HS1C50SB-02[25] (2)HS1C50SA-04[25]

(3)EC1-2[10] (4)EC4-2[10]

Test Hans model Current model

5 10 15 20 25 30 35 400Axial shortening (mm)

0

500

1000

1500

2000

2500A

xial

load

(kN

)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=02

Test Hans model Current model

0

200

400

600

800

1000

1200

1400

Axi

al lo

ad (k

N)

10 20 30 40 500Axial shortening (mm)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=04

Test Hans model Current model

1 2 3 4 5 6 7 80Axial shortening (mm)

0

500

1000

1500

2000

2500

Axi

al lo

ad (k

N)

t=4 mm fＳ=43456 MPaf＝=1105 MPa e=0133

Test Hans model Current model

0

500

1000

1500

2000A

xial

load

(kN

)

2 4 6 8 100Axial shortening (mm)

t=4mm fＳ=43456 MPaf＝=1105 MPa e=0433

Figure 12 Comparisons between experimental and simulational result

paper is accurate in simulating the eccentric behavior ofCFSST columns

4 Conclusions

This paper numerically investigated the eccentric behavior ofCFSST columns The finite element analysis found that theconfinement effect of steel tube on concrete was seriouslyweakened with the increasing of eccentricities Thereforeexisting models tended to overestimate the mechanicalbehavior of CFSST columns and were not applicable whenthe CFSST columns were under eccentric loadingThis paperproposed a new stress-strain model of CFSST introducinga new parameter to consider the influence of eccentricity

on the confinement effect Comparisons between simula-tional results and experimental results from different sourcesvalidated the accuracy the proposed model has a higherapplicability to simulate the eccentric behavior of CFSSTcolumns especially during the strain-softening stage

Nomenclature

119860119888 Cross-sectional area of concrete119860 119904 Cross-sectional area of the steel tubeD119890 Eccentric distance119864119862 Elastic modulus of concrete119864119878 Elastic modulus of steel119890 Eccentrical ratio1198911015840119888 Cylinder strength of the concrete

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

10 Mathematical Problems in Engineering

(1)HS1C50SB-02[25] (2)HS1C50SA-04[25]

(3)EC1-2[10] (4)EC4-2[10]

Test Hans model Current model

5 10 15 20 25 30 35 400Axial shortening (mm)

0

500

1000

1500

2000

2500A

xial

load

(kN

)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=02

Test Hans model Current model

0

200

400

600

800

1000

1200

1400

Axi

al lo

ad (k

N)

10 20 30 40 500Axial shortening (mm)

t=57 mm fＳ=5145 MPaf＝=553 MPa e=04

Test Hans model Current model

1 2 3 4 5 6 7 80Axial shortening (mm)

0

500

1000

1500

2000

2500

Axi

al lo

ad (k

N)

t=4 mm fＳ=43456 MPaf＝=1105 MPa e=0133

Test Hans model Current model

0

500

1000

1500

2000A

xial

load

(kN

)

2 4 6 8 100Axial shortening (mm)

t=4mm fＳ=43456 MPaf＝=1105 MPa e=0433

Figure 12 Comparisons between experimental and simulational result

paper is accurate in simulating the eccentric behavior ofCFSST columns

4 Conclusions

This paper numerically investigated the eccentric behavior ofCFSST columns The finite element analysis found that theconfinement effect of steel tube on concrete was seriouslyweakened with the increasing of eccentricities Thereforeexisting models tended to overestimate the mechanicalbehavior of CFSST columns and were not applicable whenthe CFSST columns were under eccentric loadingThis paperproposed a new stress-strain model of CFSST introducinga new parameter to consider the influence of eccentricity

on the confinement effect Comparisons between simula-tional results and experimental results from different sourcesvalidated the accuracy the proposed model has a higherapplicability to simulate the eccentric behavior of CFSSTcolumns especially during the strain-softening stage

Nomenclature

119860119888 Cross-sectional area of concrete119860 119904 Cross-sectional area of the steel tubeD119890 Eccentric distance119864119862 Elastic modulus of concrete119864119878 Elastic modulus of steel119890 Eccentrical ratio1198911015840119888 Cylinder strength of the concrete

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 11

119891119888119896 Characteristic strength of the concrete119891119888 Cube compressive strength of concrete119891119910 Nominal yield strength of steel119891119905119910 Yield strength of the steel119896 Confinement coefficient119873119906 Load carrying capacity119872119906 Moment carrying capacity119875119865119864 Peak load recorded from FEA119875119905119890119904119905 Peak load recorded from experiment119905 Wall thickness of the steel tube of CFSST120572119904 Steel ratio of steel tube (= 119860 119904119860119888)120576 Strain120590 Stress120585119888 Confinement factor of CFST (=119860 119904119891119905119910119860119888119891119888119896)

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the Open Foundationof Key Laboratory of Concrete and Prestressed ConcreteStructure of Ministry of Education under CPCSME2018-06 and the Fundamental Research Funds for the CentralUniversities under 3205009601

References

[1] L-H Han W Li and R Bjorhovde ldquoDevelopments andadvanced applications of concrete-filled steel tubular (CFST)structures membersrdquo Journal of Constructional Steel Researchvol 100 pp 211ndash228 2014

[2] Y Huang Y Sun H Sun andQWang ldquoTheoretical analysis onmechanical behavior of axially loaded recycled aggregate con-crete filled steel tubesrdquo Mathematical Problems in Engineeringvol 2015 Article ID 270469 14 pages 2015

[3] J Ma Y Liu Q I Gao and K Hou ldquoInvestigating the hystereticbehavior of concrete-filled steel tube arch by using a fiberbeam elementrdquo Mathematical Problems in Engineering vol2015 Article ID 409530 7 pages 2015

[4] M T Stephens D E Lehman and C W Roeder ldquoSeismicperformance modeling of concrete-filled steel tube bridgesTools and case studyrdquo Engineering Structures vol 165 pp 88ndash105 2018

[5] Q Zhou H Fu F Ding et al ldquoSeismic behavior of a newthrough-core connection between concrete-filled steel tubularcolumn and composite beamrdquo Journal of Constructional SteelResearch vol 155 pp 107ndash120 2019

[6] T Fujimoto A Mukai I Nishiyama and K Sakino ldquoBehaviorof eccentrically loaded concrete-filled steel tubular columnsrdquoJournal of Structural Engineering vol 130 no 2 pp 203ndash2122004

[7] D Liu ldquoBehaviour of high strength rectangular concrete-filledsteel hollow section columns under eccentric loadingrdquo in-Walled Structures vol 42 no 12 pp 1631ndash1644 2004

[8] Y-F Yang and L-H Han ldquoBehaviour of concrete filled steeltubular (CFST) stub columns under eccentric partial compres-sionrdquoin-Walled Structures vol 49 no 2 pp 379ndash395 2011

[9] X Wang and J Liu ldquoBehavior and design of slender squaretubed-reinforced-concrete columns subjected to eccentric com-pressionrdquoin-Walled Structures vol 120 pp 153ndash160 2017

[10] G Li B Chen Z Yang and Y Feng ldquoExperimental andnumerical behaviour of eccentrically loaded high strengthconcrete filled high strength square steel tube stub columnsrdquoin-Walled Structures vol 127 pp 483ndash499 2018

[11] L Han Y Ye and F Liao ldquoEffects of Core Concrete InitialImperfection on Performance of Eccentrically Loaded CFSTColumnsrdquo Journal of Structural Engineering vol 142 no 12 pp1ndash13 2016

[12] T Sheehan X H Dai T M Chan and D Lam ldquoStructuralresponse of concrete-filled elliptical steel hollow sections undereccentric compressionrdquo Engineering Structures vol 45 pp 314ndash323 2012

[13] L-H Han G-H Yao and Z Tao ldquoPerformance of concrete-filled thin-walled steel tubes under pure torsionrdquo in-WalledStructures vol 45 no 1 pp 24ndash36 2007

[14] M N S Hadi and I B R Widiarsa ldquoAxial and flexuralperformance of square RC columns wrapped with CFRP undereccentric loadingrdquo Journal of Composites for Construction vol16 no 6 pp 640ndash649 2012

[15] L H Xu Z X Li and Y Lv ldquoNumerical study on nonlinearsemiactive control of steel-concrete hybrid structures usingMR dampersrdquoMathematical Problems in Engineering vol 2013Article ID 401410 9 pages 2013

[16] L Bisby and M Ranger ldquoAxial-flexural interaction in circularFRP-confined reinforced concrete columnsrdquo Construction andBuilding Materials vol 24 no 9 pp 1672ndash1681 2010

[17] X Fan and M Zhang ldquoBehaviour of inorganic polymer con-crete columns reinforced with basalt FRP bars under eccentriccompression An experimental studyrdquo Composites Part B Engi-neering vol 104 pp 44ndash56 2016

[18] M Z Kabir and E Shafei ldquoPlasticity modeling of FRP-confinedcircular reinforced concrete columns subjected to eccentricaxial loadingrdquo Composites Part B Engineering vol 43 no 8 pp3497ndash3506 2012

[19] G Lin and J G Teng ldquoThree-dimensional finite-element anal-ysis of FRP-confined circular concrete columns under eccentricloadingrdquo Journal of Composites for Construction vol 21 no 4pp 1ndash12 2017

[20] J M Cai and J L Pan ldquoNonlinear analysis of circular concrete-filled steel tube columns under eccentric loadingrdquoMagazine ofConcrete Research vol 71 no 23 pp 1ndash12 2018

[21] D J Robert ldquoA modified mohr-coulomb model to simulatethe behavior of pipelines in unsaturated soilsrdquo Computers ampGeosciences vol 91 pp 146ndash160 2017

[22] M F Ferrotto L Cavaleri and F Di Trapani ldquoFE modeling ofPartially Steel-Jacketed (PSJ) RC columns using CDP modelrdquoComputers and Concrete vol 22 no 2 pp 143ndash152 2018

[23] M F Ferrotto O Fischer and L Cavaleri ldquoA strategy for thefinite element modeling of FRP-confined concrete columnssubjected to preloadrdquo Engineering Structures vol 173 pp 1054ndash1067 2018

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

12 Mathematical Problems in Engineering

[24] A A C I Standard Building Code Requirements for StructuralConcrete (ACI 318-11) American Concrete Institute 2011

[25] Y Du Z Chen J Y Richard Liew and M-X Xiong ldquoRectan-gular concrete-filled steel tubular beam-columns using high-strength steel Experiments and designrdquo Journal of Construc-tional Steel Research vol 131 pp 1ndash18 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom