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ResearchArticle ComparativeStudyofCFRP-ConfinedCFSTStubColumnsunder Axial Compression Ying Guo 1 and Yufen Zhang 2 1 School of Civil Engineering, Tianjin University, Tianjin 300072, China 2 School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China Correspondence should be addressed to Yufen Zhang; [email protected] Received 25 May 2018; Revised 24 June 2018; Accepted 3 July 2018; Published 18 July 2018 Academic Editor: David M. Boyajian Copyright©2018YingGuoandYufenZhang.isisanopenaccessarticledistributedundertheCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is paper presented a comparative study of concrete-filled steel tubular (CFST) stub columns with three different confinement types from carbon fiber reinforced polymer (CFRP): outer circular CFRP, inner circular CFRP, and outer square CFRP. e compressive mechanism and physical properties of the composite column were analyzed firstly aiming at investigating the confinement effect of CFRP. Ultimate axial bearing capacity of these three CFRP-confined CFSTcolumns was calculated based on Unified eory of CFSTand elastoplastic limit equilibrium theory, respectively. Meanwhile, the corresponding tests are adopted to validate the feasibility of the two calculation models. rough data analysis, the study confirmed the ultimate strength calculation results of the limit equilibrium method were found to be more reliable and approximate to the test results than those of Unified eory of CFST. en axial bearing capacity of the pure CFSTcolumn was predicted to evaluate the bearing capacity enhancement ratio of the three types of composite columns. It was demonstrated that the averaged enhancement ratio is 16.4 percent, showing that CFRP-confined CFST columns had a broad engineering applicability. rough a comparative analysis, this study also confirmed that outer circular CFRP had the best confinement effect and outer square CFRP did better than inner circular CFRP. e confinement effect of CFRP increased with the decrease of concrete strength, and it was proportional with relative proportions of CFRP and steel under the same concrete strength. 1. Introduction Carbon fiber reinforced polymers (CFRPs) have been widely used in repair and retrofit of deficient structures in recent decades, because externally bonded CFRP material in the form of sheets or plates is particularly well suited for flexure and shear [1, 2]. In many engineering fields, the CFRP-metal composite tanks or tubes have been used widely, such as gas tank used in motor vehicle and pipeline system for transporting high pressure gas or liquid used in municipal engineering or chemical engineering. CFRP materials, as external jackets for the confinement of reinforced concrete columns, can enhance strength and ductility [3–6]. e superior mechanical and physical properties of CFRP make them excellent candidates to repair and retrofit steel structures as well. Concrete-filled steeltubular(CFST)structureshavebeenstudiedandusedin civil engineering widely for many years [7]. However, steel tubes are susceptible to degradation due to corrosion and its thin-walled section before concrete hardening [8], which results in the decrease of axial strength of the CFST column [9]. erefore, the CFRP-metal tube can also be used in civil engineering, for example, the CFRP-steel composite tube in- filled with concrete has been used as the column [10], and CFRP has also been used to reinforce damaged CFSTcolumn [11]. As discussed by Gu [12], Li et al. [13], and Wang et al. [14], most of the research conducted has focused on the use CFRP for CFST structure. Carbon fiber sheets or plates are attached to a steel tube or concrete in a CFST member to increase its bearing capacity and ductility. It was concluded that the ultimate lateral strength and flexural stiffness of CFRP-repaired CFST beam-columns increased with the Hindawi Advances in Civil Engineering Volume 2018, Article ID 7109061, 8 pages https://doi.org/10.1155/2018/7109061
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Research ArticleComparative Study of CFRP-Confined CFST Stub Columns underAxial Compression
Ying Guo1 and Yufen Zhang 2
1School of Civil Engineering Tianjin University Tianjin 300072 China2School of Civil and Transportation Engineering Hebei University of Technology Tianjin 300401 China
Correspondence should be addressed to Yufen Zhang yufenzhgmailcom
Received 25 May 2018 Revised 24 June 2018 Accepted 3 July 2018 Published 18 July 2018
Academic Editor David M Boyajian
Copyright copy 2018 Ying Guo and Yufen Zhangis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
is paper presented a comparative study of concrete-filled steel tubular (CFST) stub columns with three different confinementtypes from carbon fiber reinforced polymer (CFRP) outer circular CFRP inner circular CFRP and outer square CFRP ecompressive mechanism and physical properties of the composite column were analyzed firstly aiming at investigating theconfinement effect of CFRP Ultimate axial bearing capacity of these three CFRP-confined CFSTcolumns was calculated based onUnifiedeory of CFSTand elastoplastic limit equilibrium theory respectively Meanwhile the corresponding tests are adopted tovalidate the feasibility of the two calculation models rough data analysis the study confirmed the ultimate strength calculationresults of the limit equilibrium method were found to be more reliable and approximate to the test results than those of Unifiedeory of CFSTen axial bearing capacity of the pure CFSTcolumn was predicted to evaluate the bearing capacity enhancementratio of the three types of composite columns It was demonstrated that the averaged enhancement ratio is 164 percent showingthat CFRP-confined CFST columns had a broad engineering applicability rough a comparative analysis this study alsoconfirmed that outer circular CFRP had the best confinement effect and outer square CFRP did better than inner circular CFRPe confinement effect of CFRP increased with the decrease of concrete strength and it was proportional with relative proportionsof CFRP and steel under the same concrete strength
1 Introduction
Carbon fiber reinforced polymers (CFRPs) have beenwidely used in repair and retrofit of deficient structures inrecent decades because externally bonded CFRP materialin the form of sheets or plates is particularly well suited forflexure and shear [1 2] In many engineering fields theCFRP-metal composite tanks or tubes have been usedwidely such as gas tank used in motor vehicle and pipelinesystem for transporting high pressure gas or liquid used inmunicipal engineering or chemical engineering CFRPmaterials as external jackets for the confinement ofreinforced concrete columns can enhance strength andductility [3ndash6] e superior mechanical and physicalproperties of CFRP make them excellent candidates torepair and retrofit steel structures as well Concrete-filled
steel tubular (CFST) structures have been studied and used incivil engineering widely for many years [7] However steeltubes are susceptible to degradation due to corrosion and itsthin-walled section before concrete hardening [8] whichresults in the decrease of axial strength of the CFST column[9] erefore the CFRP-metal tube can also be used in civilengineering for example the CFRP-steel composite tube in-filled with concrete has been used as the column [10] andCFRP has also been used to reinforce damaged CFSTcolumn[11] As discussed by Gu [12] Li et al [13] and Wang et al[14] most of the research conducted has focused on the useCFRP for CFST structure Carbon fiber sheets or plates areattached to a steel tube or concrete in a CFST member toincrease its bearing capacity and ductility It was concludedthat the ultimate lateral strength and flexural stiffness ofCFRP-repaired CFST beam-columns increased with the
HindawiAdvances in Civil EngineeringVolume 2018 Article ID 7109061 8 pageshttpsdoiorg10115520187109061
increasing number of CFRP layers Meanwhile the ductilityof specimens increased slightly with the number of CFRPlayers And as discussed by Tao et al [15] the CFRP cylindercan also impede buckling of the stub column leading todramatic improvements in buckling and postbuckling be-havior of the entire system Wang et al [16 17] conductedaxial compression experiments for thirty-two circular CFRP-confined CFST columns and twenty-four square CFRP-confined CFST columns Analyses of the tested resultsshow that the steel tube and its outer CFRP material cancooperate both longitudinally and transversely erefore allthese studies draw upon the concepts that complementaryaction between steel tube and concrete was strengthenedthrough the higher confinement of CFRP
Upon the abovementioned research other types ofcomposite columns have also been proposed Karimi et al[18] proposed a type of FRP-encased steel-concrete com-posite columns in which a circular FRP was placed aroundthe steel I-section and had the concrete filled between thesteel I-section and the FRP tube Feng et al [19] proposeda steel-concrete-FRP-concrete column which had a squaresteel tube as the outer layer and a circular filament-woundFRP tube as the inner layer with concrete filled both be-tween these two layers and within the FRP tube e resultsof these studies showed that the strength of concrete FRPand steel could be effectively utilized in the compositecolumns
All those research achievements confirmed that thecomposite column has its feasibility in theoretical researchand engineering practice showing a great potential for moredevelopment Compressive strength is an important pa-rameter for structural members and most of those researcheslisted above were concentrated on the superposition methodto calculate the ultimate compressive strength so differentformulas were deduced for every cross section of the CFRP-confined CFSTcolumns erefore the purpose of this paperis to build unified methods applicative to different sections ofthe composite column by the idea of Unifiedeory of CFSTand limit equilibrium theory e focus of this study is toinvestigate three different technology CFRPs to strengthenCFST stub columns through a comparative study of threedifferent confinement types outer circular CFRP inner cir-cular CFRP and outer square CFRP Compressive mecha-nism and physical properties of these three CFRP-confinedCFST columns were analyzed firstly aiming at investigatingthe confinement effect of CFRP on CFST columns Twotheoretical calculation models are presented to obtain theaxial compressive capacity of CFRP-confined CFST columnsOne is the Unified eory of CFST [20] the equivalentconfinement coefficient is proposed with consideration ofdifferent sections of steel tubes and CFRP cylinders and thenformulas are derived from Unifiedeory of CFST to predictthe bearing capacity of the composite column under com-pression e other is elastoplastic limit equilibrium methodtwin-shear unified strength theory (TDUST) [21] is applied toanalyze the ultimate state of steel tube and concrete re-spectively and then the ultimate bearing capacities of thecomposite column are obtained by the limit equilibriummethod e theoretical predictions were compared with the
experimental results to validate the feasibility of the twocalculation models Lastly the CFRP confinement effects onthe axial bearing capacity were analyzed by comparison ofthese three CFRP-confined CFST columns
2 Working Mechanism
Based on the summary of existing researches three types ofCFRP-confined CFSTcolumns are considered with differentCFRP confinements including outer circular CFRP innercircular CFRP and outer square CFRP as shown in Figure 1e CFRP cylinder is wrapped outside the circular CFSTcolumn in Type a CFRP cylinder is placed inside the squareCFST in Type b and CFRP cylinder is wrapped outside thesquare CFST column in Type c As can be seen in Figure 1steel tubes together with the confined concrete can resist theaxial compression remarkably while the CFRP cylinders canprovide the lateral confinement to the steel tube or concretedirectly and make the composite column behave betterindirectly
As we all know during the process of compression of thecomposite columns there exists horizontal deformationwhen the vertical load acts on the whole section Take theexample of Type a in Figure 1 concrete is filled in the circulartube wrapped by the CFRP sheet so its simplified model ofstress can be plotted in Figure 2
Concretersquos horizontal deformation coefficient was smallat the beginning of the axial load so the lateral stress p fromsteel tubes and CFRP sheet is not evident With the in-creasing axial compression concretersquos horizontal de-formation starts to gradually increase especially after thecolumn yielding ere would be many microcracks hap-pened in concrete after the column entered into plasticstage [22] but both the CFRP cylinder and steel tube canconfine the concrete to postpone its expansion e con-crete can be regarded as three-dimensioned compressedthe steel tubes can be regarded as thin-walled cylinders andCFRP is only tensile in the circumferential direction asshown in Figure 2 e ultimate state considers the fol-lowing failure modes of the CFRP-confined CFST columnsteel tube bucking and CFRP sheet rupturing [23 24]Although the CFRP cylinder has no direct contribution tothe axial bearing capacity the transverse fiber sheetscontribute to the strength enhancement by confining theCFST column in whole (see Type a c in Figure 1) or in part(see Type b in Figure 1) leading to a higher compressivestrength of the column erefore the wrapping CFRP canlead to a significant improvement in the inelastic axialdeformation capacity prior to buckling and an improvedload carrying capacity after buckling
3 Calculations by Unified Theory of CFST
Unified eory of CFST was presented by Professor ZhongShan-tong in 1993 [25] It considered CFST as a unifiedbody and a new composite material was used to study itsbehaviors It was a new method to design and simplify thedesign work Unified eory of CFST has been extended tocalculate the compressive strength of the composite CFST
2 Advances in Civil Engineering
columns with various confining materials and various crosssections under various loadings [26] For CFRP-confinedCFSTcolumns the concrete is still confined by the steel tubedirectly and this confining effect is absolutely strengthenedby the CFRP cylinder One composite material can also beconsidered to assess its behaviors but the confining effectshould be reevaluated deriving from the steel tube and CFRPcylinder We can extend deeper research works into CFRP-confined CFST columns so one equivalent confinementcoefficient ξssc is presented which can be expressed as
ξssc ksAsfs + kcfAcffcf
Acfck (1)
where As Ac and Acf are the cross section areas of the steeltube concrete and CFRP cylinder respectively fs and fcfare the yield strengths of steel and CFRP respectively fck isthe standard compressive strength of the concrete ks and kcfare the coefficients with consideration of section form of theconfining material Because in the composite column thereare two difform materials to confine concrete the effect ofrestraint is different from circular section to square sectionGenerally the coefficient of circular section is taken as thebasic parameter 1 and for square section it is 074 [27]
en the composite strength fssc of the stub column canbe calculated by the formula derived from Unifiedeory ofCFST and the equation can be expressed as
fssc 1212 + aξssc + bξ2ssc1113872 1113873fck (2)
where a and b reflect the contributions of confining ma-terials and concrete respectively ey can be calculated bythe following formula
a 01759fss
235 + 0974
b minus01038fck
20 + 00309
(3)
where fss is the weighted average of the confining materialsincluding both the steel tube and CFRP cylinder which iscalculated by
fss Asfs + Acffcf
As + Acf (4)
erefore it is recommended to use the following for-mula to calculate the bearing capacity of the CFRP-confinedCFST stub column
N1y Afssck (5)
where A is the cross section area of the whole column andN1
y is the bearing capacity calculated by Unified eory ofCFST
4 Calculations by Limit Equilibrium Theory
41 Basic Assumptions In this theoretical model forobtaining the axial compressive capacity we can quantita-tively analyze how much the confinement is influenced bythe steel tube and CFRPe interface between the steel tubeand the CFRP sheet is constrained the radial stress in thesteel tube is ignored and the steel tube is under biaxial stressthe CFRP material is linear elastic and only the lateral stressis considered so the stress along the fiber direction is
Steel tube
Concrete
CFRP cylinder
(a)
Steel tube
Concrete
Concrete
CFRP cylinder
(b)
CFRP cylinder
Concrete
Steel tube
(c)
Figure 1 Cross section types of CFRP-confined CFSTcolumns (a) Outer circular CFRP (b) Inner circular CFRP (c) Outer square CFRP
p
σf
pσf
Figure 2 Stress model in the composite column under compression (a) Concrete (b) Steel tube (c) CFRP cylinder
Advances in Civil Engineering 3
considered the radial stress and the longitudinal stress areignored
Based on the above assumptions the ultimate axialbearing capacity of CFRP-confined CFST columns can becalculated by
N2y Ns + Nc (6)
where N Ns and Nc are vertical bearing capacities of thesteel tube and concrete respectively N2
y is the bearing ca-pacity calculated by limit equilibrium theory In the state oflimit equilibrium every part of the composite column can beanalyzed using TSUST [21]
42 Twin-Shear Unified Strength +eory (TSUST) eTSUST considers the two larger principal shear stresses andthe corresponding normal stresses and their different effectson the failure of materials When the relationship functionbetween them reaches one ultimate value the material canbe defined as failure at this state which is formulated asfollows
F τ13 + bτ12 + β σ13 + bσ12( 1113857 C
when τ12 + βσ12 ge τ23 + βσ23(7a)
Fprime τ13 + bτ23 + β σ13 + bσ23( 1113857 C
when τ12 + βσ12 le τ23 + βσ23(7b)
where τ12 τ23 and τ13 are the principal shear stressesτ13 (σ1 minus σ3)2 τ12 (σ1 minus σ2)2 and τ23 (σ2 minus σ3)2σ12 σ23 and σ13 are the corresponding normal stresses onthe principal shear stress element σ1 σ2 and σ3 are theprincipal stresses σ1 ge σ2 ge σ3 b is a weighting coefficientreflecting the relative effect of the intermediate principalshear stress τ12 or τ23 on the strength of materials Cequals to the material strength β is the influence co-efficient of positive stress on material damage Denotingthe tension-compression strength ratio as α σtσc werewrite (7a) and (7b) in terms of principal stresses asfollows
F σ1 minusα
1 + bbσ2 + σ3( 1113857 σt when σ2 le
σ1 + ασ31 + α
(8a)
Fprime 1
1 + bσ1 + bσ2( 1113857minus ασ3 σt when σ2 ge
σ1 + ασ31 + α
(8b)
43 Formula of Ultimate Capacity By the principle of samearea the square cross section of the steel tube can betransformed into a circular one B and ts are the side lengthand thickness of the square steel tube and ro and to are theradius and thickness of the equivalent circular steel tuberespectively e formulas are shown as follows
ro Bπ
radic 05642B
to ro minus Bminus 2ts( 1113857
π
radic ro minus 05642 Bminus 2ts( 1113857
(9)
Meanwhile because the confinement of the square steelis uneven along its side the equivalent reduction factorshould be considered to reduce the same confinement of theequivalent circular steel tube Denoting thickness-sidelength ratio υ tB the expression of the equivalent re-duction factor ξ 664741υ2 + 09919υ + 041618 [28]Meanwhile there are effective and noneffective confiningzones of the concrete inside the square steel tube In thispaper the concrete strength reduction factor is considered toignore these two influences e concrete strength reductionfactor is taken as cμ 167Dminus0112
o [28] whereDo is the insidediameter of the equivalent circular steel tube
e simplified stress model of confined concrete isshown in Figure 2(a) e stresses can be explicated by0gt σ1 σ2 gt σ3 σ1 σ2 p For σ2 ge ((σ1 + ασ3)(1 + α))Substituting them into the stress expression of TSUST thefollowing expression can be obtained as
σ3 σc fck + kcp (10)
where kc is the lateral stress coefficient In TSUST kc can becalculated by cohesion and friction angle at material failurestate According to the test of Richart [22] kc has been takenas 41 simply here p is the lateral stress on the concrete andthe lateral stress on concrete is from both the steel tube andCFRP cylinder for Type a and c as shown in Figure 1 so itcan be expressed by
p σf + σrs (11)
where σf tcffcf rcf and σrs tsfsrs tcf and rcf are thethickness and radius of the CFRP cylinder respectively tsand rs are the thickness and radius of the steel tube re-spectively While for Type b in Figure 1 the concrete shouldbe divided into exterior concrete and internal concreteunder different lateral stresses Exterior concrete is onlyconfined by the steel tube but internal concrete is consid-ered both the steel tube and CFRP cylinder en the axialbearing capacity of the concrete can be expressed as
Nc fck + kcp( 1113857Ac (12)
As can be seen in Figure 2(b) the steel tube is con-strained by inside concrete so it can bear some vertical loadunder the ultimate state of the whole column η is assumedas the strength reduction factor of the steel tube and thenthe stress state of steel tubes can be explicated byσ3 σz ηfs σ2 σr 0 σ1 σθ prots For |σ3|gt σ1and σ2 ge ((σ1 + σ3)(1 + α)) substitute them into the stressexpression of TSUST the following expression can beobtained
pro
ts(1 + b)minus ηfs fs (13)
4 Advances in Civil Engineering
Tabl
e1
Com
parisonof
calculations
andtest
results
Types
Specim
ens
t cf
(mm)
fcf
(MPa
)t s
(mm)
As
(mm
2 )fs
(MPa
)fck
(MPa
)N
t(kN)
N0
(kN)
N1 y
(kN)
N2 y
(kN)
N1 y
Nt
N2 y
Nt
NCFS
T(kN)
Ntminus
NCFS
TN
CFS
T(
)Sources
a
1ndash25
017
1260
25
10132
350
4015
1294
8592
11765
12937
092
100
10605
220
[30]
1ndash35
017
1260
35
14404
310
4015
1348
9591
12854
14080
095
104
11755
147
1ndash45
017
1260
45
18802
310
4015
1698
11036
14462
15756
085
093
13417
260
2ndash25
034
1260
25
10132
350
4015
1506
8592
12933
14309
086
095
10605
420
2ndash35
034
1260
35
14404
310
4015
1593
9591
13950
15401
086
097
11755
355
2ndash45
034
1260
45
18802
310
4015
1846
11036
15054
17020
082
092
13417
376
b
SC41
0167
1500
42400
295
536
2215
18505
21758
23411
098
106
20901
59
[13]
SC42
0334
1500
42400
295
536
2275
18505
22613
24437
099
107
20901
88
SC51
0167
1500
53000
295
536
2485
20119
23264
24778
094
099
22440
107
SC52
0334
1500
53000
295
536
2585
20119
24079
23567
093
091
22440
152
SC61
0167
1500
63600
295
536
2710
21734
24728
28011
091
103
23943
132
SC62
0334
1500
63600
295
536
2775
21734
25500
26773
092
096
23943
159
c
A-1
0111
4900
35
1960
300
223
1107
9825
11663
11107
105
100
10159
90
[31]
A-2
0222
4900
35
1960
300
223
1129
9825
12723
11926
113
106
10159
111
A-3
0333
4900
35
1960
300
223
1222
9825
13802
12854
113
106
10159
203
B-1
0111
4900
35
1960
300
264
1200
10550
12605
12285
105
102
11113
80
B-2
0222
4900
35
1960
300
264
1237
10550
13657
12663
110
102
11113
113
B-3
0333
4900
35
1960
300
264
1294
10550
14726
13056
114
101
11113
164
C-1
0111
4900
35
1960
300
328
1204
11682
14093
12971
117
108
12611
minus45
C-2
0222
4900
35
1960
300
328
1300
11682
15138
13525
116
104
12611
31
C-3
0333
4900
35
1960
300
328
1400
11682
16198
14059
116
100
12611
110
D-1
0111
4900
35
1960
300
401601
12956
15780
15021
099
094
14305
119
D-2
0222
4900
35
1960
300
401742
12956
16822
16554
097
095
14305
218
D-3
0333
4900
35
1960
300
401815
12956
17878
17976
099
099
14305
269
Advances in Civil Engineering 5
en η was obtained as 065 by experimentation andstatistical data [29] so the ultimate capacity of the steel tubecan be calculated by
Ns nfsAs (14)
Lastly the ultimate capacity of CFRP-confined CFSTcolumn can be expressed as follows
N2y ηfsAs + fck + kcp( 1113857Ac (15)
5 Comparison and Analysis
e three types of CFRP-confined CFST stub columnsshown in Figure 1 have been tested under axial compression[13 30 31] Calculations N1
y and N2y obtained by Unified
eory of CFST and limit equilibrium theory respectivelyare listed in Table 1 together with the test results Nt ecalculated results both have good agreement with the testresults within small errors less than 20 Comparing thevalue of N2
yNt and N1yNt shown in Table 1 we can find that
N2y obtained by the limit equilibrium method is more ac-
curate and reliable than N1y obtained by the method of
Unified eory of CFST On the other hand the method ofUnified eory of CFST is simple and easy to realize since itjust considers the column as one composite material whilethe method of limit equilibrium method sound complicatedsince it applies TSUST to analyze every component of thecomposite column erefore these two methods can bothbe applied to investigate the axial bearing capacity of CFRP-confined CFSTstub columns and they can provide referencefor engineering design en axial bearing capacity of pureCFST columns can be predicted by the limit equilibriummethod in order to evaluate the bearing capacity im-provement due to the CFRP confinement By reviewing testresults the bearing capacity enhancement rate is describedas the expression of (Nt-NCFST)NCFSTas shown in Table 1 Itwas found that the averaged bearing capacity enhancement
rate of CFRP-confined CFSTstub columns is 164 percent incomparison with the pure CFSTcolumns Because the CFRPsheet is very thin it is demonstrated that the bearing capacityof the composite columns improves more than the corre-sponding pure CFST columns with the nearly same crosssection area erefore it is very applicable to use CFRP tostrengthen the CFST column and the composite columnscan result in significant savings in column size which ul-timately realize the material potency and bring economicbenefits
rough data analysis of the calculated and experi-mental results it can be found that concrete strength andthe relative proportions of CFRP and steel are the mainparameters to influence the axial bearing capacity of thecomposite column e confining mechanism of CFRP andaxial bearing capacity improvement needs to be validatedso the relative proportions of CFRP and steel is proposedaccording to the concept of equivalent confinement co-efficient ξssc (1) e relative proportions of CFRP and steelξcf st considers strength content and confining effect ofsection form that is
ξcfst kcfAcffcf
ksAsfs (16)
Since the test results of the bearing capacity of the stubcolumns have a certain degree of dispersion and someparameters need to be taken as the same value the calculatedaxial bearing capacity Ncc is used to describe the bearingcapacity enhancement ratio with the expression of (Ncc-NCFST)NCFST which reflects the function of the CFRPcylinder to confine the CFST column where NCFST is thecalculated value for the corresponding pure CFST columnNcc is obtained by limit equilibrium theory
e relationship between (NccminusNCFST)NCFST and ξcf stfor the three types of composite columns is shown inFigure 3 In reference to the experimental data in Table 1fck of Type b and Type c is taken as 4015MPa similar toType a and Figure 3(a) shows the relationship between
0
005
01
015
02
025
0 01 02 03 04 05 06
Outer circular CFRPOuter square CFRPInner circular CFRP
(Ncc-N
CFST
)N
CFST
ξcfst
(a)
0
005
01
015
02
025
03
035
0 01 02 03 04 05 06
fck = 223fck = 264
fck = 328fck = 40
ξcfst
(Ncc-N
CFST
)N
CFST
(b)
Figure 3 Relationship between (NccminusNCFST)NCFST and ξcfst (a) fck 4015 (b) Different fck
6 Advances in Civil Engineering
(NccminusNCFST)NCFST and ξcf st under the same concretestrength e relationship is linear and directly pro-portional to the CFRP-wrapped composite columns withthe outer circular CFRP or outer square CFRP because theouter CFRP cylinder strengthens the whole CFST columnBut for the inner circular CFRP-confined columns there isno linear proportion because inner CFRP only strengthensits inside concrete directly It can also be found that outercircular CFRP has the best confinement effect to providethe highest bearing capacity enhancement ratio at the samerelative proportions of CFRP and steel Meanwhile outersquare CFRP does better than inner circular CFRP asshown in Figure 3(a) that is CFRP as external jackets canprovide the better confinement than the internal one Onthe other hand we choose the basic parameters of outersquare CFRP-confined CFST columns in Table 1 to get therelationship between (NccminusNCFST)NCFST and ξcf st underdifferent concrete strength as shown in Figure 3(b) Forevery group the steel tube and the concrete are the same sothe bearing capacity enhancement ratio is linear and directproportional to the content of the CFRP cylinder Amongthe four groups with the decrease of concrete strength thebearing capacity enhancement ratio increases with theimprovement of relative proportions of CFRP and steel Itindicates that the confinement effect of CFRP increaseswith the decrease of concrete strengthe reason is mainlythat the contributions of the CFRP cylinder are the dis-placement resistance of the CFSTcolumn and low-strengthconcrete has the better deformation capacity to make theCFRP play better especially during the postbucklingprocess
6 Conclusions
is paper presented a comparative study of concrete-filledsteel tubular (CFST) stub columns with three differentconfinement types from carbon fiber reinforced polymer(CFRP) outer circular CFRP inner circular CFRP and outersquare CFRP CFRP-confined CFST column takes the ad-vantage of not only the good performance of CFST but alsoa substantial improvement in higher confinement of CFRPe compressive mechanism and physical properties ofthe composite column were analyzed firstly aiming at in-vestigating the confinement effects of the different CFRP onCFST Columns
Two methods based on Unified eory of CFST andelastoplastic limit equilibrium method have been applied toinvestigate the axial bearing capacity of CFRP-confinedCFST stub columns e calculated results have goodagreement with the test results rough data analysis thestudy confirmed the ultimate strength calculation results oflimit equilibrium method were found to be more accurateand reliable than that of Unifiedeory of CFST en axialbearing capacity of pure CFST columns was predicted toevaluate the bearing capacity improvement factor comingfrom the CFRP confinement It was demonstrated that theaveraged enhancement ratio is 164 percent showing thatthe three kinds of CFRP-confined CFST columns hada broad applicability
CFRP can increase CFST membersrsquo bearing capacitiessignificantly because complementary action between thesteel tube and concrete is strengthened through CFRP erelationship between the bearing capacity enhancementratio and relative proportions of CFRP and steel is nearlylinear especially for the CFRP-wrapped columns with theouter circular CFRP or outer square CFRP rougha comparative analysis this study confirmed that outercircular CFRP had the best confinement effect and outersquare CFRP did better than inner circular CFRP econfinement effect of CFRP increased with the decrease ofconcrete strength and it was proportional with relativeproportions of CFRP and CFST under the same concretestrength
Data Availability
All data used for this paper are publicly available and ac-cessible online We have annotated the entire data buildingprocess and empirical techniques presented in the paper Wehave given formal citations in article references While wedid not directly draw upon these sources for the empiricalanalysis these efforts confirmed our understanding of thescope scale and accuracy of the CFRP-confined CFSTcolumns
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to acknowledge the support providedby the Chinese National Science Foundation (Grant no51478004) Meanwhile the financial support from HebeiUniversity of Technology is also appreciated
References
[1] O Chaalal and M Shahawy ldquoPerformance of fiber-reinforcedpolymer wrapped reinforced concrete column under com-bined axial flexural loadingrdquo ACI Structure Journal vol 97no 4 pp 659ndash668 2000
[2] Y Xiao ldquoApplications of FRP composites in concrete col-umnsrdquo Advances in Structural Engineering vol 7 no 4pp 335ndash343 2004
[3] J G Teng Y L Huang L Lam and L P Ye ldquoeoreticalmodel for fiber reinforced polymer-confined concreterdquoJournal of Composites for Construction vol 11 no 2pp 201ndash210 2007
[4] J G Teng T Jiang L Lam and Y Z Luo ldquoRefinement ofa design-oriented stress-strain model for FRP-confinedconcreterdquo Journal of Composites for Construction vol 13no 4 pp 269ndash278 2009
[5] Y Zheng L F Zhang and L P Xia ldquoInvestigation of thebehaviour of flexible and ductile ECC link slab reinforced withFRPrdquo Construction and Building Materials vol 166pp 694ndash711 2018
[6] Y Zheng and L P Xia ldquoInvestigation of the ultimate capacityof NSM FRP-strengthened concrete bridge deck slabsrdquoArabian Journal of Science and Engineering vol 43pp 1597ndash1615 2018
Advances in Civil Engineering 7
[7] Z F Amir and H R Sami ldquoConfinement model for axiallyloaded concrete confined by circular FRP tubesrdquo ACIStructure Journal vol 98 no 4 pp 451ndash461 2001
[8] L H Han Concrete-Filled Steel Tube Structures-+eory andDesign Science Press Beijing China 2nd edition 2007
[9] B C Chen and T L Wang ldquoOverview of concrete filled steeltube arch bridges in Chinardquo Practice Periodical on StructuralDesign and Construction vol 14 no 2 pp 70ndash80 2009
[10] Y Che Q L Wang and Y B Shao ldquoCompressive perfor-mances of the concrete filled circular CFRP-steel tube (C-CFRP-CFST)rdquo International Journal of Advanced SteelConstruction vol 8 no 4 pp 311ndash338 2012
[11] Z Tao L H Han and L L Wang ldquoCompressive and flexuralbehaviour of CFRP repaired concrete-filled steel tubes afterexposure to firerdquo Journal of Constructional Steel Researchvol 63 no 8 pp 1116ndash1126 2007
[12] W Gu ldquoStudy on mechanics of concrete-filled CFRP-steeltube columnrdquo esis for doctor degree DaLian MaritimeUniversity Dalian China 2007
[13] G C Li L Ma and J L Yang ldquoBearing capacity of shortcolumns of high-strength concrete filled square steel tubularwith inner CFRP circular tubular under axially compressiveloadrdquo Journal of Shenyang Jianzhu University vol 24 no 1pp 62ndash66 2008
[14] Q L Wang G Y Wang and F Han ldquoExperimental study onconcentrically compressed stub columns reinforced by con-crete filled CFRP-steel tuberdquo in 4th International Conferenceon Advances in Steel Structures Elsevier Science Ltd pp671ndash676 London UK 2005
[15] Z Tao L H Han and J P Zhuang ldquoUsing CFRP tostrengthen concrete-filled steel tubular columns stub columntestsrdquo in 4th International Conference on Advances in SteelStructures Elsevier Science Ltd pp 701ndash706 London UK2005
[16] Q L Wang S E Qu Y B Shao and L M Feng ldquoStaticbehavior of axially compressed circular concrete filled cfrp-steel tubular (c-cf-cfrp-st) columns with moderate slender-ness ratiordquo Advanced Steel Construction vol 12 no 3pp 263ndash295 2016
[17] Q L Wang Z Zhao Y B Shao and Q L Li ldquoStatic behaviorof axially compressed square concrete filled CFRP-steel tu-bular (S-CF-CFRP-ST) columns with moderate slendernessrdquo+in-Walled Structures vol 110 pp 106ndash122 2017
[18] K Karimi M J Tait and W W EI-Dakhakhni ldquoTesting andmodeling of a novel FRP-encased steel-concrete composite col-umnrdquo Composite Structures vol 93 no 5 pp 1463ndash1473 2011
[19] P Feng S Cheng Y Bai et al ldquoMechanical behavior ofconcrete-filled square steel tube with FRP-confined concretecore subjected to axial compressionrdquo Composite Structuresvol 123 no 5 pp 312ndash324 2015
[20] S T Zhong Unified +eory of Concrete Filled Steel TubularStructure Tsinghua University Press Beijing China 2006
[21] M H Yu Unified Strength +eory and Its ApplicationsSpringer Press Berlin Heidelberg Germany 2004
[22] F E Richart A Brandtzaeg and R L Brown ldquoA study of thefailure of concrete under combined compressive stressesrdquoBulletin No 185 Engineering Experimental Station Uni-versity of Illinois Urbana IL USA 1928
[23] Q L Wang W Gu and Y H Zhao ldquoExperimental study onconcentrically compressed concrete filled circular CFRP-steelcomposite tubular stub columnsrdquo China Civil EngineeringJournal vol 38 no 10 pp 44ndash48 2005
[24] A H Varma R Sause and J M Ricles ldquoDevelopment andvalidation of fiber model for high strength square concrete
filled steel tube beam-columnrdquo ACI Structural Journalvol 102 no 1 pp 73ndash84 2005
[25] S T Zhong ldquoNew concept and development of research onconcrete-filled steel tube (CFST)rdquo in Proceeding of 2nd In-ternational Symposium on Civil Infrastructure Systemspp 9ndash12 Hong Kong December 1996
[26] Y F Zhang and Z Q Zhang ldquoStudy on equivalent con-finement coefficient of composite CFST column based onunified theoryrdquo Mechanics of Advanced Materials andStructures vol 23 no 1 pp 22ndash27 2016
[27] H T Chen ldquoeoretical study on continuity of basic behaviorof every-sectioned CFT stub columns under axial loadsrdquoesis for doctor degree Harbin Institute of TechnologyHarbin China 2001
[28] X W Li and J H Zhao ldquoMechanics behavior of axial loadedshort columns with concrete-filled square steel tuberdquo ChineseJournal of Highway and Transport vol 19 no 4 pp 77ndash812006
[29] Y F Zhang J H Zhao and W F Yuan ldquoStudy on com-pressive bearing capacity of concrete filled square steel tubecolumn reinforced by circular steel tube insiderdquo Journal ofCivil Engineering and Management vol 19 no 6 pp 787ndash795 2013
[30] W Gu and H N Li ldquoResearch in the properties of theconcrete filled steel tube columns with CFRP compositematerialsrdquo Advanced Materials Research vol 163-167pp 3555ndash3559 2011
[31] Q L Wang and Y B Shao ldquoCompressive performances ofconcrete filled square CFRP-steel tubes (S-CFRP-CFST)rdquoSteel and Composite Structures vol 16 no 5 pp 455ndash4802014
8 Advances in Civil Engineering
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increasing number of CFRP layers Meanwhile the ductilityof specimens increased slightly with the number of CFRPlayers And as discussed by Tao et al [15] the CFRP cylindercan also impede buckling of the stub column leading todramatic improvements in buckling and postbuckling be-havior of the entire system Wang et al [16 17] conductedaxial compression experiments for thirty-two circular CFRP-confined CFST columns and twenty-four square CFRP-confined CFST columns Analyses of the tested resultsshow that the steel tube and its outer CFRP material cancooperate both longitudinally and transversely erefore allthese studies draw upon the concepts that complementaryaction between steel tube and concrete was strengthenedthrough the higher confinement of CFRP
Upon the abovementioned research other types ofcomposite columns have also been proposed Karimi et al[18] proposed a type of FRP-encased steel-concrete com-posite columns in which a circular FRP was placed aroundthe steel I-section and had the concrete filled between thesteel I-section and the FRP tube Feng et al [19] proposeda steel-concrete-FRP-concrete column which had a squaresteel tube as the outer layer and a circular filament-woundFRP tube as the inner layer with concrete filled both be-tween these two layers and within the FRP tube e resultsof these studies showed that the strength of concrete FRPand steel could be effectively utilized in the compositecolumns
All those research achievements confirmed that thecomposite column has its feasibility in theoretical researchand engineering practice showing a great potential for moredevelopment Compressive strength is an important pa-rameter for structural members and most of those researcheslisted above were concentrated on the superposition methodto calculate the ultimate compressive strength so differentformulas were deduced for every cross section of the CFRP-confined CFSTcolumns erefore the purpose of this paperis to build unified methods applicative to different sections ofthe composite column by the idea of Unifiedeory of CFSTand limit equilibrium theory e focus of this study is toinvestigate three different technology CFRPs to strengthenCFST stub columns through a comparative study of threedifferent confinement types outer circular CFRP inner cir-cular CFRP and outer square CFRP Compressive mecha-nism and physical properties of these three CFRP-confinedCFST columns were analyzed firstly aiming at investigatingthe confinement effect of CFRP on CFST columns Twotheoretical calculation models are presented to obtain theaxial compressive capacity of CFRP-confined CFST columnsOne is the Unified eory of CFST [20] the equivalentconfinement coefficient is proposed with consideration ofdifferent sections of steel tubes and CFRP cylinders and thenformulas are derived from Unifiedeory of CFST to predictthe bearing capacity of the composite column under com-pression e other is elastoplastic limit equilibrium methodtwin-shear unified strength theory (TDUST) [21] is applied toanalyze the ultimate state of steel tube and concrete re-spectively and then the ultimate bearing capacities of thecomposite column are obtained by the limit equilibriummethod e theoretical predictions were compared with the
experimental results to validate the feasibility of the twocalculation models Lastly the CFRP confinement effects onthe axial bearing capacity were analyzed by comparison ofthese three CFRP-confined CFST columns
2 Working Mechanism
Based on the summary of existing researches three types ofCFRP-confined CFSTcolumns are considered with differentCFRP confinements including outer circular CFRP innercircular CFRP and outer square CFRP as shown in Figure 1e CFRP cylinder is wrapped outside the circular CFSTcolumn in Type a CFRP cylinder is placed inside the squareCFST in Type b and CFRP cylinder is wrapped outside thesquare CFST column in Type c As can be seen in Figure 1steel tubes together with the confined concrete can resist theaxial compression remarkably while the CFRP cylinders canprovide the lateral confinement to the steel tube or concretedirectly and make the composite column behave betterindirectly
As we all know during the process of compression of thecomposite columns there exists horizontal deformationwhen the vertical load acts on the whole section Take theexample of Type a in Figure 1 concrete is filled in the circulartube wrapped by the CFRP sheet so its simplified model ofstress can be plotted in Figure 2
Concretersquos horizontal deformation coefficient was smallat the beginning of the axial load so the lateral stress p fromsteel tubes and CFRP sheet is not evident With the in-creasing axial compression concretersquos horizontal de-formation starts to gradually increase especially after thecolumn yielding ere would be many microcracks hap-pened in concrete after the column entered into plasticstage [22] but both the CFRP cylinder and steel tube canconfine the concrete to postpone its expansion e con-crete can be regarded as three-dimensioned compressedthe steel tubes can be regarded as thin-walled cylinders andCFRP is only tensile in the circumferential direction asshown in Figure 2 e ultimate state considers the fol-lowing failure modes of the CFRP-confined CFST columnsteel tube bucking and CFRP sheet rupturing [23 24]Although the CFRP cylinder has no direct contribution tothe axial bearing capacity the transverse fiber sheetscontribute to the strength enhancement by confining theCFST column in whole (see Type a c in Figure 1) or in part(see Type b in Figure 1) leading to a higher compressivestrength of the column erefore the wrapping CFRP canlead to a significant improvement in the inelastic axialdeformation capacity prior to buckling and an improvedload carrying capacity after buckling
3 Calculations by Unified Theory of CFST
Unified eory of CFST was presented by Professor ZhongShan-tong in 1993 [25] It considered CFST as a unifiedbody and a new composite material was used to study itsbehaviors It was a new method to design and simplify thedesign work Unified eory of CFST has been extended tocalculate the compressive strength of the composite CFST
2 Advances in Civil Engineering
columns with various confining materials and various crosssections under various loadings [26] For CFRP-confinedCFSTcolumns the concrete is still confined by the steel tubedirectly and this confining effect is absolutely strengthenedby the CFRP cylinder One composite material can also beconsidered to assess its behaviors but the confining effectshould be reevaluated deriving from the steel tube and CFRPcylinder We can extend deeper research works into CFRP-confined CFST columns so one equivalent confinementcoefficient ξssc is presented which can be expressed as
ξssc ksAsfs + kcfAcffcf
Acfck (1)
where As Ac and Acf are the cross section areas of the steeltube concrete and CFRP cylinder respectively fs and fcfare the yield strengths of steel and CFRP respectively fck isthe standard compressive strength of the concrete ks and kcfare the coefficients with consideration of section form of theconfining material Because in the composite column thereare two difform materials to confine concrete the effect ofrestraint is different from circular section to square sectionGenerally the coefficient of circular section is taken as thebasic parameter 1 and for square section it is 074 [27]
en the composite strength fssc of the stub column canbe calculated by the formula derived from Unifiedeory ofCFST and the equation can be expressed as
fssc 1212 + aξssc + bξ2ssc1113872 1113873fck (2)
where a and b reflect the contributions of confining ma-terials and concrete respectively ey can be calculated bythe following formula
a 01759fss
235 + 0974
b minus01038fck
20 + 00309
(3)
where fss is the weighted average of the confining materialsincluding both the steel tube and CFRP cylinder which iscalculated by
fss Asfs + Acffcf
As + Acf (4)
erefore it is recommended to use the following for-mula to calculate the bearing capacity of the CFRP-confinedCFST stub column
N1y Afssck (5)
where A is the cross section area of the whole column andN1
y is the bearing capacity calculated by Unified eory ofCFST
4 Calculations by Limit Equilibrium Theory
41 Basic Assumptions In this theoretical model forobtaining the axial compressive capacity we can quantita-tively analyze how much the confinement is influenced bythe steel tube and CFRPe interface between the steel tubeand the CFRP sheet is constrained the radial stress in thesteel tube is ignored and the steel tube is under biaxial stressthe CFRP material is linear elastic and only the lateral stressis considered so the stress along the fiber direction is
Steel tube
Concrete
CFRP cylinder
(a)
Steel tube
Concrete
Concrete
CFRP cylinder
(b)
CFRP cylinder
Concrete
Steel tube
(c)
Figure 1 Cross section types of CFRP-confined CFSTcolumns (a) Outer circular CFRP (b) Inner circular CFRP (c) Outer square CFRP
p
σf
pσf
Figure 2 Stress model in the composite column under compression (a) Concrete (b) Steel tube (c) CFRP cylinder
Advances in Civil Engineering 3
considered the radial stress and the longitudinal stress areignored
Based on the above assumptions the ultimate axialbearing capacity of CFRP-confined CFST columns can becalculated by
N2y Ns + Nc (6)
where N Ns and Nc are vertical bearing capacities of thesteel tube and concrete respectively N2
y is the bearing ca-pacity calculated by limit equilibrium theory In the state oflimit equilibrium every part of the composite column can beanalyzed using TSUST [21]
42 Twin-Shear Unified Strength +eory (TSUST) eTSUST considers the two larger principal shear stresses andthe corresponding normal stresses and their different effectson the failure of materials When the relationship functionbetween them reaches one ultimate value the material canbe defined as failure at this state which is formulated asfollows
F τ13 + bτ12 + β σ13 + bσ12( 1113857 C
when τ12 + βσ12 ge τ23 + βσ23(7a)
Fprime τ13 + bτ23 + β σ13 + bσ23( 1113857 C
when τ12 + βσ12 le τ23 + βσ23(7b)
where τ12 τ23 and τ13 are the principal shear stressesτ13 (σ1 minus σ3)2 τ12 (σ1 minus σ2)2 and τ23 (σ2 minus σ3)2σ12 σ23 and σ13 are the corresponding normal stresses onthe principal shear stress element σ1 σ2 and σ3 are theprincipal stresses σ1 ge σ2 ge σ3 b is a weighting coefficientreflecting the relative effect of the intermediate principalshear stress τ12 or τ23 on the strength of materials Cequals to the material strength β is the influence co-efficient of positive stress on material damage Denotingthe tension-compression strength ratio as α σtσc werewrite (7a) and (7b) in terms of principal stresses asfollows
F σ1 minusα
1 + bbσ2 + σ3( 1113857 σt when σ2 le
σ1 + ασ31 + α
(8a)
Fprime 1
1 + bσ1 + bσ2( 1113857minus ασ3 σt when σ2 ge
σ1 + ασ31 + α
(8b)
43 Formula of Ultimate Capacity By the principle of samearea the square cross section of the steel tube can betransformed into a circular one B and ts are the side lengthand thickness of the square steel tube and ro and to are theradius and thickness of the equivalent circular steel tuberespectively e formulas are shown as follows
ro Bπ
radic 05642B
to ro minus Bminus 2ts( 1113857
π
radic ro minus 05642 Bminus 2ts( 1113857
(9)
Meanwhile because the confinement of the square steelis uneven along its side the equivalent reduction factorshould be considered to reduce the same confinement of theequivalent circular steel tube Denoting thickness-sidelength ratio υ tB the expression of the equivalent re-duction factor ξ 664741υ2 + 09919υ + 041618 [28]Meanwhile there are effective and noneffective confiningzones of the concrete inside the square steel tube In thispaper the concrete strength reduction factor is considered toignore these two influences e concrete strength reductionfactor is taken as cμ 167Dminus0112
o [28] whereDo is the insidediameter of the equivalent circular steel tube
e simplified stress model of confined concrete isshown in Figure 2(a) e stresses can be explicated by0gt σ1 σ2 gt σ3 σ1 σ2 p For σ2 ge ((σ1 + ασ3)(1 + α))Substituting them into the stress expression of TSUST thefollowing expression can be obtained as
σ3 σc fck + kcp (10)
where kc is the lateral stress coefficient In TSUST kc can becalculated by cohesion and friction angle at material failurestate According to the test of Richart [22] kc has been takenas 41 simply here p is the lateral stress on the concrete andthe lateral stress on concrete is from both the steel tube andCFRP cylinder for Type a and c as shown in Figure 1 so itcan be expressed by
p σf + σrs (11)
where σf tcffcf rcf and σrs tsfsrs tcf and rcf are thethickness and radius of the CFRP cylinder respectively tsand rs are the thickness and radius of the steel tube re-spectively While for Type b in Figure 1 the concrete shouldbe divided into exterior concrete and internal concreteunder different lateral stresses Exterior concrete is onlyconfined by the steel tube but internal concrete is consid-ered both the steel tube and CFRP cylinder en the axialbearing capacity of the concrete can be expressed as
Nc fck + kcp( 1113857Ac (12)
As can be seen in Figure 2(b) the steel tube is con-strained by inside concrete so it can bear some vertical loadunder the ultimate state of the whole column η is assumedas the strength reduction factor of the steel tube and thenthe stress state of steel tubes can be explicated byσ3 σz ηfs σ2 σr 0 σ1 σθ prots For |σ3|gt σ1and σ2 ge ((σ1 + σ3)(1 + α)) substitute them into the stressexpression of TSUST the following expression can beobtained
pro
ts(1 + b)minus ηfs fs (13)
4 Advances in Civil Engineering
Tabl
e1
Com
parisonof
calculations
andtest
results
Types
Specim
ens
t cf
(mm)
fcf
(MPa
)t s
(mm)
As
(mm
2 )fs
(MPa
)fck
(MPa
)N
t(kN)
N0
(kN)
N1 y
(kN)
N2 y
(kN)
N1 y
Nt
N2 y
Nt
NCFS
T(kN)
Ntminus
NCFS
TN
CFS
T(
)Sources
a
1ndash25
017
1260
25
10132
350
4015
1294
8592
11765
12937
092
100
10605
220
[30]
1ndash35
017
1260
35
14404
310
4015
1348
9591
12854
14080
095
104
11755
147
1ndash45
017
1260
45
18802
310
4015
1698
11036
14462
15756
085
093
13417
260
2ndash25
034
1260
25
10132
350
4015
1506
8592
12933
14309
086
095
10605
420
2ndash35
034
1260
35
14404
310
4015
1593
9591
13950
15401
086
097
11755
355
2ndash45
034
1260
45
18802
310
4015
1846
11036
15054
17020
082
092
13417
376
b
SC41
0167
1500
42400
295
536
2215
18505
21758
23411
098
106
20901
59
[13]
SC42
0334
1500
42400
295
536
2275
18505
22613
24437
099
107
20901
88
SC51
0167
1500
53000
295
536
2485
20119
23264
24778
094
099
22440
107
SC52
0334
1500
53000
295
536
2585
20119
24079
23567
093
091
22440
152
SC61
0167
1500
63600
295
536
2710
21734
24728
28011
091
103
23943
132
SC62
0334
1500
63600
295
536
2775
21734
25500
26773
092
096
23943
159
c
A-1
0111
4900
35
1960
300
223
1107
9825
11663
11107
105
100
10159
90
[31]
A-2
0222
4900
35
1960
300
223
1129
9825
12723
11926
113
106
10159
111
A-3
0333
4900
35
1960
300
223
1222
9825
13802
12854
113
106
10159
203
B-1
0111
4900
35
1960
300
264
1200
10550
12605
12285
105
102
11113
80
B-2
0222
4900
35
1960
300
264
1237
10550
13657
12663
110
102
11113
113
B-3
0333
4900
35
1960
300
264
1294
10550
14726
13056
114
101
11113
164
C-1
0111
4900
35
1960
300
328
1204
11682
14093
12971
117
108
12611
minus45
C-2
0222
4900
35
1960
300
328
1300
11682
15138
13525
116
104
12611
31
C-3
0333
4900
35
1960
300
328
1400
11682
16198
14059
116
100
12611
110
D-1
0111
4900
35
1960
300
401601
12956
15780
15021
099
094
14305
119
D-2
0222
4900
35
1960
300
401742
12956
16822
16554
097
095
14305
218
D-3
0333
4900
35
1960
300
401815
12956
17878
17976
099
099
14305
269
Advances in Civil Engineering 5
en η was obtained as 065 by experimentation andstatistical data [29] so the ultimate capacity of the steel tubecan be calculated by
Ns nfsAs (14)
Lastly the ultimate capacity of CFRP-confined CFSTcolumn can be expressed as follows
N2y ηfsAs + fck + kcp( 1113857Ac (15)
5 Comparison and Analysis
e three types of CFRP-confined CFST stub columnsshown in Figure 1 have been tested under axial compression[13 30 31] Calculations N1
y and N2y obtained by Unified
eory of CFST and limit equilibrium theory respectivelyare listed in Table 1 together with the test results Nt ecalculated results both have good agreement with the testresults within small errors less than 20 Comparing thevalue of N2
yNt and N1yNt shown in Table 1 we can find that
N2y obtained by the limit equilibrium method is more ac-
curate and reliable than N1y obtained by the method of
Unified eory of CFST On the other hand the method ofUnified eory of CFST is simple and easy to realize since itjust considers the column as one composite material whilethe method of limit equilibrium method sound complicatedsince it applies TSUST to analyze every component of thecomposite column erefore these two methods can bothbe applied to investigate the axial bearing capacity of CFRP-confined CFSTstub columns and they can provide referencefor engineering design en axial bearing capacity of pureCFST columns can be predicted by the limit equilibriummethod in order to evaluate the bearing capacity im-provement due to the CFRP confinement By reviewing testresults the bearing capacity enhancement rate is describedas the expression of (Nt-NCFST)NCFSTas shown in Table 1 Itwas found that the averaged bearing capacity enhancement
rate of CFRP-confined CFSTstub columns is 164 percent incomparison with the pure CFSTcolumns Because the CFRPsheet is very thin it is demonstrated that the bearing capacityof the composite columns improves more than the corre-sponding pure CFST columns with the nearly same crosssection area erefore it is very applicable to use CFRP tostrengthen the CFST column and the composite columnscan result in significant savings in column size which ul-timately realize the material potency and bring economicbenefits
rough data analysis of the calculated and experi-mental results it can be found that concrete strength andthe relative proportions of CFRP and steel are the mainparameters to influence the axial bearing capacity of thecomposite column e confining mechanism of CFRP andaxial bearing capacity improvement needs to be validatedso the relative proportions of CFRP and steel is proposedaccording to the concept of equivalent confinement co-efficient ξssc (1) e relative proportions of CFRP and steelξcf st considers strength content and confining effect ofsection form that is
ξcfst kcfAcffcf
ksAsfs (16)
Since the test results of the bearing capacity of the stubcolumns have a certain degree of dispersion and someparameters need to be taken as the same value the calculatedaxial bearing capacity Ncc is used to describe the bearingcapacity enhancement ratio with the expression of (Ncc-NCFST)NCFST which reflects the function of the CFRPcylinder to confine the CFST column where NCFST is thecalculated value for the corresponding pure CFST columnNcc is obtained by limit equilibrium theory
e relationship between (NccminusNCFST)NCFST and ξcf stfor the three types of composite columns is shown inFigure 3 In reference to the experimental data in Table 1fck of Type b and Type c is taken as 4015MPa similar toType a and Figure 3(a) shows the relationship between
0
005
01
015
02
025
0 01 02 03 04 05 06
Outer circular CFRPOuter square CFRPInner circular CFRP
(Ncc-N
CFST
)N
CFST
ξcfst
(a)
0
005
01
015
02
025
03
035
0 01 02 03 04 05 06
fck = 223fck = 264
fck = 328fck = 40
ξcfst
(Ncc-N
CFST
)N
CFST
(b)
Figure 3 Relationship between (NccminusNCFST)NCFST and ξcfst (a) fck 4015 (b) Different fck
6 Advances in Civil Engineering
(NccminusNCFST)NCFST and ξcf st under the same concretestrength e relationship is linear and directly pro-portional to the CFRP-wrapped composite columns withthe outer circular CFRP or outer square CFRP because theouter CFRP cylinder strengthens the whole CFST columnBut for the inner circular CFRP-confined columns there isno linear proportion because inner CFRP only strengthensits inside concrete directly It can also be found that outercircular CFRP has the best confinement effect to providethe highest bearing capacity enhancement ratio at the samerelative proportions of CFRP and steel Meanwhile outersquare CFRP does better than inner circular CFRP asshown in Figure 3(a) that is CFRP as external jackets canprovide the better confinement than the internal one Onthe other hand we choose the basic parameters of outersquare CFRP-confined CFST columns in Table 1 to get therelationship between (NccminusNCFST)NCFST and ξcf st underdifferent concrete strength as shown in Figure 3(b) Forevery group the steel tube and the concrete are the same sothe bearing capacity enhancement ratio is linear and directproportional to the content of the CFRP cylinder Amongthe four groups with the decrease of concrete strength thebearing capacity enhancement ratio increases with theimprovement of relative proportions of CFRP and steel Itindicates that the confinement effect of CFRP increaseswith the decrease of concrete strengthe reason is mainlythat the contributions of the CFRP cylinder are the dis-placement resistance of the CFSTcolumn and low-strengthconcrete has the better deformation capacity to make theCFRP play better especially during the postbucklingprocess
6 Conclusions
is paper presented a comparative study of concrete-filledsteel tubular (CFST) stub columns with three differentconfinement types from carbon fiber reinforced polymer(CFRP) outer circular CFRP inner circular CFRP and outersquare CFRP CFRP-confined CFST column takes the ad-vantage of not only the good performance of CFST but alsoa substantial improvement in higher confinement of CFRPe compressive mechanism and physical properties ofthe composite column were analyzed firstly aiming at in-vestigating the confinement effects of the different CFRP onCFST Columns
Two methods based on Unified eory of CFST andelastoplastic limit equilibrium method have been applied toinvestigate the axial bearing capacity of CFRP-confinedCFST stub columns e calculated results have goodagreement with the test results rough data analysis thestudy confirmed the ultimate strength calculation results oflimit equilibrium method were found to be more accurateand reliable than that of Unifiedeory of CFST en axialbearing capacity of pure CFST columns was predicted toevaluate the bearing capacity improvement factor comingfrom the CFRP confinement It was demonstrated that theaveraged enhancement ratio is 164 percent showing thatthe three kinds of CFRP-confined CFST columns hada broad applicability
CFRP can increase CFST membersrsquo bearing capacitiessignificantly because complementary action between thesteel tube and concrete is strengthened through CFRP erelationship between the bearing capacity enhancementratio and relative proportions of CFRP and steel is nearlylinear especially for the CFRP-wrapped columns with theouter circular CFRP or outer square CFRP rougha comparative analysis this study confirmed that outercircular CFRP had the best confinement effect and outersquare CFRP did better than inner circular CFRP econfinement effect of CFRP increased with the decrease ofconcrete strength and it was proportional with relativeproportions of CFRP and CFST under the same concretestrength
Data Availability
All data used for this paper are publicly available and ac-cessible online We have annotated the entire data buildingprocess and empirical techniques presented in the paper Wehave given formal citations in article references While wedid not directly draw upon these sources for the empiricalanalysis these efforts confirmed our understanding of thescope scale and accuracy of the CFRP-confined CFSTcolumns
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to acknowledge the support providedby the Chinese National Science Foundation (Grant no51478004) Meanwhile the financial support from HebeiUniversity of Technology is also appreciated
References
[1] O Chaalal and M Shahawy ldquoPerformance of fiber-reinforcedpolymer wrapped reinforced concrete column under com-bined axial flexural loadingrdquo ACI Structure Journal vol 97no 4 pp 659ndash668 2000
[2] Y Xiao ldquoApplications of FRP composites in concrete col-umnsrdquo Advances in Structural Engineering vol 7 no 4pp 335ndash343 2004
[3] J G Teng Y L Huang L Lam and L P Ye ldquoeoreticalmodel for fiber reinforced polymer-confined concreterdquoJournal of Composites for Construction vol 11 no 2pp 201ndash210 2007
[4] J G Teng T Jiang L Lam and Y Z Luo ldquoRefinement ofa design-oriented stress-strain model for FRP-confinedconcreterdquo Journal of Composites for Construction vol 13no 4 pp 269ndash278 2009
[5] Y Zheng L F Zhang and L P Xia ldquoInvestigation of thebehaviour of flexible and ductile ECC link slab reinforced withFRPrdquo Construction and Building Materials vol 166pp 694ndash711 2018
[6] Y Zheng and L P Xia ldquoInvestigation of the ultimate capacityof NSM FRP-strengthened concrete bridge deck slabsrdquoArabian Journal of Science and Engineering vol 43pp 1597ndash1615 2018
Advances in Civil Engineering 7
[7] Z F Amir and H R Sami ldquoConfinement model for axiallyloaded concrete confined by circular FRP tubesrdquo ACIStructure Journal vol 98 no 4 pp 451ndash461 2001
[8] L H Han Concrete-Filled Steel Tube Structures-+eory andDesign Science Press Beijing China 2nd edition 2007
[9] B C Chen and T L Wang ldquoOverview of concrete filled steeltube arch bridges in Chinardquo Practice Periodical on StructuralDesign and Construction vol 14 no 2 pp 70ndash80 2009
[10] Y Che Q L Wang and Y B Shao ldquoCompressive perfor-mances of the concrete filled circular CFRP-steel tube (C-CFRP-CFST)rdquo International Journal of Advanced SteelConstruction vol 8 no 4 pp 311ndash338 2012
[11] Z Tao L H Han and L L Wang ldquoCompressive and flexuralbehaviour of CFRP repaired concrete-filled steel tubes afterexposure to firerdquo Journal of Constructional Steel Researchvol 63 no 8 pp 1116ndash1126 2007
[12] W Gu ldquoStudy on mechanics of concrete-filled CFRP-steeltube columnrdquo esis for doctor degree DaLian MaritimeUniversity Dalian China 2007
[13] G C Li L Ma and J L Yang ldquoBearing capacity of shortcolumns of high-strength concrete filled square steel tubularwith inner CFRP circular tubular under axially compressiveloadrdquo Journal of Shenyang Jianzhu University vol 24 no 1pp 62ndash66 2008
[14] Q L Wang G Y Wang and F Han ldquoExperimental study onconcentrically compressed stub columns reinforced by con-crete filled CFRP-steel tuberdquo in 4th International Conferenceon Advances in Steel Structures Elsevier Science Ltd pp671ndash676 London UK 2005
[15] Z Tao L H Han and J P Zhuang ldquoUsing CFRP tostrengthen concrete-filled steel tubular columns stub columntestsrdquo in 4th International Conference on Advances in SteelStructures Elsevier Science Ltd pp 701ndash706 London UK2005
[16] Q L Wang S E Qu Y B Shao and L M Feng ldquoStaticbehavior of axially compressed circular concrete filled cfrp-steel tubular (c-cf-cfrp-st) columns with moderate slender-ness ratiordquo Advanced Steel Construction vol 12 no 3pp 263ndash295 2016
[17] Q L Wang Z Zhao Y B Shao and Q L Li ldquoStatic behaviorof axially compressed square concrete filled CFRP-steel tu-bular (S-CF-CFRP-ST) columns with moderate slendernessrdquo+in-Walled Structures vol 110 pp 106ndash122 2017
[18] K Karimi M J Tait and W W EI-Dakhakhni ldquoTesting andmodeling of a novel FRP-encased steel-concrete composite col-umnrdquo Composite Structures vol 93 no 5 pp 1463ndash1473 2011
[19] P Feng S Cheng Y Bai et al ldquoMechanical behavior ofconcrete-filled square steel tube with FRP-confined concretecore subjected to axial compressionrdquo Composite Structuresvol 123 no 5 pp 312ndash324 2015
[20] S T Zhong Unified +eory of Concrete Filled Steel TubularStructure Tsinghua University Press Beijing China 2006
[21] M H Yu Unified Strength +eory and Its ApplicationsSpringer Press Berlin Heidelberg Germany 2004
[22] F E Richart A Brandtzaeg and R L Brown ldquoA study of thefailure of concrete under combined compressive stressesrdquoBulletin No 185 Engineering Experimental Station Uni-versity of Illinois Urbana IL USA 1928
[23] Q L Wang W Gu and Y H Zhao ldquoExperimental study onconcentrically compressed concrete filled circular CFRP-steelcomposite tubular stub columnsrdquo China Civil EngineeringJournal vol 38 no 10 pp 44ndash48 2005
[24] A H Varma R Sause and J M Ricles ldquoDevelopment andvalidation of fiber model for high strength square concrete
filled steel tube beam-columnrdquo ACI Structural Journalvol 102 no 1 pp 73ndash84 2005
[25] S T Zhong ldquoNew concept and development of research onconcrete-filled steel tube (CFST)rdquo in Proceeding of 2nd In-ternational Symposium on Civil Infrastructure Systemspp 9ndash12 Hong Kong December 1996
[26] Y F Zhang and Z Q Zhang ldquoStudy on equivalent con-finement coefficient of composite CFST column based onunified theoryrdquo Mechanics of Advanced Materials andStructures vol 23 no 1 pp 22ndash27 2016
[27] H T Chen ldquoeoretical study on continuity of basic behaviorof every-sectioned CFT stub columns under axial loadsrdquoesis for doctor degree Harbin Institute of TechnologyHarbin China 2001
[28] X W Li and J H Zhao ldquoMechanics behavior of axial loadedshort columns with concrete-filled square steel tuberdquo ChineseJournal of Highway and Transport vol 19 no 4 pp 77ndash812006
[29] Y F Zhang J H Zhao and W F Yuan ldquoStudy on com-pressive bearing capacity of concrete filled square steel tubecolumn reinforced by circular steel tube insiderdquo Journal ofCivil Engineering and Management vol 19 no 6 pp 787ndash795 2013
[30] W Gu and H N Li ldquoResearch in the properties of theconcrete filled steel tube columns with CFRP compositematerialsrdquo Advanced Materials Research vol 163-167pp 3555ndash3559 2011
[31] Q L Wang and Y B Shao ldquoCompressive performances ofconcrete filled square CFRP-steel tubes (S-CFRP-CFST)rdquoSteel and Composite Structures vol 16 no 5 pp 455ndash4802014
8 Advances in Civil Engineering
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columns with various confining materials and various crosssections under various loadings [26] For CFRP-confinedCFSTcolumns the concrete is still confined by the steel tubedirectly and this confining effect is absolutely strengthenedby the CFRP cylinder One composite material can also beconsidered to assess its behaviors but the confining effectshould be reevaluated deriving from the steel tube and CFRPcylinder We can extend deeper research works into CFRP-confined CFST columns so one equivalent confinementcoefficient ξssc is presented which can be expressed as
ξssc ksAsfs + kcfAcffcf
Acfck (1)
where As Ac and Acf are the cross section areas of the steeltube concrete and CFRP cylinder respectively fs and fcfare the yield strengths of steel and CFRP respectively fck isthe standard compressive strength of the concrete ks and kcfare the coefficients with consideration of section form of theconfining material Because in the composite column thereare two difform materials to confine concrete the effect ofrestraint is different from circular section to square sectionGenerally the coefficient of circular section is taken as thebasic parameter 1 and for square section it is 074 [27]
en the composite strength fssc of the stub column canbe calculated by the formula derived from Unifiedeory ofCFST and the equation can be expressed as
fssc 1212 + aξssc + bξ2ssc1113872 1113873fck (2)
where a and b reflect the contributions of confining ma-terials and concrete respectively ey can be calculated bythe following formula
a 01759fss
235 + 0974
b minus01038fck
20 + 00309
(3)
where fss is the weighted average of the confining materialsincluding both the steel tube and CFRP cylinder which iscalculated by
fss Asfs + Acffcf
As + Acf (4)
erefore it is recommended to use the following for-mula to calculate the bearing capacity of the CFRP-confinedCFST stub column
N1y Afssck (5)
where A is the cross section area of the whole column andN1
y is the bearing capacity calculated by Unified eory ofCFST
4 Calculations by Limit Equilibrium Theory
41 Basic Assumptions In this theoretical model forobtaining the axial compressive capacity we can quantita-tively analyze how much the confinement is influenced bythe steel tube and CFRPe interface between the steel tubeand the CFRP sheet is constrained the radial stress in thesteel tube is ignored and the steel tube is under biaxial stressthe CFRP material is linear elastic and only the lateral stressis considered so the stress along the fiber direction is
Steel tube
Concrete
CFRP cylinder
(a)
Steel tube
Concrete
Concrete
CFRP cylinder
(b)
CFRP cylinder
Concrete
Steel tube
(c)
Figure 1 Cross section types of CFRP-confined CFSTcolumns (a) Outer circular CFRP (b) Inner circular CFRP (c) Outer square CFRP
p
σf
pσf
Figure 2 Stress model in the composite column under compression (a) Concrete (b) Steel tube (c) CFRP cylinder
Advances in Civil Engineering 3
considered the radial stress and the longitudinal stress areignored
Based on the above assumptions the ultimate axialbearing capacity of CFRP-confined CFST columns can becalculated by
N2y Ns + Nc (6)
where N Ns and Nc are vertical bearing capacities of thesteel tube and concrete respectively N2
y is the bearing ca-pacity calculated by limit equilibrium theory In the state oflimit equilibrium every part of the composite column can beanalyzed using TSUST [21]
42 Twin-Shear Unified Strength +eory (TSUST) eTSUST considers the two larger principal shear stresses andthe corresponding normal stresses and their different effectson the failure of materials When the relationship functionbetween them reaches one ultimate value the material canbe defined as failure at this state which is formulated asfollows
F τ13 + bτ12 + β σ13 + bσ12( 1113857 C
when τ12 + βσ12 ge τ23 + βσ23(7a)
Fprime τ13 + bτ23 + β σ13 + bσ23( 1113857 C
when τ12 + βσ12 le τ23 + βσ23(7b)
where τ12 τ23 and τ13 are the principal shear stressesτ13 (σ1 minus σ3)2 τ12 (σ1 minus σ2)2 and τ23 (σ2 minus σ3)2σ12 σ23 and σ13 are the corresponding normal stresses onthe principal shear stress element σ1 σ2 and σ3 are theprincipal stresses σ1 ge σ2 ge σ3 b is a weighting coefficientreflecting the relative effect of the intermediate principalshear stress τ12 or τ23 on the strength of materials Cequals to the material strength β is the influence co-efficient of positive stress on material damage Denotingthe tension-compression strength ratio as α σtσc werewrite (7a) and (7b) in terms of principal stresses asfollows
F σ1 minusα
1 + bbσ2 + σ3( 1113857 σt when σ2 le
σ1 + ασ31 + α
(8a)
Fprime 1
1 + bσ1 + bσ2( 1113857minus ασ3 σt when σ2 ge
σ1 + ασ31 + α
(8b)
43 Formula of Ultimate Capacity By the principle of samearea the square cross section of the steel tube can betransformed into a circular one B and ts are the side lengthand thickness of the square steel tube and ro and to are theradius and thickness of the equivalent circular steel tuberespectively e formulas are shown as follows
ro Bπ
radic 05642B
to ro minus Bminus 2ts( 1113857
π
radic ro minus 05642 Bminus 2ts( 1113857
(9)
Meanwhile because the confinement of the square steelis uneven along its side the equivalent reduction factorshould be considered to reduce the same confinement of theequivalent circular steel tube Denoting thickness-sidelength ratio υ tB the expression of the equivalent re-duction factor ξ 664741υ2 + 09919υ + 041618 [28]Meanwhile there are effective and noneffective confiningzones of the concrete inside the square steel tube In thispaper the concrete strength reduction factor is considered toignore these two influences e concrete strength reductionfactor is taken as cμ 167Dminus0112
o [28] whereDo is the insidediameter of the equivalent circular steel tube
e simplified stress model of confined concrete isshown in Figure 2(a) e stresses can be explicated by0gt σ1 σ2 gt σ3 σ1 σ2 p For σ2 ge ((σ1 + ασ3)(1 + α))Substituting them into the stress expression of TSUST thefollowing expression can be obtained as
σ3 σc fck + kcp (10)
where kc is the lateral stress coefficient In TSUST kc can becalculated by cohesion and friction angle at material failurestate According to the test of Richart [22] kc has been takenas 41 simply here p is the lateral stress on the concrete andthe lateral stress on concrete is from both the steel tube andCFRP cylinder for Type a and c as shown in Figure 1 so itcan be expressed by
p σf + σrs (11)
where σf tcffcf rcf and σrs tsfsrs tcf and rcf are thethickness and radius of the CFRP cylinder respectively tsand rs are the thickness and radius of the steel tube re-spectively While for Type b in Figure 1 the concrete shouldbe divided into exterior concrete and internal concreteunder different lateral stresses Exterior concrete is onlyconfined by the steel tube but internal concrete is consid-ered both the steel tube and CFRP cylinder en the axialbearing capacity of the concrete can be expressed as
Nc fck + kcp( 1113857Ac (12)
As can be seen in Figure 2(b) the steel tube is con-strained by inside concrete so it can bear some vertical loadunder the ultimate state of the whole column η is assumedas the strength reduction factor of the steel tube and thenthe stress state of steel tubes can be explicated byσ3 σz ηfs σ2 σr 0 σ1 σθ prots For |σ3|gt σ1and σ2 ge ((σ1 + σ3)(1 + α)) substitute them into the stressexpression of TSUST the following expression can beobtained
pro
ts(1 + b)minus ηfs fs (13)
4 Advances in Civil Engineering
Tabl
e1
Com
parisonof
calculations
andtest
results
Types
Specim
ens
t cf
(mm)
fcf
(MPa
)t s
(mm)
As
(mm
2 )fs
(MPa
)fck
(MPa
)N
t(kN)
N0
(kN)
N1 y
(kN)
N2 y
(kN)
N1 y
Nt
N2 y
Nt
NCFS
T(kN)
Ntminus
NCFS
TN
CFS
T(
)Sources
a
1ndash25
017
1260
25
10132
350
4015
1294
8592
11765
12937
092
100
10605
220
[30]
1ndash35
017
1260
35
14404
310
4015
1348
9591
12854
14080
095
104
11755
147
1ndash45
017
1260
45
18802
310
4015
1698
11036
14462
15756
085
093
13417
260
2ndash25
034
1260
25
10132
350
4015
1506
8592
12933
14309
086
095
10605
420
2ndash35
034
1260
35
14404
310
4015
1593
9591
13950
15401
086
097
11755
355
2ndash45
034
1260
45
18802
310
4015
1846
11036
15054
17020
082
092
13417
376
b
SC41
0167
1500
42400
295
536
2215
18505
21758
23411
098
106
20901
59
[13]
SC42
0334
1500
42400
295
536
2275
18505
22613
24437
099
107
20901
88
SC51
0167
1500
53000
295
536
2485
20119
23264
24778
094
099
22440
107
SC52
0334
1500
53000
295
536
2585
20119
24079
23567
093
091
22440
152
SC61
0167
1500
63600
295
536
2710
21734
24728
28011
091
103
23943
132
SC62
0334
1500
63600
295
536
2775
21734
25500
26773
092
096
23943
159
c
A-1
0111
4900
35
1960
300
223
1107
9825
11663
11107
105
100
10159
90
[31]
A-2
0222
4900
35
1960
300
223
1129
9825
12723
11926
113
106
10159
111
A-3
0333
4900
35
1960
300
223
1222
9825
13802
12854
113
106
10159
203
B-1
0111
4900
35
1960
300
264
1200
10550
12605
12285
105
102
11113
80
B-2
0222
4900
35
1960
300
264
1237
10550
13657
12663
110
102
11113
113
B-3
0333
4900
35
1960
300
264
1294
10550
14726
13056
114
101
11113
164
C-1
0111
4900
35
1960
300
328
1204
11682
14093
12971
117
108
12611
minus45
C-2
0222
4900
35
1960
300
328
1300
11682
15138
13525
116
104
12611
31
C-3
0333
4900
35
1960
300
328
1400
11682
16198
14059
116
100
12611
110
D-1
0111
4900
35
1960
300
401601
12956
15780
15021
099
094
14305
119
D-2
0222
4900
35
1960
300
401742
12956
16822
16554
097
095
14305
218
D-3
0333
4900
35
1960
300
401815
12956
17878
17976
099
099
14305
269
Advances in Civil Engineering 5
en η was obtained as 065 by experimentation andstatistical data [29] so the ultimate capacity of the steel tubecan be calculated by
Ns nfsAs (14)
Lastly the ultimate capacity of CFRP-confined CFSTcolumn can be expressed as follows
N2y ηfsAs + fck + kcp( 1113857Ac (15)
5 Comparison and Analysis
e three types of CFRP-confined CFST stub columnsshown in Figure 1 have been tested under axial compression[13 30 31] Calculations N1
y and N2y obtained by Unified
eory of CFST and limit equilibrium theory respectivelyare listed in Table 1 together with the test results Nt ecalculated results both have good agreement with the testresults within small errors less than 20 Comparing thevalue of N2
yNt and N1yNt shown in Table 1 we can find that
N2y obtained by the limit equilibrium method is more ac-
curate and reliable than N1y obtained by the method of
Unified eory of CFST On the other hand the method ofUnified eory of CFST is simple and easy to realize since itjust considers the column as one composite material whilethe method of limit equilibrium method sound complicatedsince it applies TSUST to analyze every component of thecomposite column erefore these two methods can bothbe applied to investigate the axial bearing capacity of CFRP-confined CFSTstub columns and they can provide referencefor engineering design en axial bearing capacity of pureCFST columns can be predicted by the limit equilibriummethod in order to evaluate the bearing capacity im-provement due to the CFRP confinement By reviewing testresults the bearing capacity enhancement rate is describedas the expression of (Nt-NCFST)NCFSTas shown in Table 1 Itwas found that the averaged bearing capacity enhancement
rate of CFRP-confined CFSTstub columns is 164 percent incomparison with the pure CFSTcolumns Because the CFRPsheet is very thin it is demonstrated that the bearing capacityof the composite columns improves more than the corre-sponding pure CFST columns with the nearly same crosssection area erefore it is very applicable to use CFRP tostrengthen the CFST column and the composite columnscan result in significant savings in column size which ul-timately realize the material potency and bring economicbenefits
rough data analysis of the calculated and experi-mental results it can be found that concrete strength andthe relative proportions of CFRP and steel are the mainparameters to influence the axial bearing capacity of thecomposite column e confining mechanism of CFRP andaxial bearing capacity improvement needs to be validatedso the relative proportions of CFRP and steel is proposedaccording to the concept of equivalent confinement co-efficient ξssc (1) e relative proportions of CFRP and steelξcf st considers strength content and confining effect ofsection form that is
ξcfst kcfAcffcf
ksAsfs (16)
Since the test results of the bearing capacity of the stubcolumns have a certain degree of dispersion and someparameters need to be taken as the same value the calculatedaxial bearing capacity Ncc is used to describe the bearingcapacity enhancement ratio with the expression of (Ncc-NCFST)NCFST which reflects the function of the CFRPcylinder to confine the CFST column where NCFST is thecalculated value for the corresponding pure CFST columnNcc is obtained by limit equilibrium theory
e relationship between (NccminusNCFST)NCFST and ξcf stfor the three types of composite columns is shown inFigure 3 In reference to the experimental data in Table 1fck of Type b and Type c is taken as 4015MPa similar toType a and Figure 3(a) shows the relationship between
0
005
01
015
02
025
0 01 02 03 04 05 06
Outer circular CFRPOuter square CFRPInner circular CFRP
(Ncc-N
CFST
)N
CFST
ξcfst
(a)
0
005
01
015
02
025
03
035
0 01 02 03 04 05 06
fck = 223fck = 264
fck = 328fck = 40
ξcfst
(Ncc-N
CFST
)N
CFST
(b)
Figure 3 Relationship between (NccminusNCFST)NCFST and ξcfst (a) fck 4015 (b) Different fck
6 Advances in Civil Engineering
(NccminusNCFST)NCFST and ξcf st under the same concretestrength e relationship is linear and directly pro-portional to the CFRP-wrapped composite columns withthe outer circular CFRP or outer square CFRP because theouter CFRP cylinder strengthens the whole CFST columnBut for the inner circular CFRP-confined columns there isno linear proportion because inner CFRP only strengthensits inside concrete directly It can also be found that outercircular CFRP has the best confinement effect to providethe highest bearing capacity enhancement ratio at the samerelative proportions of CFRP and steel Meanwhile outersquare CFRP does better than inner circular CFRP asshown in Figure 3(a) that is CFRP as external jackets canprovide the better confinement than the internal one Onthe other hand we choose the basic parameters of outersquare CFRP-confined CFST columns in Table 1 to get therelationship between (NccminusNCFST)NCFST and ξcf st underdifferent concrete strength as shown in Figure 3(b) Forevery group the steel tube and the concrete are the same sothe bearing capacity enhancement ratio is linear and directproportional to the content of the CFRP cylinder Amongthe four groups with the decrease of concrete strength thebearing capacity enhancement ratio increases with theimprovement of relative proportions of CFRP and steel Itindicates that the confinement effect of CFRP increaseswith the decrease of concrete strengthe reason is mainlythat the contributions of the CFRP cylinder are the dis-placement resistance of the CFSTcolumn and low-strengthconcrete has the better deformation capacity to make theCFRP play better especially during the postbucklingprocess
6 Conclusions
is paper presented a comparative study of concrete-filledsteel tubular (CFST) stub columns with three differentconfinement types from carbon fiber reinforced polymer(CFRP) outer circular CFRP inner circular CFRP and outersquare CFRP CFRP-confined CFST column takes the ad-vantage of not only the good performance of CFST but alsoa substantial improvement in higher confinement of CFRPe compressive mechanism and physical properties ofthe composite column were analyzed firstly aiming at in-vestigating the confinement effects of the different CFRP onCFST Columns
Two methods based on Unified eory of CFST andelastoplastic limit equilibrium method have been applied toinvestigate the axial bearing capacity of CFRP-confinedCFST stub columns e calculated results have goodagreement with the test results rough data analysis thestudy confirmed the ultimate strength calculation results oflimit equilibrium method were found to be more accurateand reliable than that of Unifiedeory of CFST en axialbearing capacity of pure CFST columns was predicted toevaluate the bearing capacity improvement factor comingfrom the CFRP confinement It was demonstrated that theaveraged enhancement ratio is 164 percent showing thatthe three kinds of CFRP-confined CFST columns hada broad applicability
CFRP can increase CFST membersrsquo bearing capacitiessignificantly because complementary action between thesteel tube and concrete is strengthened through CFRP erelationship between the bearing capacity enhancementratio and relative proportions of CFRP and steel is nearlylinear especially for the CFRP-wrapped columns with theouter circular CFRP or outer square CFRP rougha comparative analysis this study confirmed that outercircular CFRP had the best confinement effect and outersquare CFRP did better than inner circular CFRP econfinement effect of CFRP increased with the decrease ofconcrete strength and it was proportional with relativeproportions of CFRP and CFST under the same concretestrength
Data Availability
All data used for this paper are publicly available and ac-cessible online We have annotated the entire data buildingprocess and empirical techniques presented in the paper Wehave given formal citations in article references While wedid not directly draw upon these sources for the empiricalanalysis these efforts confirmed our understanding of thescope scale and accuracy of the CFRP-confined CFSTcolumns
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to acknowledge the support providedby the Chinese National Science Foundation (Grant no51478004) Meanwhile the financial support from HebeiUniversity of Technology is also appreciated
References
[1] O Chaalal and M Shahawy ldquoPerformance of fiber-reinforcedpolymer wrapped reinforced concrete column under com-bined axial flexural loadingrdquo ACI Structure Journal vol 97no 4 pp 659ndash668 2000
[2] Y Xiao ldquoApplications of FRP composites in concrete col-umnsrdquo Advances in Structural Engineering vol 7 no 4pp 335ndash343 2004
[3] J G Teng Y L Huang L Lam and L P Ye ldquoeoreticalmodel for fiber reinforced polymer-confined concreterdquoJournal of Composites for Construction vol 11 no 2pp 201ndash210 2007
[4] J G Teng T Jiang L Lam and Y Z Luo ldquoRefinement ofa design-oriented stress-strain model for FRP-confinedconcreterdquo Journal of Composites for Construction vol 13no 4 pp 269ndash278 2009
[5] Y Zheng L F Zhang and L P Xia ldquoInvestigation of thebehaviour of flexible and ductile ECC link slab reinforced withFRPrdquo Construction and Building Materials vol 166pp 694ndash711 2018
[6] Y Zheng and L P Xia ldquoInvestigation of the ultimate capacityof NSM FRP-strengthened concrete bridge deck slabsrdquoArabian Journal of Science and Engineering vol 43pp 1597ndash1615 2018
Advances in Civil Engineering 7
[7] Z F Amir and H R Sami ldquoConfinement model for axiallyloaded concrete confined by circular FRP tubesrdquo ACIStructure Journal vol 98 no 4 pp 451ndash461 2001
[8] L H Han Concrete-Filled Steel Tube Structures-+eory andDesign Science Press Beijing China 2nd edition 2007
[9] B C Chen and T L Wang ldquoOverview of concrete filled steeltube arch bridges in Chinardquo Practice Periodical on StructuralDesign and Construction vol 14 no 2 pp 70ndash80 2009
[10] Y Che Q L Wang and Y B Shao ldquoCompressive perfor-mances of the concrete filled circular CFRP-steel tube (C-CFRP-CFST)rdquo International Journal of Advanced SteelConstruction vol 8 no 4 pp 311ndash338 2012
[11] Z Tao L H Han and L L Wang ldquoCompressive and flexuralbehaviour of CFRP repaired concrete-filled steel tubes afterexposure to firerdquo Journal of Constructional Steel Researchvol 63 no 8 pp 1116ndash1126 2007
[12] W Gu ldquoStudy on mechanics of concrete-filled CFRP-steeltube columnrdquo esis for doctor degree DaLian MaritimeUniversity Dalian China 2007
[13] G C Li L Ma and J L Yang ldquoBearing capacity of shortcolumns of high-strength concrete filled square steel tubularwith inner CFRP circular tubular under axially compressiveloadrdquo Journal of Shenyang Jianzhu University vol 24 no 1pp 62ndash66 2008
[14] Q L Wang G Y Wang and F Han ldquoExperimental study onconcentrically compressed stub columns reinforced by con-crete filled CFRP-steel tuberdquo in 4th International Conferenceon Advances in Steel Structures Elsevier Science Ltd pp671ndash676 London UK 2005
[15] Z Tao L H Han and J P Zhuang ldquoUsing CFRP tostrengthen concrete-filled steel tubular columns stub columntestsrdquo in 4th International Conference on Advances in SteelStructures Elsevier Science Ltd pp 701ndash706 London UK2005
[16] Q L Wang S E Qu Y B Shao and L M Feng ldquoStaticbehavior of axially compressed circular concrete filled cfrp-steel tubular (c-cf-cfrp-st) columns with moderate slender-ness ratiordquo Advanced Steel Construction vol 12 no 3pp 263ndash295 2016
[17] Q L Wang Z Zhao Y B Shao and Q L Li ldquoStatic behaviorof axially compressed square concrete filled CFRP-steel tu-bular (S-CF-CFRP-ST) columns with moderate slendernessrdquo+in-Walled Structures vol 110 pp 106ndash122 2017
[18] K Karimi M J Tait and W W EI-Dakhakhni ldquoTesting andmodeling of a novel FRP-encased steel-concrete composite col-umnrdquo Composite Structures vol 93 no 5 pp 1463ndash1473 2011
[19] P Feng S Cheng Y Bai et al ldquoMechanical behavior ofconcrete-filled square steel tube with FRP-confined concretecore subjected to axial compressionrdquo Composite Structuresvol 123 no 5 pp 312ndash324 2015
[20] S T Zhong Unified +eory of Concrete Filled Steel TubularStructure Tsinghua University Press Beijing China 2006
[21] M H Yu Unified Strength +eory and Its ApplicationsSpringer Press Berlin Heidelberg Germany 2004
[22] F E Richart A Brandtzaeg and R L Brown ldquoA study of thefailure of concrete under combined compressive stressesrdquoBulletin No 185 Engineering Experimental Station Uni-versity of Illinois Urbana IL USA 1928
[23] Q L Wang W Gu and Y H Zhao ldquoExperimental study onconcentrically compressed concrete filled circular CFRP-steelcomposite tubular stub columnsrdquo China Civil EngineeringJournal vol 38 no 10 pp 44ndash48 2005
[24] A H Varma R Sause and J M Ricles ldquoDevelopment andvalidation of fiber model for high strength square concrete
filled steel tube beam-columnrdquo ACI Structural Journalvol 102 no 1 pp 73ndash84 2005
[25] S T Zhong ldquoNew concept and development of research onconcrete-filled steel tube (CFST)rdquo in Proceeding of 2nd In-ternational Symposium on Civil Infrastructure Systemspp 9ndash12 Hong Kong December 1996
[26] Y F Zhang and Z Q Zhang ldquoStudy on equivalent con-finement coefficient of composite CFST column based onunified theoryrdquo Mechanics of Advanced Materials andStructures vol 23 no 1 pp 22ndash27 2016
[27] H T Chen ldquoeoretical study on continuity of basic behaviorof every-sectioned CFT stub columns under axial loadsrdquoesis for doctor degree Harbin Institute of TechnologyHarbin China 2001
[28] X W Li and J H Zhao ldquoMechanics behavior of axial loadedshort columns with concrete-filled square steel tuberdquo ChineseJournal of Highway and Transport vol 19 no 4 pp 77ndash812006
[29] Y F Zhang J H Zhao and W F Yuan ldquoStudy on com-pressive bearing capacity of concrete filled square steel tubecolumn reinforced by circular steel tube insiderdquo Journal ofCivil Engineering and Management vol 19 no 6 pp 787ndash795 2013
[30] W Gu and H N Li ldquoResearch in the properties of theconcrete filled steel tube columns with CFRP compositematerialsrdquo Advanced Materials Research vol 163-167pp 3555ndash3559 2011
[31] Q L Wang and Y B Shao ldquoCompressive performances ofconcrete filled square CFRP-steel tubes (S-CFRP-CFST)rdquoSteel and Composite Structures vol 16 no 5 pp 455ndash4802014
8 Advances in Civil Engineering
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considered the radial stress and the longitudinal stress areignored
Based on the above assumptions the ultimate axialbearing capacity of CFRP-confined CFST columns can becalculated by
N2y Ns + Nc (6)
where N Ns and Nc are vertical bearing capacities of thesteel tube and concrete respectively N2
y is the bearing ca-pacity calculated by limit equilibrium theory In the state oflimit equilibrium every part of the composite column can beanalyzed using TSUST [21]
42 Twin-Shear Unified Strength +eory (TSUST) eTSUST considers the two larger principal shear stresses andthe corresponding normal stresses and their different effectson the failure of materials When the relationship functionbetween them reaches one ultimate value the material canbe defined as failure at this state which is formulated asfollows
F τ13 + bτ12 + β σ13 + bσ12( 1113857 C
when τ12 + βσ12 ge τ23 + βσ23(7a)
Fprime τ13 + bτ23 + β σ13 + bσ23( 1113857 C
when τ12 + βσ12 le τ23 + βσ23(7b)
where τ12 τ23 and τ13 are the principal shear stressesτ13 (σ1 minus σ3)2 τ12 (σ1 minus σ2)2 and τ23 (σ2 minus σ3)2σ12 σ23 and σ13 are the corresponding normal stresses onthe principal shear stress element σ1 σ2 and σ3 are theprincipal stresses σ1 ge σ2 ge σ3 b is a weighting coefficientreflecting the relative effect of the intermediate principalshear stress τ12 or τ23 on the strength of materials Cequals to the material strength β is the influence co-efficient of positive stress on material damage Denotingthe tension-compression strength ratio as α σtσc werewrite (7a) and (7b) in terms of principal stresses asfollows
F σ1 minusα
1 + bbσ2 + σ3( 1113857 σt when σ2 le
σ1 + ασ31 + α
(8a)
Fprime 1
1 + bσ1 + bσ2( 1113857minus ασ3 σt when σ2 ge
σ1 + ασ31 + α
(8b)
43 Formula of Ultimate Capacity By the principle of samearea the square cross section of the steel tube can betransformed into a circular one B and ts are the side lengthand thickness of the square steel tube and ro and to are theradius and thickness of the equivalent circular steel tuberespectively e formulas are shown as follows
ro Bπ
radic 05642B
to ro minus Bminus 2ts( 1113857
π
radic ro minus 05642 Bminus 2ts( 1113857
(9)
Meanwhile because the confinement of the square steelis uneven along its side the equivalent reduction factorshould be considered to reduce the same confinement of theequivalent circular steel tube Denoting thickness-sidelength ratio υ tB the expression of the equivalent re-duction factor ξ 664741υ2 + 09919υ + 041618 [28]Meanwhile there are effective and noneffective confiningzones of the concrete inside the square steel tube In thispaper the concrete strength reduction factor is considered toignore these two influences e concrete strength reductionfactor is taken as cμ 167Dminus0112
o [28] whereDo is the insidediameter of the equivalent circular steel tube
e simplified stress model of confined concrete isshown in Figure 2(a) e stresses can be explicated by0gt σ1 σ2 gt σ3 σ1 σ2 p For σ2 ge ((σ1 + ασ3)(1 + α))Substituting them into the stress expression of TSUST thefollowing expression can be obtained as
σ3 σc fck + kcp (10)
where kc is the lateral stress coefficient In TSUST kc can becalculated by cohesion and friction angle at material failurestate According to the test of Richart [22] kc has been takenas 41 simply here p is the lateral stress on the concrete andthe lateral stress on concrete is from both the steel tube andCFRP cylinder for Type a and c as shown in Figure 1 so itcan be expressed by
p σf + σrs (11)
where σf tcffcf rcf and σrs tsfsrs tcf and rcf are thethickness and radius of the CFRP cylinder respectively tsand rs are the thickness and radius of the steel tube re-spectively While for Type b in Figure 1 the concrete shouldbe divided into exterior concrete and internal concreteunder different lateral stresses Exterior concrete is onlyconfined by the steel tube but internal concrete is consid-ered both the steel tube and CFRP cylinder en the axialbearing capacity of the concrete can be expressed as
Nc fck + kcp( 1113857Ac (12)
As can be seen in Figure 2(b) the steel tube is con-strained by inside concrete so it can bear some vertical loadunder the ultimate state of the whole column η is assumedas the strength reduction factor of the steel tube and thenthe stress state of steel tubes can be explicated byσ3 σz ηfs σ2 σr 0 σ1 σθ prots For |σ3|gt σ1and σ2 ge ((σ1 + σ3)(1 + α)) substitute them into the stressexpression of TSUST the following expression can beobtained
pro
ts(1 + b)minus ηfs fs (13)
4 Advances in Civil Engineering
Tabl
e1
Com
parisonof
calculations
andtest
results
Types
Specim
ens
t cf
(mm)
fcf
(MPa
)t s
(mm)
As
(mm
2 )fs
(MPa
)fck
(MPa
)N
t(kN)
N0
(kN)
N1 y
(kN)
N2 y
(kN)
N1 y
Nt
N2 y
Nt
NCFS
T(kN)
Ntminus
NCFS
TN
CFS
T(
)Sources
a
1ndash25
017
1260
25
10132
350
4015
1294
8592
11765
12937
092
100
10605
220
[30]
1ndash35
017
1260
35
14404
310
4015
1348
9591
12854
14080
095
104
11755
147
1ndash45
017
1260
45
18802
310
4015
1698
11036
14462
15756
085
093
13417
260
2ndash25
034
1260
25
10132
350
4015
1506
8592
12933
14309
086
095
10605
420
2ndash35
034
1260
35
14404
310
4015
1593
9591
13950
15401
086
097
11755
355
2ndash45
034
1260
45
18802
310
4015
1846
11036
15054
17020
082
092
13417
376
b
SC41
0167
1500
42400
295
536
2215
18505
21758
23411
098
106
20901
59
[13]
SC42
0334
1500
42400
295
536
2275
18505
22613
24437
099
107
20901
88
SC51
0167
1500
53000
295
536
2485
20119
23264
24778
094
099
22440
107
SC52
0334
1500
53000
295
536
2585
20119
24079
23567
093
091
22440
152
SC61
0167
1500
63600
295
536
2710
21734
24728
28011
091
103
23943
132
SC62
0334
1500
63600
295
536
2775
21734
25500
26773
092
096
23943
159
c
A-1
0111
4900
35
1960
300
223
1107
9825
11663
11107
105
100
10159
90
[31]
A-2
0222
4900
35
1960
300
223
1129
9825
12723
11926
113
106
10159
111
A-3
0333
4900
35
1960
300
223
1222
9825
13802
12854
113
106
10159
203
B-1
0111
4900
35
1960
300
264
1200
10550
12605
12285
105
102
11113
80
B-2
0222
4900
35
1960
300
264
1237
10550
13657
12663
110
102
11113
113
B-3
0333
4900
35
1960
300
264
1294
10550
14726
13056
114
101
11113
164
C-1
0111
4900
35
1960
300
328
1204
11682
14093
12971
117
108
12611
minus45
C-2
0222
4900
35
1960
300
328
1300
11682
15138
13525
116
104
12611
31
C-3
0333
4900
35
1960
300
328
1400
11682
16198
14059
116
100
12611
110
D-1
0111
4900
35
1960
300
401601
12956
15780
15021
099
094
14305
119
D-2
0222
4900
35
1960
300
401742
12956
16822
16554
097
095
14305
218
D-3
0333
4900
35
1960
300
401815
12956
17878
17976
099
099
14305
269
Advances in Civil Engineering 5
en η was obtained as 065 by experimentation andstatistical data [29] so the ultimate capacity of the steel tubecan be calculated by
Ns nfsAs (14)
Lastly the ultimate capacity of CFRP-confined CFSTcolumn can be expressed as follows
N2y ηfsAs + fck + kcp( 1113857Ac (15)
5 Comparison and Analysis
e three types of CFRP-confined CFST stub columnsshown in Figure 1 have been tested under axial compression[13 30 31] Calculations N1
y and N2y obtained by Unified
eory of CFST and limit equilibrium theory respectivelyare listed in Table 1 together with the test results Nt ecalculated results both have good agreement with the testresults within small errors less than 20 Comparing thevalue of N2
yNt and N1yNt shown in Table 1 we can find that
N2y obtained by the limit equilibrium method is more ac-
curate and reliable than N1y obtained by the method of
Unified eory of CFST On the other hand the method ofUnified eory of CFST is simple and easy to realize since itjust considers the column as one composite material whilethe method of limit equilibrium method sound complicatedsince it applies TSUST to analyze every component of thecomposite column erefore these two methods can bothbe applied to investigate the axial bearing capacity of CFRP-confined CFSTstub columns and they can provide referencefor engineering design en axial bearing capacity of pureCFST columns can be predicted by the limit equilibriummethod in order to evaluate the bearing capacity im-provement due to the CFRP confinement By reviewing testresults the bearing capacity enhancement rate is describedas the expression of (Nt-NCFST)NCFSTas shown in Table 1 Itwas found that the averaged bearing capacity enhancement
rate of CFRP-confined CFSTstub columns is 164 percent incomparison with the pure CFSTcolumns Because the CFRPsheet is very thin it is demonstrated that the bearing capacityof the composite columns improves more than the corre-sponding pure CFST columns with the nearly same crosssection area erefore it is very applicable to use CFRP tostrengthen the CFST column and the composite columnscan result in significant savings in column size which ul-timately realize the material potency and bring economicbenefits
rough data analysis of the calculated and experi-mental results it can be found that concrete strength andthe relative proportions of CFRP and steel are the mainparameters to influence the axial bearing capacity of thecomposite column e confining mechanism of CFRP andaxial bearing capacity improvement needs to be validatedso the relative proportions of CFRP and steel is proposedaccording to the concept of equivalent confinement co-efficient ξssc (1) e relative proportions of CFRP and steelξcf st considers strength content and confining effect ofsection form that is
ξcfst kcfAcffcf
ksAsfs (16)
Since the test results of the bearing capacity of the stubcolumns have a certain degree of dispersion and someparameters need to be taken as the same value the calculatedaxial bearing capacity Ncc is used to describe the bearingcapacity enhancement ratio with the expression of (Ncc-NCFST)NCFST which reflects the function of the CFRPcylinder to confine the CFST column where NCFST is thecalculated value for the corresponding pure CFST columnNcc is obtained by limit equilibrium theory
e relationship between (NccminusNCFST)NCFST and ξcf stfor the three types of composite columns is shown inFigure 3 In reference to the experimental data in Table 1fck of Type b and Type c is taken as 4015MPa similar toType a and Figure 3(a) shows the relationship between
0
005
01
015
02
025
0 01 02 03 04 05 06
Outer circular CFRPOuter square CFRPInner circular CFRP
(Ncc-N
CFST
)N
CFST
ξcfst
(a)
0
005
01
015
02
025
03
035
0 01 02 03 04 05 06
fck = 223fck = 264
fck = 328fck = 40
ξcfst
(Ncc-N
CFST
)N
CFST
(b)
Figure 3 Relationship between (NccminusNCFST)NCFST and ξcfst (a) fck 4015 (b) Different fck
6 Advances in Civil Engineering
(NccminusNCFST)NCFST and ξcf st under the same concretestrength e relationship is linear and directly pro-portional to the CFRP-wrapped composite columns withthe outer circular CFRP or outer square CFRP because theouter CFRP cylinder strengthens the whole CFST columnBut for the inner circular CFRP-confined columns there isno linear proportion because inner CFRP only strengthensits inside concrete directly It can also be found that outercircular CFRP has the best confinement effect to providethe highest bearing capacity enhancement ratio at the samerelative proportions of CFRP and steel Meanwhile outersquare CFRP does better than inner circular CFRP asshown in Figure 3(a) that is CFRP as external jackets canprovide the better confinement than the internal one Onthe other hand we choose the basic parameters of outersquare CFRP-confined CFST columns in Table 1 to get therelationship between (NccminusNCFST)NCFST and ξcf st underdifferent concrete strength as shown in Figure 3(b) Forevery group the steel tube and the concrete are the same sothe bearing capacity enhancement ratio is linear and directproportional to the content of the CFRP cylinder Amongthe four groups with the decrease of concrete strength thebearing capacity enhancement ratio increases with theimprovement of relative proportions of CFRP and steel Itindicates that the confinement effect of CFRP increaseswith the decrease of concrete strengthe reason is mainlythat the contributions of the CFRP cylinder are the dis-placement resistance of the CFSTcolumn and low-strengthconcrete has the better deformation capacity to make theCFRP play better especially during the postbucklingprocess
6 Conclusions
is paper presented a comparative study of concrete-filledsteel tubular (CFST) stub columns with three differentconfinement types from carbon fiber reinforced polymer(CFRP) outer circular CFRP inner circular CFRP and outersquare CFRP CFRP-confined CFST column takes the ad-vantage of not only the good performance of CFST but alsoa substantial improvement in higher confinement of CFRPe compressive mechanism and physical properties ofthe composite column were analyzed firstly aiming at in-vestigating the confinement effects of the different CFRP onCFST Columns
Two methods based on Unified eory of CFST andelastoplastic limit equilibrium method have been applied toinvestigate the axial bearing capacity of CFRP-confinedCFST stub columns e calculated results have goodagreement with the test results rough data analysis thestudy confirmed the ultimate strength calculation results oflimit equilibrium method were found to be more accurateand reliable than that of Unifiedeory of CFST en axialbearing capacity of pure CFST columns was predicted toevaluate the bearing capacity improvement factor comingfrom the CFRP confinement It was demonstrated that theaveraged enhancement ratio is 164 percent showing thatthe three kinds of CFRP-confined CFST columns hada broad applicability
CFRP can increase CFST membersrsquo bearing capacitiessignificantly because complementary action between thesteel tube and concrete is strengthened through CFRP erelationship between the bearing capacity enhancementratio and relative proportions of CFRP and steel is nearlylinear especially for the CFRP-wrapped columns with theouter circular CFRP or outer square CFRP rougha comparative analysis this study confirmed that outercircular CFRP had the best confinement effect and outersquare CFRP did better than inner circular CFRP econfinement effect of CFRP increased with the decrease ofconcrete strength and it was proportional with relativeproportions of CFRP and CFST under the same concretestrength
Data Availability
All data used for this paper are publicly available and ac-cessible online We have annotated the entire data buildingprocess and empirical techniques presented in the paper Wehave given formal citations in article references While wedid not directly draw upon these sources for the empiricalanalysis these efforts confirmed our understanding of thescope scale and accuracy of the CFRP-confined CFSTcolumns
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to acknowledge the support providedby the Chinese National Science Foundation (Grant no51478004) Meanwhile the financial support from HebeiUniversity of Technology is also appreciated
References
[1] O Chaalal and M Shahawy ldquoPerformance of fiber-reinforcedpolymer wrapped reinforced concrete column under com-bined axial flexural loadingrdquo ACI Structure Journal vol 97no 4 pp 659ndash668 2000
[2] Y Xiao ldquoApplications of FRP composites in concrete col-umnsrdquo Advances in Structural Engineering vol 7 no 4pp 335ndash343 2004
[3] J G Teng Y L Huang L Lam and L P Ye ldquoeoreticalmodel for fiber reinforced polymer-confined concreterdquoJournal of Composites for Construction vol 11 no 2pp 201ndash210 2007
[4] J G Teng T Jiang L Lam and Y Z Luo ldquoRefinement ofa design-oriented stress-strain model for FRP-confinedconcreterdquo Journal of Composites for Construction vol 13no 4 pp 269ndash278 2009
[5] Y Zheng L F Zhang and L P Xia ldquoInvestigation of thebehaviour of flexible and ductile ECC link slab reinforced withFRPrdquo Construction and Building Materials vol 166pp 694ndash711 2018
[6] Y Zheng and L P Xia ldquoInvestigation of the ultimate capacityof NSM FRP-strengthened concrete bridge deck slabsrdquoArabian Journal of Science and Engineering vol 43pp 1597ndash1615 2018
Advances in Civil Engineering 7
[7] Z F Amir and H R Sami ldquoConfinement model for axiallyloaded concrete confined by circular FRP tubesrdquo ACIStructure Journal vol 98 no 4 pp 451ndash461 2001
[8] L H Han Concrete-Filled Steel Tube Structures-+eory andDesign Science Press Beijing China 2nd edition 2007
[9] B C Chen and T L Wang ldquoOverview of concrete filled steeltube arch bridges in Chinardquo Practice Periodical on StructuralDesign and Construction vol 14 no 2 pp 70ndash80 2009
[10] Y Che Q L Wang and Y B Shao ldquoCompressive perfor-mances of the concrete filled circular CFRP-steel tube (C-CFRP-CFST)rdquo International Journal of Advanced SteelConstruction vol 8 no 4 pp 311ndash338 2012
[11] Z Tao L H Han and L L Wang ldquoCompressive and flexuralbehaviour of CFRP repaired concrete-filled steel tubes afterexposure to firerdquo Journal of Constructional Steel Researchvol 63 no 8 pp 1116ndash1126 2007
[12] W Gu ldquoStudy on mechanics of concrete-filled CFRP-steeltube columnrdquo esis for doctor degree DaLian MaritimeUniversity Dalian China 2007
[13] G C Li L Ma and J L Yang ldquoBearing capacity of shortcolumns of high-strength concrete filled square steel tubularwith inner CFRP circular tubular under axially compressiveloadrdquo Journal of Shenyang Jianzhu University vol 24 no 1pp 62ndash66 2008
[14] Q L Wang G Y Wang and F Han ldquoExperimental study onconcentrically compressed stub columns reinforced by con-crete filled CFRP-steel tuberdquo in 4th International Conferenceon Advances in Steel Structures Elsevier Science Ltd pp671ndash676 London UK 2005
[15] Z Tao L H Han and J P Zhuang ldquoUsing CFRP tostrengthen concrete-filled steel tubular columns stub columntestsrdquo in 4th International Conference on Advances in SteelStructures Elsevier Science Ltd pp 701ndash706 London UK2005
[16] Q L Wang S E Qu Y B Shao and L M Feng ldquoStaticbehavior of axially compressed circular concrete filled cfrp-steel tubular (c-cf-cfrp-st) columns with moderate slender-ness ratiordquo Advanced Steel Construction vol 12 no 3pp 263ndash295 2016
[17] Q L Wang Z Zhao Y B Shao and Q L Li ldquoStatic behaviorof axially compressed square concrete filled CFRP-steel tu-bular (S-CF-CFRP-ST) columns with moderate slendernessrdquo+in-Walled Structures vol 110 pp 106ndash122 2017
[18] K Karimi M J Tait and W W EI-Dakhakhni ldquoTesting andmodeling of a novel FRP-encased steel-concrete composite col-umnrdquo Composite Structures vol 93 no 5 pp 1463ndash1473 2011
[19] P Feng S Cheng Y Bai et al ldquoMechanical behavior ofconcrete-filled square steel tube with FRP-confined concretecore subjected to axial compressionrdquo Composite Structuresvol 123 no 5 pp 312ndash324 2015
[20] S T Zhong Unified +eory of Concrete Filled Steel TubularStructure Tsinghua University Press Beijing China 2006
[21] M H Yu Unified Strength +eory and Its ApplicationsSpringer Press Berlin Heidelberg Germany 2004
[22] F E Richart A Brandtzaeg and R L Brown ldquoA study of thefailure of concrete under combined compressive stressesrdquoBulletin No 185 Engineering Experimental Station Uni-versity of Illinois Urbana IL USA 1928
[23] Q L Wang W Gu and Y H Zhao ldquoExperimental study onconcentrically compressed concrete filled circular CFRP-steelcomposite tubular stub columnsrdquo China Civil EngineeringJournal vol 38 no 10 pp 44ndash48 2005
[24] A H Varma R Sause and J M Ricles ldquoDevelopment andvalidation of fiber model for high strength square concrete
filled steel tube beam-columnrdquo ACI Structural Journalvol 102 no 1 pp 73ndash84 2005
[25] S T Zhong ldquoNew concept and development of research onconcrete-filled steel tube (CFST)rdquo in Proceeding of 2nd In-ternational Symposium on Civil Infrastructure Systemspp 9ndash12 Hong Kong December 1996
[26] Y F Zhang and Z Q Zhang ldquoStudy on equivalent con-finement coefficient of composite CFST column based onunified theoryrdquo Mechanics of Advanced Materials andStructures vol 23 no 1 pp 22ndash27 2016
[27] H T Chen ldquoeoretical study on continuity of basic behaviorof every-sectioned CFT stub columns under axial loadsrdquoesis for doctor degree Harbin Institute of TechnologyHarbin China 2001
[28] X W Li and J H Zhao ldquoMechanics behavior of axial loadedshort columns with concrete-filled square steel tuberdquo ChineseJournal of Highway and Transport vol 19 no 4 pp 77ndash812006
[29] Y F Zhang J H Zhao and W F Yuan ldquoStudy on com-pressive bearing capacity of concrete filled square steel tubecolumn reinforced by circular steel tube insiderdquo Journal ofCivil Engineering and Management vol 19 no 6 pp 787ndash795 2013
[30] W Gu and H N Li ldquoResearch in the properties of theconcrete filled steel tube columns with CFRP compositematerialsrdquo Advanced Materials Research vol 163-167pp 3555ndash3559 2011
[31] Q L Wang and Y B Shao ldquoCompressive performances ofconcrete filled square CFRP-steel tubes (S-CFRP-CFST)rdquoSteel and Composite Structures vol 16 no 5 pp 455ndash4802014
8 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Tabl
e1
Com
parisonof
calculations
andtest
results
Types
Specim
ens
t cf
(mm)
fcf
(MPa
)t s
(mm)
As
(mm
2 )fs
(MPa
)fck
(MPa
)N
t(kN)
N0
(kN)
N1 y
(kN)
N2 y
(kN)
N1 y
Nt
N2 y
Nt
NCFS
T(kN)
Ntminus
NCFS
TN
CFS
T(
)Sources
a
1ndash25
017
1260
25
10132
350
4015
1294
8592
11765
12937
092
100
10605
220
[30]
1ndash35
017
1260
35
14404
310
4015
1348
9591
12854
14080
095
104
11755
147
1ndash45
017
1260
45
18802
310
4015
1698
11036
14462
15756
085
093
13417
260
2ndash25
034
1260
25
10132
350
4015
1506
8592
12933
14309
086
095
10605
420
2ndash35
034
1260
35
14404
310
4015
1593
9591
13950
15401
086
097
11755
355
2ndash45
034
1260
45
18802
310
4015
1846
11036
15054
17020
082
092
13417
376
b
SC41
0167
1500
42400
295
536
2215
18505
21758
23411
098
106
20901
59
[13]
SC42
0334
1500
42400
295
536
2275
18505
22613
24437
099
107
20901
88
SC51
0167
1500
53000
295
536
2485
20119
23264
24778
094
099
22440
107
SC52
0334
1500
53000
295
536
2585
20119
24079
23567
093
091
22440
152
SC61
0167
1500
63600
295
536
2710
21734
24728
28011
091
103
23943
132
SC62
0334
1500
63600
295
536
2775
21734
25500
26773
092
096
23943
159
c
A-1
0111
4900
35
1960
300
223
1107
9825
11663
11107
105
100
10159
90
[31]
A-2
0222
4900
35
1960
300
223
1129
9825
12723
11926
113
106
10159
111
A-3
0333
4900
35
1960
300
223
1222
9825
13802
12854
113
106
10159
203
B-1
0111
4900
35
1960
300
264
1200
10550
12605
12285
105
102
11113
80
B-2
0222
4900
35
1960
300
264
1237
10550
13657
12663
110
102
11113
113
B-3
0333
4900
35
1960
300
264
1294
10550
14726
13056
114
101
11113
164
C-1
0111
4900
35
1960
300
328
1204
11682
14093
12971
117
108
12611
minus45
C-2
0222
4900
35
1960
300
328
1300
11682
15138
13525
116
104
12611
31
C-3
0333
4900
35
1960
300
328
1400
11682
16198
14059
116
100
12611
110
D-1
0111
4900
35
1960
300
401601
12956
15780
15021
099
094
14305
119
D-2
0222
4900
35
1960
300
401742
12956
16822
16554
097
095
14305
218
D-3
0333
4900
35
1960
300
401815
12956
17878
17976
099
099
14305
269
Advances in Civil Engineering 5
en η was obtained as 065 by experimentation andstatistical data [29] so the ultimate capacity of the steel tubecan be calculated by
Ns nfsAs (14)
Lastly the ultimate capacity of CFRP-confined CFSTcolumn can be expressed as follows
N2y ηfsAs + fck + kcp( 1113857Ac (15)
5 Comparison and Analysis
e three types of CFRP-confined CFST stub columnsshown in Figure 1 have been tested under axial compression[13 30 31] Calculations N1
y and N2y obtained by Unified
eory of CFST and limit equilibrium theory respectivelyare listed in Table 1 together with the test results Nt ecalculated results both have good agreement with the testresults within small errors less than 20 Comparing thevalue of N2
yNt and N1yNt shown in Table 1 we can find that
N2y obtained by the limit equilibrium method is more ac-
curate and reliable than N1y obtained by the method of
Unified eory of CFST On the other hand the method ofUnified eory of CFST is simple and easy to realize since itjust considers the column as one composite material whilethe method of limit equilibrium method sound complicatedsince it applies TSUST to analyze every component of thecomposite column erefore these two methods can bothbe applied to investigate the axial bearing capacity of CFRP-confined CFSTstub columns and they can provide referencefor engineering design en axial bearing capacity of pureCFST columns can be predicted by the limit equilibriummethod in order to evaluate the bearing capacity im-provement due to the CFRP confinement By reviewing testresults the bearing capacity enhancement rate is describedas the expression of (Nt-NCFST)NCFSTas shown in Table 1 Itwas found that the averaged bearing capacity enhancement
rate of CFRP-confined CFSTstub columns is 164 percent incomparison with the pure CFSTcolumns Because the CFRPsheet is very thin it is demonstrated that the bearing capacityof the composite columns improves more than the corre-sponding pure CFST columns with the nearly same crosssection area erefore it is very applicable to use CFRP tostrengthen the CFST column and the composite columnscan result in significant savings in column size which ul-timately realize the material potency and bring economicbenefits
rough data analysis of the calculated and experi-mental results it can be found that concrete strength andthe relative proportions of CFRP and steel are the mainparameters to influence the axial bearing capacity of thecomposite column e confining mechanism of CFRP andaxial bearing capacity improvement needs to be validatedso the relative proportions of CFRP and steel is proposedaccording to the concept of equivalent confinement co-efficient ξssc (1) e relative proportions of CFRP and steelξcf st considers strength content and confining effect ofsection form that is
ξcfst kcfAcffcf
ksAsfs (16)
Since the test results of the bearing capacity of the stubcolumns have a certain degree of dispersion and someparameters need to be taken as the same value the calculatedaxial bearing capacity Ncc is used to describe the bearingcapacity enhancement ratio with the expression of (Ncc-NCFST)NCFST which reflects the function of the CFRPcylinder to confine the CFST column where NCFST is thecalculated value for the corresponding pure CFST columnNcc is obtained by limit equilibrium theory
e relationship between (NccminusNCFST)NCFST and ξcf stfor the three types of composite columns is shown inFigure 3 In reference to the experimental data in Table 1fck of Type b and Type c is taken as 4015MPa similar toType a and Figure 3(a) shows the relationship between
0
005
01
015
02
025
0 01 02 03 04 05 06
Outer circular CFRPOuter square CFRPInner circular CFRP
(Ncc-N
CFST
)N
CFST
ξcfst
(a)
0
005
01
015
02
025
03
035
0 01 02 03 04 05 06
fck = 223fck = 264
fck = 328fck = 40
ξcfst
(Ncc-N
CFST
)N
CFST
(b)
Figure 3 Relationship between (NccminusNCFST)NCFST and ξcfst (a) fck 4015 (b) Different fck
6 Advances in Civil Engineering
(NccminusNCFST)NCFST and ξcf st under the same concretestrength e relationship is linear and directly pro-portional to the CFRP-wrapped composite columns withthe outer circular CFRP or outer square CFRP because theouter CFRP cylinder strengthens the whole CFST columnBut for the inner circular CFRP-confined columns there isno linear proportion because inner CFRP only strengthensits inside concrete directly It can also be found that outercircular CFRP has the best confinement effect to providethe highest bearing capacity enhancement ratio at the samerelative proportions of CFRP and steel Meanwhile outersquare CFRP does better than inner circular CFRP asshown in Figure 3(a) that is CFRP as external jackets canprovide the better confinement than the internal one Onthe other hand we choose the basic parameters of outersquare CFRP-confined CFST columns in Table 1 to get therelationship between (NccminusNCFST)NCFST and ξcf st underdifferent concrete strength as shown in Figure 3(b) Forevery group the steel tube and the concrete are the same sothe bearing capacity enhancement ratio is linear and directproportional to the content of the CFRP cylinder Amongthe four groups with the decrease of concrete strength thebearing capacity enhancement ratio increases with theimprovement of relative proportions of CFRP and steel Itindicates that the confinement effect of CFRP increaseswith the decrease of concrete strengthe reason is mainlythat the contributions of the CFRP cylinder are the dis-placement resistance of the CFSTcolumn and low-strengthconcrete has the better deformation capacity to make theCFRP play better especially during the postbucklingprocess
6 Conclusions
is paper presented a comparative study of concrete-filledsteel tubular (CFST) stub columns with three differentconfinement types from carbon fiber reinforced polymer(CFRP) outer circular CFRP inner circular CFRP and outersquare CFRP CFRP-confined CFST column takes the ad-vantage of not only the good performance of CFST but alsoa substantial improvement in higher confinement of CFRPe compressive mechanism and physical properties ofthe composite column were analyzed firstly aiming at in-vestigating the confinement effects of the different CFRP onCFST Columns
Two methods based on Unified eory of CFST andelastoplastic limit equilibrium method have been applied toinvestigate the axial bearing capacity of CFRP-confinedCFST stub columns e calculated results have goodagreement with the test results rough data analysis thestudy confirmed the ultimate strength calculation results oflimit equilibrium method were found to be more accurateand reliable than that of Unifiedeory of CFST en axialbearing capacity of pure CFST columns was predicted toevaluate the bearing capacity improvement factor comingfrom the CFRP confinement It was demonstrated that theaveraged enhancement ratio is 164 percent showing thatthe three kinds of CFRP-confined CFST columns hada broad applicability
CFRP can increase CFST membersrsquo bearing capacitiessignificantly because complementary action between thesteel tube and concrete is strengthened through CFRP erelationship between the bearing capacity enhancementratio and relative proportions of CFRP and steel is nearlylinear especially for the CFRP-wrapped columns with theouter circular CFRP or outer square CFRP rougha comparative analysis this study confirmed that outercircular CFRP had the best confinement effect and outersquare CFRP did better than inner circular CFRP econfinement effect of CFRP increased with the decrease ofconcrete strength and it was proportional with relativeproportions of CFRP and CFST under the same concretestrength
Data Availability
All data used for this paper are publicly available and ac-cessible online We have annotated the entire data buildingprocess and empirical techniques presented in the paper Wehave given formal citations in article references While wedid not directly draw upon these sources for the empiricalanalysis these efforts confirmed our understanding of thescope scale and accuracy of the CFRP-confined CFSTcolumns
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to acknowledge the support providedby the Chinese National Science Foundation (Grant no51478004) Meanwhile the financial support from HebeiUniversity of Technology is also appreciated
References
[1] O Chaalal and M Shahawy ldquoPerformance of fiber-reinforcedpolymer wrapped reinforced concrete column under com-bined axial flexural loadingrdquo ACI Structure Journal vol 97no 4 pp 659ndash668 2000
[2] Y Xiao ldquoApplications of FRP composites in concrete col-umnsrdquo Advances in Structural Engineering vol 7 no 4pp 335ndash343 2004
[3] J G Teng Y L Huang L Lam and L P Ye ldquoeoreticalmodel for fiber reinforced polymer-confined concreterdquoJournal of Composites for Construction vol 11 no 2pp 201ndash210 2007
[4] J G Teng T Jiang L Lam and Y Z Luo ldquoRefinement ofa design-oriented stress-strain model for FRP-confinedconcreterdquo Journal of Composites for Construction vol 13no 4 pp 269ndash278 2009
[5] Y Zheng L F Zhang and L P Xia ldquoInvestigation of thebehaviour of flexible and ductile ECC link slab reinforced withFRPrdquo Construction and Building Materials vol 166pp 694ndash711 2018
[6] Y Zheng and L P Xia ldquoInvestigation of the ultimate capacityof NSM FRP-strengthened concrete bridge deck slabsrdquoArabian Journal of Science and Engineering vol 43pp 1597ndash1615 2018
Advances in Civil Engineering 7
[7] Z F Amir and H R Sami ldquoConfinement model for axiallyloaded concrete confined by circular FRP tubesrdquo ACIStructure Journal vol 98 no 4 pp 451ndash461 2001
[8] L H Han Concrete-Filled Steel Tube Structures-+eory andDesign Science Press Beijing China 2nd edition 2007
[9] B C Chen and T L Wang ldquoOverview of concrete filled steeltube arch bridges in Chinardquo Practice Periodical on StructuralDesign and Construction vol 14 no 2 pp 70ndash80 2009
[10] Y Che Q L Wang and Y B Shao ldquoCompressive perfor-mances of the concrete filled circular CFRP-steel tube (C-CFRP-CFST)rdquo International Journal of Advanced SteelConstruction vol 8 no 4 pp 311ndash338 2012
[11] Z Tao L H Han and L L Wang ldquoCompressive and flexuralbehaviour of CFRP repaired concrete-filled steel tubes afterexposure to firerdquo Journal of Constructional Steel Researchvol 63 no 8 pp 1116ndash1126 2007
[12] W Gu ldquoStudy on mechanics of concrete-filled CFRP-steeltube columnrdquo esis for doctor degree DaLian MaritimeUniversity Dalian China 2007
[13] G C Li L Ma and J L Yang ldquoBearing capacity of shortcolumns of high-strength concrete filled square steel tubularwith inner CFRP circular tubular under axially compressiveloadrdquo Journal of Shenyang Jianzhu University vol 24 no 1pp 62ndash66 2008
[14] Q L Wang G Y Wang and F Han ldquoExperimental study onconcentrically compressed stub columns reinforced by con-crete filled CFRP-steel tuberdquo in 4th International Conferenceon Advances in Steel Structures Elsevier Science Ltd pp671ndash676 London UK 2005
[15] Z Tao L H Han and J P Zhuang ldquoUsing CFRP tostrengthen concrete-filled steel tubular columns stub columntestsrdquo in 4th International Conference on Advances in SteelStructures Elsevier Science Ltd pp 701ndash706 London UK2005
[16] Q L Wang S E Qu Y B Shao and L M Feng ldquoStaticbehavior of axially compressed circular concrete filled cfrp-steel tubular (c-cf-cfrp-st) columns with moderate slender-ness ratiordquo Advanced Steel Construction vol 12 no 3pp 263ndash295 2016
[17] Q L Wang Z Zhao Y B Shao and Q L Li ldquoStatic behaviorof axially compressed square concrete filled CFRP-steel tu-bular (S-CF-CFRP-ST) columns with moderate slendernessrdquo+in-Walled Structures vol 110 pp 106ndash122 2017
[18] K Karimi M J Tait and W W EI-Dakhakhni ldquoTesting andmodeling of a novel FRP-encased steel-concrete composite col-umnrdquo Composite Structures vol 93 no 5 pp 1463ndash1473 2011
[19] P Feng S Cheng Y Bai et al ldquoMechanical behavior ofconcrete-filled square steel tube with FRP-confined concretecore subjected to axial compressionrdquo Composite Structuresvol 123 no 5 pp 312ndash324 2015
[20] S T Zhong Unified +eory of Concrete Filled Steel TubularStructure Tsinghua University Press Beijing China 2006
[21] M H Yu Unified Strength +eory and Its ApplicationsSpringer Press Berlin Heidelberg Germany 2004
[22] F E Richart A Brandtzaeg and R L Brown ldquoA study of thefailure of concrete under combined compressive stressesrdquoBulletin No 185 Engineering Experimental Station Uni-versity of Illinois Urbana IL USA 1928
[23] Q L Wang W Gu and Y H Zhao ldquoExperimental study onconcentrically compressed concrete filled circular CFRP-steelcomposite tubular stub columnsrdquo China Civil EngineeringJournal vol 38 no 10 pp 44ndash48 2005
[24] A H Varma R Sause and J M Ricles ldquoDevelopment andvalidation of fiber model for high strength square concrete
filled steel tube beam-columnrdquo ACI Structural Journalvol 102 no 1 pp 73ndash84 2005
[25] S T Zhong ldquoNew concept and development of research onconcrete-filled steel tube (CFST)rdquo in Proceeding of 2nd In-ternational Symposium on Civil Infrastructure Systemspp 9ndash12 Hong Kong December 1996
[26] Y F Zhang and Z Q Zhang ldquoStudy on equivalent con-finement coefficient of composite CFST column based onunified theoryrdquo Mechanics of Advanced Materials andStructures vol 23 no 1 pp 22ndash27 2016
[27] H T Chen ldquoeoretical study on continuity of basic behaviorof every-sectioned CFT stub columns under axial loadsrdquoesis for doctor degree Harbin Institute of TechnologyHarbin China 2001
[28] X W Li and J H Zhao ldquoMechanics behavior of axial loadedshort columns with concrete-filled square steel tuberdquo ChineseJournal of Highway and Transport vol 19 no 4 pp 77ndash812006
[29] Y F Zhang J H Zhao and W F Yuan ldquoStudy on com-pressive bearing capacity of concrete filled square steel tubecolumn reinforced by circular steel tube insiderdquo Journal ofCivil Engineering and Management vol 19 no 6 pp 787ndash795 2013
[30] W Gu and H N Li ldquoResearch in the properties of theconcrete filled steel tube columns with CFRP compositematerialsrdquo Advanced Materials Research vol 163-167pp 3555ndash3559 2011
[31] Q L Wang and Y B Shao ldquoCompressive performances ofconcrete filled square CFRP-steel tubes (S-CFRP-CFST)rdquoSteel and Composite Structures vol 16 no 5 pp 455ndash4802014
8 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
en η was obtained as 065 by experimentation andstatistical data [29] so the ultimate capacity of the steel tubecan be calculated by
Ns nfsAs (14)
Lastly the ultimate capacity of CFRP-confined CFSTcolumn can be expressed as follows
N2y ηfsAs + fck + kcp( 1113857Ac (15)
5 Comparison and Analysis
e three types of CFRP-confined CFST stub columnsshown in Figure 1 have been tested under axial compression[13 30 31] Calculations N1
y and N2y obtained by Unified
eory of CFST and limit equilibrium theory respectivelyare listed in Table 1 together with the test results Nt ecalculated results both have good agreement with the testresults within small errors less than 20 Comparing thevalue of N2
yNt and N1yNt shown in Table 1 we can find that
N2y obtained by the limit equilibrium method is more ac-
curate and reliable than N1y obtained by the method of
Unified eory of CFST On the other hand the method ofUnified eory of CFST is simple and easy to realize since itjust considers the column as one composite material whilethe method of limit equilibrium method sound complicatedsince it applies TSUST to analyze every component of thecomposite column erefore these two methods can bothbe applied to investigate the axial bearing capacity of CFRP-confined CFSTstub columns and they can provide referencefor engineering design en axial bearing capacity of pureCFST columns can be predicted by the limit equilibriummethod in order to evaluate the bearing capacity im-provement due to the CFRP confinement By reviewing testresults the bearing capacity enhancement rate is describedas the expression of (Nt-NCFST)NCFSTas shown in Table 1 Itwas found that the averaged bearing capacity enhancement
rate of CFRP-confined CFSTstub columns is 164 percent incomparison with the pure CFSTcolumns Because the CFRPsheet is very thin it is demonstrated that the bearing capacityof the composite columns improves more than the corre-sponding pure CFST columns with the nearly same crosssection area erefore it is very applicable to use CFRP tostrengthen the CFST column and the composite columnscan result in significant savings in column size which ul-timately realize the material potency and bring economicbenefits
rough data analysis of the calculated and experi-mental results it can be found that concrete strength andthe relative proportions of CFRP and steel are the mainparameters to influence the axial bearing capacity of thecomposite column e confining mechanism of CFRP andaxial bearing capacity improvement needs to be validatedso the relative proportions of CFRP and steel is proposedaccording to the concept of equivalent confinement co-efficient ξssc (1) e relative proportions of CFRP and steelξcf st considers strength content and confining effect ofsection form that is
ξcfst kcfAcffcf
ksAsfs (16)
Since the test results of the bearing capacity of the stubcolumns have a certain degree of dispersion and someparameters need to be taken as the same value the calculatedaxial bearing capacity Ncc is used to describe the bearingcapacity enhancement ratio with the expression of (Ncc-NCFST)NCFST which reflects the function of the CFRPcylinder to confine the CFST column where NCFST is thecalculated value for the corresponding pure CFST columnNcc is obtained by limit equilibrium theory
e relationship between (NccminusNCFST)NCFST and ξcf stfor the three types of composite columns is shown inFigure 3 In reference to the experimental data in Table 1fck of Type b and Type c is taken as 4015MPa similar toType a and Figure 3(a) shows the relationship between
0
005
01
015
02
025
0 01 02 03 04 05 06
Outer circular CFRPOuter square CFRPInner circular CFRP
(Ncc-N
CFST
)N
CFST
ξcfst
(a)
0
005
01
015
02
025
03
035
0 01 02 03 04 05 06
fck = 223fck = 264
fck = 328fck = 40
ξcfst
(Ncc-N
CFST
)N
CFST
(b)
Figure 3 Relationship between (NccminusNCFST)NCFST and ξcfst (a) fck 4015 (b) Different fck
6 Advances in Civil Engineering
(NccminusNCFST)NCFST and ξcf st under the same concretestrength e relationship is linear and directly pro-portional to the CFRP-wrapped composite columns withthe outer circular CFRP or outer square CFRP because theouter CFRP cylinder strengthens the whole CFST columnBut for the inner circular CFRP-confined columns there isno linear proportion because inner CFRP only strengthensits inside concrete directly It can also be found that outercircular CFRP has the best confinement effect to providethe highest bearing capacity enhancement ratio at the samerelative proportions of CFRP and steel Meanwhile outersquare CFRP does better than inner circular CFRP asshown in Figure 3(a) that is CFRP as external jackets canprovide the better confinement than the internal one Onthe other hand we choose the basic parameters of outersquare CFRP-confined CFST columns in Table 1 to get therelationship between (NccminusNCFST)NCFST and ξcf st underdifferent concrete strength as shown in Figure 3(b) Forevery group the steel tube and the concrete are the same sothe bearing capacity enhancement ratio is linear and directproportional to the content of the CFRP cylinder Amongthe four groups with the decrease of concrete strength thebearing capacity enhancement ratio increases with theimprovement of relative proportions of CFRP and steel Itindicates that the confinement effect of CFRP increaseswith the decrease of concrete strengthe reason is mainlythat the contributions of the CFRP cylinder are the dis-placement resistance of the CFSTcolumn and low-strengthconcrete has the better deformation capacity to make theCFRP play better especially during the postbucklingprocess
6 Conclusions
is paper presented a comparative study of concrete-filledsteel tubular (CFST) stub columns with three differentconfinement types from carbon fiber reinforced polymer(CFRP) outer circular CFRP inner circular CFRP and outersquare CFRP CFRP-confined CFST column takes the ad-vantage of not only the good performance of CFST but alsoa substantial improvement in higher confinement of CFRPe compressive mechanism and physical properties ofthe composite column were analyzed firstly aiming at in-vestigating the confinement effects of the different CFRP onCFST Columns
Two methods based on Unified eory of CFST andelastoplastic limit equilibrium method have been applied toinvestigate the axial bearing capacity of CFRP-confinedCFST stub columns e calculated results have goodagreement with the test results rough data analysis thestudy confirmed the ultimate strength calculation results oflimit equilibrium method were found to be more accurateand reliable than that of Unifiedeory of CFST en axialbearing capacity of pure CFST columns was predicted toevaluate the bearing capacity improvement factor comingfrom the CFRP confinement It was demonstrated that theaveraged enhancement ratio is 164 percent showing thatthe three kinds of CFRP-confined CFST columns hada broad applicability
CFRP can increase CFST membersrsquo bearing capacitiessignificantly because complementary action between thesteel tube and concrete is strengthened through CFRP erelationship between the bearing capacity enhancementratio and relative proportions of CFRP and steel is nearlylinear especially for the CFRP-wrapped columns with theouter circular CFRP or outer square CFRP rougha comparative analysis this study confirmed that outercircular CFRP had the best confinement effect and outersquare CFRP did better than inner circular CFRP econfinement effect of CFRP increased with the decrease ofconcrete strength and it was proportional with relativeproportions of CFRP and CFST under the same concretestrength
Data Availability
All data used for this paper are publicly available and ac-cessible online We have annotated the entire data buildingprocess and empirical techniques presented in the paper Wehave given formal citations in article references While wedid not directly draw upon these sources for the empiricalanalysis these efforts confirmed our understanding of thescope scale and accuracy of the CFRP-confined CFSTcolumns
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to acknowledge the support providedby the Chinese National Science Foundation (Grant no51478004) Meanwhile the financial support from HebeiUniversity of Technology is also appreciated
References
[1] O Chaalal and M Shahawy ldquoPerformance of fiber-reinforcedpolymer wrapped reinforced concrete column under com-bined axial flexural loadingrdquo ACI Structure Journal vol 97no 4 pp 659ndash668 2000
[2] Y Xiao ldquoApplications of FRP composites in concrete col-umnsrdquo Advances in Structural Engineering vol 7 no 4pp 335ndash343 2004
[3] J G Teng Y L Huang L Lam and L P Ye ldquoeoreticalmodel for fiber reinforced polymer-confined concreterdquoJournal of Composites for Construction vol 11 no 2pp 201ndash210 2007
[4] J G Teng T Jiang L Lam and Y Z Luo ldquoRefinement ofa design-oriented stress-strain model for FRP-confinedconcreterdquo Journal of Composites for Construction vol 13no 4 pp 269ndash278 2009
[5] Y Zheng L F Zhang and L P Xia ldquoInvestigation of thebehaviour of flexible and ductile ECC link slab reinforced withFRPrdquo Construction and Building Materials vol 166pp 694ndash711 2018
[6] Y Zheng and L P Xia ldquoInvestigation of the ultimate capacityof NSM FRP-strengthened concrete bridge deck slabsrdquoArabian Journal of Science and Engineering vol 43pp 1597ndash1615 2018
Advances in Civil Engineering 7
[7] Z F Amir and H R Sami ldquoConfinement model for axiallyloaded concrete confined by circular FRP tubesrdquo ACIStructure Journal vol 98 no 4 pp 451ndash461 2001
[8] L H Han Concrete-Filled Steel Tube Structures-+eory andDesign Science Press Beijing China 2nd edition 2007
[9] B C Chen and T L Wang ldquoOverview of concrete filled steeltube arch bridges in Chinardquo Practice Periodical on StructuralDesign and Construction vol 14 no 2 pp 70ndash80 2009
[10] Y Che Q L Wang and Y B Shao ldquoCompressive perfor-mances of the concrete filled circular CFRP-steel tube (C-CFRP-CFST)rdquo International Journal of Advanced SteelConstruction vol 8 no 4 pp 311ndash338 2012
[11] Z Tao L H Han and L L Wang ldquoCompressive and flexuralbehaviour of CFRP repaired concrete-filled steel tubes afterexposure to firerdquo Journal of Constructional Steel Researchvol 63 no 8 pp 1116ndash1126 2007
[12] W Gu ldquoStudy on mechanics of concrete-filled CFRP-steeltube columnrdquo esis for doctor degree DaLian MaritimeUniversity Dalian China 2007
[13] G C Li L Ma and J L Yang ldquoBearing capacity of shortcolumns of high-strength concrete filled square steel tubularwith inner CFRP circular tubular under axially compressiveloadrdquo Journal of Shenyang Jianzhu University vol 24 no 1pp 62ndash66 2008
[14] Q L Wang G Y Wang and F Han ldquoExperimental study onconcentrically compressed stub columns reinforced by con-crete filled CFRP-steel tuberdquo in 4th International Conferenceon Advances in Steel Structures Elsevier Science Ltd pp671ndash676 London UK 2005
[15] Z Tao L H Han and J P Zhuang ldquoUsing CFRP tostrengthen concrete-filled steel tubular columns stub columntestsrdquo in 4th International Conference on Advances in SteelStructures Elsevier Science Ltd pp 701ndash706 London UK2005
[16] Q L Wang S E Qu Y B Shao and L M Feng ldquoStaticbehavior of axially compressed circular concrete filled cfrp-steel tubular (c-cf-cfrp-st) columns with moderate slender-ness ratiordquo Advanced Steel Construction vol 12 no 3pp 263ndash295 2016
[17] Q L Wang Z Zhao Y B Shao and Q L Li ldquoStatic behaviorof axially compressed square concrete filled CFRP-steel tu-bular (S-CF-CFRP-ST) columns with moderate slendernessrdquo+in-Walled Structures vol 110 pp 106ndash122 2017
[18] K Karimi M J Tait and W W EI-Dakhakhni ldquoTesting andmodeling of a novel FRP-encased steel-concrete composite col-umnrdquo Composite Structures vol 93 no 5 pp 1463ndash1473 2011
[19] P Feng S Cheng Y Bai et al ldquoMechanical behavior ofconcrete-filled square steel tube with FRP-confined concretecore subjected to axial compressionrdquo Composite Structuresvol 123 no 5 pp 312ndash324 2015
[20] S T Zhong Unified +eory of Concrete Filled Steel TubularStructure Tsinghua University Press Beijing China 2006
[21] M H Yu Unified Strength +eory and Its ApplicationsSpringer Press Berlin Heidelberg Germany 2004
[22] F E Richart A Brandtzaeg and R L Brown ldquoA study of thefailure of concrete under combined compressive stressesrdquoBulletin No 185 Engineering Experimental Station Uni-versity of Illinois Urbana IL USA 1928
[23] Q L Wang W Gu and Y H Zhao ldquoExperimental study onconcentrically compressed concrete filled circular CFRP-steelcomposite tubular stub columnsrdquo China Civil EngineeringJournal vol 38 no 10 pp 44ndash48 2005
[24] A H Varma R Sause and J M Ricles ldquoDevelopment andvalidation of fiber model for high strength square concrete
filled steel tube beam-columnrdquo ACI Structural Journalvol 102 no 1 pp 73ndash84 2005
[25] S T Zhong ldquoNew concept and development of research onconcrete-filled steel tube (CFST)rdquo in Proceeding of 2nd In-ternational Symposium on Civil Infrastructure Systemspp 9ndash12 Hong Kong December 1996
[26] Y F Zhang and Z Q Zhang ldquoStudy on equivalent con-finement coefficient of composite CFST column based onunified theoryrdquo Mechanics of Advanced Materials andStructures vol 23 no 1 pp 22ndash27 2016
[27] H T Chen ldquoeoretical study on continuity of basic behaviorof every-sectioned CFT stub columns under axial loadsrdquoesis for doctor degree Harbin Institute of TechnologyHarbin China 2001
[28] X W Li and J H Zhao ldquoMechanics behavior of axial loadedshort columns with concrete-filled square steel tuberdquo ChineseJournal of Highway and Transport vol 19 no 4 pp 77ndash812006
[29] Y F Zhang J H Zhao and W F Yuan ldquoStudy on com-pressive bearing capacity of concrete filled square steel tubecolumn reinforced by circular steel tube insiderdquo Journal ofCivil Engineering and Management vol 19 no 6 pp 787ndash795 2013
[30] W Gu and H N Li ldquoResearch in the properties of theconcrete filled steel tube columns with CFRP compositematerialsrdquo Advanced Materials Research vol 163-167pp 3555ndash3559 2011
[31] Q L Wang and Y B Shao ldquoCompressive performances ofconcrete filled square CFRP-steel tubes (S-CFRP-CFST)rdquoSteel and Composite Structures vol 16 no 5 pp 455ndash4802014
8 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
(NccminusNCFST)NCFST and ξcf st under the same concretestrength e relationship is linear and directly pro-portional to the CFRP-wrapped composite columns withthe outer circular CFRP or outer square CFRP because theouter CFRP cylinder strengthens the whole CFST columnBut for the inner circular CFRP-confined columns there isno linear proportion because inner CFRP only strengthensits inside concrete directly It can also be found that outercircular CFRP has the best confinement effect to providethe highest bearing capacity enhancement ratio at the samerelative proportions of CFRP and steel Meanwhile outersquare CFRP does better than inner circular CFRP asshown in Figure 3(a) that is CFRP as external jackets canprovide the better confinement than the internal one Onthe other hand we choose the basic parameters of outersquare CFRP-confined CFST columns in Table 1 to get therelationship between (NccminusNCFST)NCFST and ξcf st underdifferent concrete strength as shown in Figure 3(b) Forevery group the steel tube and the concrete are the same sothe bearing capacity enhancement ratio is linear and directproportional to the content of the CFRP cylinder Amongthe four groups with the decrease of concrete strength thebearing capacity enhancement ratio increases with theimprovement of relative proportions of CFRP and steel Itindicates that the confinement effect of CFRP increaseswith the decrease of concrete strengthe reason is mainlythat the contributions of the CFRP cylinder are the dis-placement resistance of the CFSTcolumn and low-strengthconcrete has the better deformation capacity to make theCFRP play better especially during the postbucklingprocess
6 Conclusions
is paper presented a comparative study of concrete-filledsteel tubular (CFST) stub columns with three differentconfinement types from carbon fiber reinforced polymer(CFRP) outer circular CFRP inner circular CFRP and outersquare CFRP CFRP-confined CFST column takes the ad-vantage of not only the good performance of CFST but alsoa substantial improvement in higher confinement of CFRPe compressive mechanism and physical properties ofthe composite column were analyzed firstly aiming at in-vestigating the confinement effects of the different CFRP onCFST Columns
Two methods based on Unified eory of CFST andelastoplastic limit equilibrium method have been applied toinvestigate the axial bearing capacity of CFRP-confinedCFST stub columns e calculated results have goodagreement with the test results rough data analysis thestudy confirmed the ultimate strength calculation results oflimit equilibrium method were found to be more accurateand reliable than that of Unifiedeory of CFST en axialbearing capacity of pure CFST columns was predicted toevaluate the bearing capacity improvement factor comingfrom the CFRP confinement It was demonstrated that theaveraged enhancement ratio is 164 percent showing thatthe three kinds of CFRP-confined CFST columns hada broad applicability
CFRP can increase CFST membersrsquo bearing capacitiessignificantly because complementary action between thesteel tube and concrete is strengthened through CFRP erelationship between the bearing capacity enhancementratio and relative proportions of CFRP and steel is nearlylinear especially for the CFRP-wrapped columns with theouter circular CFRP or outer square CFRP rougha comparative analysis this study confirmed that outercircular CFRP had the best confinement effect and outersquare CFRP did better than inner circular CFRP econfinement effect of CFRP increased with the decrease ofconcrete strength and it was proportional with relativeproportions of CFRP and CFST under the same concretestrength
Data Availability
All data used for this paper are publicly available and ac-cessible online We have annotated the entire data buildingprocess and empirical techniques presented in the paper Wehave given formal citations in article references While wedid not directly draw upon these sources for the empiricalanalysis these efforts confirmed our understanding of thescope scale and accuracy of the CFRP-confined CFSTcolumns
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to acknowledge the support providedby the Chinese National Science Foundation (Grant no51478004) Meanwhile the financial support from HebeiUniversity of Technology is also appreciated
References
[1] O Chaalal and M Shahawy ldquoPerformance of fiber-reinforcedpolymer wrapped reinforced concrete column under com-bined axial flexural loadingrdquo ACI Structure Journal vol 97no 4 pp 659ndash668 2000
[2] Y Xiao ldquoApplications of FRP composites in concrete col-umnsrdquo Advances in Structural Engineering vol 7 no 4pp 335ndash343 2004
[3] J G Teng Y L Huang L Lam and L P Ye ldquoeoreticalmodel for fiber reinforced polymer-confined concreterdquoJournal of Composites for Construction vol 11 no 2pp 201ndash210 2007
[4] J G Teng T Jiang L Lam and Y Z Luo ldquoRefinement ofa design-oriented stress-strain model for FRP-confinedconcreterdquo Journal of Composites for Construction vol 13no 4 pp 269ndash278 2009
[5] Y Zheng L F Zhang and L P Xia ldquoInvestigation of thebehaviour of flexible and ductile ECC link slab reinforced withFRPrdquo Construction and Building Materials vol 166pp 694ndash711 2018
[6] Y Zheng and L P Xia ldquoInvestigation of the ultimate capacityof NSM FRP-strengthened concrete bridge deck slabsrdquoArabian Journal of Science and Engineering vol 43pp 1597ndash1615 2018
Advances in Civil Engineering 7
[7] Z F Amir and H R Sami ldquoConfinement model for axiallyloaded concrete confined by circular FRP tubesrdquo ACIStructure Journal vol 98 no 4 pp 451ndash461 2001
[8] L H Han Concrete-Filled Steel Tube Structures-+eory andDesign Science Press Beijing China 2nd edition 2007
[9] B C Chen and T L Wang ldquoOverview of concrete filled steeltube arch bridges in Chinardquo Practice Periodical on StructuralDesign and Construction vol 14 no 2 pp 70ndash80 2009
[10] Y Che Q L Wang and Y B Shao ldquoCompressive perfor-mances of the concrete filled circular CFRP-steel tube (C-CFRP-CFST)rdquo International Journal of Advanced SteelConstruction vol 8 no 4 pp 311ndash338 2012
[11] Z Tao L H Han and L L Wang ldquoCompressive and flexuralbehaviour of CFRP repaired concrete-filled steel tubes afterexposure to firerdquo Journal of Constructional Steel Researchvol 63 no 8 pp 1116ndash1126 2007
[12] W Gu ldquoStudy on mechanics of concrete-filled CFRP-steeltube columnrdquo esis for doctor degree DaLian MaritimeUniversity Dalian China 2007
[13] G C Li L Ma and J L Yang ldquoBearing capacity of shortcolumns of high-strength concrete filled square steel tubularwith inner CFRP circular tubular under axially compressiveloadrdquo Journal of Shenyang Jianzhu University vol 24 no 1pp 62ndash66 2008
[14] Q L Wang G Y Wang and F Han ldquoExperimental study onconcentrically compressed stub columns reinforced by con-crete filled CFRP-steel tuberdquo in 4th International Conferenceon Advances in Steel Structures Elsevier Science Ltd pp671ndash676 London UK 2005
[15] Z Tao L H Han and J P Zhuang ldquoUsing CFRP tostrengthen concrete-filled steel tubular columns stub columntestsrdquo in 4th International Conference on Advances in SteelStructures Elsevier Science Ltd pp 701ndash706 London UK2005
[16] Q L Wang S E Qu Y B Shao and L M Feng ldquoStaticbehavior of axially compressed circular concrete filled cfrp-steel tubular (c-cf-cfrp-st) columns with moderate slender-ness ratiordquo Advanced Steel Construction vol 12 no 3pp 263ndash295 2016
[17] Q L Wang Z Zhao Y B Shao and Q L Li ldquoStatic behaviorof axially compressed square concrete filled CFRP-steel tu-bular (S-CF-CFRP-ST) columns with moderate slendernessrdquo+in-Walled Structures vol 110 pp 106ndash122 2017
[18] K Karimi M J Tait and W W EI-Dakhakhni ldquoTesting andmodeling of a novel FRP-encased steel-concrete composite col-umnrdquo Composite Structures vol 93 no 5 pp 1463ndash1473 2011
[19] P Feng S Cheng Y Bai et al ldquoMechanical behavior ofconcrete-filled square steel tube with FRP-confined concretecore subjected to axial compressionrdquo Composite Structuresvol 123 no 5 pp 312ndash324 2015
[20] S T Zhong Unified +eory of Concrete Filled Steel TubularStructure Tsinghua University Press Beijing China 2006
[21] M H Yu Unified Strength +eory and Its ApplicationsSpringer Press Berlin Heidelberg Germany 2004
[22] F E Richart A Brandtzaeg and R L Brown ldquoA study of thefailure of concrete under combined compressive stressesrdquoBulletin No 185 Engineering Experimental Station Uni-versity of Illinois Urbana IL USA 1928
[23] Q L Wang W Gu and Y H Zhao ldquoExperimental study onconcentrically compressed concrete filled circular CFRP-steelcomposite tubular stub columnsrdquo China Civil EngineeringJournal vol 38 no 10 pp 44ndash48 2005
[24] A H Varma R Sause and J M Ricles ldquoDevelopment andvalidation of fiber model for high strength square concrete
filled steel tube beam-columnrdquo ACI Structural Journalvol 102 no 1 pp 73ndash84 2005
[25] S T Zhong ldquoNew concept and development of research onconcrete-filled steel tube (CFST)rdquo in Proceeding of 2nd In-ternational Symposium on Civil Infrastructure Systemspp 9ndash12 Hong Kong December 1996
[26] Y F Zhang and Z Q Zhang ldquoStudy on equivalent con-finement coefficient of composite CFST column based onunified theoryrdquo Mechanics of Advanced Materials andStructures vol 23 no 1 pp 22ndash27 2016
[27] H T Chen ldquoeoretical study on continuity of basic behaviorof every-sectioned CFT stub columns under axial loadsrdquoesis for doctor degree Harbin Institute of TechnologyHarbin China 2001
[28] X W Li and J H Zhao ldquoMechanics behavior of axial loadedshort columns with concrete-filled square steel tuberdquo ChineseJournal of Highway and Transport vol 19 no 4 pp 77ndash812006
[29] Y F Zhang J H Zhao and W F Yuan ldquoStudy on com-pressive bearing capacity of concrete filled square steel tubecolumn reinforced by circular steel tube insiderdquo Journal ofCivil Engineering and Management vol 19 no 6 pp 787ndash795 2013
[30] W Gu and H N Li ldquoResearch in the properties of theconcrete filled steel tube columns with CFRP compositematerialsrdquo Advanced Materials Research vol 163-167pp 3555ndash3559 2011
[31] Q L Wang and Y B Shao ldquoCompressive performances ofconcrete filled square CFRP-steel tubes (S-CFRP-CFST)rdquoSteel and Composite Structures vol 16 no 5 pp 455ndash4802014
8 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
[7] Z F Amir and H R Sami ldquoConfinement model for axiallyloaded concrete confined by circular FRP tubesrdquo ACIStructure Journal vol 98 no 4 pp 451ndash461 2001
[8] L H Han Concrete-Filled Steel Tube Structures-+eory andDesign Science Press Beijing China 2nd edition 2007
[9] B C Chen and T L Wang ldquoOverview of concrete filled steeltube arch bridges in Chinardquo Practice Periodical on StructuralDesign and Construction vol 14 no 2 pp 70ndash80 2009
[10] Y Che Q L Wang and Y B Shao ldquoCompressive perfor-mances of the concrete filled circular CFRP-steel tube (C-CFRP-CFST)rdquo International Journal of Advanced SteelConstruction vol 8 no 4 pp 311ndash338 2012
[11] Z Tao L H Han and L L Wang ldquoCompressive and flexuralbehaviour of CFRP repaired concrete-filled steel tubes afterexposure to firerdquo Journal of Constructional Steel Researchvol 63 no 8 pp 1116ndash1126 2007
[12] W Gu ldquoStudy on mechanics of concrete-filled CFRP-steeltube columnrdquo esis for doctor degree DaLian MaritimeUniversity Dalian China 2007
[13] G C Li L Ma and J L Yang ldquoBearing capacity of shortcolumns of high-strength concrete filled square steel tubularwith inner CFRP circular tubular under axially compressiveloadrdquo Journal of Shenyang Jianzhu University vol 24 no 1pp 62ndash66 2008
[14] Q L Wang G Y Wang and F Han ldquoExperimental study onconcentrically compressed stub columns reinforced by con-crete filled CFRP-steel tuberdquo in 4th International Conferenceon Advances in Steel Structures Elsevier Science Ltd pp671ndash676 London UK 2005
[15] Z Tao L H Han and J P Zhuang ldquoUsing CFRP tostrengthen concrete-filled steel tubular columns stub columntestsrdquo in 4th International Conference on Advances in SteelStructures Elsevier Science Ltd pp 701ndash706 London UK2005
[16] Q L Wang S E Qu Y B Shao and L M Feng ldquoStaticbehavior of axially compressed circular concrete filled cfrp-steel tubular (c-cf-cfrp-st) columns with moderate slender-ness ratiordquo Advanced Steel Construction vol 12 no 3pp 263ndash295 2016
[17] Q L Wang Z Zhao Y B Shao and Q L Li ldquoStatic behaviorof axially compressed square concrete filled CFRP-steel tu-bular (S-CF-CFRP-ST) columns with moderate slendernessrdquo+in-Walled Structures vol 110 pp 106ndash122 2017
[18] K Karimi M J Tait and W W EI-Dakhakhni ldquoTesting andmodeling of a novel FRP-encased steel-concrete composite col-umnrdquo Composite Structures vol 93 no 5 pp 1463ndash1473 2011
[19] P Feng S Cheng Y Bai et al ldquoMechanical behavior ofconcrete-filled square steel tube with FRP-confined concretecore subjected to axial compressionrdquo Composite Structuresvol 123 no 5 pp 312ndash324 2015
[20] S T Zhong Unified +eory of Concrete Filled Steel TubularStructure Tsinghua University Press Beijing China 2006
[21] M H Yu Unified Strength +eory and Its ApplicationsSpringer Press Berlin Heidelberg Germany 2004
[22] F E Richart A Brandtzaeg and R L Brown ldquoA study of thefailure of concrete under combined compressive stressesrdquoBulletin No 185 Engineering Experimental Station Uni-versity of Illinois Urbana IL USA 1928
[23] Q L Wang W Gu and Y H Zhao ldquoExperimental study onconcentrically compressed concrete filled circular CFRP-steelcomposite tubular stub columnsrdquo China Civil EngineeringJournal vol 38 no 10 pp 44ndash48 2005
[24] A H Varma R Sause and J M Ricles ldquoDevelopment andvalidation of fiber model for high strength square concrete
filled steel tube beam-columnrdquo ACI Structural Journalvol 102 no 1 pp 73ndash84 2005
[25] S T Zhong ldquoNew concept and development of research onconcrete-filled steel tube (CFST)rdquo in Proceeding of 2nd In-ternational Symposium on Civil Infrastructure Systemspp 9ndash12 Hong Kong December 1996
[26] Y F Zhang and Z Q Zhang ldquoStudy on equivalent con-finement coefficient of composite CFST column based onunified theoryrdquo Mechanics of Advanced Materials andStructures vol 23 no 1 pp 22ndash27 2016
[27] H T Chen ldquoeoretical study on continuity of basic behaviorof every-sectioned CFT stub columns under axial loadsrdquoesis for doctor degree Harbin Institute of TechnologyHarbin China 2001
[28] X W Li and J H Zhao ldquoMechanics behavior of axial loadedshort columns with concrete-filled square steel tuberdquo ChineseJournal of Highway and Transport vol 19 no 4 pp 77ndash812006
[29] Y F Zhang J H Zhao and W F Yuan ldquoStudy on com-pressive bearing capacity of concrete filled square steel tubecolumn reinforced by circular steel tube insiderdquo Journal ofCivil Engineering and Management vol 19 no 6 pp 787ndash795 2013
[30] W Gu and H N Li ldquoResearch in the properties of theconcrete filled steel tube columns with CFRP compositematerialsrdquo Advanced Materials Research vol 163-167pp 3555ndash3559 2011
[31] Q L Wang and Y B Shao ldquoCompressive performances ofconcrete filled square CFRP-steel tubes (S-CFRP-CFST)rdquoSteel and Composite Structures vol 16 no 5 pp 455ndash4802014
8 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
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Control Scienceand Engineering
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wwwhindawicom Volume 2018
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International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
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